PSI - Issue 45

Koji Fujimoto et al. / Procedia Structural Integrity 45 (2023) 74–81 Koji Fujimoto / Structural Integrity Procedia 00 (2019) 000 – 000 Table 1. Convergence of stress intensity factors and T -stresses at the crack tip A with the increase of the number of the collocation points, . ( 0 = 1 √ , Ref.*: Isida and Noguchi (1983)) / = 2 / = 1.1 2 / 1 =0.1 2 / 1 =10 IA / 0 A / 1 IA / 0 A / 1 IA / 0 A / 1 IA / 0 A / 1 1 0.9074408 -0.9074408 0.7515203 -0.7515203 10 2.7161414 -14.6567749 0.4544448 2.7126456 2 0.9335960 -0.8676975 0.6681555 -0.0702653 20 2.5984897 -13.4389571 0.4600481 2.6757869 3 0.9348751 -0.8663121 0.6573643 0.1967704 30 2.5984379 -13.0758262 0.4605230 2.6343954 4 0.9349255 -0.8666076 0.6610359 0.2519280 40 2.5985163 -12.9918203 0.4605413 2.6251490 5 0.9349279 -0.8668310 0.6643882 0.2483729 50 2.5985186 -12.9749462 0.4605418 2.6233251 6 0.9349280 -0.8669092 0.6661148 0.2351489 60 2.5985186 -12.9718520 0.4605418 2.6229904 7 0.9349280 -0.8669305 0.6668687 0.2237933 70 2.5985186 -12.9713149 0.4605418 2.6229321 8 0.9349280 -0.8669357 0.6671720 0.2158338 80 2.5985186 -12.9712250 0.4605418 2.6229223 9 0.9349280 -0.8669368 0.6672875 0.2106358 90 2.5985186 -12.9712103 0.4605418 2.6229207 10 0.9349280 -0.8669371 0.6673297 0.2073507 100 2.5985186 -12.9712080 0.4605418 2.6229204 20 0.9349280 -0.8669372 0.6673521 0.2022280 150 2.5985186 -12.9712075 0.4605418 2.6229204 30 0.9349280 -0.8669372 0.6673521 0.2022030 200 2.5985186 -12.9712075 0.4605418 2.6229204 50 0.9349280 -0.8669372 0.6673521 0.2022029 250 2.5985186 -12.9712075 0.4605418 2.6229204 100 0.9349280 -0.8669372 0.6673521 0.2022029 300 2.5985186 -12.9712075 0.4605418 2.6229204 200 0.9349280 -0.8669372 0.6673521 0.2022029 400 2.5985186 -12.9712075 0.4605418 2.6229204 Ref.* 0.9349 0.6671 500 2.5985186 -12.9712075 0.4605418 2.6229204 Using the method described in the previous chapter, we can obtain T -stresses together with stress intensity factors. Table 1 shows the convergence of the calculated T -stresses and stress intensity factors at the crack tip A with the increase of the number of the collocation points . In particular, Table 1 (b) is the case that the crack tip A is very close to the interface. In such cases, it is difficult to obtain accurate numerical solutions in general but this table indicates good convergence of the numerical solutions obtained by using the proposed method. Fujimoto and Nagata (2022) obtained the solutions of T -stresses and stress intensity factors of the same problem, not using Chebyshev polynomial. (a) 2 / 1 = 23.077, 1 = 0,35, 2 =0,3 , Plane strain. (Material 1: aluminum, Material 2: epoxy) (b) / = 1.01, 1 = 2 =0,3 , Plane strain. 79 6

3.2. Row of equally spaced parallel cracks

I /( √ )

/

/

Fig. 3. Row of equally spaced parallel cracks.

Fig. 4. Relation of T-stress, stress intensity factor and the interval of cracks.