Elasto-plastic fracture criterion for structural components with sharp V-shaped notches

Abstract

Mode I fracture of plate specimens with sharp V-shaped notches is studied analytically and numerically. Within computations, elastic-perfectly plastic constitutive behaviour is assumed. The crack initiation from the tip of the V-shaped notch is described with the help of a modified Leonov–Panasyuk–Dugdale model using an additional parameter, namely, the diameter of the plasticity zone. Under small-scale yielding conditions in the presence of a singularity of the stress field in the vicinity of the V-shaped notch tip, a coupled fracture criterion is proposed. A strain-based fracture criterion is formulated at the real notch tip, and a force-based criterion operating with averaged normal stresses is considered at the fictitious crack tip. The diagrams of quasi-brittle fracture of specimens from structured material are constructed. The propagation of the plastic zone in the notched plates under quasi-static loading is simulated numerically. The plastic zone size in the vicinity of the V-shaped notch tip is assessed; in the limiting case, the V-notch degenerates into an edge crack. The generalized stress intensity factor for a crack growing from a sharp V-shaped notch is obtained by the finite element method. It is shown that under small-scale yielding, the analytical predictions of the critical load agree with the numerical results for a wide range of opening angles.