## 112 Conclusions

Fatigue performance of glass fiber-reinforced plastics under complex stress states was considered in this study. Prediction of operational life of structures made of said materials is feasible and can be based on measurements of fatigue strength and stiffness degradation.

Quadratic failure tensor polynomial criterion, FTPF, forecasts satisfactorily material response under off-axis and multiaxial loading for all cases of stress ratio R considered in this study. Application of FTPF assumes the experimental determination of three S-N curves along principal material directions. Efficiency of the criterion is proved through comparison of theoretical predictions and experimental fatigue strength data. Fatigue strength variation with off-axis angles is similar to static strength variation, irrespective of stress ratio R. Off-axis experimental strengths, both in static and fatigue loading, are well predicted in most of the cases by failure tensor polynomial criterion.

For on-axis loaded coupons, 0°, it is shown that fatigue strength is higher in tensile loading (R = 0.1) than in compressive (R = 10) for N < 106. This is not the case, however, for all the other sets of coupons tested, where it was clearly demonstrated that compressive fatigue strength is higher than tensile strength for any off-axis loading orientation.

Constant life diagrams, composed for the median survival probability point out that for on-axis loading constant life curves are closer to a parabolic curve than to a Goodman straight line. This suggests that the use of the Goodman relation, along with the Palmgren-Miner rule, could lead to conservative design decisions. On the other hand, however, high cycle fatigue results, especially in the T-T sector of the oa — om plane and off-axis strength results, in general, suggest that a Goodman-like relationship between oa and om is very optimistic.

During fatigue life the stiffness of a structural element is decreased. Observed stiffness degradation is correlated to the damage accumulated in the material. Herein, coupons cut at several off-axis angles from a multidirectional laminate [0/(±45)2/0]r, were subjected to cyclic loading and their stiffness changes were investigated. Longitudinal Young's modulus is defined as the average slope of the stress-strain loop and is a function of the number of cycles, N. Its variation, depending on the applied stress ratio and off-axis load orientation, is modeled by a simple empirical equation that produces acceptable fits of the experimental data.

Records of stiffness reduction for various R values were used to define fatigue design curves corresponding to specific modulus degradation and not to failure. The corresponding, stiffness-controlled, fatigue design curves, Sc-N, can serve better the requirements of design and full-scale testing of structural components made of FRP materials.

It was shown that Sc-N and S-N curves of 95% reliability can be correlated and, therefore, it was possible to define design allowables corresponding to predetermined levels of stiffness degradation and survival probability.

acknowledgments Part of this study was supported by the Greek General Secretariat of Research and Technology under contract EPET II #573 and by the Center for Renewable Energy Sources (CRES). Composite plates were prepared by rotor blade manufacturers Geobiologiki S.A. The authors gratefully acknowledge their assistance.

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