Induced Plastic Anisotropy Research Articles

An advanced elastoplastic framework accounting for induced plastic anisotropy fully coupled with ductile damage

We present in this investigation an advanced phenomenological approach combining the computational efficiency of classical phenomenological plasticity models and the accuracy and high resolution of multiscale crystal plasticity schemes. Within this advanced approach, a new phenomenological constitutive framework has been developed and implemented into ABAQUS/Standard finite element (FE) code. Compared to classical approaches, this framework allows accounting for initial and induced plastic anisotropy, isotropic nonlinear hardening and the full coupling with isotropic ductile damage. Material parameters corresponding to this phenomenological constitutive framework are identified based on multiscale polycrystalline simulations, where the self-consistent scheme is used to ensure the transition between the single crystal and polycrystal scales. The single crystal mechanical behavior is assumed to be elastoplastic (rate-independent), and microscopic material degradation is well-considered by introducing a scalar damage variable at each crystallographic slip system for each individual grain. The evolution of polycrystalline yield surfaces, induced by the evolution of crystallographic texture, is accurately reproduced by the new constitutive modeling, where the anisotropy parameters are assumed to evolve during plastic deformation. Their evolution laws are identified based on multiscale simulations. The different identification procedures are presented and extensively discussed. The robustness and reliability of this advanced model are analyzed through some relevant numerical predictions obtained by applying a combined tensile/shear test.

On a general numerical scheme for the fractional plastic flow rule

This paper presents a general numerical scheme for the fractional plastic flow rule, dedicated to a wide class of materials manifesting the non-normality of plastic flow and induced plastic anisotropy. To determine the vector of the plastic flow, a special numerical procedure has been developed, which is applicable for any smooth and convex yield function. The obtained approximation is verified based on an analytical solution. The paper also presents a set of numerical results for the generalised Drucker–Prager model.

Modeling of the induced plastic anisotropy fully coupled with ductile damage under finite strains

The introduction of the kinematic hardening induced distortion of the yield surface is expected to enhance the capability of the model in simulating the material behavior under complex loading paths occurring during sheet metal forming processes.In this work non-associative elastoplastic anisotropic constitutive equations accounting for mixed nonlinear hardening and fully coupled with isotropic ductile damage, is improved by considering the distortion of the yield subsequent surfaces. A convenient “distortion” deviatoric stress tensor S̲d is used in both yield criterion and plastic potential instead of the usual classical deviatoric stress tensor S̲. Accordingly, the yield surface distortion is controlled by three adequate material parameters named Xl1c, Xl1p and Xl2c. A parametric study is conducted under simple loading paths (tension and torsion) in order to explore the capabilities of the model in describing the yield surface distorsion. Comparisons with experimental results on aluminum alloy, taken from the literature, are also given. Moreover, the influence of the subsequent yield surfaces distortion under complex non-proportional loading paths on the evolution of the plastic flow with hardening and the ductile damage are also discussed and highlighted.

Non‐normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study

SummaryIn this paper, an implementation of fractional plastic flow rule in the framework of implicit and explicit procedures is under consideration. The fractional plastic flow rule is obtained from a generalisation of the classical plastic flow rule utilising fractional calculus. The key feature of this new concept is that in general, the non‐associative flow is obtained without necessity of additional potential assumption. If needed, the model can cover the anisotropy induced by plastic deformation. Illustrative examples showing the unusual flexibility of this model are also presented. Copyright © 2015 John Wiley & Sons, Ltd.

Inherent and induced anisotropic finite visco-plasticity with applications to the forming of DC06 sheets

In the current work we present a finite visco-plasticity model accounting for inherent and induced plastic anisotropy as well as Bauschinger effect for the interstitial free (IF) steels and its application to a forming process simulation of DC06 sheets. The inherent plastic anisotropy uses a Hill-48 type structural tensor whereas the induced anisotropy is modeled via its evolution accounting for dynamic (active) and latent (inactive) parts. The latter appears to be an eminent requirement for predicting the qualitative effect of the evolving dislocation microstructures under orthogonal loading path changes, i.e., the cross hardening. A nonlinear isotropic and Armstrong–Frederick type kinematic hardening is also involved. Finally, the rate dependence of the plastic response is incorporated using Johnson–Cook type formulation. The model is implemented as VUMAT user defined material subroutine for ABAQUS and used in a set of sensitivity analyses to present mentioned model features. The model parameters are identified based on a set of experiments involving monotonic shear, uniaxial tension, forward to reverse shear and plane strain tension followed by shear tests. Finally, the channel forming process of a DC06 sheet is simulated. A good agreement with the experimental findings is observed, in both the tool response history curves and the extent of spring-back which is conclusive on the final product geometry.

New interpretation of cyclic Swift effects

Abstract The generally accepted view is that induced plastic anisotropy is the main reason for accumulation of axial strains during monotonic and cyclic free-end torsion. In this paper, analytical results and numerical simulations using an elastic/plastic model with yielding described by the isotropic form of Cazacu et al. (2006) criterion and isotropic hardening point to another important cause of this phenomenon. It is shown that such phenomenon can occur in an isotropic material, a slight difference between the uniaxial yield stresses in tension and compression of the material leading to a build-up of inelastic axial strains during cyclic torsion at constant strain amplitude. It is demonstrated that the ratio between the uniaxial yield stresses in tension and compression dictates whether permanent shortening or lengthening of the specimen occurs. Furthermore, it is predicted that by axially preloading the material below its plastic threshold and then subject it to strain controlled cyclic torsion under constant axial load, the axial effects may be either reinforced or reduced. Thus, for any given isotropic material it is possible to estimate the value of the constant load and the strain amplitude that need to be prescribed in order to eliminate these effects.

On the simulation of multi‐stage forming processes: invariance under change of the reference configuration

AbstractThe need to change the reference configuration can naturally appear during the numerical simulation of multi‐stage metal forming processes. In the current work, a refined approach to the consideration of previously induced plastic anisotropy is discussed, which is based on such configuration change. The model of finite strain viscoplasticity proposed by Shutov and Kreißig is considered in this study as a practical tool, suitable to capture the evolution of mechanical properties of material during inelastic deformation. The initial plastic anisotropy can be considered within this model by a special choice of initial conditions imposed on the relevant internal variables. A simple transformation law which is based on the isochoric change of the reference configuration is obtained in the current study. This transformation allows to obtain relevant initial conditions with respect to a new reference configuration. Thus, the initial conditions are formulated using the simulation results from the foregoing loading. The advocated approach is exemplified by the numerical simulation of equal channel angular pressing of cylindrical billets. The plastic anisotropy accumulated during a single ECAP pass is estimated using a series of virtual tension tests. These tests were performed on samples cut from processed billet with their gage lengths in different directions. Finally, the impact of the plastic anisotropy on the rotation of the workpiece within the output channel during ECAP is numerically estimated.

Multiscale modelling of the induced plastic anisotropy in bcc metals

This paper presents a new framework to predict the qualitative and quantitative variation in local plastic anisotropy due to crystallographic texture in body-centered cubic polycrystals. A multiscale model was developed to examine the contribution of mesoscopic and local microscopic behaviour to the macroscopic constitutive response of bcc metals during deformation. The model integrated a dislocation-based hardening scheme and a Taylor-based crystal plasticity formulation into the subroutine of an explicit dynamic FEM code (LS-DYNA). Numerical analyses using this model were able to predict not only correct grain rotation during deformation, but variations in plastic anisotropy due to initial crystallographic orientation. Optimal results were obtained when {1 1 0}〈1 1 1〉, {1 1 2}〈1 1 1〉, and {1 2 3}〈1 1 1〉 slip systems were considered to be potentially active. The predicted material heterogeneity can be utilised for research involving any texture-dependent work hardening behaviour, such as surface roughening.

A composite dislocation cell model to describe strain path change effects in BCC metals

Sheet metal forming processes are within the core of many modern manufacturing technologies, as applied in, e.g., automotive and packaging industries. Initially flat sheet material is forced to transform plastically into a three-dimensional shape through complex loading modes. Deviation from a proportional strain path is associated with hardening or softening of the material due to the induced plastic anisotropy resulting from the prior deformation. The main cause of these transient anisotropic effects at moderate strains is attributed to the evolving underlying dislocation microstructures. In this paper, a composite dislocation cell model, which explicitly describes the dislocation structure evolution, is combined with a BCC crystal plasticity framework to bridge the microstructure evolution and its macroscopic anisotropic effects. Monotonic and multi-stage loading simulations are conducted for a single crystal and polycrystal BCC metal, and the obtained macroscopic results and dislocation substructure evolution are compared qualitatively with the published experimental observations.

Evolution of Plastic Anisotropy during Deformation of Metal Sheets

Evolution of Plastic Anisotropy during Deformation of Metal Sheets

Inelastic behaviour of polycrystalline metals under complex loading condition

In this paper, a simple mechanical model of polycrystal is suggested on the basis of the crystal plasticity. This model incorporates interactions among grains in polycrystal and interactions among slip systems in a crystal grain component. Especially, an equation for a slip strain of slip system is based on a theory of thermo-activation motion of dislocation. In this way, the model can take into account rate (creep) properties and temperature effects as well as an induced plastic anisotropy depending on deformation path, under multi-axial condition. Some computations are done by using the model for typical sets of strain paths and compared with corresponding experimental results of aluminum alloy at 200°C. The computational results reproduce accurately typical features observed in the experiments.

On Mechanism of Induced Plastic Anisotropy of Polycrystalline Metals

The experimental results concerning the plastic behaviour of metals along the strain path with a corner have demonstrated some common and fundamental features of the induced plastic anisotropy of polycrystalline metals, for example, the fading memory, the saturation property of prestrain effect and the delay effect. It is shown that the mechanism of the induced plastic anisotropy is closely related with the internal stress due to the interaction among grains of deformed polycrystalline metals and the common features are related closely with the internal stress. Computations using a simple mathematical model of polycrystal proposed in relation to the idea of internal stress show a very good qualitative agreement with the experimental results obtained from some typical strain paths by using a thin-walled tubular specimen of brass.

Mechanism of induced plastic anisotropy on polycrystalline metals

Induced plastic anisotropy is demonstrated by precise tension-torsion experiments on thin-walled polycrystalline tubes. After a sudden change of the deformation mode (e.g. tension to torsion) the stress direction delays with respect to the direction of the strain increment. This delay effect is interpreted in terms of the theory of plasticity of a polycrystal. A good qualitative agreement between experimental results and theoretical predictions is achieved. There are indications that the main mechanism responsible for induced plastic anisotropy is the internal stress arising among plastically deformed grains in the polycrystalline aggregate. Induzierte plastische Anisotropie wird durch genaue Zug-Drehungs-Experimente an dunnwandigen polykristallinen Rohren demonstriert. Nach plotzlicher Anderung des Deformationsmodus (z. B. Zug in Drehung) verzogert sich die Spannungsrichtung in Richtung des Verformungsinkrementes. Dieser verzogerte Effekt wird durch die Plastizitatstheorie des Polykristalles interpretiert. Eine gute qualitative Ubereinstimmung zwischen experimentellen Ergebnissen und den theoretischen Voraussetzungen wird erreicht. Es gibt Anzeichen, das der fur die induzierte plastische Anisotropie verantwortliche Hauptmechanismus die innere Spannung ist, die von den plastisch deformierten Kornern in den pol ykristallinen Aggregaten herruhrt.

A hardness law for inelastic deformation

Certain formulations of elastic-viscoplastic constitutive equations lead to inelastic deformations being governed by a functional relation between the plastic deformation rate and the stress. A parameter that appears in certain forms of this equation can be interpreted as an internal variable measure of the overall resistance of the material to plastic flow. In this paper, it is taken to be a second order tensor and designated the “hardness stress.” A procedure for calculating changes in the hardness stress parameter for general multiaxial loading histories is proposed in this paper. These evolutionary equations lead to induced plastic anisotropy. Stress-strain relations that would be predicted by this procedure appear to be consistent with experimental results for various multiaxial loading histories including proportional and non-proportional cyclic loading.