Modelling and Crystal Plasticity Analysis for the Mechanical Response of Alloys with Non-uniformly Distributed Secondary Particles

The relationship between yield stress and the distribution of microscopic plastic deformation was numerically investigated by using a crystal plasticity finite element method (CP-FEM) in the model where particles were randomly distributed. It was in order to reveal which particle spacing. i.e., the maximum, minimum or average particle spacing, can be taken as the representative length which controls yielding. The critical resolved shear stress for the onset of the slip deformation in any element was defined under the extended equation in the Bailey-Hirsch type model. The model includes the term of the Orowan stress obtained from the local values of the representative length. Each particle spacing was distributed with a standard deviation of approximately 2 to 3 times larger than the average particle spacing. The macroscopic mechanical properties obtained with CP-FEM were in good agreement with those experimentally obtained. The onset of microscopic slip deformation depended on the particle distribution. Plastic deformations started first in the area where the particle size is larger, then the plastic region grows in the areas where the particle spacing is smaller. Slip deformation had occurred in 90% of the matrix phase by the macroscopic yield point. The length factor in the Orowan equation was the average spacing of the particles in the model, which is in good agreement with Foreman and Makin. The CP-FEM indicated that in dispersed hardened alloys, microscopic load transfer occurred between the areas where the large particles spacing and the small one at the yielding.