Stress multiaxiality factor for crack growth prediction using the strain energy density theory
Abstract
The multiaxiality factor defined as the ratio of the von-Misses equivalent stress to the volumetric stress has been reported to be related to the initiation and progression of failure in structures. It is demonstrated in the present paper that the location around the crack tip where the multiaxiality factor obtains minimum value is an indicator of the direction of minimum material fracture resistance for crack propagation. It is also proposed that the location along the direction of crack propagation path where multiaxiality factor obtains minimum value is considered as the critical distance away from the crack tip, where the strain energy density should be evaluated and compared to its critical value. Theoretical predictions correlate well with the test results for the investigated cases. _ 2006 Elsevier Ltd. All rights reserved.
Keywords: Multiaxiality factor; Crack growth; Strain energy density; Crack orientation
1. Introduction
It is well recognized that the stress state ahead of a crack tip plays an important role for the crack behaviour of a structural component. It is also recognized that the multiaxility factor, i.e. the ratio of the von Misses equivalent stress to the volumetric stress is a characteristic measure of the local stress state. The multiaxiality factor (q) has been reported to be related to the initiation and progression of failure in structures. In [1], the crack formation in aluminium tensile specimens is predicted using the stress multiaxiality and the equivalent strain values. In [2], it is suggested that the location of fracture initiation in steel specimens lies at the point where the multiaxiality quotient is minimum. In present, the multiaxiality factor in the vicinity of the crack tip is considered as a parameter capable to correlate the stress state with the material damage mechanisms and the fracture resistance. Specifically, it is proposed that large values of the multiaxiality factor are related to the predominance of yielding mechanisms increasing the fracture resistance of the material, while small values of q are related to the increase of the brittleness of the material

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