A New Numerical Analysis for Rectangular Tensile Sheet with Double Edge Cracks
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LETTER TO THE EDITOR
A New Numerical Analysis for Rectangular Tensile Sheet with Double Edge Cracks Xiangqiao Yan • Baoliang Liu • Zhaohui Hu
Submitted: 16 March 2010 / in revised form: 8 April 2010 / Published online: 29 April 2010 Ó ASM International 2010
Dear Editor: This letter uses the hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan [1], to provide a new numerical analysis for the stress intensity factors (SIFs) of rectangular tensile sheets with double edge cracks. It was found from the previous investigations [1–12] that the boundary element method is simple, yet accurate for analyzing general plane elastic crack problems. This letter presents the SIFs of a rectangular plate with double edge cracks, Fig. 1, which is a model used frequently used in fracture mechanics [13]. The plane elastic problem has been widely studied using the complex variable method [14], the asymptotic approximation method [15], and the body force method [16]. Murakami [17] reported the detailed solutions to the SIF when H/W is very large (greater than 2; when H/W [ 2 the effect of H/W on the SIFs is negligible). However, to the author’s knowledge, detailed solutions to the SIFs for the plane elastic problem have not been obtained when H/W is smaller than 2. This letter presents the solutions. The hybrid displacement discontinuity method is used to calculate the SIFs of the plane elastic crack problem shown in Fig. 1. In these analyses, symmetric conditions of the cracked plates are used. The following cases are considered,
are discretized according to the limitation that all boundary elements have approximately the same length [1]. The pffiffiffiffiffiffi calculated SIFs normalized by r pa are given in Table 1, also see Fig. 2. For the comparison purpose, Table 1 also lists the numerical results reported in [17]. It is found from Table 1 that the present numerical results are in good agreement with those reported in the documented reference [17]. It can be seen from Table 1 that it is necessary to consider the effect of H/W on the SIFs because: (1) even though a/W = 0.1, the SIF when H/W = 0.4 is 16% larger than that when H/W = 2; (2) with increase of a/W, this
a=W ¼ 0:1; 0:2; 0:3; 0:4; 0:5; 0:6; 0:7 H=W ¼ 0:4; 0:5; 0:6; 0:7; 0:8; 0:9; 1:0; 1:2; 1:5; 2:0 Thirty boundary elements with an equal size, a/30, are meshed on the right edge crack, and the other boundaries X. Yan (&) B. Liu Z. Hu Research Laboratory on Composite Materials, Harbin Institute of Technology, Harbin 150001, People’s Republic of China e-mail: [email protected]
Fig. 1 Rectangular tensile sheet with symmetric double edge cracks
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J Fail. Anal. and Preven. (2010) 10:253–254
References
Table 1 Normalized SIFs of double edge cracks a/W 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.4
1.2902 1.6499 2.0845 2.5464 2.9943 3.3400 3.3959
0.5
1.2344 1.4900 1.8093 2.1422 2.4333 2.5980 2.5553
0.6
1.2007 1.3879 1.6213 1.8537 2.0329 2.1104 2.0776
0.7
1.1773 1.3139 1.4813 1.6393 1.7521 1.8006 1.8032
0.8
1.1596 1.2576 1.3750
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