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 lamin￾ates. 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.