2.3L 133...... My. . m“ .5 :3 mix“ .- . :us...‘ fin?! 5. ran“. um z... o uh LA... . .2: v x' F}; n.- :15»). 30%|" .2 .. t V .31.... t 93213.13: 1. .h wing}...- t....ma..nn.m .. 3 .._ I‘IN I < I 303.35): K v 3» 2. 2| I 1.3.5.1! . . . .. s. i p n. .1 ‘2‘ . ., , . .V .E . Jauwauaufi!’ 5 .0 z... .. » 3:3.“ ‘4 in... v».... .3. x7:)».:.\ v .fi!’ ‘ aft .9 fl. xv.I.. . 932.04.}...i 3.5.3! 3 . ‘31.); ..x\ ‘ a v u. H2...L5..7.1 L. 593)).‘273 4.9...6 \ I .uttit: x:(iv‘... . .3 . 7 A vhf. 3)..J: ‘1‘... ,s..l‘r A )9“. ufifZQa 513:7 v y...\ I .-.I .. 131.12.: .5..x...u.u.\v. THEBMi Date 0-7 639 \"\\\;\\\\1\\§\\£\9\\\3\\\\(\§1 41 1 l\\\ \lllllllllllllllll This is to certify that the thesis entitled DATA ACQUISITION AND ANALYSIS OF TRANSIENT CREEP DEFORMATION IN Ti-47Al—2Cr-2Nb presented by Chih-Huei Wu has been accepted towards fulfillment of the requirements for Master's Materials Science degree in 0 / 7 I f M Major professor Thomas R. Bieler August 4, 1995 MS U is an Affirmative Action/Equal Opportunity Institution w or“ meant-w l tichigan State! University PLACE II RETURN BOX to man thb checkout from your record. TO AVOID FINES mum on or before data duo. DATE DUE DATE DUE DATE DUE DATA ACQUISITION AND ANALYSIS OF TRANSIENT CREEP DEFORMATION IN Ti-47Al-2Cr-2Nb By Chih-Huei Wu A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Materials Science and Mechanics 1995 ABSTRACT DATA ACQUISITION AND ANALYSIS OF TRANSIENT CREEP DEFORMATION IN Ti-47Al-2Cr-2Nb By Chih-Huei Wu A low cost and high efficiency automated data acquisition was developed for tran- sient creep testing. The data analysis was accomplished using a modified 9—projection equation for creep. The fitting parameters of the 9—projection equation exhibited similar stress exponent and thermal activation energy as steady state creep data. Stress and temperature change creep experiments under a compression shear stress state were conducted on PST (Polysynthetically Twinned) and polycrystal (duplex) speci- mens of 'Ii-47Al-2Cr-2Nb at 25 ~87MPa and 760~810 0C. Transient creep of PST and polycrystal after stress and temperature change exhibited ‘normal’ behavior and suggests Class M type creep deformation in TIAl. The stress exponent of n=5.6 and the activation energy of Q = 135 i 70 KJ/mole for the PST indicating that dislocation glide aided by pipe diffusion is the dominant mechanism of creep deformation in this test regime. The values of n=2~3 and Q=229 i 60 KJ/mole for polycrystal in Ar and n=2~3 and Q=574 i 90 KJ/mole in air were obtained, respectively. Varying values of the stress exponent and the activation energy for the polycrystal may due to the effect of dynamic recrystallization, and a mixture mechanism suggesting that a composite mode is needed to describe the polycrystal creep behavior of TiAl. ACKNOWLEDGEMENTS I would like to express my deepest appreciation to my academic advisor, Professor Thomas R. Bieler, for his guidance and encouragement throughout my graduate studies at Michigan State University. I also wish to thank the members of my committee, Professor Gary L. Cloud and Professor David S. Grummon, for their valuable suggestions and com- ments on this work. I also thank my parents and family for their never-ending love and support during my educational career. ii TABLE OF CONTENTS LIST OF TABLES ....................................................................................... LIST OF FIGURES ..................................................................................... CHAPTER I. INTRODUCTION ............................................................... CHAPTER 11. REVIEW OF CREEP ........................................................ 2.1. DEFINITION OF HIGH TEMPERATURE CREEP ........................ 2.2. STAGES OF CREEP ........................................................................ 2.3. STRESS AND TEMPERATURE EFFECT ..................................... 2.4. POWER LAW EQUATION ............................................................. 2.5. DEFORMATION MECHANISMS .................................................. 2.5.1. Diffusional creep ...................................................................... (a) Nabarro-Herring creep ..................................................... (b) Coble creep ....................................................................... 2.5.2. Dislocation creep ..................................................................... (a) Dislocation glide rate-controlled ...................................... (b) Dislocation climb rate-controlled ..................................... 2.5.3. Mechanisms map ..................................................................... 2.6. STRESS AND TEMPERATURE CHANGE CREEP ...................... 2.6.1. Class M behavior ..................................................................... 2.6.2. Class A behavior ...................................................................... viii ix 1 3 3 3 6 8 10 10 10 10 12 12 12 14 16 16 19 2.6.3. Incubation period and anelastic strain ..................................... 20 CHAPTER III. THE O—PROJECTION CONCEPT ............................... 22 3.1. CONSTITUTIVE CREEP EQUATION ........................................... 22 3.2. MODIFICATIONS OF O—PROJECI'ION CONCEPT .................... 25 3.3. INTERPRETATION OF THE PARAMETERS ............................... 26 3.3.1. Hardening and weakening parameter ...................................... 27 3.3.2. Rate constant parameters ......................................................... 27 3.3.3. Minimum strain rate ................................................................. 29 3.3.4. Prediction of rupture life .......................................................... 29 3.4. MODIFICATION FOR OUR ANALYSIS ....................................... 30 CHAPTER IV. REVIEW OF TiAl CREEP ............................................... 32 4.1. STRUCTURE OF TIA] ..................................................................... 32 4.1.1. Crystal lattice structure ............................................................ 32 4. 1.2. Microstructure .......................................................................... 34 4.1.3. PST crystal .............................................................................. 37 4.2. ALLOYING ...................................................................................... 38 4.3. CREEP 1N TIA] ................................................................................ 38 4.3.1. No steady state regime ............................................................. 40 4.3.2. No instantaneous strain ........................................................... 40 4.3.3. Dynamic recrystallization ........................................................ 40 4.4. MECHANISMS OF CREEP IN TiAl ............................................... 41 4.4.1. Diffusion controlled creep ....................................................... 41 4.4.2. Dislocation controlled creep ................................................... 42 (a) Dislocation climb .............................................................. 42 (b) Twinning ........................................................................... 43 4.4.3. Composite model ..................................................................... 44 4.5. SUMMARY OF CREEP DATA FOR y-TiAl ALLOYS .................. 45 CHAPTER V. DATA ACQUISITION SYSTEM ...................................... 48 5.1. HARDWARE .................................................................................... 48 5.1.1. Computer .................................................................................. 48 5.1.2. Data acquisition board ............................................................. 48 (a) Analog input ..................................................................... 50 (b) Precision ........................................................................... 53 (c) Data acquisition ................................................................ 53 5.2. SOFTWARE ..................................................................................... 54 5.3. NOISE ............................................................................................... 54 5.3.1. Hardware techniques ................................................................ 56 5.3.2. Software techniques ................................................................. 57 CHAPTER VI. EXPERIMENTAL PROCEDURES ................................ 58 6.1. SPECIMEN DESIGN ..................... 58 6.2. MATERIAL AND SPECIMEN PREPARATION ............................ 62 6.3. CREEP TEST SYSTEM ................................................................... 63 6.3.1. Precision ................................................................................... 64 6.3.2. Noise ........................................................................................ 66 (a) Hardware .......................................................................... 66 (b) Software ........................................................................... 68 vi 6.4. CREEP TEST PROCEDURES ........................................................ 69 CHAPTER VII. RESULTS ......................................................................... 73 CHAPTER VIII. ANALYSIS AND DISCUSSION ................................. 80 8.1. CREEP BEHAVIOR ......................................................................... 80 8.1.1. Stress exponent ........................................................................ 81 (a) PST ................................................................................... 81 (b) Polycrystal ........................................................................ 84 8.1.2. Activation energy ..................................................................... 85 (a) PST ................................................................................... 85 (b) Polycrystal ........................................................................ 87 8.1.3. Stress and temperature change ................................................. 87 8.1.4. Composite model .................................................................... 89 8.2. IMPLICATIONS OF THE FITTING PARAMETERS .................... 90 8.2.1. Parameter A (strain hardening parameter) ............................... 90 8.2.2. Parameter 0t (rate constant) ...................................................... 91 CHARPTER IX. CONCLUSION .............................................................. 100 APPENDIX. PROGRAM CODES FOR CREEP TEST .......................... 102 REFERENCES ............................................................................................. l 18 vii 2.1. 4.1. 4.2. 4.3. 5.1. 6.1. 6.2. 7.1. 7.2. 7.3. 8.1. LIST OF TABLES Different n and Qc values associated with dislocation and diffusional creep occurring with pure metals .......................................................... The different heat treatment conditions and features for four types microstructures in TiAl based alloy ...................................................... ~ Alloying effects the properties of TiAl ................................................... The creep properties of several y—TiAl alloys ........................................ Actual range and measurement precision versus input range selection and gain .................................................................................. Chemical composition of Ti-47Al-2Cr-2Nb specimens ......................... The conditions for each test .................................................................... The fitting parameters for PST specimen in Ar ..................................... The fitting parameters for Polycrystal specimen in air ........................... The fitting parameters for Polycrystal specimen in Ar ........................... The grain sizes of PST and polycrystal for Coble creep ......................... viii 15 35 39 46 52 62 71 77 78 79 86 LIST OF FIGURES 2.1. Strain/time curves for low temperatures (T< 0.4Tm). (a) strain-time curve (b) strain rate-strain curve ...................................... 2.2. Three stages of high temperature creep curve ........................................ 2.3. (a) Stress effect and (b) temperature effect on the creep curve .............. 2.4. The temperature-compensated secondary creep rate data (or Z) for polycrystalline copper. The activation energy of 130 KJ/mole is used for this figure. ........................................................................................ 2.5. Schematic of (a) Nabarro-Herring creep (b) Coble creep ...................... 2.6. Schematic representation of the leading dislocation passes an obstacle by climbing ........................................................................... 2.7. Deformation mechanism map for a pure polycrystalline metal .............. 2.8. Schematic of two types of creep transient after stress changes (a) Class M type (b) Class A type ........................................................ 2.9. Schematic of (a) incubation period tinc(b) anelastic strain ALan ............ 3.1. The 6 projection concept envisages normal creep curves in terms of primary stage and secondary stage .................................................. 3.2. Rationalization of (a) Gland 93 (b) 62 and 64 for polycrystalline copper 4.1. (a) L10 lattice structure (b)DO.9 lattice structure .................................... 4.2. The central part of the Ti-Al equilibrium phase diagram ....................... 5.1. The sketch of creep test units with data acquisition system ................... 5.2. Basic data acquisition system block diagram ......................................... 5.3. Window interface control panel for creep data acquisition system ........ ll 13 14 17 21 24 28 33 36 49 51 55 6.1. 6.2. 6.3. 6.4. 7.1. 7.2. 7.3. 8.1. 8.2. 8.3. 8.4. 8.5. 8.6. 8.7. Plots of yield stress of PST TiAl in tension and compression as a function of the angle 4). The specimens were oriented so that the lamellar boundaries are perpendicular to the wider surface of specimens which is parallel to {112}(group 1) or {110}(group 2) ........................ Schematic of extensometer with compression-shear fixture and shape of specimen ................................................................................. Flow chart of data acquisition program for creep test ............................ The creep curve varies with the fluctuating data. .................................. The creep curve of PST (with fitting) (a) strain-time curve (b) strain-strain rate curve .................................. The creep curve of polycrystal in air (with fitting) (a) strain-time curve (b) strain-strain rate ............................................. The creep curve of polycrystal in Ar (with fitting) (a) strain-time curve (b)‘strain-strain rate curve ................................... The deformation mechanism maps of pure aluminium (a) grain size 10 um (b) grain size 1 mm ............................................. Plots of stress dependence of minimum creep rate for PST and polycrystal. The dash lines indicate the history of deformation. #’s next to datum points refer to Tables 7.1-7.3 ..................................... Arrhenius plots of the temperature dependence of minimum creep rate for PST and polycrystal of TiAl. The dash lines indicate the history of deformation. #’s next to datum points refer to Tables 7.1-7.3 ............... Stress dependence of strain hardening parameters A (a) PST and polycrystal of TIA] (b) CrMoV steel by K. Maruyama et at. #’s next to datum points refer to Tables 7.1-7.3 ................................... Plots of the strain hardening parameters A against temperature for PST and polycrystal of TIA]. #’s next to datum points refer to Tables 7.1-7.3 The stress dependence of rate constants on (a) PST and polycrystal (b) Ti-SOAI and Ti-SlAl by K. Maruyama et 01. #‘s next to datum points refer to Tables 7.1-7.3 ................................... The temperature dependence of the rate constants at (a) PST and polycrystal of TIA] (b) CrMoV steel by K. Maruyama et 0!. #’s next to datum points refer to Tables 7.1-7.3 ..................................... 60 61 65 7O 74 75 76 82 83 88 92 93 94 95 8.8. Plots of temperature-compensated creep rate for polycrystal in Ar ....... 98 xi CEAEIERJ. INTRODUCTION Titanium Aluminide (TiAl) based materials are candidates for high temperature structural applications because of their low density, high specific strength, stiffness at ele- vated temperature and high resistance to oxidation and creep. For service at high tempera- ture, it is very important to understand the creep behavior of TiAl based alloy. However, only limited research has been accomplished and there are still many mysteries regarding the mechanisms of creep in TiAl. The varied values of stress exponent (n=2~8) [l~13] and activation energy (80~60() KJ/mole) [l~13] suggest that complicated mechanisms of deformation are involved in the TiAl creep behavior. Therefore, some simple experiments which remove the effects of complicated rnicrostructure are very helpful to understand the fundamental mechanisms of creep in TIA]. The precise automated data acquisition system which consists of a personal com- puter with a data acquisition board provides a low cost, high efficiency and precise way to collect the data for creep test. The data analysis, combined with mathematical models that precisely characterize the creep curve, is very important in analyzing and interpreting the creep behavior. The goals of current work are to build a precise data acquisition system for creep test and then, to conduct several stress and temperature change creep tests under compres- sion shear stress on carefully oriented PST (Polysynthetically Twinned) and polycrystal specimens of ‘Y-TIAI based alloy. The results of sophisticated stress and temperature 2 change creep tests will be analyzed using the power law equation and a modified 9-projec- tion concept equation to examine the creep mechanisms from mechanical property experi- ments. These experiments will cover a range of stresses and temperatures so that stress exponents and activation energies can be obtained for these fundamental mechanisms. These initial analysis is associated with the microscopy work which is in progress by colleagues. Deeper understanding of creep deformation mechanisms in TIA] will per- mit prediction of the creep life of TIA] in high temperature applications. QEAL’IEBII REVIEW OF CREEP 2.1 DEFINITION OF HIGH TEMPERATURE CREEP Creep is defined as a time dependent deformation. Creep deformation mechanisms are strongly dependent upon temperature and applied stress. Different creep strain/time curves are usually found at different temperature (high or low). A typical low temperature (below about 0.4 Tm) creep strain/time curve is shown in Figure 2.1 [14]. Under low tem- perature conditions, the total creep strains are usually very low, typically much less than 1%, and the creep deformation rarely leads to failure. In general, creep is an important deformation phenomena at temperature conditions higher than half the melting tempera- ture (Tm) in applications such as heat engines. 2.2 STAGES OF CREEP In general, constant-load creep tests are used for engineering purposes. At high temperature the constant-load creep curve can be described by three stages: primary stage, secondary (steady state) stage, and tertiary stage (shown as Figure 2.2) [15]. In the pri- mary stage, after the instantaneous strain 80 that is a sum of elastic and plastic deformation on loading, the creep strain rate decreases and then reaches an approximate constant and minimum value of creep rate during the secondary (steady state) stage. The steady state stage of creep is interesting from an analytical point of view because it represents most of the creep curve and most of the time of deformation, even though the creep strain may be 01>02>O3 ' TI>T2>T3 (Q) , 0. or Tl strain, E f 02 or T2 / —— G3 01' T3 time, t —- ' ( b) creep \ 0, or T‘ rage’ \ Ga 01' T1 8 \ - - 03 or T3 creep strain, 8 —- Figure 2.1 Strain/time curves for low temperature (T< 0.4T...) [14]. (a) strain-time curve (b) strain rate-strain curve Strain 6 Primary creep Secondary creep Tertiary creep Fracture d——I _: - n Time t it: dt 44m minimum creep rate Figure 2.2 Three stages of high temperature creep curve [15]. 6 very small in the steady state stage. After reaching a constant strain rate for a period of time, the creep rate will increase again during the tertiary state which leads to fracture. There are still many mysteries regarding creep properties, i.e. mechanisms of creep. Researchers [16,17] usually use dislocation phenomenon to describe the strain (work) hardening (generation of dislocation) and softening (recovery and annihilation of dislocation) in models of creep behavior. At high temperature (T > 0.4Tm), dynamic recovery starts to play a more important role than it does in low temperature. The disloca- tion density increase, i.e. work hardening, causes the creep to decrease with time in the primary stage. In the secondary stage, the creep rate reaches a steady state due to a balance between work hardening and dynamic recovery (work softening). The dynamic recovery can occur by various mechanism, i.e. dislocation glide, climb, cross slip, ..... etc. The main mechanism is due to dislocation climb and annihilation (positive and negative signed dis- locations cancel out each other). The work softening factor dominates in the tertiary stage and finally causes material fracture. 2.3 STRESS AND TEMPERATURE EFFECT The shape of creep curve is strongly influenced by the temperature and stress. Figure 2.3 (a) [18] shows a series of creep curves corresponding to different stresses at the same temperature. In a similar manner, Figure 2.3 (b) shows that at constant stress, the shapes of creep curves change as temperature changes [18]. «4 T - constant O'm! Figure 2.3 (a) Stress effect and (b) temperature effect on the creep curve [18]. 2.4 POWER LAW EQUATION Considering both stress and temperature effects the empirical power law creep relation has been found to describe the steady state creep [14] -Q) . n c as = A6 exp(—— RT (1) where sis is steady state strain rate and A is a constant, 0 is the applied stress, Qc is the acti- vation energy for creep, R is the universal gas constant and T is the absolute temperature. In some cases, there is no steady-state rate regime in the creep curve, and the min- imum strain rate 8m is usually used instead of :35. The stress exponent value n can be obtained from the slope of loge es vs. logeo plot at the same temperature. Similarly, a graph of loge Es vs. lfT at constant stress will yield a straight line of gradient -Qc/R and activation energy can be calculated. The different mechanisms of creep in different stress/ temperature regimes will cause stress exponent n and activation energy Qc values to vary. By multiplying both sides of equation (1) by exp(QC /RT), it can be rearranged as Q ésexp(——C-) = Aa" = Z (2) RT The quantity Z is known as the Zener-l—lollomon parameter [19] or as the temperature- compensated creep rate [20,21]. By defining suitable value of QC, plots of log Z against log 0 allow several creep curves for different temperatures to be superimposed onto a single line, as shown in Figure 2.4 [14] 5 I 608K A 645K x 688K " v 728K 7 o ms 6:; 3"“ -4 Q d 3 . W ’U .5.” 1- 1 o I l I I 075 100 125 150 175 200 0 S L09101E " 10 I Figure 2.4 The temperature-compensated secondary creep rate data (or Z) for polycrystalline copper. The activation energy of 130 KJ/mole is used for this figure. [14] 10 2.5 DEFORMATION MECHANISMS In creep (T > 0.4Tm), depending upon the applied stress level (high, intermediate and law), there are two fundamental mechanisms of creep: diffusional creep and disloca- tion creep. 2.5.1 Diffusional creep At low stress and high temperature, mass transport by diffusion of vacancies becomes the controlling mechanism and this creep is known as diffusional creep. (a) Nabarro-Herring creep Based on Nabarro-Herrin g theory of creep [22,23], creep occurs by stress-directed vacancy flow through the crystal lattice from grain boundaries in a state of local tension to grain boundaries with a local compressive stress, as shown in Figure 2.5(a) [24]. Nabarro-Herring creep can be used to describe the creep behavior which usually is found at low stress and high temperature. In general, the stress exponent n=1 and the acti- vation energy Qc=an (self-diffusion) in those creep cases. (b) Cable creep In 1963, Cable [25] considered that the stress directed vacancy flow can go through grain boundaries instead of only through lattice as assumed by Nabarro and Herring. (see Figure 2.5(b)) [24]. In this case, the stress exponent n is also equal to l but the activation energy for creep is that for grain boundary diffusion,i.e., Qc = QGB. l] (b) Figure 2.5 Schematic of (a) Nabarro-Herrin g creep (b) Cable creep[24]. 12 2.5.2 Dislocation creep When the temperature is between 0.4Tm and 0.7Tm and at the intermediate/high stress level (10‘4 < o/G < 102), the dominant mechanism of creep is the rate of dislocation motion by glide or climb. This regime is known as dislocation creep. According to the dis— location rate-controlling mechanism, dislocation creep models can be divided into two types: dislocation glide and dislocation climb rate—controlled. (a) Dislocation glide rate-controlled The dislocation gliding in a crystal meets local obstacles, including precipitates and solute atoms; and if the impeding force of obstacles to dislocation glide is not strong, the dislocation may overcome the barrier by thermally-activated glide. Cottrell [26] and Weertman [27], who presented the models, assume that, in this case, dislocation glide is the creep rate-controlling process. (b) Dislocation climb rate-controlled The general idea of dislocation climb rate-controlled creep was developed by Weertman [28]. He considered dislocation climb as the recovery process. During deforma- tion gliding dislocations which may come from different dislocation sources move across their glide planes until the leading dislocations are held up by obstacles on their slip planes, forming a pile-up array on the same slip plane. At high temperature the disloca- tions can pass those obstacles by climbing and then continue moving on a new glide plane. In such a glide-plus-climb sequence, the dislocation climbing is a slower process and therefore, it is a rate-controlling process (see Figure 2.6). 13 climb —>- E _l_ _L O d1slocatlon source obstacle Figure 2.6 Schematic representation of the leading dislocation passes an obstacle by climbing [29] 14 2.5.3 Mechanisms map Under different stress/temperature conditions, the dominant creep mechanism will change and cause the different creep behaviors. This type of information can be conveyed by construction of ‘deformation mechanism map’[30] (see Figure 2.7). Ideal Strength 10'2 - . _. DISlOCBIIOh Glide DISlOCBIIOO Creep L: ~10“) __ —1 O 2 10-6 __ Cable Creep l _ : Nabarro : 'Heang i Creep i 10.8 I I I i 0 02 01. (I6 08 10 T/ Tm Figure 2.7 Deformation mechanism map for a pure polycrystalline metal [30]. 15 In general, theories to explain creep behavior can be based on diffusion creep and dislocation creep processes. We usually consider those two processes as independent pro- cess, and both of them contribute to the overall creep rate. Under different stress/tempera- ture conditions, one of these processes contributes much more than that of the other. We define this process as ‘dominant’, and a different dominant mechanism leads to different stress exponent n and activation energy Qc values, as shown in Table 2.1 [29]. Table 2.1 Different n and Qc values associated with dislocation and diffusional creep occurring with pure metals Creep Process Temperature Stress n value Qc value high temperature above intermediate/high > 3 ~QSD dislocation creep ~0.7Tm low temperature ~04 to intermediate/high > 3 QCORE dislocation creep ~0.7 Tm high temperature above low ~ l (251) diffusional creep ~0.7Tm (Nabarro-Her- ring) low temperature ~04 to low ~ 1 QGB diffusional creep ~0.7Tm (Cable creep) er) : the activation energy for self diffusion QCORE: the activation energy for self diffusion along dislocation cores, often termed pipe diffusion Q03 : the activation energy for grain boundary diffusion 16 2.6 STRESS AND TEMPERATURE CHANGE CREEP No matter what the rate-limiting dislocation creep mechanism is, most dislocation creep theories [16] state the secondary creep rate will vary with stress, temperature, grain size and dislocation structure. Stress or temperature change experiments result in transient creep behaviors which are used to provide some information about these microstructural factors. Temperature change has similar effect on the creep transient behavior of materials as stress change, but it is technologically more difficult to get good data, so in the follow- ing discussion, we only use the example of a stress change experiment to interpret those transient behaviors. In general, the transient behavior after stress changes depends on the material and on the sign and magnitude of the stress change. In dislocation creep, there are two classi- fied types: Metal (M) class in which dislocations can glide freely and Alloy (A) class in which is dislocations glide in a viscous manner. The different substructures and rate-con- trolling mechanisms cause those different creep behaviors. 2.6.1 Class M behavior For Class M materials, the transient behavior is shown as Figure 2.8 (a) [32]. As stress increases, instantaneous strain is followed by transient deformation in which de/dt is much greater than the previous steady state rate, and decelerates to a new steady state. In this case, the instantaneous strain consists of an elastic and a plastic component. With stress decreases, an instantaneous elastic contraction is followed by transient creep, where de/dt is much less than the previous steady state rate and accelerates to a new steady state. This type is known as ‘normal’ transient behavior. l7 (a) (b) 940) c .2 76 J l I g’ r":— Al‘ .9 >4 DJ 41" ' I040") Time Figure 2.8 Schematic diagram of two types of creep transient after stress changes (a) Class M type (b) Class A type [32]. A]e : elastic strain, Alp : plastic strain 18 The Class M creep behavior is characterized by pronounced heterogeneous dislo- cation distributian during the normal primary creep. This is clearly shown by the subgrain structure formation. The subgrain structures initially farm in the high stress concentration regions such as grain boundaries and then spread over the whole grain. The coarsening of small subgrains and refining of the coarse ones cause the heterogeneous dislocation den- sity to decrease, and a very regularly spaced network of subgrain boundaries is developed. Kuhlmann-Vlfilsdorf et al. [33] presented a theory that states that the equilibrium subgrain size depends on the dislocation density, and since the dislocation density is a function of applied stress, the relation between subgrain size and the applied stress can be found. Therefore, the transient phenomena resulting from changes of creep conditions such as stress changes or temperature changes are associated to the substructure changes. Lonsdale and Flewitt [34] showed that any change (reduction or increase) in applied stress results in a change in subgrain size that corresponds to the new applied stress, and this subgrain size is reached at the onset of the new steady state. In general, the class M type creep is thought to be governed by the dislocation climb processes, i.e. dislocation glide contributes strain but the creep rate is controlled by the rate of dislocation climb processes in which n is generally close to 5. These glide- climb processes which are associated with the formation of substructure allow rearrange- ment and annihilation of dislocations to occur. The dislocation movement during creep is also considered to be opposed by an “internal stress” or “dislocation back stress”, denoted as oi. The internal stress oi gener- ally depends on the dislocation structure, i .e. subgrain size, the applied stress, and testing temperature. The effective stress 0*: o - oi is the difference between the applied stress 0 19 and the internal stress oi and describes the stress that causes dislocation movement. The change in creep rate following a stepwise increase in the applied stress is thus due to an increase in the internal stress to a new equilibrium state, and consequently reducing the effective stress over time. Thus, after stress increases, the substructure rearrangement and annihilation of dislocations associated with decrease of effective stress 0* cause decelera- tion of creep rate. On the other hand, after a stress reduction, the coarsening of the disloca- tion structure causes an increase of the effective stress for thermally activated glide. Thus, the strain rate increases after a stress reduction. 2.6.2 Class A behavior For Class A materials, the transient behavior is shown in Figure 2.8(b) [32]. It is the ‘inverse’ of the normal transient behavior. In this case, the instantaneous strain is elas- tic. In contrast to Class M materials, the subgrain structure is seldom or not observed in the Class A creep behavior. This means the dislocations remain homogeneously distrib- uted with no formation of subgrain during the normal primary creep in the Class A materi- als. In Class A materials, the dislocation glide becomes the slowest step due to the vis- cous drag exerted on a moving dislocation by the solute atmosphere, where n is equal to 3. Weertman [35,36] presented a glide-controlled model which assumes that the creep rate depends on the mobile dislocation density, p, as e = prz (3) 20 where v- is the average dislocation velocity that is determined by the rate at which the sol- ute atoms can move along with the dislocations. b is the Burgers vector and p varies as the square of the applied stress. The solute-drag model can explain the inverse of normal pri- mary creep behavior. A low dislocation density exists prior to creep, and the creep rate is limited by the mobile dislocation density; subsequent stress increases leads to an increased dislocation density, and therefore a higher creep rate. On the other hand, since no substruc- ture forms and the solute atoms can move easily, they slow down the moving dislocation at lower stress, and the strain rate decelerates after stress decreases. 2.6.3 Incubation period and anelastic strain There are two other phenomena which are usually observed. Figure 2.9 (a) shows “incubation periods” following large enough stress drops (G-O'i < 0, where 0i is internal stress). It can be explained in term of the times taken for a dislocation network to readjust to a proper size for a new stress level [37]. Another phenomenon is time dependent, anelastic strain, following decreases in applied stress (see Figure 2.9(b)). Burton [37] describes this transient behavior as due to dislocations becoming unbowed after a suffi- cient stress drop, and give rise to a strain which is opposite in sense to the original strain. 21 (a) __ —Ao ‘ ”PAL- 1 i .c 1 I4- — ->I elongation (b) Figure 2.9 Schematic diagram of (a) incubation period tine (b) anelastic strain ALan [37] CHAEIEBJII THE O—PROJECTION CONCEPT In high temperature loading conditions,pmaterials are subjected to long-term ser- vice under an applied stress and creep deformation occurs. In order to model this long- term creep behavior from short-term creep experiment data, people analyze creep defor- mation curves by some constitutive equations. The most famous equation is power-law equation which relates é, (steady state strain rate) to stress ((5) and temperature (T) by a power law relationship (see equation (1)). Unfortunately, the stress exponent (n) and acti- vation energy (Q) are themselves functions of stress, strain and temperature so that differ- ent values of n and Q are observed as the test conditions are varied. By the way, the primary creep is an important issue for technological applications, and the steady state theory is not always helpful. On the other hand, polynomial expressions have been used [38] and good fits can be obtained. However, it is difficult to interpret the polynomial coefficients in terms of physical meaning. In order to find a model which can not only accurately describe the shape of the creep curve but also relate to physical meaning of creep deformation, the 0— projection concept has been proposed by Evans and Vlfrlshire(l985) [39]. 3.1 CONSTITUTIVE CREEP EQUATION Based on the physical understanding of creep deformation in primary and second- 22 23 ary stages, the following constitutive equation is described as e = 51+91{1 —exp(—92t)} +ést (4) where e, is the initial strain upon loading, and the second and third terms describe primary and secondary creep stages, respectively. e, is the secondary (or minimum) creep rate, and the parameters 6, and 02 are determined by curve fitting. By differentiating equation (4) we can obtain 2': = 9192exp (~02!) +2123 (5) And the primary creep rate can be rearranged as e'p = 0192exp(—92t) = 02(01—ep) (6) where primary strain rate ép = (é - é,). Equation (4) indicates a gradually decaying creep curve, and after a period of time a steady state stage (232,) is reached. 9, is a parameter of strain-like meaning and 02 is a rate parameter as shown in Figure 3.1. From equation (5, 6), it shows that the primary creep rate (ép) decreases gradually with increasing pri- mary creep strain (8p) and approaches é, (steady state strain rate). It is obvious that no tertiary creep is described by the above equation. All of the creep curve can be described by the following equation [39], 24 A I I Primary stage I Secondary i stage I I A strain . 'fi 80 02 deterrnrnes 91 3:31:me the curvature primary of prrmary strain creep T > time Figure 3.1 The 0 projection concept envisages normal creep curves in terms of primary stage and secondary stage 25 e = €i+01{1—exp(—02t)} +03{exp(94t)—1} (7) where ei is the initial strain upon loading, 01,02 33,04 are determined by regression analy- sis of the whole creep curve up to rupture. Bland 63 define the strain magnitude with respect to time, 92 and 04 describe the curvatures of primary and tertiary stages of creep, respectively. Evans and Wilshire [39] interpret the second term to represent the strain hardening term which dominates in primary creep, and the third term describes the strain weakening term which dominates in tertiary creep. The secondary stage is a consequence of dynamic balance between strain hardening (second term of equation (7)) and the strain weakening term (third term of equation(7)). It agrees qualitatively with theoretical inter- pretation of creep deformation by dislocation motion. However, a true steady State creep in the secondary stage is not predicted by this model; secondary creep is only a transition between primary and tertiary creep processes. 3.2 MODIFICATIONS OF O-PROJECTION CONCEPT Maruyama et al. [40] thought the initial strain 8, is the least reliable value of mea- surement even when high-precision test methods are used. It is because Si is determined by calculating only the difference in strain immediately before loading and immediately after loading. Therefore, in order to get a better interpretation, the following equation is 26 presented by Maruyama et al. [40], e=€0+A{1—exp(—0tt)}+B{exp(Bt)—l} (8) where 80 is an adjustable parameter instead of initial strain in the original 9-projection model. A, a, B and b are the parameters of curve fitting. a represents the rate constant of strain hardening process and [3 represents the rate constant of strain weakening process. Maruyama et al. [41] made further modifications in 1987. They discarded those creep data after a certain cutoff strain 83:13 when determining the parameters of equation (8) and simplified to, e=80+A{1—exp(—0tt)}+B{exp(oct)—1} (9) which has only one rate constant or instead of the two rate constants in equation (8). The same rate constant at for both strain hardening and weakening processes is not suitable for all materials due to complicated mechanisms during creep deformation. Actually, two rate constants may be more proper than one rate constant since changes in the microstructure lead to changes in the rate-controlling mechanism during the creep process. 3.3 INTERPRETATION OF THE PARAMETERS In order to interpret those parameters obtained from curve fitting, the linear stress/ log 91 and temperature/log 0l plots have been used. 27 3.3.1 Hardening and weakening parameters: Gland 03 (or A and B) Brown et al. [39] found Bland 03 in equation (7), which govern strains associated with the primary and tertiary stages respectively, can be rationalized simply by normaliz- ing the creep stress with respect to the Young’s modulus (or yield stress) at the creep tem- perature. (see Figure 3.2 (a)) [42]. Thus, the strain-related terms Gland 03 are temperature and stress dependent. They found a similar behavior pattern in: 1/2Cr1/2Mol/2V steel [39], type 316 austenitic steel [43] and cast superalloy IN 100 [44]. On the other hand, Maruyama et al. [45] also state that weakening parameter B in equation (8) is a function of fb(o/E)exp(-Qb/RT) where fb(o/E) is a function only of o/E, Qb=2 (QC - Qd) and Q is activation energy for minimum creep rate, Qd is activation energy for self-diffusion. But for CrMoV steel, they found that the hardening parameter A is invariant with temperature and only a function of (o/E). 3.3.2 Rate constant parameters: 02 and 94 (or or) Both Brown et al. [39,44] and Maruyama et al. [43,45] concluded these rate con- stants can be expressed as (see Figure 3.2(b)) 02, 04 or at = fa(0'/E)exp(-Q/RT) (10) where o is the creep stress, E is Young’s modulus, fa(o/E) is a function independent of temperature and Q is the activation energy for the rate constant. It is expected that the rate constants 02, 04 or at are closely related to the rate-controlled step of creep. In other words, the activation energy for those rate constants are associated with the dominant mechanism 28 0 T T I I T I 2 °774K .1h- ‘728K -1 .2 o “E «7‘ 5'3 1052 O D _J —J ‘” 93 i? o S- o o - 3 6” l I I I 1 L L 01 02 03 0'4 05 06 07 O8 STRESS/YIELD STRESS (a) E 3:2 8 3 3‘ 6’ '52 s: g 0 728 K I. 8 -‘ 0 688 K -’ x 606 K r 2 l L I l I I 10 20 30 (.0 SO 60 70 BO STRESS ,MNm‘2 (b) Figure 3.2 Rationalization of (a) Gland 93 (b) 92 and 94 for polycrystalline copper [42] 29 of primary or tertiary stage of creep. However, further understanding of the relationships between rate constant and the rate limiting deformation mechanism still needs more work. 3.3.3 Minimum strain rate By differentiating equation (7), the strain (creep) rate at any condition is is: dt 0102exp (—02t) + 0304exp (04t) (11) There is a minimum gradient (strain rate) at a time tm which is the time to reach the mini- mum strain rate, expressed as 2 00 t: l 12 m 02 + 04 93942 (12) Thus, if the 9i terms are known for a set of testing conditions, the tm can be calculated by equation (12) and therefore the minimum creep rate cm can be obtained. 3.3.4 Prediction of rupture life The four 0 functions vary with stress and temperature and can be defined by using the following equation: [44] 10g“) 9i = ai + biT + CiC + diO'T (l=1,2,3,4) (13) where ai,bi,ci, d, are constants. Similarly, by this approach, the fracture strain 8f can be expressed as ef=a+bT+co+doT (14) 30 where a,b,c,d are constants. Those coefficients describing 8f (a,b,c,d)and four 0 functions (ai,bi,ci,di) can be computed by multilinear least squares regression analysis. The relevant rupture life is defined as the time If taken to reach the 8f (fracture strain) under a particular stress and temperature condition. Therefore, 8f can be computed by equation (14) and tf can be obtained by solving the following equation: 91(1— exp (—92tf)} + 93 {exp (949) — 1} —8f = a (15) 3.4 MODIFICATION FOR OUR ANALYSIS For our experiments, we are interested in the primary and secondary stage of TIA] creep deformation, but especially the primary stage creep. The tertiary and rupture life are beyond our goals and therefore, we choose equation (4) as the constitutive equation for analyzing those curves of primary (or secondary) creep. However, a modification of equa- tion (4) due to different startin g time for a particular different test condition following a stress or temperature increase was used. The modified equation for transient creep after stress and temperature increase is e = 80+A{l-exp(—0t(t—t0))}+és(t—t0) (16) where so is an adjustable parameter, to is starting time. és is the steady state (or minimum) strain rate, A and at are curve fitting parameters. In the case of transient creep after stress 31 and temperature decrease, the constitutive equation is e = £0+Aexp(—a(t—t0)) +e3(t—t0) (17) By differentiating equation(16) it can be rearranged as e = Aocexp (—Ot(t—t0)) +555 (18) The equation (18) implies that the creep rate during the primary stage decreases gradually towards a definite “steady state” value, es, in the period of time t-to. However, these modi- fied equations (16,17) are not suitable to fit the transient creep behavior during the temper- ature and stress change, as they are applicable only for constant stress and temperature conditions. QEAELEBJX REVIEW OF TiAl CREEP TiAl is being considered as a candidate material for high temperature gas turbine jet engines due to its superior strength-to-weight ratio and good high temperature strength. Recently researchers have become more interested in the TIAl/TI3A1 two-phase com- pounds rather than the single-phase Al-rich TiAl compounds because of the better ductil- ity of the two-phase compounds. The compounds of TiAl with slightly Ti-rich compositions exhibit a two-phase microstructure which consists of the TIA] yphase and a small volume fraction of the TI3A1 a2 phase. These are often called near-gamma alloys. 4.1 STRUCTURE OF TiAl 4.1.1 Crystal lattice structure There are two basic lattice structures usually found in TIA]. One is 7 phase (TIAl) with L10 (FCT) structure (see Figure 4.1(a)) [46], and the other is at; phase (T13Al) with D019 (HCP) structure (see Figure 4.](b)) [46]. The ‘Y-TIAI has L10 type lattice crystal structure where the titanium and aluminum atoms alternately stack in sequence of ABCABC on (002) planes. It is a face-centered tet- ragonal structure with c/a ratio=l .02 that changes as A] content changes. The anisotropic crystal structure causes more complicated slip in the L10 lattice [47]. The 0:2 (Ti3Al) has D019 crystal lattice structure where the stacking sequence is 32 33 ? 0 Ti atom c/a =l.02 0 Al atom /a - 0.398 nm Figure 4.1(a) L10 lattice structure [46] COO II c =Ch¢p t (iz‘io) [2'iT01/ Elfin-.1 Figure 4.1(b) D019 lattice structure [46] 34 ABABAB. The D019 structure is based on the hexagonal closed-packed structure (HCP), but with a larger value of basal plane axis (2a) (see Figure 4.1 (b)) [46]. However, the sys- tem is often off-stoichiometric with A1 atoms in Ti sites and therefore, this causes a slightly disordered lattice. The lamellar structure occurs in the two-phase TiAl alloys with nearly stoichio- metric or Ti-rich composition. The lamellar structure is composed of alternating laths of gamma(y)-TiAl phase and avg-Ti3Al phase with the orientation relationship of [48] (111)“A] ll (0001)Ti3A1, <110>TiA1 ll <112O>Ti3Al The lamellar boundaries are parallel to (111) in TiAl (y) and (0001) in Ti3Al(0tQ). OH et al.[49] concluded the y—phase has six' possible orientations of [110] on (111) with respect to <1120> on (0001) in the or; phase. 4.1.2 Microstructure Since single phase y-TiAl suffers from low ductility and toughness at ambient tem- perature, many efforts have been made in recent years to develop two-phase 'y/atz alloys based on T i-(49~51)at%Al [50], due to the higher ductility and toughness displayed by this stoichiometry. Depending upon the heat treatments, there are four types of microstructures in these alloys: (a) fully lamellar (b) nearly lamellar (c) duplex (d) nearly-gamma. The differ- ent heat treatment conditions and features of the four types of microstructures are summa- rized in Table 4.1 [51] and illustrated in the corresponding phase diagram of the central region is shown in Figure 4.2 [52]. Table 4.1 The different heat treatment conditions and features for four types 35 microstructures in TIA] based alloy [51] Microstructure Heat-treatment condition Features Fully lamellar in the single phase or field *large grain size ~> 500 um with alternat- ing 7 and on; platelets *most brittle at room temperature, but excel- lent creep resistance Nearly lamellar just below To, in the (1+7 region *coarse lamellar grains and a small vol- ume fraction of fine 7 _ grains Duplex equal amounts of at and y in (1+7 region *grain size ~15 um which consists both single phase 7 equi- axed and lamellar (wool) structure *has the highest duc- tility at room tempera- ture Nearly-y or y low temperature in the (1+7 region *grain size ~13-50 um and banded regions consist of fine 7 and 002 grains 1600 1400 1200 Temperature (°C) 1000 800 36 Weight Percent of A] 20 25 30 35 40 45 50 I I I l I L I 30 4o 50 Atomic Percent of A1 2900 2700 2500 2300 2100 1900 1700 1500 1300 Temperature (°F) Figure 4.2 The central part of the Ti-A] equilibrium phase diagram [52]. 37 The creep properties of TIAl-base alloys are strong sensitive to the microstructure [53]. Huang [54] found the fully lamellar microstructure has most excellent creep resis- tance but poor ductility. On the other hand, the duplex microstructure is superior in ductil- ity but poor in fracture and creep resistance. The details of creep mechanisms in different microstructure regions still need more investigations. 4.1.3 PST crystal The two-phase TIA] with nearly stoichiometric or TI-rich composition were usu- ally composed of randomly oriented grains which have lamellar structure (7+orq). How- ever, if this material is remelted and resolidified in a specific direction and an appropriate rate, the single-crystal like crystals which consist of only a single at grain orientation with lamellar structure can be obtained. Fujiwara et al. [55] identify this material with single- crystal like structure as Polysynthetically Twinned (PST) crystal, since it contains a lot of thin twins that are all parallel to the lamellar boundaries. Since complicated effects of microstructure variation exist in near 'y-TiAl alloys, OH et al. [49] investigated deformation behavior in PST crystals which have the same microstructural features of lamellar grains, and obtained fundamental information about near-y T iAl deformation. They found there are two modes of deformation in PST crystal. One is the shear deformations across the lamellar boundaries (hard mode) and the other is the shear deformations parallel to the lamellar boundaries (easy mode). By systematic studies of PST crystal deformation, the lamellar orientation dependence of deformation behaviors were found. Furthermore, a PST crystal with a specific orientation of lamellar boundary can provide useful information of how the lamellar structure affects the creep 38 deformation in the near-y TIA] alloys. 4.2 ALLOYING The general composition of ’Y-TIAI which has been studied is titanium, 46~52 at% aluminum, and 1~10 at% M, where M represents at least one element from V, Cr, Mn, W, Mo, Nb and Ta [50]. Huang and Hall [56] found the highest ductility at room temperature of 'Y-TIAI is in binary TiAl alloys which have A] concentrations of 46~51 at% with the peak occurring at about 48 at% Al. The main purpose of adding alloys is to improve duc- tility (e.g. V, Cr) and oxidation resistance (e.g. Nb, Ta). These effects of adding alloys are listed in Table 4.2 [57]. 4.3 CREEP IN TiAl The mechanisms of creep deformation in TiAl are very complicated and so far only limited knowledge has been obtained. Based on those results, creep behavior in TiAl will be affected by the composition, microstructure, grain size and test conditions (stress and temperature). The microstructural variables include the structure of the lamellar grain boundaries, spacing of the (12- 'y laths, and the nature of the at;— y lath interface. However, there are still some problems of understanding creep behavior in TiAl: (1) no steady state creep regime is observed; (2) no instantaneous strain or primary creep is seen for some composition; (3) dynamic recrystallization occurs at low strains. 39 Table 4.2 Alloying effects the properties of TiAl [57] Elements Properties are effected by this element A] It strongly affects ductility by changing the microstructure. Best ductil- ity occurs in the range of 46-50 at% B Add >0.5 at% refines grain size, and improve strength and workability. C Carbon-doping increases creep resistance and reduces ductility Cr Add 1-3 at% increases the ductility of duplex alloys Add >2 at% enhances the workability and superplasticity Add >8 at% greatly improves the oxidation resistance Er Changes the deformation substructures and increase the ductility of single-phase gamma Fe Increases fluidity, but also the susceptibility to hot cracking Mn Add 1-3 at% increases the ductility of duplex alloys Mo Improves the ductility and strength of a fine-grained material Improves the oxidation resistance Ni Increases fluidity Nb Improves greatly the oxidation resistance and creep resistance slightly P Improves oxidation resistance Si Add 0.5-] at% improves the creep and oxidation resistance Improves fluidity, but reduces the susceptibility to hot cracking Ta Improves the creep and oxidation resistance Increases the susceptibility to hot cracking V Add 1-3 at% increases the ductility of duplex alloys and reduces the oxidation resistance W Greatly improves the oxidation resistance Improves the creep resistance 40 4.3.1 No steady state regime Most researchers [6,58,59] found no steady-state strain rate regime in TiAl creep behavior. Most observations of creep of near-y TIAl-based alloys reached a minimum strain rate followed by an increasing strain rate. Thus, the minimum strain rate is usually used to analyze the creep behavior in TiAl. 4.3.2. No instantaneous strain Based on the result of Oikawa’s et al. [3~5], there is no instantaneous strain observed in equiaxed gamma (Ti-53Al). A limited strain in the primary stage is observed, followed by an apparently steady state strain region. This type of creep behavior is unusual, and the mechanisms of this creep behavior have not been explained yet. 4.3.3 Dynamic recrystallization Dynamic recrystallization (DRX) has been reported [8] to be an important phe- nomenon at higher temperature (~7 60 0C) and at strains >~5% strain. The dynamic recrys- tallization nucleates along prior grain boundaries of the original microstructures and forms very fine grains at grain boundaries [58]. The dynamic recrystallization causes no steady state creep rate to be observed, and a minimum creep rate was obtained following a steep increase in the creep rate of most near-y TIA] based alloys. The minimum creep rate is affected by the easiness of dynamic recrystallization, and this may be one reason why the varied values of activation energy (80~600 KJ/mole) in TIA] were obtained [3~8,54~57]. The activation energy of the characteristic steady state associated with dynamic recovery (269 KJ/mole) is usually lower than the activation energy of the apparent steady 41 state during DRX (400 KJ/mole) [8]. 4.4 MECHANISMS OF CREEP IN TiAl There are two fundamental mechanisms of creep in TIA]: dislocation controlled creep or diffusion controlled creep. The dominant mechanism depends on the temperature and stress condition. Both of these mechanisms have been found in the creep behavior of TIA]. [l~13]. 4.4.1 Diffusion controlled creep In many cases, the activation energy for creep is associated with the activation energy of self-diffusion (lattice diffusion). The activation energy of ~29] KJ/mole was found by Kroll, Mehrer [60] for the self-diffusion in Ti-54Al. However, Ti-54A1 has a near-y TIA] structure which is composed mostly of gamma phase without much (12 phase. Thus, the activation energy value of lamellar-based TIA] may be different from that of near-y structure. Actually, a fundamental description of self diffusion in gamma TIA] with the activation energy has not been determined yet. The generally accepted value for the activation energy for grain boundary diffusion is 0.6 times the value for self-diffusion, i.e. Qb=0.6QL,where Q, is the boundary diffusion activation energy and QL is the lattice diffu- sion activation energy, respectively. The Q, is ~202 KJ/mole and QL is ~336 KJ/mole for gamma TIA] were calculated by Ashby [61]. However, the measured activation energies for creep deformation on single phase alloys (423~560 KJ/mole) [62,63] are usually higher than that required for interdiffusion within single phase garrrrna (80~168 KJ/mole) [9,64]. This suggests that creep behavior in 42 y—TiAl based alloys can not just be explained by intrinsic diffusional processes only. Phe- nomena such as dislocation/cell structure, pipe diffusion and dynamic recrystallization significantly affects the creep behavior of y— TiA] based alloys. 4.4.2 Dislocation controlled creep At higher stress conditions, dislocation creep is the dominant deformation mecha- nism in TIA] creep [7,8,59]. Twinning deformation is also an important deformation mechanism during creep of TIA] [47]. (a) Dislocation climb Hayes and McQuay [12] investigated a y—TiAl alloy with a fully transformed structure deformed in the temperature range 769~861°C and stress range 69~310 MPa. The creep behavior of the y—TiAl alloy was a dislocation climb-controlled process which was aided by diffusion. Stress exponent n of ~5 and activation energy of ~335 KJ/mole was found. Hayes and London [7] also reported in the temperature range 704 ~850 0C and stress range 103.4~241.3 MPa for TI-48Al-1Nb ‘Y-TIAI with duplex microstructure, the activation energy is 326.4 KJ/mole and a stress exponent n=4.95. The value of the stress exponent is in agreement with dislocation climb process and the value of activation energy is also within the range for y—TiAl alloys where creep rate is controlled by volume diffu- sion. Thus, it suggested that if dislocation climb is the rate-controlled mechanism, the expected creep activation energy is close to that of self diffusion and a stress exponent is in the range of 4~5. In general, the dislocations in TIA] creep specimens are 1/2<110] nor- mal dislocations [55]. 43 (L3) Twinning Mechanical twinning during creep deformation in TIA] has been reported by sev- eral researchers [3,58,65,66]. Twinning is known as the dominant deformation mechanism in TIA] for many crystal orientations. During primary creep, the fine mechanical twins ini- tiate from a grain boundary at the intersections between horizontal twin layers and the grain boundary and grow into the grain interior. The continuous emission of twinning dis- locations which were identified to be 1/6 <112] Shockley partials were found to be emitted from the grain boundary due to the local stress concentration. If the local stress were large enough to keep moving those dislocations, the propagation of the fine mechanical twins across the entire grain to reach the opposite grain boundary will occur. Fine mechanical twins were formed at the grain triple points during creep [66]. The contribution of mechanical twinning to creep deformation in TIA] is signifi- cant at a relatively low temperature and a high stress. In general, mechanical twinning dur- ing creep is significantly increased as the creep temperature decreases. Huang and Kim [11] found no evidence of mechanical twinning during creep deformation at 900 0C. On the other hand, mechanical twinning has more important effects on the creep deformation in TIA] at a higher stress. Jin [67] also found 1/2 <110] normal dislocation in TiAl creep. According to his researches in TI-48Al-2Nb-2Cr (duplex), subboundaries were observed both in equiaxed gamma grains and within gamma laths in lamellar grains after a multi-stress drop test at 765 0C. By' those analyses of subboundaries, the creep deformation mode in TIA] was identified as pure metal type (Class M). 4.4.3 Composite model Since the mechanisms of creep of TIA] are complicated, the models of composite theory were used to help interpretation. The composite model is based on the contribu- tions of different individual mechanisms and determined by using a simple rule-of-mix- tures approach. For the fully lamellar TI-48Al-2Cr-2Nb at the high temperature, Hofman and Blum [31] presented a simple composite model which assumes that the total strain rate results from the local strain rates $8 in the globular and e] in the lamellar regions as e = (l—f,)eg+f,e, (19) where f, is the volume fraction of lamellar regions and ég and él are expressed by the den- sity pf and the velocity 7 of free dislocation: é - -”- (7) (o*)'" 1' " Mpr 1' j=g,1 (20) where M=3 is the Taylor factor, b is burgers vector. B(’T) and m are constants. The effec- tive stresses 6* are determined by the difference between applied stress and internal stress and can be expressed as: 0*8 = o—aMGbJp} (21) 6*, = o—acMijp—f—o, (22) 45 where at is constant, G is shear modulus and 01 represents the amount of the strengthening contribution of the lamellae. Another composite model was presented by Soboyejo and Lederich [10]. In their model, the creep behavior of gamma based alloys with duplex (12 and 7 structure can mod- elled by recognizing that the two-phase alloys are composites that consist of or; and 7 phases. By the composite theory and rule-of-mixtures, the total strain rate is determined by the contributions from alpha2-gamma phase and gamma phase in which a number of mechanisms contribute to creep deformation. The composite strain rate is thus given by e=f [e +e +21: +é 9.1+ [é +é +é +é] c a2 DCorZ 1)an cm2 NHa fy DCY DoY Cr "”7 (23) where subscripts DC, DG, C, NH represent the dislocation climb, dislocation glide, Cable creep, and Nabarro-Herring creep, respectively, and f is the phase volume fraction. 4.5. SUMMARY OF CREEP DATA FOR SEVERAL y—TiAl ALLOYS Only limited knowledge on the creep behavior exists for ’Y-TIAI since it varies with composition, stress, temperature and microstructure. Table 4.3 shows power law creep constants for several y—TiAl alloys. 46 Table 4.3 The creep properties of several ‘y—TiAl alloys Alloy(at.%)/ Microstructure 0' range Temp n Q REF processing (MPa) (0C) (KJ/ mole) Ti-50 AI/HIM/ Lamellar+y at 100-251 677-877 7.9 359 1 As-cast colony bound- aries TI-50.3 Al/PM/ Lamellar + y 103-241 700-950 4 300 2 HE at 1413 0c d7 = 60 um: 001- +HT ony:50-100 um ”Tr-53.4 Al Equiaxed 7 80-400 677-927 8.0(L) 600 3~5 4.5(H) 360 Tr-SOAl/com- Equiaxed 7, 100-400 827 7.7 600 6 pression creep d=179~90 um T1-48.7 Al-2.2 Lamellar; yat 103-241 700-950 5.5 370 2 W/same as TI- colony bound- 50.3 Al/PM aries; W-rich par- ticles at phase boundaries Ti-48 Al- Duplex 103-241 704-850 5-4.46 320- 7 1Nb(0.09 wt% 34] O)/ISR+HIP 47 Table 4.3 The creep properties of several y—TiAl alloys (cont’d) Alloy(at.%)/ Microstructure 0' range Temp n Q REF processing (MPa) (0C) (KJ/ v mole) TI-48Al-2Cr- Duplex 103-300 705-815 3(L) 300(L) 8 2Nb/VAR+HIP 7(I-l) 410(H) Tr-48Al-2Cr/ Duplex 330 800 4.3 460 9 HIM TI-48Al-2Cr/ Nearly lamellar 200 700 2.4 292 10 HIM 900 3.5 292 Tr-47Al-1Cr- Fully lamellar, 138-276 900 5.8 ND 1 l 1V-2.5 Nb/ fine 7 at colony Cast+HIP+extr boundaries usion at 1290 0C. HT: 1360 0c«-10000c Tr-48Al-2Mn- Fully lamellar 69.4- 760-871 4.6 335 12 2Cr 310 Ti-49.5Al- Equiaxed 7, 75-200 850-1377 ND 411 13 2.5Nb-1.1Mn/ d=125 um cast +HIP CHAPTER 2 DATA ACQUISITION SYSTEM The automated data acquisition system is used for creep testing based on two rea- sons: time-savings and precise data are needed. Thus, an automated data acquisition sys- tem, consisting of a PC with data acquisition board, was developed for our creep experiments. 5.1 HARDWARE The hardware of our automated data acquisition system consists of a computer and data acquisition board (DAB). 5.1.1 Computer An IBM PS/2 model 30 with 80286 rrricroprocessor is used. The benefits of PC- compatible machines are their low cost, expandability and relatively fast processor speed. Computer performance was enhanced by an Intel 80287 math coprocessor and 4 Mbyte of expansion RAM. Peripheral devices included 20 Mbyte hard disk and an IBM dot matrix printer. A sketch of the system is shown in Figure 5.1. 5.1.2 Data Acquisition Board The Data Acquisition Board (DAB) used is the AT—MIO-16 made by National Instruments Corporation. The AT-MIO-l6 board is a high-performance multifunction _48 49 User l I Wintpw interface [nenu | IBM PS/Z Computer AT-Bus Furnace control system ”PW“? expansion board Analog- Digital input/outpu AT—MlO-16 bottom temp rtnin channel A ATS control unit Analog input uninchnnnel B Figure 5.1 The sketch of creep test units with data acquisition system tunnmrA 50 analog, digital and timing I/O board for PC. It contains a 12-bit ADC (Analog-Digital Converter) with up to 16 analog input channels, two l2-bit DACs (Digital-Analog Con- verter) with voltage outputs, eight lines of TTL-compatible digital I/O, and three 16-bit counter/timer channels for timing 1/0. The basic data acquisition system operation is shown in Figure 5.2 [69]. One of the goals of current work is to build a precise data acquisition system for creep test. Therefore, in the following pages, those important issues related to the preci- sion of creep data, data acquisition time, and noise will be mentioned and discussed. (a) Analog input The AT-MIO-l6 board has three different input modes: non-referenced single- ended (NRSE) input, referenced single-ended (RSE) input, and differential (DIFF) input. The single-ended input configurations use 16 channels with common analog ground. The DIFF input configurations use 8 channels where each input signal has its own reference and the difference between each signal and its reference is measured. On the other hand, for NRSE input mode, which uses 16 channels, all the input signals are referenced to the same common mode voltage, but this common mode voltage is allowed to float with respect to the analog ground of the board. For the RSE input mode, it also uses 16 signal input channels as the NRSE mode does, but the RSE mode refers all input channels to a common ground point that is tied to the analog input group of the AT—MIO-l6 board rather than floating with respect to ground of the board (NRSE mode). The AT-MIO-16 board offers two input range conditions: unipolar and bipolar input and two input ranges: 10V and 20V. The actual input range depends on the polarity, range configuration and gain (see Table 5.1) [70]. The precision values in Table 5.1 51 a? R < a 2- a g .5." a a o. l l Digital Discretes 1 £12.10? Signal Analog/digital I/O u p ex Conditioning converter Control tuetueoeldstp—> mom ———> arnsserd ——> Computer l nter i I f I I DIsk or Tape] " , , '1 l I l Figure 5.2 Basic data acquisition system block diagram [69] 52 Table 5.] Actual range and measurement precision versus input range selection and gain [70] Range Configuration Gain Actual Input Range Precision" Oto +10V 1 0to+10V 2.44 mV 2 0 to +5 V 1.22 mV 4 O to +2.5 V 610 11V 8 0 to +1.25 V 305 uV 10 0 to +1 V 244 [JV 100 0 to +0.1 V 24.4 [IV 500 0 mV to +20 mV 4.88 [IV -5 to +5 V l -5 to +5 V 2.44 mV 2 -2.5 to +2.5 V 1.22 mV 4 -1.25 to +1.25 V 610 [IV 8 -0.625 to +0.625 V 305 11V 10 -0.5 to +0.5 V 244 [IV 100 -50 mV to +50 mV 24.4 11V 500 -10 mV to +10 mV 4.88 IN -10to +10V l -10to +10V 4.88 mV 2 -5 to +5 V 2.44 mV 4 -2.5 to +2.5 V 1.22 mV 8 -1.25 to +1.25V 610 [IV 10 -l to +1 V 488 11V 100 —0.1 to +0.1 V 48.8 uV 500 -20 mV to +20 mV 9.76 uV * The value of 1 least significant bit (1 LSB) of the 12-bit ADC, that is, the voltage increment corresponding to a change of ] count in the ADC 12-bit count. 53 represents the value of 1 least significant bit (LSB) of the 12-bit ADC, the voltage incre- ment corresponds to a change of 1 count in the ADC 12-bit count. ( p ) Precision For a l2-bit A/D converter, the l2-bit resolution allows the converter to resolve the input range into 4096 different steps (212:4096). For example, the least significant bit (LSB) for 20V, bipolar input range with gain = 1 is LSB = 20 / 212 = 4.88 mV The precision of this input range and gain combination is 4.88 mv. The value of LSB (pre- cision) vary with the value of input range and gain. As the Table 5.] shows, the higher gain value, the higher resolution (precision) can be obtained. (9) Data acquisigion The data acquisition is controlled by the onboard sample counter. There are three data acquisition possibilities: single-channel data acquisition, multiple-channel (scanned) data acquisition with continuous scanning and multiple-channel data acquisition with interval scanning. For single-channel data acquisition, all A/D conversion data are read from a single channel. The multiple-channel data acquisition performs a multiple-channel scanning which is controlled by the multiplexer (mux) counter and the mux-gain memory. The continuous scanning means scanning cycles through the mux-gain memory without any delays between cycles. On the other hand, interval scanning assigns a time interim] which is called the scan interval to each cycle through the mux-gain memory. Data acquisition rates (number of samples per second) are determined by the con- version period of the ADC plus the sample-and-hold acquisition time. The rate varies from 37,000 samples/sec to 100,000 samples/sec with scanning mode (single or multiple 54 channel) and type of board (high level or low level). The data acquisition rates (sampling rate) should be a proper rate which can recon- struct the sampled signal accurately without collecting unnecessary information. Accord- ing to the Shannon and Nyquist sampling theorem [71], the sampling rate must be greater than twice the highest frequency component of the waveform being sampled to allow the signal being sampled to be reconstructed accurately. 5.2. SOFTWARE The AT-MIO- 16 board can be controlled by Labwindows software provided by the National Instruments Corporation. The Labwindows enhances Microsoft QuickBASIC and C with an interactive development environment, function panels to generate source code, and a library for data acquisition, instrument control, data analysis and presentation. By programming QuickBASIC with Labwindows libraries, a window user interface appli- cation of data acquisition for creep testing was developed (see Figure 5.3). 5.3 NOISE Since accurate data are needed for a creep experiment, especially for stress and temperature change processes (need record 1 point /per mV changes), the‘error caused by noise has a significant effect on the recorded data. Unfortunately, signals are affected by noise in the laboratory environment, even though modern data acquisition systems already contain many features to reduce noise. The possible sources of noise are electrical noise, magnetic noise, electrostatic or capaci- tive noise, radio frequency (RF) noise [71]....etc. To reduce the noise to an acceptable 55 Creep Test length area load strain A strain B temp-T temp-B time final strain - - GO Creep Curve final time - m“ change PtsPerChan rate -I - Quit W“ counts #pts / - I E: strain rate recently s.r. - - A...) Message window start date start time VINC #AVG zoom in min time max time zoom out Figure 5.3 Window interface control panel for creep data acquisition system levt (II 2. 56 level, both hardware techniques and software techniques have to be employed. 5.3.1 Hardware techniques First of all, calibrate the data acquisition board before using. Keeping cables (wires) short and avoiding unnecessary connections (using one line rather than connecting two lines or more) are the primary principle that should be followed. Using a common ground for all equipment is also very important. Electrostatic noise is produced by capacitive coupling between signal-carrying wires and other conductors or the ground. The most effective way to reduce this noise is to shield signal-carrying wires by wrapping them in a conductor that is grounded [71]. In most cases, the shield should be grounded at the signal source. Separating signal-carrying wires and AC power lines can reduce magnetic noise. A high-pass filter is helpful to remove 60 Hz AC power interference which causes electri- cal noise. Floating signal sources, i .e. strain gauge transducers,thermocouples, have isolated ground reference points. Coaxial cable should be used to make shielded connections to the floating signal source. Mechanical vibration can also induce noise, especially for a strain gauge trans- ducer. The sources of mechanical vibration include noisy machine with heavy vibration and pressure variations in water pipes used for cooling system. In summary, short and well-shielded coaxial cable is good for signal—carrying and helps reduce noise. Use of a common ground for all equipment is necessary. 57 5.3.2 Software techniques If the noise is randomly distributed, signal averaging is one software technique that has been widely used to reduce noise. The standard deviation of signal average is inversely proportional to (N)” 2 [71] where N is the number of data to be collected. There- fore, as more samples are taken, the standard deviation of signal average is reduced, and the average value becomes close to the true value. The signal-to-noise ratio is thus improved. Curve-fitting is another way to approach the true value of those random data. The fitting function is chosen according to the shape of the signal waveform. As mentioned in Chapter III, the 9-projection constitutive equation is good for creep data analysis and was used for creep data analysis. CHAEIFJIJZI EXPERIMENTAL PROCEDURES 6.1 SPECIMEN DESIGN Fujiwara,Yamaguchi and colleagues [55,72] identified the room temperature deformation modes of PST crystal as { lll }<112] twinning and {111}<110] normal dislo- cation slip. These twinning and slip systems are still operative at high temperatures, but some different results were found for the different test conditions. Soboyejo et al. [73] found the twinning activity is limited and slip involves 1/2 [110] unit dislocations and [10]] and [112] superlattice dislocation in Ti-49Al-3.4Nb (at%) at 815 0C and 982 0C. However, Huang and Kim [11] found the 1/2<1 10] type dislocations in both gamma grains and gamma lamella in Ti-47Al-lCr-lV-2.5Nb (at%) at 900 0C, but no superlattice disloca- tion and twin deformation were observed. On the other hand, Jin and Bieler [65,66] found a significant contribution of mechanical twinning to creep deformation at a relatively low temperature of 700 0C. As the temperature increases to 815 0C, the contribution of mechanical twinning to creep is significantly decreased. The reasons for these different results are not yet clear. The deformation conditions, chemical compositions and micro- structure are believed to be some important factors which affect the deformation modes of creep in TIA]. For lamellar microstructure, there are two deformation modes: the shear deforma- tion across the lamellar boundaries (hard mode) and the shear deformation parallel to the lamellar boundaries (easy mode). Therefore, the deformation properties are affected 58 59 significantly by the orientation between the lamellar boundaries and the loading axis. Yamaguchi et al. [72] did a series of experiments on PST crystals in different orientations. Some specimens had lamellar boundaries oriented so that the deformation shear strains in the gamma lamellae were parallel to the lamellar boundaries, and other orientations required shear across the lamellar boundaries and lamellae of the (12 phase. The relation- ship between the yield stress of PST crystal and the angle a, which describes the angle between the lamellar boundaries and the loading axis, was plotted as shown in Figure 6.1 [72]. From Figure 6.1, we observe that the yield stress of TiAl is high when the lamellar boundaries are parallel or perpendicular to the loading axis, due to the difficulty of shear perpendicular to lamellae. On the other hand, for those angles ¢=30°~ 60° orientations, the easy shear deformation which parallels to lamellae results in low yield stress value, espe- cially in the maximum resolved shear stress orientation, ¢=45°. In order to examine creep mechanisms under maximum resolved shear stress state, a compression fixture with the orientation of 45° to the tensile axis was used (see Figure 6.2). The compression test was used since it was more convenient than a tension test for a small specimen. By careful orientation, the {11]} lamellar planes were parallel to the sur- face 45° from the loading axis and normal dislocation <110> directions were parallel to the principle resolved shear stress. Polycrystalline specimens were used for comparison. More experiments will be done on { 111 }<112] twinning-type deformation mode in future experiments by a colleague who is investigating this in more detail. -o- Group-1 in compression 500 +- —o- Group-2 in compression o Group-1 in tension I Group-2 in tension i— 1? A O. 2 400b a) m Q) l- :3 U) '0 73-2 200- )- 0 30 60 90 O (degree) Figure 6.1 Plots of yield stress of PST TIA] in tension and compression as a function of the angle a. The specimens were oriented so that the lamellar boundaries are perpendicular to the wider surface of specimens which is parallel to { 112}(group 1) or { 1101(gTOUP 2) [72] 61 Figure 6.2 Schematic of extensometer with compression-shear fixture and shape of specimen 62 6.2 MATERIAL AND SPECIMEN PREPARATION Two types of TiAl were chosen for this research. One is polycrystalline which was made by Howmet Corp., Whitehall, MI. The fabrication process consists of a series of heat treatments which include hot isostatically pressed (HIPed) at 172 MPa and 1260 °C for 4 hours and then heat treated in Ar at 1300 °C for 20 hours and gas fan cooled at a cooling rate of 65 °C/min. The microstructure before creep deformation was duplex with (y+at.2) lamellar grains plus equiaxed y grains. The other type is a PST crystal which was grown in the LSRM facility at the University of Pennsylvania. The PST crystal was grown from the polycrystalline material using the ASGAL optical floating zone furnace in a flowing argon environment. The seed and feed was translated vertically through the hot zone to obtain a growth rate of 5 mm/hr. Both PST and polycrystal specimens have similar composition as shown in Table 6.1 [66]. Table 6.1 Chemical composition of Ti-47Al-2Cr-2Nb specimens [66] T1 Al Nb Cr Fe Cu Si O N H (wt%) bal 32.85 4.47 2.95 0.03 <0.01 0.02 555 53 23 PPm PPm PPm (at%) bal 47.4 1.9 2.2 Three specimens were made for three different compression creep tests. Two poly- crystalline specimens were cut in the form of 5x5x3 mm bricks to fit the compression- shear fixture for testing in air or in flowing argon. One PST crystal specimen was cut in the 63 same form as polycrystalline specimen (5x5x3 mm brick), but the orientation was care- fully determined by using a Laue camera and X-Ray diffraction so that the { 111} lamellar plane was parallel to the 5x5 mm surface and the <110> direction was normal to one of the other surfaces. The compression extensometer with compression-shear fixture and the form of specimen are shown in Figure 6.2. 6.3 CREEP TEST SYSTEM Three creep tests were done under compression by using an ATS series 2710 creep testing machine, and the creep data were recorded by the data acquisition system built for creep tests. The ATS system is designed to perform either creep testing (constant load) or stress relaxation testing (constant strain). The machine has a lever arm ratio of 20:1 to pro- vide high load capacity and loading rate. The creep frame controller unit, which was made by ATS and Electronic Instrument Research Corp.(EIR), allows automatic control mode for constant load or stress creep test. The strain was measured by Linear Variable Capacitance Transducers (LVCT) which perform precise and stable specimen gaging. A small change in length is measured as a change in capacitance. Two LVCTs were used so that if one fails there would be a backup. The LVCTs connect to the specially designed extensometer for compression creep test, and they directly measure the change in length during the creep test. The measure- ment from the LVCT and load cell are input into the control unit and show on a display panel. The control unit also provides the analog outputs of strain and load to allow the user to connect to the data acquisition system. The analog outputs are limited on -10~10V and the initial position of LVCT was adjusted to be within this limit. 64 The furnace has three heating zones that were controlled by a furnace control unit (LFE model 2010). The temperature can reach as high as 1200 °C and temperature gradient between top and bottom of the chamber can be controlled by careful adjustment of three heating zones. K-type thermocouples were used for measurement of temperature and were displayed on the panel of the furnace control unit. The furnace control unit also provides one analog output channel that was monitored by the data acquisition system. The data acquisition system consists of IBM PS/2 286 computer and AT-MIO- 16L-25 multifunction data acquisition board (for details see Chapter V). The five analog input channels were scanned and the values of load, displacements (A & B), temperatures (top and bottom of the specimen) were recorded. A sampling rate of 5000 pts/sec was used. The flow chart of the data acquisition program for creep test is shown in Figure 6.3 and program codes are shown in APPENDIX Time-savings and precise data recording were obtained by using the data acquisi- tion system. Since precise data are needed for creep tests, especially for stress and temper- ature change processes, the precision and noise are two issues that require more concern. 6.3.1 Precision High resolution data are needed for the analysis of the stress and temperature change process. For example, in order to resolve elastic changes of a 3 mm tensile speci- men of TIA] in a 10 MPa stress change, we need to record 1 data point for every 2 mV change (=5.08x10'4 mm change in displacement) since the elastic changes is ~5. 1x10'4 mm in this stress change. Rough data points will significantly influence the experimental result. Start ‘0 Get file name 65 "° read all data from old file update the lot Yes hput test parameters N0 Start point 7? Yes ' . Do loop tar scanning data No Yes Wt’l ‘ to data W'MNC to buffer Average 20 pts Figure 6.3 Flow chart of data acquisition program for creep test No Yes Write data to file 66 The precision of the data acquisition board can be improved by increasing the gain. Table 5.1 shows the overall input range and precision according to the input range configuration and gain used. VVrth the proper gain setting, the full resolution of the Analog/Digital Converter can be used to measure the input signal. For our AT—MIO-16L- 25 board, the gain has four possible choices: 1, 10, 100 and 500. The highest precision of 4.88 11V can be obtained by using the combination of 0 to 10 V input range and gain of 500. In our application, the combination of -10V to 10V input range and gain of 1 was used because the -10 to 10 V input range is wide enough for measurement of larger strain and easy for setting the position of LVCT. However, the low precision of 4.88 mV caused some inaccuracies during the recording of stress and temperature change process data. The gain of 10 with higher precision (488 11V) may account for this problem. However, the narrower input range of -1 to IV for a gain of 10 was not convenient for long-term creep test since only 2V (0.508 mm) range is allowed for LVCT to monitor the heat-up process and measure the strain. The accommodation between the wide input range (enough range for measurement of large strain) and high precision (enough for measurement of small voltage changes) requires practical compromise. 6.3.2 Noise In order to minimize the noise, the both hardware and software techniques should be used. (a) Hardwam In general, acceptable operation of the test system in test control and data 67 acquisition depends on the minimization of noise pickup, primarily 60 Hz. A common grounding system for all devices was implemented. The LVCTs were also grounded through the connection to the control unit of the ATS machine. Since the LVCTs were cooled by the cooling system, the temperature-induced noise was avoided. Furthermore, the extensometer was electrically isolated from the specimen and the specimen grips, and also from the load frame. The common grounding is a very important procedure to mini- mize the noise in the data. By the recommendation of the AT-MIO-l6 User Manual, individually shielded, twisted-pair wires were used to connect analog input signals to the AT-MIO-l6 board. Dif- ferential analog input connections were also used to reject the possible noise in the com- mon ground mode. By the way, carefully separated the signal lines from high-current or high-voltage lines to reduce the magnetic-induced noise. Another possible source of noise in our creep tests is the mechanical vibration due to a noisy machine that generates heavy vibration in the laboratory from time to time. The calibration of the data acquisition system is helpful to acquire precise data. For analog input calibration, the measurement accuracy within 11/2 least significant bit (LSB) is recommended by the AT—MIO-l6 User Manual [74]. The LSB of the input range we used (-10~+10V) is 4.88 mV and measurement accuracy should be within i 2.44 mV. A constant was added to the signal obtained from the data acquisition board to bring the DAS value within i 1 mV of the value obtained from the LVCT. Actually, the biggest unexpected variation of displacement fluctuation is due to the loading compensation feedback system of the ATS machine. The constant load was maintained by the ATS control unit and a slow moving DC motor adjusted the tension on 68 the loading arm to maintain a constant load. The window of the feedback loop was within _-i_-_ 1%. The measured value of displacement fluctuated as the load increased or decreased to maintain the constant-load value. In the way of a hardware technique, narrowing the load range between high and low limits will lower the fluctuation on loading and displace- ment. my; Using software techniques, the signal-averaging method was used to reduce the noise caused by fluctuation of loading or other sources. By sampling at a higher rate and using the signal-averaging method, it is a possible to minimize the errors. In our applica- tion, the sampling rate of 5000 pts/sec for 5 channels, i.e. 1000 pts/sec per channel, was used. Thus, each data point represents an arithmetic mean of 1000 data points sampled at 1 kHz frequency. Each data point was evaluated with respect to a change criteria called VINC, which is calculated by the equation: VINC = FS * LO * 10000(mV) / 0.1(in) / N(pts) (24) where FS is the final strain, L0 is the initial length of specimen and N is the number of points to be recorded. For example, if the final strain of a creep test is 10% (0.1) and initial length of specimen is 0.] in, and if 250 points data are expected to be recorded during this creep deformation process up to 0.] strain, data should be taken and stored for every 4 mV change according to equation (24). The noise effect caused by fluctuation of loading or other noise will influence the 69 shape of creep curve, as Figure 6.4 shows. The fluctuation value between high and low limits can also be averaged by using a signal-averaging method. A data value was temporarily stored in a circular buffer if this value was greater than the value of the previ- ous value (Vi)+VINC. After 20 data points were stored in the buffer, the average of those 20 points was calculated and compared with the value of Vi+VINC. If the average of 20 points was greater than Vi+VINC, this average was stored. If not, no data point would be taken until the 20 points average is greater than Vi+VINC. Since the window interface operation panel was created, the complicated com- puting processes slowed the performance of the computer. This problem is not serious during the constant load and temperature creep condition, but it is a very serious problem during the stress or temperature change process due to the high frequency of recording data that is necessary under this condition. To solve this problem, the data was stored to the memory temporarily during the stress and temperature change processes and after that it was written to disk. 6.4 CREEP TEST PROCEDURES Three compression creep tests were done in air or Ar over the temperature range 760 °C ~ 810 °C. A series of stress and/or temperature changes were conducted for each test (see Table 6.2). In the beginning, the specimen was initially heated up to 760 °C step by step (~100 °C/hr) and the temperature difference between specimen top and bot- tom was controlled in 10 °C. The thermal expansion was compensated by using draw head adjustment so that constant load was maintained during the heat-up process. The 70 High limit Low limit strain Time Figure 6.4 The creep curve varies with the fluctuating data. Table 6.2 The conditions for each test Specimen Polycrystalline- 1 Polycrystalline-2 PST Microstructure Duplex Duplex Fully lamellar Test temperature 764~775 OC 765~800 0C 760~806 0C Test stress 68.8 ~87.8 MPa 75.7~82 MPa l9~3l MPa Final strain 0.274 0.457 0.068 Test atmosphere air Ar Ar 72 specimens were initially loaded slowly at a strain rate on the order of 10'4 S‘1 at 760 °C and a defined primary stage followed by a minimum strain rate region was obtained. Fol- lowing a period well into the minimum strain rate region, the stress or temperature was increased from this level to the next level. The response to the change exhibited a transient decelerating strain rate followed by a minimum strain rate. Following a stress or tempera- ture decrease, the response exhibited strain contraction followed by an accelerating strain rate until a nearly steady value was reached. This process was repeated for each stress and temperature level applied. Top and bottom sample temperatures were held within -_l-_ 1°C. The values of specimen load, displacement, temperature and elapsed time of the experiment were digitally recorded by computer and saved as data file in ASCH format. Assuming perfect shear deformation, i.e., no compression strain 7 = (2)“2 Al/t, where A] (m): 2.54x10'4 AV (mV) and t=3 mm, the shear stress and strain data were determined using spreadsheet programs. The creep data was analyzed by using the curve fitting soft- ware (T ableCurve 3.11) with a modified creep equation of the O-projection concept. APT I RESULTS The experimental results are shown in Figures 7.1-7.3. Every data point shown on the plots represents the average of 20 points calculated by the method described in the sec- tion 6.3.2. The resolution of 4.88 mV(=l.24x10'3 mm) was used for the creep tests and the error of data was i 0.124%. The lines in the data come from a curve fitting procedure by using the modified creep equation of the B-projection concept described in section 3.4. The fitting parameters for PST and polycrystal in Ar and air are shown in Tables 7.1-7.3 and the fit standard errors are 3~5x10'4. “Normal” transient behaviors were observed for the PST and polycrystal speci- mens (in Ar or air) after stress or temperature change. As the stress or temperature increases, an instantaneous extension is followed by creep which decelerates toward the new (higher) steady state. On the other hand, as the stress or temperature decreases, an instantaneous contraction is followed by transient creep which accelerates to a new (lower) steady state. 73 74 TiAl-PST[110] at Ar Strain rate 0.07 WT I I I I o I T I 06 c osflf" 8- - - ~ 0 l 0.06 - 2 .1 0.05 " -( 31 MPa 0.04 ~ l—l . I. ..... _ 0.03 - 0:19 MP3 0.02 =- ' ' _ _ _ — - - — stress changing history 0.01 -------- temperature changing history . 1 2 3 4 5 6 7 e 9 Time(sec) x 105 (a) TlAl-PSTI110] at Ar .4 10 : I I I I I I i I l > 1 10-5 f 0 1:1 E f : o 10“: :3 10-7 nakgx 3.416% M 1 ; 5 o7 1 10.85r 10 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Shear straln (b) Figure 7.1 The creep curve of PST (with fitting) (a) strain-time curve (b) strain-strain rate curve 75 TIAl-poly in Air 0.3 I I l T I ' T T 0.25 - ‘ 764 0c """" 0.2—-----------------'---" """""" "J .5 (6 5 g °-‘5 “ 75 MPa ' q 5 _--_--_--_--_l (I) . ' 69 MPa 01 — L ' ' - ‘ _ - .. — stress changing history 0.05 ‘ -------- temperature changing history 0 2 4 6 8 10 12 14 16 18 T'Ime(sec) x105 (21) 5 TIAI—poly In Air 10- 1 I f ' ' 2 t! c: _ .1 'a . . a : ' CD . . _ o 10's? 3 I o 1 10‘9 l 1 l 1 1 0 0.05 0.1 0.15 0.2 0.25 0.3 Shear strain (b) Figure 7.2 The creep curve of polycrystal in air (with fitting) (a) strain-time curve (b) strain-strain rate curve 76 TIAi—poly in Ar 0.5 0.45 0.4 0.35 .c 0.31 g i 0 25 5 0.2- ----- 0.15 o 1 _ — - - — stress changing history ‘ ......... temperature changing history 0.05 0 2 4 6 8 10 12 Time(sec) x 105 (a) TiAl-poly in Ar -5 10 i' I I I I I I I I I . I 1 L . 11 3 -. 7 : 5 . g o l 9 o g . c 0 o O 8 4 'a Q :3 [KW 7: W0 12 o 6 10-7 _ 1 0 I 10.8 1 1 1 ' 4 1 1 1 1 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Shear strain 0)) Figure 7.3 The creep curve of polycrystal in Ar (with fitting) (a) strain-time curve (b) strain-strain rate curve 77 Table 7.1 The fitting parameters for PST specimen in Ar Fit stage Conditions 80 A or 03 t0(sec) strain standard error 1 19.0 MPa 8.16 6.05 5.10 5.37 0 0.0123 5.3—3E-04 760 0C E-04 E-03 E-05 E-08 2 22.0 MPa 1.44 1.55 1.54 8.03 120420 0.0220 4.95E-04 760 oC E-02 E-03 E-04 E-08 3 25.3 MPa 1.65 7.01 2.04 8.23 212544 0.0306 3868-04 760 0C E-02 E-03 E-04 E-08 4 25.1 MPa 3.35 4.50 4.40 7.73 301320 0.0378 5205-04 773 OC E-02 E-04 E-04 E-08 5 25.1MPa 4.22 4.52 3.47 5.21 352620 0.0412 5.38E-04 760 0C E-02 E-03 E-04 E-08 6 25.0 MPa 4.28 4.60 5.83 1.20 423144 0.0482 4.70E-04 790 0C E-02 E-04 E-04 E-07 7 25.1MPa 4.80 2.51 1.04 4.80 471492 0.0498 3.74E-04 761 OC E—02 E-04 E-04 152—08 8 25.1MPa 5.38 4.93 7.30 1.52 537048 0.0588 5.84E-04 806 0C E-02 E-04 E-04 E-O7 9 25.1MPa 5.98 1.91 1.38 3.04 597147 0.0618 2.01E-04 766 0C E-02 E-04 E-04 E-08 10 31MPa 6.15 4.53 7.50 9.51 705708 0.0675 2.36E-04 762 0C 15-02 E-03 E-04 E-08 11 25 MPa 6.68 2.50 1.14 3.80 740736 0.0681 5.52E-04 763 0C E-02 E-04 E-04 E-08 78 Table 7.2 The fitting parameter for Polycrystal specimen in air Fit stage Conditions. 80 A 0t 83 t0(sec) strain standard error ========3=E 1 75.7 MPa 3.92 1.89 2.41 1.14 0 0.1076 1.17E-03 764 OC E-03 E-02 E-05 E-07 2 87.8 MPa 1.17 2.20 6.87 1.87 767160 0.1564 4.52E-04 764 0C E-01 E-03 E-05 E-07 3 75.2 MPa 1.65 1.50 2.23 1.28 1022760 0.1854 2.76E-O4 764 oC E-Ol E-03 E-05 E-O7 4 75.1MPa 1.84 1.00 8.30 2.36 1186560 0.2633 4.66E-04 774 0C E-Ol E-03 E-05 E-07 5 68.8 MPa 2.60 4.97 3.12 1.95 1533960 0.2742 2.30E-04 775 0C E—01 E-03 E-OS E-O7 Table 7.3 The fitting parameters for Polycrystal specimen in Ar 79 Fit stage Conditions 80 A or 68 to(sec) strain standard error 1 75.7 MP3 2.89 3.94 5.19 3.21 0 0.0993 8.72E-04 765 0c E-03 E-02 E-OS E-O7 2 75.7 MP3 1.00 1.97 3.81 3.25 147276 0.1301 2.30E-04 770 0C E-Ol E-03 E-04 E-07 3 82.0 MPa 1.36 2.73 2.08 3.84 233784 0.1684 1.03E-03 770 0C E-01 E-03 E-04 E-07 4 75.7 MP3 1.64 1.00 1.11 2.66 301680 0.1848 2.4lE-04 770 0C E-01 E-03 E-04 E—07 5 75.7 MPa 1.86 1.69 2.57 4.44 386424 0.2296 3.95E—04 780 0C E-01 E-03 E-04 E-07 6 75.7 MP3 2.33 1.02 9.43 2.38 483732 0.2925 2.185-04 770 0C E-01 E-03 E-05 E-07 7 75.7 MP3 2.94 2.90 7.43 5.62 745560 0.3054 3395-04 790 0C E-Ol E-03 E-04 E-07 8 75.7 MP3 3.12 1.01 7.43 2.66 771696 0.3220 9.18E-04 770 0C E-Ol E-03 E-05 E-07 9 82.0 MPa 3.31 1.26 1.84 2.87 849456 0.3544 9.87E-04 770 0C E-Ol E-03 E-04 E-07 10 75.7 MPa 3.53 1.03 4.84 2.32 925920 0.3679 **** 770 OC E-01 E-03 E-05 E-07 11 75.7 MP3 3.70 3.40 9.84 7.63 1001412 0.4361 1.16E-03 800 OC E-01 E-03 E-04 E-07 12 75.7 MPa 4.35 3.03 9.84 4.02 1083816 0.4576 4005-04 770 0C E-Ol E-03 E-05 E-O7 *: Too few data to fit QHAPIER yIII ANALYSIS AND DISCUSSION 8.1 CREEP BEHAVIOR The creep curves of PST and polycrystalline specimens with stress and tempera- ture change are shown on the Figures 7.1-7.3. As the stress or temperature increases, an instantaneous extension is followed by creep which decelerates toward the new (higher) steady state rate. On the other hand, as the stress or temperature decreases, an instanta- neous contraction is followed by transient creep which accelerates to a new (lower) steady state. This is a typical form of “normal” transient behavior and consistent with the TEM observation of dislocation network observed by Jin et al. [67]. J in et al. [67] found that the creep deformation mode in TrAl is pure metal type (Class M) and subgrain boundaries were observed both in equiaxed gamma grains and within gamma laths in lamellar grains in the creep deformed specimen of duplex structure. Since there is no long term steady state creep rate in TiAl, the minimum creep rate is used as a basis for comparison for the power law equation. The values of minimum creep rate were obtained by fitting the modified 0-projection equations (Equation 16,17), and the minimum strain rate as usually used to represent the steady state creep rate in the 0-projection equation. In the 0-projection equation, the minimum creep rate represents a balance between the hardening term and softening term. This is similar to the dislocation theory of steady state deformation presented by Gottstein and Argon [75]. According to their model, a master equation based on the accepted dislocation theory, considering 80 81 various recovery mechanisms, was derived. This equation can account for creep and CSR (constant strain rate) tests with respect to compatibility, transients and steady state defor- mation because both modes of deformation have similar microstructure development. 8.1.] Stress exponent (a )PST As there is no deformation mechanism map for “A1 available in the literature, and as the creep behavior of TiAl is closer to FCC Al than to HCP Ti for the temperature examined, the creep deformation map for pure Al was considered (see Figure 8.1). For the stress and temperature regime examined (T~1/2 Tm =760 oC, O'~19-31 MPa), the normalized shear stress (CS/G) was in the high temperature creep regime for both 10pm and 1mm grain size Al (0:03-12 x 10'2’F/K) GPa) [68], i.e. the power-law creep by dislocation glide-plus-climb. This dislocation glide-plus-climb process is limited by the lattice-diffusion controlled climb. According to the power law equation (Equation 1), at each temperature, the stress exponent is given by the gradient of the logeS [logo plot. This gradient is shown for each stress change as the experiment progressed, as indicated by the dashed lines in Figure 8.2. Thus, by comparing the minimum creep rates following stress changes in the strain range of 1%;3% and 6%~7%, the stress exponents n=3 and n=5.6 were obtained, respectively (see Figure 8.2). The stress exponent of n=3 is characteristic of dislocation glide creep and n=5 for dislocation climb creep. There are two possible ways to explain stress exponent of n=3, one is no steady state was reached in the strain range of 1% ~3%, so, this value can be 82 TEMPERATUREJU n‘ 'H '. .. g E. I L. H i- .- 2‘2 "2"..32‘" L — .4 Eye: A; ngIgu | I ' o a. \a 9 571cm ' 10" U . 5'. 75" 423$?an , a 6. 50' SHEAR 510555 11 3001((MN/m’) NORMALISEO SHE AR SI RESS ‘0' ,_...... - . .. . . l \ \1 \ " . 1 ' “$173336... 1'1“}:ng ‘°0 02 0:. 06 ca 10 HOMOLOGOUS YSMPERHURE, '/_ (a) rcupenxrunm'o . ° . 9° 9 '90 39° :00 ‘9 ’°° '°° '° ._..'...¢.u 122-4." 1:..- w w u d ' in. 000’ r I PLASTICITY E 3‘6 1 . Ire-vsuum'o. - y JH— _ I ' W. \\\‘ng‘ A ”WN iy\.dk ‘jT—l‘l—l-‘>O €5.13 05 8 \.\ 5 6, a...) _ g. . \ 4 S i\ '1 a g I&.ICIIU \ g ' e ' o P O a 1 lutCltl'i 9' ‘ m ‘23 '° I : Powcp-uw\ CREEP\ g 3 1 ' I {11' z m c lr_ 1X \\ cf IO “A3 '. 1.0.. . I ‘ 0 HAQPER: OORN CREE’ L . ....__s. _..i o r o a o o 61' to HOMOLOGOUS Ycupcnnun: V,“ (b) Figure 8.1 The deformation mechanism maps of pure aluminium. (a) grain size 10 um (b) grain size 1 mm [76] . . . -1 Minimum strain rate,(sec ) 83 Stress exponent for TiAl -6 O PST (Mu AT) 10 T '1 . Ci polycrystaKAir) . _ o polycrystaKAr) 1. (£1.54 at AT) 1- "-2 3 1 ’ 30:92.3 1 n-Z1d. 5 :n- 2 .. 774°C 3 3- ; 5' ”-3 i .7 _, _, 1° : 764°C : i- -1 1 0 100 Shear stress, MPa Figure 8.2 Plots of stress dependence of minimum creep rate for PST and polycrystal. The dash lines indicate the history of deformation. #‘s next to datum points refer to Tables 7.1-7.3. 34 doubted. On the other hand, the pipe diffusion did not contribute to creep deformation in the early stage (1%~3% strain) since fewer dislocations. In the latter stage (6%~7% strain), more dislocations lead larger contributions of pipe diffusion and cause the stress exponent of n=3 increased by 2. i b) Pglyggstal For polycrystal in air, the stress exponents of n=2 for 774 0C and n=3 for 764 0C were obtained (see Figure 8.2). The position of the normalized stress and temperature on the mechanism boundary of the deformation mechanism map for Al, suggests that for this temperature regime, there is no single dominant deformation mechanism, and lies near the dislocation climb controlled and dislocation glide controlled creep boundary. The stress exponent n=3 is commonly associated with the dislocation glide-limited creep process. But dislocation glide-limited deformation usually causes the “inverse” tran- sient behavior after stress or temperature changes rather than normal transients we observed. One possible interpretation for n=3 is Coble creep (n=l) modified by the pipe diffusion which usually increases the stress exponent by 2 [8]. However, from the defor- mation mechanism map in Figure 8.1(a)(b), the applied stress of 75~87 MPa seems too high for Coble creep to be the dominant mechanism. According to the Coble creep equa- tion [25], (25) where 2': is the Coble creep rate, Db is the grain boundary diffusion coefficient, 5,, is the effective grain boundary width, Q is the atomic volume, (1 is the grain size and Bc is the 85 constant (=l48). Grain sizes for Coble creep were estimated and shown on the Table 8.1 using the range data for FCC metal of Frost and Ashby [76]. Since only small volume fraction of (12 phase is presented, only 7 phase was considered to estimate the grain size for Coble creep. Critical grain size range of 10 tim~28 ttm for PST, and 12 tim~34 ttm for polycrystal were calculated for Coble creep, which are smaller than the average measured grain size (>50 pm) of polycrystal specimen we used. Therefore, if Coble creep occurs, then it must occur in lamellar microstructure regions, which have sizes < ~10 pm. Since the test conditions of the polycrystal may lie in the transition regime of dif- ferent mechanisms, the amount of the contribution of each deformation mechanism to the creep deformation becomes a more complicated problem, especially since the microstruc- ture also plays a important role for interpretation of creep behavior. Therefore, more experiments in a wider test conditions are necessary to gain better understanding and interpretation of those unsolved problems. For polycrystal in Ar, the stress exponent n=2~3 was calculated at 770 0C (see Fig- ure 8.2). It is similar to that of polycrystal in air and there seems to be no significant influ- ence on the stress exponent by different atmospheres (air or Ar). 8.1.2 Activation energy (011151 The activation energy QC 2 137 i 70 KJ/mole was obtained for PST in the temper- ature range of 760 0C~806 0C (see Figure 8.3). This value is similar to the activation energy Q=150 KJ/mole for interdiffusion in y-TiAl which was reported by Ouchi et al. [64]. The lower activation energy maybe due to the easy mode deformation. A similar 86 Table 8.1 The grain sizes of PST and polycrystal for Coble creep PST polycrystal Applied stress 0’ (MPa) 22 88 Steady state strain rate (s'l) 82338 1-87E'7 Temperature (K) 1033 1037 Grain size for Coble creep(|.tm) 10~28 12~34 * Q, = 150 KJ/mole was assumed. * 8r)b for FCC metals: 9.1x10'23~2.1x10'21 m33'1 * o =1.18x10'29 m3 for TiAl 87 activation energy value of 130 KJ/mole for thermally activated glide of screw dislocation in y—TlAl at room temperature was reported by Appel et al. [77]. (biPolycgstal The activation energy of 574 i 90 KJ/mole and 229 i 60 KJ/mole were computed for air and Ar atmosphere, respectively (see Figure 8.3). The value of 229 i 60 KJ/mole (in Ar atmosphere) is lower than the general accepted value Q =29l KJ/mole for T1 diffu- sion in '1‘1-54A1 which was reported by Kroll et al. [60]. On the other hand, a high activa— tion energy QC =574 i 90 KJ/mole was obtained in air and it is not common for stress exponent of n=2~3. This value is unreliable since only two temperature changes. Dynamic recrystallization has been reported [8] to be a important phenomenon at higher tempera- ture (~76O OC) and at strains > ~ 5% it may cause this high activation energy for the poly- crystal in air. However, this unsolved problem needs more experiments in the wider range of temperature and stress since QC=574 i 90 KJ/mole for the polycrystal in air was deter- mined by interpreting only two data points of different temperatures. Since the uncertainty of activation energy for polycrystal in air, it is not known about the influence of atmo- sphere (Ar and air) by the comparison of activation energy. 8.1.3 Stress and temperature change In general, the stress change experiment is usually used to study the substructure phenomenon during the creep deformation since it is easy to conduct. The temperature change experiment is seldom used because it is not easy to control the temperature fluctu- ation after temperature changes. From our observations after temperature changes, the 88 Activation energy for TiAl 806°C 790°C 770°C 10'5_...,r..,.4fi,... I j. l mJT . . . -1 Minimum strain rate(sec ) 10" r 1 : Q -‘I 37170 KJ/mole 5 i- 7 .- .9 T o PST (1113.10.11 as Ac) P O polycrystal(Ar) (#1.2.3.9 a M) D polycrystal(Air) (111.2.5 u M) 10.3 . . L 1 . . . 1 . . . 1 L L . 9 9.2 9.4 9.6 9.8 10“/T (K") Figure 8.3 Arrhenius plots of the temperature dependence of minimum creep rate for PST and polycrystal of TiAl. The dash lines indicate the history of deformation. #‘s next to datum points refer to Tables 7.1-7.3 89 temperature generally fluctuated in the range of TC(creep temperature): 5-7 0 C for half hour before TC settled down. This feature may result in some uncertainties in the interpretations of transient behaviors. However, normal transients were still observed after temperature changes as well as stress Changes. This suggests that stress and temperature have similar influence on the substructure during the creep deformation. From the loading history plots in Figure 8.2. 8.3, as stress or temperature increases, the creep rate ém increases to a new value (> em) and then back to a lower value (< .6...) after stress or temperature reduction. This process can result from subgrains that were formed by dislocation climb processes that harden the specimen in the primary stage. These substructures in primary creep are evident in the results of Jin et al. [67] and indi- cated that the creep behavior in TiAl is Class M type behavior. 8.1.4 Composite model Since the mechanisms of creep of in TiAl are complicated, the composite model has been presented by several researcher [10,68]. Those composite models may provide a possible way to understand those unsolved mysteries of the creep deformation in poly- crystal. The composite model uses a simple rule-of-mixture equation to combine all defor- mation mechanisms which contribute the creep deformation. This is a useful method to describe creep behaviors which have more than one deformation mechanism. A less sophisticated, empirical model and analysis is explored next, 8C = 2V '6‘. (26) i l 90 éc is the total creep rate, 6, is the creep rate of mechanism i, Vi is the volume fraction dom- inated by mechanism 1. The analysis needed to identify the operative mechanism is beyond the scope of this thesis. 8.2 IMPLICATIONS OF THE FITTING PARAMETERS A modified O-projection concept equation [39] was used for the data analysis of creep to explore the creep behavior. The constitutive equation for transient creep after stress and temperature increase is e:80+A{1—exp(—0t(t—t0))}+és(t—t0) (16) where 80 is an adjustable parameter, to is starting time. e, is the steady state (or minimum) strain rate, A and a are curve fitting parameters. In the case of transient creep after stress and temperature decrease, the constitutive equation is e = 80+Aexp(—Ot(t—to)) +és(t—t0) (17) 8.2.1. Parameter A (strain hardening parameter) The strain hardening parameter A represents the saturation strain of primary creep. The parameters A are plotted against O/G in Figure 8.4(a) and show that the parameter A depends on stress. The values of A increase as the applied shear stress increases for PST and polycrystal specimens. This is consistent with the results found on CrMoV steels by Maruyama and Oikawa [45] which presented A = fa(G/E), where fa(o/E) is a function only 91 of o/E (see Figure 8.4(b)). These results also suggest that the stress increase was associ- ated with the microstructure change. The values of A are also plotted against the temperature, as shown in Figure 8.5. Strain hardening parameter A is independent of temperature for the PST. On the other hand, no matter what atmosphere (Ar or air), the values of A of polycrystal appear to increase as temperature increases. It indicated that the microstructure of polycrystal is more harden with temperature increase than PST in the temperature range of 760 °C ~ 800 0C. 8.2.2. Parameter or ( rate constant) The stress and temperature dependence of the rate constant or for the PST and polycrystal are shown in Figures 8.6(a), 8.7(a), respectively, and show the parameter 0: increases as stress or temperature increases. It is consistent with other observations using the 0-projection concept (see Figure 8.6(b), 8.7 (b)). Those studies of the 0-projection concept [39,43~45] suggest that or can be expressed in the form of OL = fa(o/E)D where D = Doexp(-QD/RT) (10) where D is the self-diffusion coefficient and QD is the activation energy for the rate con- stant Brown et al. [44] considered that or has the common activation energy as the self diffusion. Maruyama et.al. [79] stated that in the case of dislocation creep controlled by diffusion, the rate constant or of TiAl can be formed as on = CDO'm+2, where C is a con- stant, D is the diffusion coefficient, m is the effective stress exponent for dislocation velocity and the stress exponent of 2 comes from the stress dependence of dislocation 92 10° I ‘ ‘ O PST < O polycrystal(Ar) :9: D poiycrystal(Air) ‘ 3 10" :- '5 9 E : 8 ~ : .3 ~ 0‘ 1 '9 10'2 " s '1 g E 10 . 1 .5 . " e .1 e . 330. 10'3 =- 2 1 t 1 1 1 1 . .11 1 1 1 1 1 1 11" 10“ 10'3 10'2 O/G, Pa (2!) 100 I I I r 1 I v 50. tCrMoV tZCrMoVNb SCrM0VNb‘ 773 K 0 823 K A A D ‘0 .873 K ' D 0____ N 5 923 K . ‘ l O o d :9 i /D’ i q .1.-. .A’ . q ‘-°*::ofiijg—tfifiu—e __ . I L__l ’ __ -1 O/ma I l l 1 ,, _, 0410 i I i i ll .05 1 J 5 . 1 1 . 0-4 0-5 0-7 1.0 2 O 3 0 (O/E). 10‘3 (b) Figure 8.4 Stress dependence of strain hardening parameters A. (a) PST and polycrystal of TiAl (b) CrMoV steel by K. Maruyama er al. [45] #’s next to datum points refer to Tables 7.1-7.3 Strain hardening parameter A 93 1040 1050 1060 1070 1080 (K) 410'3 _ .fi..........,..-.1r...,. e PST ; o polycrystaKAr) n 3 C D polycrystaKAir) 2 -3 I. .1 3 10 1 : t I t 1 C 1 .3 : 4 I 2 10 t" s 0 '2 I: D o s : b 4 : I 10" :- 0 1 t 4 O 0 j t o —e O : o : L l l L l l L l L l J l l 1 l l l l 1 l J L L l : O 10 760 770 780 7900 800 810 Temperature( C) ‘ Figure 8.5 Plots of the strain hardening parameters A against temperature for PST and polycrystal of TiAl. #’s next to datum points refer to Tables 7.1-7.3 Rate constant a 94 10""t . . o PSTat760°C 1 o Win-177W: n Wurmnflc. 1:? n-3 'YT 10“ F '3 - n-7 P 5 10-5 L l L 1 1 1 1 10" 10'3 10'2 o/G, Pa (a) 10'.2 l l I .1 ’ Tl-SlnolXAl- 1100 K 0'3 0 47m / ‘ 1 - I 9711. I - " A 10811- ‘ 3/5 ' A 7 104v / o/" \ ‘ =5.6/!/./ « S I o 8 1 7 /'/6/ Ti-SOmleAl _6 A/o 0 33qu 10 r' / D 39‘“! d ’ 6 501m ‘ 0 561m ‘0’, L L l 50 100 150 200 250 d / MPa 0)) Figure 8.6 The stress dependence of rate constants a (a) PST and polycrystal of ’IlAl (b) Ti-SOAI and 'I‘i-SlAl by K. Maruyama et al.[79] #’s next to datum points refer to Tables 7 .1-7.3. 9S 10¢ BOG‘E 790°C 770°c : ' - ' 00-294 .160 KJ/molé I 0 3 _ (10.133 .120 KJ/mole ‘ 1 1 ‘ -1 00-412 1 90 KJ/rn'ok, E PST at 25.1 MP. polycrystaKAr) at 75.7 MP: polycryst-KAIr) at 75.1 upl- "" Rate constant a ‘1 l LDC. PA 9 9.2 9.4 ‘ 9.6 , 9.8 10‘/T(I<") ‘ (a) ‘04 1- O/ExLSflO.’ 1000 9150 900 050 000 10" b v v I fi| I 1 J 7 1 ‘ I \ 1 \ .q 1 . 1 o 1 7m I0 5 ' -- \0. 137.6 kJ-mol" . . #5110110”, 4' U ,5 __O.s352kJ-fli°l" \ lO '— O T . ‘ I 0.:353 4 10" - c ICrMoV I “51‘.“ _. 'ICrMOV 0 0129mm? I \ l ‘ ‘ .3 1 1 1 1 1 01.00 1.05 1.10 1.15 1.70 1.25 1.30 7", 10311" (b) Figure 8.7 The temperature dependence of the rate constants or (21) PST and polycrystal of TiAl (b) CrMoV steel by K. Maruyama et al. [45] #’s next to datum points refer to Tables 7.1-7.3. 96 density. Some reports [8,75] have shown that the stress exponent can be increased by a factor of 2 when pipe diffusion is rate-controlling during intermediate temperature creep deformation. From the stress dependence of the rate constant plot in Figure 8.6 (a), the slopes n =5.5 for PST and n= 3 for polycrystal are close to the stress exponents which were obtained for steady state creep (n=5.6 for the PST and n=2~3 for the polycrystal in Ar). Figure 8.6(b) also shows similar result of slope n~5.6 in 'Ii-SOAI and Ti-SOAI by K. Maruyama et al. [79]. However, these stress exponents in Figure 8.6(a)(b) include a factor of 2 which is contributed from pipe (core) diffusion. Therefore, the n=5.5 suggests dislo- cation glide (n~3) aided by pipe diffusion to be the dominant deformation mechanism in PST since higher dislocation density causes the significant contribution of the pipe diffu- sion. On the other hand, dynamic recrystallization that occurs in polycrystal results in fewer dislocations and consequently less pipe diffusion, and so the n=3 was obtained. The high stress exponent of n=7 for the polycrystal in air is much higher than the stress expo- nent n=2~3 which was obtained for steady state creep. This may be due to a slope with error resulting from only two points or a curve fit for one of these is incorrect. The activation energies QD of the rate constant for PST and polycrystal were calcu- lated by the Arrhenius plots of the temperature dependence of or, and the QD =133 i 20 KJ/mole for PST, QD =294 _+_- 60 KJ/mole for polycrystal in Ar and Q, =412 i 90 KJ/mole for polycrystal in air were given, respectively (see Figure 8.7). For the PST crystal, the value of Q, = 133 i 20 KJ/mole is close to the apparent activation energy of creep, QC=137 -_l~_ 70 KJ./mole, calculated from the temperature depen- dence of minimum creep rate. The interpretation of the activation energy for the rate 97 constant provides that the same rate-limiting thermal activation process occurs in transient steady state creep. Therefore, the activation energy QC=135 i 70 KJ/mole for the easy deformation mode creep of PST should be a reasonable interpretation. For the polycrystal in Ar, the activation energy QD =294 i 60 KJ/mole for rate constant is higher than activation energy QC=229 i 60 KJ/mole which was obtained from the Arrehenius plot of temperature dependence of minimum creep rate. The Q, =294 i 60 KJ/mole is closer to a general accepted activation energy value (Q = 291KJ/mole) for gamma TrAl in this temperature and stress regime [60]. However, plots of temperature- compensated creep rate (Zener-Hollomon parameter Z = as exp(Qc /RT)[19] in Figure 8.8 shows that the lower activation energy causes better superimposition data onto a single line. It implies that the QC =229 KJ/mole or 150 KJ/mole better describes this creep defor- mation process. From the interpretation of steady state creep rate and the fitting parameters of 0- projection equation, the stress exponent of n=5.6 for PST appears to be due to the disloca- tion glide (n~3) aided by pipe diffusion. The occurrence of pipe diffusion is supported by the low activation energy QC=135 i. 70 KJ./mole. For the polycrystal, fewer dislocations existed due to dynamic recrystallization, this can account for the stress exponent of n~3 and high activation energy of QC=229 ;I_- 60 KJ/mole (in Ar) and QC=574 i 90 KJ/mole (in air). Even though dislocation glide (n~3) usually causes “inverse” transient behavior, the n~3 is still acceptable for the “normal” transient observations in PST and polycrystal. Weertman and Weertman [80], who have shown that, when glide and climb distances (velocities) are similar, dislocation climb can occur with n=3 rate law. Similar result also was found by Gottstein and Argon [75]. According to their dislocation theory model, the 98 Polycrystal In Ar 109 ...1,...1,11..'....11.r. o 770 9 o x 780 Q=294 KJ/mole 107 A 790 O 800 105 3 ° 8 8’ Q-229 KJ/mole .J 103 10‘ I o Q-1SO KJ/mole 10.111111.1..1111111111111g1 4.5 4.6 4.7 4.8 4.9 S Log(stress/G X105),Pa Figure 8.8 Plots of temperature-compensated creep rate for polycrystal in Ar 99 stress exponent of n=3 was found when only recovery by climb is taken into account. Finally, from the interpretation of stress exponent and activation energy, we found the quality of data in PST appears better than in polycrystal in spite of the fact of that fewer data in PST causes greater uncertainties in curve fit. That indicated the simpler deformation process occurs in the PST and that the PST data are sufficient reliable. CHAPTER IX CONCLUSION The automated data acquisition system which consists of PC-based computer and data acquisition board was developed for transient creep test. The purpose of time-savings was achieved and accurate data were obtained for transient creep test. The effect of noise was minimized by using hardware (common ground) and software (signal-averaging) techniques. ‘Normal’ transient creep after stress and temperature change were observed on the PST and polycrystal (duplex) specimens. This suggests that Class M type creep deforma- tion and subgrain structures were formed during the primary creep stage. The stress exponent of n=5.6 at 25 ~31 MPa and activation energy Q: 135 i 70 KJ/mole at 760 ~806 0C for the PST suggest that the dislocation glide aided by pipe diffu- sion is the dominant mechanism of creep deformation in this microstructure condition. For the polycrystal, the stress exponent n=2~3 and the activation energies of Q: 229 j; 60 KJ/ mole (in Ar), Q: 574 :90 KJ/mole (in air) were found. The high activation energy and low stress exponent suggests that dynamic recrystallization occurs that the dislocation net- work forms, due to the normal transient, but glide is limiting. Creep characteristics of polycrystal are affected by dynamic recrystallization could cause the complicated creep behaviors which were observed. A composite model can account for multiple deformation mechanisms is suggested for interpretation of this kind of complicated creep behavior. The data analysis was aided by the modified G-projection equations for creep. The 100 101 implication of fitting parameters of G—projection equation provide a remarkable informa- tion to interpret the complicated creep behavior in TrAl. APPENDIX APPEN 21X PROGRAM CODES FOR CREEP TEST REM $INCLUDE: 'creep.inc' REM ***************************************************** REM * some important parameters: REM * REM * VL : the load REM * VSA : the strain of channel A(min volts) REM * VSB : the strain of channel B(min volts) REM * TCl : the temperature of specimen top REM * TC2 : the temperature of specimen bottom REM * FS : the final strain REM * FF : the final time REM * L0 : the initial specimen length REM * A0 : the initial specimen area REM * ID : the specimen ID REM * REM ***************************************************** REM DECLARE SUB get.data(V L,VSA,VSB,TC1,TC2) DECLARE SUB write.data(FILENAME$) DECLARE SUB average.data(Iavg%,VAVG,CTIME,VL,VSA,VSB,TCl) ************* REM declare the parameters ********4:*3101:3101:***************************** DEFDBL A-Z COMMON SHARED /data.buf/data.buf%() COMMON SHARED /chans/chans%() COMMON SHARED /gains/gains% () COMMON SHARED /volts.buf/volts.buf#() COMMON SHARED /CDATA/CDATA#() . COMMON SHARED /AVG/AVG#() COMMON SHARED /NUMPOINTS/NUMPOINTS AS INTEGER COMMON SHARED RATE/RATE AS DOUBLE COMMON SHARED NSBO/VSBO AS DOUBLE COMMON SHARED /dspace/dspace as string COMMON SHARED /Ikeep/Ikeep as integer COMMON SHARED /X/X#() COMMON SHARED /Y/Y#() 102 103 COMMON SHARED /hPanel/hPane1 as integer COMMON SHARED /count/count as integer COMMON SHARED /handle/handle as integer COMMON SHARED /Ifull/Ifull as integer CONST NUMCHANS% = 5 REM define data buffers for storing DIM data.buf%(5000) DIM volts.buf#(5000) DIM chans%(NUMCHANS%) DIM gains%(NUMCHANS%) DIM CDATA#(NUMCHANS%,SOO) DIM AVG#(4,20) DIM NOWDATE AS STRING * 20 DIM FILENAME AS STRING * 81 DIM buf as string * 80 DIM STARTDATE as string * 15 DIM STARTIME as string * 10 DIM scanarray#(10) DIM X#(2000) DIM Y#(2000) i% = 0 k..err% = 0 quitloopl% = O quitloop2% = 0 quitloop3% = 0 hPanel% = 0 varPanel%= 0 ctrl% = 0 numTimeOutTicks& = 0 NDAYS% = 0 PTSPERCHAN% = 200 ' the # of input channels ' buffer for storing binary data ' buffer for storing voltage data ' array storing channels ' array storing gains ' 6 channels of averaged data ' array to average 10 pts ’ the string storing current date ’ the output filename ' the string buffer ' the start date ' the start time ' the arrry for the data scanning from buf$ ' x-axis graph data(time) ' y-axis graph data(strain) ' loop counter and array index ' holds error code ' loop control flag#1 ' loop control flag#2 ' loop control flag#3 ' creep test panel handler ' VarChange panel handler ' control ID ' tick count for Timeout_Confi g '# of days of the experiment period ' the # of data to acquire per channel NUMPOINTS% = NUMCHANS%*PTSPERCHAN% ' total number of points ' to RATE = 5000# ’acquire ' sampling rate REM display the value of NUMCHANS,PTSPERCHAN,RATE ************ PRINT "Current acquisition parameters are: " PRINT NUMCHANS%; "channels" PRINT PTSPERCHAN%; "pts/chan" 104 PRINT RATE; "points/sec" REM fill the channel and gain arrays for MID-16 ************************** WHILE i% < NUMCHANS% chans%(i%) = i% gains%(i%) = 1 i% = i% + l WEND REM initializing the AT-MIO—l6 Board k..err% = Init.DA.Brds%(1, boardType%) k..err% = OpenlnterfaceManager% 'open the interface numTimeOutTicks& = (NUMPOINTS% / RATE) * 20 IF numTimeOutTicks& < 20 THEN numTimeOutTicks& = 20 END IF k..err% = Timeout.Config%(l, numTimeOutTicks&) REM iflpllt the output filenamc *************=1:*************************** k..err% = FileSelectPopup("","*.dat","The Output Filename " ,0,0,1,FILENAME$) SELECT CASE k..err% CASE 0 k..err% = FileSelectPopup("","*.dat","The Output Filename " ,0,0,l, FILENAME$) CASE 1 quitloop2% = CASE 2 quitloop2% = 0 CASE ELSE STOP END SELECT REM open and display panel *alnk**************************************** hPanel% = LoadPane1% ("creep.uir", CT %) varPanel% = LoadPanel%("creep.uir",VC%) k..err% = DisplayPanel% (hPanel%) 105 k..err% = HidePanel%(varPanel%) i..dummy% = SetCteral%(hPanel%, CT .ppc%, PTSPERCHAN%) i. .dummy%- — SetCteral%(hPanel%, CT .rate%, RATE) dspace$- -- " " IF quitloop2% = 1 THEN REM the continuing experiment REM Read the initial data 211******************************************** handle%=OpenFile(FILENAME$,0, 1, 1) IF handle% = -1 THEN i..dummy% = SetCteral%(hPanel%,CT.mw%,"error opening file") STOP ELSE END IF position& = SetFilePtr(handle%, O, O) n% = Readline(handle%,buf‘$,79) print buf$ n% = Scan (buf$, "%s>%5f[x]",scanarray#()) L0 = scanarray#(O) 'specimen length A0 = scanarray#(l) 'specimen area FS = scanarray#(Z) 'estimated final strain FT = scanarray#(3) 'estimated final time ID= scanarray#(4) 'specimen ID n%- — Readline(handle%, buf$ .79) n%- — Scan (buf$, ",%s>%s[xt44]%s[xt44]%4f[x]" STARTDATE$, ,STARTIME$ ,scanarray#()) CTIME = scanarray#(O) 'the time VL = scanarray#(l) 'the load VS A0 = scanarray#(2) 'the initial strain-A VSBO = scanarray#(3) 'the initial strain-B n% = Scan(STARTDATE$, "%s>%i[x]%i[x]", STARTMON%,STARTDAY%) n% = Scan(STARTIME$ , "%S>%i[x]%i[x]%i[x]", STARTHR% ,STARTMIN% ,STARTSEC%) i..dummy% = SetCteral%(hPanel%, CT.Sdate%, STARTDATE$) i..dummy% = SetCteral%(hPanel%, CT.Stime%, STARTIME$) REM decide to update plot or not 3k3k***=1:3k*alt*al:#3101:11:31:31:********************** k..err% = ConfirmPopup ("Would you like reload stored file to update plot?") IF k..err% = 1 THEN lkeep% = 0 Pts% = 0 WHILE quitloop1% = 0 n% = Readline (handle%, buf$, 79) 106 IF n% = -2 THEN quitloop1% = 1 ELSE END [F n% = Scan (buf$, "%s>%s[xt44]%s[xt44]%5f[x]" ,STARTDATES,STARTIME$,scanarray#()) CDATA#(I, Ikeep%) = scanarray#(l) CDATA#(3, Ikeep%) = scanarray#(3) CDATA#(4, Ikeep%) = scanarray#(4) IF Ikeep% < 4 or Ikeep% > 498 THEN Ikeep% = 4 ELSE ENDIF X#(pts%) = scanarray#(O) Y#(pts%) = scanarray#(3) - VSBO Ikeep% = Ikeep% + 1 Pts% = Pts% + l WEND i..dummy% = PlotXY% (hPanel%,CI‘.creepcurvel%,X#(),Y#() ,2000,4,4,2,2, 1,12) ELSE Ikeep% = 4 END IF i..dummy% = SetCteral%(hPanel%, CT .Pts%, Pts%) ELSE REM the new experiment i..dummy% = SetActiveCtrl%(CT.Ilength%) i..durruny% = SetCteral%(hPanel%, CT.mw%, " Please input specimen lengthz") i..dummy% = SetCteral%(hPanel%, CT .mw%, " Specimen areaz") i..dummy% = SetCteral%(hPanel%, CT.mw%, " Estimate final strainz") i..dummy% = SetCteral%(hPanel%, CT .mw%, " Specimen IDz") i..dummy% = SetCteral%(hPanel%, CT.mw%, " Estimeat final time:") REM display those initial data on the panel =1:*******>k********************** k..err% = GetUserEvent% (l, hPanel%, ctrl%) i - _0 fl. fl. .dummy% = GetCteral (hPanel%, CT .Ilength%, L0) .dummy% = GetCteral (hPanel%, CT .Iarea%, A0) ..dummy% = GetCteral (hPanel%, CT .Fstrain%, FS) ..dummy% = GetCteral (hPanel%, CT .Ftime%, FI‘) ..dummy% = GetCteral (hPanel%, CT .ID%, ID) 107 quitloop1% = 0 i..dummy% = SetCteral%(hPanel%, CT.mw%, "***ABOUT 1000 DATA TAKEN") i..dummy% = SetCteral%(hPanel%, CT.mw%, "BUT MORE AT FIRST STAGE***") CDATA#(O, 0) = L0 CDATA#(l, O) = A0 CDATA#(Z, 0) = FS CDATA#(3, 0) = FT CDATA#(4, 0) = ID REM Loop that waits for starting experiment ***************************** WHILE quitloopl% = O CTIME = 0 CALL get.data(VL, VSA,VSB, TCl, TC2) i..dummy% = SetCteral%(hPanel%, CT .Ctime%, CTIME) i..dummy% = SetCteral%(hPanel%, CT.Cstress%, VL) i..dummy% = SetCteral%(hPanel%, CT.Cstraina%, VSA) i..dummy% = SetCteral%(hPanel%, CT.Cstrainb%, VSB) i..dummy% = SetCtera1%(hPanel%, CT .Tc1%, TCl) i..dummy% = SetCteral%(hPanel%, CT.Tc2%, TC2) i..dummy% = SetCteral%(hPanel%, CT.Sdate%, DATE$) i..dummy% = SetCteral%(hPanel%, CT .Stime%, TIME$) k..err% = ConfirmPopup ("Is this the starting point?") IF k..err% = 1 THEN i..dummy% = SetCteral%(hPanel%, CT .Sdate%, DATES) i..dummy% = SetCteral%(hPanel%, CT .Stime%, TIMES) n% = Scan(DATE$, "%s>%i[x]%i[x]", STARTMON%, STARTDAY%) n% = Scan(TIME$, "%s>%i[x]%i[x]%i[x]", STARTHR% , STARTMIN%, STRATSEC%) VDO = VL VSAO = VSA VSBO = VSB TClO = TCl TC20 = TC2 CDATA#(O, l) = 0 CDATA#(I, l) = VLO 108 CDATA#(Z, 1) = VSAO CDATA#(3, 1) = VSBO CDATA#(4, 1) = TClO CDATA#(S, 1) = TC20 quitloop1% = l ELSE quitloopl% = 0 END IF WEND REM storing those initial data to output file ****************************** handle%=OpenFile (FILENAME$,0, 1, 1) IF handle% = -1 THEN i..durruny% = SetCteral% (hPanel%,CT.mw%,"error opening file") STOP ELSE END IF FOR I%=0 TO 4 n%=Fthile (handle% , "%s<%f[w0p4]%s",CDATA#(I%,0),dspace$) NEXT 1% . i..dummy% = SetCteral% (hPanel%,CT.mw%,"writing initial data to file") n%= Writefile (handle% ,CHR$(10), 1) IF n% = -1 THEN i..dummy% = SetCteral% (hPanel%,CT.mw%,"error writing to file") ELSE END IF n% = CloseFile (handle%) count% = 0 Ikeep% = 1 Pts% = 1 CALL write.data (FILENAME$) Ikeep% = 4 ENDIF quitloopl% = 0 VINC = FS * L0 * 10*1000 / .l /300 ’ the criteria of taking data datapointsl% = 700 datapoint32% = 300 StressChange% = 10 109 TempChange% = 20 count% = 0 TINC = FT/400 ' final time / 400 TNEXT = TINC ' time indicator of whether it is time to take data lavg% = 0 VAVG = 0 [full% = 0 print "tnext="; tnext i..dummy% = SetCteral% (hPanel%, CT .Ilength%, L0) i..dummy% = SetCteral% (hPanel%, CT .Iarea%, A0) i..dummy% = SetCteral% (hPanel%, CT .ID,ID) i..dummy% = SetCteral% (hPanel%, CT.Fstrain%, FS) i..dummy% = SetCteral% (hPanel%, CT.Ftime%, FT) i..dummy% = SetCteral% (hPanel%, CT .mw%,"Press Go for starting test or ") i..dummy% = SetCteral% (hPanel%, CT.mw%, "Press Quit for stop ...... ") REM Loop that takes the data, more rapidly for first .2% ******************** WHILE quitloop1% = 0 k..err% = GetUserEvent% (1, hPanel%, ctrl%) SELECT CASE ctrl% CASE CT .quit% quitloopl% = ConfirmPopup% ("Do you want to quit??") CASE ELSE WHILE quitloopl% = 0 k..err% = GetUserEvent% (O, hPanel%, ctrl%) SELECT CASE ctrl% CASE CT.quit% quitloopl% = ConfirmPopup% (”Do you want to quit??") CASE CT .zoomin% i..dummy% = SetCteral% (hPanel%, CT.mw%,"Set Mintime and Maxtime") i..dummy% = SetCteral% (hPanel%, CT .mw%, "and Press Zoomin again") n% = SetActiveCtrl (CT. MinTime%) 110 k..err% = GetUserEvent% (1, hPanel%, ctrl%) i..dummy% = GetCteral (hPanel%, CT .MinTime%, Tmin) i..dummy% = GetCteral (hPanel%, CT .MaxTime%, Tmax) n% = ConfigureAxes (hPanel%,CT.meepcurvel%,0,Tmin,Tmax,1,0,0) i..dummy% = SetCteral% (hPanel%, CT.mw%,"Press Zoomout to return") i..dummy% = SetCteral% (hPanel%, CT.mw%,"to auto time-scaling mode") CASE CT .zoomout% n% = ConfigureAxes (hPanel%,CTcreepcurvel %,l ,0,0, 1,0,0) i..dummy% = SetCteral% (hPanel%, CT .mw%, "Press Go for continuing") CASE CT .VarChange% n% = HidePanel (hPanel%) n% = InstallPopup (varPanel%) quitloop3% = 0 WHILE quitloop3% = 0 k..err% = GetPopupEvent% (1,ctrl%) SELECT CASE ctrl% CASE VC.rate% n% = PromptPopup ("Enter New rate value: ",buf$,10) n% = Scan (bufiB , "%s>%f[x]", RATE) n% = SetCteral% (varPanel%, VC.newrate%,RATE) n% = SetActiveCtrl% (VC.ppchan%) CASE VC.ppchan% n% = PromptPopup ("Enter New PtsPerChan value: ",buf$,10) n% = Scan (buf$ , "%s>%i[x]", PTSPERCHAN%) n% = SetCteral% (varPanel%, VC.newppc%,PTSPERCHAN%) n% = SetActiveCtrl% (VC.SChange%) NUMPOINTS% = NUMCHANS%*PTSPERCHAN% CASE VC.SChange% n% = PromptPopup ("Enter New Stress Changes:(Default value is 10)” ,buf$,10) n% = Scan (buf$ , "%s>%i[x]", StressChange%) n% = SetCteral% (varPanel%, VC.NewSC%,StressChange%) n% = MessagePopup ("Be sure to change VINCl before you start !!") 111 n% = SetActiveCtrl% (VC.TChange%) CASE VC.TChange% n% = PromptPopup ("Enter new Temp Changes: (Default value is 20)" ,buf$,10) n% = Scan (buf$ , "%s>%i[x]", TempChange%) n% = SetCteral% (varPanel%, VC.NewTC%,TempChange%) n% = MessagePopup ("Be sure to change VINC] before you start !!") n% = SetActiveCtrl% (VC.VINC1%) CASE VC.VINC1% n% = MessagePopup ("VlNCl = FS * LO * 10*1000 / .1 /datapointsl") n% = PromptPopup ("Enter new VINCl value: (# of datapoints) ",buflB,10) n% = Scan (buf$ , "%s>%i[x]", datapointsl%) VINC1= FS * L0 * 10*1000 / .1 /datapointsl% n% = SetCteral% (varPanel%, VC.NewVINC1%,VINC1) n% = SetActiveCtrl% (VC.OK%) CASE VC.VINC2% n% = MessagePopup ("VINC2 = FS * L0 * 10*1000 / .1 /datapoint82") n% = PromptPopup ("Enter new VINC2 value: (# of datapoints) ",buf$, 10) n% = Scan (buf$ , "%s>%i[x]", datapoints2%) VINC2 = FS * L0 * 10*1000 / .1 /datapoints2% n% = SetCteral% (varPanel%, VC.NewVINC2%,VINC2) n% = SetActiveCtrl% (VC.OK%) CASE ELSE quitloop3% =1 END SELECT WEND n% = RemovePopup(0) n% = DisplayPanel (hPanel%) i..dummy% = SetCteral% (hPanel%, CT.rate%, Rate) i..dummy% = SetCteral% (hPanel%, CT.ppc%,PTSPERCHAN%) CASE CT .storedata% Ikeep% = Ikeep% + 1 Pts% = Pts% + 1 CDATA#(O, Ikeep%) = CTIME 112 CDATA#(l, Ikeep%) = VL CDATA#(2, Ikeep%) = VSA CDATA#(3, Ikeep%) = VSB CDATA#(4, Ikeep%) = TCl CDATA#(S, Ikeep%) = TC2 CALL write.data(FILENAME$) Ikeep% = Ikeep% + count% count% = 0 CASE ELSE i..dummy% = SetCteral%(hPanel%, CT .mw%,"Creep test is proceeding...") REM calculate the time from last time to now ***************** n% = Scan (DATE$, "%s>%i[x]%i[x]" ,NOWMONTH% ,NOWDAY%) n% = Scan (THVIE$, "%s>%i[x]%i[x]%i[x]", NOWHR%,NOWMIN%, NOWSEC% ) SELECT CASE NOWMONTH% CASE 1,2,4,6,8,9,11 NDAYS% = NOWDAY% - STARTDAY% + (NOWMONTH%- STARTMON%)*31 CASE 3 NDAYS% = NOWDAY% - STARTDAY% + (NOWMONTH%- STARTMON%)*28 CASE 5,7,10,12 NDAYS% = NOWDAY% - STARTDAY% + (NOWMONTH%- STARTMON%)*30 END SELECT CALL get.data(VL, VSA, VSB,TC1, TC2) CTIME = (NDAYS% * 24)+(NOWHR%-STARTHR%)+ (NOWMlN%-STARTMIN%)/60+(NOWSEC%-STARTSEC%)/36OO IF X#(Ikeep%-1)- CT [ME = 0 THEN recently = 0 ELSEIF X#(Ikeep%-3)-X#(lkeep%-l) = 0 THEN strainrate = O ELSE recently=(Y #(Ikeep%-1)-VSB+VSBO)*0.0000 1/LO/ (X#(Ikeep%- l )-CTIME)/ 3 600 strainrate=(Y#(Ikeep%-3)-Y#(Ikeep%-1))*0.00001/L0/ (X#(Ikeep% -3)—X#(lkeep%- 1 ))/ 3600 END IF fl. - ~o - flo Ho fl. ~o ~o “I 113 .dummy% = SetCteral%(hPanel%, CT .sr%, strainrate) .dummy% = SetCteral%(hPanel%, CT.recently%, recently) ..dummy% = SetCteral%(hPanel%, CT.Ctime%, CT IME) .dummy% = SetCteral%(hPanel%, CT.Cstress%, VL) ..dummy% = SetCteral% (hPanel%, CT .Cstraina%, VSA) .dummy% = SetCteral% (hPanel%, CT .Cstrainb%, VSB) .dummy% = SetCteral% (hPanel%, CT .Tc1%, TCl) ..dummy% = SetCteral% (hPanel%, CT .Tc2%, TC2) ..dummy% = SetCteral% (hPanel%, CT Pts%, Pts%) .dummy% = SetCteral% (hPanel%,CT.count%,count%) vs = ABS (VSB - CDATA#(3,]keep%)) so = ABS (VL - CDATA#(1,Ikeep%-3)) TC = ABS (TCl - CDATA#(4,Ikeep%-3)) REM Check if the stress changes greater than StressChanges% REM (Default value is 10) OR REM the temperature changes greater than TempChange% REM (Default value is 20) IF SC > StressChange% OR TC > TempChange% THEN VINCl = FS * LO * 10*1000 /0.1/ datapointsl% VINC = VINC] ELSE VINC2 = FS * L0 * 10*1000 / .1 /datapoints2% VINC = VINC2 END IF i..dummy% = SetCteral% (hPanel%, CT.VINC%, VINC) REM Check if need to store data in keeping array ************************* IF VS > VINC AND VINC = VINC] THEN Ikeep% = Ikeep% + 1 Pts% = Pts% + 1 count% = count% + l CDATA#(O, Ikeep%) = CTIME CDATA#(l, Ikeep%) = VL CDATA#(2, Ikeep%) = VSA CDATA#(3, Ikeep%) = VSB CDATA#(4, Ikeep%) = TC] CDATA#(S, Ikeep%) = TC2 ELSEIF VS > VINC AND VINC = VINC2 THEN CALL average.data (lavg%,VAVG,CTIME,VL,VSA,VSB,TC1) i..dummy% = SetCteral% (hPanel%,CT.Iavg%,Iavg%) 114 IF ABS (VAVG - CDATA#(3,]keep%)) > VINC AND ABS(V AVG) > 0 THEN lavg% = 0 lfull% = 0 Ikeep% = Ikeep% + 1 Pts% = Pts% + l CDATA#(O, Ikeep%) = CT IME CDATA#(I, Ikeep%) = VL CDATA#(2, Ikeep%) = VSA CDATA#(3, Ikeep%) = VSB CDATA#(4, Ikeep%) = TCl CDATA#(S, Ikeep%) = TC2 CALL write.data (FILENAME$) Ikeep% = Ikeep% + count% count% = 0 ELSE END IF ELSE END IF TNEXT = CTIME+ TINC i..dummy% = SetCteral% (hPanel%,CT.Iavg%,Iavg%) REM ChCCk if Ikeep% > 500 *****31:************************************* IF Ikeep% > 498 THEN CALL write.data (FILENAME$) count% = 0 Ikeep% = 3 ELSE END IF END SELECT WEND END SELECT WEND REM Close all files and interfaces ************************************** n%=CloseFile (handle%) k..err% = Init.DA.Brds% (l, boardtype%) k..err% = CloselnterfaceManager% REM subprogram for data acquirization ********************************* 115 SUB get.data (VL, VSA, VSB, TCl, TC2 ) k..err% = SCAN.Op% (1,NUMCHANS%,chans%(),gains%(), data.buf%(),NUMPOINTS%,RATE,0.0#) k..err% = DAQ.Scale (l,1,numpoints%,data.buf%(),volts.buf#()) 1% = 0 VL = 0 VSA = 0 VSB = 0 TC] = 0 TC2 = 0 WHILE 1% < NUMPOINTS% —1 VL = VL + volts.buf#(J%) VSA = VSA + volts.buf#(J% + 1) VSB = VSB + volts.buf#(J% + 2) TCl = TCl + volts.buf#(J% + 3) TC2 = TC2 + volts.buf#(J% + 4) J% = 1% + NUMCHANS% WEND J% = NUMPOINTS%/NUMCHANS% VL = (VL/J%)*1000 -5 VSA = (VSA/J%)*1000 VSB = (VSB/J%)*1000 TCl =(TC1/J%)*1000 TC2 = (TC2/J%)*1000*100 END SUB REM subprogram for Store data to file *aI::Ic=1:*akak*akakakak*********************** SUB write.data (FILENAME$) handle%=OpenFile (FILENAME$,0, l, 1) IF handle% = -1 THEN i..dummy% = SetCteral% (hPanel%,CT.mw%,"error opening file") STOP ELSE END IF Ikeep% = Ikeep% - count% FOR K% = 0 TO count% n%=Fthile (handle% , "%s<%s[wl4]%s[w2]%s[w9]%s[w2]" ,DATE$,dspace$,TIME$,dspacc$) FOR I%=0 TO 4 n%=Fthile (handle% , "%s<%f[w9p2]%s[w2]" 116 ,CDATA#(I%,Ikeep%+K%),dspace$) NEXT 1% i..dummy% = SetCteral% (hPanel%,CT.mw% ,"writing data to file") i..dummy% = SetCteral% (hPanel%,CT.count%,K%) n%=Writefile (handle% , CHR$(10),1) IF n% = -1 THEN i..dummy% = SetCteral% (hPanel%,CT.mw% ,"error writing to file") ELSE END IF X#(Ikeep%+K%) = CDATA#(O, Ikeep%-I—K%) Y#(Ikeep%+K%) = CDATA#(3, Ikeep%+K%) - VSBO REM plot the graph********************31¢***************************** i..dummy% = PlotXY% (hPanel%,CT.creepcurvel%,X#(),Y#() ,2000,4,4,2,2,], 12) NEXT K% n% = CloseFile(handle%) END SUB REM subprogram for averaging data *akakak*akak>1:2k>1:*akakak*********************** SUB average.data (lavg%,VAVG,CTIME,VL,VSA,VSB,TCl) AVG#(O, lavg%) = CTIME AVG#(l, lavg%) = VL AVG#(2, lavg%) = VSA AVG#(3, lavg%) = VSB AVG#(4, lavg%) = TCl lavg% = lavg% + 1 IF lavg% = 20 THEN VL = 0 VSA = 0 VSB = 0 TC] = 0 FOR 1% = 0 TO 19 VL = VL + AVG#(1,I%) VSA = VSA + AVG#(2,1%) VSB = VSB + AVG#(3, 1%) TC] = TCl + AVG#(4, 1%) NEXT 1% AVG#(O,20) = AVG#(0,0) CTIME = (AVG#(0,lavg%-l)+AVG#(0,lavg%))/2 VL = VL/20 VSA = VSA/2O END IF END SUB 117 VSB = VSB/20 VAVG = VSB TCl = TC1/20 Ifull% = l lavg% = 0 ELSEIF Ifull% = 1 THEN VL = 0 VSA = 0 VSB = 0 TC] = 0 FOR 1% = 0 TO 19 VL = VL + AVG#(1,I%) VSA = VSA + AVG#(2, 1%) VSB = VSB + AVG#(3, 1%) TCl = TCl + AVG#(4, 1%) NEXT 1% AVG#(O,20) = AVG#(0,0) CTIME = (AVG#(0,Iavg%-l)+AVG#(0,Iavg%))/2 VL = VL/20 VSA = VSA/20 VSB = VSB/20 VAVG = VSB TCl = TCI/ZO ELSE VAVG = O LIST OF REFERENCES W [1] T. 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