The Role of Geometry and Crack Growth on Constraint and Implications for Ductile/Brittle Fracture

Abstract

A family of self-similar fields provides the two parameters required to characterize the full range of high- and low-triaxiality stress states that can exists near the tip of a mode I stationary crack. The two parameters, J and Q, have distinct roles: J sets the size scale of the zone of high stresses and large deformations, while Q scales the near-tip stress distribution relative to a high triaxiality reference stress state corresponding to a long crack in an infinitely large body. The evolution of mode I near-tip fracture states under plane strain conditions is addressed in two parts. We begin by discussing crack geometry and load effects on near-tip constraint for a non-growing crack. Details aside, increased loading (plastic deformation) in finite size geometries is accompanied by a steady loss of constraint. This behavior is explained and quantified relative to a high triaxiality reference stress state, or the Q=0 state, using results from several crack geometries. The second part of this work focuses on crack growth effects on constraint. Here steady-state crack growth provides a basic result. First, crack growth under well-contained yielding elevates near-tip constraint. Second, the maximum stress elevation due to growth is set by the steady-state high triaxiality stress state. The competing effects of constraint elevation due to crack growth and constraint loss due to increased plastic deformation in a finite size geometry offers insight into the transition to a brittle fracture mode after some amount of ductile tearing.