Finite Strain Viscoplasticity Research Articles

Macro-scale modeling of finite strain viscoplasticity in irradiated F/M steels: a continuum thermodynamic framework

The European reduced activation ferritic/martensitic steel Eurofer97 in irradiated states displays significant nonlinear material behavior involving irradiation hardening, loss of strain hardening, and uniform elongation, as well as irradiation-induced embrittlement. Nonlinear behavior of irradiated steel modeled on the continuum scale will help to estimate the maximum operating range of the irradiated components beyond the onset of localized plastic flow. In this work, a thermodynamic framework for modeling irradiation-influenced deformation is established based on irradiation defect density and a thermodynamically consistent finite strain formulation of an existing viscoplastic model using the Dual Variables concept is presented. The model is implemented in ABAQUS allowing the simulation of tensile tests conducted on irradiated and unirradiated materials which shows the model’s ability to capture the post-yield and post-necking behavior observed in experiments up to ductile failure.

Topology optimization for designing periodic microstructures based on finite strain viscoplasticity

This paper presents a topology optimization framework for designing periodic viscoplastic microstructures under finite deformation. To demonstrate the framework, microstructures with tailored macroscopic mechanical properties, e.g., maximum viscoplastic energy absorption and prescribed zero contraction, are designed. The simulated macroscopic properties are obtained via homogenization wherein the unit cell constitutive model is based on finite strain isotropic hardening viscoplasticity. To solve the coupled equilibrium and constitutive equations, a nested Newton method is used together with an adaptive time-stepping scheme. A well-posed topology optimization problem is formulated by restriction using filtration which is implemented via a periodic version of the Helmholtz partial differential equation filter. The optimization problem is iteratively solved with the method of moving asymptotes, where the path-dependent sensitivities are derived using the adjoint method. The applicability of the framework is demonstrated by optimizing several two-dimensional continuum composites exposed to a wide range of macroscopic strains.

Finite Element Simulation of the Presta Joining Process for Assembled Camshafts: Application to Aluminum Shafts

This work shows a sequence of numerical models for the simulation of the Presta joining process: a well-established industrial process for manufacturing assembled camshafts. The operation is divided into two sub-steps: the rolling of the shaft to widen the cam seat and the joining of the cam onto the shaft. When manufactured, the connection is tested randomly by loading it with a static torque. Subsequently, there are three numerical models using the finite element method. Additionally, a material model of finite strain viscoplasticity with nonlinear kinematic hardening is used throughout the whole simulation process, which allows a realistic representation of the material behavior even for large deformations. In addition, it enables a transfer of the deformation history and of the internal stresses between different submodels. This work also shows the required parameter identification and the associated material tests. After comparing the numerical results with experimental studies of the manufacturing process for steel-steel connections, the models are used to extend the joining process to the utilization of aluminum shafts.

Simulation of the Presta process – Transfer of deformation history

AbstractThe Presta joining process is the world's leading manufacturing method for assembled camshafts. It is a multi‐stage forming process separated in different steps. First, the rolling of the shaft creates a local widening of the intended cam seat. Within the subsequent joining process, the cam is forced onto the widened cam seat to form a tight fit. The two substeps are modelled and simulated using FEM. Within the process large local deformations occur, which requires an appropriate material model. The phenomenological material formulation of finite strain viscoplasticity implemented in the introduced simulation model enables the transfer of the deformation history to a new reference configuration. Hence, at the change of simulation models this feature is applied by passing the material model's internal state variables of the rolling step to the initial FE‐mesh of the joining step. This work shows the simulation models of the Presta joining process and gives a detailed insight into the change of the reference configuration. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On operator split technique for the time integration within finite strain viscoplasticity in explicit FEM

AbstractIn this contribution, the operator split technique is applied to the time integration within viscoplasticity for explicit FEM. As an example, the finite strain viscoplastic material model of Shutov and Kreißig is analyzed. In the new solution scheme, some evolution equations are solved using an explicit update formula for implicit time stepping. The solution procedure is split into three steps: an elastic predictor and two viscoplastic corrector steps. Aspects of accuracy and stability of the algorithm are discussed. As shown, the proposed method is superior compared to a fully explicit integration of evolution equations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Distribution of dislocation density and residual stresses in plastically deformed specimens: numerical studies

AbstractA two‐scale approach to the simulation of mechanical properties of metallic materials is considered. On the macroscopic level, the material behavior is described by a phenomenological model of finite strain viscoplasticity with nonlinear kinematic hardening. In particular, the process‐induced plastic anisotropy is captured by backstresses. On the microstructural level, the so called “load path sensitive two‐population dislocation cell model” is implemented. It describes an evolving dislocation cell structure with dislocation populations for dislocation cell walls and the cell interior. Owing to the coupling with the phenomenological plasticity model, it can describe the evolution of the dislocation densities depending on the load path. The applicability of the multiscale approach to the FEM simulation of severe plastic deformation processes such as Equal Channel Angular Pressing is demonstrated. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Automatic differentiation for stress and consistent tangent computation

In the field of nonlinear finite element analysis, the linearization within the Newton–Raphson and the Multilevel-Newton–Raphson algorithm requires the computation of the stresses and the so-called consistent tangent operator. There are several possibilities for coding the derivatives either by deriving analytical expressions, by using numerical differentiation schemes, or by applying the concept of automatic differentiation. In this article, the three possibilities are compared for three different kinds of constitutive models in order to ascertain particular differences. These models are a finite strain hyperelasticity relation, a more sophisticated finite strain viscoplasticity model, and a small strain von Mises-type thermo-viscoplasticity model. Especially for the last example, it is required to provide a number of tangents to be derived within a monolithic, fully coupled finite element computation. Numerical examples investigate the advantages and disadvantages of analytical, numerical, and automatic differentiation. It is shown that the latter one is a very helpful tool in the developing stage of constitutive modeling.

Accelerating constitutive modeling by automatic tangent generation

AbstractWithin the framework of finite elements the linearization within a Newton‐like method requires the computation of the so‐called consistent tangent operator. There are several possibilities to get these derivatives. Three methods, namely analytical, numerical and automatic differentiation, for tangent generation will be analyzed concerning the simulation time and applicability for three different constitutive models. These models are a finite strain hyperelasticity model, finite strain viscoplasticity model for metal powders and a small strain thermoviscoplasticity model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Simulation of distortional hardening by generalizing a uniaxial model of finite strain viscoplasticity

In this paper we generalize a uniaxial model of finite strain viscoplasticity (proposed by Shutov and Kreißig) using the so-called concept of representative directions. As a result, a new three-dimensional phenomenological material model is obtained. The original model takes the nonlinear isotropic and kinematic hardening into account, but it does not cover the distortional hardening. Using a series of numerical computations we show that the isotropic and kinematic hardening is completely retained during the process of generalization. Moreover, the distortional hardening effects are automatically induced by the concept itself. This is demonstrated by simulating combined tension–torsion tests on thin-walled tubular specimens. Furthermore, the generalized material model is validated by a comparison with real experimental data concerning the shape of the yield surface. A good correspondence between the simulation results and the measurements is observed.

On the simulation of nonlinear hardening in metallic materials using the concept of representative directions

AbstractWe generalize a uniaxial model of finite strain viscoplasticity using the concept of representative directions. As a result, a new phenomenological material model is obtained, which can describe the mechanical behavior under arbitrary loading conditions. The original uniaxial model takes the nonlinear isotropic and kinematic hardening into account, but it does not cover the distortional hardening. We show that the isotropic and kinematic hardening is completely retained during the process of generalization. Moreover, the distortional hardening effects are naturally induced by the concept. The resulting material model is validated by a comparison with real experimental data. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A phenomenological model of finite strain viscoplasticity with distortional hardening

AbstractIn this paper we suggest a thermodynamically consistent approach to the simulation of a rate dependent material response at finite strains. The nonlinear mechanical phenomena which are covered by the proposed material model include distortional, kinematic, and isotropic hardening. Firstly, we present a new two‐dimensional rheological model of distortional hardening, which predicts the yield curve in the stress space to be a limaçon of Pascal. Such effects like the distortion of the yield surface in the stress space and its orientation depending on the loading path are captured by the rheological model in a vivid way. Next, the rheological model serves as a guideline for the construction of the constitutive equations. In particular, the kinematic assumptions, the ansatz for the free energy, and the form of the yield function are motivated by the rheological model. Further, two types of flow rules are considered in this study: a normality rule and a radial rule, both thermodynamically consistent. Moreover, we formulate explicitly the constraints on the material parameters, which guarantee the convexity of the yield surface. Furthermore, implicit time‐stepping methods are considered which exactly preserve the incompressibility of the inelastic flow. Finally, the basic features of the predicted material response are illustrated by a series of numerical simulations. In particular, the simulation results are compared to the real experimental data.

A cell model study of crazing and matrix plasticity in rubber-toughened glassy polymers

The competition between crazing and matrix shear yielding in rubber-toughened glassy polymers is investigated by detailed finite element simulations. To this end the microstructure is represented by an axisymmetric unit cell of glassy matrix containing a single cavitated rubber particle which is modeled as a void. The behavior of the matrix material is described in the framework of finite strain viscoplasticity while a cohesive surface model is employed for crazing. The influence of the matrix yield behavior, the craze response, the rubber content, and the overall loading state are analyzed.

Stress and strain‐driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements

AbstractThis work deals with the formulation and implementation of finite deformation viscoplasticity within the framework of stress‐based hybrid finite element methods. Hybrid elements, which are based on a two‐field variational formulation, are much less susceptible to locking than conventional displacement‐based elements. The conventional return‐mapping scheme cannot be used in the context of hybrid stress methods since the stress is known, and the strain and the internal plastic variables have to be recovered using this known stress field. We discuss the formulation and implementation of the consistent tangent tensor, and the return‐mapping algorithm within the context of the hybrid method. We demonstrate the efficacy of the algorithm on a wide range of problems. Copyright © 2009 John Wiley & Sons, Ltd.

Editorial

This special issue of the Journal of Engineering Materials and Technology (JEMT) contains selected papers from the first symposium organized on shear; SHEAR07 in Nancy, France, 4–7 September, 2007. All papers have successfully gone through the regular peer-review process of JEMT.Shear deformation is one of the basic deformation modes in testing and metal forming. It usually permits to reach much larger strains than in other deformation modes. The main objective of this issue is to provide an insight into the large variety of topics that are related to shear and to publish new advances in testing, material behavior and modelling.Although the selected papers cannot cover all topics related to shear, the present collection represents a good discussion about effects related to large strain shear (torsion), hardening behavior, adiabatic shear bands at high strain rates, specific rules for dynamic recrystallization in shear, advanced crystal plasticity analyses, texture development and testing of polymers. One can present the essential of the contributions as follows:After an analysis of the shear process and grain refinement in Equal Channel Angular Extrusion, the paper entitled “Plastic Behavior of Metals at Large Strains: Experimental Studies Involving Simple Shear” presents a new model on Stage IV strain hardening.There are two papers on high strain torsion of an intermetallic alloy, the NiAl: “Texture Formation and Swift Effect in High Strain Torsion of NiAl” and “Microstructure Development During High Strain Torsion of NiAl.” They present original experimental data on texture and microstructure at large strains and varying temperatures together with good simulation results concerning the Swift effect. The latter is always important in free-end torsion and is shown to be related to the evolution of the crystallographic texture.The contribution entitled “Analysis of Large Strain Hot Torsion Textures Associated With ‘Continuous’ Dynamic Recrystallization” presents new principles and successful modelling for the dynamic recrystallization process that changes the texture at higher temperatures during shear.The torsion of non-axisymmetric initial textures is analyzed in the paper “Texture and Mechanical Behavior of Magnesium During Free-End Torsion” including polycrystal plasticity modelling of the texture development and new ideas about dynamic recrystallization in hexagonal materials.There are two theoretical papers that give insight into the shear process in metal forming and the selection of slip systems: “Identification of Simple Shear in Plane Strain Deformation” and “Shear on the Flow Surface of Metallic Crystals.”A complex shock-related problem is addressed in the paper “Numerical Study of Impact Penetration Shearing Employing Finite Strain Viscoplasticity Model Incorporating Adiabatic Shear Banding” for the case of dynamic plasticity of high-strength metallic materials.The hardening characteristics of polymers strongly depends on the crystalline phase which deforms mainly by simple shear as shown in the paper “Determination of Critical Strains in Isotactic Polypropylene by Cyclic Loading-Unloading.”Finally, I thank gratefully all the authors for their excellent contributions to this special issue and the Editors of JEMT, Professors Hussein Zbib and Huseyin Sehitoglu for giving the opportunity to publish the most relevant contributions of the SHEAR07 symposium. Special thanks to Professor Christian GSell, the Chairman of SHEAR07 for bringing the scientific community together on shear processes and related phenomena.

Numerical Study of Impact Penetration Shearing Employing Finite Strain Viscoplasticity Model Incorporating Adiabatic Shear Banding

This work brings forward a twofold contribution relevant to the adiabatic shear banding (ASB) process as a part of dynamic plasticity of high-strength metallic materials. The first contribution is a reassessment of a three-dimensional finite deformation model starting from a specific scale postulate and devoted to cover a wide range of dissipative phenomena, including ASB-related material instabilities (strong softening prefailure stage). The model, particularly destined to deal with impacted structures was first detailed by (Longère et al. 2003, “Modelling Adiabatic Shear Banding Via Damage Mechanics Approach,” Arch. Mech., 55, pp. 3–38; 2005, “Adiabatic Shear Banding Induced Degradation in a Thermo-Elastic/Viscoplastic Material Under Dynamic Loading,” Int. J. Impact Eng., 32, pp. 285–320). The second novel contribution concerns numerical solution of a genuine ballistic penetration problem employing the above model for a target plate material. The ASB trajectories are shown to follow a multistage history and complex distribution pattern leading finally to plugging failure mechanism. The corresponding analysis and related parametric study are intended to put to the test the pertinency of the model as an advanced predictive tool for complex shock related problems.

Numerical treatment of a finite strain viscoplasticity model based on a double multiplicative split

AbstractA viscoplastic material model of overstress type is analyzed. The model is based on the kinematic assumption of a double multiplicative split in order to simulate a nonlinear kinematic hardening. We investigate theoretically and numerically two implicit time–stepping methods, which were used lately in engineering literature to integrate the evolution equations in the context of multiplicative plasticity/viscoplasticity. A common feature of both methods is that the plastic incompressibility constraint is exactly satisfied. Moreover, we show that both methods preserve the symmetry of internal variables, which is inherent to the problem. According to testing results, both methods are equivalent regarding robustness, accuracy, and computational efficiency. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On plastic incompressibility within time-adaptive finite elements combined with projection techniques

This article treats the interpretation of quasi-static finite elements applied to constitutive equations of evolutionary-type as a solution scheme to solve globally differential-algebraic equations. This concept is applied to finite strain viscoplasticity based on a model with non-linear kinematic hardening under the assumption of plastic incompressibility. The model is based on multiple multiplicative decomposition both for the deformation gradient into an elastic and an inelastic part as well as for the inelastic part into a kinematic hardening (energy storage) and a dissipative part. Both intermediate configurations are described by inelastic right Cauchy–Green tensors satisfying inelastic incompressibility in the theoretical context. The attention in view of the numerical treatment within finite elements is focused on diagonally implicit Runge–Kutta methods which destroy the assumption of plastic incompressibility during the time-integration due to an additive structure of the integration step. In combination with a Multilevel-Newton algorithm these algorithms embed the classical strain-driven radial-return method. To this end, a concept of geometric numerical integration is applied, where the plastic incompressibility condition is taken into account as an additional side-condition. Since the literature states large integration errors if the side-condition is not taken into account, a particular focus lies on the application of a time-adaptive procedure. Accordingly, the article investigates (i) the algorithmic treatment of kinematic hardening within time-adaptive finite elements, (ii) the influence of the Perzyna-type viscoplasticity approach in view of an order reduction phenomenon, and (iii) the influence of taking into account the exact fulfillment of plastic incompressibility using a projection method having the advantage of simple implementation.

Finite strain viscoplasticity with nonlinear kinematic hardening: Phenomenological modeling and time integration

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of Armstrong–Frederick type. Two implicit time-stepping methods are adopted for numerical integration of evolution equations, such that the plastic incompressibility constraint is exactly satisfied. The first method is based on the tensor exponential. The second method is a modified Euler-backward method. Special numerical tests show that both approaches yield similar results even for finite inelastic increments. The basic features of the material response, predicted by the material model, are illustrated with a series of numerical simulations.

Modeling and computation of metal powder compaction processes

AbstractIn this short communication the numerical treatment of a thermomechanical consistent finite strain viscoplasticity model for metal powder compaction is discussed. The convex single surface yield function evolves according to two evolution equations and remains convex under all loading conditions. The very challenging numerical treatment on local level for integrating the constitutive model requires particular globally convergent Newton‐like method with inequality constraints so that a stable solution scheme results. This is embedded into a time‐adaptive finite element program which makes use of diagonally‐implicit Runge‐Kutta methods combined with a Multilevel‐Newton algorithm. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)