## GR CTmax1 R

where ox(a1, a2, 0) is the static strength in the x direction and Xr is the static strength in the reference direction.

As can be seen from Eq. (1.8), function g is introduced to account for different stress ratios R. When stress ratio for the reference S-N curve (Rr) is the same as the stress ratio of the S-N curve under prediction, then g = 1, while for R = 1, g = 0.

Recently, Jen and Lee [26, 27] modified Tsai-Hill failure criterion to cope with cyclic loading, and as shown in [26], fatigue life prediction of AS4 carbon/PEEK APC-2 laminates at various stress ratios was quite successful. The failure functions read:

where n, = n,(N, R, v), / = 1,2,6 are the applied cyclic stresses and = Oi(N,R,v) denote the respective fatigue strengths in principal material coordinates, being functions of cycle number N, stress ratio R, and frequency v.

Depending on the loading, tension-tension (T-T), compression-compression (C-C), or T-C, at in Eq. (9) are derived from experiments under similar loading conditions.

A modification of failure tensor polynomial [30] to account for fatigue loading, henceforth denoted by FTPF, was used in [20] to predict fatigue strength under multiaxial stress. The failure tensor polynomial for orthotropic media expressed in material principal coordinate system, under plane stress, is given by:

F110? + F220I + 2F12O1O2 + F101 + F2O2 + F66026 - 1<0, (1.10) with the components of the failure tensors given by:

0maxr 0minr where X, X' stand for tension and compression strengths along direction 1 of the material symmetry coordinate system, Y, Y' are the corresponding values for the transverse direction, while S is the shear strength. Failure tensor polynomial criterion with the form of Eq. (1.10) is valid for orthotropic materials or materials of higher symmetry. The choice of the off-diagonal term of failure matrix Ftj, F12 was shown to lead to completely different failure theories [31]. Nevertheless, for simplicity, the form of F12 used in this study is given by [32]:

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