10

103 104 105 106 107 108 N

FIGURE 1.23 Effect of stress ratio R on 95% survival probability S-N curves. Off-axis, 45°, loading.

To comply with the needs of designing a composite structure against variable amplitude fatigue, that is, spectrum loading, strength data are projected in the plane having as coordinates stress amplitude and mean stress, oa — om. Radial lines emanating from the origin are expressed by:

and thus, every such curve of the family corresponds to a constant R value. Therefore, points along these lines are points of the S-N curve for that particular stress ratio R. Constant life diagrams are formed by joining points of consecutive radial lines, all corresponding to a certain value of cycles, N. Some useful characteristics of (oa — om) plane are shown in Fig. 1.24. As shown, the positive half-plane is divided into three sectors, the central one being of double surface area. The tension-tension sector is bounded by the radial lines R = 1 and R = 0, the former corresponds to static loading and the latter to tensile cycling with amin = 0. The S-N curves, that is, radial lines belonging to this sector have positive R values smaller than unity. Similar type comments for the other sectors can be derived from the annotations shown in Fig. 1.24. It is interesting also to mention that to every radial line with 0 < R < 1, that is, in the T-T sector, corresponds its symmetric with respect to the oa axis, which lies in the C-C sector and whose R value is the inverse of the tensile one, for example, R = 0.1 and R = 10.

For the experimental data presented in Tables 1.7-1.10 and using the model parameters shown in Table 1.14, it is possible to form constant life diagrams, for each off-axis loading configuration, corresponding to any specific survival

FIGURE 1.24 oa — am-plane notation for constant life diagrams.

FIGURE 1.25 Constant life diagram for [0/(±45)2/0]r laminate at 0°. UTS = 244.84 MPa, UCS = —216.68 MPa.

FIGURE 1.25 Constant life diagram for [0/(±45)2/0]r laminate at 0°. UTS = 244.84 MPa, UCS = —216.68 MPa.

probability. Such an exercise was performed for a 50% reliability level, and the results were shown in Figs. 1.25-1.27 for 0 = 0°, 45°, and 90°, respectively.

For on-axis loading (Fig. 1.25) constant life curves are closer to a Gerber-like prediction rather than a Goodman straight line. Since several design codes, for composite structures, suggest the use of Goodman criterion to account for variable

FIGURE 1.26 Constant life diagram for [0/(±45)2/0]T laminate at 45°. UTS = 139.1 MPa, UCS = -101.59 MPa.
0 0

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