13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 1 2 , 0, 0, 0 , 0, 0, 0 CR CR CR cr cr PZ PZ PZ pz pz k X if X and if X k X if X and if X , (3) where 1k , and 2k are the kinetic coefficients, which are evaluated experimentally. Evaluation of CL driving forces requires a computation of SIF and crack opening displacement (COD). In this paper we present a semi-analytical method of SIF and COD computations. The method is illustrated by solution for three geometries: a semi-infinite crack in an infinite solid; a single-edge notched specimen, standard PENT specimen (ASTM F 1473) and a stiff constant-K (SCK) specimen. The approximate formulas for SIF and COD are expressed as superposition of two elastic solutions for the listed above samples due to: 1) remote load or F ; and 2) closing force dr . The close form solution for a semi-infinite crack in an infinite homogeneous and linear elastic solid is used as the basic expression. The solution for any finite specimen geometry is constructed by introducing a geometry correction factor to the basic expression. The Green’s functions technique is effectively used to construct analytical expressions for SIF and COD. Then, the approximate expressions for SIF and COD are employed in computations of the CL driving forces and simulations of the slow fracture propagation process in HDPE [8, 13]. 2. Semi-Infinite Crack in an Infinite Plate 2.1. SIF Formula The decomposition shown in Fig. 1 is first applied to the semi-infinite crack in an infinite homogeneous and linear elastic solid subjected to a distributed load over L and a crack closing load dr on PZ (see Figure 2 below). L is the length of CL, which is the summ of actual crack length cr and PZ size pz , i.e., cr pz L . The SIF Green’s function for the semi-infinite crack is well known: 2 SIF G x x , (4) where the origin of the coordinates is placed at the crack tip. Figure 2. Decomposition of the problem of a semi-infinite crack in an infinite plate subjected to a distributed load and a closing force dr on PZ. For the boundary conditions and loading shown in Figure 2 a and b, SIFs are readily obtained by the standard application of Green’s function: Boundary Condition a: 0 2 2 ( ) L SIF I L K K G x dx ; (5)
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