Comparison of two potential-based cohesive models to predict the critical load of a finite orthotropic plate with oblique crack

Abstract

The boundary-value problem of the theory of elasticity for a finite orthotropic plate with an oblique edge crack is considered. A tensile load is applied to a cracked body, and the crack is located along the orthotropy axis, which is not aligned with the loading direction. A cohesive zone model for the mixed fracture mode is used to study crack growth mechanisms. The traction— separation laws are represented in the potential form. In this case, normal and tangential tractions are given by partial derivatives of the dissipation potential with respect to the corresponding separations. Two cohesive laws of different mixity forms are constructed basing on the pure-mode fracture models (normal separation and transverse shear) with no mode mixity parameters. An algorithm for the determination of critical state parameters of a crack using the finite-element method is constructed. An example of the calculation of critical load parameters and the corresponding stress field for the two cohesive laws of mixed-mode fracture is given. The impact of the mode-mixity form on the critical state parameters is studied. For the investigated range of orthotropic parameters, it is established that the mode-mixity of two cohesive laws well-known in the literature gives an error in determining the critical load to be less than five percent. This discrepancy decreases simultane ous ly with the cohesive length.