magnitudes of stress for unidirectional composites.For fabric composites, however,Equations(2.42c and d)indicate failure of the fibers oriented along the 2-direction. 2.5.2 Maximum Strain Failure Criterion The maximum strain criterion assumes that failure of any principal plane of the lamina occurs when any in-plane strain reaches its ultimate value in uniaxial tension,compression,or pure shear.Failure should occur when any of the following equalities are satisfied (Table 2.1): E=eT (2.43a) e=-ec (2.43b) E,-e] (2.43c) E2=ef (2.43d) Y12=e6 (2.43e) Y12=-e6 (2.43f0 In these expressions,the symbol e represents the magnitude of the ultimate strain.If any of the above conditions become satisfied,failure is assumed to occur by the same mechanism leading to failure in uniaxial loading or pure shear loading.Similar to the maximum stress criterion,the maximum strain criterion has the ability of predicting the failure mode. 2.5.3 Tsai-Wu Failure Criterion Tsai and Wu [29]proposed a second-order tensor polynomial failure criter- ion for prediction of biaxial strength,which takes the following form for plane stress: F1+F2o2+F1o+F22o2+F6t2+2F12012=1 (2.44) Failure under combined stress is assumed to occur when the left-hand side of Equation(2.44)is equal to or greater than one.All of the parameters of the Tsai-Wu criterion,except F12,can be expressed in terms of the basic strengths (Table 2.1). ©2003 by CRC Press LLCmagnitudes of stress for unidirectional composites. For fabric composites, however, Equations (2.42c and d) indicate failure of the fibers oriented along the 2-direction. 2.5.2 Maximum Strain Failure Criterion The maximum strain criterion assumes that failure of any principal plane of the lamina occurs when any in-plane strain reaches its ultimate value in uniaxial tension, compression, or pure shear. Failure should occur when any of the following equalities are satisfied (Table 2.1): (2.43a) (2.43b) (2.43c) (2.43d) (2.43e) (2.43f) In these expressions, the symbol e represents the magnitude of the ultimate strain. If any of the above conditions become satisfied, failure is assumed to occur by the same mechanism leading to failure in uniaxial loading or pure shear loading. Similar to the maximum stress criterion, the maximum strain criterion has the ability of predicting the failure mode. 2.5.3 Tsai-Wu Failure Criterion Tsai and Wu [29] proposed a second-order tensor polynomial failure criter￾ion for prediction of biaxial strength, which takes the following form for plane stress: (2.44) Failure under combined stress is assumed to occur when the left-hand side of Equation (2.44) is equal to or greater than one. All of the parameters of the Tsai-Wu criterion, except F12, can be expressed in terms of the basic strengths (Table 2.1). ε1 1 = eT ε1 1 =− eC ε2 2 = eT ε2 2 =− eC γ 12 6 = e γ 12 6 = −e FF F F F F 1 1 2 2 11 1 2 22 2 2 66 12 2 12 1 2 σ σ σ σ τ σσ ++ + + + = 2 1 TX001_ch02_Frame Page 26 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC