Hussein, M. I.3; Borg, Ulrik2; Niordson, Christian Frithiof4; Deshpande, V. S.3
1 Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark2 Department of Mechanical Engineering, Technical University of Denmark3 University of Cambridge4 Centre for oil and gas – DTU, Center, Technical University of Denmark
The shear and equi-biaxial straining responses of periodic voided single crystals are analysed using discrete dislocation plasticity and a continuum strain gradient crystal plasticity theory. In the discrete dislocation formulation the dislocations are all of edge character and are modelled as line singularities in an elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Over the range of length scales investigated, both the discrete dislocation and strain gradient plasticity formulations predict a negligible size effect under shear loading. By contrast, under equi-biaxial loading both plasticity formulations predict a strong size dependence with the flow strength scaling approximately inversely with the void-spacing. Excellent agreement is obtained between predictions of the two formulations for all crystal types and void volume fractions considered when the material length scale in the non-local plasticity model chosen to be $0.325\mu m$ (around ten times the slip plane spacing in the discrete dislocation models).