A Discrete Dislocation Analysis of Crack Growth under Cyclic Loading
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2 H.H.M. CLEVERINGA , E. VAN DER GIESSEN' and A. NEEDLEMAN 'Delft University of Technology, Koiter Institute Delft, Mekelweg 2, 2628 CD Delft, The Netherlands 2 Brown University, Division of Engineering, Providence, RI 02912, USA
ABSTRACT Cyclic loading of a plane strain mode I crack under small scale yielding is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic solid. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a nonsingular complementary solution that enforces the boundary conditions, which is obtained from a linear elastic, finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. An elastic relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, which permits crack initiation and crack growth to emerge naturally. It is found that crack growth can occur under cyclic loading conditions even when the peak stress intensity factor is smaller than the stress intensity required for crack growth under monotonic loading conditions. INTRODUCTION The nucleation and growth of cracks under cyclic loading conditions is arguably the most important mode of failure in engineering applications. Nevertheless, although much is known about fatigue fracture from both the materials science and engineering perspectives
[1], a basic quantitative understanding of the mechanisms involved is limited. In practice, phenomenological relations between the amplitude of the applied stress intensity factor and the crack growth rate are used to quantify fatigue crack growth, e.g. [2]. However, outside a limited range of conditions, additional variables are needed in a phenomenological relation for it to have predictive capability, e.g. [3, 4, 5]. Quite recently, Nguyen et al. [6] have analyzed fatigue crack growth using a cohesive surface framework to characterize the separation process and conventional continuum plasticity to characterize the material behavior. It was found that when the cohesive relation was taken to be elastic and the crack subject to cyclic loading, shake down occurred in that the deformation became elastic and the crack arrested. Crack growth was found for a cohesive relation with unloading-reloading hysteresis. Simulations of fatigue crack growth using discrete dislocation models have also been carried out, e.g. [7, 8, 9, 10, 11]. In such studies, dislocations nucleated from the crack tip are allowed to glide on specific presumed slip planes around the crack tip. Crack growth in [10, 11] is taken to be deformation controlled in that the crack is assumed to grow by emitting dislocations from the crack tip. In this paper, we carry out an analysis of crack growth under cyclic loading
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