13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Table 1 Cases of layered rocks containing a rectangular crack Case no. Layered rocks of infinite extent 1 The homogeneous solid of infinite extent consists of fine-grained sandstone. 2 The sandwich solid consists of two semi-infinite extents of mudstone and the mid-layer of fine-grained sandstone. 3 The homogeneous solid of infinite extent consists of mudstone. 4 The sandwich solid consists of two semi-infinite extents of fine-grained sandstone and the mid-layer of mudstone. (1) Case 1 and case 2 For case 1, there are no relative sliding displacements along the crack surfaces because of symmetry of geometry and loads. Due to the same reasons, there are no relative sliding displacements for case 2 (h1=1m). For case 2, the COD values increase and the KI values also increase in comparison with case 1. This is because the elastic module of mudstone in semi-infinite domain is less than the one of fine-grained sandstone. For case 2 (h1≠1m), the absolute values of displacements along the upper surface increase and the ones along the lower surface decrease. This leads to the appearance of the sliding discontinuous displacements along the crack surface. Due to the non-uniform load on the crack surfaces, there are different SIF values at the crack fronts x m2 ′ =± whilst there are the same SIF values at the crack fronts y m1 ′ =± . In the following, the SIF values at the crack fronts x m2 ′ =± and y m1 ′ =− are discussed. Fig. 7 shows the variation of the SIF values at the crack fronts x m2 ′ =± and y m1 ′ =− . The KI values are positive and the KII values are negative. Obviously, these phenomena are related to the load on the crack surfaces and the relative position of the crack in this medium. Along the crack front y m1 ′ =− , the larger the load, the larger the absolute values of KI and KII. As the crack surface approaches to the interface, the absolute values of KI and KII increase. 0 2 4 6 8 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 L (a) KI vs. L x'=2m y'=-1m x'=-2m D C B A KI/π1/2 (MPa.m-1/2) Case 1 Case 2 h1=1.0m, h1=0.7m h1=0.5m, h1=0.3m 0 2 4 6 8 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 x'=2m y'=-1m x'=-2m D C B A KII/π1/2 (MPa.m-1/2) Case 1 Case 2 h1=1.0m, h1=0.7m h1=0.5m, h1=0.3m L Fig. 7 SIF values of rectangular crack subjected to linear loads (Cases 1 and 2) (2) Case 3 and case 4
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