Evaluation of the elastic T-stress in surface-cracked plates using the line-spring method

Abstract

The elastic T-stress has been found to be an important parameter in characterizing the very near tip elastic-plastic stress state under 2-D plane strain conditions (Larsson and Carlsson [1]; Bilby et al. [2]; Beteg6n and Hancock [3]; etc.). Several computational methods have been developed to evaluate the T-stress (Larsson and Carlsson [1]; Kfouri [4]; Sham [5]). However, none of these methods can be readily adapted to calculate the elastic T-stress in a surface-cracked plate (SCP), which is essentially 3-D in nature. In this paper, the line-spring method, which has proven effective in computing the stress intensity factor of SCPs, is used to evaluate the elastic T-stress along the crack front. SCPs with same length and width, but different crack geometries, from low aspect ratio (a/c=0.24) to high aspect ratio (a/c=0.70), under both remote tension and bending, are studied using the line-spring method. Detailed, threedimensional continuum finite element (FE) solutions of some 'extreme' cases, in terms of both aspect ratio and crack depth, under either remote tension or bending, are compared with the line-spring solutions. The line-spring solutions are in excellent agreement with the 3-D elastic FE solutions, but use 2 to 3 orders of magnitude less computational time and considerably less preparation and post-processing efforts. A concluding example demonstrates the utility of the T-stress in more accurately describing the crack front elastic-plastic field in a SCP at load levels up to moderate scale yielding.

Three-dimensional evaluation of the T-stress in centre cracked plates

“…Generally, very fine meshes are required to accurately determine the T-stress when using this method. The domain over which the stresses are calculated is arbitrary but it should not be too far away from the crack tip as higher order terms become more significant [9].…”

Variation of elastic T-stresses along slightly wavy 3D crack fronts

“…2/ao, Z/H >> 1, the problems can be studied using the 'line spring' concept originally developed by Rice and Levy [37] for treating part-through cracks in elastic plates. The line-spring method has already been applied to calculate the T-stress for surfacecracked plate by Wang and Parks [17]. On the other hand, for short wavelength perturbations, i.e.…”

“…The fact that T significantly affects the stress triaxiality in the very near-tip elastic-plastic fields has motivated the development of a two-parameter characterization methodology [9][10][11][12][13][14][15][16][17]. Such two-parameter characterization using J and T for the elasti~plastic crack-tip fields has been shown, in the literature quoted above, to provide exceptional improvement in describing local crack-tip stress triaxiality on the scale of fracture process zone size, as compared to any single-parameter crack-tip description, for a variety of crack configurations and loadings.…”

“…In an attempt to extend the 2D crack stability analysis of Cotterell and Rice [3] to a three-dimensional regime, carried out a perturbation analysis for slightly non-planar half-plane cracks and found that while the stability of the crack against deflection in the x -x2 plane is dominantly controlled by the 2D T-component, Tll, the other two components, T33 and T13 , affect the stability against non-planar crack surface perturbations parallel to the crack front, such as those leading to the so-called en-echelon crack front segmentation. Numerical schemes based on 3D finite elements for calculating the distribution of T-stresses along a curved 3D crack front have been devised by Parks and coworkers [16,17,[19][20][21] to facilitate the application of the J-T two-parameter criteria to surface-cracked geometries.…”

Interfacial crack-tip constraints and J-integral for bi-materials with plastic hardening mismatch

“…The requirement of elastic-plastic FE analyses together with many variables to be considered may hamper the use of the J-Q-M theory in practical application. This aspect has been discussed in detail in a recent paper of Thaulow et al (2004), and they suggested that constraint and mismatch corrections can be made available in practice by line-spring calculations (Wang and Parks 1992;Lee and Parks 1995;Jayadevan et al 2005). As the effects of mismatch in yield strength have been extensively investigated, it would be useful to characterize interfacial crack tip stress fields for another limiting case of bi-materials having the mismatch in plastic strain hardening with the same yield strength.…”