Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria

Abstract

A numerical parametric study on the crack growth direction under mixed mode conditions (I+II) is introduced. An eccentric asymmetric four-point bending of a single edge notched beam specimen is considered as an example, since various levels of mode mixity can be thus obtained. The crack growth direction is estimated using the maximum tangential stress (MTS) criterion, the strain energy density (SED) criterion and the crack tip displacement (CTD) criterion. Multi-parameter fracture mechanics based on description of the stress and deformation fields in the cracked body by means of their approximation using several initial terms of the Williams power series is employed. It was found out that whereas the use of the CTD and SED criteria should be accurate enough even in their classical (or two-parameter) form for most geometries and distances of their application from the crack tip, the generalized form of the MTS criterion with at least four terms of the series should be applied, if the distance of its application is not less than 0.01 of the specimen width. Moreover, it is able to describe the typical dependence of the initial kink angle on the distance from the crack tip where the criterion is applied.