4 Performance The performance of an engineering material is judged by its properties and behavior under tensile,compressive,shear,and other static or dynamic loading conditions in both normal and adverse test environments.This information is essential for selecting the proper material in a given application as well as designing a structure with the selected material.In this chapter,we describe the performance of fiber-reinforced polymer composites with an emphasis on the general trends observed in their properties and behavior.A wealth of property data for continuous fiber thermoset matrix composites exists in the published literature.Continuous fiber-reinforced thermoplastic matrix com- posites are not as widely used as continuous fiber-reinforced thermoset matrix composites and lack a wide database. Material properties are usually determined by conducting mechanical and physical tests under controlled laboratory conditions.The orthotropic nature of fiber-reinforced composites has led to the development of standard test methods that are often different from those used for traditional isotropic materials.These unique test methods and their limitations are discussed in relation to many of the properties considered in this chapter.The effects of environmental conditions,such as elevated temperature or humidity,on the physical and mechanical properties of composite laminates are presented near the end of the chapter.Finally,long-term behavior,such as creep and stress rupture,and damage tolerance are also discussed. 4.1 STATIC MECHANICAL PROPERTIES Static mechanical properties,such as tensile,compressive,flexural,and shear properties,of a material are the basic design data in many,if not most, applications.Typical mechanical property values for a number of 0 laminates and sheet-molding compound(SMC)laminates are given in Appendix A.5 and Appendix A.6,respectively. 4.1.1 TENSILE PROPERTIES 4.1.1.1 Test Method and Analysis Tensile properties,such as tensile strength,tensile modulus,and Poisson's ratio of flat composite laminates,are determined by static tension tests in accordance 2007 by Taylor Francis Group.LLC
4 Performance The performance of an engineering material is judged by its properties and behavior under tensile, compressive, shear, and other static or dynamic loading conditions in both normal and adverse test environments. This information is essential for selecting the proper material in a given application as well as designing a structure with the selected material. In this chapter, we describe the performance of fiber-reinforced polymer composites with an emphasis on the general trends observed in their properties and behavior. A wealth of property data for continuous fiber thermoset matrix composites exists in the published literature. Continuous fiber-reinforced thermoplastic matrix composites are not as widely used as continuous fiber-reinforced thermoset matrix composites and lack a wide database. Material properties are usually determined by conducting mechanical and physical tests under controlled laboratory conditions. The orthotropic nature of fiber-reinforced composites has led to the development of standard test methods that are often different from those used for traditional isotropic materials. These unique test methods and their limitations are discussed in relation to many of the properties considered in this chapter. The effects of environmental conditions, such as elevated temperature or humidity, on the physical and mechanical properties of composite laminates are presented near the end of the chapter. Finally, long-term behavior, such as creep and stress rupture, and damage tolerance are also discussed. 4.1 STATIC MECHANICAL PROPERTIES Static mechanical properties, such as tensile, compressive, flexural, and shear properties, of a material are the basic design data in many, if not most, applications. Typical mechanical property values for a number of 08 laminates and sheet-molding compound (SMC) laminates are given in Appendix A.5 and Appendix A.6, respectively. 4.1.1 TENSILE PROPERTIES 4.1.1.1 Test Method and Analysis Tensile properties, such as tensile strength, tensile modulus, and Poisson’s ratio of flat composite laminates, are determined by static tension tests in accordance 2007 by Taylor & Francis Group, LLC
-38 mm (1.5 in.)Gage length +2(width) +中-38mm(15in.)+ End tab End tab Width Tab 25 thickness LSpecimen thickness Tab thickness FIGURE 4.1 Tensile test specimen configuration. with ASTM D3039.The tensile specimen is straight-sided and has a constant cross section with beveled tabs adhesively bonded at its ends (Figure 4.1). A compliant and strain-compatible material is used for the end tabs to reduce stress concentrations in the gripped area and thereby promote tensile failure in the gage section.Balanced [0/90]cross-ply tabs of nonwoven E-glass-epoxy have shown satisfactory results.Any high-elongation (tough)adhesive system can be used for mounting the end tabs to the test specimen. The tensile specimen is held in a testing machine by wedge action grips and pulled at a recommended cross-head speed of 2 mm/min (0.08 in./min). Longitudinal and transverse strains are measured employing electrical resistance strain gages that are bonded in the gage section of the specimen.Longitudinal tensile modulus Eu and the major Poisson's ratio v12 are determined from the tension test data of o unidirectional laminates.The transverse modulus E22 and the minor Poisson's ratio vz are determined from the tension test data of 90 unidirectional laminates. For an off-axis unidirectional specimen (0<0<90),a tensile load creates both extension and shear deformations (since 416 and 4260).Since the specimen ends are constrained by the grips,shear forces and bending couples are induced that create a nonuniform S-shaped deformation in the specimen (Figure 4.2).For this reason,the experimentally determined modulus of an off- axis specimen is corrected to obtain its true modulus [1]: Etrue =(1-m)Eexperimental, where 356 7=3,356/5）+2L/wT' (4.1) 2007 by Taylor Francis Group,LLC
with ASTM D3039. The tensile specimen is straight-sided and has a constant cross section with beveled tabs adhesively bonded at its ends (Figure 4.1). A compliant and strain-compatible material is used for the end tabs to reduce stress concentrations in the gripped area and thereby promote tensile failure in the gage section. Balanced [0=90] cross-ply tabs of nonwoven E-glass–epoxy have shown satisfactory results. Any high-elongation (tough) adhesive system can be used for mounting the end tabs to the test specimen. The tensile specimen is held in a testing machine by wedge action grips and pulled at a recommended cross-head speed of 2 mm=min (0.08 in.=min). Longitudinal and transverse strains are measured employing electrical resistance strain gages that are bonded in the gage section of the specimen. Longitudinal tensile modulus E11 and the major Poisson’s ratio n12 are determined from the tension test data of 08 unidirectional laminates. The transverse modulus E22 and the minor Poisson’s ratio n21 are determined from the tension test data of 908 unidirectional laminates. For an off-axis unidirectional specimen (08 < u < 908), a tensile load creates both extension and shear deformations (since A16 and A26 6¼ 0). Since the specimen ends are constrained by the grips, shear forces and bending couples are induced that create a nonuniform S-shaped deformation in the specimen (Figure 4.2). For this reason, the experimentally determined modulus of an offaxis specimen is corrected to obtain its true modulus [1]: Etrue ¼ (1 h) Eexperimental, where h ¼ 3S2 16 S2 11[3(S66=S11) þ 2(L=w) 2 ] , (4:1) ≥58 Specimen thickness Tab thickness Tab thickness End tab Width 38 mm (1.5 in.) Gage length + 2 (width) 38 mm (1.5 in.) End tab FIGURE 4.1 Tensile test specimen configuration. 2007 by Taylor & Francis Group, LLC.
FIGURE 4.2 Nonuniform deformation in a gripped off-axis tension specimen. where L is the specimen length between grips w is the specimen width Su,S16,and S66 are elements in the compliance matrix (see Chapter 3) The value of n approaches zero for large values of L/w.Based on the investigation performed by Rizzo [2],L/w ratios >10 are recommended for the tensile testing of off-axis specimens. The inhomogeneity of a composite laminate and the statistical nature of its constituent properties often lead to large variation in its tensile strength. Assuming a normal distribution,the average strength,standard deviation, and coefficient of variation are usually reported as Average strength Cave= Standard deviation =d= (n-1) 100d Coefficient of variation= (4.2) Jave where n is the number of specimens tested o;is the tensile strength of the ith specimen Instead of a normal distribution,a more realistic representation of the tensile strength variation of a composite laminate is the Weibull distribution. Using two-parameter Weibull statistics,the cumulative density function for the composite laminate strength is F(o)=Probability of surviving stress o=e exp (4.3) 2007 by Taylor&Francis Group.LLC
where L is the specimen length between grips w is the specimen width S11,S16, and S66 are elements in the compliance matrix (see Chapter 3) The value of h approaches zero for large values of L=w. Based on the investigation performed by Rizzo [2], L=w ratios >10 are recommended for the tensile testing of off-axis specimens. The inhomogeneity of a composite laminate and the statistical nature of its constituent properties often lead to large variation in its tensile strength. Assuming a normal distribution, the average strength, standard deviation, and coefficient of variation are usually reported as Average strength ¼ save ¼ Xsi n , Standard deviation ¼ d ¼ Pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ si save 2 (n 1) s , Coefficient of variation ¼ 100d save , (4:2) where n is the number of specimens tested si is the tensile strength of the ith specimen Instead of a normal distribution, a more realistic representation of the tensile strength variation of a composite laminate is the Weibull distribution. Using two-parameter Weibull statistics, the cumulative density function for the composite laminate strength is F(s) ¼ Probability of surviving stress s ¼ exp s s0 a , (4:3) FIGURE 4.2 Nonuniform deformation in a gripped off-axis tension specimen. 2007 by Taylor & Francis Group, LLC.
1.0 0.8 [90] 0.6 [0/性45/90] 0.4 0.2 0 7.48.29.0 9.810.6Y5567 79148181214 Ultimate stress(ksi) FIGURE 4.3 Tensile strength distribution in various carbon fiber-epoxy laminates. (Adapted from Kaminski,B.E.,Analysis of the Test Methods for High Modulus Fibers and Composites,ASTM STP,521,181,1973.) where a is a dimensionless shape parameter oo is the location parameter(MPa or psi) The mean tensile strength and variance of the laminates are 0= =(告9）-r(t (4.4) where I represents a gamma function. Figure 4.3 shows typical strength distributions for various composite lamin- ates.Typical values of a and oo are shown in Table 4.1.Note that the decreasing value of the shape parameter a is an indication of greater scatter in the tensile strength data. EXAMPLE 4.1 Static tension test results of 22 specimens of a 0 carbon-epoxy laminate shows the following variations in its longitudinal tensile strength (in MPa):57.54,49.34, 68.67,50.89,53.20,46.15,71.49,72.84,58.10,47.14,67.64,67.10,72.95,50.78 63.59,54.87,55.96,65.13,47.93,60.67,57.42,and67.51.Plot the Weibull distribution curve,and determine the Weibull parameters a and oo for this distribution. 2007 by Taylor Francis Group,LLC
where a is a dimensionless shape parameter s0 is the location parameter (MPa or psi) The mean tensile strength and variance of the laminates are s ¼ s0G 1 þ a a , s 2 ¼ s2 0 G 2 þ a a G2 1 þ a a , (4:4) where G represents a gamma function. Figure 4.3 shows typical strength distributions for various composite laminates. Typical values of a and s0 are shown in Table 4.1. Note that the decreasing value of the shape parameter a is an indication of greater scatter in the tensile strength data. EXAMPLE 4.1 Static tension test results of 22 specimens of a 08 carbon–epoxy laminate shows the following variations in its longitudinal tensile strength (in MPa): 57.54, 49.34, 68.67, 50.89, 53.20, 46.15, 71.49, 72.84, 58.10, 47.14, 67.64, 67.10, 72.95, 50.78, 63.59, 54.87, 55.96, 65.13, 47.93, 60.67, 57.42, and 67.51. Plot the Weibull distribution curve, and determine the Weibull parameters a and s0 for this distribution. 1.0 0.8 [90] [0] [0/±45/90] 0.6 0.4 0.2 0 7.4 8.2 9.0 9.8 10.6 55 67 Ultimate stress (ksi) Probability of survival 79 148 181 214 FIGURE 4.3 Tensile strength distribution in various carbon fiber–epoxy laminates. (Adapted from Kaminski, B.E., Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP, 521, 181, 1973.) 2007 by Taylor & Francis Group, LLC.
TABLE 4.1 Typical Weibull Parameters for Composite Laminates Shape Location Parameter, Material Laminate Parameter,o oo MPa (ksi) Boron-epoxy O 24.3 1324.2 (192.0) [90 15.2 66.1 (9.6 [02/±45s 18.7 734.5 (106.6 [0/±45/90s 19.8 419.6 (60.9) [902/45]s 19.8 111.9 (16.1) T-300 Carbon-epoxy5 [Os] 17.7 1784.5 (259) [016d 18.5 1660.5 (241) E-glass-polyester SMCe SMC-R25 7.6 74.2 (10.8) SMC-R50 8.7 150.7 (21.9) a From B.E.Kaminski,Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP,521,18L,1973. bFrom R.E.Bullock,J.Composite Mater.,8,200.1974. e From C.D.Shirrell,Polym.Compos..4.172.1983. SOLUTION Step 1:Starting with the smallest number,arrange the observed strength values in ascending order and assign the following probability of failure value for each strength. i P= n+l: where i=1,2,3,,n n=total number of specimens tested P 46.15 1/23=0.0435 2 47.14 2/23=0.0869 2 47.94 3/23=0.1304 21 72.84 21/23=0.9130 22 72.95 22/23=0.9565 Step 2:Plot P vs.tensile strength o to obtain the Weibull distribution plot (see the following figure). 2007 by Taylor&Francis Group.LLC
SOLUTION Step 1: Starting with the smallest number, arrange the observed strength values in ascending order and assign the following probability of failure value for each strength. P ¼ i n þ 1 , where i ¼ 1, 2, 3, . . . , n n ¼ total number of specimens tested i s P 1 46.15 1=23 ¼ 0.0435 2 47.14 2=23 ¼ 0.0869 3 47.94 3=23 ¼ 0.1304 ... ... ... ... ... ... 21 72.84 21=23 ¼ 0.9130 22 72.95 22=23 ¼ 0.9565 Step 2: Plot P vs. tensile strength s to obtain the Weibull distribution plot (see the following figure). TABLE 4.1 Typical Weibull Parameters for Composite Laminates Material Laminate Shape Parameter, a Location Parameter, s0 MPa (ksi) Boron–epoxya [0] 24.3 1324.2 (192.0) [90] 15.2 66.1 (9.6) [02=±45]S 18.7 734.5 (106.6) [0=±45=90]S 19.8 419.6 (60.9) [902=45]S 19.8 111.9 (16.1) T-300 Carbon–epoxyb [08] 17.7 1784.5 (259) [016] 18.5 1660.5 (241) E-glass–polyester SMCc SMC-R25 7.6 74.2 (10.8) SMC-R50 8.7 150.7 (21.9) a From B.E. Kaminski, Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP, 521, 181, 1973. b From R.E. Bullock, J. Composite Mater., 8, 200, 1974. c From C.D. Shirrell, Polym. Compos., 4, 172, 1983. 2007 by Taylor & Francis Group, LLC