Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques

Abstract

Bounds on the hydrostatic plastic strength of voided polycrystals and implications for linear-comparison homogenization techniques Bornes de la résistance plastique hydrostatique des polycrystaux poreux et leurs implications sur des techniques basées sur des milieux linéaires de comparaison

An approximate yield criterion for porous single crystals

“…By adopting a quadratic approximation for the regularized criterion (i.e n = 2), we get a Hill-type anisotropic material, for which (19) which leads to the expression of the plastic multiplierλ…”

“…The reader is referred to [12,13] for a critical assessment of these criteria. On the other hand, variational nonlinear homogenization approaches [14,15,16,17] have been applied to textured viscoplastic polycrystals with intergranular cavities [18] and perfectly plastic voided polycrystals subjected to a hydrostatic loading [19], among others. Besides, full-field numerical simulations have been performed to study void growth and coalescence within polycrystalline aggregates [18,20].…”

Bounding the plastic strength of polycrystalline voided solids by linear-comparison homogenization techniques

“…22%) as those reported above for the high-symmetry ionic solid. Additional calculations as a function of porosity [20,28] reveal that the impact of the variational relaxation on these linear-comparison bounds is independent of porosity level. Finally, because the HS bounds grow faster with slip contrast than the SC bounds, the non-relaxed HS bounds for the hydrostatic strength cease to be sharper than the relaxed SC" bounds above a certain contrast.…”

“…The SC results also predict a substantial change in the interplay between porosity and crystallinity when the crystals are deficient. Indeed, additional calculations [20,28] reveal that when the crystals are not deficient, the bounds for the hydrostatic strength follow a dilute scalinḡ σ c m ∼ f −1/2 . But while the bounds for hexagonal systems undergoing basal+prismatic slip ( J = 4) also follow this dilute scaling, the bounds for ionic systems undergoing B-type slip ( J = 3) follow the slower dilute scalingσ c m ∼ f −1 .…”

“…The bounds served to discriminate between two linear-comparison theories of polycrystalline plasticity, but were quite far from predictions obtained by full-field simulations. More recently, Idiart & Ramos Nervi [20] have reported linear-comparison bounds for the hydrostatic strength of cubic systems which confirm that the relaxation can have a significant impact in the presence of a voided phase. Here, linear-comparison bounds of the HS and the SC types 1 are reported for cubic and hexagonal voided polycrystals with isotropic texture and varying degrees of crystal anisotropy, subject to axisymmetric loading conditions.…”