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

Abstract

The monotonic and cyclic crack growth rate of cracks is strongly influenced by the microstructure. Here, the growth of cracks emanating from pre-cracked micron-scale elastic particles and growing into single crystals is investigated, with a focus on the effects of (i) plastic confinement due to the elastic particle and (ii) elastic modulus mismatch between the reinforcement and matrix phases. Due to the small sizes of the particles and cracks, plasticity in the ductile crystal is modelled using a 2D discrete dislocation plasticity framework wherein dislocations are modelled as line singularities in an isotropic elastic isotropic material. Crack growth is modelled using a cohesive surface. Calculations reveal a threshold for fatigue crack growth and a transition to Paris power-law behavior, both depending on the existence of the elastic particle and the modulus mismatch. For a matched-modulus particle, the threshold is reduced by 25% and is attributed to slip blockage by the particle. For a high-modulus particle, the threshold is reduced by 50% due to the enhanced stress intensity factor caused by elastic mismatch and due to some slip blockage. However, crack growth halts after some amount of crack advance due to the decreasing effect of elastic mismatch and slip blocking as the crack moves away from the particle. The broad results here are compared with experimental observations in the literature, and are consistent in a number of respects. These results show that fatigue crack growth from micron-scale particles is strongly influenced by plasticity size effects, elastic mismatch, and particle constraints on plastic flow, all of which are captured within a discrete dislocation plasticity framework.

Keywords:

• discrete dislocations
• cracked particle
• crack growth
• defects in solids

Acknowledgements

The authors gratefully acknowledge support of this work by Northrop–Grumman Corporation and by the National Science Foundation through the Materials Research Science and Engineering Center on Nano- and Micromechanics of Materials at Brown University, grant no. DMR-0520651.