A Fracture Criterion with Biaxial Constraints of Deformations along the Front of a Normal Rupture Crack

Abstract

In this article, a new fracture criterion is formulated for a normal rupture crack, the most common in practice, based on the assumption that the tangential stresses in the prefracture zone are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account the nonsingular Тхx and Тzz stresses included in the asymptotic stress distribution according to Williams and characterizing the two-dimensional local constraint of deformation along the crack front in three-dimensional bodies. An expression for the effective stress intensity factor is obtained. In addition to the classical stress intensity factor, it includes the ratios of the Тxx and Тzz stresses to the yield strength. This makes it possible to take into account the restriction of deformations in the transverse (due to Тxx stresses) and longitudinal (due to Тzz stresses) directions in the vicinity of the crack front. Verification of the developed software tools and the proposed fracture criterion has been carried out. Examples of the implementation of the developed criterion for assessing crack resistance of a plate stretched in one or two directions with a coaxial transverse crack are given.