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FIGURE 1.27 Constant life diagram for [0/(±45)2/0]T laminate at 90°. UTS = 84.94 MPa, UCS = 83.64 MPa.

amplitude cyclic loading, this would lead to conservative design decisions, along with Palmgren-Miner damage accumulation rule. Another interesting aspect of this graph, already mentioned, is that the material proved to be stronger in tension, than in compression, for small number of cycles, while the opposite holds true with an increasing number of cycles. The same trend was reported for a similar material and stacking sequence by other researchers [14], and their results were

FIGURE 1.28 Constant life diagram for GRP laminate composed of (0/ ± 45) fabrics. UTS = 467 MPa, UCS = -318 MPa. Data from [14].

reproduced in Fig. 1.28 for comparison. It is worthwhile noting in this figure that at the high-cycle range (N > 107), even the Goodman straight line is an optimistic approach to the real oa — om relation.

Off-axis loading reveals the anisotropic nature of the GRP laminate investigated since, as observed in Figs. 1.26 and 1.27, for 0 = 45° and 90°, respectively, the fatigue response of the material differs significantly from what was discussed already. What is common in these figures is the higher fatigue strength in com-pressive rather than in tensile stress ranges, and the poor performance of Goodman law in describing the relation between mean stress and cyclic amplitude.

1.11.2 Fatigue Strength Prediction

Efficient and reliable prediction of fatigue life of any structural component under complex stress states is of paramount importance in design. Such a task can be carried out by means of the FTPF criterion, discussed in Section 1.9.1, which for plane stress conditions is expressed by Eq. (1.17). For the formulation of the criterion in the principal material directions of a laminate possessing similar strength symmetries as the one investigated herein, the S-N curves along the two orthogonal symmetry directions as well as the respective shear fatigue strength must be known. Determination of the latter, always under the same R value loading, is performed using the methodology proposed in Section 1.10.2.1, Eq. (1.34).

Comparison of FTPF prediction with experimental data from various material systems as well as with theoretical predictions from other strength criteria can be found in [20]. For the experimental off-axis data presented in Tables 1.7-1.9 under R = 10, —1 and 0.1, respectively, calculations following the aforementioned

FIGURE 1.29 Comparison of experimental data and FTPF predictions (R = 10).

FIGURE 1.30 Comparison of experimental data and FTPF predictions (R = -1).

methodology were performed, and the results are presented in Figs. 1.29-1.34. Shear strength S-N formulation is derived for all cases by fitting the experimental data of smaller off-axis angles, that is, 30° for R = 10, —1 and 15° for R = 0.1. Reliable predictions, that is, conservative, of the criterion are produced that way for the other off-axis directions.

The results of Figs. 1.29-1.31 were derived by solving Eq. (1.34) for ox. The expressions used for X(N), Y(N), and S(N) are given in Table 1.15 and

FIGURE 1.31 Comparison of experimental data and FTPF predictions (R = 0.1).

FIGURE 1.32 FTPF predictions vs. experimental data from woven GRP cylindrical specimens biaxially loaded at 0° [20].

correspond to the median survival probability approximately. If a higher reliability level is required, the procedure for the determination of S(N) has to be repeated by using values for X(N), Y(N), and off-axis test results to be fitted by Eq. (1.34), corresponding at that survival probability.

As concluded from Figs. 1.29-1.31 the predictions of the FTPF criterion for off-axis orientations such as 60° or 75° are good and always on the safe side. The same is valid also for 45°, but the predictions are too conservative. However,

FIGURE 1.33 FTPF predictions vs. experimental data from woven GRP cylindrical specimens biaxially loaded at 45° [20].

FIGURE 1.34 FTPF predictions vs. experimental data from woven GRP cylindrical specimens loaded under combined tension-torsion [20].

TABLE 1.15 Experimental Fatigue Strength Equation along Principal Material Directions of [0/(±45)2/0]r GRP Laminate (in MPa)
0 0

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