Recent developments in polycrystalline theories of viscoplasticity

M. I. IDIART

Montpellier

Workshop; MIST Workshop: Friction, Fracture, Failure [microstructural effects]; 2015

Instituto de Radioprotección y Seguridad Nuclear (Francia)

The elastoplastic response of polycrystalline metals and minerals above their brittle-ductile transition temperature is to a great extent dictated by the morphology, lattice orientation, and elastoplastic response of each individual single-crystal grain composing the aggregate. In many deformation processes these microscopic properties evolve and induce significant changes on the macroscopic response. An accurate description of such processes thus requires multiscale theories that explicitly account for the polycrystalline nature of the solid. Now, due to their inherent microstructural randomness, microscopically cognate polycrystals do not exhibit a single response but a ---hopefully narrow--- range of responses. Therefore, one can either develop estimates that yield a single representative response or derive bounds for the entire range of possible responses of polycrystalline solids belonging to a certain class. This talk will present recent developments on nonlinear homogenization techniques to bound and estimate the elastoplastic response of polycrystalline solids.The first part of this talk will pertain to bounds. We will present new bounds for polycrystalline solids made up of elastically rigid and plastically non-hardening grains. The bounds follow from a homogenization technique proposed by Idiart & Ponte Castañeda [Proc. R. Soc. A 463 (2007) 907?924] which incorporates up to second-order microstructural statistics. A wide range of cubic and hexagonal solids is considered to assess the role of crystal anisotropy on the macroscopic response. In all cases, the new bounds are the sharpest available to date. Improvements over earlier bounds are particularly significant in the case of voided polycrystals. Interestingly, bounds of the Self-Consistent type assert that voided aggregates of crystals with four independent systems can accommodate arbitrary deformations, those with three independent systems can dilate but not distort, and those with less than three independent systems cannot deform at all.The second part of this talk pertains to estimates. Amongst the various quasi-analytical techniques available, the so-called `generalized-secant´ technique proposed Liu & Ponte Castañeda [J. Mech. Phys. Solids 52 (2004) 467-495] seems to deliver the most accurate estimates to date. In its original formulation, this technique delivers estimates for the overall strain-rate-stress response of polycrystalline solids. These estimates are computationally inexpensive relative to full-field simulations but they still require the numerical resolution of a large set of nonlinear algebraic equations. This fact can become an issue when simulating mechanical processess where deformations are imposed, which require inversion of the constitutive description in order to express stresses in terms of strain rates. We will present new generalized-secant estimates derived directly for the problem formulated in terms of strain rates as recently proposed by Idiart & Vincent [C.R. Mecanique 343 (2015) 179-186].The talk will conclude with a brief presentation of new estimates for heterogeneous elastoplastic systems undergoing infinitesimal deformations, which could be useful for quantifying residual stresses in polycrystalline solids. The estimates follow from an incremental homogenization technique recently proposed by Idiart & Lahellec [submitted for publication]. The derivation relies on the use of `comparison solids´ which, unlike comparison solids considered previously, are pointwise rather than piecewise heterogeneous. Predictions are confronted with full-field simulations for particulate composites under cyclic and rotating loading conditions. Good agreement is found for all cases considered. In particular, elasto-plastic transitions, tension-compression asymmetries (Bauschinger effect) and strain-rate effects are all well captured.