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Single-fiber pull-out from a microcomposite test
Composltes Science and Technology 48 (1993) 5-10
SINGLE-FIBER P U L L - O U T FROM A MICROCOMPOSITE TEST Yiping Qiu* & Peter Schwartz$ Fiber Science Program, CorneU University, Ithaca, New York 14853-4401, USA (Received 29 June 1992; revised version received 22 September 1992; accepted 16 November 1992)
Abstract Technical details and statistical analysis methods for a new fiber pull-out technique, single-fiber pull-out from a microcomposite, are discussed. The technique has been proved to be a versatile tool for the study of fiber~matrix interracial properties for various fiber/matrix systems. The specimen geometry can be controlled by adjusting the distance between the two plates, the tension on the fibers, and the amount of matrix applied. Appropriate statistical analysis is crucial for correct interpretation of the experimental resuits. A regression analysis using fiber volume fraction as an additional independent variable is recommended to detect the change of the interracial shear strength for different samples. Keywords: interface, fiber pull-out, bond strength, test methods, composite materials 1 INTRODUCTION Mechanical properties of fiber-reinforced composites depend on not only the properties of the fibers and the matrix but also the fiber/matrix interfacial properties, which have a complex structure, as described by Hughes. ~ The interracial properties are determined by the material properties such as the adhesion of the fiber surface to the matrix, as well as fiber volume fraction. If a fiber has neighboring fibers too close to it, which is the case when the fiber volume fraction is large, the interracial shear strength (IFSS), defined as peak load divided by embedment area, decreases because of the shear stress concentration induced by the neighbouring fibers. 2. In addition, the properties of the matrix may change when fibers are too close to each other, according to Williams et al. 3 The strength of the fiber/matrix interface is * Present address: Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. ~:To whom all correspondence should be addressed.
Composites Science and Technology 0266-3538/93/$06.00 © 1993 Elsevier Science Publishers Ltd.
measured by means of various test methods, among which the most popular are the fiber pull-out test, 4'5 the single-fiber composite test, 6 microbond test, 7 and the micro-indentor push-through test. a In the fiber pull-out test and the microbond test a fiber is pulled out of bulk matrix; this test is easy to perform but yields no information about a fiber volume fraction effect on interfacial properties. The single-fiber composite test has the same problem, as the fiber is also embedded in bulk matrix. Furthermore, it is not easy to separate frictional and debonding effects, which is one of the reasons why it is difficult to relate the fiber pull-out test results to the mechanical properties of the composites. Micro-indentation, on the other hand, can provide information fiber volume fraction effects and can be used for in situ experiments. However, the disadvantages of the test are: (1) calculation of the IFSS is complex and (2) it cannot be used for some fiber-reinforced composites, e.g. aramids. Recently, a new technique, known as the single-fiber pull-out from a microcomposite (SFPOM) test, has been developed in our laboratory. 9 The technique has been used for various systems and has proved to be a versatile tool for the investigation of fiber/matrix interracial properties and the effect of fiber volume fraction on the IFSS. This paper discusses some technical details of specimen fabrication and data analysis of the SFPOM test by using updated experimental results obtained in our laboratory.
2 SFPOM EXPERIMENTS 2.1 Fiber/epoxy systems To explore the potential application of SFPOM tests to fiber/matrix systems, several combinations of fiber and matrix were tried, viz. Kevlar-149/epoxy (a 7:3 blend of DER 331 and DER 732, and 12.74 phr DEH 26), S-glass/epoxy, Kevlar-149/S-glass/epoxy, Kevlar49/epoxy, and E-glass/b-staged-epoxy with arrangements of fibers shown in Fig. 1. Except for the E-glass/b-staged-epoxy system sample preparation was as follows.9 On each sample-holder, there were
Y. Qiu, P. Schwartz
All Kevlar-149
All S-glass
Kevlar-149 pull-out from an S-glass bundle
Fig. 1. Cross-section of the SFPOM specimens. two hexagonal plates of silicone rubber (Fig. 2). At each corner of the plate, a notch was cut to locate the fiber, to ensure the hexagonal geometry of the microcomposite. A slot reaching the center of the plate allows positioning of the central fiber. Individual springs hung as weights provided 2 . 5 + 0 - 1 m N of tension to each fiber. After all fibers were hung, the central fiber was coated with a layer of epoxy about 3 #m thick. A single 4.5 denier Dacron @ fiber was used to tie a knot bonding the six surrounding fibers to the central one. For the first three systems, specimens were cured at 80°C for 3 h and 100°C for 2 h. After curing, the samples were mounted on a sample-holding paper with cyanoacrylate adhesive. The pull-out tests were performed at 21°C and 65% relative humidity using an Instron Model 1122 tensile testing machine. The gauge length was 3 0 m m and the strain rate was 0-033 min -~. Typical views of S-glass/epoxy, Kevlar149/S-glass/epoxy and Kevlar-149/epoxy SFPOM specimens are shown in Figs 3-5.
Fig. 3. Typical S-glass/epoxy SFPOM specimen.
2.2 Sample geometry control One of the problems encountered in constructing SFPOM specimens is how to control the geometry of the specimens. It is difficult to control embedment
Fig. 4. Typical Kevlar-149/S-glass/epoxy SFPOM specimen, i
Microcomposite D
.....~ ......
Weight
Fig. 2. Illustrationof sample preparation.
Fig. 5. Typical Kevlar-49/epoxy SFPOM specimen.
Single-fiber pull-out from microcomposite test
length to a predetermined dimension, which makes the test more likely to be an observational experiment. In addition, if the fiber is weak, one may not be able to fabricate specimens with appropriate embedment lengths to pull the fiber out before the fiber fails. However, it is still possible to control the size of the specimens to a certain extent by means of changing sample preparation procedures as discussed below.
2. 2. I Embedment length control The specimens were prepared on a frame shown in Fig. 2, where the fibers are hanging over two plates. The distance between the two plates, D, determines the angle, y, between the central fiber and the surrounding fibers, which controls the embedment length. When y is too small, a longer part of the fiber bundle will be bonded by a certain amount of epoxy resin, resulting in a greater embedment length. There are two ways to adjust y: (1) changing the distance between the two plates; (2) varying the tension or the weight hanging on the surrounding fibers, which increases the torque on the part of the fibers close to the knot. The fiber used to tie the knot has to have an appropriate diameter to ensure the correct shape and length of the microcomposite; a thicker fiber makes the cross-section of the bundle more elliptical and results in a greater embedment length, and if the tie fiber is too thin, it will not be able to hold the fibers together if the tension is high. Another method to control the size of the microcomposite is by adjusting the amount of the epoxy resin. Of course, less resin on the central fiber before tying the knot results in a shorter embedment length and larger fiber volume fraction. However, too little resin could result in poor adhesion between the fiber and the matrix, or even a loosening bundle.
2. 2. 2 Fiber volume fraction control Fiber volume fraction can be adjusted using approaches similar to those described above. Increasing D leads to a larger fiber volume fraction, as does decreasing the weight pulling the fibers down. At the same time, less resin should be used, to avoid an increase of embedment length, because the space per unit length occupied by the resin is contained by the surrounding fibers. On the other hand, there is a positive correlation (R 2 ~ 0 . 4 for our data) between fiber volume fraction and embedment length if the cross-section of the microcomposite and y do not change, i.e. fiber volume fraction increases when embedment length increases. Thus, if the tension on the fibers and distance between the plates are constant, shorter embedment length usually generates a larger fiber volume fraction.
7
2.3 Working with solid matrices Solid matrices include b-staged epoxy resin and thermoplastic resin, which are solid at room temperature. The problem with these matrices is how to apply them on the central fiber before tying a knot. Generally, it is not possible to construct the specimens at elevated temperature, and the use of solvent may change the properties of the matrix. One solution is to spin the matrix into very short fibers (about twice the expected embedment length) with a diameter roughly 2-4 times that the central fiber, then place the small resin fiber on the center fiber parallel to the fiber axis, and melt the matrix using a heat source. Next, the knot is tied at the location of the matrix. 3 ANALYSIS OF THE RESULTS 3.1 Fiber volume fraction calculation The dimensions to be measured for fiber volume fraction calculation are determined by the calculation method. There is another method to calculate fiber volume fraction in addition to that described in Ref. 9. As, in most cases, the microcomposite has an elliptical cross-section, it is better to assume that the cross-section is an ellipse, with a and b as the intercepts of the ellipse on the x and y axis at the middle of the bundle, and d as the intercept on the x at the top (Fig. 6). If we use the upper part of the bundle, which has a length of L1, to calculate fiber volume fraction, the following equation can be used: Vf --
3a(6r2~/[(d - a) 2 + L2] 1/2+ L l r 2} bLl(a 2 + ad + d 2)
(1)
where rs and rc are diameters of the surrounding fiber and the central fiber, respectively. 3.2 Statistical analysis of the results Because of the high variability involved in this type of test, adequate statistical analysis is necessary to interpret the results correctly. As a common practice,
d
Fig. 6. Geometry used to calculate fiber volume fraction.
8
Y. Qiu, P. Schwartz
one should calculate the confidence intervals (CIs) for the slopes and intercepts in regression analysis for the relationship such as peak load vs embedment length. It is well known that the peak load will not increase beyond a certain embedment length when IFSS decreases with embedment length. 5 If this is the case, comparison between mean IFSS for two or more sets of data, say different treatments for the same fiber/matrix system, is not sensitive, as it involves variations created by large e m b e d m e n t length. Using peak load as a function of embedment length, e.g. using the equation suggested by Piggott 4 or Penn and Lee 5 as a basic relation, we can perform a regression analysis to examine the differences between the treatments. As an example, if we assume that the relation between peak load and embedment length obeys Fa ocL, the following regression model can be used:
FAi = flO + fllLi + r2 T r e a t / + (f13 Treati x Li) + ei
(2)
where FA is the peak load, L the e m b e d m e n t length, flo-fl3 are regression coefficients, ei are errors independently identically distributed with N(0, o2), and {~ i f T r e a t m e n t l Treat = if Treatment 2 Here r3 is the difference between the slopes of peak load vs L for the two treatments. If the two curves are parallel, the interaction term, T r e a t × L, can be eliminated from the above model. 1° r2 represents the difference of peak load between the two treatments at a constant embedment length. In the SFPOM test, it is important to employ an appropriate statistical model to handle the data because the fiber volume fraction effect on IFSS increases the variance of the peak load. From the following example, it is easy to see that the method used to analyze the data directly influences the conclusions we draw. In studying the role of the interfacial properties in the hybrid effect of a Kelvar-149/S-glass/epoxy system, 11 we collected two data sets: pure Kevlar-149 microcomposites (in which a Kevlar fiber is pulled out of Kevlar microcomposites) and Kevlar pulled out of S-glass microcomposites. To see the difference between the two treatments, we first compare the mean IFSS of the two treatments using a t-test; no difference was detected (P > 0.05). Then, we adopted eqn (2) as the regression model but replaced L with embedment area; again, no significant difference was discovered. However, when we looked at the plot of IFSS vs fiber volume fraction for the two treatments, we found that the IFSS decreases with the increase of fiber volume fraction slower (smaller slope) for Kevlar in glass than for Kevlar in Kevlar (P < 0.05). If we ignore this difference in slopes, the average IFSS for Kevlar in
glass is 8.67 MPa (95% CI = (5-09 MPa, 12.25 MPa)) larger than that for Kevlar in Kevlar at the same fiber volume fraction. Why do we have significant difference in IFSS vs fiber volume fraction but no difference in peak load vs embedment area for the two treatments? The reason is that the fiber volume fractions with the same embedment area for the two treatments are different ( P < 0 . 0 5 , 95% C I = (8-649%, 17-495%)). Therefore, when assessing whether there is any difference between the peak load of the two treatments at the same e m b e d m e n t area, we have to take fiber volume fraction effect into account, which can be accomplished by using fiber volume fraction as an additional independent variable (or a concomitant) in a regression analysis, where the regression model is
FAi =
r 0 q- fll A r e a / + r2 T r e a t / +
fl3Vfi .~L (f14 Area/
x Treat/) + (f15 A r e a / x Vfi) + (fl6 Treatit x Vfi) + ei
(3) where Treat =
{01 i f K e v l a r i n g l a s s if Kevlar in Kevlar
Vf is fiber volume fraction, flo-fl6 are regression coefficients, and Area x Treat, Area x Vf, and Treat x Vf are interaction terms between the independent variables. The regression analysis showed that the two interaction terms, A r e a x Vf and Treat x Vf, were not significant at re=0-05, but A r e a × T r e a t was significant, and the estimated regression equation is FA = 8.12 - 11.5 Treat - 0.183Vf + 0-0032 Area + 0.00146 (Area x Treat)
(4)
Using this model, we found that there did exist a difference (P < 0.05) between the peak loads of the two treatments, when fiber volume fraction and embedment area are kept constant. Additionally, the slope of peak load vs area at constant Vf, i.e.
aFA
- = 0-0032 + 0.00146 Treat 0Area
(5)
increases for Kevlar in Kevlar. However, the increase is so small that it could not compensate for the decrease in the intercept ( l l . 4 4 m N ) . Using the equation for the relation between the peak load and the shear stress proposed by Piggott and Wang, 12 FA ---- ~'iu Area + Fo
(6)
where riu is a constant shear stress, which is equivalent to the regression coefficients fll for Kevlar in glass and fll + r4 for Kevlar in Kevlar in our case for a constant fiber volume fraction, and F0 is the intercept believed to be caused by environmental factors, such as meniscus, and temperature changes. 12
Single-fiber pull-out from microcomposite test As only a slight difference in riu was observed, the major difference in IFSS at a constant fiber volume fraction came from the intercepts (note that our definition of IFSS is different from tin). In this study, the curing conditions for the two samples were the same, as were the testing conditions. Also, the geometries of the two types of specimens were similar. The difference has to come from the properties of the surrounding fibers, which created a different environment for the central fiber. Thus, we not only found a difference between the two treatments but also isolated the source of the difference. This result helped to explain the source of the hybrid effect. H Thus, the above regression model is r e c o m m e n d e d for SFPOM data analysis.
3.3 Visual examination of specimens after testing When the central fiber is pulled out, the failure can occur at the fiber/matrix interface, the interphase (a very thin layer of matrix from the fiber surface), in the matrix, or even in the fiber. To detect the location of the failure is an important but difficult task, especially when there is only a trace of the matrix adhering on the surface of the fiber or a trace of the fiber peeling off the matrix. The methods that should be employed in these two cases have been discussed by U. G a u r (1992, pets. comm.). H e r e , we want to show how the failure modes which can be visually observed under microscope could affect the results of SFPOM test. Examining the pure S-glass fiber/epoxy SFPOM specimens, we found that most of the fibers pulled out of the microcomposite had a cone-shaped matrix adhering to them. 11 In the plot of IFSS vs fiber volume fraction (Fig. 7), it is obvious that no relationship between the two ( R 2 = 0 . 0 1 8 ) can be claimed, which is easy to understand because we were testing shear strength of the matrix. Matrix failure can also be such that a fiber is pulled out with a tube of matrix (a thick and rather uniform layer of matrix) as observed in E-glass fiber/b-staged matrix specimens.
8O
6O
oO
o
5O 40
0
0
0
~0
0 2O
8
%
~0
40
o
10
ii 2O
If matrix failure occurs, IFSS is not an appropriate term to use for peak load divided by e m b e d m e n t area.
4 ADVANTAGES AND DISADVANTAGES The advantages of the single-fiber pull-out from a microcomposite test are as follows: (1) the test can be used to measure the fiber volume fraction effect on IFSS; (2) different types of fibers can be used to construct one specimen; (3) it is easy to observe the failure mode if matrix failure occurs; (4) calculation of the results is simple compared with the micro-indentation test. The disadvantages of SFPOM tests are as follows: (1) specimen geometry is not easy to control; (2) it is difficult to make specimens with very weak fibers; (3) defects in the microcomposites are hard to detect. 5 CONCLUSION (1) SFPOM can be used for various types of systems with one or more types of fiber in one specimen, and liquid or solid matrix before curing. (2) The geometry of the specimens can be adjusted by altering the distance between the two plates, the tension on the fibers, and the amount of matrix applied. (3) Statistical analysis has to be carried out carefully to include the fiber volume fraction effect. A regression analysis using the fiber volume fraction as an additional independent variable is necessary to detect the change in interracial shear strength for different treatments.
REFERENCES
0
7O
9
/10
60
70
Fibre" volume f r a ~ o n (%)
Fig. 7. Relation between IFSS and fiber volume fraction in S-glass/epoxy SFPOM tests.
1. Hughes, J. D. H., The carbon fiber/matrix interface--a review. Composites Sci. Technol., 41 (1991) 13-45. 2. Greszczuk, L. B., Theoretical studies of the mechanics of the fiber-matrix interface in composites. Interfaces in Composites, ASTM STP 452. American Society for Testing and Materials, Philadelphia, PA, 1969, pp. 42-56. 3. Williams, J. G., Donnellan, M. E., James, M. R. & Morris, W. L., Properties of the interphase in organic matrix composites. Mater. Sci. Eng., A216 (1990) 305-12. 4. Piggott, M. R., Debonding and friction at fiberpolymer interfaces. I: Criteria for failure and sliding. Composites Sci. Technol., 30 (1987) 295-8. 5. Penn, L. S. & Lee, S. M., Interpretation of
10
Y. Qiu, P. Schwartz
experimental results in the single pull-out filament test. J. Composites Technol. Res., 11 (1989) 23-30. 6. Netravali, A. N., Henstenburg, R. B., Phoenix, S. L. & Schwartz, P., Interracial shear strength studies using the single-filament-composite test. Polym. Composites, 10 (1989) 226-41. 7. Miller, B., Muff, P. & Rebenfeld, L., A microbond method for determination of the shear strength of a fiber/resin interface. Composites Sci. Technol., 28 (1987) 17-32. 8. Mandell, J. F., Grande, D. H., Tsiang, T. H. & McGarry, F. J., Modified microdebonding test for direct in situ fiber/matrix bond strength determination in fiber composites. Composite Materials: Testing and Design (Seventh Conference), ASTM STP 893, ed. J. M. Whitney. American Society for Testing and Materials, Philadelphia, PA, 1986, pp. 87-108.
9. Qiu, Y. & Schwartz, P., A new method for study of the fiber-matrix interface in composites: single fiber pull-out from a microcomposite. Adhesion Sci. Technol., 9 (1991) 741-56. 10. Neter, J., Wasserman, W. & Kutner, M. H., Applied Linear Statistical Models: Regression, Analysis of Variance and Experimental Designs, 3rd edn Richard D. Irwin, Boston, MA, 1990, 271-314. 11. Qiu, Y. & Schwartz, P., Micromechanical behavior of Kevlar 149/S-glass hybrid seven-fiber microcomposite. I: Tensile strength of the hybrid composite. Composites Sci. Technol. (in press). 12. Piggott, M. R. & Wang, Z. N., Relations between polymer and fiber-polymer interface properties. Proc. Am. Soc. Composites, American Society of Composites, Albany, NY, 1991, pp. 725-31.
SINGLE-FIBER P U L L - O U T FROM A MICROCOMPOSITE TEST Yiping Qiu* & Peter Schwartz$ Fiber Science Program, CorneU University, Ithaca, New York 14853-4401, USA (Received 29 June 1992; revised version received 22 September 1992; accepted 16 November 1992)
Abstract Technical details and statistical analysis methods for a new fiber pull-out technique, single-fiber pull-out from a microcomposite, are discussed. The technique has been proved to be a versatile tool for the study of fiber~matrix interracial properties for various fiber/matrix systems. The specimen geometry can be controlled by adjusting the distance between the two plates, the tension on the fibers, and the amount of matrix applied. Appropriate statistical analysis is crucial for correct interpretation of the experimental resuits. A regression analysis using fiber volume fraction as an additional independent variable is recommended to detect the change of the interracial shear strength for different samples. Keywords: interface, fiber pull-out, bond strength, test methods, composite materials 1 INTRODUCTION Mechanical properties of fiber-reinforced composites depend on not only the properties of the fibers and the matrix but also the fiber/matrix interfacial properties, which have a complex structure, as described by Hughes. ~ The interracial properties are determined by the material properties such as the adhesion of the fiber surface to the matrix, as well as fiber volume fraction. If a fiber has neighboring fibers too close to it, which is the case when the fiber volume fraction is large, the interracial shear strength (IFSS), defined as peak load divided by embedment area, decreases because of the shear stress concentration induced by the neighbouring fibers. 2. In addition, the properties of the matrix may change when fibers are too close to each other, according to Williams et al. 3 The strength of the fiber/matrix interface is * Present address: Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. ~:To whom all correspondence should be addressed.
Composites Science and Technology 0266-3538/93/$06.00 © 1993 Elsevier Science Publishers Ltd.
measured by means of various test methods, among which the most popular are the fiber pull-out test, 4'5 the single-fiber composite test, 6 microbond test, 7 and the micro-indentor push-through test. a In the fiber pull-out test and the microbond test a fiber is pulled out of bulk matrix; this test is easy to perform but yields no information about a fiber volume fraction effect on interfacial properties. The single-fiber composite test has the same problem, as the fiber is also embedded in bulk matrix. Furthermore, it is not easy to separate frictional and debonding effects, which is one of the reasons why it is difficult to relate the fiber pull-out test results to the mechanical properties of the composites. Micro-indentation, on the other hand, can provide information fiber volume fraction effects and can be used for in situ experiments. However, the disadvantages of the test are: (1) calculation of the IFSS is complex and (2) it cannot be used for some fiber-reinforced composites, e.g. aramids. Recently, a new technique, known as the single-fiber pull-out from a microcomposite (SFPOM) test, has been developed in our laboratory. 9 The technique has been used for various systems and has proved to be a versatile tool for the investigation of fiber/matrix interracial properties and the effect of fiber volume fraction on the IFSS. This paper discusses some technical details of specimen fabrication and data analysis of the SFPOM test by using updated experimental results obtained in our laboratory.
2 SFPOM EXPERIMENTS 2.1 Fiber/epoxy systems To explore the potential application of SFPOM tests to fiber/matrix systems, several combinations of fiber and matrix were tried, viz. Kevlar-149/epoxy (a 7:3 blend of DER 331 and DER 732, and 12.74 phr DEH 26), S-glass/epoxy, Kevlar-149/S-glass/epoxy, Kevlar49/epoxy, and E-glass/b-staged-epoxy with arrangements of fibers shown in Fig. 1. Except for the E-glass/b-staged-epoxy system sample preparation was as follows.9 On each sample-holder, there were
Y. Qiu, P. Schwartz
All Kevlar-149
All S-glass
Kevlar-149 pull-out from an S-glass bundle
Fig. 1. Cross-section of the SFPOM specimens. two hexagonal plates of silicone rubber (Fig. 2). At each corner of the plate, a notch was cut to locate the fiber, to ensure the hexagonal geometry of the microcomposite. A slot reaching the center of the plate allows positioning of the central fiber. Individual springs hung as weights provided 2 . 5 + 0 - 1 m N of tension to each fiber. After all fibers were hung, the central fiber was coated with a layer of epoxy about 3 #m thick. A single 4.5 denier Dacron @ fiber was used to tie a knot bonding the six surrounding fibers to the central one. For the first three systems, specimens were cured at 80°C for 3 h and 100°C for 2 h. After curing, the samples were mounted on a sample-holding paper with cyanoacrylate adhesive. The pull-out tests were performed at 21°C and 65% relative humidity using an Instron Model 1122 tensile testing machine. The gauge length was 3 0 m m and the strain rate was 0-033 min -~. Typical views of S-glass/epoxy, Kevlar149/S-glass/epoxy and Kevlar-149/epoxy SFPOM specimens are shown in Figs 3-5.
Fig. 3. Typical S-glass/epoxy SFPOM specimen.
2.2 Sample geometry control One of the problems encountered in constructing SFPOM specimens is how to control the geometry of the specimens. It is difficult to control embedment
Fig. 4. Typical Kevlar-149/S-glass/epoxy SFPOM specimen, i
Microcomposite D
.....~ ......
Weight
Fig. 2. Illustrationof sample preparation.
Fig. 5. Typical Kevlar-49/epoxy SFPOM specimen.
Single-fiber pull-out from microcomposite test
length to a predetermined dimension, which makes the test more likely to be an observational experiment. In addition, if the fiber is weak, one may not be able to fabricate specimens with appropriate embedment lengths to pull the fiber out before the fiber fails. However, it is still possible to control the size of the specimens to a certain extent by means of changing sample preparation procedures as discussed below.
2. 2. I Embedment length control The specimens were prepared on a frame shown in Fig. 2, where the fibers are hanging over two plates. The distance between the two plates, D, determines the angle, y, between the central fiber and the surrounding fibers, which controls the embedment length. When y is too small, a longer part of the fiber bundle will be bonded by a certain amount of epoxy resin, resulting in a greater embedment length. There are two ways to adjust y: (1) changing the distance between the two plates; (2) varying the tension or the weight hanging on the surrounding fibers, which increases the torque on the part of the fibers close to the knot. The fiber used to tie the knot has to have an appropriate diameter to ensure the correct shape and length of the microcomposite; a thicker fiber makes the cross-section of the bundle more elliptical and results in a greater embedment length, and if the tie fiber is too thin, it will not be able to hold the fibers together if the tension is high. Another method to control the size of the microcomposite is by adjusting the amount of the epoxy resin. Of course, less resin on the central fiber before tying the knot results in a shorter embedment length and larger fiber volume fraction. However, too little resin could result in poor adhesion between the fiber and the matrix, or even a loosening bundle.
2. 2. 2 Fiber volume fraction control Fiber volume fraction can be adjusted using approaches similar to those described above. Increasing D leads to a larger fiber volume fraction, as does decreasing the weight pulling the fibers down. At the same time, less resin should be used, to avoid an increase of embedment length, because the space per unit length occupied by the resin is contained by the surrounding fibers. On the other hand, there is a positive correlation (R 2 ~ 0 . 4 for our data) between fiber volume fraction and embedment length if the cross-section of the microcomposite and y do not change, i.e. fiber volume fraction increases when embedment length increases. Thus, if the tension on the fibers and distance between the plates are constant, shorter embedment length usually generates a larger fiber volume fraction.
7
2.3 Working with solid matrices Solid matrices include b-staged epoxy resin and thermoplastic resin, which are solid at room temperature. The problem with these matrices is how to apply them on the central fiber before tying a knot. Generally, it is not possible to construct the specimens at elevated temperature, and the use of solvent may change the properties of the matrix. One solution is to spin the matrix into very short fibers (about twice the expected embedment length) with a diameter roughly 2-4 times that the central fiber, then place the small resin fiber on the center fiber parallel to the fiber axis, and melt the matrix using a heat source. Next, the knot is tied at the location of the matrix. 3 ANALYSIS OF THE RESULTS 3.1 Fiber volume fraction calculation The dimensions to be measured for fiber volume fraction calculation are determined by the calculation method. There is another method to calculate fiber volume fraction in addition to that described in Ref. 9. As, in most cases, the microcomposite has an elliptical cross-section, it is better to assume that the cross-section is an ellipse, with a and b as the intercepts of the ellipse on the x and y axis at the middle of the bundle, and d as the intercept on the x at the top (Fig. 6). If we use the upper part of the bundle, which has a length of L1, to calculate fiber volume fraction, the following equation can be used: Vf --
3a(6r2~/[(d - a) 2 + L2] 1/2+ L l r 2} bLl(a 2 + ad + d 2)
(1)
where rs and rc are diameters of the surrounding fiber and the central fiber, respectively. 3.2 Statistical analysis of the results Because of the high variability involved in this type of test, adequate statistical analysis is necessary to interpret the results correctly. As a common practice,
d
Fig. 6. Geometry used to calculate fiber volume fraction.
8
Y. Qiu, P. Schwartz
one should calculate the confidence intervals (CIs) for the slopes and intercepts in regression analysis for the relationship such as peak load vs embedment length. It is well known that the peak load will not increase beyond a certain embedment length when IFSS decreases with embedment length. 5 If this is the case, comparison between mean IFSS for two or more sets of data, say different treatments for the same fiber/matrix system, is not sensitive, as it involves variations created by large e m b e d m e n t length. Using peak load as a function of embedment length, e.g. using the equation suggested by Piggott 4 or Penn and Lee 5 as a basic relation, we can perform a regression analysis to examine the differences between the treatments. As an example, if we assume that the relation between peak load and embedment length obeys Fa ocL, the following regression model can be used:
FAi = flO + fllLi + r2 T r e a t / + (f13 Treati x Li) + ei
(2)
where FA is the peak load, L the e m b e d m e n t length, flo-fl3 are regression coefficients, ei are errors independently identically distributed with N(0, o2), and {~ i f T r e a t m e n t l Treat = if Treatment 2 Here r3 is the difference between the slopes of peak load vs L for the two treatments. If the two curves are parallel, the interaction term, T r e a t × L, can be eliminated from the above model. 1° r2 represents the difference of peak load between the two treatments at a constant embedment length. In the SFPOM test, it is important to employ an appropriate statistical model to handle the data because the fiber volume fraction effect on IFSS increases the variance of the peak load. From the following example, it is easy to see that the method used to analyze the data directly influences the conclusions we draw. In studying the role of the interfacial properties in the hybrid effect of a Kelvar-149/S-glass/epoxy system, 11 we collected two data sets: pure Kevlar-149 microcomposites (in which a Kevlar fiber is pulled out of Kevlar microcomposites) and Kevlar pulled out of S-glass microcomposites. To see the difference between the two treatments, we first compare the mean IFSS of the two treatments using a t-test; no difference was detected (P > 0.05). Then, we adopted eqn (2) as the regression model but replaced L with embedment area; again, no significant difference was discovered. However, when we looked at the plot of IFSS vs fiber volume fraction for the two treatments, we found that the IFSS decreases with the increase of fiber volume fraction slower (smaller slope) for Kevlar in glass than for Kevlar in Kevlar (P < 0.05). If we ignore this difference in slopes, the average IFSS for Kevlar in
glass is 8.67 MPa (95% CI = (5-09 MPa, 12.25 MPa)) larger than that for Kevlar in Kevlar at the same fiber volume fraction. Why do we have significant difference in IFSS vs fiber volume fraction but no difference in peak load vs embedment area for the two treatments? The reason is that the fiber volume fractions with the same embedment area for the two treatments are different ( P < 0 . 0 5 , 95% C I = (8-649%, 17-495%)). Therefore, when assessing whether there is any difference between the peak load of the two treatments at the same e m b e d m e n t area, we have to take fiber volume fraction effect into account, which can be accomplished by using fiber volume fraction as an additional independent variable (or a concomitant) in a regression analysis, where the regression model is
FAi =
r 0 q- fll A r e a / + r2 T r e a t / +
fl3Vfi .~L (f14 Area/
x Treat/) + (f15 A r e a / x Vfi) + (fl6 Treatit x Vfi) + ei
(3) where Treat =
{01 i f K e v l a r i n g l a s s if Kevlar in Kevlar
Vf is fiber volume fraction, flo-fl6 are regression coefficients, and Area x Treat, Area x Vf, and Treat x Vf are interaction terms between the independent variables. The regression analysis showed that the two interaction terms, A r e a x Vf and Treat x Vf, were not significant at re=0-05, but A r e a × T r e a t was significant, and the estimated regression equation is FA = 8.12 - 11.5 Treat - 0.183Vf + 0-0032 Area + 0.00146 (Area x Treat)
(4)
Using this model, we found that there did exist a difference (P < 0.05) between the peak loads of the two treatments, when fiber volume fraction and embedment area are kept constant. Additionally, the slope of peak load vs area at constant Vf, i.e.
aFA
- = 0-0032 + 0.00146 Treat 0Area
(5)
increases for Kevlar in Kevlar. However, the increase is so small that it could not compensate for the decrease in the intercept ( l l . 4 4 m N ) . Using the equation for the relation between the peak load and the shear stress proposed by Piggott and Wang, 12 FA ---- ~'iu Area + Fo
(6)
where riu is a constant shear stress, which is equivalent to the regression coefficients fll for Kevlar in glass and fll + r4 for Kevlar in Kevlar in our case for a constant fiber volume fraction, and F0 is the intercept believed to be caused by environmental factors, such as meniscus, and temperature changes. 12
Single-fiber pull-out from microcomposite test As only a slight difference in riu was observed, the major difference in IFSS at a constant fiber volume fraction came from the intercepts (note that our definition of IFSS is different from tin). In this study, the curing conditions for the two samples were the same, as were the testing conditions. Also, the geometries of the two types of specimens were similar. The difference has to come from the properties of the surrounding fibers, which created a different environment for the central fiber. Thus, we not only found a difference between the two treatments but also isolated the source of the difference. This result helped to explain the source of the hybrid effect. H Thus, the above regression model is r e c o m m e n d e d for SFPOM data analysis.
3.3 Visual examination of specimens after testing When the central fiber is pulled out, the failure can occur at the fiber/matrix interface, the interphase (a very thin layer of matrix from the fiber surface), in the matrix, or even in the fiber. To detect the location of the failure is an important but difficult task, especially when there is only a trace of the matrix adhering on the surface of the fiber or a trace of the fiber peeling off the matrix. The methods that should be employed in these two cases have been discussed by U. G a u r (1992, pets. comm.). H e r e , we want to show how the failure modes which can be visually observed under microscope could affect the results of SFPOM test. Examining the pure S-glass fiber/epoxy SFPOM specimens, we found that most of the fibers pulled out of the microcomposite had a cone-shaped matrix adhering to them. 11 In the plot of IFSS vs fiber volume fraction (Fig. 7), it is obvious that no relationship between the two ( R 2 = 0 . 0 1 8 ) can be claimed, which is easy to understand because we were testing shear strength of the matrix. Matrix failure can also be such that a fiber is pulled out with a tube of matrix (a thick and rather uniform layer of matrix) as observed in E-glass fiber/b-staged matrix specimens.
8O
6O
oO
o
5O 40
0
0
0
~0
0 2O
8
%
~0
40
o
10
ii 2O
If matrix failure occurs, IFSS is not an appropriate term to use for peak load divided by e m b e d m e n t area.
4 ADVANTAGES AND DISADVANTAGES The advantages of the single-fiber pull-out from a microcomposite test are as follows: (1) the test can be used to measure the fiber volume fraction effect on IFSS; (2) different types of fibers can be used to construct one specimen; (3) it is easy to observe the failure mode if matrix failure occurs; (4) calculation of the results is simple compared with the micro-indentation test. The disadvantages of SFPOM tests are as follows: (1) specimen geometry is not easy to control; (2) it is difficult to make specimens with very weak fibers; (3) defects in the microcomposites are hard to detect. 5 CONCLUSION (1) SFPOM can be used for various types of systems with one or more types of fiber in one specimen, and liquid or solid matrix before curing. (2) The geometry of the specimens can be adjusted by altering the distance between the two plates, the tension on the fibers, and the amount of matrix applied. (3) Statistical analysis has to be carried out carefully to include the fiber volume fraction effect. A regression analysis using the fiber volume fraction as an additional independent variable is necessary to detect the change in interracial shear strength for different treatments.
REFERENCES
0
7O
9
/10
60
70
Fibre" volume f r a ~ o n (%)
Fig. 7. Relation between IFSS and fiber volume fraction in S-glass/epoxy SFPOM tests.
1. Hughes, J. D. H., The carbon fiber/matrix interface--a review. Composites Sci. Technol., 41 (1991) 13-45. 2. Greszczuk, L. B., Theoretical studies of the mechanics of the fiber-matrix interface in composites. Interfaces in Composites, ASTM STP 452. American Society for Testing and Materials, Philadelphia, PA, 1969, pp. 42-56. 3. Williams, J. G., Donnellan, M. E., James, M. R. & Morris, W. L., Properties of the interphase in organic matrix composites. Mater. Sci. Eng., A216 (1990) 305-12. 4. Piggott, M. R., Debonding and friction at fiberpolymer interfaces. I: Criteria for failure and sliding. Composites Sci. Technol., 30 (1987) 295-8. 5. Penn, L. S. & Lee, S. M., Interpretation of
10
Y. Qiu, P. Schwartz
experimental results in the single pull-out filament test. J. Composites Technol. Res., 11 (1989) 23-30. 6. Netravali, A. N., Henstenburg, R. B., Phoenix, S. L. & Schwartz, P., Interracial shear strength studies using the single-filament-composite test. Polym. Composites, 10 (1989) 226-41. 7. Miller, B., Muff, P. & Rebenfeld, L., A microbond method for determination of the shear strength of a fiber/resin interface. Composites Sci. Technol., 28 (1987) 17-32. 8. Mandell, J. F., Grande, D. H., Tsiang, T. H. & McGarry, F. J., Modified microdebonding test for direct in situ fiber/matrix bond strength determination in fiber composites. Composite Materials: Testing and Design (Seventh Conference), ASTM STP 893, ed. J. M. Whitney. American Society for Testing and Materials, Philadelphia, PA, 1986, pp. 87-108.
9. Qiu, Y. & Schwartz, P., A new method for study of the fiber-matrix interface in composites: single fiber pull-out from a microcomposite. Adhesion Sci. Technol., 9 (1991) 741-56. 10. Neter, J., Wasserman, W. & Kutner, M. H., Applied Linear Statistical Models: Regression, Analysis of Variance and Experimental Designs, 3rd edn Richard D. Irwin, Boston, MA, 1990, 271-314. 11. Qiu, Y. & Schwartz, P., Micromechanical behavior of Kevlar 149/S-glass hybrid seven-fiber microcomposite. I: Tensile strength of the hybrid composite. Composites Sci. Technol. (in press). 12. Piggott, M. R. & Wang, Z. N., Relations between polymer and fiber-polymer interface properties. Proc. Am. Soc. Composites, American Society of Composites, Albany, NY, 1991, pp. 725-31.