Multiparametric presentation of the crack-tip fields in the vicinity of longitudinal shear crack

The article is devoted to the study of the stress field at the tip of a longitudinal shear crack based on a multiparametric asymptotic representation of the stress field at the crack tip in a linearly elastic isotropic material. The performed asymptotic analysis of the fields at the tip of a longitudinal shear crack is a natural continuation of the studies conducted for multiparametric stress fields at the tips of cracks of normal separation and transverse shear, as well as mixed loading. Despite the simplicity of analyzing the contribution of higher approximations to the general representation of the stress field at the tip of a type III crack, multicoefficient representations of the stress field near this type of crack have not been previously studied. It is shown that higher-order approximations must necessarily be taken into account for 1) accurate representation of the stress field and 2) expansion of the range of asymptotic expansions. It has been found that the greater the distance from the crack tip, the more components of the series must be stored near the crack tip.