Effective behavior of composites with combined kinematic and isotropic hardening based on additive tangent Mori–Tanaka scheme

Abstract

The goal of the present work is to propose a multi-scale approach for composite materials which accounts for kinematic hardening in the phases. For that purpose, the additive/sequential interaction rule and tangent linearization of viscoplastic response proposed for elastic-viscoplastic material can be extended in a straigthforward manner. A two phase composite where each phase is elastic-viscoplastic is considered. The viscoplastic flow is governed by a J 2 flow theory with an overstress. To find the overall behavior of the composite, a Mori-Tanaka model is applied. Numerical validation of the proposition is carried out by considering a representative volume element with 30 inclusions. Various configurations have been tested: hard or soft inclusion cases with or without isotropic hardening. It is shown that the quality of the model predictions is not affected by the introduction of the kinematic hardening component in the local constitutive behavior. Namely, in most cases considered in the paper the overall stress-strain response as well as the average stress-strain response per phase is accurately estimated. It has been also verified that the obtained back-Article published in Composites Part B 174 (2019) 1-65 stress components are consistent with the ones predicted by Finite element calculations with ABAQUS Software.

An incremental‐secant mean‐field homogenization model enhanced with a non‐associated pressure‐dependent plasticity model

“…The plastic multiplier Γ is then computed, as in the case in which the residual is considered, by means of a Newton-Raphson algorithm, with the derivatives following from Equations ( 43)- (45) without the residual stress. The updated expressions when neglecting the residual stress of…”

“…The direct linearization approach for the definition of the LCC is used in the secant formulation by Berveiller and Zaoui, 36 Tandon and Weng 37 and so forth, a formulation which allows representing visco-plastic behaviors under proportional and monotonic loading conditions. Other approaches are the affine formulation [38][39][40] and so forth, which is valid for arbitrary loading history of visco-plastic models, the incrementally affine formulation, 41,42 or the incremental-tangent formulation, 19,[43][44][45] and so forth, which allow representing arbitrary loading. There is one main drawback when using the affine, incrementally-affine and incremental-tangent formulations, which is the anisotropicity of their tangent operators.…”

Cyclic response of electrodeposited copper films. Experiments and elastic–viscoplastic mean-field modeling

“…By the definition of the tangent compliance tensor, the slip system backstress has been treated as an internal variable independent of the stress state, similarly to the recent development of the additive interaction law combined with the Mori-Tanaka scheme for two-phase composite materials presented in Mercier et al (2019).…”

“…Moreover it is clear that for cyclic loading, Bauschinger effect is present. Therefore a Mori-Tanaka scheme for two-phase materials with kinematic hardening was recently developed in Mercier et al (2019) and compared well with finite element predictions. It was shown that the additive tangent interaction law is capable to manage kinematic hardening with good efficiency.…”

Influence of Different Strain Hardening Models on the Behavior of Materials in the Elastic–Plastic Regime under Cyclic Loading

“…Three spatial limit hexagons of plasticity 1-2, 2-3 and 1-3 as the intersections of the limit prism of plasticity and three coordinate planes are also marked in Figure 3 . The axis of the respective area is identical to the so-called hydrostatic axis which passes through the origin of the coordinate system and is equidistant from all three major axes [ 24 , 25 , 26 , 27 , 28 , 29 ].…”