Scaling of discrete dislocation predictions for near-threshold fatigue crack growth

Abstract

Analyses of the growth of a plane strain crack subject to remote mode I cyclic loading under small scale yielding are carried out using discrete dislocation dynamics. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation being incorporated through a set of constitutive rules. An irreversible relation is specified between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip in order to simulate cyclic loading in an oxidizing environment. Calculations are carried out with different material parameters so that values of yield strength, cohesive strength and elastic moduli varying by factors of three to four are considered. The fatigue crack growth predictions are found to be insensitive to the yield strength of the material despite the number of dislocations and the plastic zone size varying by approximately an order of magnitude. The fatigue threshold scales with the fracture toughness of the purely elastic solid, with the experimentally observed linear scaling with Young's modulus an outcome when the cohesive strength scales with Young's modulus.

Fatigue crack growth from a cracked elastic particle into a ductile matrix

“…These discrete dislocation (DD) models have been shown to predict a host of phenomena, such as sizeeffects in yielding, fracture, sliding, indentation, and polycrystals [16][17][18][19][20][21][22], not accounted for in conventional continuum plasticity. In particular, DD studies of fatigue crack growth have been carried out [17,18,[24][25][26][27] that provide insight and guidance into fatigue crack growth problems where continuum plasticity and standard fatigue laws may be inapplicable. Most importantly for our current work is that these DD analyses predict that fatigue crack growth arises naturally under cyclic loading conditions without introducing additional parameters.…”

“…Most importantly for our current work is that these DD analyses predict that fatigue crack growth arises naturally under cyclic loading conditions without introducing additional parameters. The DD studies of fatigue in single-crystal materials have shown the existence of a threshold, a Paris power-law regime, striations, scaling with material properties and a short-crack regime [17,18,24].…”

An atomistic investigation into the nature of near threshold fatigue crack growth in aluminum alloys

“…Discrete dislocation (DD) dynamics simulations are not generally plagued by this problem as they can accommodate a much larger spatial domain, while still explicitly modeling every dislocation. However, DD models do not explicitly represent the atomic scale complexities that occur at a crack tip [9][10][11][12][13], and thus cannot illuminate the atomic mechanisms by which a crack tip propagates.…”

Multi-asperity contact: A comparison between discrete dislocation and crystal plasticity predictions

“…The formulation was presented by Van der Giessen and Needleman in [15] and has been used to solve a variety of two and three dimensional boundary value problems, for example, [16][17][18][19][20][21]. In the calculations here a two dimensional discrete dislocation plasticity formulation is used with the dislocations all of edge character and modeled as line singularities in an isotropic linear elastic solid.…”

“…However, there are circumstances involving plastic deformation in small volumes where long-range elastic dislocation interactions dominate which permits a wide range of complex phenomena involving plastic deformation to be represented qualitatively, e.g. [4,17,23], and, to a remarkable extent even quantitatively, e.g. [16,24].…”