= 21.44N-0.06940

FIGURE 1.35 Sampling distribution of stiffness degradation data. R = 0.1, 15° off-axis.

this was observed for static strength results also (see Fig. 1.3) and it is due to the presence of fiber bundles along ±45°, that is, the GRP laminate investigated is not in essence a homogeneous orthotropic medium. For unidirectional glass epoxy laminates tested off-axis, it was shown in [20] that predictions of fatigue strength by the FTPF criterion were corroborated satisfactorily by the experimental data for the entire range of off-axis directions. Then, it is logical to conclude that the quadratic version of the failure tensor polynomial is adequate for design calculations, where one needs safe and reliable predictions, but if higher accuracy is needed, from the material characterization point of view, higher order tensor formulation [44] could be necessary.

Besides uniaxial loading test cases, the FTPF criterion was shown to predict satisfactorily fatigue strength under multiaxial cyclic loads as well [20]. Theoretical predictions were compared to experimental data of Owen and Griffiths [18] on woven glass polyester cylinders cycled under biaxial hoop, ahp, and axial, aax, stresses. Two separate loading cases were reported at 0° and 45° with respect to the fiber's direction. Suitable experimental data were also found in a study by Fujii and Lin [19], from an experimental program consisting of fatigue tests under tension-torsion loading on cylindrical specimens made of woven glass/polyester.

The stress ratio R considered was equal to 0, that is, amin = 0, while the test frequency was limited to 2 Hz.

Predicted failure locii by the FTPF criterion plotted against experimental data from [18] are shown in Figs. 1.32 and 1.33 for 1-106 cycles. Failure locii for the cylindrical specimens loaded at 0° with respect to the fibers direction are shown in Fig. 1.32, while corresponding locii for the specimens loaded at 45° off-axis are shown in Fig. 1.33. In both figures, Aaax and Aahp denote ranges of axial and hoop stress, respectively.

The applicability of FTPF criterion in reliably predicting fatigue strength under multiaxial loading is further demonstrated in Fig. 1.34, where predicted fatigue failure locii for 1-106 cycles are shown along with experimental data from [19].

It is clearly shown in both cases examined that predictions made by the FTPF criterion are very close to, and are corroborated well by, the experimental data from multiaxial cyclic loads.

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