scholarly journals A stochastic solver based on the residence time algorithm for crystal plasticity models

2021 ◽  
Author(s):  
Qianran Yu ◽  
Enrique Martínez ◽  
Javier Segurado ◽  
Jaime Marian
Keyword(s):  
Residence Time ◽  
Crystal Plasticity ◽  
Evolution Equations ◽  
Time Algorithm ◽  
Dislocation Motion ◽  
Crystalline Materials ◽  
Stochastic Fluctuations ◽  
Dislocation Behavior ◽  
Plastic Localization ◽  
Large Material

AbstractThe deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

Elasto-Plastic Models with Continuously Distributed Dislocations and Disclinations

2012 ◽  
Vol 504-506 ◽  
pp. 125-130
Author(s):  
Sanda Cleja-Tigoiu
Keyword(s):  
Mathematical Model ◽  
Evolution Equations ◽  
Second Order ◽  
Lattice Defects ◽  
Screw Dislocations ◽  
Crystalline Materials ◽  
Distributed Dislocations

The paper deals with a mathematical model able to describe the presence of lattice defects of the crystalline materials, such as dislocation and disclination. Within the constitutive framework of second order plasticity developed by the author, the evolution equations to describe the disclinations that are compatible with the screw dislocations are derived.

Numerical Implementation of Continuum Dislocation Dynamics with the Discontinuous-Galerkin Method.

2014 ◽  
Vol 1651 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Mehran Monavari ◽  
Thomas Hochrainer
Keyword(s):  
Discontinuous Galerkin ◽  
Crystal Plasticity ◽  
Evolution Equations ◽  
Total Curvature ◽  
Time Integration ◽  
Three Dimensional ◽  
Conserved Quantity ◽  
Dislocation Dynamics ◽  
Slip Systems ◽  
Continuum Dislocation Dynamics

ABSTRACTIn the current paper we modify the evolution equations of the simplified continuum dislocation dynamics theory presented in [T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, Continuum dislocation dynamics: Towards a physical theory of crystal plasticity. J. Mech. Phys. Solids. (in print)] to account for the nature of the so-called curvature density as a conserved quantity. The derived evolution equations define a dislocation flux based crystal plasticity law, which we present in a fully three-dimensional form. Because the total curvature is a conserved quantity in the theory the time integration of the equations benefit from using conservative numerical schemes. We present a discontinuous Galerkin implementation for integrating the time evolution of the dislocation state and show that this allows simulating the evolution of a single dislocation loop as well as of a distributed loop density on different slip systems.

Diffusion Effects Induced by Dislocations in Crystalline Materials Subjected to Large Strains

2015 ◽  
Vol 651-653 ◽  
pp. 89-95
Author(s):  
Raisa Paşcan ◽  
Sanda Cleja-Ţigoiu
Keyword(s):  
Evolution Equations ◽  
Plane Stress State ◽  
Large Strains ◽  
Slip Systems ◽  
State Variables ◽  
Equilibrium Equations ◽  
Crystalline Materials ◽  
Dislocation Densities ◽  
Differential Type ◽  
Non Local

Abstract. We reconsider here the FEM-algorithm for solving the initial and boundary value problems performed within the viscoplastic constitutive framework and proposed in our paper [1]. The problems concerning the deformation of a sheet composed of a single fcc-crystal, generated by different slip systems simultaneously activated, are solved numerically for an in-plane stress state. The variational formulation is associated to the incremental equilibrium equations and is coupled with an update procedure for the state variables, which are described by the differential type equations, as well as for the non-local evolution equations of the dislocation densities. The length scale parameter is introduced into the model through the diffusion-like parameter which enters the evolution equations for dislocation densities. For more accuracy of the simulation, the shape functions have been chosen polynomials with higher than one degree. We do not consider that once a slip system was activated it remains active for the rest of simulation. The activation condition is a key point in the numerical algorithm. As a numerical example, we perform a tensile test of a rectangular and non-rectangular metallic sheet, comparring the results of the simulation when two, respectively eight slip systems are considered.

scholarly journals Zbigniew Stanislaw Basinski, O.C. 28 April 1928 – 12 August 1999

2001 ◽  
Vol 47 ◽  
pp. 1-17 ◽  
Author(s):  
Archie Howie
Keyword(s):  
Crystal Plasticity ◽  
Dislocation Motion ◽  
Experimental Investigations ◽  
Lifelong Partner

Zbigniew Basinski, widely known as Bas, was exposed early in life to turbulent events in Poland, Russia and Palestine. He studied chemistry at Oxford, then performed research in metal physics with Jack Christian (F.R.S. 1975). There he met Sylvia Pugh, his wife and lifelong partner, in an enduring and passionate study of crystal plasticity pursued largely in Canada. Over most of the period since the dislocation concept transformed the problem of explaining crystal weakness into one of explaining crystal strength, Basinski's experimental investigations of the obstacles to dislocation motion surpassed in quality and variety those of any other worker.

Numerical Study on Bicrystalline Micropillar Compression Using High-Order Gradient Crystal Plasticity

2019 ◽  
Vol 794 ◽  
pp. 65-70
Author(s):  
Yuichi Tadano
Keyword(s):  
Grain Boundary ◽  
Crystal Plasticity ◽  
Numerical Study ◽  
Boundary Effect ◽  
Large Angle ◽  
Dislocation Motion ◽  
Element Analysis ◽  
Metallic Material ◽  
Micropillar Compression ◽  
Grain Boundary Effect

Dislocation structures at crystalline scale play an important role in the scale effect of materials. The higher-order crystal plasticity, in which a dislocation information is introduced as the gradient of slip and affects the hardening behavior of slip, is a useful model to describe a scale dependency of metallic material. In this study, a large deformation finite element analysis of a bicrystalline micropillar is demonstrated to investigate the grain boundary effect on the dislocation motion. The effect of condition on the grain boundary is numerically discussed. It is suggested that the large angle grain boundary and the coherent twin boundary can be represented by boundary conditions of non-penetration and penetration of dislocation.

Simulation on Nanostructured Metals Based on Multiscale Crystal Plasticity Considering Effect of Grain Boundary

2012 ◽  
Vol 706-709 ◽  
pp. 1751-1756 ◽  
Author(s):  
Yoshiteru Aoyagi ◽  
Tomotsugu Shimokawa ◽  
Kazuyuki Shizawa ◽  
Yoshiyuki Kaji
Keyword(s):  
Grain Boundary ◽  
Crystal Plasticity ◽  
High Strength ◽  
Nanostructured Metals ◽  
Hardening Law ◽  
Crystal Plasticity Model ◽  
Ultrafine Grained ◽  
Dislocation Behavior ◽  
Strain Responses ◽  
Peculiar Behavior

Ultrafine-grained metals whose grain size is less than one micron have attracted interest as high strength materials. Whereas nanostructured metals produced by severe plastic deformation express remarkably peculiar behavior in both material and mechanical aspects, its mechanism has been clarified by neither experimental nor computational approaches. In this study, we develop a multiscale crystal plasticity model considering an effect of grain boundary. In order to express release of dislocation from grain boundaries, information of misorientation is introduced into a hardening law of crystal plasticity. In addition, carrying out FE simulation for FCC polycrystal, the stress-strain responses such as increase of yield stress due to existence of grain boundary are discussed. We investigate comprehensively the effect of dislocation behavior on the material property of nanostructured metal.

Residual Meso Stresses in Multilevel Crystal Plasticity Models

2014 ◽  
Vol 1040 ◽  
pp. 576-580 ◽  
Author(s):  
Pavel S. Volegov ◽  
Peter V. Trusov ◽  
Dmitry S. Gribov
Keyword(s):  
Plastic Deformation ◽  
Crystal Plasticity ◽  
Inelastic Deformation ◽  
Stress Relief ◽  
Crystal Lattices ◽  
Crystalline Materials ◽  
Level Model ◽  
Multi Level ◽  
Individual Grains ◽  
Two Level Model

The problems related to the construction of multi-level mathematical models of inelastic deformation of crystalline materials based on crystal plasticity are considered. The example of the two-level model for description the severe plastic deformation of fcc polycrystals is discussed. The issues relating to the description of hardening and rotations of crystal lattices of the grains are discussed. The focus is on the formation of residual mesostresses in individual grains in the case of polycrystalline stress relief with a representative volume in general.

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