EFFECT OF LOCAL CRYSTAL ORIENTATIONS ON THE ADIABATIC SHEARING AND
CRACKING IN THE FORMATION OF SEGMENTED TI-6AL-4V CHIPS FROM TURNING
By
Jiawei Lu
A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Materials Science and Engineering– Doctor of Philosophy
2023
ABSTRACT
The Ti-6Al-4V (Ti64) alloy has been widely used as a light-weight structural material due to
its excellent corrosion resistance and high strength even at elevated temperatures. However, the
poor machinability of Ti64, leading to higher costs, has severely limited its application. The
formation of segmented chips rather than smooth continuous chips, caused by the intrinsic low
thermal conductivity of Ti64, is of great interest and significance for investigation.
Ti64 bars with various microstructures, namely mill-annealed (MIL), elongated (ELO),
solution treated and aged (STA), and lamellar (LAM), were machined at 61, 91, and 122 m/min.
The chips were collected, and their microstructures were characterized by scanning electron
microscopy (SEM) and electron backscattered diffraction (EBSD). The morphology of these chips
was also measured, and observations of the smooth and segmented sides were also made and
compared.
For STA chips, nano-indentation and EBSD were used to investigate local shear strain
phenomena. An existing continuum model based upon material constants and mechanical
properties was used for shear band width prediction at various cutting speeds and the predicted
values were compared with the measured values and discussed. In addition, a model based on the
morphology of the segmented chips was adopted to calculate the homogeneous shear strains in the
segments and catastrophic shear strains within the shear bands. Representative examples of chips
were characterized by EBSD and analyzed using the stress tensor obtained from finite element
numerical simulation. Finally, the chips were annealed at 500, 600 and 650 ℃ to investigate their
response to annealing, revealing effects of the chip deformation history. For LAM, a few EBSD
scans were also carried out to show the correlation between chip morphology and local orientations.
Overall, the work presented in this study demonstrates an approach to investigating the
formation of segmented chips and the severe deformation during turning. It can be further applied
to the chips obtained from other machining methods and to identify effects of higher cutting speeds.
Copyright by
JIAWEI LU
2023
ACKNOWLEDGEMENTS
I would like to thank Dr. Bieler, my primary advisor, for the invaluable opportunities to work
on this project, to visit IMDEA for research, and to present my work in many conferences and
peer-reviewed journals. His expertise, enthusiasm, and constructive feedback have helped me
overcome the obstacles in my research career and greatly contributed to the completion of this
dissertation. I will always keep in mind his motivation and attitude, and pass it on as I keep on my
research career.
Next, I would like to express my gratitude to Dr. Kwon, as well as Dr. Khawarizmi, who
carried out the turning experiments and helped me with finite elements analysis using Deform 2D.
In addition, many research results in this paper have been discussed with Dr. Kwon and Dr.
Khawarizmi during our weekly meetings. Their insights and expertise have been instrumental in
shaping the direction and scope of this work.
I would also like to thank the rest of my committee members, Dr. Guo and Dr. Eisenlohr, as
well as professors from metal group, Dr. Crimp, Dr. Boehlert, for their valuable suggestions and
guidance in my qualifying and comprehensive exams, and their efforts on responsible conduct of
research.
Besides my committee members, I would also like to express my gratitude to Dr. Jon Molina-
Aldareguia and Dr. Miguel Monclús for their help with nano-indentation experiments and
suggestions on analysis of the results.
Last but not least, I would like to thank my colleagues, Dr. Per Askeland, Dr. Zhuowen Zhao,
Genzhi Hu and many other graduate students from metal group for their kindly suggestions, as
well as my family and friends Yining He, Dr. Shengyuan Bai, Dr. Quinn Sun, Dr. Danqi Qu,
Haining Du, Tianhong Ying, Dr. Zinan Wang and many others for their support and care
v
throughout my endeavors.
The present work was supported by the U.S. National Science Foundation (NSF) (NO.
1727525), and the Talent Attraction program of the Comunidad de Madrid (reference 2016-
T3/IND-1600).
vi
TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION .................................................................................................... 1
CHAPTER 2 METHODOLOGY ................................................................................................. 40
CHAPTER 3 UNDEFORMED MICROSTRUCTURES OF THE AS-RECEIVED BARS ....... 47
CHAPTER 4 AS-CUT STA, MIL, ELO AND LAM CHIPS ...................................................... 55
CHAPTER 5 SHEAR BAND WIDTH PREDICTION AND SHEAR STRAIN ESTIMATION
IN STA CHIPS ............................................................................................................................. 83
CHPATER 6 EFFECT OF LOCAL ORIENTATION AND CUTTING SPEED ON THE
FORMATION OF SEGMENTED STA CHIPS......................................................................... 101
CHAPTER 7 ANNEALING TREATMENT OF STA CHIPS................................................... 133
CHAPTER 8 CONCLUSIONS AND FUTURE WORK ........................................................... 148
BIBLIOGRAPHY ....................................................................................................................... 153
XXX
vii
CHAPTER 1 INTRODUCTION
Titanium was discovered in 1791 by the British reverend, mineralogist, and chemist William
Gregor. He found it while examining magnetic sand from a river in Cornwall, England, and
isolated a substance called "ilmenite" by removing the iron with a magnet and treating the sand
with hydrochloric acid. He named the impure oxide of the new element "mechanite" after the
location. Around the same time, the Berlin chemist Martin Heinrich Klaproth also isolated titanium
oxide from a Hungarian mineral known as "rutile". Klaproth named it after the titans, who were
children of Uranos and Gaia in Greek mythology, as they were similarly imprisoned in the earth's
crust like the hard-to-extract ore[1].
It wasn't until over 100 years later that Matthew Albert Hunter from Rensselaer Polytechnic
Institute in Troy, N.Y. was able to isolate the metal in 1910 by heating titanium tetrachloride
(TiCl4) with sodium in a steel bomb. The father of the titanium industry is Wilhelm Justin Kroll
from Luxembourg, who in 1932 produced significant quantities of titanium by combining TiCl4
with calcium. When World War II began, Kroll fled to the United States and demonstrated at the
U.S. Bureau of Mines that titanium could be extracted commercially by reducing TiCl4 using
magnesium instead of calcium. This method, known as the "Kroll process", is still widely used
today.[1].
The initial applications of titanium alloys have been in aerospace industries like aero-engine
and airframe manufacture, due to their excellent properties, mainly high specific strength and
excellent corrosion resistance [1]. Over the past few decades, titanium and its alloys have been
experiencing extensive development in industrial applications, such as petroleum refining, surgical
implantation, nuclear waste storage, chemical and food processing, automotive, and marine
applications [2], [3]. Among all the titanium alloys, Ti-6Al-4V is most commonly adopted in the
1
above mentioned applications, which accounts for around 45-60% of the titanium products in
practical use [2], [3].
1.1 Representative microstructures of Ti-6Al-4V alloy
For Ti64, the α-β phase transformation temperature is ~995℃ [12, 13]. The α phase is
transformed to the β phase when heated above 995℃. The idealized orientation relationship
between α and β unit cells of Ti64 are shown in Fig. 1.1. However, the lattice parameters of α and
β don’t match perfectly and thus strains are necessary when phase transformation takes place. As
indicated in Fig. 1.2, an expansion of ~10% along [21̅1̅0]𝛼 , a contraction of ~10% along [011̅0]𝛼
and a contraction of ~1% along [0001]𝛼 are required to become [100]𝛽 , [011̅]𝛽 , and[01̅1]𝛽 ,
respectively. As a result of this imperfect matching, one of the < 111 >𝛽 directions need to be
rotated by ~5° to align itself with one of the < 21̅1̅0 >𝛼 directions, leading to 6 possible β variants
when transformed from one α grain, as illustrated in Fig. 1.2. Therefore, the misorientation
between each two of these 6 β variants can be either 10°, 50°, 60° and 70°.
Figure 1.1 Idealized orientation relationship between α and β crystal structures [12].
2
Figure 1.2 Atomic positions of α and β crystal structures are close so phase transformation is
easy to take place [4].
When the β phase is transformed to α upon cooling, one < 21̅1̅0 >𝛼 direction is parallel to
one of the two < 111 >𝛽 directions on one of the {110} planes. Since there are six different {110}
planes within a β crystal, the c-axis of a daughter α crystal has six directions as well, and each
direction has two variants which can be rotated about the c-axis by ~10° from each other.
In general, the aluminum equivalent and molybdenum equivalent equations (in wt.%) are
adopted to describe the degree of stability of the α and β phases. Aluminum is one of the most
important alloying elements due to its potent solid solution strengthening effect on the α phase [5].
Also, the addition of aluminum can reduce the density of titanium alloys. Molybdenum and
vanadium can also solid solution strengthen the β phase and are two of the most popular β-
stabilizing additives [6]
As a result, titanium alloys can be classified based on the phases present in their
microstructure, due to the addition of different alloying elements. α alloys are consisting of mainly
α phase while the alloys with the presence of a small amount of β phase are termed near-α alloys.
Commercially pure (CP) titanium alloy is a typical α alloy. CP titanium is usually graded by
oxygen and iron content. Compared with the β alloys, CP titanium is usually preferred for superior
creep resistance and high-temperature applications [7]. On the other hand, α alloys have reduced
3
ductility and poor forgeability and a two-orders-of-magnitude lower diffusion rate. Typical near-
α alloys include Ti-3Al-2.5V, Ti-8Al-1Mo-1V, and Ti-6Al-2Sn-4Zr-2Mo, which are mainly used
at temperatures between 400-520℃ [7]. When the alloys have a mixture of both α and β phases,
the alloys are classified as α+β alloys. Most common α+β alloys include Ti-6Al-4V, Ti-6Al-2Sn-
4Zr-6Mo, Ti-6Al-2Sn. The microstructure and properties of α+β alloys can be controlled by heat
treatment at temperatures between 315-400℃. If the alloys show the microstructure of mainly β
phase at room temperature, the alloys are called β alloys [8]. Representative β alloys are Ti-15V-
3Cr-3Al-3Sn, Ti-15Mo-2.7Nb-3Al-0.2Si, Ti-3Al-8V-6Cr-4Mo-4Zr and Ti-10V-2Fe-3Al [7].
(a) (b)
Figure 1.3 (a) Solution treated and furnace cooled Ti64 at 0.42°C s-1 from 1100°C×10 min
[9];(b) Cooled from the β phase field at more than 1°C s−1 [10].
β-annealing requires heating the alloy into the β phase field (~1100℃) for a certain time, then
followed by furnace cooling or air cooling or even quenching for different purposes. Usually, the
β-annealing results in coarse prior β grains so the annealing temperature and time should be kept
to the minimum. Matsumoto et. al [9] heated Ti64 to1100°C for10 min and then furnace cooled at
the speed of 0.42°C s-1 and the resulting microstructure had coarse lamellar α+β phases (Fig. 1.3
(a), showing white α phase and black β phase). This is because α-laths nucleated at the grain
boundaries of prior-β grains and grew inward as large α-colonies. However, when increasing the
4
cooling rate, a basket-weave α+β phase microstructure (Fig. 1.3 (b)) was formed [10] with finer
and shorter α-laths with increasing cooling rate. An increased driving force led to the nucleation
and growth of α-laths at both prior-β grains boundaries and boundaries between the newly formed
α-laths. Both reasons led to the formation of the microstructure as shown in Fig. 1.3 (b).
Figure 1.4 Optical micrographs of the microstructure isothermally held at (a) 970℃, (b) 950℃;
(c) 930℃; and (d) 900℃ for 30 min [11].
Zhang et al. [11] investigated the effect of thermal history on the microstructure evolution of
Ti64 during solidification. Typical α-Widmanstätten colonies were formed when cooling directly
from 1700℃. To further study the special microstructure at 950℃, the microstructures at 970℃,
930℃, and 900 ℃ were investigated. The microstructure at 970℃ (Fig. 1.4 (a)) consisted of
primary α particles and secondary α lamellar structure, which is referred to as bimodal
microstructure. The tendency of α breakdown (forming small primary α grains) was higher at 970℃
than at 950℃. When the temperature decreased to 930℃ (Fig. 1.4 (c)), the microstructure was
5
coarse α lamellae scattered with small fine lamellar colonies. The microstructure obtained at 900℃
was mainly coarse α lamellae, as shown in Fig. 1.4 (d).
The average width for primary α lamellae (i.e. α that forms from during the isothermal hold
below the β transus) decreased from 9 μm to 3 μm with decreasing temperature from 970℃ to
900℃. The growth of the primary α was dominated by the diffusion mechanism when the
specimens were isothermally held, resulting in coarser primary α with increasing temperature.
Another feature was that the volume fraction of primary α decreased with increasing isothermal
holding temperature. This is because the driving force for the nucleation and further transformation
of primary α at 970℃ was weaker than at 900 ℃. The primary α was coarser and had a higher
tendency of breakdown with increasing holding temperature. The breakdown of primary α can be
ascribed to Ostwald ripening and boundary splitting mechanisms during isothermal holding. When
the temperature was below the β transus, the primary lamellar α nucleated at the grain boundaries
or at the interior of the grains. The subsequent isothermal holding led to the coarsening of the
primary lamellar α by diffusion mechanism. EDS results showed that the vanadium concentration
increased in the retained β grains, leading to a lower phase transformation temperature. The grain
boundaries of primary α provided nucleation sites and inhibited the growth of secondary lamellar
α.
6
(a) (b)
(c) (d)
Figure 1.5 Microstructures of Ti64 when cooling from 1100 ℃ at the cooling rate of (a)5.1℃s-1;
(b)3.4 ℃s-1; (c) 0.81 ℃s-1; (d)0.23 ℃s-1 [12].
Gil et al. [12] conducted experiments on the microstructure and mechanical properties of Ti64
at different cooling rates. As can be seen from Fig. 1.5, martensite was formed when the cooling
rate was 5.1℃s-1. The thickness of α-Widmanstätten plates increased with decreasing cooling rate
(~4μm at 3.4℃s-1 and ~8μm at 0.23℃s-1). The high diffusivity at low cooling rate allowed the
atoms to move faster so that the α-Widmanstätten plate was thicker. The increase of β grain size
can lower the starting β to α transformation. The β phases with a grain size of 600 μm had a ~250℃
lower starting transformation temperature than those with a grain size of 100 μm. The mechanical
properties for a lamellar microstructure are mainly determined by prior β grain size, the size of the
α+β lamellae, thickness of α lamellae, and the morphology of the interlamellar interface (β phase)
[13]. Refined prior β grains and thinner α lamellae can result\ in a higher tensile strength, which
can also explain the higher strength for the Widmanstätten microstructures.
7
(a) (b)
Figure 1.6 Backscattered electron (BSE) images of the microstructure of mill-annealed Ti64 (a)
in-plane view (b) cross-section view[14].
Mill annealing for Ti64 is usually carried out in the temperature range of 700-800℃ for 1-4
h, followed by air cooling. The main purpose of mill annealing is to retain the wrought-state
microstructure. Mulay et al. [14] compared the microstructure and mechanical properties of Ti64
manufactured by direct metal laser melting (DMLM) and mill annealing. The in-plane
Backscattered electron (BSE) image (Fig. 1.6) shows globular α grains (dark phase) with the β
phase (bright phase) decorating the grain boundaries. The cross-section view exhibited elongated
α grains and β grains were located along the grain boundaries. The compressive yield strength of
mill annealed Ti64 (1059 MPa) was comparable to that of the DMLM sample (1066 MPa).
Figure 1.7 (a) bimodal; and (b) lamellar microstructure of Ti64 alloy [15].
Recrystallization annealing is heating the alloy into the upper end of α+β field (~950℃) for
8
up to 2 h, followed by furnace cooling. After annealing, the α and β phases are both essentially
dislocation free [10]. Liu et al. [15] obtained two different microstructures by annealing at 950℃
for 1 h, followed by air cooling, and annealing at 1020℃ for 1 h, followed by air cooling,
respectively. Fig. 1.7 (a) exhibits the bimodal microstructure when annealed at 950℃ and Fig. 1.7
(b) shows the lamellar microstructure when annealed at 1020℃. The bimodal microstructure
consists of primary α phase and lamellar α+β phase while the lamellar microstructure is mainly
lamellar α+β phase.
Meyer et al. [16] investigated the quasi-static and dynamic compressive tests and impact tests
of Ti64 with different microstructures (as shown in Fig. 1.8) obtained by different heat treatments.
The bimodal microstructure (Fig. 1.8 (b)) exhibited a higher yield stress than coarse lamellar
microstructure (Fig. 1.8 (a)), which was 1040 MPa and 960 MPa, respectively. The coarse-grained
martensite microstructure (Fig. 1.8 (c)) and the globular primary α microstructure (Fig. 1.8 (d))
exhibited even higher yield strengths (1120 MPa and 1170 MPa, respectively).
9
(a) (b)
(c) (d)
Figure 1.8 Optical microstructures of Ti64(a) annealed at 1065℃, furnace cooling; (b) annealed
at 955℃ and furnace cooling; (c) annealed at 1065℃ and water quenching; (d) annealed at
900℃, water quenching and aged at 600℃ [16].
On the other hand, the specific energy consumption of the bimodal microstructure (310 J/cm3)
was much higher than those of the other three (coarse lamellar: 125 J/cm3, coarse-grained
martensite: 120 J/cm3, and globular primary α: 260 J/cm3), indicating a better deformability among
these four microstructures. This may be ascribed to the residual-stress-free state after annealing at
955℃ and followed by furnace cooling.
10
Figure 1.9 Optical micrograph of the bimodal Ti64 microstructure showing primary α and
lamellar α+β structure [17], similar to that after recrystallization annealing.
A typical duplex annealing for Ti64 includes 870-950°C for 0.2-1.0 h, followed by air cooling,
and 680-730°C for 2-4 h, again followed by air cooling [10]. The first stage of annealing controls
the fraction and morphology of α phase while the second stage allows the precipitation of acicular
secondary α phase in the metastable β phase. The Ti64 alloy was solution-treated 925℃ for 1 h,
fan air cooled and then stabilized at 700℃ for 2 h by Nalla et al. [17]. As can be seen from Fig.
1.9, the microstructure after duplex annealing consists of equiaxed primary α and lamellar α+β,
similar to that after recrystallization annealing.
1.2 Improvements of cutting tools and other approaches
Titanium is not actually a rare substance as it ranks as the ninth most plentiful element and
the fourth most abundant structural metal in the Earth’s crust exceeded only by aluminum, iron,
and magnesium. Unfortunately, it is seldom found in high concentrations and never found in a
pure state [1]. However, the poor machinability of Ti and its alloys, which leads to high costs of
finished parts, has severely limited their applications [18]. The poor machinability of Ti alloys
11
arises from their extremely low thermal conductivity ( ~7.5 W/Km [2]). Also, the phase
transformation from α to β may occur at high cutting speeds [19], which can be detrimental to the
cutting tool since the β phase is much more chemically active, with 4-5 orders of magnitude faster
diffusivity [8].
Machinability has not been accurately defined but it should at least take the following aspects
into account: tool life, removal rate of work materials, cutting force, surface finish and chip shape
[20]. Tool life is the machining time by which a fresh tool can work before a specified amount of
tool wear is obtained [21]. To be specific, tool life when machining titanium can be defined as the
machining time by which a fresh tool can work before the flank wear reaches a specified amount.
If the experiments are carried out at the same cutting speed, the cutting length can be utilized
instead of the machining time in some cases. However, titanium and its alloys are notoriously
known for its poor machinability (low machining efficiency and severe tool wear), which can be
attributed to their extremely low thermal conductivity and high hardening rate [2], [20]–[22].
There have been many attempts to improve the tool life in different ways. Nabhani [23] used
cubic boron nitride (CBN) and polycrystalline diamond (PCD) inserts as cutting tools for titanium
alloys. The higher critical temperature at which adhesion and welding started to develop indicated
that PCD (760C) and CBN (900C) coated inserts had higher cratering wear resistance than the
bare carbide tool (740C). Schrock et al. [19] investigated the crater wear condition of both PCD
and carbide inserts at different cutting speeds. For PCD inserts, the rake face wear was uneven,
fractured and rough, indicating attrition at 61 m/min. A smooth crater developed at 122 m/min,
showing a diffusion/dissolution wear mechanism. For carbide inserts, the rake face showed
smooth craters at both cutting speeds. Amin et al. [3] investigated the effectiveness of uncoated
WC-Co and PCD inserts in end milling of Ti64 alloy. The results show that average surface
12
toughness produced by PCD inserts is lower than that produced by carbide inserts. As can be seen
from Fig. 1.10, total volume of metal removal per tool life for PCD insert is much larger than that
for carbide inserts over a much higher cutting speed range. At the cutting speed of 120 and 160
m/min, the volume of metal removal of PCD inserts is almost 3 times as large as that of carbide
inserts. The applicable cutting speed for uncoated carbide should be 40 m/min while for PCD tool
it should be 120 m/min.
Figure 1.10 Total volume of metal removed per tool life shows the coated PCD tool has superior
ability of cutting titanium alloys, compared with the tungsten carbide insert [3].
Three PCD tools made of different diamond grain sizes (CTB002 (2μm), CTB010 (10μm)
and CTM302 (2-30μm)) were examined by turning experiments [24]. The flank wear of tools
CTB002 and CTB010 developed steadily as indicated by the linearly increasing tangential force
and the maximum width of flank wear (VBs). For CTM 302, large-scale fracture happened at the
beginning of the cutting and the fracture at the tip restricted the development of flank wear. On the
rake faces, scattered adhesion layers were found on the rake faces of the tools CTB002 and
CTB010. An intact adhesion layer was preserved on the rake face of the tool CTM302. In addition
to the elements from PCD inserts (Co) and workpiece material (Ti), oxygen was found on the tool
13
rake faces due to the oxidation of the adhered titanium alloy. Plus, the oxygen content was related
to the cutting temperature at the tool/chip interface.
Since the coated tools are costly but not as effective as expected in improving the wear
resistance in dry machining process, other clean and sustainable cutting approaches have drawn
the attention. Many researchers [25]–[33]turned to the minimum quantity lubrication (MQL)
approach, which consumes very small amount of fluids (typically 20-150mL/hr [34]). Compared
with conventional flooding method, which obviously is a non-clean cutting approach, even with
the clean and sustainable dry cutting, MQL is cost-efficient and guarantees the safety for both
environment and the worker. Wang et al. [32] machined Ti-6Al-4 V alloy using various turning
approaches such as dry, wet cooling, MQL cooling. It can be concluded that coefficient of friction
under MQL turning at higher cutting speed was much lower than dry turning and flood cooling,
and ultimately resulted in enhanced lubrication at the tool-chip contact surface. In contrast with
the dry cutting condition, temperature and the consequent tool wear is significantly decreased
using MQL strategy [35]. Some other researchers [36]–[38], [39, p. 2], [40]–[42] adopted
cryogenic cooling approach, using liquid nitrogen (LN2) or CO2-snow to lower the high
temperature caused by cutting in order to extend the tool life. Compared to dry and flood
machining, both flank wear and rake wear were reduced during cryogenic machining at 150 m/min.
In addition, the cutting forces decreased by 15% and 44% at 100 m/min and 150 m/min,
respectively [37]. Nevertheless, the consumption of LN2 can add considerably to the total
machining cost [38]. However, both cutting strategies still lead to segmented chips.
1.3 Formation of segmented chips
Since the coatings are not so cost-effective in extending tool life, a better understanding of
the formation of segmented chips might be the key to improving the machinability of Ti64. In
14
previous research work, the thermo-plastic instability took place when the critical cutting speed of
0.15 m/s (9 m/min) was exceeded [43], [44]. Also, the shear bands started to show up when the
chip load (the cutting speed times the feed rate) is around 0.004 m2/min [43], [45]. Ye et al. [46]
validated that the transition of the flow pattern from continuously serrated to discontinuously
segmented almost always occurs when the input energy is equal to or greater than the total energy
dissipation during the whole shear band relaxation process.
There have been two theories concerning the formation of the segmented Ti chips obtained
from machining. One possibility is the propagation and growth of cracks from the outer surface
of the chips [43], [47]. The other one attributes segmented chip formation to adiabatic shear bands
caused by localized shear deformation resulting from the predominance of thermal softening over
strain hardening [48], which is also frequently referred to as a thermoplastic instability. According
to Vyas and Shaw [47], a shear crack will initiate at the free surface at point D in Fig. 1.11, where
the shear stress is maximal, and will proceed downward along the shear plane toward the tool tip
(point O). Initially, the crack will be continuous across the width of the chip, which is called a
gross crack, but will become discontinuous as higher crack arresting normal stresses are
encountered. These disconnected localized cracks are called microcracks.
15
Figure 1.11 mechanism of saw tooth formation due to the crack propagation along the maximal
shear direction [47].
Continuum isotropic models for segmented chips have been developed, where the width of
the shear band can be calculated based upon the model developed by Molinari et al. [22], [49]:
12√2𝑚cos(𝜃 − 𝜔)𝑘𝑇𝑟
𝑡=
𝑎𝑡0 𝑉𝑐𝑜𝑠𝜃
where 𝜃 is the shear angle, 𝜔 is the tool rake angle (0 in this study), 𝑚 and 𝑎 are non-dimensional
strain hardening and thermal softening coefficients of the material, 𝑘 is the thermal conductivity,
𝑇𝑟 is room temperature, 𝑡0 is the shear flow resistance and 𝑉 is the cutting speed. The non-
dimensional thermal softening parameter 𝑎 can be calculated based on [22], [50]:
𝛼𝜅0
𝑎= × (𝑏𝜀̇0 )𝑚
𝜌𝑐
16
where 𝜅0 is the yield strength, 𝜌 is the density, 𝑐 is the specific heat capacity, 𝜀̇0 is the reference
strain rate and 𝑏 is a physical constant of the material. The parameters used for the calculation can
be obtained in [22]. Ye et al. [51] proposed the concept of shear band evolution degree and that
the evolution degree is the ratio of current shear displacement to the critical shear displacement.
When the evolution degree is less than 1, the shear band is not fully mature, and this will influence
the shear band spacing as a result of the shear stress in the shear band. Once the shear displacement
reaches the critical value of 1, the shear stress in the shear band vanishes [51] and the shear band
stops growing in width because the propagation process of shear bands is stress-controlled [52].
From orthogonal cutting experiments, Ye et al. determined that the evolution degree can be worked
out from the fluctuation of the cutting force:
𝐹𝑚𝑖𝑛
𝑋 =1−
𝐹𝑚𝑎𝑥
Liu et al. [22] investigated the milled Ti64 chips and shear band widths at 250 m/min and 500
m/min were measured to be 5.8 and 5.9 μm, respectively. According to the model, the shear band
width is inversely proportional to the cutting speed, thus the shear band width at 250 m/min should
be twice that at 500 m/min. On the other hand, the evolution degree at 250 m/min was calculated
to be half of that at 500 m/min. Finally, these two cutting speeds resulted in similar as-measured
shear band widths at 250 and 500 m/min.
In general, the homogeneous shear strain 𝛾𝑠𝑒𝑔 between shear bands is given by [53]–[55]:
1 2𝜆ℎ cos(𝜌𝑠𝑒𝑔 ) 1
𝛾𝑠𝑒𝑔 = √𝜆ℎ 2 − + 2
𝜆ℎ 𝑠𝑖𝑛𝜙𝑠𝑒𝑔 sin(𝜙𝑠𝑒𝑔 + 𝜌𝑠𝑒𝑔 ) 𝑠𝑖𝑛 (𝜙𝑠𝑒𝑔 + 𝜌𝑠𝑒𝑔 )
where 𝜙𝑠𝑒𝑔 is the direction of the localized shear, 𝜌𝑠𝑒𝑔 is the complementary angle of 𝜙𝑠𝑒𝑔 . 𝜆ℎ is
the chip compression ratio that can be obtained by the ratio of the deformed chip thickness, ℎ𝑐 ,
and the undeformed chip thickness, ℎ, or the ratio of cutting speed, 𝑣𝑐 , and chip flow speed, 𝑣𝑐ℎ ,
17
as illustrated in Fig. 1.12:
ℎ𝑐 𝑣𝑐
𝜆ℎ = =
ℎ 𝑣𝑐ℎ
The catastrophic shear strain, 𝛾𝑐 , and the strain in the shear band, 𝛾𝑠𝑏 , are:
𝑝𝑠𝑏
𝛾𝑐 =
𝛿𝑠𝑏
𝛾𝑠𝑏 = 𝛾𝑠𝑒𝑔 + 𝛾𝑐
where 𝑝𝑠𝑏 is the shear displacement (referred to as “shear band projection” in their context [55])
and 𝛿𝑠𝑏 is the shear band width. This model provides the means to investigate the correlation
between the shear strain and the chip morphology and potentially better understanding for the
formation of segmented chips. Results of these models can be compared with the criteria that
adiabatic instability happens when the slope of true stress-true strain curve becomes zero [56], [57].
18
Figure 1.12 Shear strain calculation based upon the chip segment geometry [55].
When investigating the formation of segmented chips, finite element (FE) simulation is a
powerful and useful methodology that has been widely adopted in modeling of the machining
process [58]. The modeling procedure is a challenging task using even the most advanced software
since the machining process is under severe deformation condition such as high strain, high strain
rate, high stress and high temperature. Therefore, most of the published research work was
performed under the assumption of orthogonal cutting, the simplest configuration of machining.
The main issues in FE simulation of machining operations are:
1. To provide accurate material constitutive and damage models, over a wide range of strains
(0.1-10), strain rates (105-106 s-1), and temperatures (800-900°C or even higher when machining
hard-to-cut materials) (material nonlinearity).
19
2. To define mechanical and thermal contacts at the tool-chip and tool-workpiece interfaces
correctly.
3. To overcome the severe element distortion due to chip formation (geometric nonlinearity).
4. To calculate both temperatures and displacements simultaneously in a highly nonlinear,
coupled thermomechanical dynamic process.
The tool is mostly considered as a rigid body due to its high stiffness compared with the
workpiece [59], [60]. Al-Zkeri et al.[61] compared the results obtained using rigid and elastic tools.
The simulation started with a rigid tool model to minimize the simulation time. After reaching
steady state cutting temperature and forces, the tool was switched to an elastic body and the elastic
tool stresses were computed. The results showed that the stress in the elastic tool model is only 2%
lower than the rigid body model, attesting the validity of the FE modeling with the assumption of
considering the tool as a rigid part.
Only a portion of the workpiece is modeled as a planar rectangle (2D simulation) with a
relatively short length compared to the actual workpiece, for simplicity. the plane strain condition
was usually assumed in orthogonal turning tests when the uncut chip thickness (feed) was much
smaller (5-10 times) than the width of cut.
The equations of motion for 2D cutting problems are as following [62]:
𝜕𝜎𝑥𝑥 𝜕𝜎𝑥𝑦 𝜕 2 𝑢𝑥
+ + 𝜌𝑏𝑥 = 𝜌
𝜕𝑥 𝜕𝑦 𝜕𝑡 2
𝜕𝜎𝑦𝑥 𝜕𝜎𝑦𝑦 𝜕 2 𝑢𝑦
+ + 𝜌𝑏𝑦 = 𝜌
𝜕𝑥 𝜕𝑦 𝜕𝑡 2
where 𝜎 is the Cauchy stress, 𝜌 is density, 𝑏 is the body force, 𝑡 is time, 𝑢 is the material
displacement, and 𝑥 − 𝑦 is the reference coordinate system.
Heat transfer during the machining process is governed by the energy equation as following
20
[63]:
𝜕𝑇 𝜕𝑇 𝜕𝑇 𝜕 2𝑇 𝜕 2𝑇
𝜌𝑐 ( + 𝑉𝑥 + 𝑉𝑦 ) = 𝑘 ( 2 + 2 ) + 𝑄̇𝑔
𝜕𝑡 𝜕𝑥 𝜕𝑦 𝜕𝑥 𝜕𝑦
where 𝑐 and 𝑘 are specific heat capacity and thermal conductivity, 𝑉𝑥 and 𝑉𝑦 are the material
velocities in the 𝑥 and 𝑦 directions. Also, 𝑄̇𝑔 is the sum of heat generations from two sources
during machining: plastic work in the primary and secondary deformation zones and frictional
work on the tool-chip interface. The heat generation equation is [63]:
𝑄̇𝑔 = 𝜂𝑃 𝑊̇𝑃 + 𝜂𝐹 𝑊̇𝐹 = 𝜂𝑃 (𝜎𝜀̇𝑃 ) + 𝜂𝐹 (𝜏𝑉𝑐ℎ )
where 𝜂𝑃 and 𝜂𝐹 are the fraction of plastic work converted to heat and the fraction of friction work
converted to heat. 𝑊̇𝑃 and 𝑊̇𝐹 are in turn the rate of plastic work per unit material volume and the
rate of frictional work per unit contact area. 𝜎, 𝜀̇𝑃 , 𝜏 and 𝑉𝑐ℎ are flow stress, effective plastic strain
rate, frictional shear stress at the tool-chip interface, and chip velocity along the tool-chip interface,
respectively.
The conduction heat transfer between the chip and tool:
𝑄̇ = ℎ𝑖𝑛𝑡 (𝑇𝑐ℎ − 𝑇𝑡 )
where ℎ𝑖𝑛𝑡 is t he thermal conductance coefficient between chip and tool, 𝑇𝑐ℎ and 𝑇𝑡 are the
temperatures of chip and tool, respectively.
Similarly, convection heat transfer between the chip and the surrounding ambient is:
𝑄̇ = ℎ(𝑇𝑐ℎ − 𝑇𝑎 )
where ℎ is the convection heat transfer coefficient between the chip surface and the ambient, 𝑇𝑐ℎ
and 𝑇𝑎 are the temperatures of chip and ambient, respectively.
It has been well recognized that the material model in the FE simulation of machining process
cannot be identified using quasi-static tests, due to the fact that the material undergoes high strain,
21
strain rate, and temperature during cutting process. Therefore, alternative techniques such as high-
speed compression tests, impact tests, and split pressure Hopkinson bar (SPHB) tests have been
extensively used in determining material constitutive and damage models in FE simulation. The
commonly used material constitutive models include: Johnson-Cook [64], Power law, Zerilli-
Armstrong [65], Usei-Maekawa-Shirakashi [66], Oxley [67], Marusich [68], among which
Johnson-Cook is the most commonly adopted one:
𝜀̇ 𝑇 − 𝑇𝑟 𝑚
𝜎 = (𝐴 + 𝐵𝜀 𝑛 ) (1 + 𝐶𝑙𝑛 ) [1 − ( ) ]
𝜀̇0 𝑇𝑚 − 𝑇𝑟
where 𝜎 is the equivalent flow stress, 𝜀 is the equivalent plastic strain, 𝜀̇ is the equivalent plastic
strain rate, 𝜀̇0 is the reference equivalent plastic strain rate, 𝑇 is the workpiece temperature, 𝑇𝑚 is
the material melting temperature, 𝑇𝑟 is the room temperature. Different values of the material
constants (𝐴, 𝐵, 𝑛, 𝑚) for Ti64 based upon researchers’ experimental work [69]–[72] can be found
in [73].
Among all the friction models, the constant Coulomb friction coefficient at the entire tool-
chip interface shear friction model is most commonly used [58], the friction factor is defined as
following:
𝜏
𝑚=
𝜏𝑌
Where 𝜏 is the frictional shear stress and 𝜏𝑌 is the work material shear flow stress.
There have been many other attempts [74]–[79] to obtain good agreement between the
experimental and simulation results in terms of the cutting forces and chip morphologies, by
modifying and comparing the constitutive models. Calamaz et al. [78] carried out numerical
analysis of chip formation and shear localization in the cutting process of Ti64 alloy, using a
modified Johnson-Cook model. The result showed that the best agreement was obtained when
22
using a high friction coefficient of 2, together with the introduced strain softening parameter a of
0.11. Ducobu et al. [79] investigated three different models for simulations:
First model: Lagrangian with Johnson–Cook law (LJC), taking only crack propagation into
account.
Second model: Arbitrary Lagrangian Eulerian (ALE) with TANH law (ALETHAN), taking
only strain softening into account.
Third model: Lagrangian with TANH law (LTANH), taking both crack propagation and strain
softening into account.
As shown in Fig. 1.13, The first model leads to many highly deformed elements, but no
apparent serrated chips can be observed. This is mainly due to the unavailability of continuous
remeshing in Abaqus/ Explicit v6.8. The second model produces a chip with small teeth. In contrast,
the third model produces a saw-toothed chip with a morphology that is observed in the
experimental results [80].
23
Figure 1.13 Von Mises stress contours during chip formation using different material models
LTANH model shows the appearance of cracks [79].
Zang et al. [81] made attempts to explain the segmented chip formation mechanism with FE
simulation. The results showed that the temperature of adiabatic shear zone is obviously higher
than the surrounding segments. At each cutting speed, a crack was observed right next to the
adjacent shear band (Fig. 1.14). Both the crack length and the segmented degree of the chips
increased with increasing cutting speed. Indeed, the primary shear zone initiates around the tool
tip and propagates toward the free surface, and then the crack initiates from the free surface of the
chip. A similar conclusion has been made in the paper by Molinari et al. [74]. In their investigation
of adiabatic shear band formation in cutting Ti64 alloy, it has been found that the shear bands are
generated at the tool tip and propagate towards the chip free surface. Shear bands grow within the
chip formation region as the chip flows away from the workpiece. As shown in Fig. 1.15, the shear
24
band has no time to reach the free surface of the chip, as the shear band propagation time is longer
than the shear band convection time. As a result, the shear bands are not fully developed.
Figure 1.14 Micrographs of serrated chips and the temperature profiles of simulated adiabatic
shear bands for Ti- 6Al-4V (a) 80, (b) 120, and (c) 160 m/ min [81]. The temperature within the
adiabatic shear band shows the shear band is triggered by the secondary shear zone.
25
Figure 1.15 Chip morphology and strain isoclines at the cutting speed of 350 m/s with the feed of
0.1 mm [74]. The strain field indicates how the adiabatic shear band originates from the
secondary shear zone.
Sima et al. [73] conducted serrated chip formation simulation of the Ti64 alloy using
constitutive models with non-temperature-dependent parameters (Model 1), with temperature-
dependent parameters (Model 2), and with temperature-dependent parameters and strain softening
(Model 3), all of which are based upon J-C constitutive model. Predictions using Model 3 resulted
in the closest matches to the experimental forces and cutting and thrust forces for the other two
uncut chip thickness conditions. According to Model 3, effective shear strain in the shear bands is
much higher than that in the chip segments (Fig. 1.16). However, their results showed that effective
shear stress within the primary shear zone is much higher (Fig. 1.17), which is contrary to the
thermo-plastic instability hypothesis.
26
Figure 1.16 Effective strain values along a path into the segmented chip with adiabatic shearing
[73]
Figure 1.17 Effective stress values along a path into the segmented chips [73].
Many papers [2], [22], [46], [82] have revealed that the transition of chip morphology from
continuous chips at a cutting speed as low as 0.05 m/s, to more or less regular serrated with
localized shearing and possible presence of cracks at the cutting speed from 1 - ~40 m/s, and
discontinuous chips at very high cutting speeds. In addition, the chip morphology is also dependent
on the depth of cut [83], initial microstructure of the workpiece [84], and even the wear condition
of the cutting tool [85], [86].
Only one paper published in 2022 focused on the effect of initial orientations of workpiece
on the formation of segmented chips, to the author’s best knowledge. The effect of both initial
27
texture and strain hardening on the formation of Ti64 chips in orthogonal cutting has been
investigated by Palaniappan et al. [87]. The texture modification was induced by cold-rolling Ti64
plates with thickness reductions of 30%, 40%, 45% and 47%. A gradual transition from
heterogeneous to homogeneous deformation has been observed in optical images of the chips
machined from Ti64 plates with increasing thickness reduction (Fig. 1.18). The initial texture of
the plate influenced the ease of deformation in intense shear bands leading to crack formation,
while strain hardening determined the stress increment required to reach a value for fracture to
initiate at the free surface of chip. Prism slip turned out to have the highest Schmid factor in the
annealed as-received Ti64 plate with respect to the shear direction in the primary shear plane. In
addition, among all the slip systems, prism slip has the lowest CRSS and thus it is easy for
severe shear deformation to take place in annealed as-received material. In contrast, basal slip
has highest Schmid factor in the cold-rolled Ti64 plates [87]. However, the Schmid factors are
calculated based upon the general texture, not the local grain orientations. Also, the investigation
basically attributed the formation of segmented chips to the preferred slip systems depending on
the texture detected.
28
Figure 1.18 Optical micrographs of chips machined from plates subjected to different thermo-
mechanical processing conditions: as-received(AR), as-received material annealed and cold-
rolled (ARA) and the number indicates the cold rolling reduction percentage [87].
1.4 Shear bands in other severe deformation process
Adiabatic shear deformation is used to describe the localization of plastic flow that occurs in
many metals and alloys when they are deformed at high strain rates to large plastic strains, for
instance, in high speed torsion and compression, ballistic impact, machining and explosive
fragmentation [88]. It is usually manifested as zones of intense shear deformation and/or
microstructural modification of the original material, up to hundreds of microns wide, interspersed
between regions of lesser and relatively homogeneous deformation. Adiabatic shear has been
interpreted theoretically in several ways. Flow localization in shear is attributed to the destabilizing
effect of the thermal softening which can outweigh the effects of strain and strain rate hardening
in a deforming region when the local rate of heat generation resulting from the plastic flow exceeds
the rate of dissipation into the surrounding material. By assuming negligible stain rate sensitivity,
29
and that the onset of shear localization coincides with the maximum in the local shear stress-shear
strain curve, the susceptibility of metals to adiabatic shear banding can be easily predicted. The
observations of the frequent occurrence of shear bands in aluminum, titanium, uranium, and steels
during the ballistic impact is in accord with these predictions. Adiabatic shear banding is an
important deformation mode and the shear zones later become sites for eventual failure of the
material. Once intense shear localization has commenced, steep strain, strain rate and temperature
gradients are generated perpendicular to the plane of localization and change with time. These
parameters and the evolution of the shear bands have not been well understood, but material
properties definitely play an important role in determining the final widths and structures of these
shear bands.
Shear bands in metals and alloys can be classified as either transformed or deformed, on the
basis of their metallographic appearances. The transformed shear bands refer to those with a
permanent change in microstructure, whereas deformed shear bands are manifested as zones of
intense shear deformation consisting of the original microstructure. The temperature rise in the
transformed shear bands is thus supposed to be higher than the deformed one. In steels, the
transformed shear band is generally martensitic, and the shear deformation is sufficiently localized.
Shear bands in α+β titanium alloys exhibit broadly similar behavior. This implies that the
transformed shear band is associated primarily with phase transformation in the shear band, and
hence restricting the number of alloy systems in which it can form. The resistance to adiabatic
shear deformation of different alloys was evaluated via critical strain and relative critical strain
rate to form shear zones of comparable width and plotted in Fig. 1.19. It can be seen that metals
with low thermal diffusivity and low resistance to adiabatic shear localization are more susceptible
to the formation of transformed shear band. CP Ti, Ti64 and 4130 steel tend to form transformed
30
shear bands, while 1020steel and aluminum alloys tend to form deformed shear bands. Pure copper
and pure aluminum rarely form discrete shear bands, but rather zones of diffuse shear. Low thermal
diffusivity may cause the local temperature to rise rapidly at an early stage of deformation, to
exceed the transus temperature, or even perhaps to melt the shear band material under extreme
conditions. The phase transformation may be achieved by the rapid diffusion of various atomic
species at elevated temperatures within a very short time (typically up to tens of microseconds).
For instance, it is noteworthy that in pure titanium the self-diffusion coefficient of pure α jumps
from 10-12 to 10-9 cm-2s-1 for β at the transformation temperature.
Figure 1.19 Thermal diffusivity at room temperature of different metals plotted against their
resistance to adiabatic shear localization (note different logarithmic scales in (a) and (b)). Solid
symbols: metals tend to form transformed shear bands (region Ⅰ); half-open symbols: metals tend
to form deformed shear bands (region Ⅱ); open symbols: metals do not tend to form discrete
shear bands (region Ⅲ) [88].
The adiabatic shear bands of AM50 and Ti64 alloys in the shear compression tests were
investigated by Rittel et al. [89]. The true stress and strain curves show three stages in the shear
compression process (Fig. 1.20). Stage 1 extends from 𝜀 = 0 to 𝜀(𝜎𝑝𝑒𝑎𝑘 ). In this stage, plastic
deformation is uniform, without localization. The temperature increases modestly with increasing
31
strain. The measured temperature rise is always less than the calculated rise, indicating that some
of the energy is stored in the material. Stage 2 spans from the strain at peak stress to the strain at
which the measured and calculated thermal curves intersect. In this stage the stress is decreasing,
and the measured temperature exceeds the calculated limit past the intersection point. The
deformation is not strictly homogeneous, but not yet fully localized either. Generally, the measured
temperature below the calculated value, indicating that the underlying assumption of strain
homogeneity is still valid to some extent for temperature rise estimation. Stage 3 starts when the
calculated temperature is lower than the measured one, showing that all of the mechanical energy
transforms into heat. The intersection point of the two temperature curves indicates the onset of
the intense localization corresponding to the ASB. The true stress- strain curve no longer represents
the real status of the deforming gauge as a result of shear localization and thermal softening is
dominant in this stage. Elongated dimples are seen on the fracture surface of Ti64 alloy while
extensive wear features are observed for AM50.
Figure 1.20 Typical stress and temperature vs. strain for (a) AM50 and (b) Ti6Al4V alloys for a
strain rate is around 3000s-1. The temperature is measured at three locations and recorded
channels 2, 3, and 5, and compared with calculated value (dashed line) [89].
The evolution of multiple adiabatic shear bands of commercially pure titanium and Ti-6Al-
4V alloy in a thick-walled implosion experiment is investigated by Xue et al. [52]. The sample
32
was sandwiched between a copper driver tube and a copper stopper tube and is collapsed inward
during the test at a strain rate of ~104s-1. The shear bands nucleated at the internal surface of the
specimens and construct a periodic distribution at an early stage. The thickness of the shear band
varied with respect to the distance from its tip. The largest shear band thickness in CP Ti is
approximately 10 µm. It is observed that a number of microstructure changes could and did occur
within the shear bands, including dynamic recovery and recrystallization, phase transformation
and even amorphization, depending on the temperature that can be reached within the shear band.
The presence of fine equiaxed subgrains within the shear band, with an average diameter of 0.2
µm provided direct evidence for dynamic recrystallization. The deformation time is lower by
orders of magnitude than that required for diffusion. Thus, a rotational recrystallization mechanism
by Derby [90] in the classification of dynamic recrystallization, was proposed for the shear bands.
In their study, bifurcation (Fig. 1.21) of shear bands is geometrically necessary due to the spiral
trajectory of the bands, starting on the internal surface. Similar bifurcation features have been
observed in other research [15], [91]. The propagation mechanism of shear bands is a rotation
mechanism as illustrated in Fig. 1.22 [92]. Fig. 18 shows the nucleation, growth, elongation and
rotation, and the coalescence of the voids within the shear bands. Similar phenomena (Fig. 1.23)
are also observed in the SHPB compression tests [15].
33
Figure 1.21 Shear band bifurcation and induced damage in Ti– 6Al–4V alloy [52].
Figure 1.22 Void nucleation and growth inside a shear band in Ti–6Al-4V alloy: (a) nucleation
of voids within a shear band; (b) growth of voids; (c) elongation and rotation of voids; (d)
coalescence [52].
34
Figure 1.23 The nucleation, growth, and coalescence of micro-voids in the interfaces
between ASBs and matrix bulk [15].
Adiabatic shear bands are usually studied by the method of ballistic impact tests. Meyers et
al. [92] investigated the microstructure of the adiabatic shear band in commercially pure titanium
in the ballistic impact test. A CP Ti plate with a thickness of 12.5 mm, was impacted by a
cylindrical steel projectile with a diameter of 3 mm at the velocity of 600 m/s. The penetration into
the target was about 6 mm. ~15 shear bands were observed on the section along the axis of
projectile. The widths of the bands varied between 1 and 10 microns. Regions away from the shear
bands, but close to the impact surface show abundant twinning. In the boundary between the shear
band and matrix, very small grains and well-defined grain boundaries within the shear bands can
be observed. The selected area diffraction (SAD) pattern of the matrix shows HCP reflections from
one crystal ([11̅01] zone axis), while the SAD pattern of the shear band shows a discontinuous
HCP ring, indicating multiple small grains. The micro-grain morphology doesn’t change
significantly from the center of the band toward the matrix, indicating that the material did not
melt. Solidification would most probably produce columnar grains in the vicinity of the shear
band-matrix interface. The grain size ranges from 0.05 to 0.3 microns. The dislocation density in
the micro-grains is in general not very high. It seems to be somewhat higher in larger grains.
Parallel and regularly spaced Moire fringes indicate that no dislocations exist in small grains.
35
To better understand the deformation behavior of pure titanium, an adiabatic stress-strain
curve was developed. The interpolation of the isothermal stress-strain curves was made by
assuming a linear stress strain response at all temps for the tests conducted by Conrad et al. [93],
and discussed by Meyers [92]. Low strain-rate data was used due to the unavailability of high
strain-rate date. The temperature computation was finished after a shear strain increment of 0.1. In
each increment, the area under the stress strain curve was computed and the energy was fully
converted to the temperature increase by using the temperature-dependent heat capacity.
Catastrophic shear will occur at a plastically deforming location within a material when the slope
of the true stress-true strain function becomes zero [57] and is in accordance with the result by
Meyers et al. [92]. From Fig. 1.24, the instability sets in at 𝛾 = 1 at a temperature of approximately
350 ℃. The critical shear strain predicted by Culver et al. [94] was 1.2-1.4, which is surprisingly
close to what was obtained in this study. In some metals, the shear strain within a shear band has
been found to reach values of even more than 500. For the Ti64 tested under similar conditions, a
shear strain of 5 was found.
Figure 1.24 Isothermal (straight lines) shear stress-strain response of commercially pure titanium
between 100 and 1000 K; adiabatic shear stress-strain curve showing maximum at 𝛾 = 1 [92].
36
A micromechanical mechanism for the propagation of shear bands has been proposed (as
illustrated in Fig. 1.25), although any proposed mechanism for the formation and propagation of
the shear bands is speculatory at this point. The temperature rise and thermal softening within the
bands were caused by the adiabaticity. As the plastic deformation continued, the band region
underwent dynamic recrystallization, leading to the grain size reduction. An equilibrium
temperature was achieved at which deformation took place primarily by micrograin boundary
sliding. This mechanism is also favored by creep and super-plasticity at high temperature. It is
noteworthy that the central part of the micrograin won’t undergo significant plastic deformation
and the deformation within the shear band will take place without deforming the grains to the same
extent as the global strain. The shear band width could be constant due to the rotations of the
micrograins. Also, the dislocations whose generation and motion is the shear mechanism can be
annealed out at such high temperature.
Figure 1.25 Proposed mechanism for shear band propagation involving micrograin rotation and
sliding of micrograin boundaries. (A) Microngrain rotating by 2π and translating by 2πr in
process; hatching indicates regions in which substantial plastic deformation has to take place. (B)
Array of rotating micograins producing translation of upper part of band with respect to lower
part [92].
37
1.5 Critical assessment of understanding of adiabatic shear in Ti64 cutting
Although many attempts have been made over the past decades regarding machining Ti64
alloy, there is still lack of understanding of the formation of the segmented chips. Relevant
questions include:
1) Which mechanism is dominant when forming the segmented chips, cracking or adiabatic
shearing?
2) How to estimate the homogeneous shear strain and the catastrophic shear strain and how
does the cutting speed affect them?
3) What is the correlation between the shear strains and the two mechanisms of segmented chip
formation?
4) Does the microstructure and local crystal orientation influence the morphology of the
segmented chips? If so, how do they influence and what crystal orientation is beneficial for
the formation of adiabatic shear?
5) Is there direct evidence of the α → β phase transformation during cutting?
Thus, the aim of the present study is to further investigate the formation of segmented chips
from the perspective of materials science, based upon the local stress tensor revealed by FE
simulation and local orientations characterized by electron backscattered diffraction (EBSD).
In the present dissertation, stress tensor obtained from finite element numerical simulation
will be adopted for Schmid factor analysis and compared with the simplified plane strain
compression assumption. Detailed information on the constitutive model and material constants,
as well as other experimental methodologies will be introduced in Chapter 2. Chapter 3 contains
the initial microstructures of solution treated and aged (STA), mill annealed (MIL), elongated
(ELO) and lamellar (LAM) grade Ti64. Preliminary observations of the chips obtained from
38
cutting these four grades are introduced in Chapter 4. In Chapter 5, the model that predicts the
shear band width and another model that calculates both the homogeneous shear and catastrophic
shear in the chips, are introduced and adopted to compare the effect of cutting speeds on the
formation of segmented STA chips. More cases are incorporated, analyzed, and discussed in detail
in Chapter 6, in order to reveal the rationale behind the nucleation of cracks and adiabatic shear
band. Annealing of STA chips at 500, 600 and 650 ℃ were carried out to examine how the
deformation microstructure responds to heat treatment as a forensic means to infer the state of the
deformed chip, and the results are discussed in Chapter 7.
39
CHAPTER 2 METHODOLOGY
2.1. Turning experiments
The chips used in this study were obtained from dry turning experiments performed on a
solution-treated and aged (STA) Ti64 bar with a diameter of 12.7 cm and a length of 64.8 cm,
obtained from Rolled Alloys Inc. Fig. 2.1 shows three schematic views of the turning experiment
where the observed cross section of the chip is illustrated in Fig. 2.1 (c). The original as-received
bar microstructure was characterized on the surface perpendicular to the radial direction, which is
the same material orientation that is viewed on the chip. The bar was turned at cutting speeds of 1,
1.5, and 2 m/s (61, 91, and 122 m/min), respectively, where 1 m/s is a typical industrial cutting
speed. The 1.2 mm depth of cut and 0.127mm/rev feed rate were kept constant for all turning
experiments. The cutting tools were uncoated H13A grade tungsten carbide (WC) tool from
Sandvik Coromant© with 6% cobalt binder, 0◦ rake angle, and 15◦ leading angle. Additional
information about the tool, cutting geometry, and the turning machine are available in [84].
40
Figure 2.1 Geometry of the turning experiment (a) top view; (b) side view along the turning axis;
(c) view from the bar radial direction, which is close to the observation direction of the
segmented chips [95].
2.2. Mounting the chips
Since the chips were curved in a three-dimensional way, a steel supporting clip was used to
hold the chips so that the intended cross section could be polished after mounting them in
conductive Bakelite using a hot press. The stainless-steel clip also provided the means to maintain
a stiff load path between nano-indenter and the base platen in the nanoindentation machine. After
mounting, the chips were ground using 400 to 2000 grade SiC papers until a thickness reduction
of ~ 0.8 mm to observe the middle of the chip since the stress state on the two sides and in the
middle are quite different (as discussed in Chapter 3). The samples were then polished using OPS
(Oxide Polishing Suspension) 0.8 μm Colloidal Silica for 2-3 h to achieve mirror-like surfaces.
41
2.3. Nanoindentation arrays
A Hysitron TI 950 Triboindenter equipped with a Berkovich indenter was used for the
nanoindentation arrays on as-received material, 1 m/s and 2 m/s chips. A matrix of 400 (20 × 20)
indents covering an area of 30 μm × 30 μm was used with a spacing of 1.5 μm. Nanoindentation
measurement arrays were obtained using the high-speed mode of the instrument, with loading-
holding-unloading times of 0.1-0.1-0.1 s and a maximum load of 3000 μN, resulting in penetration
depths in the range of 100–150 nm. Hardness and reduced modulus were derived using the Oliver
and Pharr method [96].
2.4. SEM and EBSD characterization
The microstructure of the as-received material and chips obtained after cutting at 1 m/s and 2
m/s were observed using a Tescan Mira or an Orsay Holding scanning electron microscope (SEM)
with an accelerating voltage of 25 keV, working distance of 15 mm, under the backscattered
electron (BSE) detector. Orientation mapping of both the as-received material and the chips was
investigated using an Ametek (TSL) orientation imaging microscopy (OIM) system on the
TescanMira, or using an hkl system (Oxford Instruments) on the Orsay Holding SEM with a step
size of 0.25 μm. Analysis and cleanup of EBSD data (including one iteration of neighbor
confidence index (CI) correlation followed by grain CI standardization clean-up) was conducted
using OIM Analysis software v.8.5.0. The method for identifying the width of shear bands is based
upon discontinuities in the shapes of deformed αp grains that were sheared. The shear band width
is determined to be the distance between the parallel lines where the shape of the equiaxed αp
grains become severely elongated, as illustrated schematically in Fig. 2.2.
42
Figure 2.2 Schematic illustration showing shear band width determination. The distance
between discontinuities in the shape of globular αp grains is used to define the shear band width
(𝜎𝑠𝑏 ). The shear band usually contains multiple highly sheared αp grains [95].
2.5 Finite element analysis
To estimate the interaction between the tool and the work material, a 2-D FEA numerical
simulation of the Ti64-STA machining was performed using DEFORM-2D v.11.2 commercial
software [97]. The numerical model was based on a plane strain orthogonal cutting geometry that
approximates turning using a Lagrangian approach that allows continuous remeshing in the highly
deformed chip. The tool was modeled as a mechanically rigid body but with a meaningful thermal
conductivity to allow the temperature to rise during cutting. A heat transfer coefficient of 20 kW/℃
was used to allow fast heat conduction from workpiece into the tool, all initially at 20℃. The initial
mesh had 6043 elements for the workpiece and 2477 elements for the tool. A 5 μm mesh size was
used in the workpiece close to the cutting zone with a constant shear friction coefficient of 0.9
between the tool and workpiece. There are two approaches utilized to simulate the formation of
segmented chips [73], by using damage or material failure models [98]–[100], or by using
modified material models with temperature-dependent flow softening based adiabatic shearing
[75], [101]. In the present work, the isotropic Cockroft-Latham model damage criterion value was
adjusted to a value of 2000 to make the chip segmentation size closer to experimental values. The
43
morphology of the simulated chip is consistent with the actual chips. More detailed information
can be seen in [97].
2.6 IPF maps and pole figures
(110) and (11̅0)inverse pole figure (IPF) maps can also be used to visualize the soft and hard
orientations better with respect to the shear direction. However, rotations about the < 0001 >,<
̅̅̅̅ > and < 112̅0 > by any degrees will still exhibit red, blue and green colors. This is the
1010
intrinsic problem with IPF maps and as a result no choice is perfect. The (001) IPF maps, most
commonly referred to as the normal direction IPF maps, are widely used. In the present study, the
normal IPF maps are used consistently.
Figure 2.3 Confidence index (CI) distribution of the selected orientation (Eulers=[93.2, 120.4,
201]) shows that CI>0.1 can eliminate a number of noise from the scan.
The normal IPF mapping of the as-received Ti-4Al-6V bar is shown in Fig. 2.3. The pole
figures of the scan show a pronounced peak with the Euler angles of [93.2, 120.4, 201]. A partition
44
of this orientation has been made to further analyze this corresponding peak on the pole figure.
The CI distribution map showed that most of these data points have CI<0.1. This indicates that
these are the noise points that contribute to the majority of this peak. So CI>0.1 is crucial for
omitting the noise points. For the as-received material, both the αp and βt (α laths in βt) can be
indexed and the criterion to distinguish the two microconstituents in a course scan is their image
quality (IQ) value. Presumably αp has higher IQ values than βt. As can be seen in Fig. 2.4, the pole
figures of these two microconstituents look similar and βt has made slightly higher contributions
to the micro-texture. It is interesting to note that the transformed β has a strong orientation
relationship with the primary α. It is important to make this clear since no information of βt in the
chips can be collected in deformed chips, probably due to the severe deformation in the material.
In summary, the pole figures are plotted with CI>0.1 and IQ > 50%.
Figure 2.4 The pole figures based upon the contributions of αp and βt microconstituents show that
βt contribute a little more to the peak intensity than αp.
2.7 Rotation of stress tensor from FE simulation
To apply the stress tensors from the FE simulation to the crystal orientations for Schmid factor
calculation purpose, they have to be rotated between the two coordinate systems. The stress tensors
obtained from the simulation results are in the coordinate system with x-axis pointing down and
45
y-axis pointing to the right. They need to be rotated when calculating the Schmid factors in the
coordinate system with x-axis pointing up and y-axis pointing to the left. The rotation matrix is
determined to be:
𝑐𝑜𝑠𝜋 −𝑠𝑖𝑛𝜋 0 −1 0 0
𝑅 = [ 𝑠𝑖𝑛𝜋 𝑐𝑜𝑠𝜋 0] = [ 0 −1 0]
0 0 1 0 0 1
Taking the stress tensor at point #5 for example, the stress tensor in the EBSD coordinates
is determined to be:
303 −279 0 303 −279 0
′
𝜎𝑃5 = 𝑅 ∗ [−279 45 0 ] ∗ 𝑅 ′ = [−279 45 0 ] = 𝜎𝑃5
0 0 174 0 0 174
This indicates that the stress tensor stays in the same form as in the cutting simulation setting,
because the stress tensor is symmetric. The illustration of the three principal stresses (in chapter 5)
also reveals the symmetry of the stress tensor so that the rotation about z-axis by 180° doesn’t
change the stress tensor.
46
CHAPTER 3 UNDEFORMED MICROSTRUCTURES OF THE AS-RECEIVED BARS
The microstructures and micro-textures of the four as-received Ti64 bars were first
investigated in order to provide the basis for comparing the chips from the various grades.
Observations of the segmented surface, smooth surface and the cross-section of the various chips
will be presented in the next chapter.
3.1 Microstructure and textures
Four 4 different grades of Ti-6Al-4V alloy bars were studied, namely solution treated and
aged (STA), mill annealed (MIL), elongated (ELO) and lamellar (LAM). The representative
microstructures of the STA, MIL, ELO and LAM Ti64 alloys are shown in Fig. 3.1. The STA alloy
in Fig 3.1 (a,e) has the typical bimodal microstructure, consisting of ~50 vol. % primary αp (darker
grains), and ~50 vol. % transformed βt, which is also referred to as lamellar α+β regions (brighter
regions) [84]. The MIL grade alloy in Fig. 3.1 (b,f) exhibits equiaxed dark α grains with white β
phases on the grain boundaries. In contrast, elongated α grains with β phases on the grain
boundaries are present in ELO grade in Fig. 3.1 (c,g). The images of the LAM grade in Fig. 3.1
(d,h) have fine β lamellae (straight white lines) and large prior β grain size.
47
Figure 3.1 Representative microstructure of (a) solution treated and aged (STA); (b) mill
annealed (MIL); (c) elongated (ELO), (d) lamellar (LAM) Ti-6Al-4V ;(e)(f)(g)(h) show the
microstructures at a higher magnification. The images at two magnifications share the same scale
bar, respectively.
48
Figure 3.1 (cont’d)
Fine EBSD scans of STA, MIL and ELO alloys can be seen in Fig. 3.2. In general, the β phase
in all three alloys cannot be indexed by OIM. In the STA alloy, the secondary α phase in the
lamellar regions can be indexed. Lamellar regions may be composed of multiple colonies with
various orientations. For the LAM alloy, the size of colonies showing the same orientation is much
larger compared to the other three grades, as shown in Fig. 3.3. The prior β grain size can be greater
than 1 mm and this leads to a significantly different chip morphology as described in Chapter 4.
49
Figure 3.2 Electron backscattered diffraction (EBSD) normal direction inverse pole figure (IPF)
mapping of (a) STA; (b) MIL; (c) ELO Ti64 alloy.
50
Figure 3.2 (cont’d)
Figure 3.3 EBSD normal direction IPF mapping and BSE image of lamellar (LAM) Ti64 alloy.
The grain size of LAM alloy is huge compared to STA, MIL and ELO grades.
51
Figure 3.4 EBSD normal direction inverse pole mapping and corresponding pole figures that
show the macro-texture of (a) STA; (b) MIL; (c) ELO Ti64 alloy.
52
Figure 3.4 (cont’d)
There are many orientations in the STA alloy where each cluster of grains has a similar
orientation leading to the presence of micro-texture. For instance, the two clusters with green color
located in the upper mid and mid part, the red and blue clusters in the lower mid parts of the IPF
color map in Fig. 3.4. These clusters are the reason for the appearance of many peaks on the pole
figures. In the MIL-grade alloy, the right margin of the IPF map shows red-colored orientation and
the left margin shows green-colored orientations, which explains the presence of three dominant
(001) components on the pole figure. The IPF map of ELO alloy shows an overall red-colored
orientation, with non-red-colored orientation appearing on the lower right part. The pole figure
exhibits a strong basal texture as a result. As described in later chapters, the micro-textureed
regions have a strong impact on the machinability of the alloy and the formation of each segment.
53
3.2 Conclusions
The undeformed microstructures of STA, MIL, ELO and LAM grade Ti64 alloys were
investigated. LAM grade has a very large grain size compared to the other three grades and it will
affect the formation of segmented chips.
54
CHAPTER 4 AS-CUT STA, MIL, ELO AND LAM CHIPS
In this chapter, the chips obtained from solution treated and aged (STA), mill annealed (MIL),
elongated (ELO), and fully lamellar (LAM) grade Ti-6Al-4V bars are investigated. The initial
microstructures of these alloys have been discussed in Chapter 3. Images of the serrations, chip-
tool contact surface, and the segmented surface of these chips are compared. In addition, EBSD
scans of the LAM chips showed pronounced effect of the initial orientation on the morphology of
LAM chips. The favorable slip systems are discussed based upon the maximal Schmid factor
calculation under the plane strain compression boundary condition. EBSD and nano-indentation
analysis of STA chips reveal the low strain hardening rate of titanium. Portions of this chapter
describing the STA microstructure are adapted from a published paper1.
4.1 As-received STA chips from stable cutting stage
4.1.1 Cross-section observation
The chip morphologies at various scales with the cutting speeds of 1, 1.5 and 2 m/s are shown
in Fig. 4.1 The 1 m/s chips were much more curled than the 1.5 and 2 m/s chips. The mounted
chips were ground to the approximate middle of the chip for cross-section observation (removed
~0.8 mm). Unlike chips machined at 1.5 and 2 m/s, the micro-morphologies of chips cut at 1 m/s
show a number of undeveloped serrations, which can be considered as a transition from continuous
to serrated chips [22], [37], [83], [96], [102] (serrations and oscillating load occurs above 0.15
m/s). According to Wan et al. [103], the chips obtained from turning at the cutting speed of 30.2
m/s showed only incipient separation of segments. In the present work, the segments/teeth at 1m/s
is much more developed compared with their observation but still less developed than 1.5 and 2
1 Effect of Cutting speed on Shear Band Formation and Chip Morphology of Ti-6Al-4V alloy using Nanoindentation and EBSD
Mapping, Jiawei Lu, Ryan Khawarizmi, Miguel Monclús, Jon Molina-Aldareguia, Patrick Kwon, Thomas R. Bieler, Materials
Science and Engineering A 862 (2023) 144372, DOI: 10.1016/j.msea.2022.144372.
55
m/s. The microstructure of the chips show that the shear bands in the primary shear zone were
oriented about 45° from the chip flow direction.
Figure 4.1 The 1 m/s chip is more curled than 1.5 and 2 m/s chips and the serrations resulting
from the primary shear zones between serrations are more regularly spaced at higher cutting
speeds.
The parameters characterizing the morphology of the chips include: peak height ℎ𝑝 , valley
height ℎ𝑣 , and the distance between two neighboring shear bands 𝑆. These lead to the definitions
of segmentation degree,
ℎ𝑝 −ℎ𝑣
𝐺𝑠 = (1)
ℎ𝑝
shear angle,
𝜋
𝜃 = 2 − 𝜃′ (2)
where θ' is the angle between the smooth surface of the chip and the direction of primary shear
zone [83], the equivalent thickness,
ℎ𝑝 +ℎ𝑣
𝑡𝑒 = (3)
2
56
and the segmentation frequency,
𝑉𝑐
𝑓= (4)
𝑆
From ~70 measurements of segmented chips, all parameters are compared in Fig. 4.2. A
slight increase occurred in peak height, equivalent thickness, and shear band spacing from 1 to 2
m/s with a corresponding decrease in the valley height. The shear angle was nearly the same at
each speed (42.8°, 43.4°, 43.1°, respectively), which agreed with the observation that the
dependence between shear angle and cutting speed in orthogonal cutting is weak at high cutting
speeds [49], [104]. The segmentation degree increased significantly from 0.34 at 1 m/s to 0.45 at
1.5 m/s, and further to 0.48 at 2 m/s, indicating that the chip was more segmented with increasing
cutting speed. For all of these metrics, the spread of the standard deviation for all three speeds
overlap. The frequency of segmentation went up in proportion to the cutting speed, but the
frequency at 2 m/s was less than twice that at 1m/s, consistent with an increase in shear band
spacing at higher cutting speed.
(a) (b)
Figure 4.2 Chip segmentation metrics following definitions in [83] vary slightly with increasing
cutting speed, with spreads that overlap.
57
4.1.2 Segmented surface observation
Figure 4.3 segmented surface of the chips obtained at the cutting speed of (a) 1 m/s; (b) 1.5 m/s;
(c) 2 m/s. Top and bottom sides are non-symmetric.
58
Figure 4.3(cont’d)
The segmented surface of the chips at 1, 1.5 and 2 m/s are shown in Fig. 4.3. It is interesting
to note that the two edges (top and bottom) of the chips are non-symmetric, at all cutting speeds.
The top side is rectangular shaped with a certain amount of height while the bottom side is cut
from the workpiece with the height of zero, which indicates that the formation of segmented chips
initiates from the free-surface side, not the constrained side. This is consistent with the proposal
of Vyas and Shaw [47] that the segmented chip is formed due to the initiation of cracks on the free
surface of the chip. The chip flow direction on this figure is from right to left as shown by the cyan
arrow. This asymmetry is the reason that the cross-section of the chip in the present work is
observed in the middle of the chip (removal of ~0.8mm).
4.1.3 Smooth surface observation
The smooth side observations before polishing are shown in Fig. 4.4. At all cutting speeds,
there are grooves on the tool-chip contact surface. In addition, it shows that there is not much
material removed from tool-chip contact surface on the 1m/s chip surface while many particles
59
have been pulled out at 2 m/s, leaving the scar-like features on the surface, and potentially these
particles form the adhesion layer on the crater surface of the cutting tool. The histograms of both
teeth spacings and scars are investigated and plotted on Fig. 4.5. The results in Table 4.1 show that
the peak of teeth spacing coincides with the peak of scar spacing, especially at 2 m/s, same for the
histogram itself. This indicates that material being pulled out on the chip-tool contact surface is
highly correlated to the formation of the primary shear zone. A possible explanation for this
correlation is the occurrence of α to β phase transformation in the primary shear zone due to higher
temperature increase at the cutting speed of 2 m/s. β phase is much softer and stickier than α and
thus large chunks of material is adhered to cutting tool. This hypothesis is supported by the
observation in Fig. 4.8.
60
Figure 4.4 morphology of the smooth side of the chips before polishing, magnification of 100X
(a) 1m/s; (b)1.5 m/s; (c) 2 m/s and (d) magnification of 500X, 2 m/s.
61
Figure 4.5 the histograms of teeth spacing and scar spacings at the cutting speed of (a) 1 m/s;
(b)(d) 1.5 m/s; (c)(e) 2 m/s.
Table 4.1 peak spacing of the teeth and scars showing the stick slip is highly related to the
formation of PSZ
1 m/s 1.5 m/s 2 m/s
Peak of teeth spacing (μm) 95 102 102
Peak of scar spacing (μm) N/A 115 103
Figure 4.6 Tool-chip contact surfaces at different cutting speeds from [46].
Similar smooth side observation is reported in the work by Ye et al. [46] (Fig. 4.6). When the
cutting speed is as low as 0.05 m/s, the tool-chip contact surface is quite smooth. At the cutting
62
speed of 7.8 m/s, the removal of material can be seen in Fig. 4.6 (a). The features in the green box
are considered as elongated dimples. The regularly distributed dimple structure on the tool-chip
contact surface is related to the periodical shear banding inside the PSZ because their spacings are
in accordance. Also, the periodic dimples indicate that the chip movement on the tool rake face is
stick slip in nature. At cutting speeds of about 69 m/s, local melting occured at the PSZ root on
the rake face. This can be inferred from the formation of fully melted shear bands to render fully
discontinuous chips as further increasing the cutting speed.
Figure 4.7 Left figure: phase determination on the smooth surface of the 1 m/s, 1.5 m/s and 2 m/s
chips. Right figure: Phase analysis of micro-chips formed in micro-milling the (a) first,
(b)second, (c) third, and (d) fourth micro-slot [86].
The XRD results on the smooth side of the chips in our investigation (Fig. 4.7 left image)
failed to show the presence of β phase. However, XRD results on the milling chips by Wang et al.
[86] did attest the appearance of β phase. In addition, the volume fraction of β phase increased
slightly with increasing cutting time. The smooth surface after slight polishing without any
grinding can be seen in Fig. 4.8. The samples were prepared by only polishing without grinding in
order to see the microstructure as close to the tool-chip contact face as possible. The PSZ lines are
more pronounced at 2 m/s compared to 1.5 m/s, but they can be barely seen at 1 m/s. Within these
PSZ lines, more β phase (white color) can be seen with increasing cutting speed. The volume
63
fraction of β phase on the tool-chip contact face is determined by ImageJ. The result show that β
volume fraction increased from 50% (as-received), to 60% at 1m/s, 62% at 1.5 m/s and further to
68% at 2 m/s, as listed in Table 4.2. This provides direct evidence for the phase transformation at
higher cutting speed (2m/s). The TEM selected area diffraction results of the chip obtained from
turning at 59.6 m/s [103] can also support the phase transformation hypothesis. The diffraction
pattern shows the presence of both α and β phases in the ASB [103]. When the cutting speed
increases to 126.6 m/min, multi electron diffraction ring pattern appeared, which indicated
nanocrystalline in ASB [103].
Figure 4.8 microstructure of the smooth side of the chips after slight polishing without grinding:
(a)(d): 1 m/s; (b)(e)1.5 m/s; (c)(f): 2 m/s.
64
Table 4.2 β volume fraction increased with increasing cutting speed
As-received 1 m/s 1.5 m/s 2 m/s
β volume fraction 50% 60% 62% 68%
4.1.4 The chip morphology at the beginning and end of cutting phase
At the beginning phase of cutting (Fig. 4.9), the chips at all cutting speeds show similar
features as those obtained from the stable stage. 1 m/s chips still show less developed segments
and the saw-teeth were more developed with increasing cutting speed. However, near the end phase
of cutting (Fig. 4.10), the chip morphologies are so distinctive from both the beginning and steady
stages. At 1 and 1.5 m/s, the segmented surface of the chips was no longer smooth, indicating more
unstable deformation occurring at the end of cutting due to excess tool wear. The chips at 1 m/s
show further transgranular crack propagation from the crack tip formed during the cutting,
probably resulting from the increased vibration and chatter at the end of cutting. For the 1.5 m/s
chip, the valley height is much larger than those obtained at the beginning and steady stages, while
it is the opposite case in 2 m/s chips. In addition, there seems to be more shearing on the prior
turned side of the chip. This might be the result of tool with excess wear cannot remove the as
much material as in the previous stage, most likely due to the build-up edge and adhesion layer.
Figure 4.9 Morphologies of the chips obtained at the beginning stage of turning: (a) 1 m/s; (b)
1.5 m/s; (c) 2 m/s.
65
Figure 4.10 Morphologies of the chips obtained at the end stage of turning at various
magnifications: (a) 1 m/s; (b) 1.5 m/s; (c) 2 m/s.
4.1.5 Nano-indentation analysis
As mentioned in as-received workpieces part, though the EBSD software was set to identify
both αp and βt orientations, most of the pixels in the βt (lamellar α+β regions) were identified as α
phase in the EBSD map (Fig. 4.11 (b)) because the β laths are so thin and account for only ~3-8
vol. % of the alloy [105], [106]. As a result, BSE image as shown in Fig. 4.11 (a) is necessary to
distinguish αp and βt regions. On the hardness map, αp grains can be seen clearly as they exhibit
66
consistently higher hardness the βt (lamellar α+β) regions. The orientations of αp grains and their
corresponding hardness values are plotted on the inverse pole figure in Fig. 4.11 (d). The hardness
of αp grains are highly dependent on their orientations. For instance, grain #16 had the highest
hardness value (6.65 GPa) among the 18 grains, while grains #1, 5, 7 and 8 (4.89, 4.9, 5.22, 5.22
GPa, respectively) were much softer due to their softer orientations, as shown in Fig. 4.11. Grains
with similar orientations had very similar hardness values (e.g. Grain #3, 4, 6).
(d)
Figure 4.11 (a) Backscattered electron (BSE) image after nano-indentation of the as-received Ti-
6Al-4V; (b) corresponding electron backscattered diffraction (EBSD) normal direction inverse
pole figure (IPF) mapping; (c) corresponding hardness map; and (d) inverse pole figure (IPF)
shows that the hardness depends on the primary α grain orientation (same color scale as the
hardness map).
67
Figure 4.12 (a) The hardness and reduced modulus of the αp in as-received STA Ti64 and
commercial pure (CP) Ti data from literature [107] decrease with declination angle; (b) The
cutting speed of 1.5 m/s shows lower hardness at low declination angles than 1 and 2 m/s.
Table 4.3 Maximum, minimum and average hardness values of αp / βt phase, the (Max-Min)/Avg
ratio shows hardness variation of β phase is larger than α phase
(Max-
Max Min Avg (Max-
Material Phase Min)
(GPa) (GPa) (GPa) Min)/Avg
(GPa)
α 5.51 4.24 4.77 1.27 0.27
CP Ti [24]
β N/A N/A N/A N/A N/A
Ti-6Al-4V As- αp 6.77 4.60 5.52 2.17 0.39
received βt 5.68 3.91 4.55 1.77 0.39
αp 6.43 4.98 5.51 1.45 0.26
Ti-6Al-4V 1m/s
βt 5.78 4.12 4.83 1.66 0.34
αp 6.38 4.47 5.20 1.91 0.37
Ti-6Al-4V 1.5m/s
βt 5.94 3.90 4.68 2.04 0.44
αp 6.49 4.94 5.52 1.55 0.28
Ti-6Al-4V 2m/s
βt 5.89 3.82 4.97 2.07 0.42
The hardness of the αp grains in as-received Ti64 bar was highly dependent on the c-axis
direction as indicated in Fig. 4.12. The reduced elastic modulus followed a similar decreasing
trend with increasing declination angles between the c-axis of αp grain and the indenter direction.
The highest hardness of 6.72 GPa was obtained when the declination angle was ~2.8°. A similar
trend in commercial purity (CP) Ti was also reported by Britton et al. [107], but its hardness is
about 20% lower (square symbols in Fig. 4.12 (a)). This differs from the observations of Han et
68
al. [106] , where no relationship between hardness and orientation was apparent, but that material
shows significant orientation gradients and sub-grain boundaries in the αp grains and the t had an
acicular shape suggesting that a high cooling rate was used. The systematically higher hardness in
the present work is mainly due to the solid solution strengthening effect of aluminum in αp grains.
Also, the present measurements show that the t has a similar hardness as CP Ti but is not as hard
as the αp component in the Ti64 microstructure, indicating the lack of Al solid solution
strengthening in the dominant α fraction of the t, and/or the presence of the softer phase. The
reduced modulus of the αp is slightly lower than CP Ti, but the t component is about 10% more
compliant, as BCC Ti has a lower stiffness [108]. Average values in Table 4.3 show that the
hardness of βt is consistently lower than the αp phase, and bold values show that the variation in
the hardness of βt is larger than that of αp. These measurements show that the properties of titanium
are very anisotropic, which is important for interpreting the detailed analysis of chip geometry in
the following sections.
4.2 MIL chips
The cross-section of MIL chips are shown in Fig. 4.13. These serrations are more regularly
spaced and fully developed with increasing cutting speed. The primary shear zone has the
appearance of a lamellar microstructure, unlike the STA chips. Like the STA chips, a small number
of shear bands are bifurcated in the 1.5 m/s chip. The chip-tool contact surface is illustrated in Fig.
4.14. Some of the black spots on these images are the voids and the others are particles on the
surface. In addition to the fine grooves aligned with the chip flow direction, there are more scar-
like features with higher cutting speeds. In Fig. 4.15, the upper part of the image is the outward
facing edge of the chip, while the lower part of the image is the constrained edge of the chip next
to the workpiece, which shows bent and more evenly spaced finer surface ridges. The top and
69
bottom edges of the chips are non-symmetric. The top side has geometric features with a consistent
height while the bottom side is pulled away from the workpiece. These features indicate that the
formation of segmented chips initiates from the free-surface side, not the constrained side. This is
consistent with the proposal of Vyas and Shaw [47] that the segmented chip is formed due to the
initiation of cracks on the free surface of the chip. The chip flow direction on this figure is from
right to left as shown by the cyan arrow. To avoid complications from the asymmetry, the cross-
sections of chips in the present work are observed in the middle of the chip (removed ~0.8mm).
Figure 4.13 MIL chips at 1, 1.5 and 2 m/s. Periodic primary shear zone and secondary shear zone
can be seen clearly and the serrations at higher cutting speed are more regularly spaced.
70
Figure 4.14 Smooth side of the MIL chips at low and high magnifications before sectioning and
polishing. In addition to the grooves, the number of scar-like features increased with cutting
speed.
Figure 4.15 Representative images of the segmented side of MIL chips. The top and bottom sides
show asymmetric features.
71
4.3 ELO chips
The cross-section of ELO chips, as shown in Fig. 4.16, shows similar features as the MIL
chips. The serrations become more and more pronounced and regularly spaced with increasing
cutting speed. The initial microstructure of the ELO chips consists of equiaxed alpha grains and
beta phase on the grain boundaries of alpha. Similar to the MIL chip, the primary shear zone
appears to have more of the lighter beta phase. At the 2 m/s cutting speed, the microstructure
appears similar to STA grade. The chip-tool contact surface at all cutting speeds also shows groove
and scar-like features at the 2 m/s cutting speed (Fig. 4.17). The segmented side of the chip is also
very similar to the MIL chip (Fig. 4.18).
Figure 4.16 ELO chips at 1, 1.5 and 2 m/s. Periodic primary shear zone and secondary shear
zone can be seen clearly and the serrations at higher cutting speed are more regularly spaced.
72
Figure 4.17 Smooth side of the ELO chips before polishing at low and high magnifications.
More scar-like features are apparent at higher cutting speeds in addition to the grooves.
Figure 4.18 Representative images of the segmented side of MIL chips. The top and bottom sides
show asymmetric features.
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4.4 LAM chips
4.4.1 Morphology of LAM chips
In general, the morphology of the LAM chips at all three cutting speeds exhibited more
variability compared with the MIL, ELO and STA chips. In contrast to the other three grade chips,
the variability of serrations in the LAM chip increased significantly with increasing cutting speed,
as shown in Fig. 4.19. For the two smaller serrations, the primary shear zone can be clearly seen,
which is composed of the lamellar microstructure. In contrast, no obvious primary shear zone can
be observed in the huge serration in Fig. 4.19. The substantial variability can also be seen even on
the chip-tool contact surface (Fig. 4.20). There is a large amount of damage on both the top and
bottom side of the chip as shown in Fig. 4.20. For the LAM chips at all three cutting speeds, the
groove feature is still obvious and visible, but the scar-like feature is not as pronounced as with
chips of the other grades. The damage can also be seen from the segmented side of the chip as
shown in Fig. 4.21 This observation is consistent with the flank wear results by Nguyen et al. [84].
The flank wear of insert for LAM grade machining is substantial especially at 91 and 122 m/min.
Figure 4.19 LAM chips at 1, 1.5 and 2 m/s. Periodic primary shear zone and secondary shear
zone can be seen clearly and the serrations at higher cutting speed show more variability.
74
Figure 4.20 Smooth side of the LAM chips before polishing at low and high magnifications.
There are more scar-like features visible at higher cutting speeds in addition to the grooves.
Figure 4.21 Representative images of the segmented side of LAM chips. Top and bottom sides
show asymmetric features.
75
4.4.2 EBSD scans of LAM chips
The variability of the chip morphology is highly dependent on the initial orientation of the
lamellar colony. In Fig. 4.22, the serrations with an average segmented degree of 0.49 show blue
orientations (Morphology I). Basal slip is favored with the maximal Schmid factor of 0.62
under the plane strain condition. The light green orientation of neighboring lamellar colony favors
pyramidal slip with the maximal Schmid factor of 0.56, but slip has a 3-times higher
CRSS than the basal slip. In addition, the Schmid factor of basal slip is even higher than
the Pyramidal slip. It is likely that the blue orientation colony experienced more
deformation compared with the light green colony.
The second type of morphology with an average segmented degree of 0.59 is correlated with
green orientations (Fig. 4.23). Also, there are uneven lamellar widths in the microstructure
compared with the first type. Pyramidal slip is favored with the maximal Schmid factor of
0.53 under the plane strain compression boundary condition. The red orientation of another
lamellar colony favors pyramidal slip with an even higher maximal Schmid factor of 0.61. It
can be inferred that the green orientation is highly favored by pyramidal clip. Compared with
the serrations with blue orientations, the adiabatic shear bands are very narrow, and evident by a
slightly lighter shade of gray, and where beta laths terminate at the ASB on the BSE image. Also,
the average segmented degree of the green orientations is a little bit higher than that of the blue
orientations.
The serrations are exaggerated (Morphology III) in Fig. 4.24, where the average segmented
degree is 0.7, compared with 0.49 for Morphology I and 0.59 for Morphology II. Similar to
Morphology II, the adiabatic shear band is very narrow, and in one location, perpendicular to the
smooth surface of the SSZ. Schmid factor calculations show that the preferred slip system for the
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golden orientation is the pyramidal slip with the maximal Schmid factor of 0.54. The
magenta color with a slightly different orientation may be the result of large regions of cooperative
deformation during the cutting, which is different from other orientations of the lamellae colonies.
Pyramidal slip has the highest CRSS among all of the hexagonal Ti slip systems, so the
resistance to deformation from the cutting force in Morphology III is the highest. As a result, , the
cutting force fluctuation for forming ASBs is large when cutting LAM chips, especially at the
cutting speed of 2 m/s. This is consistent with the large variability in chip morphologies at all
cutting speeds indicated in Fig. 4.19. The effect of initial grain orientation on the morphology of
the chips is pronounced for LAM grade since the grain (lamellar colony) size of LAM is huge
compared with STA, MIL, ELO grades (Nguyen et al. [84] showed that the LAM sample had the
largest colony size of 743 μm and STA and MIL samples with lamellar colonies each had a similar
lamellar colony size of around 20 μm). The large lamellar colonies with hard orientations (golden
colored) account for the exaggerated serrations, and those with soft orientations (blue and green
colored) lead to the smaller serrations.
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Figure 4.22 Morphology I with the average segmented degree of 0.49 showing maximal Schmid
factor value of 0.62 (basal slip) under the plane strain condition.
78
Figure 4.23 Morphology II with the average segmented degree of 0.59 showing maximal Schmid
factor value of 0.53 (pyramidal slip) under the plane strain condition.
79
Figure 4.24 Morphology III with the average segmented degree of 0.7 showing maximal Schmid
factor value of 0.54 (pyramidal slip) under the plane strain condition.
4.5 Conclusion
1. The chips cut at 1, 1.5 and 2 m/s all show segmented morphology. With increasing cutting speed,
there is a slight increase in peak height, equivalent thickness, and shear band spacing, together
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with a slight decrease in valley height. The shear angle remained stable around 43 °. The chips are
more and more segmented with increasing cutting speed since the segmented degree increased
significantly.
2. The constrained side of the chip is more homogeneous while the free surface side is apparent
segmented. At the cutting speed of 1 m/s, the tool-chip contact surface of the chip is smooth and
scar-like features are more apparent with increasing cutting speed, which may account for the
formation of adhesion layer on the tool rake face.
3. The hardness of both αp and βt in Ti64 alloy was highly dependent on its orientation both before
and after machining, ranging from 4.5 and 3.9 GPa (c-axis perpendicular to indenter direction) to
6.7 and 5.7 GPa (c-axis parallel to indenter direction), respectively, and the hardness of αp was
consistently higher than that of βt. The modulus shows the same trend; The hardness of αp after
machining was close to those before machining, indicating that a balance of strain hardening and
thermal recovery took place during deformation.
4. The images of the tool-chip contact surface provide evidence of phase transformation during the
cutting process.
5. The chip morphologies at the beginning phase are similar to the chip morphologies from the
steady stage. At the ending phase of cutting, the chips at 1 m/s showed further transgranular crack
propagation from the crack tip formed during the cutting. For the 1.5 m/s chip, the valley height is
much larger than those obtained at the beginning and steady stages, while it is the opposite case in
2 m/s chips.
6. The scar-like features on the smooth side of the chips are more pronounced with increasing
cutting speed for all grades. The morphology of the chips show higher variability with increasing
cutting speed, especially the LAM grade.
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7. The initial microstructure has a substantial impact on the morphology of the segmented chips.
The LAM grade shows exaggerated serrations and obvious variability due to the huge prior β
grains and α colonies. The morphology of MIL and ELO chips were similar to the STA chips and
show more uniform geometry.
8. For the LAM chips, the orientations that favor basal lead to the segmented chips with the
lowest segmented degree and a diffuse shear band, while orientations that pyramidal
resulted in the segmented chips with the highest segmented degree and an extremely narrow shear
band.
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CHAPTER 5 SHEAR BAND WIDTH PREDICTION AND SHEAR STRAIN
ESTIMATION IN STA CHIPS
In order to check the variability of the crack depth along the chip width, the fracture surfaces
were investigated when a chip was bent in the way shown in Fig. 5.1 (a). Ideally, there will be a
straight valley line, as indicated in Fig. 5.1 (b). However, the valley line throughout the chip width
is not a perfect straight line, as can be seen from Fig. 5.1 (c). Fig. 5.1 (d) and (e) shows the
counterparts of the fracture surfaces, with the detailed features labeled on both surfaces. In Fig.
5.1 (d), there are scoring marks all over the region above the valley line, which corresponds to the
tool-chip contact surface observation in Chapter 4. A large amount of shearing features can be seen
in Fig. 5.1 (e) and similar features can be seen right below the valley line in Fig. 5.1 (d), showing
evidence that the crack propagates past the valley. In contrast to the relatively straight valley line
in Fig. 5.1 (d), the shear crack length in Fig. 5.1 (e) varies dramatically throughout the chip width.
For instance, it can be seen from Fig. 5.1 (e) that the crack propagation stops at point A, B and C,
leading to a large variation in the crack length. This variability of crack propagation may be directly
related to the local stress state and surrounding orientations. It also reveals that the morphology of
a particular position on the chip is highly dependent on the depth of the cross-section observation
plane, which depends on slip behavior in the local crystal orientations. Hence, investigations of
crystal orientations in cross sections will reveal which slip systems are more likely and affected
crack growth at each location, and correlation between the formation of crack and the local
orientations is sought2.
The chip morphology becomes more uniform and regularly spaced with increasing cutting
2 This chapter is adapted from a published paper, Effect of Cutting speed on Shear Band Formation and Chip Morphology of Ti-
6Al-4V alloy using Nanoindentation and EBSD Mapping, Jiawei Lu, Ryan Khawarizmi, Miguel Monclús, Jon Molina-Aldareguia,
Patrick Kwon, Thomas R. Bieler, Materials Science and Engineering A 862 (2023) 144372, DOI: 10.1016/j.msea.2022.144372.
83
speed. As a result, 2 m/s chips are investigated first to try to reveal the correlation between the
formation of cracks and the local orientations. In contrast, 1 m/s chips exhibited large variability
in chip morphology, homogeneous shear strain, and crack length. It would be a good idea to check
whether the correlation still makes sense in the cases where there are more variations. Finally, the
intermediate cutting speed was also investigated.
Figure 5.1 (a) Illustration of bending a chip; (b) schematic plot of the fracture surface; (c) the
fracture surface tilted at low mag; (d) and (e) the corresponding fracture surfaces on both sides,
(d) is the prior turned flank surface and (e) is the shearing side.
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Figure 5.1 (cont’d)
In this chapter, a model that predicts the shear band width, as well as the model that calculates
both the catastrophic shear strain within the ASB and the homogeneous shear strain in the segments,
are introduced and adopted. The teeth where nanoindentations were tested on were selected and
discussed. This methodology will be applied to tens of teeth at each cutting speed in the next
85
chapter to provide a statistical perspective.
5.1 Shear band width calculation
During the cutting process, the homogeneous shear strain rate is related to the shear angle 𝜃,
tool rake angle 𝜔 (0 in this study), cutting speed 𝑉𝑐 , and the spacing perpendicular to the shear
band 𝑆 [51], [109]:
𝑉𝑐 𝑐𝑜𝑠𝜔
𝛾̇ = √2
(5)
2× ×𝑆×𝑐𝑜𝑠(𝜃−𝜔)
2
The shear strain rates were calculated to be ~13,000, 16,000, and 20,000 s-1 at cutting speeds
of 1, 1.5 and 2 m/s, respectively. Thimm et al. determined the shear strain rate in linear orthogonal
cutting at a range of cutting speeds between 1.33 and 2 m/s (the strain rate decreased with
increasing depth of cut) with a rake angle of 0 and a depth of cut of 0.1 and 0.2 mm using digital
image correlation (DIC) [110], resulting in a range of ~14,000 and 28,000 s-1. The calculated
results in the present work agreed with their measurements since feed rate in the present turning
experiment was 0.127 mm/rev, which is between 0.1 and 0.2 mm/rev in Thimm’s orthogonal
cutting [110].
The width of the shear band can be calculated based upon the model developed by Molinari
et al. [22], [49]:
12√2𝑚cos(𝜃−𝜔)𝑘𝑇𝑟
𝑡= (6)
𝑎𝑡0 𝑉𝑐𝑜𝑠𝜃
where 𝜃 is the shear angle, 𝜔 is the tool rake angle (0 in this study), 𝑚 and 𝑎 are non-dimensional
strain hardening and thermal softening coefficients of the material, 𝑘 is the thermal conductivity,
𝑇𝑟 is room temperature, 𝑡0 is the shear flow resistance and 𝑉 is the cutting speed. The non-
dimensional parameter 𝑎 can be calculated using [22], [50]:
𝛼𝜅0
𝑎= × (𝑏𝜀̇0 )𝑚 (7)
𝜌𝑐
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where 𝜅0 is the yield strength, 𝜌 is the density, 𝑐 is the specific heat capac`ity, 𝜀̇0 is the reference
strain rate and 𝑏 is a physical constant of the material. The parameters used for the calculation are
from Liu et al. [22]. In addition, a shear flow resistance of 950 MPa and yield strength of 1050
MPa at the reference strain rate of 14000 s-1 at room temperature was adopted [111], since the
strain rate was determined to be between 10000 and 20000 s-1 when the cutting speed was at 1.33
and 2 m/s in linear orthogonal cutting experiments in [110]. The shear flow stress is nearly the
same for shear strain rates from 1×104 to 5×104 s-1 in split Hopkinson pressure bar (SHPB) tests
[112].
The predicted shear band widths based upon equation (6) are 10.5, 7 and 5.2 μm at the cutting
speeds of 1, 1.5 and 2 m/s. However, the measured shear band widths from BSE images are ~1.3
μm at 1 and 1.5 m/s, and ~2μm at 2 m/s, which are 1/10-1/4 of the model predictions. For the
segmentations that formed a crack rather than a distinct shear band, the width of the shear band
near the end (tip) of the crack is used for the calculation in 4.2.
The measurements show discrepancies between inverse proportionality between shear band
width and cutting speed, which is the fundamental basis for this model. One reason for the six-ten
times thinner shear band width measurements may come from using the shear flow resistance and
yield strength from a lamellar Ti64 microstructure while experimentally, a bi-modal microstructure
was used, which has higher yield strength and hardness [113]. Also, material constants such as
thermal conductivity, specific heat capacity, strain hardening and thermal softening coefficients
can vary at elevated temperatures [70], but these are not likely to account for the factor of 4 to 10
reduction in shear band width. As the flow softening commonly observed in hot working results
from microstructural evolution [113], a microstructural instability could also facilitate reaching
high enough temperatures for transformation to β, which would cause an even more concentrated
87
shear instability. It is possible that adiabatic heating causes transformation to β, and because the
β phase is much softer, the shear band would become even more localized and could account for
the small observed shear band widths (the model does not consider a phase transformation to a
softer structure).
In addition to the microstructure change, the shear band width also depends on its degree of
evolution [36, 42]. The evolution degree is the ratio of current shear displacement to the critical
shear displacement. When the evolution degree is less than 1, the shear band is not fully mature
and this will influence the shear band spacing as a result of the shear stress in the shear band. Once
the shear displacement reaches the critical value of 1, the shear stress in the shear band vanishes
[51] and the shear band stops growing in width because the propagation process of shear bands is
stress-controlled [52]. From orthogonal cutting experiments, Ye et al. [51] determined that the
evolution degree can be worked out from the fluctuation of the cutting force, showing that the
degree of shear band evolution increased gradually with increasing initial shear strain rate in the
primary shear zone. A study of the milling Ti64 showed shear band widths at 250 m/min and 500
m/min to be 5.8 and 5.9 μm, respectively. The evolution degree at 250 m/min was half of that at
500 m/min. According to the model, the shear band width is inversely proportional to the cutting
speed. These two opposing aspects resulted in similar as-measured shear band widths at 250 and
500 m/min. In the present study, the evolution degrees are calculated in Table 5.1 and the shear
bands width values are listed in Table 5.2. By taking the evolution degree into account, predicted
shear band widths are 6.2, 2.9 and 1.6μm which is much closer to the average as-measured widths
of 1.3, 1.3 and 2μm at 1, 1.5, and 2 m/s,respectively, but this does not account for the opposite
trend in width from the observations, nor the variability in chip geometry observed in the chips.
According to the full width half max (FWHM) method, the shear band widths from the simulated
88
results (Fig. 5.2) are consistently around 15 μm, which does not agree with the as-measured or the
predicted values. As mentioned in Chapter 2, the mesh size of the simulation is 5 μm and this may
account for the large shear band width result since no features below 5 μm can be obtained using
such mesh size. In Chapter 5, there is a pronounced variability in shear band width of chips cut at
1 m/s when a lot more cases are included, which is of interest and will be discussed. For 1.5 and 2
m/s chips, the shear band widths are consistently as narrow as 1-2 μm.
However, none of this research focused on the local orientation of the αp grains. The model
by Molinari et al. [22], [49] showed that the shear band is only affected by the cutting speed while
the theory by Ye et al. [95] indicates that the evolution degree depends on the cutting speed. This
may not be sufficient, if the heterogeneous deformation in titanium alloys is taken into account.
In a thick-walled implosion test, the initiation of the shear bands was considered as a heterogeneous
nucleation process by Xue et al. and the initiation sites may be located at favorably oriented grains
or even defects [52]. This work shows that nucleation of shear bands requires a critical shear strain
at a certain stress. Hence, finding the shear strain in a shear band is needed.
Figure 5.2 (a) Simulated chip morphology that shows consistent peak/valley heights and segment
spacing with the experimental results; (b) effective strain distribution along the lines in (a), for
shear band width estimation.
Table 5.1 Evolution degree (X) calculated by cutting forces
89
Fmax (N/mm) Fmin(N/mm) X=1-Fmin/Fmax
1m/s 487.9 202.7 0.59
1.5 m/s 443.7 262.7 0.41
2 m/s 400.4 278.0 0.31
Table 5.2 The shear band width comparison of Molinari model, as-measured, and FE simulation
1 m/s 1.5 m/s 2 m/s
Molinari model [22], [49] 10.5 μm 7 μm 5.2 μm
Modified by evolution degree
6.2 μm 2.9 μm 1.6 μm
(X) [95]
As-measured 1.3 μm 1.3 μm 2 μm
FE simulation (FWHM) 15.8 μm 15.8 μm 15.7 μm
5.2 Shear strain calculation
The shear bands in serrated chips are widely separated, so the homogeneous shear and
localized catastrophic shear strains can be calculated from geometric considerations. In general,
the homogeneous shear strain 𝛾𝑠𝑒𝑔 between shear bands is given by [53]–[55]:
1 2𝜆ℎ cos(𝜌𝑠𝑒𝑔 ) 1
𝛾𝑠𝑒𝑔 = 𝜆 √𝜆ℎ 2 − + 𝑠𝑖𝑛2 (𝜙 , (8)
ℎ 𝑠𝑖𝑛𝜙𝑠𝑒𝑔 sin(𝜙𝑠𝑒𝑔 +𝜌𝑠𝑒𝑔 ) 𝑠𝑒𝑔 +𝜌𝑠𝑒𝑔 )
where 𝜙𝑠𝑒𝑔 is the direction of the localized shear, 𝜌𝑠𝑒𝑔 is the complementary angle of 𝜙𝑠𝑒𝑔 . 𝜆ℎ is
the chip compression ratio that can be obtained by the ratio of the deformed chip thickness ℎ𝑐 and
the undeformed chip thickness ℎ, or the ratio of cutting speed 𝑣𝑐 and chip flow speed 𝑣𝑐ℎ ;
ℎ𝑐 𝑣
𝜆ℎ = ℎ
= 𝑣𝑐 , (9)
𝑐ℎ
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The catastrophic shear strain 𝛾𝑐 and the strain in the shear band 𝛾𝑠𝑏 are:
𝑝
𝛾𝑐 = 𝛿𝑠𝑏 (10)
𝑠𝑏
𝛾𝑠𝑏 = 𝛾𝑠𝑒𝑔 + 𝛾𝑐 (11)
where 𝑝𝑠𝑏 is the shear band projection and 𝛿𝑠𝑏 is the shear band width.
Figure 5.3 (a) Homogeneous shear strain calculated in each segment in an increasing order, (b)
catastrophic shear strain calculated in each adiabatic shear band at three cutting speeds. The
presence of crack is correlated with smaller homogeneous shear strain.
Shear strains were calculated from this model in several locations in 1, 1.5, and 2 m/s chips
as shown in Fig. 5.3, where the homogeneous shear strain varied from ~0.4 to 0.9. There is a slight
decrease from ~0.7 to ~0.4 with increasing cutting speed (excluding some special cases). This
homogeneous shear strain is smaller than the homogeneous shear strain value of 1.15 from a single
pass of equal channel angular extrusion (ECAE) process with a channel angle of 90° [114], due to
the expansion in the width direction of the chip and the presence of shear bands. In contrast, the
91
catastrophic shear in Fig. 5.3 (b) exhibited a decreasing trend from 60-75 at 1 m/s, to 40-60 at 2
m/s (which is much higher than the calculated shear strain (~28) in high speed cutting of a
30CrNi3MoV steel [115]). In the thick-walled cylinder implosion experiment, the shear strain in
the shear band increased significantly from 4 to 41 and further to over 200 with increasing global
shear strain, which can even generate melting [52]. The inaccuracy in calculating catastrophic
shear strain lies in the determination of shear band width. The shear bands formed in the solution
treated-quenched-aged Ti64 in the present study can be composed of both αp and βt, but only the
sheared αp grains can be identified in BSE images and EBSD maps. As a result, the measured shear
band width might be slightly smaller.
At all three cutting speeds, the homogeneous shear strain decreased with increasing size of
cracks. A possible explanation for the formation of crack is that the initiation of shear bands is
strain controlled and also orientation dependent. When the homogeneous strain reached a critical
value and the local orientations of αp grains were soft to form a potential shear band, a shear band
would form and a strain instability developed. Consequently, shear stain between shear bands
stopped due to the strain localization in the shear band. At some point, either micro-voids appeared
and kept growing to coalescence, or a crack nucleated at the free surface. If the crack is formed
from the free surface of the chip, as proposed by Vyas and Shaw [47], the shear strain between
shear bands could be lower than that needed for an adiabatic shear band to form. This would be
favored when the orientations of αp grains where a crack forms (near the tip of an emerging tooth)
are hard to deform. It is possible that some of the cracks formed from the free surface of the chip
while others were the result of coalescence of voids within a shear band. As no stretched micro-
void features were observed in the examples in the present study, it seems likely that the cracks
initiated from the free surface of the chip, especially for the straight cracks (green #3, blue #4, #5).
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A partially developed shear band is illustrated in the 1 m/s chip labelled as ‘1’ in Fig. 5.3 (a),
with the lowest catastrophic shear strain of 24.6, which is approximately one third of the shear
strain values of 60.4 and 75.9 in the other two shear bands analyzed at the same cutting speed.
From more detailed analysis below, the shear stress needed to deform this shear band is lower than
the other two locations, leading to much less energy absorbed per unit volume during the cutting
process, making this adiabatic shear band “less adiabatic”. Also, the spacing between the shear
bands at this location is ~30 μm, approximately one third of more typical spacings of ~80 μm
where the shear strains are three times as large. In addition, the segmented degree at this location
is only 0.19, much smaller than the other two locations (0.43 and 0.52), indicating that this chip
morphology is closer to a continuous chip. The large morphology variation in the 1 m/s chips
accounts for the large error bar shown in Fig. 4.2 in Chapter 4. These considerations suggest that
the crystal orientations within this shear band are beneficial for the cutting process. As the energy
input is more homogeneous in this part of the chip, the cutting tool will also experience a more
uniform force.
5.3 Slip modes activated in the shear bands
In hexagonal metals, there are several dislocation slip and twinning systems with different
critical resolved shear stresses (CRSS) that can be activated during the plastic deformation. The
most easily activated systems are basal 〈a〉 slip, prismatic 〈a〉 slip, but pyramidal 〈a〉 slip (Burger’s
1
vector 〈a〉 = 3 〈112̅0〉), as well as first- and second-order pyramidal slip with the Burger’s vector
1
〈c + a〉 = 3 〈112̅3〉 are activated to a lesser degree because they have higher CRSS values [105].
At room temperature, basal slip has a CRSS that is ~23% higher than prismatic slip, but this ratio
is temperature dependent, and at elevated temperatures, basal and prism slip have CRSS values
that are more similar [116]. Twinning has a CRSS that is higher than prism or basal slip, but not
93
as high as the CRSS of 1st order 〈c+a〉 slip, which is ~2.6 times higher than prism 〈a〉 slip so that
prismatic slip is easier to occur. The Schmid law indicates that a slip system can be activated if
the resolved shear stress reaches or exceeds its CRSS. In machining conditions, the stress and
strain rates are high, so it is likely that all slip system families are activated during deformation.
2nd order pyramidal 〈c+a〉 slip is seldom observed but it is discussed in investigations such as slip
transfer [117], [118], and in a study on Ti64 texture evolution during the machining process that
indicated that 2nd order pyramidal 〈c+a〉 slip made a large contribution to the ‘C’ shear texture.
When a crystal orientation has a higher Schmid factor (SF) for a particular slip system, it is more
likely to be activated. Therefore, SF analysis is widely used to predict the activation of
deformation modes, but it is defined for uniaxial stress state [119], [120]. In the present discussion,
2nd order pyramidal 〈c+a〉 slip is not discussed further since the calculated Schmid factors of 2nd
order 〈c+a〉 slip are generally similar to those of 1st order 〈c+a〉 slip, so both 1st and 2nd order 〈c+a〉
slip would have similar driving force in these high stress conditions.
The generalized Schmid factors3 of αp grains near the shear band are estimated under the
assumption that these grains were deformed under the plane strain compression stress tensor
−1 0 0
[ 0 1 0]. This tensor provides the maximum shear stress on two 45 planes in the material,
0 0 0
rather than just the one that is relevant to the turning process. Based upon inspection of slip systems
with high generalized Schmid factors, only those with slip planes close to the primary shear
direction are considered.
The maximum Schmid factor of relevant basal 〈a〉, prism 〈a〉, pyramidal 〈a〉 and pyramidal
〈c+a〉 slip is labeled on each αp grain in blue, red, green and orange, respectively, in Fig. 5.4 (a)
3 The Schmid factor is defined for uniaxial deformation, which has a maximum value of 0.5. Extending this to a general stress
tensor leads to a maximum generalized Schimd factor of √2/2, corresponding to simple shear.
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and Fig. 5.5 (a) for two exemplary shear bands. In the 1 m/s chip in Fig. 5.4, the orientation of
grain #11, a red grain orientation in the (001) inverse pole figure map in Fig. 5.4 (a), was highly
favored with a Schmid factor of 0.7 for prism 〈a〉 slip (the c-axis is perpendicular to the page). The
crystal rotated only about the c-axis as dislocation glide on prism planes would not change the
orientation of the c-axis or the dominant slip mode. Basal 〈a〉 slip in Grain #10 has a Schmid factor
of 0.61, which is also a facile slip system with a high Schmid factor. Clearly, most of the grains
near the shear band were easily deformed by prism or basal slip. Hence, the shear stress in the
shear band was low for two reasons: i) the high Schmid factors on facilitate slip systems enables
activation of slip at a low resolved shear stress; ii) the CRSS of basal 〈a〉 and prism 〈a〉 slip is
lowest among all the slip systems. Combined with the aforementioned small shear strain (24.6) in
the shear band, the overall shear strain was spread out over a wider area, leading to less
concentrated energy dissipation per unit volume than in other shear bands, which seems
counterintuitive, given the ease of deformation. As a result of the more uniform strain, the
temperature did not reach the level required for phase transformation to β.
95
Figure 5.4 BSE image of the first location (less developed serration) in 1 m/s chip, with maximal
SF labeled on each grain; (b) (001) IPF map. (c) dominant slip systems in Grains 11 and 10 are
easily activated. Maximum Schmid factors (based upon plain strain compression) are labeled:
blue: basal slip; red: prism slip; green: pyramidal slip; orange: pyramidal
slip.
In the shear band in Fig. 5.5, the pyramidal 〈a〉 slip Schmid factor of grain #4 in Fig. 5.5 (a)
was 0.52. With dislocation glide on the pyramidal plane, the initial orientation rotated to the new
orientation of grain #4-2 in the shear band, making it more favored for basal 〈a〉 slip (SF: 0.63),
resulting in texture-softening. Since the CRSS of pyramidal 〈a〉 slip was initially higher than basal
or prism slip and the strain rate and the shear strain was high (31.06), the dissipated energy
was much higher than it would have been at 1 m/s. With a higher stress leading to more dissipated
96
strain energy, more adiabatic heating took place, making it more likely that a phase transformation
from α to β may have occurred. Two possible transformed β variants (among the six possibilities)
with the highest Schmid factors (0.69 in both cases) are illustrated in Fig. 5.5 (d), whose
orientations were found based upon transforming the αp grain #4-2 to its parent β orientation [121],
[122]. Following deformation, cooling causes the β to transform back to α by the conventional
orientation relationship: {110}β//(0001)α and 〈111〉β//〈21̅1̅0〉α, which would result in orientations
with the basal plane parallel to the shear band. While this is not obvious due to the high strains in
the shear band, this is the subject of continuing investigations.
Figure 5.5 (a) BSE image of representative location in 2 m/s chip, with maximal SF labeled on
each grain; (b) (001) IPF map. (c) the dominant slip system in grain 4 and shear band. (d) two
possible beta variants based on G4-2 orientation. Maximal Schmid factors are labeled: blue:
basal slip; red: prism slip; green: pyramidal slip; orange: pyramidal slip.
(same coordinate system as in Fig.5.4).
97
Fig. 5.6 shows four additional cases of either cracks or shear bands that occurred at the cutting
speed of 2 m/s. It has been reported that the nucleation, growth and coalescence of micro-voids
will form the cracks within the shear band due to large shear strains [52]. In Fig 5.6. (c) and (d),
it is interesting to see that the αp grains in the vicinity of a potential shear band show large SF
values in the 45° shear direction, yet cracks formed rather than shear bands. On the other hand,
the calculated shear strains in these two cases are 0.46 and 0.41, respectively, smaller than those
two with adiabatic shear bands (0.48 and 0.49). This suggests that the cracks may be formed by
nucleation from the outer surface of the chip [43], [123] rather than due to the large shear strain
within the shear band. The morphology of these two cracks is different from the cracks formed by
the micro-voids as well. The cracks in Fig. 5.6 (c) and (d) show no evidence of coalescence of
micro-voids. However, the crack in Fig. 5.6 (c) shows straight fracture feature and was blunt at
the end, whose propagation mechanism is mode Ⅱ (sliding mode), while a feature similar to the
bifurcation of the shear band was observed in the crack in Fig. 5.6 (d). A systematic assessment
of cracks vs. shear bands with respect to crystal orientation is the subject of further investigation
(Chapter 6).
98
Figure 5.6 The chips cut at 2 m/s: (a) pure shear band; (b)both shear and crack; (c) crack that
show straight features; (d) crack that show features like shear band bifurcation.
5.4 Conclusion
1. The as-measured shear band widths from BSE images are ~1.3 μm at 1 and 1.5 m/s, and ~2μm
at 2 m/s, which are only 1/10 to 1/3 of the model predictions (12, 8, 6 μm, respectively). This
substantial discrepancy can be explained by both the parameters utilized in this calculation model
and the evolution degree. However, the essential reason is that this model considers the material
to be homogeneous, which is not the reality in Ti64 alloy;
2. The homogeneous shear strains in the segments vary from ~0.4 to ~0.7, depending on local
orientation and cutting speed. There is a slightly decreasing tendency in homogeneous shear strain
with increasing cutting speed. In addition, there appears to be a correlation between the presence
of crack and small homogeneous shear strain;
3. The slip systems activated within the shear band include prism , pyramidal and basal
. Prism slip occurs with a lower stress in theory and a smaller catastrophic shear strain by
calculation, and as a result the temperature rise is small and less likely to reach the β transus
temperature. Also, the neighboring αp grains in the segment, with soft orientations, exhibited large
99
homogeneous shear strain, which is beneficial to the cutting tool. In contrast, the deformation due
to the activation of pyramidal slip leads to higher stress and larger catastrophic shear strain.
Thus, α to β phase transformation could have happened in this condition. It is also interesting to
note that the orientation of this αp grain was rotated slightly due to the deformation and became
more favored by basal slip.
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CHAPTER 6 EFFECT OF LOCAL ORIENTATION AND CUTTING SPEED ON THE
FORMATION OF SEGMENTED STA CHIPS
The crack variability and cases from a few chip locations in the previous chapter reveals the
importance of the local crystal orientations. Both the nucleation of the crack near the chip free
surface and the generation of adiabatic shear from the secondary shear zone are highly dependent
on the local crystal orientations. In this chapter, tens of teeth are investigated using a systematic
methodology introduced in Chapter 5, in order to reveal the rationale behind the formation of crack,
adiabatic shear band or both in each tooth.
6.1 Chips at 2 m/s
6.1.1 Crack length, segment spacing and homogeneous shear strain distribution of 2 m/s
chips
The chips cut at 2 m/s are illustrated in Fig. 6.1. As discussed in the previous chapter, all the
teeth are fully developed compared to the 1 m/s chips. Among 32 locations investigated, only 7
exhbited pure shear band without crack (location # 2, 4, 10, 11, 24, 31, 32, as can be seen in Fig.
6.2). Generally speaking, the αp grains within the shear bands do not exhibit a large aspect ratio,
indicating a more uniform shear deformation compared with 1 m/s (this will be further discussed
in Chapter 6.2). To explore correlations between geometric features such as crack length, spacing
between shear bands, and homogeneous shear strain indicated by grain aspect ratios, these metrics
are plotted with respect to position in Fig. 6.2. Segment spacings are in the range of 50 and 95 μm
and exhibited a normal distribution (Fig. 6.3). Similarly, the homogeneous shear strains within the
segments also followed a normal distribution and its range is between 0.4 and 0.7. In contrast, the
distribution of crack lengths does not follow normal distribution, which means the occurrence of
crack is not random but resulted from some reason. Most of the cracks are shorter than 45 μm,
101
while only 4 cracks have a length of 60-100 μm. Fig. 6.4 shows a trend of decreasing crack length
with increasing homogeneous shear strain. A possible explanation is that the adiabatic shear band
in the primary shear zone is shear strain induced and shear stress controlled. When the
homogeneous shear strain accumulates to a certain extent, the temperature increase will be large
enough to trigger the thermo-plastic instability and an adiabatic shear band happens as a result.
When the shear band is well developed, the crack, which is another way to form segmented chips,
is suppressed. The segment spacing also tends to decrease with increasing homogeneous shear
strain. The segment spacing is determined once the shear band is formed, and thus the spacing is
smaller when the shear band is easier to form (larger homogeneous shear strain). This phenomenon
should result in decreasing crack length with decreasing segment spacing.
Figure 6.1 2m/s chips on which segment spacing, shear strain, and crack length are investigated
(The locations are label with C or S which represents the presence of crack or only shear band.).
Measurements of crack length, segment spacing, and homogeneous shear strain within the
segment is illustrated.
102
Figure 6.2 The distribution of crack length, segment spacing, and homogeneous shear strain
within each segment, with respect to their actual locations at 2 m/s.
Figure 6.3 The histogram of crack length, segment spacing, and homogeneous shear strain within
each segment.
Figure 6.4 Correlation between crack length, segment spacing, and homogeneous shear strain
within each segment.
6.1.2 Schmid factor analysis
To estimate what slip systems are likely to be active in a given shear band, the stress tensor
is needed. A simulation was performed as part of this project, using a Johnson-Cook material
103
model optimized to match the geometry of the observed chips by DEFORM 2D v.11.2 commercial
software. The tool was modeled as a mechanically rigid body but with a meaningful thermal
conductivity to allow the temperature to rise during cutting. A cutting length of 1 mm was used in
the FE simulation to see multiple segments while minimizing the computation time. A value of
2000 for the Cockroft-Latham model damage criterion was used to make the chip segmentation
size closer to experimental values. Detailed information of the Johnson-Cook constitution model,
material constants of STA Ti64, shear friction coefficient and heat transfer coefficient of the tool,
and other simulation parameters can be referred to in [97].
The simulation for chips cut at 2 m/s is shown in Fig. 6.5. The effective stress distribution
shows an adiabatic shear band, within which the effective stress is much lower than that in the
segment. As can be seen in Fig. 6.5, the stress tensors at 15 points were extracted from FE
simulation by DEFORM 2D. Using the local stress tensors at location P5, generalized Schmid
factors were computed for crystal orientations present in each segment in Fig 6.6.
The two prevailing theories concerning the formation of segmented chips are (i) propagation
and growth of cracks from the outer surface of the chips [47] and (ii) adiabatic shear bands caused
by localized shear deformation [48], respectively. According to the bending fracture surface
observation in Fig. 5.1., and the correlation between the crack length and homogeneous shear strain,
these two mechanisms are competing with each other in forming segmented chips, depending on
the local crystal orientations. Orientations of the αp grains near the tip of each tooth and the
corresponding locations prior to shear on the other side of the shear band were identified using
electron backscatter diffraction (EBSD). The stress tensor at point 5, the tip of teeth within the
potential shear band (labeled on Fig. 6.5 (e)) is determined to be:
303.47 −279.2 0
𝜎𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = [−279.22 44.83 0 ].
0 0 174.14
104
Using this stress tensor and Schmid factors were computed and the slip systems with the top five
values were recorded.
(e)
(PSZ
)
e
sh
ea
rz
on
y
ar
Pr
im
Secondary shear zone (SSZ)
(g) (f)
Tool Rake Face
Face
Tool Flank
Figure 6.5 Illustration of 2-D segmented chip formation cycle (a-d) caused by localized shear,
where the pair of red dots identify positions that were once adjacent prior to cutting. The blue
and magenta shaded area represents the regions that are highly stressed. The effective stress (e),
strain (f) and temperature (g) in the 2 m/s FEM simulation illustrate formation of a shear band at
the time when a tooth emerges. The position labeled P15 was used to extract a local stress tensor
[97].
On the other hand, the plane strain compression stress tensor used in Chapter 5, where the
cracks tended to occur in segments with lower homogeneous shear strain, was also used to compare
with the simulation result. This prior correlation is in agreement with the above discussion of Fig.
6.4, which is based upon a much larger sample size. It is reasonable to compare the stress tensor
105
from the simulation and the plane strain stress tensor:
−300 0 0
𝜎𝑝𝑙𝑎𝑛𝑒𝑠𝑡𝑟𝑎𝑖𝑛 = [ 0 300 0].
0 0 0
Since the shear only happens in one of the two 45° directions, the top three highest Schmid factors
with slip in the direction observed will be used because those revealing the shearing in the other
45°direction did not actually occur. The results are shown in Fig. 6.7.
Figure 6.6 Top five Schmid factors calculated under the stress tensor from FE simulation
(𝜎𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛 ) show the presence of crack with pyramidal slip activated.
106
Figure 6.7 Top three Schmid factors calculated under the plane strain compression condition
(𝜎𝑝𝑙𝑎𝑛𝑒𝑠𝑡𝑟𝑎𝑖𝑛 ) show the activation of non slip at all locations.
The Schmid factors calculated for dominant orientations described using the stress tensors
from the FEM simulation are plotted in Fig. 6.6, for each characterized segment in the 2 m/s chip.
About half of the segments show high Schmid factors for slip, 4 for basal, 7 for prism, and 6
on pyramidal planes. All 6 segments without cracks are included in this set. There are 10 segments
with much higher Schmid factors for pyramidal slip, all of which are correlated with cracks.
As is well-known, the CRSS of slip systems are much higher than basal , prism
and pyramidal . Given the high strain rate sensitivity of stress at strain rates above about 100
s-1 [70], and the fact that different slip systems have different strain rate sensitivity [124] is likely
that the stress state is saturated, and is high enough to activate significant slip, though it
may not account for the majority of strain. Given that the CRSS is at least 3 times higher for
slip the degree of slip that occurred would generate at least 3 times as much heat for
the same amount of strain as slip. As a result, the thermal instability could be triggered at a
lower strain than in conditions dominated by slip, leading to the nucleation and growth of
micro-voids and/or crack formation along the shear band. Another possibility is that the shear crack
107
initiated at the free surface and kept propagating toward the tip of tool until a stress state or softer
material at higher temperature that could arrest the crack was encountered. The variability in
temperature based upon different amounts of work and adiabatic heating could account for variable
crack depths.
The plane strain compression boundary condition leads to Schmid factors that are ~20%
higher than those calculated using the FE simulation stress tensor (Fig. 6.7), and the Schmid factors
for slip systems were highly favored at all except 2 locations where systems were
favored. This differs significantly from the FE simulation stress tensor results. Only slip system
Schmid factors where the slip plane was aligned with the shear bands were considered. Though
both approaches may approximate what actually occurred, it is unclear whether a kinematic plane
strain compression boundary condition is more descriptive than a stress-based condition from the
simulation based upon isotropic properties. As it is reasonable that the stored elastic strain energy
would be high in slip systems, and higher stored energy would favor crack nucleation, the
simulation stress states are probably more meaningful.
108
6.1.3 Representative cracks and shear bands in 2 m/s chips
Fig. 6.8 gives examples of the orientations favored by prism , basal , pyramidal ,
pyramidal slip and orientations that are resistant to deformation. In the order of from left to
right, higher stress level is needed and decreasing likelihood of happening for these slip systems.
According to the shear displacement, the grain near the valley to the left of the shear band/crack
was adjacent to the one near the tooth. It is thus meaningful to compare their orientations and the
orientations of other grain pairs that were adjacent prior to cutting.
Figure 6.8 Crystal orientations with slip systems aligned with the plane of shear in order of
likelihood of happening.
109
Figure 6.9 2 m/s chip segments with localized shear bands and elongated grains favoring prism
slip. Blue dashed arrows on the first SEM image illustrate the sense of shear. White dashed
lines on EBSD maps indicate the center of the shear bands.
110
In Fig. 6.9, four examples of shear bands without cracks are illustrated. In C8, dashed arrows
identify the location of the ASB in the map beneath the valley. C8 and S11 have narrower shear
bands than S31 and S32. They share the characteristic that the αp grains show a large amount of
shear have the same red orientation that favors prism slip systems. In C8, the αp grain near
the upper right peak has a hard-to-shear orientation (A’) and the one near the valley (A) also has a
green orientation but is relatively much easier to shear. Prior to cutting the two grains were located
next to each other, and their orientations can be similar (due to the commonly seen micro-texture
in Ti alloys) or very different. In this case, they have distinctively different orientations. This
might give rise to the tiny crack that is right on top of the sheared αp grain with red orientation.
Since the easy-to-shear grain has made main contributions to the shear displacement required to
form the segmented chip, the crack is trivial and may reflect the small green orientation. In addition,
this case supports the proposal that the adiabatic shear band may originate from the secondary
shear zone by Molinari et al. [74]. As can be seen in the EBSD scans in previous work [97], the
elongated grain B has the same orientation as the grain below it that transitions from the secondary
shear zone to the primary shear zone as half of it is sheared horizontally and the other half is
sheared in the 45 ° direction. In the other three cases, a number of prism favored red
orientations were detected in the vicinity of the shear bands, for both the peaks and valleys. This
makes good sense since the prism slip is the easiest to activate slip system in hexagonal Ti
alloys.
111
Figure 6.10 2 m/s chip segments with localized shear bands and elongated grains favoring prism
slip. Blue dashed arrows on the first SEM image illustrate the sense of shear. White dashed
lines on EBSD maps indicate the center of the shear bands.
112
Fig. 6.10 provides four examples of long straight Mode II cracks. Looking at the orientations
in the crucial regions where the upper right peak and the region to the left of the valley were
adjacent prior to cutting, there are many αp grains with red orientations that favor prism slip
near the shear bands, suggesting that prism orientations may be helpful but not sufficient to prevent
cracking. In C7, the homogeneous shear strain in this segment is 0.6 (large enough to induce the
adiabatic shear band at 2 m/s), but unlike uncracked ASBs, other crystal orientations above the
valley side of C7 are present that may have prevented uniform deformation of red grains. If the
long straight crack initiated at the tip of the tooth and propagated to the crack tip, then it was
arrested at a ductile red grain that has a high aspect ratio to the right of crack tip, where the material
was hotter and softer. At the tip of the tooth, orientations are red and blue, where the blue
orientation is favorably oriented for basal slip, and this grain was originally opposite the nearly
circular green grain (marked B and B’). As the green grain is a harder orientation that was initially
adjacent to a soft “blue” basal orientation, a plastic strain incompatibility resulted, and the fracture
surface ledge discontinuity is located here. Other αp grains near this elongated αp grain also have
orientations favored by prism slip, but they remained nearly equiaxed or globular. Two
hypotheses could account for this: The first one is that the shear band initiated from hot and soft
SSZ and propagated toward the cooler and stronger free surface of the chip, as proposed by
Molinari et al. [74] based upon their simulation results. The temperature around the peak is much
lower than the SSZ and the stress is much higher, making a crack is easier to nucleate. The second
one is that localized shear deformation and crack propagation are two competing mechanisms
during the formation of segment chips. One argument that supports the two competing mechanisms
is the crack length. Vyas and Shaw [47] mentioned in their work that the crack length was
controlled by the frequency of segmentation. The higher the frequency is, the shorter the crack
113
length will be. The present work shows that the crack lengths are random at each speed and there
is no obvious trend with increasing cutting speed, as either (frequency increases with increasing
cutting speeds [125]). This supports the hypothesis that the formation of cracks is dependent on
the local orientations and cracks are competing with and complementary with the ASBs in order
to satisfy the shear displacement between the peak-valley pair to form segmented chips.
ASB C12 has some similar characteristics, as C7, as prism red regions at the tip of the tooth
are also present on the upper valley side, but beneath that B’ has soft orientation but B has hard
orientations, resulting in incompatible strains on two sides. Further beneath B-B’ pair, at locations
C-C’, the tooth has hard orientations that would also lead to incompatible strain on the two sides.
Above the valley of C12, there are many red grains that are elongated horizontally, reflecting
compression prior to forming the ASB/crack. In contrast, those below this cluster have very small
amounts of deformation. This shows that the so-called homogeneous shear strain within the
segment is not homogeneous across the segment. The rounded valley to the left of the crack
suggests ductile deformation and formation of a smooth rather than notched peak, but the
subsurface strain incompatibility may have triggered the crack beneath the softer tooth tip volume.
This scenario is more exaggerated in in C22, where the volume of ductile red orientations is larger,
but harder blue orientations are beneath the surface of the adiabatic shear band. However, in this
case, there was no evidence of forming a smoother tooth, and instead, a wider crack opening took
place, and this suggests that the crack nucleated deep beneath the surface. A similar set of features
is present in C23, where a deep crack nucleation may have taken place due to harder orientations
in the ASB regions. Furthermore, the calculated homogeneous shear strains in C22 and C23 are
low, 0.44 and 0.45, which can account for the absence of adiabatic shear bands because the
nucleation of adiabatic shear bands is strain induced and then the propagation of the shear bands
114
is stress controlled [52].
Figure 6.11 Wide-open cracks provide evidence of mode I propagation.
115
Figure 6.11 (cont’d)
Fig 6.11 shows four examples of cracks with a strong mode I opening component in addition
to the mode II shear component. In addition, the crack arrest, which makes these cracks much
shorter than those long straight cracks, indicated that both the crack and shear band are responsible
for the formation of segmented chips simultaneously, and the two mechanisms are competing with
each other.
Figure 6.12 Rough-interface cracks indicate the coalescence of micro-voids.
The cracks in Fig. 6.12 show rough features that may have resulted from the growth and
coalescence of micro-voids within the shear bands. Also, the two cracks branched, just like the
shear band bifurcation in [52]. Shear localization precedes failure mechanisms such as voids and
116
cracks. A well-developed shear band is often accompanied with voids and cracks within it. These
defects accelerate localization and localized deformation creates fresh nucleation of micro-voids
and cracks.
6.1.4 Deformation twins in 2 m/s chips
In hexagonal closed packed metals, such as magnesium, zirconium, and titanium, basal
and prism slip are the dominant deformation mechanisms due to their low CRSS. However,
the activation of these two slip systems cannot accommodate either extension or compression
along c-axis [126]. In addition to the second-order slip, twinning is another important mode
to accommodate the deformation along c-axis, including {101̅2} < 1̅011 > and {112̅1} <
1̅1̅26 > that lead to extension along c-axis, and {112̅2} < 112̅3̅ > and {101̅1} < 1̅012 > that
give rise to contraction along c-axis [126]–[129].
Figure 6.13 Representative T1-type twins in the chip segments exhibiting misorientation angle of
~89° (twin boundary is labeled with yellow lines).
A few twins were observed in the 2 m/s chips, which were also observed in 1 and 1.5 m/s
chips. The misorientation angle between the parent and twined grains are approximately 85° and
they have a common a-axis (Fig. 6.13). The twinning mode is {101̅2} < 1̅011 > extension
twinning. In commercially pure titanium (CP Ti), a large fraction of both extension {101̅2} <
1̅011 > twins and contraction {112̅2} < 112̅3̅ > twins have been observed [130]. In contrast,
117
mechanical twining as a deformation mode is much less prevalent in α-Ti-6Al-4V alloy. It has been
reported that the addition of Al is responsible for the suppression of twinning mechanisms. The
accommodation of deformation along c-axis can be replaced by the activation of slip on
pyramidal planes or extra deformation in the β phase. When the Al content is higher than 5 at. %,
twinning is almost fully suppressed in single crystals [131], [132]. However, there is research
reporting on very small fraction of twins in Ti64 alloy at high strains and strain rates, such as cold-
rolling and equal channel angular extrusion (ECAE) [128], [131], [133]. The shear strain within
the segments at 2 m/s is between 0.4 and 0.65 as can be seen in Fig. 6.3, which is smaller than the
theoretical homogeneous shear strain value of 1.15 from a single pass of ECAE process with a
channel angle of 90° [114]. The shear strain rate of 2 m/s is calculated to be ~20000 s-1. Both
explain why deformation twins take place in the chips.
6.2 Chips at 1 m/s
6.2.1 Crack length, segment spacing and homogeneous shear strain distribution of 1 m/s
chips
The morphology of chips cut at 1 m/s can be seen in Fig. 6.14. Compared to the 2 m/s chip,
1 m/s chip exhibited much more variations in the chip peak/valley heights, segment spacing, and
crack length. For instance, a few segments in the middle look similar to those at 2 m/s and large
cracks occurred at these locations (C8-C13), while the segments on the right are much less
segmented and fewer cracks were observed. This observation is also reflected in the metrics shown
in Fig. 6.15, where the long red bars and short blue bars are located in the middle whereas the short
red bars and long blue bars are on the right.
Figure 6.14 1m/s chips on which segment spacing, shear strain, and crack length are investigated.
118
Figure 6.15 The distribution of crack length, segment spacing, and homogeneous shear strain
within each segment, with respect to their actual locations at 1 m/s (the blue horizontal line
indicates the theoretical shear strain value (1.15) in ECAP process).
The histogram of segment spacings show that the range of segment spacing is between 30
and 90 μm and exhibited a normal distribution (Fig. 6.16), which is smaller than those of 2 m/s
chips (50-95 μm). Most of the cracks are shorter than 40 μm, while only 4 cracks have the lengths
up to 85 μm. It is noteworthy that the homogeneous shear strain in the segments are between 0.4
and 1.4 at 1 m/s, which is much higher than the shear strain at 2 m/s (0.4-0.7). At the cutting speed
of 1 m/s, the deformation stress is lower than at 2 m/s. As a result, more strain (deformation energy)
is needed to cause temperature increase that triggers thermos-plastic instability. As indicated in
Fig. 6.17, the crack length decreased with increasing shear strain, and the segment spacing shows
a similar decreasing trend. Correspondingly, the segment spacing increased with increasing crack
length. This phenomenon is the same as 2 m/s chips.
119
Figure 6.16 Histograms of segment spacings, crack lengths, and homogeneous shear strain
within each segment.
Figure 6.17 Correlation between crack length, segment spacing, and homogeneous shear strain
within each segment.
6.2.2 Representative cracks and shear bands in 1 m/s chips
The cracks in Fig. 6.18 show both wide-open and long straight features, which provide
evidence of both mode I and mode II propagation mechanisms activated during the propagation
process. None of the αp grains in the vicinity of the cracks have the red orientation, which depressed
the formation of shear bands and promoted the cracking mechanism. In Fig. 6.20, the elongation
and coalescence of the micro-voids took place within the shear band. One possibility for this
phenomenon is that as higher normal stresses are encountered when a shear crack progresses
downward from the free surface toward the tool tip, a continuous gross crack may gradually be
converted into a discontinuous microcracked region [47]. On the other hand, Bieler et al. [134]
observed that the cavity nucleation in lamellar Ti64 during upset forging process was located in
boundaries with hard orientations present on one side, thus giving rise to large strain variations
120
between neighboring colonies. Even though the stress state in upset forging is much more
complicated, it is still possible that the nucleation of the micro-voids in the present study may
result from the 90°-misorientation of the colonies on two sides.
Figure 6.18 Cracks at 1 m/s are usually wide open. The arrows indicate the hard-oriented αp
grains.
121
Figure 6.19 1 m/s chip segments with wide shear band regions with prism favored
orientations.
Compared with 2 m/s chips, αp grains were less severely sheared in 1 m/s chips and the shear
bands can be much wider, as can be seen in the PSZs in Fig. 6.19. According to the EBSD maps,
the sheared αp grains all exhibited red orientations which are favored by prism slip. In S3 in
Fig. 6.19, the shearing in PSZ is closely related to the SSZ. There are αp grains in the SSZ sheared
horizontally and gradually transitioning to the 45° shearing in PSZ. This observation is in
agreement with the simulation result by Molinari et al [74], in which the shear bands are generated
at the tool tip and propagate toward the chip free surface. However, his simulated chip morphology
at 350 m/s showed no segmented features at all. Their explanation is that the shear bands did not
122
have enough time to reach the chip free surface, which is an interesting but controversial idea.
In S3 in Fig. 6.19, the homogeneous shear strain is 0.6 and is high enough to trigger the
adiabatic shear band. The localized shear strain in this shear band is estimated to be 4.38 due to a
wide shear band width (15.2 μm, as shown in Fig. 6.21 (a)). In contrast, the homogeneous shear
strain in S7 in Fig. 6.19 is 0.55 and the adiabatic shear band is even less localized so that the width
between the two yellow arrows is much wider. The shear strain between the right two blue arrows
is determined to be 1.46, which is much smaller than the localized shear strain in S3. Unlike the 2
m/s serrated chip, there is much greater variability of the shear band width in the 1 m/s, as
illustrated in Fig. 6.21, where the shear band width varies from 15.2 μm to 1.3 μm. The 1.5 and 2
m/s chips show consistent shear band widths of approximately 1.5-2 μm. This observation agrees
with the proposed model [135] that the shear band width is inversely proportional to the cutting
speed. Using this model, the catastrophic shear strains in Fig. 6.21 are 6, 9 and 25, respectively.
Using measurements of the aspect ratio of the sheared αp grains provides catastrophic shear strain
values of 17, 20, 31, which follow the same trend, but the model predicts much lower values, and
a larger range. The potential crack is not considered by the model, which could also account for
the shear displacement and thus the catastrophic shear strain will be smaller (in what case?). In
addition, the model calculates the “average” catastrophic shear strain within the shear band, which
also shows difference from the physical measurements that reflects the shear strain of specific αp
grains.
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Figure 6.20 Evidence showing the elongation and coalescence of micro-voids (a) C6 ;(b) C12.
Figure 6.21 Shear band width variation (a) S3; (b) C2; (c) C18.
6.2.3 Deformation twins in 1 m/s chips
A few twins were also observed in the 1 m/s chip. The misorientation angle between the parent
and twinned grains are approximately 85° and they have a common a-axis (Fig. 6.22). The
twinning mode is identified to be {101̅2} < 1̅011 > extension twinning.
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Figure 6.22 Representative T1-type twins in the chip segments exhibiting misorientation angle of
~85° (twin boundary is labeled with yellow lines).
6.3 1.5 m/s chips
6.3.1 Crack length, segment spacing and homogeneous shear strain distribution of 1.5 m/s
chips
The morphology of chips cut at 1.5 m/s can be seen in Fig. 6.23. Compared to the 1 m/s chip,
1.5 m/s chip are much more uniform in the chip peak/valley heights, segment spacing, and crack
length, and are a little more uniform than the 2 m/s chips as well. Another important difference is
that the αp grains are more uniformly deformed compared to the other two cutting speeds. There
are no αp grains showing extreme shear deformation, except for only a few in the vicinity of the
shear bands. This conclusion can also be seen in Fig. 6.24. The homogeneous shear strain is
uniformly distributed and so is the segment spacing.
From Fig. 6.25, the segment spacing is between 55 and 80 μm, similar to the 2 m/s chip. Most
of the cracks are shorter than 40 μm, and only 2 cracks have the length of 60-70 μm, and are shorter
than those in 2 m/s. It is noteworthy that the homogeneous shear strain in the segments is between
0.46 and 0.52, which is much smaller than the shear strain at 1 m/s (0.4-1.4) and is close to the
shear strain at 2 m/s (0.4-0.7) but more homogeneously distributed. As indicated in Fig. 6.26, the
crack length decreased with increasing shear strain, and the segment spacing shows a similar
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decreasing trend. Therefore, the segment spacing increased with increasing crack length. These
parameters at all three cutting speeds show the same trend.
Figure 6.23 1.5 m/s chips on which segment spacing, shear strain, and crack length are
investigated.
Figure 6.24 The distribution of crack length, segment spacing, and homogeneous shear strain
within each segment, with respect to their actual locations at 1.5 m/s.
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Figure 6.25 Histograms of segment spacings, crack lengths, and homogeneous shear strain
within each segment.
Figure 6.26 Correlation between crack length, segment spacing, and homogeneous shear strain
within each segment.
6.3.2 Representative cracks and shear bands in 1.5 m/s chips
In both C6 and C8 in Fig. 6.27, there is a small crack after the arrest of the long straight crack.
In the blue box shown in C6, this minor crack resulted from the elongation and coalescence of
micro-voids within the shear band. The shear band is so thin that the micro-voids are small and as
a result the elongation of the voids is not as pronounced. It is reasonable to infer that the small
crack in C8 is also created by the coalescence of micro-voids.
Pole figures in Fig. 6.28 shows the texture evolution after cutting at three speeds (the observation
directions of as-received bar and chips are consistent.). In Fig. 6.28, the as-received material has
various peaks with different intensities on the (0001) pole figure, indicating the existence of a few
predominant orientations. After being cut, the chips have a texture with a strong peak in the center
of the (0001) pole figure, especially at 1 and 2 m/s. This means that the crystals preferentially
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rotated to orient the c-axis transverse to the chip flow direction as the material deforms, which can
be accomplished with prism slip. The difference in the 1.5 m/s chips lie in the intensity of the
peaks. Maximal intensity is not in the center but located at the upper right peak.
Figure 6.27 Long straight crack with small opening at the chip valley (1.5 m/s chip).
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Figure 6.28 Pole figures of as-received material (radius direction) and chips (transverse
direction) showing the texture evolution.
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Figure 6.29 Shear bands where not much shearing in αp is seen.
In the uncracked 1.5/s chips S3 and S4, shear bands are narrower, showing highly sheared
primary α grains such as those shown in Fig. 6.29, indicating more localized shear deformation 1
and 2 m/s chips. EBSD scans show two grains that were sheared to very thin proportions, shown
by arrows in S3 (a prism favored orientation) and S4 (a basal favored orientation). In both cases,
the lower part of the shear band in the PSZ is highly correlated with the SSZ. From the FEM
simulation, the temperature is much higher at the SSZ than in the PSZ, and the lack of cracking
combined with favorable orientations for shear suggests that the PSZ was initiated by the shear
taking place in the SSZ. On the other hand, the upper part of the shear band is far away enough
from SSZ and thus is less associated with SSZ but more related to the orientations of its
surrounding material.
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6.3.3 Deformation twins in 1.5 m/s
A few twins were also observed in the 1.5 m/s chip. The misorientation angle between the
parent and twined grains are approximately 85° and they have a common a-axis (Fig. 6.30). The
twinning mode is identified to be {101̅2} < 1̅011 > extension twinning.
Figure 6.30 Representative T1-type twins in the chip segments exhibiting misorientation angle of
~85° (twin boundary is labeled with yellow lines).
6.4 Conclusion
1. At all three cutting speeds, the crack length decreases with increasing homogeneous shear strain
in the segment, indicating that the adiabatic shear is more likely to take place with higher
homogeneous shear strain and cracking and thus adiabatic shear are two competing mechanisms
for the formation of segmented chips. This makes sense because the observations show that
cracking usually nucleates at the subsurface of the tooth tip while the adiabatic shear always
generates from the secondary shear zone due to elevated temperature from friction, both depending
on the local crystal orientations. Cracks usually form when there are hard-to-cut orientations on
one side (causing deformation incompatibility on two sides) or both sides, while adiabatic shear
bands keep propagating when there are easy-to-cut orientations.
2. The shear band width at 1 m/s varies from 1.3 μm to 15.2 μm but barely changes at 1.5 and 2
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m/s (~1.3 μm at 1.5 m/s and ~2 μm at 2 m/s). Wider shear band widths indicate less localized shear
and this is consistent with the fact that calculated homogeneous shear strains at 1 m/s is between
0.4 and 1.4, which is much higher than at the other two cutting speeds, and is much more uniform
at both 1.5 m/s (0.4 - 0.5) and 2 m/s (0.4 - 0.6). The shear strain calculations are believable in that
the strains at 2 m/s are much lower compared with those at 1 m/s.
3. The prism favored red orientation is dominant in and beneficial for the formation of
adiabatic shear bands at both 1 and 2 m/s. This makes sense as prism slip is the slip system
with the lowest critical resolved shear stress among all the slip systems in hexagonal titanium.
However, no dominant orientations have been observed from the 1.5 m/s chips.
4. {101̅2} < 1̅011 > extension twinning, as a minor deformation mode, was observed at all three
cutting speeds. There are only a few twins among all the locations investigated, because the
deformation during cutting is large and twinning can only contribute a very small amount of
deformation.
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CHAPTER 7 ANNEALING TREATMENT OF STA CHIPS
The aim of annealing heat treatment on the as-received STA chips is to reduce dislocation
density without modifying microstructure so that it will be easier to obtain high quality EBSD
scans of the shear bands after annealing. In addition, higher temperature heat treatments provide
a means to investigate the beginning of recrystallization and thus provide indirect evidence for
locations with high shear strain and the nature of stored defect energy. Investigating the effect of
the annealing temperature and time on microstructure change due to recovery and recrystallization
provides insights about the nature of defects present in the as-formed chip.
7.1 Annealing at 500℃
From the BSE image and orientation maps, orientations within the shear band are
undetectable after a 4h-anneal (Fig. 7.1) as no apparent recovery or recrystallization took place at
this temperature. In Figs. 7.1 and 7.2 with 12 h-anneal, BSE images, the lamellar structure in the
βt region is still present after the annealing. The grain reference orientation deviation (GROD) map
in Fig. 7.1(c) reveals the misorientation in each αp grain where the white color indicates that the
misorientation is greater than the maximum scale value of 15°.
In 1 m/s chips annealed for 12 or 16 h, in Figs. 7.2 and 7.3(a), orientations in the βt regions
away from the shear band could be indexed, but the orientations within the shear band in the 2 m/s
chip are less clearly seen (Fig. 7.3(b)). In Figs. 7.2 and 7.3, there are some small orientations that
are larger than single indexed points, where orientations within the shear band have a blue or cyan
orientation that would favor basal slip. The 500℃ temperature is still too low for recovery to
reveal most orientations within the βt shear band region, and it did not cause recrystallization in a
measurable way.
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Figure 7.1 1m/s chip annealed at 500℃ for 4h (a) BSE image; (b) IPF mapping in the red box in
(a); (c) grain reference orientation deviation (GROD) map of (b) with a maximum misorientation
of 15 °, white color indicates that the misorientation is great than 15 °. White dashed line on the
IPF map indicates where the potential shear band is located.
Figure 7.2 1m/s chip annealed at 500℃ for 12h.
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·
Figure 7.3 (a) 1m/s chip (b) 2m/s chip annealed at 500℃ for 16 h.
7.2 Annealing at 600℃
After annealing at 600℃ for 16h, orientations within the shear bands can be detected clearly
in both the 1 m/s chips in Fig. 7.4 and 2 m/s chips in Fig. 7.5. All of these shear bands exhibited a
similar orientation that would favor basal slip (blue, cyan color). The αp grains in the vicinity
of the shear band are clearly indexed, which indicates a low dislocation density in the deformed
grains. Nevertheless, the initial lamellar microstructure of the βt region is not clearly indexed, and
it is difficult to identify what took place in these areas. This 600 ℃ microstructure reflects
sufficient temperature to generate indexible grains within most of the shear band in only 1 of the
4 cases, in Fig. 7.4(a). In the GROD maps for all four chips, there are slight misorientation
gradients along the blue basal favored strip (ribbon in 3-D) within the shear band, indicating that
recovery rather than recrystallization took place within the shear band. This indicates that 600℃
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annealing is not high enough to annihilate all of the dislocations within the shear band.
It is of great significance that there is a crystal orientation change from the red, prism
favored orientation to blue, basal favored orientation in Fig. 7.5 (b). The orientation of this
specific αp grain would favor prism slip, which is the easiest to activate due to the lowest
critical resolved shear stress. However, the severely sheared portion of this same grain, composing
the shear band, has an orientation favored by prism and a misorientation angle of 90°, which
is a possible misorientation angle of the two α variants before and after α-β-α phase transformation,
which is discussed in more detail below.
Figure 7.4 Two scans of 1m/s chip annealed at 600℃ for 16h.
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Figure 7.5 Two scans of a 2m/s chip annealed at 600℃ for 16h.
7.3 Annealing at 650℃
When the annealing temperature was increased to 650 ℃ and annealed for 20 h (Fig. 7.6),
the microstructure of the 1 m/s chip has two distinct regions. In the vicinity of the shear band (PSZ),
indicated by a white arrow, there is a fine microstructure of equiaxed α grains with β on their grain
boundaries, similar to the mill-annealed microstructure. In contrast, the lamellar structure can still
be seen far from the shear band (indicated by the black arrow). Enlarged images of these two
distinct microstructures are provided in Fig. 7.7 illustrating β lamellae in Fig. 7.7 (a) and ultra-fine
recrystallized α grains in Fig. 7.7 (b). The change in microstructure reflects the different strain
paths in the segments and shear bands during the cutting process. Within the segment far from the
shear band, the homogeneous shear strain is much smaller than the localized shear in the shear
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band and thus the microstructure is not much affected by the 650 ℃ annealing. The highly distorted
area near the shear band has enough driving force for complete recrystallization with many
nucleation sites that lead to a new fine-grained microstructure.
Figure 7.6 Two scans of 1m/s chip annealed at 650℃ for 20h. the black arrow indicates the
remaining βt lamellar structure, and the white arrow indicates the newly formed equiaxed fine-
grain structure.
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Figure 7.7 Representative images at the same magnification of (a) lamellar microstructure (black
arrow in Fig. 7.6) in the segment; (b) equiaxed α grains with β on the grain boundaries (white
arrow in Fig. 7.6) near the shear band.
Similar phenomena are observed in the 2 m/s chips. Annealing the 2 m/s chip for only 8 h
leds to a similar microstructure as annealing the 1 m/s chip for 20 h, which suggests that the shear
strain is more localized and distortion energy is higher at the cutting speed of 2 m/s. It is noteworthy
that all the shear bands indexed in the annealed chips have the same blueish color and orientation
that would favor basal slip that was observed in the 600C chips. In the three 1 m/s examples
in Fig. 7.8, the extent of recrystallization is quite different; in the first, nearly all of the βt is
recrystallized (blue orientations in the GROD plot), but a lesser fraction is recrystallized in the
other two shear band regions. There are also recrystallized grains in the SSZ in addition to those
in the PSZ. The αp grains did not recrystallize, as the orientation gradients are still present within
them.
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Figure 7.8 Three scans of 2m/s chip annealed at 650℃ for 8h. the black arrow indicates the
remaining lamellar structure, and the white arrow indicates the newly formed structure.
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7.4 Discussion
The blue basal shear band orientations show a difference from the prism slip favored
orientation often found in uncracked shear bands in the as-received chips. For basal slip,
homogeneous deformation would lead to a rotation of the c axis. In contrast, homogeneous strain
due to the activation of prism slip will not change the c-axis direction. The measured
misorientation angle between these two orientations is close to 90°. One possible phase
transformation mechanism that could account for this is that the blue orientation revealed after
annealing at 600 or 650℃ might be a result of the phase transformation to β during cutting.
Zhao et al. [136] carried out equal channel angle pressing (ECAP) of Ti64 samples with a
shear strain of ~1.125 in each pass. Fast recrystallization was observed when annealing the sample
after four passes at 620℃ for only 5 mins. In addition, an increasing fraction of β phase was
observed after a pulsed electric current treatment. In contrast, the shear strain in the vicinity of
ASB in the present study is much larger than 4.5. The microstructure after the 650℃ anneal in the
present study (Fig. 7.7 (a)) is similar to the results from Zhao et al. [136]. Therefore, it is believable
that the recrystallization took place when heat treated at 650 ℃ for 20 h and 8 h for the 1 and 2
m/s chips, respectively. The fact that many βt regions are not indexed implies that local grain or
sub-grain sizes are too small to generate a dominant Kikuchi pattern. Dynamic recrystallization
(DRX) may have taken place during the cutting but the nano-scale grain from DRX in the as-cut
chips is too small to be detected by EBSD [137]. If so, the grains grew to become measurable as
1-2 μm grains in Fig. 7.7 (b), but it is not clear whether this took place by static recrystallization
of a DRX sub-micron grain microstructure, or if the deformed and quenched microstructure
recrystallized during a static anneal.
The misorientation angle distribution of the as-received bar, is compared with regions without
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the ASB vicinity and only the ASB vicinity of 2 m/s chips after annealing in Fig. 7.9. Compared
with the misorientation angle distribution of undeformed Ti64 and Ti64 with the tensile strain of
0.59 by Bieler et al. [138], similar peaks located at 30°, 60° and 90° that reflect the transformation
from β to α, have also been observed in Fig. 7.9. In addition, the peaks at ~75° may have been
caused by the large deformation during cutting, which was also observed after a hot tensile strain
of 0.59 [138], a strain similar to strains between shear bands in the chips. The ASB vicinity in the
annealed 2 m/s chip is similar to the as-received bar, which indicates that the α grains in the vicinity
of ASB have misorientations caused by the phase transformation. This may reflect preferred
misorientations from transformation that persisted during grain growth, as these misorientation
have a Burgers orientation relationship.
Figure 7.9 The misorientation angle of the ASB vicinity in the annealed 2 m/s chip shows a
similar distribution as the as-received bar.
The pole figures of 1 and 2 m/s chips were made by merging about 15 scans so that the texture
is representative. It can be seen in Fig. 7.10 that the peaks on (0001) pole figure are roughly near
the center, and they have similar maximal intensities. In addition, the as-cut 1 and 2 m/s chips
show similar texture except for the intensities. The strong peak near the center of the (0001) pole
figure indicates that the crystals rotate toward the orientation of c-axis perpendicular to the page
as they deform during the cutting.
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Figure 7.10 Pole figures of the 2 m/s chip (annealed at 650 ℃ for 8 h) and 1 m/s chip (annealed
at 650 ℃ for 20 h).
It is noteworthy that the orientations of the ASB before and after annealing show an apparent
and consistent differenec at both 1 and 2 m/s. The ASBs before annealing in Chapter 5 exhibited
red color that favors prismatic slip, while the ASBs after annealing in the present work have
blue color that would favor basal slip. Also, the blue ribbons after annealing are much
narrower compared with any red shear bands that were detected before annealing. One possible
explanation for the blue-ribbon orientation that favors basal slip is the β-α phase transformation.
If the βt region transformed to β during the cutting process, it would be much softer than the
hexagonal orientations in the βt. This would facilitate and accelerate a plastic shear instability that
would favor even more strain that could be accomplished by the α grain orientations. With large
strain in the ASB, two two β variants that are likely to form due to large strain with the highest
possible Schmid factors in the direction of shear are presented at the top of Fig. 7.11. According
to the orientation relationship between α-Ti and β-Ti [139], there are 12 possible α variants that
could transformed from β phase orientations. The orientations of α crystal in red boxes are
consistent with the orientations detected in Fig. 7.8 (a), which have the basal plane parallel to a
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{110}β plane. Compared with other possible {110}β planes, this specific orientation of α is
favorably biased among all the 12 variants because the dislocation slip on the {110}β plane parallel
to the shear plane resulted in lattice defects and thus preferentially favored this {110}β plane to
become the basal plane of the α crystal [4]. Hence, the presence of the thin band of blue basal
orientation could not have resulted as convincingly from deformation of the α phase.
The typical phase diagram of the Ti64 alloy [8], [140], [141] illustrates that the β-transus
temperature is 994 ℃ when there is 6% Al present. However, the partition of Al and V in primary
α and transformed β makes phase transformation more complicated. The phase diagram plotted in
Fig. 7.12 overlays the Al and V binary phase boundaries. Assuming that there is 50% α and 50%
β during the sub-transus heat treatment for the STA microstructure, then Al is an α stabilizer, and
is partitioned in primary α, at a concentration of about 12wt. % Al, so the beta transus temperature
is ~1080 ℃. Similarly, V is a β stabilizer, and at about 8 wt. % V, the β transus is about 750 C.
The starting and finishing temperatures for a martensitic phase transformation is 780 and 650 ℃,
with a cooling rate larger than 20 ℃/s [140]. Such a cooling rate is likely following cutting, and
the temperature near ASB can reach even much higher than the predicted temperature of 750℃
since the shear is more localized compared with the FE simulation (from Chapter 4). It thus is
likely that the βt regions within/near ASB transformed to β phase during the cutting and then
experienced a large amount of shear deformation along the ASB direction, and finally transformed
to the martensitic α’ during the air cooling after being cut. This may also account for the fact that
the regions near the ASB usually cannot be detected by EBSD. The αp grains near ASB would not
be able to transform to β because the transus temperature is as high as 1080 ℃ due to Al
partitioning, and the observation that they remained intact, even though severely stretched after
cutting.
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When annealed at 600 or 650C, the martensitic α’ was able to transform back to β due to the
V partition in martensitic α’, because vanadium didn’t have enough time to diffuse during the air-
cooling process. When withheld at 650C for 8 hr, there was sufficient time for β to transform to
α+ a small amount of β, in the form of the extremely narrow blue ribbon (compared to the wide
shear band widths with red orientations), with grain growth sufficient to make the orientations
visible by EBSD. In Fig. 7.8 (c), the narrow blue ribbon was still present even when the A-A’ and
B-B’ pairs showed prism favored soft orientations. This indicates that the βt contributes to the
adiabatic shear despite the soft αp at 2 m/s.
While Fig. 7.12 shows one plausible path to account for the observed ribbon of basal
orientations in the shear plane, other β orientations could have been present after transformation
to β. The intense shear could easily have led to rotations leading to orientations similar to the two
terminal orientations of β due to large strain, and consequently back transformation to a blue basal
orientation, as well. The fact that there are discontinuities in the blue ribbon is consistent with
variations in β grain orientations undergoing severe shear. The presence of many dislocations on
(110) planes in the plane of shear provides defects that could favor formation of the basal variant
of the 12 possible β-α phase variants [139].
Figure 7.11 Two terminal β orientations that favor maximal shear. The red- boxed α orientations
among 12 possible α variants are consistent with the α orientation detected after annealing, as
shown in Fig. 7.8 (a).
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Figure 7.12 Phase diagram of titanium and the partitioned Al/V.
7.5 Conclusion
1. When annealed at 500 ℃, the ASB was still invisible to EBSD, and no recrystallization was
observed because the temperature is not high enough for sufficient recovery and/or
recrystallization processes to grow large enough grains to generate a dominant Kikuchi pattern. At
600 ℃, some parts of the ASB can be indexed but recrystallized grains were not indexable. After
650 ℃ annealing, both ASB and the recrystallized grains can be clearly seen and indexed by EBSD.
In addition, microstructure near ASB consisted of fine equiaxed α grains with β on the grain
boundaries, whereas the microstructure in the less deformed βt segments remained lamellar and
recovered sufficiently to be indexable, identifying high shear strains near the ASB, low shear
strains within the segment and the gradient between them.
2. The GROD map of the shear band annealed at 650 ℃ has many grains with local misorientation
gradients of 0 °, which indicates that the shear band has no GNDs that cause a gradient, and hence,
have recrystallized. DRX may have taken place during the cutting process but the nano-scale grain
from DRX in the as-cut chips is too small to be detected by EBSD. If so, the grains grew to become
146
measurable as 1-2 μm grains but it is not clear whether this took place by static recrystallization
of a DRX sub-micron grain microstructure, or if the deformed and quenched microstructure
recrystallized during a static anneal.
3. All of the narrow ribbons detected after annealing show the same blue orientation that would
favor basal slip, which differs by nearly 90 from the red orientation so commonly observed
in uncracked (and some cracked) ASBs in as-machined chips at both cutting speeds. The blue
ribbons can be best explained by a strong variant selection from transforming the βt into the β
phase above 750 ℃, from which back transformation to a highly favored α with basal planes
parallel to the high dislocation density β {110} planes occurs. This observation provides evidence
for the βt → β phase transformation during the cutting at 2 m/s, and accounts for the more
homogeneous chip morphology at 2 m/s compared with the 1 m/s chips.
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CHAPTER 8 CONCLUSIONS AND FUTURE WORK
8.1 Conclusions
This thesis demonstrates an approach to understanding the formation of segmented chips and
their deformation history during turning, using EBSD, nanoindentation and annealing heat
treatments. Preliminary results in Chapter 4 show that primary α exhibits high anisotropy in the
hardness, and is consistently higher hardness than transformed β. Before and after cutting, the
hardness of primary α generally remained unchanged, which may result from the low work
hardening rate at high temperatures even under high strain rates [142]. Considering many cases,
the calculated homogeneous shear strain in the segments at 1 m/s is much higher at 1 m/s than at
1.5 and 2 m/s, indicating a high strain rate sensitivity of homogeneous deformation in Ti64.
Cracking originating from the surface or subsurface of the chip and the adiabatic shear generated
near the tool tip are the two competing yet also complementary mechanisms for the formation of
segmented chips, both depending on the local crystal orientations. Hard-to-cut orientations of
primary α at tooth emergence sites will more likely lead to the nucleation of cracks. In contrast,
primary α with soft orientations near the tooth emergence site is beneficial for the formation of an
uncracked adiabatic shear band that is wider, and does not get as hot or unstable. Both cracks and
adiabatic shear instabilities will result in a periodic load drop and hammering effect on tool. One
observation of a prism favored orientation resulted in a much “less localized” shear at 1 m/s
and the chip morphology is more “continuous”. The Schmid factor analysis based upon many cases
also indicates that orientations that favor both basal and prism slip are usually related to
the occurrence of adiabatic shear bands without cracks, and more homogeneous deformation in
and near the adiabatic shear band.
The phase diagram suggests that the transformed β half of STA microstructure to soft β can
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occur at temperatures above ~750℃ due to partitioned vanadium. This implies that the
transformed β part of the microstructure will transorm to β, deform more easily than the primary
α, and then re-transform upon rapid cooling to martensitic α that cannot be indexed due to the high
density of defects. This happens to a greater degree with increasing speed, and this can account
for observations of increased tool damage due to tool dissolution as diffusivity is orders of
magnitude faster in the β phase than the α phase. After annealing at 650 ℃, static recrystallization
or grain growth of dynamically recrystallized nanograins in the deformed transformed β leads to
large enough grains to be indexed by EBSD, which develop preferentially in the vicinity of
adiabatic shear bands. This indicates a stronger driving force to form new grains, in higher strain
regions, in contrast to the lamellar βt microstructure away from the shear band which remains intact.
While this work has clarified many aspects of deformation during turning, deformation is
locally heterogeneous and very sensitive to local crystal orientations. It is still difficult to
systematically understand the orientation and crystal structure evolution of the adiabatic shear
band during deformation, as interpretations aided by annealing are still challenging to untangle.
Nevertheless, the questions raised at the end of literature review can be answered with confidence:
1) Which mechanism is dominant when forming the segmented chips, cracking or adiabatic
shearing?
In most cases, both mechanisms are activated, and pure adiabatic shearing is less common
(~20%). The activation of cracking is more likely when hard-to-deform orientations are located
where a tooth emerges. When most of the material has a soft orientation in the shear band volume,
the lower flow stress enables adiabatic shear bands to form that do not reach a high enough
temperature to transform to β phase and become unstable enough to form a shear crack.
2) How to estimate the homogeneous shear strain and the catastrophic shear strain and how
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does the cutting speed affect them?
A model based on the shape of the tooth was adopted to calculate the shear strains. The
homogeneous shear strain within the segment decreased significantly with increasing cutting speed
due to the increasing strain rate. However, it can be seen from C12 in Fig. 6.10 that the so-called
homogeneous shear strain is not homogeneous across the segment. The prsim favored
orientations have more deformation in the αp than other orientations. The catastrophic shear in the
shear band increased dramatically with increasing cutting speed since the shear band width
generally decreased with increasing cutting speed. There is a much greater shear band width
variation at 1 m/s, where the likelihood for forming cracks is lower due to a lower flow stress in
the material (and hence, less adiabatic heating). The aspect ratio of the sheared αp grains in the
adiabatic shear band at three locations (Fig. 6.2) of pure adiabatic shear bands are also used and
compared with the catastrophic shear strain. The catastrophic shear strains according to the model
are 6, 9 and 25 while the aspect ratio measurements can be used to estimaate the catastrophic shear
strain to be 17, 20 and 31. The model gives smaller values than the aspect ratio method and they
they are similar in magnitude and show similar increasing trend in these cases. A possible
explanation for this slight difference is that the model provides the “average” shear strain within
the shear band (which consists of a few sheared αp grains and βt regions) while the aspect ratio
measurement reflects the shear strains of the αp grains in the center of the shear band.
3) What is the correlation between the shear strains and the two mechanisms of segmented
chip formation?
The adiabatic shearing tends to take place when the homogeneous shear strain within the
segment is higher while the cracking shows the opposite trend.
4) Does the microstructure and local crystal orientation influence the morphology of the
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segmented chips? If so, what is the influence and what crystal orientation is beneficial for the
formation of adiabatic shear?
The microstructure and local crystal orientation have significant influence on the morphology
of the chips. Easy-to-cut orientations such as orientations that favor prism or basal slip are
beneficial for the formation of adiabatic shearing with wide ASBs and minimizing cracking. For
LAM chips, the basal favored orientations result in less segmented chips. For STA, adiabatic
shearing propagates when the prism favored orientations are present.
5) Is there direct evidence of the α → β phase transformation during cutting?
Simulations that match the material behavior of the shear band also provide a lower bound
on the temperature in the shear band, indicating that temperatures exceeding 750℃ are reached up
to about 100 μm from the tip of the tool, which can cause transformation of βt to β in the adiabatic
shear band due to the enriched V. After annealing, consistent observation of thin basal oriented
(blue) bands are present at the center of the shear band can most easily be explained by
transformation of the βt in the adiabatic shear band to β, followed by intense shearing that rotates
the β orientation to a terminal orientation with {110} < 111 > aligned with the shear plane and
direction. With rapid cooling, transformation to the α’ martensite orientation with (0001) <
21̅10 > aligned with the shear plane and direction in the volume that sheared preferentially as β
results in a ribbon of α that becomes detectable with heat treatment. Also, the EBSD scan in Fig.
7.5 (a) shows a red, prism favored αp grain but the sheared portion of it has a blue, basal
favored orientation, which shows a misorientation angle of 90°. This observation provides direct
evidence of the phase transformation taking place within the shear band during the machining
process.
151
8.2 Future work
As discussed above, the formation of cracks and adiabatic shear bands should be reduced to
improve the tool life. However, it is impractical to manipulate the texture of Ti64 to become what
is desired for cutting. On the other hand, the present study identified the root cause for the
formation of segmented chips, which is the build-up of stress and strain combined with low thermal
conductivity that leads to unstable adiabatic shearing and cracking. Cryogenic machining may be
a potential environmental-friendly and efficient approach to extending tool life, yet the chips will
remain segmented, and the lower temperature may result in higher loads on the tool. Hence,
tougher and chemically resistant tools are needed to enable faster machining or longer tool life. It
will be meaningful and interesting to carry out annealing with in-situ observations to better
understand how the deformed state can be understood by the outcomes of heat treatment and
provide improved understanding of how particular shear bands developed.
152
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