An elasto-plastic self-consistent model with hardening based on dislocation density, twinning and de-twinning: Application to strain path changes in HCP metals

Abstract

a b s t r a c tIn this work, we develop a polycrystal mean-field constitutive model based on an elastic-plastic selfconsistent (EPSC) framework. In this model, we incorporate recently developed subgrain models for dislocation density evolution with thermally activated slip, twin activation via statistical stress fluctuations, reoriented twin domains within the grain and associated stress relaxation, twin boundary hardening, and de-twinning. The model is applied to a systematic set of strain path change tests on pure beryllium (Be). Under the applied deformation conditions, Be deforms by multiple slip modes and deformation twinning and thereby provides a challenging test for model validation. With a single set of material parameters, determined using the flow-stress vs. strain responses during monotonic testing, the model predicts well the evolution of texture, lattice strains, and twinning. With further analysis, we demonstrate the significant influence of internal residual stresses on (1) the flow stress drop when reloading from one path to another, (2) deformation twin activation, (3) de-twinning during a reversal strain path change, and (4) the formation of additional twin variants during a cross-loading sequence. The model presented here can, in principle, be applied to other metals, deforming by multiple slip and twinning modes under a wide range of temperature, strain rate, and strain path conditions.

Comparison of 2 methodologies developed for the determination of residual stresses through X-ray diffraction: application to a textured hcp titanium alloy

“…We denote by A the rotation matrix between the two references frames (sample and diffraction), such that ‡′ > = ‰ z ‰ >{ ‡ z{ (18) where ‡ z{ and ‡′ > are the components of a given tensor, expressed in the reference frames linked to the sample and to diffraction respectively. This rotation matrix reads…”

“…Only the principal equations relating stress and strain tensors (or stress and strain rate tensors) will be recalled below, and the reader is referred to the work of Turner, Tome et al [4,6,17,18] for further details concerning this model. It is important to note that during plastic deformation, the model not only allows the quantifications of these tensors but also to calculate the grain shapes and texture evolutions due to slip on several systems within each grain.…”

Serrated Yielding: Crystal Viscoplastic Models

“…Во многих моделях использу-ется разделение дислокаций на различные типы (мобильные -иммобильные [34,41,42,43,44,68,76,98,99], статистически накопленные и геометрически необходимые [95]). …”

“…К данному направлению относится упругопластическая модель, изложенная в работе [99]. В модели различаются следующие типы дислокаций: дислокации леса, положитель-ные и отрицательные мобильные дислокации на СС.…”

Explicit incorporation of deformation twins into crystal plasticity finite element models

“…It is assumed that all slip and twin systems within the same deformation mode share the same values for critical resolved shear stress (CRSS). This hardening law has been successfully used to model deformation of several metals within mean-field self-consistent codes, differing in crystal structure, such as Haynes 25 [47], AA6022 [48], Nb [49,50], Ta [51,52], Mg [53][54][55], Zr [46,56,57], Be [10,58], and U [4,59,60]. Here, we integrate the same hardening law for U in CPFE and enable the existing CPFE to model the orthorhombic structure.…”