A higher order elasto-viscoplastic model using fast Fourier transforms: Effects of lattice curvatures on mechanical response of nanocrystalline metals

Abstract

In this work a couple stress continuum based elasto-viscoplastic fast Fourier transform model is developed with the intent to study the role of curvatures-gradient of rotation-on the local meso scale and effective macroscale mechanical response of nanocrystalline materials. Development of this model has led to the formulation of an extended periodic Lippmann Schwinger equation that accounts for couple stress equilibrium. In addition to the standard boundary conditions on strain rate and Cauchy stresses, the model allows imposing non-standard couple stress and curvature rate boundary conditions. Application to representative nanocrystalline microstructures reveals that elastic and plastic curvatures accommodate a part of the local and macroscopic Cauchy stresses. Next, grain boundary interfaces are characterized using curvatures that are representative of their structure and defect content. Depending on the magnitude and distribution of these curvatures, local stresses in the grain boundary neighborhood are generated that activate slip systems besides those fulfilling the Schmid criterion. Generation of both polar dislocations and disclinations as a possible plasticity mechanism

A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

“…For polycrystals, the different constitutive regimes solved with FFT-based methods include: linear elasticity (Lebensohn, 2001;Brenner et al, 2009); linear viscosity (Lebensohn et al, 2005); thermoelasticity (Vinogradov and Milton, 2008;Anglin et al, 2014;Donegan and Rollett, 2015); rigid-viscoplasticity (Lebensohn, 2001;Lebensohn et al, 2008Lebensohn et al, , 2009Lee et al, 2011;Rollett et al, 2010); smallstrain crystal plasticity elasto-viscoplasticity, i.e. CP-EVPFFT Grennerat et al, 2012;Suquet et al, 2012); large-strain elasto-viscoplasticity (Eisenlohr et al, 2013;Shanthraj et al, 2015;Kabel et al, 2016;Vidyasagar et al, 2018;Lucarini and Segurado, 2018); dilatational plasticity ; lower-order (Lucarini and Segurado, 2018) and higher-order strain-gradient plasticity (Lebensohn and Needleman, 2016); curvature-driven plasticity (Upadhyay et al, 2016); transformation plasticity (Richards et al, 2013;Otsuka et al, 2018); fatigue (Rovinelli et al, 2017a,b); and quasi-brittle damage (Li et al, 2012;Sharma et al, 2012). FFT-based methods were also applied to field dislocation mechanics (FDM) and field disclination mechanics (Brenner et al, 2014;Berbenni et al, 2014;Djaka et al, 2015;Berbenni et al, 2016;Djaka et al, 2017;Berbenni and Taupin, 2018), and discrete dislocation dynamics (DDD) problems (Bertin et al, 2015;Graham et al, 2016;…”

A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals

“…The different constitutive regimes solved with FFT-based methods include: linear elasticity (Lebensohn, 2001;Brenner et al, 2009); linear viscosity (Lebensohn et al, 2005); linear elasticity with eigenstrains or thermoelasticity (Vinogradov and Milton, 2008;Anglin et al, 2014;Donegan and Rollett, 2015;Eloh et al, 2019); rigid-viscoplasticity (Lebensohn, 2001;Lebensohn et al, 2008Lebensohn et al, , 2009Lee et al, 2011;Rollett et al, 2010); small-strain crystal plasticity elasto-viscoplasticity, i.e. CP-EVPFFT (Lebensohn et al, 2012;Grennerat et al, 2012;Suquet et al, 2012); large-strain elasto-viscoplasticity (Eisenlohr et al, 2013;Shanthraj et al, 2015;Kabel et al, 2016;Vidyasagar et al, 2018;Lucarini and Segurado, 2019); dilatational plasticity ; lower-order (Haouala et al, 2020) and higher-order (Lebensohn and Needleman, 2016) straingradient crystal plasticity; curvature-driven plasticity (Upadhyay et al, 2016); transformation plasticity (Richards et al, 2013;Otsuka et al, 2018); twinning (Mareau and Daymond, 2016;Paramatmuni and Kanjarla, 2019), fatigue (Rovinelli et al, 2017(Rovinelli et al, , 2018Lucarini and Segurado, 2019); and quasi-brittle damage (Li et al, 2012;Sharma et al, 2012). FFT-based methods were also applied to field dislocation mechanics (FDM) and field disclination mechanics (Brenner et al, 2014;Berbenni et al, 2014;…”

A continuum model for slip transfer at grain boundaries

“…Equations (48,49,50) are regularity conditions for the computation of the dislocation density tensor α through Eq. (25).…”

“…In doing so, nonlocal interactions between domains B − and B + across the interface are enhanced, because values of the plastic distortion at limit points on either sides of the interface have to be equal. Of course, the interface conditions (48,49,50) ) and a normal stretch jump p 33 in pressure-sensitive materials. However, compatibility conditions between these normal discontinuities arise when several interfaces with respective discontinuities of the plastic distortions U p i , i ∈ (1, 2 .…”