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A Discrete Dislocation Analysis of Crack Growth under Cyclic Loading

Published online by Cambridge University Press:  15 February 2011

H.H.M. Cleveringa,
E. Van Der Giessen and
A. Needleman
H.H.M. Cleveringa
Affiliation:
Brown University, Division of Engineering, Providence, RI 02912, USA
E. Van Der Giessen
Affiliation:
Delft University of Technology, Koiter Institute Delft, Mekelweg 2, 2628 CD Delft, The Netherlands
A. Needleman
Affiliation:
Brown University, Division of Engineering, Providence, RI 02912, USA
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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.

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