10.1 Basic Equations 189 Maximum Stress Theor 0 一一·Tai-Hill Theory -·-。-。Maximum Strain Theory Fig.10.8.Comparison between the three failure envelopes Figure 10.8 shows the three failure envelopes of the maximum stress theory, the maximum strain theory,and the Tsai-Hill theory superimposed on the same plot for comparison. 10.1.4 Tsai-Wu Failure Theory The Tsai-Wu failure theory is based on a total strain energy failure theory.In this theory,failure is assumed to occur in the lamina if the following condition is satisfied: F1o7+F22o+F66T2+Fo1+F2+2012≤1 (10.17) where the coefficients F11,F22,F66,F1,F2,and F12 are given by: y F1= (10.18) 1 F2= (10.19) F=- 11 7 (10.20) 11 = 昭 (10.21) 1 F66= () (10.22) and F12 is a coefficient that is determined experimentally.Tsai-Hahn deter- mined F12 to be given by the following approximate expression:10.1 Basic Equations 189 Fig. 10.8. Comparison between the three failure envelopes Figure 10.8 shows the three failure envelopes of the maximum stress theory, the maximum strain theory, and the Tsai-Hill theory superimposed on the same plot for comparison. 10.1.4 Tsai-Wu Failure Theory The Tsai-Wu failure theory is based on a total strain energy failure theory. In this theory, failure is assumed to occur in the lamina if the following condition is satisfied: F11σ2 1 + F22σ2 2 + F66τ 2 12 + F1σ1 + F2σ2 + F12σ1σ2 ≤ 1 (10.17) where the coefficients F11, F22, F66, F1, F2, and F12 are given by: F11 = 1 σT 1 σC 1 (10.18) F22 = 1 σT 2 σC 2 (10.19) F1 = 1 σT 1 − 1 σC 1 (10.20) F1 = 1 σT 2 − 1 σC 2 (10.21) F66 = 1  τ F 122 (10.22) and F12 is a coefficient that is determined experimentally. Tsai-Hahn deter￾mined F12 to be given by the following approximate expression: