Effects of finite chain extensibility on the stress fields near the tip of a mode III crack

Abstract

We carried out a detailed analysis of the asymptotic stress and deformation fields at the tip of a mode III crack in a hyperelastic solid described by Gent's model. This model accounts for finite chain extensibility so that the deformation everywhere in the solid, including the crack tip, is bounded. We also present an exact solution for the 'small-scale yielding' problem where the region of large deformation is small compared with specimen dimensions. Our result shows that the crack tip stress field is non-separable. In addition, an infinite number of parameters are needed to completely specify the angular variation of crack tip stress field.

Crack tip fields in soft elastic solids subjected to large quasi-static deformation — A review

“…However, this discontinuity is due to an approximation to describe the rapidly changing stress fields across /2. A discussion of this approximation can be found in Long and Hui [48]. The above solution has several interesting features:…”

“…They first introduced image patterns to the crack tip region by means of shadowgraph and then determined the displacement field by correlating small elements in the reference and deformed images based on the introduced patterns. A similar method based on particle tracking was used in Chen et al 48 [93] to measure the crack tip velocity field for subsonic and supersonic dynamic cracks. There are at least two aspects in the experiments that can be further improved.…”

“…Fortunately, the class of isotropic strain energy density functions consistent with antishear deformation are those that depends only on 1 II which is the main interest of this review. In this section, we will first summarize the crack tip solutions for GNH solids obtained by Knowles [47] and then those for Gent solid from Long and Hui [48]. In light of (74), we only need to present the true stress components 3 for crack tip stress fields.…”

“…For more general loading conditions, for example, when the applied stresses are sufficiently large so that the SSY condition is violated, the leading order terms of the stresses were found to be [48]: (80c)…”

“…The amplitudes of these singular stress and deformation fields are governed by far-field loading conditions and are analogous to the stress intensity factors in LEFM [33,23]. These pioneering works inspired further studies to understand the local stress and deformation fields near cracks in homogeneous hyper-elastic solids, which can be roughly divided into five categories: plane strain cracks in compressible materials [34,35,36,37,38], plane strain cracks in incompressible materials [39,40,41], plane stress cracks in compressible materials [42,43,44], plane stress cracks in incompressible materials [45,46], and anti-plane shear cracks (Mode III) [47,48]. In addition, a number of analyses were devoted to interface cracks between two dissimilar hyperelastic materials, either in plane stress [49,50,51] or in plane strain [52,53,54,55] condition.…”