On higher order parameters in cracked composite plates under far‐field pure shear

Abstract

This paper presents the analytical solution of the crack tip fields as well as the crack parameters in an infinitely large composite plate with a central crack subjected to pure shear loading. To this end, the complex variable method is employed to formulate an asymptotic solution for the crack tip fields in an anisotropic plane. Using a stress-based definition of the crack tip modes of loading, only the mode II crack parameters are found to be non-zero under pure shear load. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non-singular term, ie, the T-stress. Unlike the isotropic materials, in which the T-stress is zero under pure shear, it is found that the T-stress is non-zero for the case of anisotropic materials, being the only material-dependent crack tip stress parameter. The veracity of our exact crack tip fields is assessed and verified through a comparison made with respect to the finite element (FE) solution. Finally, we demonstrate the significance of the T-stress on stresses near the crack tip in composite plates under pure shear loads.

Crack tip fields in anisotropic planes: a review

“…To illustrate the impact of higher order coefficients on the crack tip stress field, we herein refer to a representative numerical example from the literature (Shah et al, 2006b;Tran and Mear, 2018;Ayatollahi et al, 2020). The problem geometry is shown in mesh grid in Fig.…”

“…Thereafter, Lee (2016Lee ( , 2018 continued their previous study (Lee et al 1996) and analysed the propagating crack in an anisotropic medium, with stress and displacement fields given along with a generic solution for all the crack parameters in dynamic fracture. More recently, Ghouli et al (2020); Nejati et al (2021b) suggested infinite series solutions for stress, strain and displacement fields in cracked anisotropic planes, while decomposing fracture modes according to a stress-based definition. These authors also devised exact analytical solutions for all crack tip coefficients in centrally cracked infinite anisotropic plates.…”

“…crack tip coefficients) so as to have an over-determined system of displacement equations. Treating such problem with the least squares scheme will finally output the sought-after crack tip parameters (Ayatollahi and Nejati 2011;Ayatollahi et al 2020;Yao et al 2020a). • Extended finite element method (XFEM): Another well-known FEM-based approach is the extended finite element method which utilises enriched shape functions for elements at the crack tip.…”

Crack tip asymptotic field and K-dominant region for anisotropic semi-circular bend specimen

“…The characteristic equation normally returns distinct complex roots (µ µ 1 2 ) in general anisotropic problems. Ghouli et al [35] put forward a stress-based definition for the anisotropic fracture modes based on the criterion that at =°= 0 , 0…”

“…Evaluated from Eqs. (7) and (8), the coefficients of the second terms, A 2 and B 2 , construct two physical parameters, T and [35]:…”