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thesis entitled

Silica Coatings on Bismaleimide Substrates

presented by

Chinmoy Mukherjee

has been accepted towards fulfillment
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Master's degree in Materials Science

 

 

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ma alumna-41659.14

SILICA COATINGS ON BISMALEIMIDE SUBSTRATES
By

Chinmoy Mukherjee

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

1999

ABSTRACT

SILICA COATINGS ON BISMALEIMIDE SUBSTRATES
By

Chinmoy Mukherjee

Neat (unreinforced) BMI specimens were coated with a thin, protective layer of a dense
silicate ceramic material. Vickers indentation testing on the coated and uncoated BMI
specimens was carried out to get an idea of point contact damage to a first approximation.
Amount of silica coating spalled off from an indentation was measured as a function of
indentation load and for different curing temperatures. Spalling for BMI specimens
having coatings cured at 175°C for one hour (0.5% to 5%) was considerably less
compared to spalling for BMI specimens (15% to 25%) with coatings cured at ”0°C for
20 minutes. Crack spacings were characterized at constant loads for unabraded and
abraded coatings, and their distribution studied. Mean crack spacings were independent
of the indentation load for BMI specimens with coatings cured at 150°C for twenty
minutes. However for BMI specimens with coatings cured at 175°C for one hour, the
mean crack spacing increased 47% over a load range of 2.94 N to 196 N. The mean

crack spacing normalized with respect to half the total crack dimension when plotted
against Indentation load is consrstent With the power law relationship, ,u/a = (p P .
In addition, the silica coating slowed the uptake of water during water-immersion

testing 1.7 times. An expression for the mass change as a function of time due to the

diffusion of water into the BMI specimens was developed in Section 3.6.

ACKNOWLEDGEMENTS

I would like to thank my advisor Dr. Eldon D. Case, whose performance as an
advisor was exemplary. His guidance and motivation enabled to bring out the best in me.
I would like to thank my family for their support and encouragement. Also I would like
to thank Ann Xiang (MS Candidate, MSM department, MSU) for her help in Visual
Basic programming. This work was funded by the Research Excellence Fund of the State

of Michigan, administered through the Composite Materials and Structures Center.

iii

TABLE OF CONTENTS

List of Tables

List of Figures

1.

2.

INTRODUCTION

1.1 Polymer-ceramic combinations

1.2 Bismaleimide chemistry

1.3 Silica coatings on BMI

EXPERMENT AL PROCEDURE

2.1 Materials used

2.2 Specimen preparation

2.3 Characterization of coated BMI

2.4

2.5

2.6

2.7

2.8

2.3.1 Vickers indentation technique
2.3.2 Rockwell indentation technique

2.3.3 Measurement of silica film island gaps and crack lengths on
silica coated BMI specimens

2.3.4 Measuring percentage of coating spalled off from an
indentation

Scanning electron microscopy

Coating thickness measurements using ESEM
Inter crack spacing measurements

Abrading silica coated BMI specimens

Mass change upon immersion in water

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3. RESULTS AND DISCUSSION

3.1 Uncured BMI and coating quality

3.2 Coating thickness effects

3.3 Vickers indentation damage

3.4

3.5

3.3.1 Comparison of the semi-macro indentor with the micro
indentor

3.3.2 Study of Vickers indentation damage
3.3.3 Spalling area fraction as a function of curing conditions

3.3.4 Indentation dimension analysis as a function of load for
Vickers indents

3.3.5 Vickers indent dimension as a function of loading rate and
load time

Rockwell indentation damage
ESEM observations and statistical analysis of crack pattern
3.5.1 Mean crack Spacing as a function of indentation load

3.5.2 Comparison of scatter in spacings of abraded coatings
versus unabraded coatings at constant loads

3.5.3 Scatter increase with distance from the center of the indent

3.5.4 Order statistics study to determine distribution of crack
spacings

3.6 Mass change measurements

4. CONCLUSIONS

5. FUTURE STUDIES

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APPENDICES

Appendix A. Curing and coating conditions for specimens used to measure
coating thicknesses (Section 3.2).

Appendix B. Curing and coating conditions for specimens used in mass
absorption experiments, along with dimensions and time of water
immersion (Section 3.6).

Appendix C. Curing and coating conditions for specimens used in scatter
spacing measurements, along with R-square values for order statistic plots
for different loads (Section 3.5).

Appendix D. Curing and coating conditions for specimens used to make
Vickers Indentations and study effect of not precuring specimens (Section
3.3.42 and Section 3.3.4).

Appendix E. Curing and coating conditions for specimens used to study
Hertzian indents (Section 3.4).

Appendix F. Curing conditions and dimensions for uncoated Specimens
used in varying load time and loading rate Vickers indentations (Section
3.3.5).

Appendix G. Curing and coating conditions for specimens used to
calculate fractional spalled of area from indentations (Section 3.3.3).

Appendix H. Visual basic macro program to calculate the lowest P value
corresponding to point (1), in a set of crack spacings for any given
indentation load (Section 3.5.3).

Appendix 1. Raw crack spacings data for 2.94 N and 4.9 N indentation
loads for BMI specimen with unabraded silica coating cured at 150°C for
20 minutes (Figures 20 and 21) and 175°C for one hour (Figures 28 and
29).

Appendix J. Raw crack spacings data for 9.8 N and 49 N indentation loads
for BMI specimen with unabraded silica coating cured at 150°C for 20
minutes (SUAl, Figure322 and 23 ) and 175°C for one hour (CR1, Figures
30 and 31) and, BMI with abraded coating cured at 150°C for 20 minutes.

Appendix K. Raw crack spacings data for 98 N and 196N indentation
loads for BMI specimen with unabraded silica coating cured at 150°C for
20 minutes (SUAl, Figures 24 and 25 ) and 175°C for one hour (CR1,
Figures 32 and 33).

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Appendix L. Indent dimension raw data, which was included in Figures
5a and 5b. Averages of indent dimensions (6 to 10 indents) were taken,
when plotting indentation dimension versus indentation load. 137

vii

LIST OF TABLES

Table 1. The average of 6 total crack dimension values 2D, for
indentations at 3 different loads in the semi-macro indentor (Specimen B,
Appendix D) and the micro indentor (Specimen B 1 , Appendix D).

Table 2. The crack dimension measurement of a 9.8 N indent made by the
semi macro indentor on specimen Bl (Appendix D), measured by the
optical read out in the semi macro indentor and the micro indentor.

Table 3. Average Total indent dimension (2a) raw data as a function of
indentation loads for figures 5a and 5b.

Table 4. Average of mean crack spacings for six indentations at each
indentation load for the specimens listed in Appendix C.

Table 5. The pre-exponent (p and exponent 8 obtained from least squares
fitting of of figure 19 using equation 5.

Table 6. Mean crack spacing data for various indentation loads for BMI
Specimens with unabraded coatings cured at 150°C at 20 minutes and cured
at 175°C at 60 minutes. -

Table 7. MSFA values (equation 4) for BMI with unabraded and abraded
coatings cured at 150°C for 20 minutes and BMI with unabraded coatings
cured at 175°C for 20 minutes.

Table 8. Number of concentric cracks/unit length as a function of
indentation load for BMI with unabraded and abraded silica coatings, cured
at 150°C for 20 minutes and for unabraded silica coatings cured at 175°C
for 1 hour.

Table 9. The standard deviations from mean crack spacings for BMI
specimens with unabraded and abraded coatings cured at 150°C for twenty
minutesand BMI specimens with unabraded coatings cured at 175°C for
one hour.

Table 10. The distance of point, (i), from the center of the indent, along
with the r) values (equation 9), for various indentation loads.

Table 11. Coefficients 0t and B obtained from the least-squares fit of
equation 17b to the MN versus t"2 data.

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Table A. Curing and coating conditions for specimens used to measure
coating thicknesses (Section 3.2).

Table B. Curing and coating conditions for specimens used in mass
absorption experiments, along with dimensions and time of water
immersion (Section 3.6).

Table C1. Curing and coating conditions for specimens used in scatter
spacing measurements, along with mean spacing values at different loads
(Section 3.5).

Table C2. R-square values for order statistics plots for indentations made
on specimens listed in table C1.

Table D. Curing and coating conditions for specimens used to make
Vickers Indentations and study effect of not precuring specimens (Section
3.3.42 and Section 3.3.4).

Table E. Curing and coating conditions for specimens used to study
Hertzian indents (Section 3.4).

Table F. Curing conditions and dimensions for uncoated specimens used
in varying load time and loading rate Vickers indentations (Section 3.3.5).

Table G. Curing and coating conditions for specimens used to calculate
fractional spalled of area from indentations (Section 3.3.3).

Table 1. Raw crack spacings data for 2.94 N and 4.9 N indentation loads
for BMI specimen with unabraded silica coating cured at 150°C for 20
minutes (Figures 20 and 21) and 175°C for one hour (Figures 28 and 29).

Table J. Raw crack spacings data for 9.8 N and 49 N indentation loads for
BMI specimen with unabraded silica coating cured at 150°C for 20 minutes
(SUAl, FiguresZZ and 23 ) and 175°C for one hour (CR1, Figures 30 and
31) and, BMI with abraded coating cured at 150°C for 20 minutes.

Table K. Raw crack spacings data for 98 N and 196N indentation loads
for BMI specimen with unabraded silica coating cured at 150°C for 20
minutes (SUAl, Figures 24 and 25 ) and 175°C for one hour (CR1, Figures
32 and 33).

Table L. Indent dimension raw data, which was included in Figures 5a

and 5b. Averages of indent dimensions (6 to 10 indents) were taken, when
plotting indentation dimension versus indentation load.

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137

LIST OF FIGURES

Figure 1. The thickness of silica coating on BMI substrates as a function
of the spinning speed. The BMI (BMPM:DABPA=1:1.13 and
BMPMzDABPA = 1:1, Appendix A) substrates were first precured at
200°C for 1 hour, then the coated specimens were cured at 150°C for 20
minutes.

Figure 2. Micrograph of z 2.5 micron thick silica coating on BMI showing
separated islands of the coating. The specimen, with substrate
stoichiometry BMPM:DABPA=1:1 (Appendix A), was pre cured at 200°C
for 1 hour, coated at 500 rpm for 20 seconds and then cured at 150°C for 20
minutes.

Figure 3(a). Schematic of delaminated Silica coating on BMI substrate and
Figure 3(b). Schematic of a spalled region of the silica coating on a BMI
substrate.

Figure 4. Schematic of Vickers indent impressions on (a) an uncoated BMI
specimen and (b) a coated BMI specimen.

Figure 5 (a). Logarithmic plot for indentation dimension versus
indentation load for uncoated and coated BMI specimens of different
chernistries (BMPMzDABPA = 1:1, 1:0.82, 1:1.13, Appendix D) and
Figure 5 (b). Logarithmic plot for indentation dimension versus
indentation load for uncoated and coated BMI specimens of the same
stoichiometry (BMPMzDABPA = 1:1, Appendix D).

Figure 6. Micrograph of a Vickers indent made at a load of 49 N on an
uncoated BMI specimen (BMPM: DABPA = 1:1, Specimen CR1,
Appendix G). The BMI was precured at 200°C for 1 hour and again cured
at 150°C for 20 minutes.

Figure 7. Micrograph of 9.8 N Vickers indent made on coated BMI
specimen where the coating thickness was = 0.15 microns. The specimens
were precured at 200°C for 1 hour, coated at 3500 rpm for 20 seconds a)
cured at 150°C for 20 minutes (Specimen CR1, Appendix G) and, b) cured
at 175°C for one hour (Specimen CR3, Appendix G).

Figure 8. For the same indented specimen as shown in Figure 7a, a higher
magnification view of the array of concentric cracks that comprise the
indentation crack field. The center of the indent impression and a spalled
region of the coating are shown.

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Figure 9. Fraction of silica film spalled off from an indentation as a
function of indentation load, for BMI with unabraded silica coatings cured
at O - 150°C for 20 minutes, and A - 175°C for 1 hour.

Figure 10. Micrograph showing a coating delamination and crack
associated with a pair of closely spaced 49 N Vickers indentations on a
coated BMI specimen (BMPMzDABPA = 1:1, Specimen K2, Appendix D)
This is the only example of a coating delamination that was observed in
this study.

Figure 11. Micrograph showing a pair of closely Spaced 9.8 N Vickers
indentations on a coated BMI specimen (BMPMzDABPA = 1:1, Specimen
CR2, Appendix G).

Figure 12. Indentation dimension plotted as a function of indentation load
time at a loading rate of 50 microns/second, at loads of 4.9 N and 49 N for
uncoated BMI specimens of three different chemistries (L1, L2 and L3,

Appendix F).

Figure 13. Indentation dimension plotted as a function of loading rate at a
load time of 10 seconds at loads of 4.9 N and 49 N, for uncoated BMI
Specimens of three different chemistires (L1, L2 and L3, Appendix F).

Figure 14. Rockwell indentation on the HRF scale depicting concentric
circular crack pattern on a silica coated BMI specimen (R1, Appendix E).

Figure 15. Micrograph depicting the transition region from complete
Hertzian cracks to incomplete hertzian cracks, in the same indent as Figure
14.

Figure 16. Micrograph depicts the incomplete Hertzian cracks at a higher
magnification for the same indent as Figure 14.

Figure 17. Micrograph depicting the radial cracks originating from the end
of the region that included the incomplete Hertzian cracks on the same
indent as Figure 14.

Figure 18. Mean crack spacing data plotted versus various indentation
loads for BMI Specimens with unabraded coatings cured at 150°C at 20
minutes and cured at 175°C at 60 minutes.

Figure 19. Logarithmic plot of mean crack spacing data versus various

indentation loads for BMI specimens with unabraded coatings cured at
150°C at 20 minutes and cured at 175°C at 60 minutes.

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Figure 20. Crack spacing data dij, for a Vickers indent made at a load of
2.94 N, on specimen SUAl (Appendix C), plotted against the radial
position from the center of the indent.

Figure 21. Crack spacing data dij, for a Vickers indent made at a load of
4.9 N, on specimen SUAl (Appendix C), plotted against the radial position
from the center of the indent.

Figure 22. Crack spacing data (in, for a Vickers indent made at a load of
9.8 N, on specimen SUAl (Appendix C), plotted against the radial position
from the center of the indent.

Figure 23. Crack spacing data dii, for a Vickers indent made at a load of
49 N, on specimen SUAl (Appendix C), plotted against the radial position
from the center of the indent.

Figure 24. Crack spacing data dij, for a Vickers indent made at a load of 98
N, on specimen SUA4 (Appendix C), plotted against the radial position
from the center of the indent.

Figure 25. Crack spacing data dig, for a Vickers indent made at a load of
196 N, on specimen SUA4 (Appendix C), plotted against the radial
position from the center of the indent.

Figure 26. Crack spacing data dii, for a Vickers indent made at a load of
9.8 N, on specimen SAl (Appendix C), plotted against the radial position
from the center of the indent.

Figure 27. Crack spacing data dij, for a Vickers indent made at a load of
49 N, on specimen SAl (Appendix C), plotted against the radial position
from the indent.

Figure 28. Crack spacing data dij, for a Vickers indent made at a load of
2.94 N, on an silica coated BMI specimen cured at 175°C for one hour (CR
3, Appendix C), plotted against the radial position from the center of the
indent.

Figure 29. Crack spacing data dij, for a Vickers indent made at a load of
4.9 N, on an silica coated BMI specimen cured at 175°C for one hour
(CR3, Appendix C), plotted against the radial position from the center of
the indent.

Figure 30. Crack spacing data dij, for a Vickers indent made at a load of
9.8 N, on an silica coated BMI specimen cured at 175°C for one hour
(CR3, Appendix C), plotted against the radial position from the center of
the indent.

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Figure 31. Crack spacing data dij, for a Vickers indent made at a load of 49
N, on an silica coated BMI specimen cured at 175°C for one hour (CR3,
Appendix C), plotted against the radial position from the center of the
indent.

Figure 32 .Crack spacing data dij, for a Vickers indent made at a load of
98 N, on an silica coated BMI specimen cured at 175°C for one hour (CR3,
Appendix C), plotted against the radial position from the center of the
indent.

Figure 33. Crack spacing data dii, for a Vickers indent made at a load of
196 N, on an silica coated BMI Specimen cured at 175°C for one hour
(CR3, Appendix C), plotted against the radial position from the center of
the indent.

Figure 34. Crack spacing data d“, for a Hertzian indent made on the HRF
scale, on specimen SUA3 (Appendix C), plotted against the radial position
from the center of the indent impression.

Figure 35. Point (21, normalized by radial crack field dimension “a” for
coated BMI specimens (SUAl, SUA4, Appendix C), plotted as a function
of indentation load.

Figure 36. Schematic depicting uniform distribution of residuals.

Figure 37. For the distance between the i‘h and j‘h crack, dij, ordered
residual spacings versus expected value of order statistics for a 2.94 N
indent on an silica coated BMI specimen (SUA4, Appendix C) with an
unabraded coating.

Figure 38. For the distance between the i“ and ju‘ crack, dij, ordered
residual spacings versus expected value of order statistics for a 49 N
indent on an silica coated BMI specimen (SUA4, Appendix C) with an
unabraded coating.

Figure 39. For the distance between the iih and jth crack, dig, ordered
residual crack spacings versus expected value of order statistics for a 9.8
N indent on an silica coated BMI specimen (SUAl, Appendix C) with an
unabraded coating.

Figure 40. For the distance between the iih and jth crack, dij, ordered
residual spacings versus expected value of order statistics for a 49 N
indent on an silica coated BMI Specimen (SUAl, Appendix C), with an
unabraded coating.

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Figure 41. For the distance between the ith and j‘h crack, (in, ordered
residual crack spacings versus expected value of order statistics for a 98 N
indent on an silica coated BMI specimen (SUA4, Appendix C), with an
unabraded coating.

Figure 42. For the distance between the i‘h and jth crack, dij, ordered
residual crack spacings versus expected value of order statistics for a 196
N indent on an silica coated BMI specimen (SUA4, Appendix C), with an
unabraded coating.

Figure 43. For the distance between the iih and j‘h crack. dij. ordered
residual spacings versus expected value of order statistics for a 9.8 N
indent on a coated BMI specimen (SAl, Appendix C) with an abraded
silica film.

Figure 44. For the distance between the iih and j'h crack, dii, ordered
residual spacings versus expected value of ordered statistics for a 49 N
indent on a coated BMI specimen (SAl, Appendix C) with an abraded
silica film.

Figure 45. For the distance between the i'h and j'h crack, d.i, ordered
residual spacings versus expected value of ordered statistics for a 2. 94 N
indent on a coated BMI specimen cured at 175 0C for one hour (CR3,
Appendix H) with an abraded Silica film.

Figure 46. For the distance between the i"I and j'h crack, d.i, ordered
residual spacings versus expected value of ordered statistics for a 9. 8 N
indent on a coated BMI Specimen cured at 175 0C for one hour (CR3,
Appendix C) with an abraded silica film.

Figure 47. For the distance between the ilb and j‘h crack, dig, ordered
residual spacings versus expected value of ordered statistics for a 9. 8 N
indent on a coated BMI specimen cured at 175 0C for one hour (CR3,
Appendix G) with an abraded silica film.

Figure 48. For the distance between the i"1 and j‘h crack, d.i, ordered
residual spacings versus expected value of ordered statistics for a 49 N
indent on a coated BMI specimen cured at 175 0C for one hour (CR3,
Appendix C) with an abraded silica film.

Figure 49. For the distance between the i‘h and jth crack, dfi, ordered
residual spacings versus expected value of ordered statistics for a 98 N
indent on a coated BMI specimen cured at 1750 C for one hour (CR3,
Appendix C) with an abraded silica film.

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Figure 50. For the distance between the i'h and j‘h crack, d.i, ordered
residual spacings versus expected value of ordered statistics for a 196 N
indent on a coated BMI specimen cured at 175 0C for one hour (CR3,
Appendix C) with an abraded Silica film.

Figure 51. For the distance between the iih and jth crack, dig, ordered
residual spacings versus expected value of order statistics for a Rockwell
indent on a coated BMI specimen (SUA3, Appendix C), with an
unabraded silica film.

Figure 52. For the distance between the iih and j'11 crack, dii, from the
center of the indent until the point (i), ordered residual spacings versus
expected value of order statistics for a 49 N Vickers indent on a coated
BM] specimen (SUAl, Appendix C), with an unabraded silica film.

Figure 53. For the distance between the iih and jth crack, dij, from the point
4) to the end of the indent, ordered residual spacings versus expected value
of order statistics for a 49 N Vickers indent on a coated BMI specimen
(SUAl, Appendix C), with an unabraded silica film.

Figure 54. For the distance between the iih and j‘h crack, dij, from the
center of the indent until the point 6, ordered residual spacings versus
expected value of order Statistics for a 196 N Vickers indent on a coated
BMI specimen (SUA4, Appendix C), with an unabraded silica film.

Figure 55. For the distance between the im and j‘h crack, dij, from the
point (i) to the end of the indent, ordered residual spacings versus expected
value of order statistics for a 196 N Vickers indent on a coated BMI
specimen (SUA4, Appendix C), with an unabraded silica film.

Figure 56. Schematic of the diffusion of water into the BMI during water
immersion testing.

Figure 57. Normalized mass change, MN, versus t"2 for BMI specimens
with (a) all 6 sides coated and (b) uncoated BMI specimens
(BMPMzDABPA = 1:0.82). The solid curves represent a least -squares fit
of the data to equation (17b).

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1.0 INTRODUCTION

1.1 Polymer ceramic combinations

This thesis deals with applying continuous ceramic coatings to polymeric
materials. Although continuous ceramic coatings on polymeric materials are relatively
novel, additions of ceramics to bulk polymeric materials are common, especially for
ceramic fiber reinforcement of polymers such as in fiberglass. In addition, for biomedical
use, several weight percent barium sulfate (BaSO4) dispersed in PMMA bone cement (a
fixative for medical implants composed mainly of a monomeric methyl methacrylate and
particulate PMMA) makes the bone cement radiopaque and hence renders the bone cement
“readable” on medical x-rays [1]. Powdered silica, calcium carbonate, and clay are often
used as inexpensive extenders for polymers [2]. Mica platelets can increase the impact
strength and the flexural modulus, improve resistance to chemical attack, and decrease
moisture up-take for therrnoplastics [3]. However, each of these applications feature
ceramics in particulate, fiber, or platelet form being added to the bulk of a polymer material,
rather than producing a ceramic coating on the surface of the polymer.

Duchatelhard et al. applied thin alumina films to PMMA using RF magnetron
sputtering [4,5]. Alumina coatings improve the wetability of PMMA, which is
advantageous in dental applications, where saliva wetability of materials is quite
important [6]. This thesis however focuses on a technique for depositing and
characterizing a thin, adherent coating on the surface of bismaleirnide (BMI), which is a
polymeric material that is of considerable interest for aerospace applications due to its (i)

ease of processing and (ii) excellent high temperature properties. Prior to crosslinkin g,

BMI is a viscous liquid, enabling BMI to be processed with methods similar to those used
to process epoxy resin. Upon curing, the glass transition temperature of BMI is about
300°C, which can be considered for aerospace applications.

However, as is the case for many polymeric systems, the physical and mechanical
properties of BMI are affected by organic solvents and moisture [15]. In addition, BMI-
carbon composites are susceptible to galvanic corrosion when in contact with metallic
surfaces. Thus, although BMI has the advantages of processing ease and good thermal
properties, BMI’S performance could be substantially improved by decreasing its
susceptibility to solvent attack, ingress of water, and (in the case of BMI-carbon
components) galvanic corrosion. A thin continuous surface coating might be able to seal
out moisture and solvents, and if the layer were electrically insulating, it could reduce
galvanic corrosion. To be effective such a coating would need to adhere well to the BMI

surface.

1.2 Bismleimide Chemistry

The cure reaction characteristics and kinetics in the liquid and glassy-state of BMPM-
DABPA BMI composite matrices have been studied by Fourier transform infrared
spectroscopy (FI‘IR), differential scanning calonmetry (DSC) and gel permeation
chromatography (GPC) [7, 8, 9, ll, 12]. In the 100-2000C range the BMPM BM] reacts
with the DABPA to form an "ene" adduct. The "ene" adduct is pentafunctional as a result of
(i) three carbon-carbon double bonds, capable of chain extension and crosslinking, and (ii)

two hydroxyl groups capable of etherification by hydroxyl dehydration.

BMI is a crosslinked polymer glass and as such its mechanical properties depend on the
detailed topography of the crosslinked network [13]. For example, depending on the
crosslinked conditions, the elastic modulus of BM] varies from 3.55 GPa to 4.12 GPa [15]
and the room temperature density changes from 1.2375 g/cm3 to 1.2473 g/cm3 [16].

The relative rates in the liquid-state and the principal cure reactions involving the five
reactive "ene" group species have been fully characterized in the 2000-3500C temperature
range [12]. Morgan et. a1 [7] have used the infrared bands at 3473 cm'l and 1179 cm’1 to
monitor the disappearance of hydroxyl groups and appearance of the ether groups
respectively for the etherification reaction by hydroxyl dehydration. Recent work [14] has
identified infrared bands associated with the cure reactions of the allyl (A) at 915 cm’I and
995 cm", propenyl (B) at 931 cm" and 975 cm" and maleirrude (C) at 690, 713, 827 and

1639 cm”1 double bonds respectively.

1.3 Silica coatings on BMI

This thesis investigates fabricating continuous silica coatings on unreinforced
BMI substrates. Spin rates and curing conditions are adjusted to obtain uniform,
apparently uncracked silica coatings on BMI substrates. Coating thicknesses are
measured for varying spin rates. Vickers indentations were made on uncoated and silica
coated BMI substrates and their indentation pattern evaluated. Spalling area fractions on
Vickers indentation and uniformity of silica coatings for the silica coated BMI substrate

was studied as a function of indentation load for varying curing temperatures.

Crack spacings in silica coated BMI substrates were evaluated at constant
indentation loads for BMI with unabraded and abraded (Section 2.7 and Section 3.5.2)
silica coatings cured at 150°C, and for BMI with unabraded silica coatings cured at 150°C
and 175°C. Scatter in crack spacings was evaluated as a function of the radial position
from the indent at at a constant indentation load (Section 3.5 .3). Mean crack spacings
were plotted as a function of indentation loads for the curing temperatures of 150°C and
175°C (Section 3.5.1). Distribution of crack spacings was studied by doing an order
statistic study (Section 3.5.4). Water uptake at room temperature was compared for

uncoated and silica coated BMI (Section 3.6).

2. EXPERIMENTAL PROCEDURE

2.1 Materials Used.

The Bismaleimide (BMI) resin system (MatrimidTM 5292, Ciba-Geigy [14]),
used was a two component system based on 4,4’-bismaleimidodiphenylmethane (BMPM)
and 0,0’-diallyl bisphenol alcohol (DABPA). The amber, viscous DABPA liquid
monomer was poured into a magnetic stir-activated beaker and heated on a hot plate at
130°C, then yellow BMPA crystalline powder was added slowly and mixed until a .
homogeneous solution was achieved. This prepolymer mixture was degassed in a
vacuum oven set at a temperature of 130°C for 20 minutes. This mixture was then
poured into a preheated (90°C) mold and cured in a nitrogen atmosphere oven for 1 hour
at 177°C followed by additional 1 hour curing at 200°C. During processing, the
stoichiometric ratio of BMPAzDABPA was varied such that the BMI specimens included
in this study had BMPM: DABPA ratios of 120.82, 1:1 and 1:1.13. All BMI substrates
included in this study were initially cured for 1 hour at 177°C followed by a cure for one
hour at 200°C. Depending on the curing conditions, the elastic modulus of BMI varies
from 3553 MPa to 4122 MPa [15], the room temperature density ranges from 1.2375
g/cm3 to 1.2473 g/cm3 [16], the activation energy for diffusion varies from about 21.8
kJmol" to 33.5 kJmol".

The silica coatings that were applied to the BMI were an organic-based liquid
(Emulsitone company, New Jersey) that was spun-onto the BMI substrates. The liquid is

converted to an amorphous silica film upon pyrolysis.

2.2 Specimen Preparation

Using a low speed diamond saw (IsometTM Buehler), the BMI substrate
specimens were cut into 1 cm X 1 cm X 0.4 cm sections. Tap water was used as coolant
instead of oil to prevent contamination of the BMI. After sectioning with the diamond
saw, the specimens were ground using a 600-grit abrasive paper and then polished using
5 um, 0.3 um, and 0.05 pm alumina abrasive powders.

The polished BMI specimens were pre-cured (The specimens when received had
already been cured at 177°C/1hour and then at 200°C/1hour) prior to coating in order to
reduce shrinkage of the BMI during the subsequent coating procedure. The precuring
was done in air for 60 minutes to 120 minutes in a resistively-heated oven (Stabil-
Therm® Gravity oven, Model — B-2729-Q, Blue Signal) at temperatures ranging from
180°C to 265°C. A mercury thermometer, with a least count of 2°C was used to record
temperature in the furnace.

The BMI specimen surfaces to be coated were cleaned first with deionized water,
then with acetone and then blotted dry with a paper towel. Afterwards the silica coating
was applied to the BMI surface.

The BMI specimens were adhered to the center of a petri-dish with an adhesive
tape and placed on the high speed spinner which holds the petri-dish by vacuum assist.
The spinner was turned on before applying the film and the spin rate and timer settings
were adjusted to that needed in the experiment.

Five to six drops of the silica film solution was applied on the center of the BMI
surface using a pasteur pipette. The specimens were then spun for 20 seconds on a

substrate spinner at rates ranging from 500 to 4000 rpm to yield a range of coating

thicknesses. The specimens were then cured in air at 150°C i 2°C for 20 minutes in the
resistively-heated oven.

Two coating protocols were used for coating the BMI: (1) only one specimen
surface coated and (2) all Six-specimen surfaces coated (for mass absorption experiments,
Section 3.6). To coat all six sides, 5 sides of a precured BMI specimen were coated,
leaving the bottom surface uncoated. The coated specimen was then cured in air at 150°C
for 20 minutes, then the single uncoated specimen surface was coated with Silica coating
at 3000 rpm for 20 seconds. The entire specimen was cured using the same temperature
and time used to cure the other five specimen surfaces.

Two coated BMI specimens SA] and 8A2 (Appendix C) were used in scatter
spacing studies (Section 3.5.2). The curing and coating conditions are given in Appendix
C. After curing the two BMI coated substrates, the specimens were polished on a
polishing wheel at 175 rpm for 45 seconds to introduce defects larger than the pre-
existing defects. Both specimens were cleaned using de-ionized (DI) water and blotted

dry using Kleenex paper.

2.3 Characterization of coated BMI

In this study, we evaluate the BMI coatings using two types of tests: (1) Vickers
and Hertzian indentation damage and (2) mass change upon water immersion. For the
indentation tests we compared the single-side coated and uncoated specimens. For the
water immersion tests, we compare uncoated specimens with specimens coated on all six

surfaces.

2.3.1 Vickers Indentation technique

All indented BMI specimens were polished and precured prior to indentaton.
Two commercial hardness testers were used to generate Vickers indentation cracks in
both uncoated and single-side coated specimens using a loading rate of 70
microns/second, a loading hold time of 10 seconds. The semi-macro indenter (Buehler,
Lake Bluff, IL) had a load range of 2.94 N to 196N and the micro indenter (Model : M-
400-Gl, LECO Corporation) had a load range of 0.098 N to 9.8 N. The dimensions of
the resulting crack damage were measured using a digital readout attachment to the
Vickers indenters (both the indenters had a similar digital readout attatchment), which

could be read to i- 0.1 micron.

2.3.2 Rockwell Indentation Technique

Single-side coated BMI specimens were cleaned and dried prior to indentation. A
standard Rockwell indenter (Wilson Mech. Instrument CO. INC., N.Y.) was used at a
load of major load of 60 kg and 1.5875 X 10'3m steel ball indentor at a loading time of 10
seconds. This scale is the Rockwell-F scale. A minor load of about 10kg is first applied to
set the penetrator in position on the specimen, and a reference position is established on
the dial gauge. The dial is then set at zero before the major load (between 60kg and
150kg) is subsequently applied. This major load is the total load applied and the depth
measurement (hardness calculated from depth) depends solely on the increase in depth
due to the load increase from minor to major. The specimen was then removed and

imaged using scanning electron microscopy.

2.3.3 Measurement of silica film island gaps and crack lengths on silica coated

BMI specimens

BMI specimens with chemistries (BMPMzDABPA = 1:1, 1:0.82, 1:1.13) were
coated at speeds varying from 500 to 4000 rpm. All of the above BMI specimens were
observed under an optical microscope at 200 X prior to indentation. The optical lens
used was the one attached to the semi-macro Vickers indentor. The specimens on which
the silica film formed islands (Figure 2) were subjected to measurements on the optical
microscope. The gaps between islands of silica film were measured were made using the
digital readout, which was attached to the lens. Two cursors are placed at the two points
between which you want the measurements taken and the reading is observed from the
digital readout. For each specimen 10 readings were taken and the average calculated.
For the specimens on which film was absent but some surface cracks were present, the
crack lengths and the distances between the parallel cracks were measured with the

optical microscope. Results were calculated from average of five readings.

2.3.4 Measuring percentage of coating spalled off from an indentation

Three BMI specimens with coating thickness of approximately 0.15 microns,
were indented at loads ranging from 2.94 N to 196 N and imaged using scanning electron
microscopy. Micrographs were taken at magnifications ranging from 300 X to 720 X.
The fractional spalled area was calculated using an image analysis software NIH image
FAT 5.0. The fractional spallation area, f3, was calculated from fs = spalled area/total
indented area. Grid point method was used to verify the results from the image analysis

software, and agreed to within i 2%. For the grid point method the fractional spalled

area fs = number of grid points intersecting the spalled area/total number of grid points

intersecting the diamond-shaped crack zone.

2.4 Scanning electron microscopy

Scanning electron microscopy was used in imaging coated and uncoated BMI
specimens. Two different scanning electron microscopes were used. One was an SEM
(JEOL, LaB6) and the other was an environmental scanning electron microscope
OSSEM, Philips-Electroscan 2020 environmental scanning electron microscope, equipped
with a LaB6 filament).

Surfaces to be imaged of all indented specimens used for SEM studies was gold
coated using an Emscope Sputter coater at a current of 20 mA, vacuum of 0.08-0.12 Torr
and coating time of 90 to 120 seconds. Specimen sides were made conductive by
applying carbon paint.

Specimens imaged using ESEM, did not have to be gold coated nor painted using

carbon paint, as the ESEM allows imaging of non conductive specimens.

2.5 Coating Thickness Measurements Using ESEM

The environmental scanning electron microscope was used to estimate the
thickness of the silica coating on the BMI. BMI specimens of chemistries
(BMPMzDABPA = 1:1 and 1:1.13 and 1:0.82, Appendix A) precured at 200°C for 1 hour
were coated at spinning speeds varying from 500 rpm to 4000 rpm with the silica coating

and then cured in air at 150°C for 20 minutes. The coated specimens were sectioned,

10

using a low speed diamond saw, so that the thickness values could be measured near the
center of the specimen.

Coated BMI specimens were then placed in the ESEM at tilt angles varying from
70 to 120 and at an accelerating voltage of 20 kV in order to facilitate the coating
thickness measurements. The true coating thickness h is given by h = hw/COSB where hw
is the measured coating thickness and 0 the tilt angle in the ESEM.

Since the ESEM allows observation of nonconductive specimens without an
electrically-conductive coating, no conductive coating was applied to the surfaces of
either the silica coated or the uncoated BMI specimens. The lack of a conductive coating
is an advantage in this study, as such a coating could obscure details of cracks and other

surface features on the BMI specimens.

2.6 Inter-crack spacing measurements

For this set of experiments only coated BMI and abraded coated BMI specimens
were considered. Six of the BMI specimens were precured at 200°C for 1 hour, then
coated with silica film at 4000 rpm for 20 seconds and finally cured at 150°C for 20
minutes, but one of the specimens were cured at 175°C for 60 minutes. For the BMI with

abraded coatings the specimen surface after coating was polished using 0.03 um alumina

polishing powder solution on a wheel for 45 seconds to abrade the surface. In all 7 BMI
specimens of chemistries (BMPMzDABPA = 1:1, Appendix C) were used. Two types of
indents considered:

a) Vickers Indent at indentation loads ranging from 2.94 N to 196 N

b) Rockwell-F scale Indent at 588 N indentation load

11

The specimens were imaged using scanning electron microscopy at
magnifications of 3000K to 3500X, and an accelerating voltage of 20 kV. The BMI
specimen was held to the specimen holder by an adhesive tape. For the Vickers Indent,
images were taken along a radial crack till the end of the crack zone.

The crack spacing were individually measured from the micrographs by using a
ruler with a least count of 1 m. If the crack spacing measured from the ruler was (1 mm,
then the true length of the spacing was given by

D0 = (W) X 1000 microns
where,

M = magnification

The crack spacings were plotted as a function of radial spacing using MS Excel
software.

Similarly, the crack spacings were calculated along one of the radii for the
Rockwell indent and plotted as a function of radial position. The Rockwell indent
spacings also were imaged at magnifications of 3000X to 3500X using scanning electron

microscopy.

2.7 Abrading silica coated BMI specimens
Silica coated BMI specimens after curing were abraded on a polishing cloth using
a 0.03 micron alumina polishing solution for 30 to 45 seconds. The polishing wheel was

spun at 175 rpm. The specimen was held by hand without any other mechanical pressure.

12

2.8 Mass change upon immersion in water
The coated (all six sides) and uncoated BMI were weighed using an electronic
balance (Denver Instrument Company, M-Series Analytical balance, Model M-220D), to

an accuracy of i0.0001 g. The coated and uncoated BMI were placed in two separate

beakers containing room temperature deionized water. The ratio of the volume of
water/specimen surface area ranged from 50 cm to 60 cm for each of the water
immersion trials. After two hours the uncoated and coated BMI were removed from the
deionized water. The specimen was dried using tissue paper and exposing it to air for 3
to 4 minutes. The masses of the uncoated and coated BMI were measured. The uncoated
and coated BMI specimens were returned to their respective deionized water containers.
The mass measurement procedure was repeated every two hours up to 10 hours after the

initial immersion in the deionized water.

13

3. RESULTS AND DISCUSSION

3.1 Uncured BMI and coating quality

Four BMI specimens (Appendix D) that were not precured prior to coating
showed sets of nearly parallel cracks which were about 70 to 140 microns apart that were
distributed uniformly over the 1 cm X 1 cm specimen faces. The cracks were about 3 to
5 mm long, with side-branching cracks that extended about 1 to 3mm from the main
cracks. On average there were about 1 or 2 branching cracks that originated from one of
the set of parallel cracks. The specimens were observed in an optical microscope
attached to the Semi-Macro Indentor at 200x. All measurements were made using the

digital readout attatched to the Semi-Macro Indentor, as discussed in Section 2.3.3.

3.2 Coating thickness effects

Spin rates between 500 rpm and 4000 rpm produced (after curing) coating
thicknesses from 2.5 microns to 0.15 microns (Figure l). Coating thickness were
measured as a function of spin rates for silica coated BMI specimens of varying
stoichiometry. Thirty specimens were used, six each of T1, T2 and T3 types of specimens
(BMPM:DABPA = 1:1.13, Appendix A), six of T4 specimens (BMPM:DABPA = 1:1,
Apendix A) and six of T7 (BMPM:DABPA = 1:0.82, Appendix A).

The coated surfaces were observed as a function of the spinning speed. For this
six each of T5 (BMPM:DABPA = 1:1.13, Appendix A), T6 (BMPM:DABPA = 1:1,
Appendix A), and T8 types of specimens were used (BMPM:DABPA = 1:0.82,

Appendix A), none of which had to be sectioned, as they were not used for thickness

14

measurements. For coating thickness in the thickness range between 1.66 (1000 rpm) to
2.5 microns (500 rpm), the coating was discontinuous, as determined both by unaided eye
observations and a 200X optical microscope connected to the Semi-Macro indentor. For
coatings spun at 500 rpm and 1000 rpm, islands of silica coating (Figure 2) were
observed. For the 500 rpm specimens the distance between the silica islands was on
average about 12 microns, and for 1000 rpm specimen the distance between the islands
was about 6.3 microns. The measurements were made using the digital readout
connected to the semi-macro indentor as described in Section 2.3.3.

Coatings spun at 1500 rpm (coating thickness z 0.6 microns) had parallel cracks
with spacings of about 100 to 150 microns with lengths ranging from 3 to 4 mm, with
occasional side branching cracks that ranged in length from about 1m to 2.5mm.
Coatings with thicknesses less than about 0.3 microns (corresponding to spin rates of
2000 rpm and greater) were not cracked and no gaps were apparent in either the optical
microscope or the ESEM for the 0.8 cm x 1 cm (TS, Appendix A) and 1 cm x 1 cm (T6
and T7) specimen surfaces.

Coatings with thicknesses less than about 0.3 microns (2000 rpm and above)
were not cracked and no gaps were apparent in either the optical microscope or the

ESEM for the 0.8 cm X 1 cm (T5, Appendix A) and 1 cm x 1 cm (T6 and T7) specimen

surfaces.

15

 

 

 

 

 

 

 

 

 

3
A BMPM:DABPA = 1:1.13
OBMIM:DABPA=1:1
A DBMHVIzDABPA=l:0.82
32. A
U)
3
if D
.E-‘f
1~ A
o
-‘-r Ital J
0 . . L?! U a
0 1000 2000 3000 4000

Stimuspeedmm)

Figure 1. The thickness of silica coating on BMI substrates as a function of the spinning
Speed. The BMI (BMPM:DABPA=1:1.13 and BMPM:DABPA = 1:1, Appendix A)
substrates were first precured at 200°C for 1 hour, then the coated specimens were cured
at 150°C for 20 minutes.

16

 

Figure 2. Micrograph of z 2.5 micron thick silica coating on BMI showing separated
islands of the coating. The specimen, with substrate stoichiometry BMPM:DABPA=1:1
(Appendix A), was pre cured at 200°C for 1 hour, coated at 500 rpm for 20 seconds and
then cured at 150°C for 20 minutes.

3.3 Vickers Indentation damage

This thesis shall discuss the coating damage in terms of cracks, delaminations,
and spalls. We shall use the term delanrination to denote a fracture along or near the
coating/specimen interface for which part of the coating remains attached to the
surrounding coating (Figure 3(a)). If the fracture along or near the coating /specimen
interface entirely separates a portion of the coating from the surrounding coating, we

shall refer to that as spallation damage (Figure 3(b)).

3.3.1 Comparision of the Semi Macro indentor with the Micro indentor

A Semi-Macro Indentor and a micro indentor were used to produce Vickers
indentations, as stated earlier in section 2.3.1. Indentations taken on the Semi-Macro
indentor (specimen B, Appendix D) and the micro indentor (specimen Bl, Appendix D)
were compared for loads of 2.94 N, 4.9 N and 9.8 N each.

Six readings were taken at each load, on each of the indentors and averages
compared. Also, an indent made at 9.8 N on specimen B1 on the semi-macro indentor
was measured using the digital readout on the semi-macro as well as the micro indentor.

The indentations made on the semi-macro and micro indentors are very much
comparable at the same loads (Tables 1 and 2) with regards to nature of the indent
impressions and their dimensions. Thus, we use both the indentors at various loads to

extend the range of loads at which we make indentations.

18

Table 1. The average of 6 total crack dimension values 2a, for indentations at 3 different
loads in the semi-macro indentor (Specimen B, Appendix D) and the micro indentor
(Specimen Bl, Appendix D).

 

 

 

Specimen Indentor *2aooat (Hm) / P (N)
B (Appendix 4) Semi-Macro 122.3 / 2.94 167.7 / 4.9 239.5 / 9.8
Bl (Appendix 4) Micro 124.27 / 2.94 165.17 / 4.9 236.7 / 9.8

 

 

 

 

 

 

 

* Each 2am, reading is an average of 6 readings.

Table 2. The crack dimension measurement of a 9.8 N indent made by the semi macro
indentor on specimen Bl (Appendix D), measured by the optical read out in the semi
macro indentor and the micro indentor.

 

 

 

Optical read-out Load (N) Indentor used 23m, (um)
used

Senri-macro 9.8 N Semi-macro 237.1
Micro 9.8 N Semi-macro 237.3

 

 

 

 

 

 

l9

3.3.2 Study of Vickers Indentation Damage

The indentation behavior of brittle films on brittle substrates, has been considered
in number of studies [18, 19, 20]. However, we will consider the point contact damage
by doing Vickers indentation on a brittle (silica) film on a compliant (polymer —- BMI)
substrate. Vickers indentation damage to a first approximation compares well with
damage caused during handling and fabricating components [21].

For the silica-coated BMI specimens, the adhesion of the silica coatings to the
BMI is surprisingly strong. Both uncoated and silica-coated BMI specimens were
indented using a Vickers Semi-macroindentor at loads of 2.94 N to 196 N and a
rnicroindentor at loads of 0.098 N to 9.8N G‘igures 4 (a), 4 (b), 5 (a) and 5 (b)). The
uncoated specimens showed a square-pyramidal indent impression. The total crack
dimension, 2a.,ncoa. (Note: For coated BMI we call the total crack dimension 2am, and
for the uncoated BMI the total crack dimension is called 2auncom, Figures 5 (a), 5 (b) and
6), for the uncoated BMI varied from about 530 microns at 2.94 N to about 1040 microns
at 196 N. The absence of radial cracks in the uncoated BMI, is interesting as polymers
tend to have low fracture toughness values Kic (Kic — fracture toughness in plain strain,
[22]). This absence of radial cracks can be attributed to the low hardness value, H (H =
P/2a2), where P is Vickers indentation load and, “a” is half the total crack dimension for a
Vickers indentation), and high critical load , Pc (the critical load required to initiate a
crack) to initiate cracks. Pc is proportional to (K,C)“/(H)3 {Pc = 2.0 (r(,,)“/(H)3 H23, 24, 25],
where he is a geometric constant, which is about 1.6 x 104 for a Vickers indentation [25].

From the above relationship, Pc = A0 (Kic)4/(H)3 [25], we estimate the critical Vickers

indentation load required to propagate radial cracks in BMI to be 322 N to 840 N

20

(assuming Kic (BMI) = 1 MPa m"2 , Hardness (BMI) = 317.48 :t 50.03 from Section

3.3.4 ). Since the Pc for BMI (322 N to 840 N), was higher than the maximum
indentation load (196 N), which could be obtained using the Semi-macro Vickers
indentor, it is consistent with the fact that we did not obtain any radial cracks.

For the silica-coated specimens, Vickers indentation produced cracks in the silica
coating in a pattern of concentric diamond-shaped cracks, centered on the indent
impression (Figures 4(b), 7 (a), 7 (b) and 8). The outer edge of the array of diamond
shaped cracks corresponded very well with the indent impression for the uncoated BMI
specimens. Cracks towards the outer region tend to bow outward slightly, than compared
to the cracks towards the center of the indent impression (Figures 7 (a) and 7 (b)). The
total crack dimension 2a,,ncoa. for the uncoated specimen and the outer edge of the “crack
zone” , 23cm. , for the coated material agree to within about two-percent in all cases. Also
the crack zone dimension 23 agrees very closely even for specimens coated at different
spinning speeds and different chemistries (BMPM:DABPA = 1:1 , 1:082 and 1:1.13,
Figures 5 (a) and 5 (b)). Twelve specimens (Appendix D) were used in this study. Of the
twelve specimens four were uncoated specimens and eight were coated. All crack field
measurements were made using the digital readout attached to the semi-macro indentor.
For each load, the crack-region measurements 2a, was an average of readings from 6 to
10 indentations. The 2a, for each indentation was an average of the two diagonals of the
Vickers indentation (Figures 4(a) and 4(b)). A total of 514 Vickers indentations were

made in this study.

21

Coating

 

Substrate

Figure 3 (a). Schematic of delaminated silica coating on BMI substrate

Coating

/

/

 

 

Substrate

Figure 3 (b)- Schematic of a spalled region of the silica coating on a BMI substrate

22

 

INDENT IMPRESSION

 

 

2auncoat

 

 

 

 

 

 

(a)
CONCENTRIC
CRACKS RADIAL CRACKS
CRACK \
SPACING
d,j /
’4 / Za t

 

 

(b)

Figure 4. Schematic of Vickers indent impressions on (a) an uncoated BMI specimen and
(b) a coated BMI specimen.

23

 

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10000

 

 

 

 

 

 

 

1000 a

a 100 ~

on

3

10 ~ , _
O Uncoated specrmens A, D, F1 and A1
El Coated specimens B, C, E, B1, C1 and F2
A Specimen R1 for Hertzian indents
l 1 r r r
0.01 0.1 1 10 100 1000

Log (P), Newtons

Figure 5a. Logarithmic plot for indentation dimension 2a versus indentation load for
uncoated and coated BMI specimens of different chemistries (BMPM:DABPA = 1:1,
1:082 and 1:1.13, Appendix D).

25

 

10000

 

1.... flax
- P

 

100-

 

 

Log 28, (Inn)

 

0 Uncoated BMI, Specimen A
El Coated BMI, Specimen B
10 J A Coated BMI, Specimen C
O Uncoated BMI, Specimen Al
+ Coated BMI, Specimen B1

- Coated BMI, Specimen C1

)K Rockwell indents, Specimens GI and G2
1 I l l l l
0.01 0.1 1 10 100 1000

Log (P), Newtons

 

 

 

 

Figure 5b. Logarithmic plot for indentation dimension versus indentation load for
coated and uncoated BMI specimens of the same stoichiomery (BMPM:DABPA = 1:1,

Appendix D).

26

 

Figure 6. Micrograph of a Vickers indent made at a load of 49 N on an uncoated BMI
specimen (BMPM: DABPA = 1:1, Specimen CR1, Appendix G). The BMI was precured
at 200°C for 1 hour and again cured at 150°C for 20 minutes.

27

 

Figure 7. Micrograph of 9.8 N Vickers indent made on coated BMI specimen where the
coating thickness was = 0.15 microns. The specimens were precured at 200°C for 1 hour,
coated at 3500 rpm for 20 seconds a) cured at 150°C for 20 minutes (Specimen CR1,
Appendix G) and, b) cured at 175°C for one hour (Specimen CR3, Appendix G).

28

...4 M" '1“ “f.

i.‘

1.

7,.
a

.. ”e, x

 

Figure 8. For the same indented specimen as shown in Figure 7a, a higher magnification

view of the array of concentric cracks that comprise the indentation crack field. The
center of the indent impression and a spalled region of the coating are shown.

29

 

<> cured at 175 deg C for one hour

 

O cured at 150 deg C for 20 minutes

 

 

 

 

 

 

f8, Spalling area fraction

 

 

 

 

 

 

 

 

 

0'1 l Mean = 0.031
A +0 A _____________ ,
Yv‘f ‘ "' ' “:3.
"""""" v““:’5’"-mg if“;
VI
1 v 1 ‘1
0 so 100 150 200

Indentation load (Newtons)

Figure 9. Fraction of silica film spalled off from an indentation as a function of
indentation load, for BMI with unabraded silica coatings cured at O - 150°C for 20
minutes, and A - 175°C for 1 hour.

30

Vickers indentation damage of the coated BMI specimens yielded evidence of
coating delamination (Figure 10) only in one case. For specimen K1, (Appendix D) two
Vickers indentations at loads of 49 N were made so that the center of each indent was
480 microns apart. Some more close sets of indentations were carried out to check for
other occurrences of delaminations.

Six additional pairs of closely spaced indentations at 49 N were made on specimens
K1 and K2 (Appendix D). In addition to the above pairs of indents, two sets of four
closely spaced indents were made at 49 N on specimen K2 (Appendix D), so that the
center of the indents were about 400 to 460 microns from each other. In one case two
closely spaced indents were made at, 98 N on specimen K2, so that the center of indents
were 700 microns apart. In two cases a pair of indents of loads of 9.8 N were made so
that the center of indents were 180 microns apart (specimen CR2, Appendix G).

None of the closely spaced indentations, other than the one shown in Figure 10,
produced a delamination that could be observed by either optical microscopy or by
ESEM observations (Figure 11). However, spallation of the coatings was observed over
a small fraction of the indentation-damaged coatings (Figures 3(b), 7 (a), 7 (b) and 8).

The lack of coating delaminations in all but one case, suggests that the delamination
produced in that one case (Figure 10), may be due to an interfacial coating defect, near
the indentation site. We can also say the film delamination on indentation is not a trend.
This observation, is in agreement with the work done by Li et a1 [26], who observed
coating cracking on indenting 0.1 micron thick DLC coatings on a polycarbonate
substrate using a diamond like three sided Berkovich indentor. The substrate/coating

system that was indented by Li et a1 [26], was comparable in Young’s modulus values for

31

both the substrate and coating and coating thickness values. Young’s moduli of
polycarbonate and DLC are 3.3 GPa and 130 GPa respectively [26], as compared to the
Young’s moduli of BMI and fused silica, which are 3.6 GPa — 4.1 Gpa [15] and 72 Gpa
[27] respectively. The silica coating indented by us was 0.15 to 0.3 microns thick
compared to the 0.1 micron thick DLC coating indented by Li et a1 [26]. However
indentation loads used in this study ranged from 0.098 to 196 N, compared to the 0.7 N

load used by Li et a1 [26]

3.3.3 Spalling area fraction as a function of curing conditions

Three coated BMI specimens were cured at varying conditions as listed in
Appendix G. To quantify the extent of coating spallation as a function of indentation
load, the three BMI specimens with coating thicknesses of approximately 0.15 microns,
were indented at loads ranging from 2.94 N to 196 N and imaged using scanning electron
microscopy. Micrographs were taken at magnifications ranging from 300 X to 720 X.
The fractional spalled area were calculated as described in Section 2.3.4

Fractional spalled area, fs,, was calculated for nine indents at each load (Figure 9),
for the BMI cured at different conditions. For the indents on the BMI cured at 150°C for
20 minutes, f5, varied from 0.14 to 0.25 (Figure 7 (a)). However the indents for the BMI
specimen cured at 175°C for one hour had a much reduced f5, ranging from 0.02 to 0.05
(Figure 7 (b)). The indents for the coated BMI cured at 200°C for one hour and 250°C
for one hour also had fs, in the range 0.02 to 0.04 However these specimens had a

network of cracks.

32

Thus at curing conditions of 175°C for one hour, the adhesion of the silica coating
to the BMI is very good and might be of further interest in fabrication of the film on a
larger scale, due to the narrow temperature window which controls the adhesion. The

cracking of silica film at the higher curing temperatures ( 2 200°C) might have been due

to relief of thermal stresses, but should be further investigated.

3.3.4 Indent dimension analysis as a function of load for Vickers indents.
As determined by least-squares fitting, the load, P, versus indentation damage
dimension (Figures 5a and 5b) was consistent with the relationship
P = 2Ban (1)
where the parameter “a” measures the dimension of: (1) half the indent dimension for the
uncoated BMI specimens (Figure 4a) or (ii) the crack damage field of concentric
diamond-shaped cracks for the silica-coated BMI specimens (Figure 4b). The B value
from least squares fitting was 317.48 i 50.03 MPa, and exponent n was 1.933 MPa i
0.05. The form of equation 1 is consistent with the functional form of load-crack length
relationships found in the literature for brittle materials [21], i.e.
P = 2Ha2 (2)
Thus B corresponds to the hardness values H, which can be approximated to be
same for both the coated and uncoated specimens, as the “2a” values for uncoated and

coated BMI agreed to within 32% of each other for the various indentation loads. Thus

we can say the Hardness value, is hardness of the BMI substrate itself. This confirms
with the fact that the thin silica coatings (0.15 microns to 0.3 microns), did not affect the

value of H, measured from Vickers indentations, in the indentation load we considered.

33

The hardness value obtained from Vickers indentations, are consistent with hardness
values in literature for other rigid polymers like epoxy resin, acrylic resin, and a series of
aromatic polyesters, ranging from 200 MPa to 400 Mpa [23, 28, 29, 30]. Also the HIE
values, where the elastic modulus, E, ranges from 3.6 GPa to 4.1 GPa for BMI is
approximately 0.07 and are consistent with H/E ratios found in literature PMMA [28].
The constant slope of the log (2a) versus log (P) plot (Figures 5 (a) and 5 (b)), implies
that hardness of BMI is independent of the indentation load. This is consistent with data
from the literature for other rigid polymers, where the hardness of PMMA, high density
polyethylene, an epoxy resin and an acrylic resin is load independent at higher Vickers
indentation loads [23, 31, 32].

To understand the array of diamond-shaped cracks, one can think of an analogy to
loading a membrane with a circular punch. Such loading will result in a conical
depression of circular cross section. For the BMI, which has a relatively low elastic
modulus, the subsidence of the surface local to the indentor (for the case of a Vickers
indentation crack) may roughly correspond to a cone of pyramidal cross section. Thus

the regions of the coating that are significantly deflected undergo cracking.

34

 

Figure 10. Micrograph showing a coating delamination and crack associated with a pair
of closely spaced 49 N Vickers indentations on a coated BMI specimen (BMPM:DABPA
= 1:1, Specimen K2, Appendix D) This is the only example of a coating delamination
that was observed in this study.

35

 

Figure 11. Micrograph showing a pair of closely spaced 9.8 N Vickers indentations on a
coated BMI specimen (BMPM:DABPA = 1:1, Specimen CR2, Appendix G).

36

3.3.5 Vickers Indentation dimension as a function of loading rate and load time

Three uncoated BMI specimens (Appendix F) of different stoichiometries
(BMPM:DABPA = 1:1, 1:082 and 1:1.13) were indented at loads of 4.9 N and 49 N at
varying loading rates and load times. The load time was varied from 5 to 35 seconds at a
loading rate of 50 microns/second for both the 4.9 N and 49 N indentation loads. The
indentations were measured immediately after they were made and again 72 hours later
and plotted as a function of the load time (Figure 12). The indentation dimensions for all
the stoichiometries and the two loads varied little as a function of loading time [23, 32]
and also recovered much after 72 hours. A similar lack of sensitivity to indentation time
was observed by Paglia et al for the polymeric materials epoxy (KIT 36) and acrylic
(moulding transoptic powder) [23]. For the indentations we made the indentation
dimensions increased by about 3% to 5% (Figure 12) over the range of indentation load
time we considered (5 seconds to 35 seconds). Thus BMI’s viscoelasticy will not affect
the hardness readings, which are calculated from the Vickers indent dimension 23, which
in turn depends on the viscoelastic nature of the material. The indentations measured 72
hours later, showed a recovery in crack dimension of 0.01% to 0.05%. Thus elastic
recovery is almost absent, and indentation dimension changes very little as a function of
elapsed time since indentation.

The three BMI specimens used for the varying load times experiment were also
used to study the dependence of indentation dimension on loading rates at loads of 4.9 N
and 49 N at a load time of 10 seconds. The indent dimensions 2a varied 0.5 % to 1% on

varying loading rates from 40 microns/second to 200 microns/second (Figure 13).

37

Thus varying load rates and indentation load times would have given us, very
similar hardness values. Also indentations measured after a certain time would give us

similar hardness values.

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

500 -
400 4
.5. 300 -
«‘3
200 -
A 1" \ l \ < A > A @
Vail ‘ v ’ ‘ ’ V
0 2a measured at a load of 4.9 N at zero hours
100 d El 2a measured at a load of 4.9 N, 72 hours later
A 2a measured at a load of 49 N, at zero hours
0 2a measured at a load of 49 N, 72 hours after later
0 l l l l I l l 1
0 5 10 15 20 25 30 35 40

Load Time (seconds)

Figure 12. Indentation dimension plotted as a function of indentation load time at a
loading rate of 50 microns/second, at loads of 4.9 N and 49 N for uncoated BMI
specimens of three different chemistries (L1, L2 and L3, Appendix F).

39

 

 

 

 

 

 

 

 

 

 

 

W R 3 5
U
500 —
400 -
E
5’: 300 .
Q
N
200 .
"'l E 1'"! H
E—J L_l L_l l._l 5
100 a
El Indentation load of 4.9 N
O Indentation load of 49 N
0 T 1 t l 1
0 50 100 150 200 250
Loading rate (um/sec)

Figure 13. Indentation dimension plotted as a function of loading rate at a load time of
10 seconds at loads of 4.9 N and 49 N, for uncoated BMI specimens of three different
chemistires (L1, L2 and L3, Appendix F).

40

3.4 Rockwell Indentation damage

Two coated BMI specimens (Appendix E) were indented using the Rockwell
Hardness Tester, on the Rockwell-f Scale (Load 588 N). Rockwell indentation on the
silica coated BMI produced cracks in the silica coating in a pattern of concentric circular
shaped cracks (Figures 14 and 15), centered on the indent impression. Radial cracks
originated from the edge of the indent (Figure 17) and were 450 to 850 microns long.
There was a transition region between the edge of the indent and the beginning of the
radial cracks (Figures 15 and 16) which comprised of incomplete Hertzian cracks. The
transition region measured from 75 to 85 microns. For five Hertzian indents 0.06 to 0.08
of the total indent area was spalled off.

The fraction spalled off fs was calculated using a grid point method. Eight
micrographs were required to cover the Hertzian indent at a magnification of 600 X.
Grids were drawn on the eight micrographs and the fractional spallation area, f5, was
calculated from fs = number of grid points intersecting the spalled area/total number of
grid points intersecting the circular crack zone. The diameter of the circular indent
region was approximately 1340 microns (this measurement excludes the transition region
and the outgoing radial cracks).

The total indentation dimension (1340 microns) for the hertzian indent when
plotted on Figures 5 (a) and 5 (b), was 30% lesser than that the indentation dimension at
588 N from extrapolating the least squares fit for the Vickers indents data. From this we
can conclude that the load dominates the indentation damage, with very little dependence

on the shape and material of the diameter.

41

 

Figure 14. Rockwell indentation on the HRF scale depicting concentric circular crack
pattern on a silica coated BMI specimen (R1, Appendix E).

42

  
 

 

!.;:.‘-uu. nuuwr'n, MW”;

  

 

; I
.1, 3
| i
l

5.

l

.1

1

l1

1
, .,......-..-a.~..m...u. , .... . .

 

 

 

 

 

 

. .....-....... ...._ .Awa-» -

“2;, tam-=1 Inad- ‘

Figure 15. Micrograph depicting the transition region from complete Hertzian cracks to
incomplete hertzian cracks, in the same indent as Figure 14.

43

 

Figure 16. Micrograph depicts the incomplete Hertzian cracks at a higher magnification
for the same indent as Figure 14.

. ,3
fi‘" « -

40 [mi

 

Figure 17. Micrograph depicting the radial cracks originating from the end of the region
that included the incomplete Hertzian cracks on the same indent as Figure 14.

45

3.5 ESEM observations and statistical analysis of crack pattern

3.5.1 Mean crack spacing as a function of indentation load

Seven specimens (Appendix C) were indented at loads ranging from 2.94 N to
196 N, using the semi macro Vickers indentor. Hertzian indents were made using the
Rockwell Hardness Tester on the F-scale. Crack spacings dij (distance along the radius
between one crack and the adjacent crack, (Figure 4 (b)) were measured (Section 2.6).
For each of the eighty-four Vickers indents (six at each indentation load) and for the six
Rockwell indents made on the F-scale, crack spacing values were plotted as a function of
the radial position from the center of the indent.

The mean crack spacings fl were calculated for each indent by using the following

equation

(3)

where
N = the total number of cracks for an indent in between the center of the indent

dimension and the end of the indent dimension.

The average of six mean crack spacing values, MS were calculated for each

indentation load (Table 4).

46

The ratio of mean crack spacings at two different loads can be calculated by

 

MSF = M53 (4)
M

Where
MSF = Ratio in average of six mean crack spacing values of indents made at load of
x Newtons to an average of six mean crack spacing values of indents made at a

load of y Newtons.

MS, = Average of six mean crack spacing values for x Newton load indents on a coated

BMI specimen

MS, = Average of six mean crack spacing values for y Newton load indents on a coated

Blvfl specimen.

47

Table 4. Average of mean crack spacings for six indentations at each indentation load
for the specimens listed in Appendix C.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen M8194 MS“ MS 9,3 M549 M593 MS 196 M53“;
(um) (um) (um) (um) (um) (run) (um)

SUAl 4.7 4.8 4.6 4.6

SUA2 4.7 4.7

SUA3 4.6

SUA4 4.7 5.0 4.7

8A] 4.4 4.5

5A2 4.4 4.3

CR1 4.9 5.3 6.0 6.3 6.7 7.2

 

48

 

For the specimens SUAl and SUA2 with unabraded coatings cured at 150°C for
20 minutes (Appendix C) crack spacings were plotted as a function of the radial position
from the center of the indent for Vickers indents made at loads of 2.94 N (Figure 20), 4.9
N (Figure 21), 9.8 N (Figure 22), 49 N (Figure 23), 98 N (Figure 24) and 196 N (Figure
25). Thirty-six such indents were made, six each for each of the six loads. The mean
crack spacings, ,u, for six indents at each of the loads were calculated and averages MS
taken for the six readings (Table 4). The mean crack spacing varied from 4.3 microns to
5.0 microns for the BMI specimens with unabraded coatings (Tables 4 and 6, Figure 18)
for the various indentation loads. The MSF values for the specimens with unabraded
coatings ranged from 0.98 to 1.01 (Table 7).

Similarly for the BMI specimens SAl and SA2 (Appendix C), with coatings
cured at 150°C for 20 rrrinutes and then abraded using the 0.03 um alumina polishing
cloth (Section 2.7), six indentations each at 9.8 N and 49 N (Table 4) were made. The
mean crack spacings were calculated for each of the indentations and the averages MS for
the mean crack spacings calculated at each indentation load. The averages MS of the
mean crack spacing y for various indentation loads varied in between 4.3 microns and
4.7 microns (Table 4). The MSF value for the BMI specimen with abraded coatings was
0.97 (Table 7).

From the MSF values for both the abraded and unabraded coated BMI specimens
(MSFMMM = 0.97, MSFMW = 1.01), we can say that, the average of mean crack
spacings varied only by i 3% for the range of loads at which mean crack spacings were
measured (2.94 N to 196 N, change in load factor of 66.67). Thus we can say that the

mean crack spacing is a very weak function of indentation load.

49

To further investigate the nature of crack spacings, six Rockwell indents on
specimen SUA3 (Appendix C, Table 4). Crack spacings were plotted as a function of the
radial position from the center of the indent (Figure 34). The average MSka of six mean
crack spacing values for the Rockwell-f scale indent was 4.6 pm (Table 4). The Rockwell
indents were not performed on the same specimen as the Vickers was.

MSF values were calculated by comparing the average of the mean crack spacing
for the Rockwell indent to the average of the mean crack spacings for various Vickers
indentation loads varied from 0.98 to 1.01 (Table 7). Thus we can say that the average
mean crack spacing values for the Vickers indents are within i 2% to the mean crack
spacing values for the Rockwell-f scale indent. Thus even after increasing indentation
loads by a factor of 200 (2.94 N to 588 N) the average of mean crack spacing values
changed only by i 2%. Thus the mean crack spacing value is a very weak function of
indentation load. Changing the indenter material (diamond to steel) and shape (diamond
pyramid to spherical) varied average of the mean crack spacings by i- 2%. This
observation confirms with the fact that the mean crack spacing is a weak function of the
indentor material and shape.

For the coated BMI with unabraded coatings cured at 175°C for one hour (CR1,
Appendix C), the crack spacings, dij, were plotted as a function of radial position from the
center of the indent for indentation loads of 2.94 N to 196 N (Figures 28, 29, 30, 31, 32
and 33). However for the coated BMI cured at 175°C for one hour the mean crack
spacings showed a clear dependence on indentation load as compared to the BNII

specimens with unabraded coatings cured at 150°C for twenty minutes. The average of

50

the mean crack spacings increased with increase in indentation loads from 4.9 microns at
2.94 N, to 7.2 microns at 196 N (an increase of 47%, Table 6, Figure 18).

The mean crack spacings normalized by half the total indent dimension “a”
plotted as a function of the indentation load for the BMI specimens with unabraded
coatings cured at 150°C for twenty minutes and 175°C for one hour (Figure 19) using the
log-log scale on least squares fitting gives R2 values of 0.997 and 0.996 respectively.
From this we can say that the mean crack spacings normalized by the half the total indent

‘6 ’7

dimension a , is consistent with the power law relationship

”[3 = (p P8 (5)

where

(p = pre-exponential factor
8 = exponent

From the standard error of estimates of (p (0.006 and 0.005) for the two curing
conditions 150°C/20 minutes and 175°C/1 hour listed in Table 5, we can say that the (p

values can be considered similar, as the s.e.e. values (0.005 and 0.006) are greater than

the difference in (p values for the two different curing conditions (0.1230-0.1224 = 0.0006
= s.e.e ((p)/10 ). Similarly for the two curing conditions 150°C/20 minutes and 175°C/l
hour, we can say that the 8 values can be considered different, as the s.e.e. values (0.0253
and 0.023) are less than the difference in 8 values for the two different curing conditions
(-0.4153 + 0.4981 = 0.0828 = 4 x s.e.e. (8)). Thus the 8 values might be influenced by

the two different curing temperatures but must be further explored.

51

Table 5. The pre-exponent (p and exponent 8 obtained from least squares fitting of of
figure 19 using equation 5.

 

 

 

Specimen curing conditions (p i s.e.e. * e i s.e.e. **
150”C/20 nrinutes 0.1224 i 0.006 -O.4981 i 0.0253
175rC/1 hour 0.1230 x 0.005 —0.4153 i 0.0230

 

 

 

 

 

a: o (175/1) - (p (150/20) = 0123001224 = 0.0006 < s.e.e. ((p)

** a (175/1) — s (150.20) = —0.4153 + 0.4981 = 0.0828 > s.e.e (e)

52

The number of cracks/unit length were calculated (Table 8), and varied from
0.20 pm1 to 0.22 pm" for the BMI with unabraded and abraded coatings cured at 150°C

for 20 minutes. However the number of cracks/unit length for the BMI with unabraded
coatings cured at 175°C for one hour decreased with increase in indentation load, from

0.21 um’l to 0.14 p.m'l (Table 8) as the indentation load went up from 2.94 N to 196 N

respectively.

53

Table 6. Mean crack spacing data for various indentation loads for BMI specimens with
unabraded coatings cured at 150°C at 20 minutes and cured at 175°C at 60 minutes.

Indentation Load (N) CR1 A1

4
4.
4.
4
4.
4.
4.
4.
4.
4.
4.

 

54

 

7.5

6.5 -

6i

 

Mean crack spacings - p. (um)

 

 

 

 

4 .4
3.5 i
3 r l l l
0 50 100 150 200 250

Indentation Load (Newtons)

Fig 18. Mean crack spacing data plotted versus various indentation loads for BMI
specimens with unabraded coatings cured at 150°C at 20 minutes and cured at 175°C at

60 minutes.

55

 

 

 

 

     

 

 

 

1
0 cured at 175 deg celsius for one hour
[1 cured at 150 deg celsius for 20 minutes
0.1 -
y = 0.123 1(0.4153
a R2 = 0.9959
3.
0.01 e
0.001 r r
1 1 O 100 1 000

Indentation load (Newtons)

Figure 19. Logarithmic plot of mean crack spacing data versus various indentation loads
for BMI specimens with unabraded coatings cured at 150°C at 20 minutes and cured at
175°C at 60 minutes.

56

Table 7. MSFA values (equation 4) for BMI with unabraded and abraded coatings cured
at 150°C for 20 minutes and BMI with unabraded coatings cured at 175°C for 20 minutes.

 

 

 

 

 

 

 

 

 

 

 

 

 

MSF 4 SUA“ SA" CRV
MSFu/z,“ 0.98 1.08
MSF9,3/2,94 1.01 1.22
MSF49/2,94 0.99 1.29
MSF93/2,94 0.98 1.37
MSF 196/2,94 1.01 1.47
MSF49/9,3 0.98 0.97

MSmezm 0.98

MSFRocmy 0.98

MSFRock/og 0.97

MSFRxmg 0.99

MSFRocmg 1.01

MSF Rock/196 0.99

 

 

 

 

 

 

4 MS values used to calculate MSF are an average of 6 readings for each indentation

load.
* MSF values for BMI with unabraded silica coatings cured at 150°C for 20 minutes.
** MSF values for BMI with abraded silica coatings cured at 150°C for 20 minutes.

VMSF values for BMI with unabraded silica coatings cured at 175°C for one hour.

57

Table 8. Number of concentric cracks/unit length as a function of indentation load for
BMI with unabraded and abraded silica coatings, cured at 150°C for 20 minutes and for
unabraded silica coatings cured at 175°C for 1 hour.

 

 

 

 

 

 

 

Indentation load NSUA“ NSA** NCRV
(Newtons) (11m)1 (11m).1 (14111).1

2.94 0.21 0.21

4.9 0.22 0.19

9.8 0.22 0.22 0.17

49 0.21 0.22 0.16

98 0.22 0.15

196 0.21 0.14

 

 

 

 

 

 

* Number of concentric cracks/unit length for BNfl with unabraded silica coatings cured
at 150°C for 20 minutes.

** Number of concentric cracks/unit length for BMI with abraded silica coatings cured at
at 150°C for 20 minutes.

V Number of concentric cracks/unit length for BMI with unabraded silica coatings cured
at 175°C for one hour.

58

 

12

10— o

 

 

 

Crack spacing - du(um)
as

 

 

 

O I I T I I F
0 10 20 30 40 50 60 70
Radial position (urn)

Figure 20. Crack spacing data dij, for a Vickers indent made at a load of 2.94 N, on
specimen SUAl (Appendix C), plotted against the radial position from the center of the

indent.

59

 

 

Crack spacing - (1“ (pm)
9
Z
8
:1
11
P
W
t
3
O
O

 

 

 

0 'ii- I I l l
O 20 4O 6O 80 100

Radial position (um)

Figure 21. Crack spacing data dij, for a Vickers indent made at a load of 4.9 N, on
specimen SUAl (Appendix C), plotted against the radial position from the center of the
indent.

6O

 

 

Crack spacing - d“ (m)
u:

 

 

 

0 r r
0 50 100 150
Radial position (um)

Figure 22. Crack spacing data dij, for a Vickers indent made at a load of 9.8 N, on
specimen SUAl (Appendix C), plotted against the radial position from the center of the

indent.

61

 

 

 

 

 

12
o
10 ~
E o
‘7... 8 ‘ 0 ,
1:
$5 + o O ’ ° °
.5 6 q ......................................................... . .......... . ........................
o 0
§- . o o .’ o ’ .
. . . - 0
g 4 __._,_, . ,_Mean:_4.3_mmmns__
00¢
09‘ . .9 . - o ’ Q o
2 _+‘ .-.-.-.; ...... .. ................... ; -... ...............................................
o O
O I l l I fit —fil
0 50 100 150 200 250 300
Radial position (um)

Figure 23. Crack spacing data dij, for a Vickers indent made at a load of 49 N, on
specimen SUAl (Appendix C), plotted against the radial position from the center of the

indent.

62

 

 

 

 

 

 

 

14
12‘ Mean=4.7p.m .
104 O
E
i 84 . o . . .
é, o O 9 o .
E ' """""""""""""" ; """" 3 ''''''' Q """ ' "."""""";'°'; """""""
‘3 6’ ’ o l.’ ’ . . I ’ o
5 9 0 r a
4. “9“ o 0 " o
O 0 ‘ O
..... 0 32-....." -.-.: .-.- -.0..-.-.-
2 o 9 g o 8 8 o
9
0T 7 l T l I l T
0 50 100 150 200 250 300 350 400
Radial position (um)

Figure 24. Crack spacing data dij, for a Vickers indent made at a load of 98 N, on
specimen SUA4 (Appendix C), plotted against the radial position from the center of the
indent.

63

 

12

 

 

 

 

 

 

10 - ,
o
o o
A 8 "‘ O Q 0
i . ’ . o
a: o o + o
30 ------------------------- +- ------------- 93¢ ----------- -- --------------------
.E 6 — o o ’ o o.
8 o o o .0 o
3‘ . u o g o o . o
I: 7.9 L . J A . a . 9
U _
is w . ”‘5 Mean _ 5.0 urn . O
o 4 _ o o o o
. o o o o o 0. _ o
- ................................... 0 .......................... ¢ _ - ............
o o o o
a: .’ 09
o
2 —1
o
0 I I I I I
0 100 200 300 400 500 600
Radial position (um)

Figure 25. Crack spacing data dij, for a Vickers indent made at a load of 196 N, on
specimen SUA4 (Appendix C), plotted against the radial position from the center of the

indent.

o4

 

 

 

 

 

 

o
o
6 4 o
.. .................. '1" -g ........ 0 ..... .0. ........................................................
o
‘3’, 5 ‘ o o 0
“=1 0
3° 0 Mean = 4.5 pm
'5 VT 0 a
“e”- .
E4— ’
U 0
- 0’ .
I ........................................ a .......... a .............................. o. ..........
o
3 s
o o
o
o
o
2 r r
O 50 100 150
Radial position (um)

Figure 26. Crack spacing data dij, for a Vickers indent made at a load of 9.8 N, on
specimen SAl (Appendix C), plotted against the radial position from the center of the
indent.

65

 

 

 

 

 

 

o
. o o
6 -
9 +0 0
""""""""" 6'66 "'3’o‘63’""3’"""""'"""'3""‘3'3“""""""""

5 2 O ”o co .
A o
5' lfi... Mean = 4.5 um ..
:1- 0 00 o 9“
I? 4 7 O O «0 o o .
s a ’
'5 . .................. '. .Q-._.-.-.-.-._.-.. ...............................................
2.
£2 3 ~ 3.
O
E 9
U o

2 a 0 ’ °

1 -

O I I I T I r

0 50 100 150 200 250 300 350
Radial position (um)

Figure 27. Crack spacing data dij, for a Vickers indent made at a load of 49 N, on
specimen SAl (Appendix C), plotted against the radial position from the indent.

66

 

 

 

 

 

8 A O
7 " 9
+0
.. ....... . ................................................................................. ..

a“ t
'9” 5 . Mean 4.921111?
2‘ O
“a O
“ O
at 4 4
CD
.2
° ..-.-.-.-.-.-.-.-.-.-.¢_.Q .......................... T 9 .................................. -
5 o o

3 1

2 _

l -.

O I I I I f Ft

0 10 20 3O 4O 50 6O 7O
Radial position (pm)

Figure 28. Crack spacing data do" for a Vickers indent made at a load of 2. 94 N, on an
silica coated BMI specimen cured at 175 0C for one hour (CR3, Appendix C), plotted
against the radial position from the center of the indent.

67

 

 

Crack spacing - d“ (pm)
M
O
O

 

 

 

O I I I I
0 20 4O 60 80 100

Radial position (um)

Figure 29. Crack spacing data dij, for a Vickers indent made at a load of 2.94 N, on an
silica coated BMI specimen cured at 175°C for one hour (CR3, Appendix C), plotted
against the radial position from the center of the indent.

68

12

 

 

 

 

 

10 ~ 0
O
A 8 “L ........... f S ...........................................................................
5 . .
'6: O . . .
g 6 - Mean = 6.0 um‘ ‘ .
a
a.
m 9 O
. t ‘
L .......... T .......................................... - .................................
u 4 _ . O O
O
2 —+
O I I fl r 1 ‘A
O 20 40 60 80 100 120
Radial position (um)

Figure 30. Crack spacing data dij, for a Vickers indent made at a load of 9.8 N, on an
silica coated BMI specimen cured at 175°C for one hour (CR3, Appendix C), plotted
against the radial position from the center of the indent.

69

 

 

 

 

 

 

16
14 — .
O
12 ~ .
’ o
5;, 1°“ .......................................... 3. ................................... t 9 ......
'1; § ‘ . .
.2: 8 ~ . O O
a; Mean = 6.3 pm 0 O
5 6 - . a ‘
O . 0 . .
’ o» ’ .
4 ~ 0. O O
.-. ........................................................ T 5? .......
‘ . o ' o
2 . O O
O I I I I T
o 50 100 150 200 250 300
Radial position (um)

Figure 31. Crack spacing data dij, for a Vickers indent made at a load of 49 N, on an
silica coated BMI specimen cured at 175°C for one hour (CR3, Appendix C), plotted
against the radial position from the center of the indent.

7O

 

16

 

 

 

 

 

14 ~ 9 9
O
O

12 ~
:3. 10 1 Q
.5:- - ............................. 4- .................... a} .q.‘ ...... -. ...........
Q Q .
E” 8 ~ 9 O O O .9
g O .O . . 9 .Mean=66ufi
g 6 ~ . . o .

41 39.-.-.. ..... . ............... 2 ............. .- .q ......... . .............

. O O
2 _ t
0 I T I
0 100 200 300 400
Radial position (um)

Figure 32 .Crack spacing data dij, for a Vickers indent made at a load of 98 N, on an
silica coated BMI specimen cured at 175°C for one hour (CR3, Appendix C), plotted
against the radial position from the center of the indent.

71

16

 

 

 

 

 

l4 4 C] E]
El
12 .
CID
E 10 DD D D D +0
3» D """""""""" B """"""""" EE’CIEEJ‘E] """""""""
3g 8. 51 1:1 1:1 '3 [:1 BED DD
3. D D D Mgan=1.2 “m
=5. 6 p {:1 [31:1 [:1 Ebflj E] E]
8 DC] [In D [1:] -o
....... EMMEI.-. .-.-.IIJ.CI.-.-._%-.-.-.-.-.-.-.-.-D.-.-._._.-.-.-.-..
4- I] [JD
[:1
2 -~ [:1
0 I . . T .
0 100 200 300 400 500 600

Radial position (um)

Fig 33. Crack spacing data dij, for a Vickers indent made at a load of 196 N, on an silica
coated BMI specimen cured at 1750C for one hour (CR3, Appendix C), plotted against
the radial position from the center of the indent.

72

12

 

 

 

 

 

 

10 ~ .
o
’ o
E, 8 I o O o
C: . o o ”o
«a: o . ’
w -.-.-..II.'.Q. ........ Q ..... Q ........................ _ - .........
-§ 5 .1 o o “ ’
a 0 o 09.0 . .
2 . . o o o
a Mean = 4.6 pm " o O O. A
5 .0 0 ° ” o w o
4 ‘ 0 ° ° 9 o
o o . ‘ 0.. “, ” ’
..-._.-.:..Q' ...... 4 tum: ....... .1... ........................... . -.-.-
O . .. O. O
2 . o
. o
o o
0 I * r I I I I
0 1 00 200 300 400 500 600 700
Radial position (um)

Figure 34. Crack spacing data dij, for a Hertzian indent made on the HRF scale, on
specimen SUA3 (Appendix C), plotted against the radial position from the center of the
indent impression.

73

3.5.2 Comparison of scatter in spacing of abraded coatings versus unabraded
coatings at constant loads.

The standard deviation, 0, from the mean crack spacing values for Vickers
indentations at 2.94 N, 4.9 N, 9.8 N, 49 N, 98 N and 196 N for BMI specimens with
unabraded coatings cured at 150°C for twenty minutes (Figures 20, 21, 22, 23, 24 and 25)
were 02.94 = 2.1 pm, 049 = 2.1 pm, 0'93 = 1.9 um, 0'49 = 1.9 pm, 093 = 2.1 pm and 0.96 =
1.6 um (Table 9) respectively. For the BMI specimens with unabraded coatings cured at
175°C for one hour the 0 values varied from 1.6 pm to 3.0 um (Table 9, Figures 28, 29,
30, 31, 32 and 33), for indentation loads of 2.94 N to 196 N.

For indentation loads of 9.8 N and 49 N the specimen with the coating abraded
abraded (on 0.03 pm alumina polishing wheel, Section 2.7) prior to indentation showed
standard deviations in mean spacing values of 09.3 = 1.2 pm (Figure 26, Table 9) and 049
= 1.0 pm (Figure 27, Table 9) respectively.

The statistical differences between the standard deviations of the crack spacing
data for the unabraded specimen versus the abraded specimen were explored using the F-
test [33]. The statistical analysis was performed using MS Excel software. The F-test
returns a P value for two sets of data. The two data sets are not required to have the same
number of items. In our case the two data sets were the crack spacings for the unabraded
coated BMI (SUAl) and the abraded coated BMI (SAl). The spacing data was compared
between SUAl and SA] for both the 9.8N as well as the 49N indent. As the P value
increases, the statistical significance of the difference in standard deviations of the two
data sets decreases. The maximum P value is l and the minimum P value is zero. The

cutoff P value used generally is 0.05, below which values the statistical significance of

74

the difference in standard deviation values are considered to be significant [33]. Thus if
the two data sets returned P values less than 0.05 then the difference in standard
deviations of the two data sets can be considered significant.

The P value for the corresponding spacing data of the 9.8 N indents on abraded
(SAl - data set from figure 16) and unabraded silica coated BMI (SUAl — data set from
Figure 14) specimens worked was P = 0.046. Similarly the P value for the corresponding
spacing data of the 49 N indents on abraded (SAl — data set from Figure 17) and
unabraded silica coated BMI (SUAl — data set from Figure 15) specimens worked out to
be P: 9.97 x106.

From the low P values (P = 4.6 X 10'2 and 9.97 X 10'6 < 0.05), for both the 9.8
N and 49 N sets of crack spacing data, and the fact that the 0 values for crack spacing
data on the silica coated BMI specimen with unabraded coating {0493 = 1.9 mm, 049 = 1.9
pm} are greater than the standard deviations for the BMI specimen with an abraded
coating {09.3 = 1.2 um, 0'49 = 1.0 um}, we can conclude that abrading the coating prior to
indentation considerably reduces the scatter.

The dimensions of the indentation-damaged zone was larger for the abraded
coatings (SAl and SA2, Appendix C) at the same load than for the unabraded coatings
(SUAl, SUA2 and SUA3, Appendix C). The half-diagonal length of the diamond shaped
region “a” for the unabraded coatings at 9.8 N was approximately 116 microns, where as
for abraded coatings it is approximately 135 microns. Similarly the radius of the overall
crack dimension D in the specimens with unabraded coatings at 49N was approximately

260 microns, where as for the specimen with abraded coatings it is approximately 295

75

microns. That is, BMI with abraded coatings have crack dimensions around 1.15 times

greater than that of BMI specimens with unabraded coatings.

76

Table 9. The standard deviations from mean crack spacings for BMI specimens with
unabraded and abraded coatings cured at 150°C for twenty minutesand BMI specimens
with unabraded coatings cured at 175°C for one hour.

 

 

 

 

 

 

 

Indentation load a (SUA)* 0 (SA)** 0 (CR)V
(Newtons) (um) (um) (um)

2.94 2.1 1.6

4.9 2.1 2.2

9.8 1.9 1.2 1.8

49 1.9 1.0 3.0

98 2.1 2.7

196 1.6 2.5

 

 

 

 

 

 

77

3.5.3 Scatter increase with distance from the center of indent.

The scatter in the crack spacing measurements increased with increasing radial
distance from the indent center (Figures 20, 21, 22, 23, 24 and 25) for the BMI specimens
with unabraded coatings cured at 150°C for twenty minutes. For an interval from the
indent center to a point (13, the scatter in crack spacing was markedly less compared to the
scatter from ¢ to the edge of the cracked region. The point 41 depends on the indentation
load. When normalized by the radial crack field dimension “a”, (2) corresponds to
approximately 0.4 irrespective of the indentation load (Figure 35).

Point ¢, was determined by using MS Excel software. For each indentation load
the crack spacing data was subdivided into two sets. If there were “11” items in a set of
crack spacing data “”,z the F-test was performed for two data sets “Z1” and “22".
Minimum number of items in either set “21” or “Z2” was fixed to be = n/3, as a criterion,
to get good results from the F—test, where,

Set 21 = d), 2 to d5“, M, and Set 22 = dM, M.) to dN-1,~ (6)
2n/3 > M > n/3 (7)
and “d” represents measured crack spacing values.

The F-test was performed for the range of, M, specified by equation (7). The M that
corresponded to the minimum P value (i.e. if P < 0.05), M', was calculated and used to
calculate ¢ in the following manner.

m—l

¢ = d1. j (8)

1.2

78

The minimum P value was determined using a Visual basic macro program (Appendix H)
which was run using MS Excel software.

Thus the F-test was also performed on individual sets of crack spacing data
comparing data for two different regions on the same crack region. One data set
represented the crack spacings for cracks positioned between the indent center and point
¢, and the other data set represented crack spacings for cracks located between point
(1) and the outer edge of the indentation crack field.

Point ¢ was determined (Figure 35, Table 10) using the method explained above
for the six different loads (2.94 N, 4.9, 9.8 N, 49 N, 98 N and 196 N) for unabraded
coated specimens (SUAl, SUA4, Appendix C). For the 2.94 N indentation load the point
¢ was'determined to be 36.1 microns from the center of the indent (Table, Figures 20 and
35). The P value for the F-test carn'ed out on the two sets of data for the 2.94 N indent
was PR = 0.03 (i.e. PR < 0.05).

Similarly for the 4.9 N, 9.8 N, 49 N, 98 N and 196 N indentation loads ¢was
calculated to be 39.8 um, 46.6 um, 94.3 mm, 162.1 um, 214.6 pm respectively. The P
values for the 4.9 N, 9.8 N, 49 N, 98 N and 196 N were 0.01, 0.0004, 0.00003, 0.007,
0.0001 (i.e. P < 0.05) respectively.

The standard deviations from mean crack spacing, for crack spacing data from the
center of the 2.94 N indent to point ¢ = 36.05 microns, and from point (11 to the end
of the indent were 1.30 microns and 3.49 microns respectively. Now let the ratio of the

distances from point ¢ to the edge of the indent and center of the indent to point ¢ be

ahead _ (9)

79

where

on“ = Standard deviation of the crack spacing data from the mean for the data ranging
from point (I), to the end of the indent.

00¢ = Standard deviation of the crack spacing data from the mean for the data ranging
from center of the indent to point ¢.

The n values fer the 2.94 N, 4.9 N, 9.8 N, 49 N, 98 N and 196 N
indentation loads were calculated using equation 9. Table 10 lists the (D, aofld, 0'00 and
17 values for the 2.94 N, 9.8 N, 49 N and 196 N indentation loads. From the greater than
one, 7] values (ranged from 1.8 to 2.7, Table 10), we can conclude that the standard

deviations from mean crack spacing for the crack spacings in the region in between point
(I), to the end of the indent is greater compared to the standard deviations from mean crack

spacings for the crack spacings in between the region from the center of the indent to

point (I).

80

Table 10. The distance of point (D from the center of the indent, along with the 17 values

(equation 9), for various loads.

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Load C- w ac... Um I]
(Newtons) (microns) (microns) (microns) unitloss

SUA4 2.94 36.5 1.3 3.5 2.68
SUAl 4.9 39.8 1.2 2.8 2.31
SUAl 9.8 46.6 1.2 2.5 2.09
SUAl 49 94.3 1.0 2.1 2.01
SUAl 98 162.1 1.1 2.0 1.80
SUA4 196 214.6 1.0 1.8 1.77

 

* C-¢ represents the distance from the center of the indent to the point (11.

81

 

Thus from the low P values (i.e. < 0.05) and the 7] values, that are greater than one
(1.8 to 2.7) we conclude that the scatter is considerably greater in the region from the
center of the indent to point (0 than for the region between point ¢ and end of the cracked
region.

A similar test was performed on the abraded specimen to determine if scatter is
high towards the end of the crack region as in the abraded specimen (SAl, Appendix C).
For the abraded coatigns P values for loads of 9.8 N and 49 N were 0.86 and 0.54
respectively (i.e. P > 0.05).

The P values for the abraded BMI are greater than 0.05 (0.54 to 0.86). Thus the
difference in, O’ values from mean crack spacings for a region in-between the center of
the indent and point (11 compared to the 0 values from mean crack spacing for a region in-
between point 11) and end of the indent is not statistically significant. Thus we can
conclude that the scatter in crack spacings from the mean does not increase with radial
position from the center of the indent for the BMI with abraded coatings as compared to
the BMI with unabraded coatings were scatter increased with radial position from center

of the indent.

82

 

P
\o
l

9
oo
1

p
\l
1

A

0.6 1

A

p
M
1

 

8&{200
0

Point 111 normalized by radial crack dimension "3"

«>09

 

 

0.3 -
0.2 ~
0.1 —
o . T r .
o 50 100 150 200

Indentation load (Newtons)

 

'_‘—_“_'1

250

Figure 35. Point “¢”, normalized by radial crack field dimension “a” for coated BMI
specimens (SUAl, SUA4, Appendix C), plotted as a function of indentation load.

83

3.5.4 Order statistics study to determine distribution of crack spacings

If we assume an uniform crack spacing, then the residuals (difference between the
observed value and expected value) and are normally distributed [34]. This is consistent
with a random variation with respect to the mean crack spacing. The assumption that the
residuals are distributed in a manner similar to the crack spacings itself is true for any
distribution [34].

An order statistics study [34] compared the distribution of the crack spacings with
the uniform distribution. For the crack spacing data for a single indentation, mean crack
spacings, ,u , was subtracted from each individual crack spacing dij, for one particular
indent, to obtain the residual crack spacings. The residual crack spacings were arranged
in ascending order and numbered 1 through N, where N was the total number of crack
spacings for that particular data set. We label the order set of crack spacings is an

ordered statistic of the experimental data R.

The set S is defined by
S1: (I-3/8)/(N+1/4) (10)
where

S1: The Ith item in the new data set S,
I = 1 through N,
N = defined earlier as total number of items.
Equation 10, removes a bias that is based on a detailed explanation in [34].
From set S, a new set E was created using the NORMSINV function in MS Excel

software. NORMSINV returns the inverse of the standard normal cumulative distribution

84

(standard normal deviate) [34] with a mean of zero and standard deviation of one. Set E
is the expected value of order statistic.

The ordered residual spacings (set R) from measured values was plotted against the
expected order statistic values using MS Excel software (Figures 37, 38, 39, 40, 41, 42,
43, 44, 45, 46, 47, 48, 49, 50 and 51). The least squares fit for the figures, gave very
good R-square values ranging from 0.904 to 0.986. Thus we can say the distribution of
our residual spacings is a Gaussian [34]. Since the distribution of residuals is a gaussian,
we can conclude that the assumption we had made of the crack spacings being uniformly
distributed is true.

Similar plots of ordered residual crack spacings were plotted against expected
order statistic values for the crack spacings data for an indentation load in the region in-
between the center of the indent to point ¢, and for regions in-between point ¢ and the
end of the indent dimension (Figures 52, 53, 54 and 55). The least-squares fit for the
figures 37 though 55, gave R2 values ranging from 0.971 to 0.986. Thus we can say that
the crack spacings are also uniformly distributed in regions between center of indent and

point (I), and in regions in-between point ¢, and end of the indent.

85

Crack
Spacings
dii

 

[du ' H]

 

 

I I I
I I I
I I I I I I I
I I I I I
I I I
I
Radial position

Figure 36. Schematic, describing uniform distribution of crack spacings.

86

 

 

Ch

 

 

 

 

8 o
.2
a
>
E 4“
5
g R2=0.904
E
E
2-
.8
,5:- O
3 ’—.——‘—T— — r r 8 F. 1. r r — ’m
:9
a -2 -15 -1 -05 90 05 1 15 2
a O
8
E-i
E O
_4_
E
0
'E
o
.6 J

 

Expected value of order statistic

Figure 37. For the distance between the 1th and jth crack, dij, ordered residual spacings
versus expected value of order statistics for a 2.94 N indent on an silica coated BMI
specimen (SUA4, Appendix C) with an unabraded coating.

87

Ch

 

 

 

I
W

 

I Ordered residual spacings [du-p] (pm), from measured values

 

 

 

 

Expected value of order statistic

Figure 38. For the distance between the ith and 3"” crack, dij, ordered residual spacings
versus expected value of order statistics for a 4.9 N indent on an silica coated BMI
specimen (SUA4, Appendix C) with an unabraded coating.

88

Ia

 

 

 

Ordered residual spacings [du-u] (pm), from measured values
1'6
N

 

 

 

 

Expected value of order statistic

Figure 39. For the distance between the iih and jth crack, dij, ordered residual crack
spacings versus expected value of order statistics for a 9.8 N indent on an silica coated
BMI specimen (SUAl, Appendix C) with an unabraded coating.

89

vn'Ii—flfl.’ .‘l'll-Ialfll": 'F-lilI-_ ‘F...-\ -III. I.“ 3::CI‘IVI‘IPI Illll-lflutllll Iliilur-rl c

Ordered residual spacings, [du'lll (pm), from measured values

do

 

6z 0
O
4‘ 2
R=0.938 o
O
O
2-
O

 

 

 

I
W
'51
|—4
.—
Cb
r——+
Na

 

 

 

A
'U

 

Expected value of order statistic

Figure 40. For the distance between the iih and j‘h crack, dij, ordered residual spacings
versus expected value of order statistics for a 49 N indent on an silica coated BMI
specimen (SUAl, Appendix C), with an unabraded coating.

90

Ordered [cu-,1] (pan), from measured values

Figure 41. For the distance between the 1th and jth crack, dij, ordered residual crack
spacings versus expected value of order statistics for a 98 N indent on an silica coated

 

GO

 

 

 

 

 

R2 = 0.938
4 7 o
o
g,»
o
o
2 _.
O
-2 -1 /x 1
-2 —
o ooe’
-4 4
Expected value of order statistic

BMI specimen (SUA4, Appendix C), with an unabraded coating.

91

 

Ch

 

 

 

 

 

Ordered residual crack spacings we'll] (pm), from measured
values

 

 

 

A
'U

 

Expected value of order statistic

Figure 42. For the distance between the ith and jth crack, dij, ordered residual crack
spacings versus expected value of order statistics for a 196 N indent on an silica coated
BMI specimen (SUA4, Appendix C), with an unabraded coating.

92

L»)

 

 

 

 

l
W

 

Ordered residual crack spacings [du-p] (11m), from measured values

 

 

 

 

Expected value of order statistic

Figure 43. For the distance between the iilri and jth crack, dij, ordered residual spacings
versus expected value of order statistics for a 9.8 N indent on a coated BMI specimen
(SAl, Appendix C) with an abraded silica film.

93

taxi-I-a) -'¢'o--ml.flw4‘-F- IF-n‘u-n‘ AFFI-\ Fch ..‘h .dlitflo‘le:rfi ~IIVIlllr: l1.11l.~

 

h»)

 

 

 

l
w

 

 

Ordered residual crack spacings [du-u] (pm), from measured values

 

 

 

Expected value of order statistic

Figure 44. For the distance between the iih and j‘h crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 49 N indent on a coated BMI specimen
(SAl, Appendix C) with an abraded silica film.

94

Ordered residual crack spacings We'll], from measured
values

4}

 

2 -l.5

 

R2 = 0.932

 

.______._ __._T__

 

A
"r

1.5

L‘
‘v

 

 

Expected value of order statistic

Figure 45. For the distance between the iih and jth crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 2.94 N indent on a coated BMI specimen
cured at 175°C for one hour (CR3, Appendix C) with an abraded silica film.

95

Ordered residual crack spacings [du'lil (pm), from
measured values

Figure 46. For the distance between the iih and jth crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 9.8 N indent on a coated BMI specimen

 

LII

 

 

 

 

Expected value of order statistic

cured at 175°C for one hour (CR3, Appendix C) with an abraded silica film.

96

 

w

 

 

 

 

Ordered residual crack spacings [tin-11] (pm), from measured values

 

 

 

 

A
"7

Expected value of order statistic

 

Figure 47. For the distance between the iih and ju‘ crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 9.8 N indent on a coated BMI specimen
cured at 175°C for one hour (CR3, Appendix C) with an abraded silica film.

97

n-
CD

 

 

 

 

'8

i 81 t
E R2=0.936 ’
E 6 " 9

a: .Q

a 4»

".5

1:

E 2 r

m 8

3:.” 13

3 > e . e T .
3'

a: -B -2 -l 1 2 I
8

z: -2 .

To

.5 O

Q 0 O '4

9

a -6 .

o

 

 

 

 

Expected value of order statistic

Figure 48. For the distance between the ii” and jth crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 49 N indent on a coated BMI specimen
cured at 175°C for one hour (CR3, Appendix C) with an abraded silica film.

98

GP

 

 

 

 

I
W
t-‘
w

 

Ordered residual crack spacings [dn-u] (pm), from
measured values

 

 

 

 

Expected value of order statistic

Figure 49. For the distance between the iill and jth crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 98 N indent on a coated BMI specimen
cured at 175°C for one hour (CR3, Appendix C) with an abraded silica film.

99

qo

 

 

 

 

Ordered residual crack spacings [du-u] (pm), from measured
values

 

 

 

Q
'0

Expected value of order statistic

 

Figure 50. For the distance between the iih and jth crack, dij, ordered residual spacings
versus expected value of ordered statistics for a 196 N indent on a coated BMI specimen
cured at 175°C for one hour (CR3, Appendix C) with an abraded silica film.

100

 

 

 

 

1
w

 

Ordered residual crack spacings [du-p] (pm),
from measured values

 

 

 

 

Expected value of order statistic

Figure 51. For the distance between the i“1 and jth crack, dij, ordered residual spacings
versus expected value of order statistics for a Rockwell indent on a coated BMI specimen
(SUA3, Appendix C), with an unabraded silica film.

101

up

 

 

 

Ordered residual crack spacings [dfi-u] (pm), from center of
indent to pornt ¢, from measured values

 

 

 

 

 

Expected value of order statistic

Figure 52. For the distance between the iih and jth crack, dij, from the center of the indent
until the point ¢, ordered residual spacings versus expected value of order statistics for a
49 N Vickers indent on a coated BMI specimen (SUAl, Appendix C), with an unabraded
silica film.

102

 

‘7
I

 

measured values
W

 

Ordered Idu'lll (pm), from point (p to end of indent , from

 

 

 

 

Expected value of order statistic

Figure 53. For the distance between the iih and j“1 crack, dij, from the point 41 to the end of
the indent, ordered residual spacings versus expected value of order statistics for a 49 N
Vickers indent on a coated BMI specimen (SUAl, Appendix C), with an unabraded silica
film.

103

 

R2 = 0.975

 

I
w

l
N '1

' —<
h:

CD 1— N u 4:.
K L 1 1

H 1
N _.

to point (p, from measured values

 

Ordered residual crack spacings [du-p] (pm), for center of indent

 

 

 

 

Expected value of order statistic

Figure 54. For the distance between the iih and 1"" crack, dij, from the center of the indent
until the point (I), ordered residual spacings versus expected value of order statistics for a

196 N Vickers indent on a coated BMI specimen (SUA4, Appendix C), with an
unabraded silica film.

104

 

 

 

 

l
w

 

Ordered residual crack spacngs [dfi-p] (pm), from point (11
to end of the indent, from measured values

 

 

 

 

Expected value of order statistic: Standard normal distribution

Figure 55. For the distance between the iii] and im crack, dij, from the point (I) to the end
of the indent, ordered residual spacings versus expected value of order statistics for a 196
N Vickers indent on a coated BMI specimen (SUA4, Appendix C), with an unabraded
silica film.

105

3.6 Mass change measurements

An expression for the mass change as a function of time due to the diffusion of
water into the BMI specimens can be developed by first considering the concentration
C(x,t) for a semi-infinite medium with a planar interface [35] with the time independent
concentration C, defined as C(0,t) = C, and the initial concentration C(x,0) = C0, then

C(x,t) can be written as [35]

C(x,t)-C, _e x

C0—C, #25 (11)

 

where C; = C(0,t) = time-independent concentration at the planar interface and Co =
C(x,0) = initial concentration of diffusant in the host. From Fick’s first law, the flux, J, of
water diffusing into the BMI specimen (Figure 56) is related to the concentration gradient

by [351

8C

D(C0 -Cl)
J = D— =——
{ 3x150 JnDt

(12)

where D is the diffusivity of water in the BMI. The total mass of water, M., which has

diffused into BMI in time 1:, is given by

_ (13)
M, —J;Jdt.

Upon integration Mrcan be written as

l
M. = 2(C. -C.)(-Z—t)5 +1: “4)

106

Direction of diffusion of water

 

BMI surface (x=0)

 

 

 

 

 

 

Figure 56. Schematic of the diffusion of water into the BMI during water immersion
testing.

107

which displays parabolic kinetics (that is, the mass change is a function of the square root

of time). Physically, the constant k corresponds to M0. In terms of the M r, we can rewrite
equation (14) as

l

1
Mr —M0 = 2(C0 — C,)(—:23)52'3 (15)

We define the normalized mass change MN per unit surface area as

= M (16)

” MOA
where Mr is the instantaneous mass at time t = 7, M0 is the initial mass at time t = 0
hours, and A is the total specimen surface area. Thus the time dependence of M, can be

written as in terms of MN
I
= (M. -Mo) = on; (17a)

In equation 17a, for t = 0, MN = 0 since M1: M0 at time t = 0. However, we fit the MN

1/2

versus t data to equation 17b

M % ,8 (17b)
Nzat +

where the coefficients aand [3 are determined from the least-squares fit, and ,6 allows for
a non-zero intercept of the regression line. The on values for coated and uncoated BMI

(Table 11) show that at any time, t, the mass change of coated BMI will be less than the

108

uncoated BMI. Comparing with equation (15), we can see that physically the coefficient
acorresponds to
1
a = 251093394 g)? (18)
Thus, ais the slope of the MN versus tm curve (Figure 57), where dis a function
of the concentration difference (Co-C1) as well as the diffusivity D, specimen surface area
A, and initial specimen mass Mo. A least-squares fit of the MN versus rm data (Figure 57)
shows a linear trend for both the coated and uncoated BMI, where coefficient of
determination, R2, is 0.992 and 0.946 for the uncoated and coated specimens respectively.
If '15“ is the time required for the BMI to become saturated with water then for
time r<<15AT we expect parabolic kinetics, as predicted by equation 14. In this study,
after ten hours of immersion in water at 21°C the values of the relative mass change
AM/Mo = (M. - M0)/Mo were 0.0032 and 0.0048, for the uncoated and the coated
specimens, respectively. However, for BMI at water saturation, AMSM/Mo = (MSM -
MoMWo = about 0.04 to 0.05 [17], where MSAT denotes the specimen mass in the water-
saturated condition. Thus the relative mass change, AM/Mo, observed in this experiment
is about an order of magnitude less than MSM/Mo, which is again consistent with the
parabolic kinetics, observed in this study [35].
As described in Section 3.2, “islands” of the silicate coating were observed by
optical microscopy for the four specimen “edges” of the specimen, although the larger
specimen surfaces were coated continuously and uniformly. The discontinuous silica

coating on the four edges of the specimen was likely the reason that the moisture uptake

109

by the coated BMI specimens was higher than would be expected for a perfectly
continuous coating. Methods for producing a more uniform silicate coating on all
specimen surfaces, including the edges, will be explored in future work, including

methods in which the coating is brushed or sprayed on the edges.

”0

Table 11. Coefficients a and B obtained from the least-squares fit of equation (17b) to
the MN versus t"2 data.

 

 

 

 

 

 

 

Surface Uncoated Coated
a (g/secm) 4.2266 2.4172
s.e.e(or) 0.179 0.391
c.v. %(oc) 4.24% 16.16%
B (m4) 0.3652 0.6508
s.e.e(B) 0.318 0.401
c.v. %(B) 87% 61.7%

 

 

 

 

 

s.e.e = standard error estimate, determined by Sigmaperthoftware

111

 

16

14 i O Uncoated BMI
Cl Coated BMI

  
 

 

 

 

 

 

MN(m.2)
co

 

 

 

Figure 57. Normalized mass change, MN, versus t"2 for BMI specimens with (a) all 6
sides coated and (b) uncoated BMI specimens (BMPM:DABPA = 1:0.82). The solid
curves represent a least -squares fit of the data to equation (17b).

112

4. CONCLUSIONS

This study employed a total of 72 specimens in all. Using a spin-on process, neat
(unreinforced) precured BMI polymeric substrates were coated with a silicate coating.
Six specimens each of T1, T2, T3, T4 and three specimens of T7 (Appendix A) were
used to determine coating thicknesses as a function of the spin-rate. Curing the coated
specimen at 150°C for 20 minutes produced silicate coatings roughly 0.15 to 2.5 microns
thick. The silica coating thickness decreases as the speed increases, however the coating
thickness becomes relatively constant at 0.15 microns for spin rates greater than 3000
rpm.

The surfaces of six specimens each of T5, T6, T7 types (Appendix A) were
observed using optical microscopy and scanning electron microscopy. For coating
thickness in the thickness range between 1.66 (1000 rpm) to 2.5 microns (500 rpm), the
coating was discontinuous. For coatings spun at 500 rpm and 1000 rpm, islands of silica
coating (Figure 2) were observed. For the 500 rpm specimens the distance between the
silica islands was on average about 12 microns, and for 1000 rpm specimen the distance
between the islands was about 6.3 microns. Coatings spun at 1500 rpm (coating
thickness z 0.6 microns) had parallel cracks with spacings of about 100 to 150 microns
with lengths ranging from 3 to 4 mm, with occasional side branching cracks that ranged
in length from about 1m to 2.5mm. Coating spun at 2000 rpm and greater speeds were
uniform and continuous, and showed no cracking or gaps when observed using optical

microscopy and scanning electron microscopy. For the BMI specimens included in this

113

study the minimum spinning speed required to obtain a uniform and continuous coating is
approximately 2000 rpm.

For Vickers indentation experiments 12 specimens (Appendix D) were used, of
which 4 were uncoated. A concentric, diamond shaped array of cracks were induced in
the silica coatings upon loading with a Vickers indentor (Figures 4b, 7a, 7band 8). Over
a load range from 0.098 N to 196 N the diagonal length of the crack array 2a (Figures 4b,
5a, and 5b) for the coated specimens were essentially identical to the radial crack length
for the uncoated specimens (Figures 4a, 5a and 5b). Within the crack array there was
only very minor spalling of the coating from the BMI substrate (roughly 22 percent) and
coating delaminations were not observed in any of the indents (Figure 10), but one
indentation (Figure 11).

Vickers indentation dimension was found to be independent of indentation load
times in the range of 5 seconds to 35 seconds (Figure 12). These dimensions were
measured right after making the indents and also 72 hours later. The recovery after 72
hours was minimal (Figure 12). Thus the BMI is not viscoelastic enough to affect the
indentation dimension readings with loading time, which is used to determine hardness
values using equation (2). Also varying loading rate experiments were carried out, and

the indentation dimension did not change much with loading rate (13).

Two coated BMI specimens (Appendix E) were indented using a Rockwell-F

scale, which uses a steel ball indentor with a diameter of 1.5875"‘10’3 and a load of 588N.

A concentric, circular shaped array of cracks was produced, and no delamination was

114

observed. Fraction of the region spalled of was 0.08. Thus, it appears that the silica
coatings adhered exceptionally well to the polymeric substrates.

Seven specimens (Appendix C) in all were studied for observing the crack
spacings. Since the MSF values for the silica coated BMI specimens cured at 150°C for
twenty minutes ranged between 0.97 to 1.02 (Table 7, Section 3.5.1) we can say that the
mean spacing is a very weak function of the indentation load if at all. Also the mean

crack spacing for the rockwell indent was within 1 2% of the various vickers indents

(Table 7, Section 3.5.1). Thus on changing the indentor material and shape the mean
crack spacing did not change much. Thus mean crack spacings was independent of the
indentation load and material for BMI specimens with unabraded and abraded coatings
cured at 150°C for twenty minutes.

However for BMI specimens with unabraded coatings cured at 175°C for one
hour (Appendix C, CR3), the mean crack spacing increased with indentation loads and
was 47% greater than BMI with coatings cured at 150°C for twenty minutes at the highest
load of 196 N. The mean crack spacing normalized with respect to half the total crack

dimension when plotted against indentation load shows a power law relationship

,u/a=(pP€

for the two different curing temperatures, with similar pre-exponential factors of (p =
0.123 i 0.005 and (p = 0.1224 1' 0.006 for curing conditions of 175°C/1 hour and
150°C/20 minutes respectively. However the exponent, e, was significantly different for

the two different curing conditions. For the 175°C/l hour and 150°C/20 minute curing

conditions the, 8, were 8 = -0.4153 :1: 0.0230 and 04153 i 0.0253 respectively. Thus the

exponent 8, may be varying with curing conditions.

115

The scatter in crack spacings is considerably reduced when the coating is
abraded and the crack region seems to be bigger than that of the unabraded specimen
(Section 3.5.2). The scatter in crack spacing is more towards the end of the crack region
than near the indent (Section 3.5.3). The residual distribution is pretty much normal from
the ordered statistics plot (Section 3.5.4).

For mass absorption experiments eight specimens (Appendix B) were studied, 4
of which were coated and 4 uncoated. The extent of water absorption was 1.7 times more
for the coated BMI compared to the uncoated BMI (Figure 56). For immersion in de-
ionized water at 21°C for 10 hours, MN, the normalized mass change per unit surface area
(equation 16) was 13.64 m'z, for the uncoated BMI and 8.06 m'2 for the coated BMI. The
larger than expected mass change MN for the coated BMI may be related to gaps in silica

coating on the edges of the specimen.

116

5. FUTURE STUDIES

Future work should include coating BMI substrates with coatings having other
chemistries (i.e. other than silicate coatings). Silica coating on substrates other than BMI
should be investigated and a comparison made with the silica/BMI system, which would
be of interest from an application and even, from a scientific point of view.

The silica coating should be subjected to more severe chemical and environmental
attacks, than just absorption of DI water. A model connecting coating thickness,
indentation load, crack spacings and surface strains should be developed. Reasons for
why the silica coating adheres to the BMI substrate must be investigated thoroughly.

The effect of different curing temperatures on the exponent, a, in equation 5
(Section 3.5.1), needs to be further investigated, to come up with an explanation for how
the different curing conditions are related to the exponent e.

The percentage of coating that spalls of on indentation for BMI with coatings
cured at of 175°C ranges from 2% to 5%. An attempt to further reduce the percentage of
coating that spalls off on indentation should be made, as that would show enhanced

adhesion of silica coating to the BMI.

117

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17. J. E. Lincoln, “Effects of cure and initial monomer stoichiometry on the physical,
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18. C. A. Gamlen, E. D. Case, D. K. Reinhard and B. Huang, “Adhesion of
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19. D. G. Lee, J. M. Fitz-Gerald, and R. K. Singh, “Novel method for adherent diamond
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21. B. R. Lawn, B. J. Hockey and H. Richter, “Indentation analysis - application in the
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24. B. R. Lawn, T. R. Jensen and A. Arora, “Brittleness as an indentation size effect”,
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(1956).

120

Appendix A.

Table A. Curing and coating conditions for specimens used to measure coating
thicknesses (Section 3.2).

 

 

 

 

 

 

 

 

 

Specimen Pre Coating Coating Curing No. of Dimensions
curing speed time temp(°C) specimens lxbxh cm°
temp(°C) range (seconds) [time
[time (rpm) (mins)

(hours)

*Tl 200/1 500 to 20 150/20 6 1x1x0.45
4000

*T2 200/1 500 to 20 150/20 6 1x1x0.38
4000

*T3 200/1 500 to 20 150/20 6 1x1x0.38
4000

**T4 200/1 500 to 20 150/20 6 1x1x0.41
4000

*TS 200/2 500 to 20 150/20 6 lx0.8x0.33-
4000

"T6 200/1 500 to 20 150/20 6 1X1X0.41
4000

***T8 200/1 500 to 201 150/20 6 1x1x0.36
4000

***T8 200/1 500 to 20 150/20 6 1x1x0.36
4000

 

 

 

 

 

 

 

 

 

* T1, T2, T3 and T5 specimens had a BMPM:DABPA = 1:1.13
* * T4 and T6 specimens had a BMPM:DABPA = 1:1
**** T7 and T8 had a BMPM:DABPA = 1:0.82

121

Appendix B.

Table B. Curing and coating conditions for specimens used in mass absorption
experiments, along with dimensions and time of water immersion (Section 3.6).

 

 

 

 

 

 

 

 

 

 

Specimen"I Precuring Coating Curing Time of Dimensions
temp(°C)/ speed temp(°C)/ immersion lxbxh cm3
time (rpm)/ time in water
(hours) Time (mins) (hours)

(seconds)

WCl 265/1 3000/20 150/20 10 1x1x0.42

WUCl 265/1 Uncoated 150/20 10 1x1x0.42

WC2 265/2 3000/20 150/20 10 1x1x0.42

WUC2 265/2 Uncoated 150/20 10 1x1x0.42

WC3 200/2 3000/20 150/20 10 1x1x0.42

WUC3 200/2 Uncoated 150/20 10 1x1x0.42

WC4 265/1 3000/20 150/20 500 1x1x0.42

WUC4 265/1 Uncoated 150/20 500 1x1x0.42

 

 

 

 

 

 

*All specimens had a BMPM:DABPA = 1:0.82

122

 

Appendix C.

Table C1. Curing and coating conditions for specimens used in scatter spacing
measurements, along with mean spacing values at different loads (Section 3.5).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen“ Precuring Coating Curing Abraded Number
temp(°C)/ speed temp(°C)] (Y es/No) of
time (rpm)/ time indents
(mins) time (mins)

(seconds)

SUA1** 200/60 4000/20 150/20 NO 8

SUA2“ 200/60 4000/20 150/20 NO 8

SUA3*** 200/60 4000/20 150/20 N O 8

SUA4" 200/60 4000/20 150/20 NO 2

SAP” 200/60 4000/20 _ 150/20 YES 8

SA2” 200/60 4000/20 150/60 YES 4

CR3! 200/60 4000/20 175/60 NO 6

 

* All specimens had a BMPM:DABPA = 1:1

* * SUAl, SUA2, SUA4, SA], and SA2 were used to make Vickers indents only

*** SUA3 was used to make the Hertzian indent only
! CR3 specimen was also used in spalling area fraction calculations

123

 

Table C2. R-square values for order statistics plots for indentations made on specimens

 

 

 

 

 

 

 

 

 

 

 

 

 

 

listed in table C1.
Indentation SUAl SUA4 SUA3 SAl CR3
Load
(R2) (R2) (R2) (R2) (R’)
(N)
2.94 0.904 0.932
(Figure 37) (Figure 46)
4.9 0.941 0.938
(Figure 38) (Figure 47)
9.8 0.937 0.986 0.953
(Figure 39) (Figure 43) (Figure 48)
49 0.938 0.953 0.936
(Figure 40) (Figure 44) (Figure 49)
98 0.938 0.916
(Figure 41) (Figure 50)
196 0.963 0.963
(Figure 42) (Figure 51)
588 0.970
(Rockwell) (Figure 45)

 

124

 

Appendix D.

Table D. Curing and coating conditions for specimens used to make Vickers
Indentations and study effect of not precuring specimens (Section 3.3.42 and Section
3.3.4).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Precuring Coating BMPM: Curing Load Dimensions
Specimen temp(°C)! speed DABPA temp(°C) range (N) lxbxh cm3

time (rpm)/ /time

(hours) Time(s) (mins)
A 200/1 Uncoated 1:1 150/20 2.94-196 1x1x0.45
B 200/1 3000/20 1:1 150/20 2.94-196 1x1x0.38
C 200/1 4000/20 1:1 150/20 2.94-196 1x1x0.45
D 200/1 Uncoated 1:0.82 150/20 2.94-196 1x1x0.38
E 200/1 3000/20 1:0.82 150/20 2.94-196 1x1x0.38
A1 200/1 Uncoated 1:1 150/20 0.245-9.8 1x1x0.38
B1 200/1 3000/20 1:1 150/20 0.245-9.8 1x1x0.38
C1 200/1 4000/20 1:1 150/20 0.245-9.8 1x1x0.38
F3 200/1 Uncoated 1:1.13 150/20 2.94-196 1x1x0.45
F4 200/1 3000/20 ’ 1:1.13 150/20 2.94-196 1x1x0.45
G1 200/1 3500/20 1:1 150/20 588 1x1x0.36
GZ 200/1 3500/20 1:1 150/20 588 1x1x0.36
K1 Not pre 3000/20 1:1 150/20 9.8-98 1x1x0.36
Ki-yorm cured
K2 200/1 3000/20 1:1 150/20 9.8-98 1x1x0.45

 

 

 

 

 

 

 

125

 

Ar

Ta
(S

r—g—T

 

Appendix E.

Table E. Curing and coating conditions for specimens used to study Hertzian indents
(Section 3.4).

 

 

 

*Specimen Pre Coating Coating Curing N o. of Dimensions
curing speed time temp(°C)! indents lxbxh cm3
temp(°C) (rpm) (seconds) time
[time (mins)

(hours)
R1 ZOO/1 3500 20 ISO/20 3 1X1x0.45
R2 200/1 3500 20 150/20 3 lxlXO.45

 

 

 

 

 

 

 

 

 

*All specimens had a BMPM:DABPA = 1:1.13

126

Appendix F.

Table F. Curing conditions and dimensions for uncoated specimens used in varying load
time and loading rate Vickers indentations (Section 3.3.5).

 

 

 

 

Specimen BMPM:DABPA Precuring Dimensions
temp(°C)/time lxbxh cm3
(hours)

L1 1:1 200/1 1x1x0.45

L2 1:0.82 200/1 1X1x0.45

L3 1:1.13 200/1 1x1x0.45

 

 

 

 

 

 

127

Appendix G.

Table G. Curing and coating conditions for specimens used to calculate fractional
spalled of area from indentations (Section 3.3.3).

 

 

 

 

 

*Specimen Pre Coating Curing No. of Dimensions
curing speed temp(°C)/ indents lxbxh cm3
temp(°C) (rpm)l Time
[time Time (5) (mins)

(hours)

CR1 200/1 3500/20 150/20 24 1x1x0.45

CR2 200/1 3500/20 150/20 30 1x1x0.45

CR3! 200/1 3500/20 175/60 24 1x1x0.45

CR4 200/1 3500/20 175/60 30 1x1x0.45

 

 

 

 

 

 

 

 

* All specimens had a BMPM:DABPA = 1:1

! CR3 specimen also used in crack spacing measurements

128

Appendix H. Visual basic macro program to determine point (1), corresponding to the
lowest P value in a set of crack spacings for any given indentation load (Section
3.5.3). The program compares a series of P values comparing two sets for the same
indent and returns the minimum P value obtained. Section 3.5.3 describes the procedure
in detail.

Private Sub CommandCancel_Click()

FormTestSeries.IIide

End Sub

Private Sub CommandOkay_Click()

Dim ThisSheet As Worksheet

D im Fl‘estResults As Range

Dim RangeNum As Integer

Dim Ranges, RangeE As Integer

Dim NOver3 As Integer

Dim FT estR As Double

Dim TopEnd, BottomStart As Integer

RangeS = Val(Right(RangeStart.Text, Len(RangeStartText) - 1))

RangeE = Val(Right(RangeEnd.Text, Len(RangeEnd.Text) - 1))

Col = Left(RangeStart.Text, 1)

RangeNum = RangeE - RangeS + 1

NOver3 = Int(RangeNum / 3)

TopEnd = Ran geS + NOver3

BottomStart = RangeE - NOver3

Worksheets(TextSheetName.Text).Activate

Set ThisSheet = WorksheetsCTextSheetName.Text)

129

Set Results = Worksheets.Add

Set FTestResults = Results.Range("A1:A" & NOver3)

Do While BottomStart > NOver3

F'I‘estR = Application.WorksheetFunction.Fl‘est(ThisSheet.Range(RangeStart.Text & "z"
& Col & Format(TopEnd)), ThisSheet.Range(Col & Format(BottomStart) & "z" &
RangeEnd.Text))

FFestResults(TopEnd - RangeS - NOver3 + l, "A") = FI‘estR

BottomStart = BottomStart - 1

TopEnd = TopEnd + 1

LOOP

MinFT est = Application.WorksheetFunction.Min(FTestResults)

FI‘estResults(1, "B") = MinFT est

MsgBox (MinFT est)

FormTestSeriesHide

End Sub

130

Appendix I.

Table 1. Raw crack spacings data for 2.94 N and 4.9 N indentation loads for BMI
specimen with unabraded silica coating cured at 150°C for 20 minutes (Figures 20 and
21) and 175°C for one hour (Figures 28 and 29).

A1 (2.94 N) CR1 (2.94 N) SUAl (4.9 N) CR1 (4.9 N)
6. 4
3.2 5.3
3.2 4.7
3.5 6.5
3.5 2.
4.7 8.1
6. 3.3

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3.
3.
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5.1
8.1
4.
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2.3
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3.3

 

131

Appendix J.

Table J. Raw crack spacings data for 9.8 N and 49 N indentation loads for BMI
specimen with unabraded silica coating cured at 150°C for 20 minutes (SUAl, Figures22
and 23 ) and 175°C for one hour (CR1, Figures 30 and 31) and, BMI with abraded
cured at 150°C for 20 minutes.
A1 (9.8 N) CR1 (9.8 N) A1 (9.8 N) A1 (49 N) (49 N) SA] (49 N)
2.5 10.1 2.2 2. 9. 3.8
2. 9.1 2.8
4. 5. 3.7
2.1 4. 4.9
1.8 5. 5
1.8 3. 5.1
4.5 7.2 5.1
7 6.3
6.8 4.5
5. 4.5
3.3 5.7
4.2 6.
5.2 5.7
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6. 3.
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Appendix K.

Table K. Raw crack spacings data for 98 N and 196N indentation loads for BMI
specimen with unabraded silica coating cured at 150°C for 20 minutes (SUAl, Figures 24
and 25 and 175°C for one hour CR1 Fi 32 and 33 .

A1 (98 N) CR1 (98 N) A1 (196 N) CR1 (196 N)
4.5
4.8
4.5
4.5
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2.7
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Appendix L.

Table L. Indent dimension raw data, which was included in Figures 5a and 5b.
Averages of indent dimensions (6 to 10 indents) were taken, when plotting indentation
dimension versus indentation load.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen Indentation Load Indent dimension - 2a Average
(11m) Indent
(N) dimension
-2a(11m)
A 2.94 132.2, 133.5, 135.8, 133.3, 135.4, 134.5
136.8, 132.8, 136.1
A 4.9 172.3, 176.1, 178.0, 177.6, 175.3, 176.0
176.2, 175.8, 176.7
A 9.8 237.1, 235.8, 238.5, 238.9, 237.9, 237.6
236.0, 238.8, 237.8
A 49 521.1, 523.4, 527.4, 524.7, 525.2, 524.4
523.6
A 98 746.2, 741.1, 745.6, 748.3, 742.9, 745.3
747.7
A 196 1036.3, 1027.9, 1031.5, 1033.1, 1031.9
1035.9, 1028.1
B 2.94 120.2, 126.4, 121.1, 124.3, 120.4, 122.3
121.4,123.1, 121.5
B 4.9 170.1, 168.8, 167.2, 166.3, 166.1, 167.7
170.4, 165.7, 166.9
B 9.8 238.1, 239.7, 241.6, 238.4, 242.3, 239.5
237 .6, 238.0, 240.1
B 49 523.4, 526.1, 529.0, 527.9, 525.1, 526.9
529.9
B 98 746.8, 751.1, 751.7, 749.2, 748.8, 749.7
750.6
B 196 1044.5, 1041.9, 1045.8, 1042.1, 1043.4
1046.0,1040.1
C 2.94 134.9, 133.6, 132.0, 129.5, 129.8, 132.5
133.2, 134.9, 132.1
C 4.9 169.4, 167.2, 166.1, 168.9, 170.3, 167.9
166.6, 169.4, 167.7
C 9.8 226.7, 229.2, 234.1, 234.4, 232.4, 231.1
228.7, 230.1, 233.3
C 49 519.2, 516.5, 516.7, 521.3, 517.0, 517.8
516.1
C 98 740.7, 743.9, 747.6, 748.1, 740.2, 744.3
746.2, 745.6
C 196 1035.6, 1039.3, 1047.4, 1049.2, 1042.3

 

 

 

 

137

 

 

1044.5, 1038.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D 2.94 121.5, 125.2, 122.9, 126.8, 121.4, 123.9
124.4, 1245.1, 122.8

D 4.9 166.2, 162.7, 173.3, 164.3, 163.8, 165.5
164.3, 166.2, 163.2

D 9.8 235.6, 229.1, 233.2, 232.6, 235.2, 232.2
231.0, 230.8, 232.9

D 49 514.7, 509.7, 510.5, 514.5, 509.3, 511.6
510.9

D 98 722.9, 717.6, 719.3, 725.1, 719.8, 721.1
721.9

D 196 1040.5, 1037.2, 1033.8, 1032.3, 1036.8
1038.8, 1038.3

E 2.94 128.1, 130.3, 133.9, 132.3, 135.6, 132
129.4, 131.8, 134.6

E 4.9 164.9, 166.8, 170.1, 168.5, 167.4, 167.2
166.1, 169.3, 164.5

E 9.8 236.4, 235.3, 230.9, 237.7, 233.6, 234.1
233.2, 235.9, 229.8

E 49 517.9, 511.5, 520.4, 513.9, 516.8, 516.3
517.3

E 98 724.3, 729.9, 725.6, 725.4, 733.8, 728.6
732.6

E 196 1034.9, 1042.4, 1045.6, 1044.1, 1042.1
1047.8, 1037.8

A1 0.098 20.5, 19.8, 20.6, 19.1, 18.7, 20.5, 22.3, 20.1
18.9, 20.2, 20.4

Al 0.245 32.1, 28.9, 28.4, 29.3, 33.5, 29.6, 30.5, 30.1
28.3, 30.0, 30.4

Al 0.49 45.4, 46.9, 49.1, 48.2, 44.6, 48.1, 49.7, 47.7
43.5, 47.9, 53.6

A1 0.98 68.9, 73.2, 71.7, 69.3, 70.5, 74.2, 68.4, 71.2
70.3, 75.1, 70.4

Al 1.96 106.8, 104.5, 103.3, 101.6, 105.6, 102.9
102.8, 99.0, 100.6, 99.2, 105.6

Al 2.94 126.8, 129.3, 128.1, 135.7, 127.6, 129.1
133.4, 128.7, 123.2

A1 4.9 170.4, 178.6, 173.9, 176.7, 179.1, 175.1
175.6, 177.2, 169.3

A1 9.8 236.9, 234.2, 231.4, 237.8, 240.1, 236.4
235.3, 238.5, 237.0

B1 0.098 19.3, 22.9, 20.6, 18.1, 20.2, 20.9, 22.1, 20.3
18.8, 19.9, 20.2

Bl 0.245 33.5, 29.6, 31.8, 34.1, 28.5, 34.6, 32.5, 32.9
33.2, 32.7, 38.5

B1 0.49 50.4, 46.9, 48.1, 48.4, 50.3, 47.2, 49.5, 48.8

 

 

 

 

138

 

 

50.2, 47.1, 49.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B1 0.98 70.1, 73.2, 68.6, 70.7, 69.4, 67.9, 72.7, 70.5
73.6, 69.0, 69.8

B1 1.96 96.3, 100.5, 104.9, 97.2, 95.6, 100.3, 99.1
95.2, 101.9, 96.7, 102.4

Bl 2.94 123.7, 120.9, 126.3, 125.4, 124.8, 124.3
128.3, 121.1, 123.9

B1 4.9 167.2, 163.8, 164.5, 166.3, 162.9, 165.2
168.4, 162.6, 165.9

B1 9.8 234.1, 239.3, 235.5, 233.8, 234.7, 236.7
236.9, 237.3, 242.0

C1 0.098 21.9, 18.9, 20.2, 18.1, 19.3, 22.5, 18.4, 19.7
19.3, 20.7, 17.7

CI 0.245 30.6, 27.2, 29.3, 26.8, 27.5, 28.1, 26.9, 28.7
27.9, 30.5, 32.2

Cl 0.49 48.3, 49.9, 45.4, 46.7, 46.1, 44.8, 50.2, 47.2
47.6, 45.1, 47.9

Cl 0.98 72.3, 69.4, 67.3, 71.8, 69.7, 68.1, 65.3, 69.8
75.8, 70.2, 68.1

Cl 1.96 104.6, 100.3, 102.7, 105.1, 104.8, 104
108.3, 99.3, 103.5, 104.1, 107.3

Cl 2.94 122.1, 123.9, 127.2, 126.8, 130.3, 125.5 -
120.4, 123.7, 129.6

CI 4.9 163.1, 160.2, 161.7, 162.4, 161.6, 162.3
160.9, 161.3, 167.2

Cl 9.8 233.8, 227.1, 229.5, 226.3, 228.2, 228.5
224.9, 230.8, 227.4

Fl 2.94 132.4, 127.9, 128.7, 133.6, 135.4, 130.8
126.1, 127.2, 135.1

F] 4.9 172.2, 175.9, 168.9, 170.4, 174.3, 171.6
171.9, 169.7, 169.5

F1 9.8 235.7, 236.3, 232.2, 238.1, 234.1, 234.9
230.5, 233.6, 238.7

F l 49 516.9, 522.4, 523.7, 518.6, 519.2, 521.2
526.4

F1 98 728.1, 724.3, 722.8, 730.1, 726.3, 725.2
719.6

F2 2.94 125.9, 118.7, 120.1, 119.3, 117.7, 120.4
118.5, 116.4, 126.6

F2 4.9 163.9, 164.8, 168.6, 162.5, 163.6, 164.6
161.9, 169.4, 162.1

F2 9.8 224.6, 223.2, 227.9, 220.1, 228.8, 224.8
224.2

F2 49 510.9, 513.8, 519.4, 516.1, 514.7, 514.3
510.7

F2 98 728.1, 725.3, 724.4, 722.6, 729.3, 725.8

 

 

 

 

139

 

 

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A total of 514 Vickers indents made in this study.

140

 

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