Vol. 1, No. 5, 2006

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Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

QiZhi Xiao and Bhushan Lal Karihaloo

Vol. 1 (2006), No. 5, 881–910

The lack of any work on the asymptotic fields at the tips of cohesive cracks belies the widespread use of cohesive crack models. This study is concerned with the solution of asymptotic fields at cohesive crack tips in quasibrittle materials. Only normal cohesive separation is considered, but the effect of Coulomb friction on the cohesive crack faces is studied. The special case of a pure mode I cohesive crack is fully investigated. The solution is valid for any separation law that can be expressed in a special polynomial form. It is shown that many commonly used separation laws of quasibrittle materials, for example, rectangular, linear, bilinear, and exponential, can be easily expressed in this form. The asymptotic fields obtained can be used as enrichment functions in the extended/generalized finite element method at the tip of long cohesive cracks, as well as short branches/kinks.

asymptotic field, cohesive crack tip, Coulomb friction, quasibrittle material, cohesion-separation laws
Received: 19 January 2006
Accepted: 5 April 2006
Published: 1 September 2006
QiZhi Xiao
School of Engineering
Cardiff University
Queen’s Buildings
The Parade
Cardiff CF24 3AA
United Kingdom
Bhushan Lal Karihaloo
School of Engineering
Cardiff University
Queen’s Buildings
The Parade
Cardiff CF24 3AA
United Kingdom