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About | ECITTT | Conference Programme | Abstracts (3.)


B L Karihaloo and Q Z Xiao
School of Engineering
Cardiff University
P O Box 686
Cardiff CF24 3TB

In many engineering problems of practical interest concerned with the presence of cracks, accurate determination of the coefficient of the first, singular term of the crack tip asymptotic field, i.e. the stress intensity factor (SIF) is of prime importance. The coefficients of the higher order terms of this field are equally important in elasto-plastic and quasi-brittle fracture.

This paper will introduce an improved hybrid crack element (HCE) with p-adaptivity in order to calculate directly (i.e. without interpolation or the use of J-integral) and accurately not only the SIF but also the coefficients of the higher order terms of the crack tip asymptotic field in bodies of finite size.

The ambiguities in the variational background, parameter matching condition and integration order of HCE that have plagued the published literature will be cleared. Numerical results of finite-size bodies with a variety of geometry show that the computed coefficients of the higher oreder terms as well as the SIF converge rapidly with p-refinement of the HCE used to represent the crack and the h-refinement of the regular elements used to discretise the remaining body. The latter elements are developed to satisfy exactly traction-free conditions on any free boundaries.

The elements are stable when the ratio of HCE size to the crack length is larger than 0.25. They do not suffer from 'shear locking'. The HCE is efficient down to very short cracks, thus enabling one to investigate the growth of shallow cracks. Several examples will be presented to demonstrate the potential of HCE.