Non-linear analysis of shallow cracks in smooth and notched plates Part 1: Analytical evaluation

Abstract

This is the first paper of two that deal with the non-linear analysis of shallow cracks. Simple formulae are given for estimating the J integral for a power-hardening elastic-plastic solid. The proposed equation for estimating J makes use of the linear elastic and the fully plastic solution to interpolate over the entire range from small-to large-scale yielding. The elastic geometry factor is obtained by means of the stress intensity factor. In the fully plastic formulation, the plastic geometry factors are obtained by considering a pure power-hardening solid, which reduces at one limit to an incompressible linear elastic solid, and at the other to a perfectly plastic solid. The solutions are given for three basic configurations: a double-edgecracked plate under tension and bending; a notched plate under tension with a crack at the root of the notch; a single-edge-cracked plate under bending. Both force control and displacement control are considered. The accuracy of the formulae is assessed using the finite element calculations in Part 2.

Non-linear analysis of shallow cracks in smooth and notched plates Part 2: Finite element validation

“…Based on dimensional arguments, it should be possible to write the path-independent contour integral J as [1] J…”

“…The J integral as defined in equation (5) requires the determination of an equivalent nominal stress ne , which can be calculated from the load and the limit load [see equation (19) in Part 1 [1]]. To find the limit load of the cracked specimens, FEA was first carried out assuming an elastic-perfectly plastic solid with yield stress Y .…”

“…To find the limit load of the cracked specimens, FEA was first carried out assuming an elastic-perfectly plastic solid with yield stress Y . The limit load Q L was taken as the asymptotic value of the total generalized load Q (force or moment) under increasing displacement u [1]. The limit load analyses were carried out under displacement control, since this gave a numerically more stable solution than under force control.…”

“…The limit load analyses were carried out under displacement control, since this gave a numerically more stable solution than under force control. By introducing the net section stress net ¼ P=A net , the constraint introduced by a crack can be represented by the constraint factor [1] ¼ net ne ð6Þ…”

“…In the last column of Table 1, the relative deviation between finite element results and closed-form solutions, as given in reference [1], are presented.…”