# Small-scale yielding interfacial crack-tip fields

- Authors
- Journal
- Journal of the Mechanics and Physics of Solids 0022-5096
- Publisher
- Elsevier
- Publication Date
- Volume
- 40
- Issue
- 3
- Identifiers
- DOI: 10.1016/0022-5096(92)80002-8

## Abstract

Abstract B y idealizing the crack surroundings as an isotropic elastic perfectly-plastic material with tensile yield strength σ bonded to a rigid or isotropic elastic substrate, the small-scale yielding (SSY) plane strain asymptotic lields for “elastically” traction-free interfacial cracks are numerically calculated. The resulting fields are described in terms of slip-line theory and elastic potentials. The oscillatory asymptotic elastic field behavior does not persist deep within the plastic zone. However, some loadings produce cusp-like boundaries separating various crack-lip sectors within the near-tip fields, coupling the stress state to the radial distance, r, in non-conventional quasi-constant-slate sectors. When the SSY interfacial load-phase angle, defined as ζ 0 = ∠ K + ɛ ln [K/σ 2 v cosh 2 (πɛ)] (where ∠ K is the phase angle of the complex tractionfree stress intensity factor K, and ɛ is the bi-material constant) is negative, inelastic sectors generally surround the crack tip in the plastically deformable medium, simultaneously producing normal and shear interfacial tractions as large as 3.29σ and σ/√3, respectively. For ζ 0 > 0, the fields usually contain an elastic crack-face sector which typically spans at least 45, a centered-fan sector, as well as various conslantand quasi-constant-state sectors, generally leading to less severe interfacial traction and strain conditions than for ζ 0 < 0. From the individual fields found at various discrete values of ζ 0, the near-tip fields are qualitatively characterised over the entire admissible range of ζ 0. At distances from the crack tip much less than the characteristic plastic zone dimension in the adjacent “yielding” domain, the logarithmically singular asymptotic stress field in the “elastic” domain is accurately described by the solution of a halfspace subject to a uniform stress parallel to its boundary and to step function discontinuities in normal and shear surface tractions at the crack tip.

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