MEAM Seminar: “A Differential Homogenization Framework for Precipitation Strengthened Metals”

Precipitation-strengthened alloys are a commercially important class of materials because their mechanical properties can be altered by changing the microstructure through heat-treatment. Specifically, precipitates are introduced into the bulk (matrix) material to interact with dislocations and affect their mobility. It is known that the size, shape, orientation and stiffness of the precipitates, which can be altered during the age-hardening process, have a strong influence on the alloy and its plastic behavior. In this talk, I will discuss a differential homogenization framework that has been developed to model elasto-viscoplastic particulate composites which exhibit hardening at the local scale. The new homogenization estimates incorporate the second moments of the local hardening fields and improve on existing formulations which only take into account the first moment. First, we’ll consider the simple case of linear viscoelasticity and show that by using differential equations instead of difference equations, the new formulation is more robust than earlier incremental approaches and recovers exact results for certain classes of composites. Next, we provide estimates for creeping single crystals with elastic particles and find that neglecting the elasticity of the crystal, an assumption which is typically made, can lead to an overestimation of the effective creep-rate. Last, we examine the role of microstructure on the effective workhardening of precipitation-strengthened crystals. We focus on the interplay between crystallographic and morphological anisotropy and how these can reduce the overall anisotropy, as well as how the choice of the crystal matrix(either FCC or HCP) leads to markedly different work-hardening behavior.