Numerical evaluation of stress distributions ahead of crack tip for finite-width center cracked specimens

Abstract

A simple approach -force balance method (FBM) -has been proposed to calculate geometric correction factors in linear elastic fracture mechanics [1]. In the method, the stress distribution ahead of the crack tip along the crack-line for a finite-width plate has to be involved, which was postulated to be associated with the stress distribution for the corresponding infinite plate, modified by a geometric correction factor. The geometric correction factor can then be determined by means of equilibrium conditions of forces and torques along the crack-line.By virtue of the FBM, a number of geometric correction factors for finite-width center cracked specimens, subjected to different configurations of loading, have been deduced e.g. [1][2][3]. They were found to be in good agreement with those reported in the literature. However, the assumption regarding the stress distribution in front of the crack tip along the crack-line in a finite-width specimen is lacking in mathematical rigour. In order to verify the applicability of the obtained geometric correction factors, it is thus essential to evaluate this assumption for various loading configurations.In [4][5][6] the stress distributions ahead of the crack tip along the crack-line for the standard center cracked tension (CCT) specimen and a finite-width plate loaded by a pair of concentrated forces on the center line of the specimen have numerically been assessed by means of the finite element method (FEM). The assumed stress distributions were found to be in good accordance with the obtained numerical results, especially in the vicinity of the crack tip. In this paper the stress distribution ahead of the crack tip along the crack-line for the center cracked specimen, loaded by uniformly distributed stresses on the center portion of the crack (see Fig. 1) is numerically evaluated by means of FEM. Int Journ of Fracture 75 R4For the loading configuration depicted in Fig. 1, the stress distribution (.~) ahead of the crack tip along the crack-line for the finite width plate (width W) is assumed to bewhere the singular term of the Westergaard function [7] available for the corresponding infinite-width plate is modified by a geometric correction factor Y.In (1), 2a is the crack length, 2b is the acting region of stresses tJ, x is the distance from the center of the crack, as shown in Fig. 1. By means of FBM, the stress intensity factor K and geometric correction factor Y can be obtained as(2) y = "~W 2-4 a 2 sin-l(b/a) Analogous to the work in [4,5], a specimen of total height L=30 with a center crack of length a=l is considered. Hence, in the range of interest (i.e., 0.2<2a/W<0.8) the minimum ratio of L over W is 3, which is acceptable from a practical point of view. Due to the symmetry only a quarter of the specimen (i.e., the right-upper part) is discretized. A typical FE-mesh corresponding to 2a/W=0.2 is displayed in Fig. 2, consisting of 690 four-node bilinear elements and 761 nodes. In view of the singularity at the crack tip the FE-mesh close to this point is relatively...

Geometric correction factors determined by force balance method for center cracked specimens. X.

“…It has been indicated by means of finite element calculations [9][10][11] that the assumed stress distributions ahead of the crack tip along the crack-line for the finite-width plate could basically delineate the situation in the neighborhood of the crack tip, but they do exhibit some discrepancy near the free-boundary of specimens especially for large relative crack length. Thus, even though the geometric correction factors deduced for various cases were found to be in good agreement with those reported in the literature, the proposed FBM should be considered as a simple approximate approach which is easy to apply and has sufficient accuracy [1211.…”

Numerical evaluation of stress distributions ahead of crack tip for finite-width center cracked specimens. IV. Loaded by a pair of splitting forces acting at an arbitrary location on the crack

“…Similar to the previous work presented in [4][5][6][7], a specimen of total height L=30 with a center crack of length a=l is considered. Hence, in the range of interest (i.e.…”

“…In [4][5][6][7] the stress distributions ahead of the crack tip along the crack-line for a center cracked plate loaded by various symmetric loading configurations have numerically been evaluated by means of the finite element method (FEM). The assumed stress distributions were found to be in fairly good coincidence with the numerical results especially in the proximity of the crack tip, although some differences can be identified near the specimen edge.…”

Geometric correction factors determined by force balance method for center cracked specimens

“…It should be pointed out that the assumed stress distributions ahead of the crack tip along the crack-line for the finite-width plate could basically represent the situation in the vicinity of the crack tip, but they do exhibit some discrepancy near the specimen edge especially for large relative crack length [20][21][22][23]. Hence the geometric correction factors deduced by virtue of the FBM should be considered to be approximate.…”