SYMPOSIA PAPER Published: 01 January 1995

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


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.

Author Information

O'Dowd, NP
Imperial College of Science, Technology & Medicine, London, UK
Shih, CF
Brown University, Providence, RI, USA
Dodds, RH
University of Illinois, Urbana, IL, USA
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Developed by Committee: E08
Pages: 134–159
DOI: 10.1520/STP14634S
ISBN-EB: 978-0-8031-5305-9
ISBN-13: 978-0-8031-2013-6