Abstract
In this paper, we consider an interface mode III crack with a process zone located in front of the fracture tip. The zone is described by imperfect transmission conditions. After application of the Fourier transform, the original problem is reduced to a vectorial Wiener–Hopf equation whose kernel contains oscillatory factors. We perform the factorization numerically using an iterative algorithm and discuss convergence of the method depending on the problem parameters. In the analysis of the solution, special attention is paid to its behaviour near both ends of the process zone. Qualitative analysis was performed to determine admissible values of the process zone's length for which equilibrium cracks exist.This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.
Highlights
The theory of brittle fracture, developed by Griffith using the energy balance approach [1] and later reformulated by Irwin in terms of stress fields, implies the existence of a stress singularity at the tip of a sharp crack
We assumed that the length of the process zone L was predefined, but in reality, for equilibrium cracks, there are two critical conditions which ensure that the fracture will not propagate and that neither end of the process zone will move
We considered the static loading of a mode III crack at the interface of two elastic materials, with a process zone modelled by relations (2.3)
Summary
The theory of brittle fracture, developed by Griffith using the energy balance approach [1] and later reformulated by Irwin in terms of stress fields, implies the existence of a stress singularity at the tip of a sharp crack. Barenblatt introduced the cohesive zone model in [5,6], describing the resisting forces that occur when material elements are being pulled apart This approach allows the elimination of the stress singularity at the crack tip, which is useful for classic finite-element modelling [7]. All models of fracture belong to the class of mixed boundary value problems which, in turn, can be reduced to Wiener–Hopf functional equations [11,12,13,14,15] This applies to modelling cracks through a formulation that is continuous, for both static and steady-state approaches [16,17]. We determine all fracture mechanics parameters, evaluate a condition for the existence of an equilibrium state of the crack under remote loading and compute the corresponding length of the process zone
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