Virtual material testing for stamping simulations based on polycrystal plasticity

In the modern practice of stamping simulation of complex industrial parts the prediction of springback still lacks accuracy. In commercial software packages various empirical constitutive laws for stamping are available. Limited to simple empirical models for material anisotropy they do not take into account in a full manner the effects of microstructure and its evolution during the deformation process. The crystal plasticity finite element method bridges the gap between the polycrystalline texture and macroscopic mechanical properties that opens the way for more profound consideration of metal anisotropy in the stamping process simulation. In this paper the application of crystal plasticity FEM within the concept of virtual material testing with a representative volume element (RVE) is demonstrated. Using virtual tests it becomes possible, for example, to determine the actual shape of the yield locus and Lankford parameters and to use this information to calibrate empirical constitutive models. Along with standard uniaxial tensile tests other strain paths can be investigated like biaxial tensile, compressive or shear tests. The application of the crystal plasticity FEM for the virtual testing is demonstrated for DC04 and H320LA steel grades. The parameters of the Vegter yield locus are calibrated and the use case demonstration is completed by simulation of a typical industrial part in PAMSTAMP 2G.     

Ductile fracture by multiple void growth and interaction ahead of a notch tip in polycrystalline plastic solids

The objectives of this paper are to study the effects of plastic anisotropy and evolution in crystallographic texture with deformation on the ductile fracture behaviour of polycrystalline solids. To this end, numerical simulations of multiple void growth and interaction ahead of a notch tip are performed under mode I, plane strain, small scale yielding conditions using two approaches. The first approach is based on the Hill yield theory, while the second employs crystal plasticity constitutive equations and a Taylor-type homogenization in order to represent the ductile polycrystalline solid. The initial textures pertaining to continuous cast Al–Mg AA5754 sheets in recrystallized and cold rolled conditions are considered. The former is nearly-isotropic, while the latter displays pronounced anisotropy. The results indicate distinct changes in texture in the ligaments bridging the voids ahead of the notch tip with increase in load level which gives rise to retardation in porosity evolution and increase in tearing resistance for both materials.     

Yield surface simulation for partially recrystallized aluminum polycrystals on the basis of spatially discrete data

The paper presents simulations of the yield surface evolution of plastically deformed aluminum polycrystals during recrystallization. The yield surfaces are calculated using a viscoplastic Taylor–Bishop–Hill strain rate polycrystal homogenization method. The input data for the yield surface calculations are the crystal orientations, their volume fractions, and their shear stresses. While the crystal orientations determine the kinematic portion of the yield surface the threshold shear stress of each individual orientation determines the kinetic portion of the yield surface. The input data for the homogenization calculations are generated through a spatially discrete simulation, where crystal deformation and primary static partial recrystallization are simulated by coupling a viscoplastic crystal plasticity finite element model with a cellular automaton. The crystal plasticity finite element model accounts for crystallographic slip and for crystal rotation during plastic deformation using space and time as independent variables and the crystal orientation and the accumulated slip as dependent variables. The cellular automaton uses a switching rule which is formulated as a probabilistic analogue of Turnbull's rate equation for the motion of grain boundaries. The actual decision about a switching event is made using a simple-sampling Monte Carlo step. The automaton uses space and time as independent variables and the crystal orientation and a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through grain boundary mobility and driving force data. The crystallographic texture and the orientation-dependent resistance to shear are for each interpolation point extracted after each time step during recrystallization. The data serve as input for the calculation of discrete yield surfaces.     

Industrial challenges for finite element and multiscale methods for material modeling

The automotive industry promotes lightweight design to reduce the CO2-emission and enhances the passenger’s safety using high strength steel grades. One limiting factor to the accuracy of modern stamping simulation are the empirical constitutive models. In particular for high strength multiphase steels the modelling techniques like multi-scale methods are becoming more interesting. However they should meet the industrial needs. Not only the accuracy but also features like time, costs and complexity are rapidly increasing. The challenge is the development of finite element technologies and multi-scale methods in an appropriate framework for industrial projects. The crystal plasticity finite element method bridges the gap between the micro level and macroscopic mechanical properties that opens the way for more profound consideration of metal anisotropy in stamping process simulation. Nevertheless new empirical constitutive models are favourable for spring back prediction in forming simulations, even if the number of material parameters and the amount of tests for their identification increases. In this paper the application of crystal plasticity FEM within the concept of virtual material testing with a representative volume element (RVE) is demonstrated.     

Numerical simulations of crack tip fields in polycrystalline plastic solids

In this paper, modes I and II crack tip fields in polycrystalline plastic solids are studied under plane strain, small scale yielding conditions. Two different initial textures of an Al-Mg alloy, viz., continuous cast AA5754 sheets in the recrystallized and cold rolled conditions, are considered. The former is nearly-isotropic, while the latter displays distinct anisotropy. Finite element simulations are performed by employing crystal plasticity constitutive equations along with a Taylor-type homogenization as well as by using the Hill quadratic yield theory. It is found that significant texture evolution occurs close to the notch tip which profoundly influences the stress and plastic strain distributions. Also, the cold rolling texture gives rise to higher magnitude of plastic strain near the tip.     

Two-scale analysis for deformation-induced anisotropy of polycrystalline metals

The anisotropic macroscopic mechanical behavior of polycrystalline metals is characterized by incorporating the microscopic constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory, which enables us to derive both micro- and macro-scale governing equations. The two-scale simulations are conducted to evaluate the macroscopic anisotropy induced by microscopic plastic deformation histories of the polycrystalline aggregate. In the simulations, the representative volume element (RVE) composed of several crystal grains is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macroscopic responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of microscopic plastic deformation process without referring to the change of crystallographic orientations.     

A new implementation of the spectral crystal plasticity framework in implicit finite elements

We present a new implementation of a computationally efficient crystal plasticity model in an implicit finite element (FE) framework. In recent publications, we have reported a standalone version of a crystal plasticity model based on fast Fourier transforms (FFTs) and termed it the spectral crystal plasticity (SCP) model. In this approach, iterative solvers for obtaining the mechanical response of a single crystal of any crystallographic orientation subjected to any deformation mode are replaced by a database of FFTs that allows fast retrieval of the solution. The standalone version of the code facilitates simulations of relatively simple monotonic deformation processes under homogeneous boundary conditions. In this paper, we present a new model that enables simulations of complex, non-monotonic deformation process with heterogeneous boundary conditions. For this purpose, we derive a fully analytical Jacobian enabling an efficient coupling of SCP with implicit finite elements. In our implementation, an FE integration point can represent a single crystal or a polycrystalline material point whose meso-scale mechanical response is obtained by the mean-field Taylor-type homogenization scheme. The finite element spectral crystal plasticity (FE-SCP) implementation has been validated for several monotonic loading conditions and successfully applied to rolling and equi-channel angular extrusion deformation processes. Predictions of the FE-SCP simulations compare favorably with experimental measurements. Details of the FE-SCP implementation and predicted results are presented and discussed in this paper.     

Crystal plasticity finite element simulations of pure bending of aluminium alloy AA7108

The crystal plasticity finite element method (CP-FEM) is used to investigate the influence of microstructure on the bending behaviour of the heat treatable aluminium alloy AA7108. The study comprises two materials obtained from the AA7108 aluminium alloy by different thermo-mechanical treatments. The first one is an as-cast and homogenized material consisting of large grains with random texture, while the second one is a rolled and recrystallized material having refined grains with weak deformation texture. The behaviour of the two materials in plane-strain bending is investigated numerically and compared qualitatively to existing experimental data. The crystallographic texture and grain morphology of the materials are explicitly represented in the finite element models. The numerical results display a strong effect of the grain morphology on the bending behaviour, the surface waviness and the development of shear bands. These results are consistent with the experimental observations. The simulations further indicate that crystallographic texture affects the bending behaviour of the rolled and recrystallized material.     

A texture discretization technique adapted to polycrystalline aggregates with non-uniform grain size

This paper presents a new procedure for the sampling of crystallographic textures into discrete lattice orientations. The method is, for example, useful in order to assign initial grain orientations in crystal-plasticity-based finite element simulation of forming processes. The discretization technique ensures that the orientation sampling is statistically representative of a known orientation distribution function (ODF). Contrary to previous discretization techniques, the new method is valid also when the model microstructure consists of grains with non-uniform size. The accuracy of the texture representation is assessed in the case of cold rolled IF steel. Crystal plasticity theory coupled to finite element modeling is used to predict mechanical planar anisotropy of the sheet. Comparison is made between model predictions assuming, respectively, a uniform or a heterogeneous grain-size distribution.     

Microstructure and texture evolution during the drawing of tungsten wires

Tungsten wires develop during their forming process a pronounced fibre texture that causes anisotropic deformation of single grains. The aim of this work is to simulate the crystallographic texture and microstructure evolution that arises during wire drawing using two different texture models. A visco-plastic self-consistent model that allows simulations using a large number of grains is compared with a crystal plasticity finite element model that provides a more detailed insight into the wire’s microstructure. Texture predictions of both models are discussed and quantitatively compared with experimental texture measurements obtained by neutron diffraction. The developed fibre texture causes plane strain deformation of single grains, which induces grain curling. The prediction of grain curling is of importance because it allows studying the residual stresses that trigger splits, at the grain level.     

Modeling the crystallographic changes in processing of Al alloys

The evolution of deformation and recrystallization (RX) textures in 6016 Al alloy is analyzed in the current study by means of experimental measurements and numerical simulations. The deformation texture is modeled with various Taylor-type homogenization models whereas the development of RX texture is analyzed by evaluation of energy stored during the plastic deformation in grains of various orientations employing crystal plasticity (CP) calculations. It is shown that the main features of texture which evolve during discontinuous RX could be reproduced by taking into consideration both a microgrowth selection criterion and orientation selection based on crystallographically resolved stored energy of deformation. The influence of the strain heterogeneities on the development of RX texture is analyzed on the basis of CP and results derived from finite element calculations.     

Application of crystal plasticity FEM from single crystal to bulk polycrystal

This article compares results of crystal plasticity FE simulations with experimental results for single, bi- and oligo crystal deformation. It is shown, that while single crystal deformation is very well reproduced by the simulations, the quality of simulation results for bicrystals strongly depends on the orientation of the grain boundary with respect to the external mechanical load. In the second part of the paper an extension of crystal plasticity FEM (CP-FEM) using texture components for the representation of the crystallographic texture of bulk material is shortly introduced and applied to the cup drawing of sheet material.     

Mesoscale Modeling of Microstructure and Texture Evolution During Deformation Processing of Metals

The application of the finite element method to model the deformation of metals at the mesoscale to study the microstructure and texture evolution is described. The finite element discretization is applied directly to the various grains, and crystal plasticity is used as the constitutive basis to model the plastic deformation by crystallographic slip, and to evolve the slip system strength and crystal lattice orientation of the material. Applications of the methodology to detailed studies of the non‐uniform deformations of individual grains, and effects of grain interactions on the distributions of deformation and stress in the microstructure are discussed.     

Evaluation of two mutliscale models for the simulation of cross-die forming of Dual Phase (DP) steels

Two micro-macro modelling approaches, one based on crystal plasticity and the other on a Mori-Tanaka mean-field model, are presented and used for the simulation of forming operations on dual phase (DP) steels. The material parameters are determined based on bending-unbending experiments while deep-drawing with a cross-shaped die is simulated based on user-defined material laws (UMAT) in the ABAQUS finite element code. It is demonstrated that accurate predictions would require a combination of both modelling approaches.     

Investigation of the effect of temper rolling on the texture evolution and mechanical behavior of IF steels using multiscale simulation

The main objective of this study is to simulate texture and deformation during the temper-rolling process. To this end, a rate-independent crystal plasticity model, based on the self-consistent scale-transition scheme, is adopted to predict texture evolution and deformation heterogeneity during temper-rolling process. For computational efficiency, a decoupled analysis is considered between the polycrystalline plasticity model and the finite element analysis for the temper rolling. The elasto-plastic finite element analysis is first carried out to determine the history of velocity gradient during the numerical simulation of temper rolling. The thus calculated velocity gradient history is subsequently applied to the polycrystalline plasticity model. By following some appropriately selected strain paths (i.e., streamlines) along the rolling process, one can predict the texture evolution of the material at the half thickness of the sheet metal as well as other parameters related to its microstructure. The numerical results obtained by the proposed strategy are compared with experimental data in the case of IF steels.     

Assessment of forming parameters influencing spring-back in multi-point forming process: A comprehensive experimental and numerical study

Like all sheet metal forming methods, one of the main characteristics of parts formed by multi-point forming is dimensional deviation caused by elastic recovery that is known as spring-back. In this paper the effects of material property, sheet thickness and anisotropy ratio along with process parameters such as elastic layer thickness, elastic layer hardness and number of punch elements on spring-back are studied utilizing finite element simulations and experimental tests. Experimental tests are carried out under various conditions by forming V-shaped and Sin-shaped geometries. Aluminum alloy 3105, stainless steel 304 and pure copper were used as sheet materials for experiments. Likewise, black rubber with shore A hardness of 50 and polyurethane with hardness of 65 and 85 were allocated as elastic layers. The Abaqus® commercial code is employed for finite element simulations. The definition of yield behavior of utilized sheet materials is fulfilled by using three yield criteria of Barlat-89, Hill-48 and Von-Mises. Since the Barlat-89 is not adopted in Abaqus, VUMAT and UMAT user defined subroutines are provided and integrated with explicit simulation of forming process and implicit simulation of spring-back phenomenon respectively. The results indicate that parameters such as material property, blank thickness and anisotropy affect spring-back in multi-point forming. Also the thickness and hardness of elastic layers are novel ideas that should be considered in order to minimize the spring-back. In general, using the elastic layer with minimum possible thickness and greater hardness beside the maximum number of pins leads to minimum spring-back.     

Constitutive modeling of ferritic stainless steel

In this work, constitutive models, including phenomenological and crystal plasticity, were used to simulate the anisotropy behavior and texture evolution of two ferritic stainless steel sheets, AISI409L and AISI430. Uniaxial tension, hydraulic bulge and disk compression tests were performed to characterize the mechanical properties of the two materials, and to determine the yield surfaces at different amounts of plastic work. Meanwhile, X-ray diffraction and electron backscatter diffraction techniques were used to analyze the texture of undeformed and deformed specimens. Crystal plasticity simulations were performed to determine the plastic behavior in selected deformation paths. The analysis of the mechanical test results showed that the yield surface shapes were changing during deformation. Crystal plasticity results indicated that texture evolution was mainly responsible for the yield surface shape change, i.e., anisotropic work-hardening, in AISI409L. For AISI430, the results were not completely consistent. More work is needed to understand the plastic behavior of this material.     

Numerical methods for the quantification of the mechanical properties of crystal aggregateswith morphologic and crystallographic texture

The influence of an anisotropic distribution of crystal orientations and an anisotropic average grain shape is analysed using finite element simulations. By the numerical approach, which is based on a statistical volume element with periodic microstructure and periodic boundary conditions, the influence of the crystallographic and the morphologic texture can be separated by combining (an)isotropic orientation distributions with (an)isotropic grain morphologies.