Plastic deformation of models of a crystalline polymer in hydrostatic tension

The strength of a rhombic model of a defective polymer crystal in hydrostatic tension has been calculated for the set of configurations assumed by the model in the process of plastic deformation. The dislocation centers and twinning curves are calculated for models with one and two coordination polygons in hydrostatic tension. It is shown that in hydrostatic tension the twinning limit of the models is considerably reduced.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 20–25, January–February, 1976.     

A crystal plasticity framework based on the Continuum Dislocation Dynamics theory: relaxation of an idealized micropillar

The motion and interaction of dislocation lines are the physical basis of the plastic deformation of metals. Although ‘discrete dislocation dynamic’ (DDD) simulations are able to predict the kinematics of dislocation microstructure (i.e. the motion of dislocations in a given velocity field) and therefore the plastic behavior of crystals in small length scales, the computational cost makes DDD less feasible for systems larger than a few micro meters. To overcome this problem, the Continuum Dislocation Dynamics (CDD) theory was developed. CDD describes the kinematics of dislocation microstructure based on statistical averages of internal properties of dislocation systems. In this paper we present a crystal plasticity framework based on the CDD theory. It consists of two separate parts: a classical 3D elastic boundary value problem and the evolution of dislocation microstructure within slip planes according to the CDD constitutional equations. We demonstrate the evolution of dislocation density in a micropillar with a single slip plane. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dislocation mechanism of the initial stage of plastic deformation of polyethylene

A unified treatment of the initial stages of the plastic deformation of the polyethylene single crystal — phase transformation from the orthorhombic to the monoclinic lattice, twinning, and crack formation — is proposed. This treatment, which makes use of dislocation theory, is based on an analysis of experiments on the deformation of the polyethylene single crystal.     

Some general results in the theory of crystallographic slip

Crystallographic slip of a Bravais lattice is analyzed utilizing the main results of a recently constructed theory of structured solids, where explicit account is taken of the influence of dislocation density identified in terms of Curl of plastic deformationG _p . In the present paper, the scope of the subject is enlarged to also include defects (other than dislocations) such as substitutional impurities and vacancies and it is shown that these point defects may also be characterized in terms of the plastic deformation fieldG _p . Several general results pertaining to the kinematics and kinetics of Crystallographic slip are proved within the scope of an appropriate constraint theory suitable for Crystallographic slip; the latter is motivated by the well-known basic mechanism of Crystallographic slip that constrains the admissible modes of plastic deformation. The constraint responses (or forces) that are necessary to maintain the active slip systems, as well as the conditions for the transitions between the slip systems, are determined. In spite of the nature of the assumption pertaining to the mechanism of Crystallographic slip on distinct slip systems, it is shown that the yield surface does not necessarily exhibit sharp corners. Instead, the shape of the yield surface is in the form of hyperplanes joined by round corners. In fact, the presence of sharp corners is mainly a result of the use of a special set of constitutive assumptions. The predictive capability of the theoretical results is further illustrated by using a two-dimensional crystal subjected to simple shear. The effect of the initial dislocation density on the response of the sheared-crystal is studied by carrying out detailed calculations for two substantially different initial dislocation densities. The calculations show that while the response of the crystal is sensitive to the initial dislocation density in the early stages of deformation, its influence diminishes with progressively larger deformations. Furthermore, the crystal exhibits a well-defined shear band which evolves naturally due to the presence of initial dislocation distribution and is easily visible at large deformations.     

Variational Phase Field Modeling of Laminate Deformation Microstructure in Finite Gradient Crystal Plasticity

The macroscopic mechanical behavior of many materials crucially depends on the formation and evolution of their microstructure. In this work, we consider the formation and evolution of laminate deformation microstructure in plasticity. Inspired by work on the variational modeling of phase transformation [5] and building on related work on multislip gradient crystal plasticity [9], we present a new finite strain model for the formation and evolution of laminate deformation microstructure in double slip gradient crystal plasticity. Basic ingredients of our model are a nonconvex hardening potential and two gradient terms accounting for geometrically necessary dislocations (GNDs) by use of the dislocation density tensor and regularizing the sharp interfaces between different kinematically coherent plastic slip states. The plastic evolution is described by means of a nonsmooth dissipation potential for which we propose a new regularization. We formulate a continuous gradient-extended rate-variational framework and discretize it in time to obtain an incremental-variational formulation. Discretization in space yields a finite element formulation which is used to demonstrate the capability of our model to predict the formation and evolution of laminate deformation microstructure in f.c.c. Copper with two active slip systems in the same slip plane. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of stage I-crack growth using a 3D-model

A three-dimensional model for stage I-short crack propagation on a single slip plane is presented. It considers elastic plastic material behaviour by allowing sliding on the active slip plane in a defined slip direction. A crack propagation law based on the crack tip slide displacement is implemented to simulate crack propagation. The model is solved numerically using the dislocation loop technique. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane constrained uniaxial extension of a single crystal strip

Within continuum dislocation theory the plane constrained uniaxial extension of a single crystal strip deforming in single or double slip is analyzed. For the single and symmetric double slip, the closed-form analytical solutions are found which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effect. Numerical solutions for the non-symmetric double slip are obtained by finite element procedures. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of nonlinear continuum dislocation theory to antiplane shear

We apply the nonlinear dislocation theory to the problem of antiplane constrained shear in a single crystal with one slip system. By taking dissipation into account, the relaxed energy functional has to be minimized. We show that, up to a threshold strain, no dislocations are nucleated and therefore the plastic slip is zero. Since this threshold value depends on the width of the specimen, a size effect takes place. The stress strain curve turns out to be a hysteresis loop exhibiting the work hardening due to the dislocation pile-up. It is shown that the Bauschinger effect holds true. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Plane constrained shear of single crystal strip with one and two active slip systems

The plane constrained shear problems of a single crystal strip with one and two active slip systems are considered within the continuum dislocation theory. Analytical solutions are found for single slip and symmetric double slip systems which exhibit the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening and the size effect. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On one mathematical model of creep in superalloys

In [Sv1] a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE's generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied.     

A meso elastoplastic constitutive model for polycrystalline metals based on equivalent slip systems with latent hardening

A meso material model for polycrystalline metals is proposed, in which the tiny slip systems distributing randomly between crystal slices in micro-grains or on grain boundaries are replaced by macro equivalent slip systems determined by the work-conjugate principle. The elastoplastic constitutive equation of this model is formulated for the active hardening, latent hardening and Bauschinger effect to predict macro elastoplastic stress-strain responses of polycrystalline metals under complex loading conditions. The influence of the material property parameters on size and shape of the subsequent yield surfaces is numerically investigated to demonstrate the fundamental features of the proposed material model. The derived constitutive equation is proved accurate and efficient in numerical analysis. Compared with the self-consistent theories with crystal grains as their basic components, the present theory is much simpler in mathematical treatment. Project supported by the National Natural Science Foundation of China (Grant No. 19732006).     

Comparison of different distortional hardening models suitable for the analysis of magnesium

HCP metals such as magnesium are characterized by a strong interplay between dislocation slip and deformation-induced twinning. These micromechanical processes result in a complex macroscopic behavior. More precisely, in addition to classical isotropic and kinematic hardening, the shape of the macroscopic yield function changes during deformation as well. This effect which is frequently referred to as distortional hardening is particularly pronounced in case of non-radial loading paths typical for most forming processes. Consequently, a physically sound distortional hardening is of utmost importance for several technically relevant applications. In the present contribution, three different of such enhanced hardening models are critically analyzed. Focus is on the modeling of magnesium. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlocal damage-viscoplastic model for high temperature creep of single crystal superalloys

A new nonlocal damage-viscoplastic model for high temperature creep of single crystal superalloys is developed. It is based on the variational formulation consisting of free energy, plastic and damage dissipation potentials. Evolution equations for plastic strain and damage variables are derived from the minimum principle for dissipation potentials [1]. The model is capable of describing different stages of creep in a unified way. The evolution of dislocation densities of gamma and gamma prime phases in superalloys incorporates plastic deformation. It results in the time-dependence of the creep rate in primary and secondary creep. Tertiary creep is taken into account by introducing local and nonlocal damage variables. Herein the nonlocal one is considered as numerical treatment to remove mesh-dependence. Numerical results and comparisons with experimental data of the single crystal superalloy LEK94 are shown. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On physics-based crystal plasticity models: Application to virtual material testing of sheet metals

It is possible to pursue a multi-scale modeling approach for sheet forming simulations by applying the concept of virtual material testing to determine the yield surface from the microstructure of a given material. Full-field simulations with phenomenological crystal plasticity models are widely used for this kind of investigations. However, recent developments focus on incorporating physical quantities like dislocation density into these models. In this work, a dislocation density based crystal plasticity model is used to investigate the plastic anisotropy of the deep drawing steel DC04. In particular, we focus on the prediction of R-values, which can be used to calibrate macroscopic plasticity models. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Are plastic yielding and work hardening sensitive to the boundary conditions?

The plane strain shear of a single crystal strip with one active slip system placed in a mixed device with one clamped and one free boundary is considered. Since dislocations pile up against only the clamped boundary, the plastic yielding and work hardening differ essentially from those of a hard device, showing clearly their sensitivity to the boundary conditions. An analytical solution to this problem within continuum dislocation theory is found explicitly which exhibits the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effects. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling thermoplastic material behaviour of dual-phase steels on a microscopic length scale

On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work a material model for the temperature dependent hardening behaviour of the ferritic phase is presented. As the dislocation structure determines the resistance to dislocation glide, dislocation densities are introduced as state variables to capture the dependence of the material behaviour on the loading history. Motivated by the elementary processes of multiplication by the Frank-Read-mechanism and annihilation by cross-slip, evolution equations for the dislocation densities are introduced. Based on the interaction of dislocations on different slip systems and the Peierls-stress, the resistance to dislocation motion with its temperature dependence is formulated to describe the hardening behaviour. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of micro-cutting considering finite deformation crystal plasticity

Micro-machining processes on metalic microstructures are influenced by the crystal structure, i. e. the grain orientation. Furthermore, the chip formation underlies large deformations. To perform finite element simulations of micro-cutting processes, a large deformation material model is necessary in order to model the hyperelastic and finite plastic material behaviour. In the case of cp-titanium material with hcp-crystal structure the anisotropic behaviour must be considered by an appropriate set of slip planes and slip directions. In the present work the impact of the grain orientation on the plastic deformation is demonstrated by means of finite element simulations of a finite deformation single slip crystal plasticity model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rate-independent plasticity and statistically stored dislocations

We present here a continuum model for the evolution of the total dislocation density in the framework of rate-independent plasticity. Three basic physical features are taken into account: (i) the role of dislocation densities on hardening; (ii) the relations between the slip velocity and the mobility of gliding dislocations; (iii) the energetics of self and mutual interactions between dislocations. We restrict attention to plastic processes corresponding to single slip. Numerical simulations showing the formation of bands are also presented.