Strength of Cross-Ply Laminates

The procedure of laminate strength analysis outlined in Section 4.5.2, with the Tsai-Hill lamina failure criterion will be illustrated for cross-ply laminates that have been cured at a temperature above their service or operating temperature in the manner of Tsai [4-10]. Thus, the thermal effects discussed in Section 4.5.3 must be considered as well. For cross-ply laminates, the transformations of lamina properties are trivial, so the laminate strength-analysis procedure is readily interpreted. 

all numbers are in hand for calculation of the stresses in the example cross-ply laminate. 

Consider a constant temperature of the laminate different from, and relative to, its stress-free curing temperature. Then, the thermal forces are, from Equation (4.105), 

By means of rather involved successive substitutions of Equation (4.108) in (4.111), in (4.13), and finally in (4.103), the stresses in the inner and outer layers can be shown to be 

The failure criterion must be applied to determine the maximum values of Nx and AT that can be sustained without failure of any layer. Actually, the failure criterion is applied to each layer separately. For the special orientation of cross-ply laminates, the Tsai-Hill failure criterion for each layer can be expressed as 

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