13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- from 1.4 to 1.6. Thus different life time ranges of 0-7 years and 0-10 years should be employed. With attention placed on seven years, seven time segments from 0-1, 1-2, 2-3, 3-4, 4-5, 5-6 and 6-7 year will be chosen for integration. In Eq. (10), 7 n= such that the condition 1 2 7 ... 1 a a a = = = = is used in Eq. (9). And same can be done to the range of 0-10 years. Ten time segments from 0-1, 1-2, …, 9-10 year will be chosen for integration. In Eq. (10), 10 n= such that the condition 1 2 10 ... 1 a a a = = = = is made. These conditions together with the weighted function ( )tα in Fig.7 are needed for determining the R-integrals and variances. Fig.7 Weighted functions Choice of weighted function ( )tα depends on several factors, It is applied to adjust the time degradation effect of the root function ( ) p t . The decay function can also be seen as a description of material degradation. 5.2.2. R-integrals and variances of crack length Application of Eqs. (9) and (10) together with the weighted functions in Fig.7, the R-integrals and the corresponding variances for the micro/macro fatigue crack growth of wire in cable no.3 are evaluated. The numerical values can be found in Tables 2-5 inclusive. Table 2 R-integrals for fatigue crack growth with 1.4 η= 1R 2R 3R 4R 5R 6R 7R 8R 9R 10 R ave R 23.4 31.7 42.7 57.5 77.1 103.1 137.4 182.4 241.2 317.6 121.4 Table 3 Variances for fatigue crack growth with 1.4 η= 1RΔ 2RΔ 3RΔ 4RΔ 5RΔ 6RΔ 7RΔ 8RΔ 9RΔ 10 RΔ 98.0 89.8 78.7 63.9 44.3 18.3 16.0 61.0 119.8 196.2 Table 4 R-integrals for fatigue crack growth with 1.6 η= 1R 2R 3R 4R 5R 6R 7R ave R 25.1 38.8 59.6 91.1 138.6 209.5 314.7 125.3 0 2 4 6 8 10 12 14 16 18 20 22 Weighted function α(t) Time t (year) η=1.6 α(t)=-0.05t2+30 η=1.4 α(t)=-0.03t2+30
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