Two-Parameter Criterion for Elastoplastic Failure of Materials with Anisotropy of Plastic Properties
V.D. Kurguzov
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia
Keywords: plastic anisotropy, mixed mode failure, crack path deflection, elastoplastic failure, critical load
Abstract
The initiation of an inclined edge crack of mixed type (modes I and II failure) in a thin strip of sheet steel under tensile loading is considered. During rolling, an initially isotropic sheet metal typically develops significant anisotropy, characterized by differences in plastic properties along the rolling and transverse directions. The quadratic Hill yield criterion is used to describe plastic anisotropy. The failure process of such materials is described using the modified Leonov-Panasyuk-Dagdale model. Under complex loading, the crack path curves, so the trajectory deflection angle is determined using the force-based integral strength criterion. In the asymptotic representation, stress components near the crack tip account for non-singular terms (T-stresses). To obtain critical failure parameters of a strip with an inclined edge crack, a two-parameter strength criterion is proposed. The parameters in the analytical model are analyzed. Dimensionless geometric parameters of the structure are determined numerically using the finite element method. A system of two nonlinear equations is obtained for the critical length of the pre-failure zone and the critical load under complex stress conditions. Using Hill’s yield criterion, the shape and size of the plastic zone near the crack tip in a plastically anisotropic material are determined.
|
