Abstract
Engineers require accurate determination of the configurational force at the crack tip, and corresponding stress intensity factors, for fracture fatigue analysis and accurate crack propagation. However, obtaining highly accurate crack tip configuration force values is challenging with methods requiring knowledge of the stress field around the crack tip a priori. This paper proposes a method which aims to remove the necessity of knowing the stress field a priori whilst producing very accurate values of the configurational force at a static crack tip. The proposed method is demonstrated to be path independent and is combined with a robust a posteriori residual error estimator which is indicative of the accuracy of the configurational force calculation. This makes it possible to generate accurate values for the configurational force acting both perpendicular and parallel to the crack edges. Accuracies are achieved which are at least 104 times more accurate than other numerical methods which make no assumption about the local tip stress field. Therefore accurate benchmarks are determined in this paper for inclined, split and tree crack problems. In addition the new method is shown to obtain very similar values for the configurational force compared to results obtained using other methods which require knowledge of the stress field at the crack tip. The techniques presented in this paper open the door to configurational force-based methods being used for fatigue analysis.
Highlights
The accurate determination of configurational forces (CF) for fracture mechanics problems is essential in order to obtain realistic predictions of fatigue life, by virtue of the stress intensity factors (SIFs), as well as determining accurate propagation paths
A highlight of this method is its simplicity, the authors appreciate that a goal-orientated error estimate for the edge term of (34) could be used to as an error measure for the CF this would require an adjoint problem to be solved at each iteration step; detracting from overall simplicity of this algorithm
This paper proposed a novel method to determine the CF at the crack tip which does that not require knowledge of the stress field about the crack tip to be known a priori
Summary
The accurate determination of configurational forces (CF) for fracture mechanics problems is essential in order to obtain realistic predictions of fatigue life, by virtue of the stress intensity factors (SIFs), as well as determining accurate propagation paths. The power released by a crack is the product of two components; the CF (or material force) and the crack tip’s configurational velocity (or crack propagation rate). Alternative methods to determine the stress intensity factors include: the equivalent domain integral method [60], determining both components of the CF directly using the near tip stress solution [17,70], the virtual crack extension method [31], virtual crack closure technique [64], or by considering the nodal CF at the crack tip in the context of a finite element CF mechanics [51]. The first integral considered the crack faces but did not include a region at the crack tip, the region at the crack tip
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