## 2

't where superscript u denotes fatigue failure stress, or else the S—N curve of the material in the corresponding direction, and subscript T stands for transverse to the fiber direction. It can be shown that any off-axis fatigue function (failure mode II) can be given as a function of fx,fT, Ts, ost and the angle 0 [23]:

Equation (1.3) can be used for the calculation of any off-axis fatigue function but also to calculate fatigue functions fT, fT from two different off-axis, experimentally obtained, fatigue functions. For the application of this criterion three S-N curves need to be defined experimentally, along with the static strengths of the material.

For multidirectional laminates [24], the situation is far more complicated. As each lamina is under a different stress field, failure may occur at a ply after a certain amount of load cycling while the other plies could be still intact. These differences, along with inherent inhomogeneity, produce interlaminar stresses, capable to cause successive failure, probably with different damage mechanisms. In order to take into account these stresses, another failure mode, interlaminar, is established and the set of equations (1.2) is supplemented by:

where superscript c denotes cyclic stress and subscript d delamination failure mode, respectively.

The Hashin and Rotem [23] failure criterion can predict fatigue behavior of a unidirectional (UD) or multidirectional (MD) laminate subjected to uniaxial or multiaxial cyclic loads provided that the discrimination between the failure modes exhibited during fatigue failure is possible.

Fawaz and Ellyin [25] proposed a fatigue strength criterion suitable for UD and MD materials under multiaxial cyclic loading. The criterion has attractive features as it needs only one experimentally obtained S-N curve and some static strengths. The multiaxiality is entered through any acceptable static failure criterion, and the predicted S -N curve is given by:

S(a1, a2, 0, R, N) = h(a1, a2, 0)[g(R)mr log(N) + br], (1.5) as a function of a reference S -N curve, known by experiment, given by:

In the above two equations, subscript r denotes reference direction and a1 is the first biaxial ratio, a1 = oy/ox, while a2 is the second biaxial ratio, a2 = Txy/ox; x and y refer to a global coordinate system rotated at an angle 0 from the principal material system and R is the cyclic stress ratio defined, as usual, by R = gmin/qmax. Functions h and g are dimensionless and are defined by:

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