Specimen (x-y) Material (1-2) 2t1(<0j 6 FIGURE 9.4 State of stress in the specimen for an off-axis tension test. 9.3 Off-Axis Tensile Strength As mentioned earlier in this chapter,the off-axis tension test has been used to examine theories proposed for prediction failure of composites under com- bined stress.In such studies,slender specimens are used for strength mea- surements to avoid the complications of end constraint effects discussed above. This leads to a stress state in the on-axis system,as given by Equations(2.12) and(2.14: 01 m2 02 =6 n2 (9.21) T12 -mn Therefore,as illustrated in Figure 9.4,the state of stress in the principal material coordinate system is biaxial. Experimental studies conducted on on-axis and off-axis specimens,e.g., in References [4,5],show that the off-axis specimen under tension fails along planes parallel to the fibers except for zero and very small angles,where failure involves fiber fractures.To predict the failure stress of the off-axis tension specimen,the on-axis stresses given by Equations(9.21)are substi- tuted into the failure criterion of choice(see Section 2.5).The maximum stress and strain criteria(see Section 2.5),yield three equations for the ultimate stress,and the appropriate strength is identified by the least of the three values.Substitution of the stresses given by Equations(9.21)into the Tsai-Wu criterion,Equation(2.44),yields a quadratic equation in o,of the type Ao)+Bo-1=0 (9.22) ©2003 by CRC Press LLC9.3 Off-Axis Tensile Strength As mentioned earlier in this chapter, the off-axis tension test has been used to examine theories proposed for prediction failure of composites under com￾bined stress. In such studies, slender specimens are used for strength mea￾surements to avoid the complications of end constraint effects discussed above. This leads to a stress state in the on-axis system, as given by Equations (2.12) and (2.14): (9.21) Therefore, as illustrated in Figure 9.4, the state of stress in the principal material coordinate system is biaxial. Experimental studies conducted on on-axis and off-axis specimens, e.g., in References [4,5], show that the off-axis specimen under tension fails along planes parallel to the fibers except for zero and very small angles, where failure involves fiber fractures. To predict the failure stress of the off-axis tension specimen, the on-axis stresses given by Equations (9.21) are substi￾tuted into the failure criterion of choice (see Section 2.5). The maximum stress and strain criteria (see Section 2.5), yield three equations for the ultimate stress, , and the appropriate strength is identified by the least of the three values. Substitution of the stresses given by Equations (9.21) into the Tsai-Wu criterion, Equation (2.44), yields a quadratic equation in , of the type (9.22) FIGURE 9.4 State of stress in the specimen for an off-axis tension test. 1 2 12 x 2 2 m n mn σ σ τ σ             = −             σx ult σx ult A B x ult x ult ( ) σ σ + −= 2 1 0 TX001_ch09_Frame Page 137 Saturday, September 21, 2002 5:01 AM © 2003 by CRC Press LLC