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For every experimental point corresponding to a coupon loaded off-axis under stress amplitude ax and failed at N cycles, one derives by means of Eq. (1.34) the corresponding S(N) value.

Static strength results from both tension and compression plotted as a function of the off-axis angle 0 are presented in Fig. 1.3. Theoretical predictions, solid

FIGURE 1.3 Off-axis static strength, ast, of [0/(±45)2/0]T GRP laminate.

FIGURE 1.3 Off-axis static strength, ast, of [0/(±45)2/0]T GRP laminate.

line, according to the FTPF criterion are also shown along with data points. To derive the calculated strengths, the multidirectional laminate is considered as homogeneous orthotropic medium. Details on failure predictions under static loading are given in [20].

The S-N curves for R = 10, —1, 0.1, and 0.5 are presented in Figs. 1.4-1.7, respectively, where the coordinates of data points correspond to stress amplitude, oa, and number of cycles to failure, N. Detailed results on life cycles for every

coupon tested under various stress ratios R and off-axis angle 0 are displayed in Tables 1.7-1.10. Linear regression curves, shown as solid lines, in Figs. 1.4-1.7 are of the form oa = aN-1/b.

As seen from these figures, fatigue strength of this specific GRP laminate is higher in tensile loading (R = 0.1) than in the respective compressive one (R = 10), only for the case of on-axis coupons, 0°, and N < 106. The opposite is suggested by the experimental data, that is, compressive strength is higher than tensile fatigue strength for any other off-axis loading configuration. It is furthermore observed that the material is more fatigue sensitive in tension than in compression as indicated from the slope of the respective S-N curves.

### 1.10.2.2 Stiffness Degradation

For all the coupons tested in fatigue, hysteresis loops were monitored continuously by recording load and cross-head displacement signals. Stiffness changes with respect to the number of cycles were studied in terms of dynamic modulus, En, determined by linear curve fitting of data samples at every stress-strain hysteresis loop. A dimensionless measure of stiffness degradation is given by the ratio En/E1,E1 being the modulus at the first load cycle, greater in general from the static Young's modulus, E0, due to the higher strain rate of deformation.

According to the simple model of Section 1.9.2, the variation of the ratio En/E1 with respect to cycle number, N, is linear, its slope depending on the cyclic stress amplitude. This was postulated for the main central life period of a coupon, excluding initiation and final failure phases. By means of Eq. (1.19), model parameters were derived by fitting the experimental data for the various stress ratios, R, and off-axis angle, 0, values; see Table 1.11.

TABLE 1.7 Number of Cycles to Failure from C-C (R = 10) Tests for Various Stress Ranges and Off-axis Loading Orientations

90 200 5500, 2161, 5607 81 180 20,776, 11,400, 6728

76.5 170 53,626, 33,052, 36,350 72 160 770,046, 437,115, 100,184 65.5 150 2,357,018, 431,315, 225,912

10,727

15,329

77,433, 142,397

1,050,000 2540

40,316

317,000, 102,412

896,316, 1,000,000" 10,595

92,141, 25,006

206,244, 658,432

2,505,659, 1,554,429

TABLE 1.8 Number of Cycles of Failure from T-C (R =

—1) Tests for Various Stress Ranges and Off-axis Loading Orientations

TABLE 1.8 Number of Cycles of Failure from T-C (R =

—1) Tests for Various Stress Ranges and Off-axis Loading Orientations

(MPa) |
0° |
30° |
45° 60° 90° |

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