Evolution Of Plastic Anisotropy Research Articles

Multi-scale modelling of evolving plastic anisotropy during Al-alloy sheet forming

Accurate modelling of local evolving texture and yield surface evolution in complex strain path are of crucial importance to the accurate sheet metal forming simulations. This work proposed a novel multi-scale computational scheme, in which the full-field crystal plasticity (CP) modelling is mapped and real-time updated into each integration point following the local strain path in the finite element (FE) model. By the real-time close-loop feedback and update between the FE model and CP model, the evolving texture and its induced anisotropic plasticity evolution are considered utilizing on-the-fly virtual tests in the full deformation field. To carefully verify the developed computational framework, a comprehensive validation including plastic anisotropy characterization, cyclic hardening tests and deep drawing tests is conducted in an AA6016-T4 aluminium sheet with strong cube texture using ESAFORM Benchmark 2021. By comparison with experimental results and the conventional approaches with constant yield surface for the forming case, the newly developed method is thoroughly validated, showing that the significant texture evolution is observed in large plastic deformation and various strain paths lead to different texture evolution. The local evolving texture induced plastic anisotropy evolution has a considerable effect on the prediction accuracy of the deep drawing simulations, such as earing profile, wall thickness and loading history. Additionally, this method does not increase too much computation cost, enabling cost-effectively simulation of complex forming processes.

Plastic anisotropy evolution of SS316L and modeling for novel cruciform specimen

In this paper, the evolution of the plastic anisotropy of stainless steel 316L samples is investigated under proportional loading paths using a customized cruciform specimen. The determination of a novel cruciform specimen by a design of experiments approach integrated with finite element simulations is described. The mechanical properties of the material are characterized under uniaxial tension applied in every 15° from the rolling direction and equibiaxial tension from hydraulic bulge experiments. The results reveal that the plastic anisotropy shown in stress and strain significantly evolves with respect to the plastic work. Based on the experiments, the material behavior is modeled using a non-quadratic anisotropic yield function, Yld2004–18p, with parameters modeled as a function of the equivalent plastic strain, assuming plastic work equivalence, and with constant parameters for comparison. The Hockett-Sherby model is also used for the strain hardening behavior to extrapolate the results to higher strain values. The models are implemented into a user material subroutine for finite element simulations. To validate the model, in-plane biaxial tension experiments are performed, using a customized specimen, to achieve greater deformation than previous designs by introducing double-sided pockets for thickness reduction and notches in the corner areas. The results are compared with finite element simulations implemented with the plasticity models.

Anisotropic work hardening behaviour in duplex stainless steel under uni-axial loading: Interplay between phase morphology and crystallographic texture

Duplex stainless steels (DSS) are characterised by vivid phase morphology and crystallographic textures. The typical microstructure consists of elongated phases (along rolling direction, RD) stacked alternatively along the normal direction (ND). In this study, uni-axial testing in multiple macroscopic directions is used to explore the anisotropic evolution of work hardening. Crystal plasticity simulations are used to gain insights into the same. The compressive stress and work hardening of samples loaded in the transverse direction (TD) are observed to be higher than those loaded in the RD and ND. Austenite and ferrite developed [110] and [111] parallel to the loading direction type fibre textures during uni-axial compression. The weak austenite texture behaves similarly to its single-phase counterparts regarding reorientation. The plastic anisotropy evolution is aided by the strong ferrite texture, which deviates from its single-phase behaviour. When loaded along TD compared to other directions, microstructural characterisation revealed the formation of deformation twins in austenite and lower effective slip length of both the phases.

Modeling plastic anisotropy evolution of AISI 304 steel sheets by a polynomial yield function

In this study, a numerical model for the evolution of plastic anisotropy is investigated for the purpose of stamping method design by Finite Element (FE) analysis and proved experimentally via process simulations of a cold-rolled austenitic stainless steel (AISI 304) sheet. The plastic anisotropy of the sheets is described with a fourth-order homogenous polynomial yield function and this modelling approach is enhanced by plastic strain dependent material coefficients. Tensile tests of coupon specimens taken along the different directions from rolling direction, and flow strength and deformation anisotropies are described with the planar variations of yield stress and plastic strain ratio computed at four plastic strain levels (0.002, 0.02, 0.05 and 0.18). A new numerical approach is, then, applied to identify polynomial coefficients ensuring an orthotropic positive-definite, convex yield surface with a well-defined stress gradient at every loading point on plane stress subspace. The developed computational model is implemented into general purpose explicit FE analysis software Ls-Dyna by a user-defined material model subroutine (UMAT) and applied in the stamping simulation of AISI 304 steel rectangular cups for the house-hold applications. The computed thickness distributions and the flange geometries were compared with measurements and it was observed that the best predictions were done with material parameters at %5 plastic strain level.

A machine learning framework to predict local strain distribution and the evolution of plastic anisotropy & fracture in additively manufactured alloys

Machine learning (ML) approaches are widely used to develop systems or frameworks with the ability to predict the properties of interest by learning and establishing relationships and inferences from data. In the present work, an ML based framework is proposed to predict the evolution of local strain distribution, plastic anisotropy and failure during tensile deformation of AlSi10Mg aluminum alloy produced by selective laser melting (SLM). The framework combines the methods involved in additive manufacturing (AM) and artificial intelligence (AI). This includes printing of test specimens using laser powder bed fusion (LPBF), x-ray computed tomography (CT) scanning to measure internal defects distribution, mechanical testing with digital image correlation (DIC) to get local strain evolution, extraction and coupling of CT and DIC data, and the development, validation and evaluation of an artificial neural network (ANN) model. The experimental data from CT and DIC measurements are used to train, validate and evaluate the proposed ANN model. Microstructural features such as the size, shape, volume fraction and distribution of porosity are used as an input to ANN. The proposed ANN model successfully predicts the evolution of local strains, plastic anisotropy and failure during tensile deformation. The intensity and location of strain hotspots as well as the shape of shear bands and the location of crack initiation are well predicted. The current research demonstrates the applicability of an ML based ANN approach to predict microstructure – property – performance relationships for engineering materials with intricate heterogeneous microstructures such as those produced additively by SLM. The success of the present approach motivates further use of ML techniques, as a mean for accelerated development of new alloys, AM process optimization and its wide scale applicability.

Evaluation of material models describing the evolution of plastic anisotropy in pearlitic steel

Rolling contact fatigue cracks often initiate in the highly deformed surface layer of railway rails. However, the behavior of the material in this region is not well known. In an earlier study by the author the behavior of a pearlitic rail steel subjected to large shear deformations was analyzed experimentally. The purpose of the present study is to evaluate the ability of four different material models, based on [Meyer et al. INT J SOLIDS STRUCT, pp. 122–132, vol 130–131, 2018], [Shi et al. INT J PLASTICITY, pp. 170–182, vol 63, 2014], [Qin et al. INT J PLASTICITY, pp. 156–169, vol 101, 2018] and crystal plasticity, to simulate these experiments. The second and third models are formulated into the finite strain framework used in the first model, and advanced kinematic hardening laws are incorporated. To enable such an evaluation, a simulation methodology of the experimental procedure is developed and presented. It is found that the model by Shi et al. could fit the experimental data most accurately. None of the models were able to predict all features observed in the experiments. Further development of constitutive models for evolving anisotropy in pearlitic steels subjected to large shear strains is therefore needed.

Prediction of necking in HCP sheet metals using a two-surface plasticity model

In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension–compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension–compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.

Modelling the plastic anisotropy evolution of AA5754-H22 sheet and implementation in predicting cylindrical cup drawing process

In this paper, constitutive models for sheet metals that take into account evolution of plastic anisotropy during material forming are developed and analyzed considering experimental data for aluminum alloy 5754-H22 sheet. The developed models are based on associated or non-associated flow rule approach and utilize simple four parametric orthotropic stress functions, quadratic Hill-48 function or non-quadratic Karafillis-Boyce function. An experimental study is performed in order to characterize the plastic anisotropy and its evolution with straining in tensile testing for the considered material. Lankford coefficient (r-value) is calculated as an instantaneous value based on the polynomial fit of the transverse versus longitudinal true plastic strain diagram. The directional dependences of yield stress ratios and instantaneous Lankford coefficients corresponding to the selected amounts of plastic work are determined. Based on the obtained data, anisotropy parameters of Hill-48 and Karafillis-Boyce stress functions are set as the polynomial functions of the equivalent plastic strain. The developed models based on associated or non-associated flow rule and Hill-48 or Karafillis-Boyce stress function with variable anisotropy parameters are analyzed in predicting the cylindrical cup drawing process for the considered material. The implicit algorithmic formulations of the analyzed constitutive descriptions are implemented into the finite element program ADINA 8.6 via user defined subroutine CUSERG. The predictions of cup drawing process are compared with the experimental data. The results demonstrate that the evolving plasticity model based on non-associated flow rule and non-quadratic Karafillis-Boyce stress function provides the best estimation of the earing profile. Based on the obtained results, the influence of plastic anisotropy evolution description on the cup drawing predictions is assessed.

Characterization of mechanical properties and formability of a superplastic Al-Mg alloy

In order to develop a reliable constitutive model for predicting formability and springback of sheet metals during superplastic forming (SPF) and quick plastic forming (QPF), characterization of elastic-plastic behavior, as well as formability of the material is essential. In the present study, the module of elasticity, uniaxial flow behavior and anisotropy, as well as the forming limit curve (FLC) of one of an SPF/QPF grade AA5083 was investigated. The variation of Young’s modulus with temperature was measured from the uniaxial tensile tests for four temperatures ranging from 25 to 500 °C. The impact of temperature and strain rate on the flow behavior of the material was investigated via uniaxial tensile tests for three temperatures (420, 450, and 480 °C) and at three strain rates (0.001, 0.01, and 0.1 s−1). The dependency of the flow stress on the material orientation with respect to the rolling direction (0, 45, and 90°) was assessed using uniaxial tensile tests at a constant temperature. In addition, the evolution of plastic anisotropy with plastic strain and strain rate was assessed by measuring the Lankford coefficient (r-value). Finally, the FLC of the material at 450 °C was characterized according to Nakazima tests procedure for three strain paths (i.e. uniaxial tension, plane strain, and biaxial tension).

Evolution of plastic anisotropy and strain rate sensitivity

In this study, it is aimed to formulate a constitutive model accounting for the evolving features of the plastic anisotropy, in terms of both stresses and r-values, and the strain rate sensitivity during the plastic deformation. For the model calibration and validation, a bcc ferritic steel is selected. The material parameters are calibrated by tensile experiments under different loading configurations and different strain rates. Nakajima tests are conducted to characterise the cold formability of the selected steel. The model prediction is compared with the experimental results and it is concluded that the formability prediction is significantly improved when considering the evolving features during the plastic deformation.

Spatial clustering strategies for hierarchical multi-scale modelling of metal plasticity

In this paper we propose a novel approach to accelerate the multi-scale simulation of metal plasticity. In macroscopic zones of nearly homogeneous strain responses, the evolution of plastic anisotropy at each finite element integration point can be approximated from the properties at a representative point within a zone. We show how these zones can be identified by a clustering algorithm and can be utilised to reduce the computational cost of the simulation. We present and analyse the results obtained for two test cases.

Latent hardening and plastic anisotropy evolution in AA6060 aluminium alloy

The crystal plasticity theory predicts that hardening on a particular slip system and its corresponding work-hardening rate will depend on the slip activity on both this slip system and all others. The exact form of this dependence is defined by the latent hardening description in form of the latent hardening matrix or the interaction matrix. It has been assumed that this matrix describes the relative strength of various dislocation interactions and is therefore the same for a wide range of alloys with the same lattice structure. Different methods have been used to estimate the values of the interaction matrix components: one is experimental and uses strain-path changes; another simulates the dislocations dynamics in a crystal directly at the microscale and estimates the strength of the forming locks. In this work, the influence of the interaction matrix (and thus latent hardening) on the development of plastic anisotropy is studied. An extruded AA6060 alloy is tested in uniaxial tension in different directions and the anisotropy of the alloy is found to evolve considerably throughout the deformation. A crystal plasticity model is used to simulate the experimental tests, and the use of different interaction matrices is evaluated. A noticeable influence on the predicted evolution of plastic anisotropy as well as on the stress–strain field and slip inside the constituent grains is found.

Effect of the grain shape on the q-value evolution of steel sheets

Two polycrystalline plasticity models, namely the ALAMEL model and the viscoplastic self-consistent (VPSC) model were used to study the effect of the grain shape on the evolution of plastic anisotropy. The latter was characterized by the q-value in this paper. The two models both predict the evolution of grain shape and texture and then can predict the effect of the initial grain shape on the texture. The final anisotropy of the materials was also assessed with the help of these models. Data of tensile tests in three directions for three low carbon steel sheets with either equiaxed or a pancake grain shape were used to evaluate the model predictions. Both models give the same trend of the grain shape effect on the evolution of the q-values. Results demonstrate that the effect of the grain shape can be clearly reflected in the x-value distribution as defined and discussed in this paper. But it is not so obvious in the predicted textures for the investigated three materials according to both models.

Damage anisotropy and its effect on the plastic anisotropy evolution under finite strains

In this work, non-associative finite strain anisotropic elastoplastic model fully coupled with anisotropic ductile damage is considered. First, the kinematics of large deformation based on multiplicative decomposition of the total transformation gradient is briefly recalled. Using a thermodynamically-consistent framework, the effective state variables are defined to introduce the effect of the anisotropic damage through the total energy equivalence assumption. For an accurate plastic anisotropy description, non-associative plasticity framework is considered for which equivalent stresses in yield function and in plastic potential are separately defined. The evolution equations governing the overall dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential, while the consistency condition is still deduced from the yield function. Applications are made to a generic material defined by selected values of material parameters and considering different typical strain controlled loading paths as uniaxial tension (UT), plane tension (PT) and equibiaxial tension (ET). For each loading path, the effect of the anisotropic damage evolution on the plastic anisotropy and vice-versa is carefully studied in the context of finite plasticity assuming small elastic strains.

Effect of Stress Triaxiality on the Flow and Fracture of Mg Alloy AZ31

The microscopic damage mechanisms operating in a hot-rolled magnesium alloy AZ31B are investigated under both uniaxial and controlled triaxial loadings. Their connection to macroscopic fracture strains and fracture mode (normal vs shear) is elucidated using postmortem fractography, interrupted tests, and microscopic analysis. The fracture locus (strain-to-failure vs stress triaxiality) exhibits a maximum at moderate triaxiality, and the strain-to-failure is found to be greater in notched specimens than in initially smooth ones. A transition from twinning-induced fracture under uniaxial loading to microvoid coalescence fracture under triaxial loading is evidenced. It is argued that this transition accounts in part for the observed greater ductility in notched bars. The evolution of plastic anisotropy with stress triaxiality is also investigated. It is inferred that anisotropic plasticity at a macroscopic scale suffices to account for the observed transition in the fracture mode from flat (triaxial loading) to shear-like (uniaxial loading). Damage is found to initiate at second-phase particles and deformation twins. Fracture surfaces of broken specimens exhibit granular morphology, coarse splits, twin-sized crack traces, as well as shallow and deep dimples, in proportions that depend on the overall stress triaxiality and fracture mode. An important finding is that AZ31B has a greater tolerance to ductile damage accumulation than has been believed thus far, based on the fracture behavior in uniaxial specimens. Another finding, common to both tension and compression, is the increase in volumetric strain, the microscopic origins of which remain to be elucidated.

Modeling and finite element simulation of loading-path-dependent hardening in sheet metals during forming

A recent material model considering the evolution of plastic anisotropy in interstitial free steels is validated for the forming process of the channel die, a complex part. In the model the evolution of the intra-granular microstructure is represented by tensor-valued internal variables. The model accounts for the cross hardening behavior observed in rheological tests of interstitial free steels. A novel cross hardening indicator which is directly derived from the constitutive model is proposed. This cross hardening indicator is a quantitative measure for the occurrence of cross hardening in the forming process of complex parts. A correlation between the occurrence of cross hardening and larger values of the stored (elastic) energy is observed. The influence of cross hardening on the forming process is investigated, in particular, the drawing forces and the geometric deviations due to springback. The influence of cross hardening on the forming process of the channel die geometry is small. The influence of cross hardening on the more complex S-Rail geometry is larger due to larger plastic deformation and more severe loading path changes. The concept of the proposed transient hardening indicator should be applicable to other models for the evolution of plastic anisotropy. A possible use of the cross hardening indicator would be the efficient choice of the material model in the context of sheet metal forming simulations.

Polycrystal plasticity models based on crystallographic and morphologic texture: Evaluation of predictions of plastic anisotropy and deformation texture

Two micro–macro scale transition models, namely the ALAMEL and visco-plastic self-consistent (VPSC) models (both predict the evolution of grain shape and texture), were used to study the effect of the initial grain shape. The evolution of plastic anisotropy was characterized by the q-value and was simulated in three directions for three low carbon steels assuming either equiaxed (hypothetical one) or a pancake (measured one) grain shape. In addition, texture evolution during rolling was investigated for one of the materials. Comparisons between the model predictions and the measured values demonstrate that the grain shape effect can be predicted well by both models. In most cases, the initial q-value can be nicely estimated by both models. VPSC is better than ALAMEL on q-value evolution prediction for simulations which consider the measured aspect ratios. For texture evolution of rolling, the effect of initial grain shape is only significant at large deformation.

Analysis of texture and R value variations in asymmetric rolling of IF steel

Asymmetric rolling (ASR) is a potential process to reach better grain refinement than in conventional rolling, thus, can lead to better mechanical properties. It is not known, however, how the introduction of a shear component will change the ideal orientations of the textures, and consequently, the evolution of plastic anisotropy. To understand the effect of the added shear on texture evolution in ASR, a stability analysis is carried out in orientation space and the variations in the position and strength of the ideal orientations are analysed as a function of the shear component. Then, modelling of R values is presented for various cases. On that basis, it is shown that there is an upper limit for the shear component in asymmetric rolling that still retains the 〈1 1 1〉 || ND fibre (ND: direction normal to the sheet) which is good for formability. It is also found that better persistence of the ND fibre can be obtained by cyclically alternating the shear component. The theoretical results are well supported by comparison to experimental evidences.

Microstructure, crystallographic texture, and plastic anisotropy evolution in an Mg alloy during equal channel angular extrusion processing

Abstract In this article, we report on the relationship between the active deformation mechanisms and the development of texture, grain size and morphology, and dynamic recrystallization (DRX) during large plastic strain deformation of an AZ31B magnesium alloy. Equal channel angular extrusion (ECAE) is used to apply a variable amount and sequence of simple shearing at 200 °C. Two different starting textures were used: basal poles either aligned with or perpendicular to the extrusion direction. A multi-scale ECAE simulation model based on crystal plasticity was employed to determine the relative contributions of different slip systems during ECAE at 200 °C. These simulations clarified how different active deformation modes were responsible for specific grain size and distribution, and grain morphology as a function of the starting textures and ECAE route. For instance, we found that relatively intense prismatic slip activity suppresses DRX, which, in turn, leads to an elongated grain structure. Room temperature mechanical testing was carried out on the processed samples along three orthogonal directions to characterize flow stress anisotropy and tension–compression asymmetry. It is shown that with proper selection of the starting texture and ECAE route, it is possible to control the level of mechanical anisotropy in the processed samples and obtain strongly or weakly anisotropic mechanical response in Mg alloys.

Plastic behaviour and forming limit during biaxial compressions of magnesium alloy AZ31 at room temperature

The plastic behaviour and compressive fracture of AZ31 magnesium alloy were examined at room temperature. The uniaxial compression tests and biaxial compression tests along linear and nonlinear strain paths were carried out until fracture using a unique biaxial compression testing machine developed by author. The results revealed the evolution of plastic anisotropy in biaxial compressions, that is the strain path dependency of work hardening. The adaptability of several forming limit criteria to the compressive fracture of AZ31 alloy was discussed. It was found that the uniform estimation of compressive forming limits by uniaxial and biaxial compressions was difficult by Freudenthal criterion and Oyane criterion. The result of Tresca energy criterion suggested that the criterion based on shear stress has possibility to predict the compressive forming limits at room temperature of AZ31 alloy.