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MEAM PhD Thesis Defense: “A Differential Homogenization Framework for Precipitation-Strengthened Metals”

September 30 at 2:00 PM - 3:00 PM

Composite materials, such as metal- and polymer-matrix composites, exhibit both elastic and dissipative effects when subjected to macroscopic loadings. Even when the phases of the composite are characterized by a simple Maxwell rheology, the complex viscoelastic interactions between the phases give rise to emergent behavior at the macroscopic scale. Incorporating these “long-memory” effects in the context of analytical homogenization is the subject of this thesis.

In particular, I will present a novel differential homogenization framework for particulate composites comprised of elasto-viscoplastic strain-hardening phases that incorporates first and second-moment information about the local hardening fields and improves upon existing formulations which only consider the corresponding first moments. The present framework is motivated by precipitation-strengthened alloys, which constitute a commercially important class of whose mechanical properties can be altered by introducing stiff precipitates into the bulk (matrix) through heat-treatment.

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 approaches and recovers exact results for certain classes of composites.

Next, we provide estimates for creeping single crystals with elastic particles and find that the long-memory effect manifests as a transient creep-rate which is strongly dependent on the elasticity of the phases as well as the morphology of the particles. We also find that the timescales associated with macroscopic creep are strongly dependent on crystal symmetry as well as the loading configuration.

Lastly, we examine the effect of microstructure on the effective behavior of precipitation-strengthened crystals. It is found that overall, stiff precipitates induce larger levels of slip-activity and work-hardening, relative to a corresponding homogeneous crystal. For FCC crystals, the precipitate stiffness plays a significant role in modulating the overall anisotropy, while for HCP crystals the overall anisotropy is mostly affected by the viscous and hardening anisotropies. Moreover, it is found that incorporating the second-moments of the local hardening fields is important for generating accurate predictions, particularly at large deformations.

Jose E. Cotelo

Ph.D. Candidate, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania


September 30
2:00 PM - 3:00 PM
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Mechanical Engineering and Applied Mechanics