Polycrystalline Plasticity Research Articles

Nano-enabled orientation alignment via extreme shear strains

It was recently shown that the crystals in an already nanocrystalline alloy (Pd–10% Au) became highly oriented under extreme shearing. No such self-ordering is seen in the coarse-grained counterpart under the same conditions. Here we use phase field dislocation dynamics and polycrystalline plasticity modeling to explore the possible causes that enabled this unusual crystallographic alignment. The results suggest that full-dislocation slip and preservation of grain boundary misorientation with at least one neighbor grain can cause the highly oriented texture observed experimentally.

Material-based design of the extrusion of bimetallic tubes

Using finite element and polycrystalline plasticity modeling, we explore the influence of die design and material behavior on the extrusion of bimetallic tubes. Three distinctly different extrusion designs are introduced and evaluated based on a range of macroscopic and microstructural criteria: die and punch stress, interface roughness, peak forming loads, and strain and crystallographic texture heterogeneities across the tube thickness. We find that an extrusion die design proposed here that differs from the conventional one is better for reduction of peak forming load satisfying objectives of the traditional design. However, when the design is more constrained and considerations of strain and microstructural heterogeneities and gradients are made part of the design criteria, we show that one die design promotes such gradients while the other minimizes them. In all three designs, large disparities in flow stress and hardening rate (>3 times) lead to larger interfacial strain gradients. These findings provide basic die designs that can be used to evaluate the degree and locations of strain and texture gradients across the tube thickness.

Effect of Texture on Plastic Flow Localization of FCC Polycrystals Using Homogenization-Based Polycrystalline Plasticity

In this study, a framework to predict the onset of plastic flow localization is introduced. The Marciniak-Kuczyński type approach, which is a classical method to predict the strain localization, and a crystal plasticity model with a homogenization-based finite element method are combined, and forming limit strains that are defined as the onset of plastic flow localization for FCC polycrystals are computed. The forming limit strains with several kinds of textures are evaluated with the present approach, and the results are compared with those obtained by the Taylor model, which is a widely used conventional polycrystalline model. Within the present application, the present method and the classical Taylor model give similar forming limit strains for FCC polycrystal sheets. According to the present results, the use of the Taylor model in the sheet necking analysis might be justified, at least for FCC polycrystal sheets with various textures.

Validation of a Multi-Scale Model for Shear Deformation of an Aluminium Sheet Alloy

Aluminium is a potential light weight alternative to steel for deep drawn sheet components, but generally does not compare well to steels in terms of formability. Research in polycrystalline plasticity indicates applying shear to rolled fcc alloys improves their deep drawability by favourably modifying their crystallographic texture. Such processing could be realised industrially by cold asymmetric rolling (ASR), but in order to gain detailed understanding of the influence of process parameters on the evolution and through thickness homogeneity of the texture a validated full field multi-scale model of the process is required. This study examines the ability of a hierarchical multi-scale approach to predict evolved textures for aluminium sheet subjected to a mechanical test exhibiting a deformation mode relevant for ASR, namely simple shear. The homogeneity of the deformation field is assessed with full field strain measurement by digital image correlation, and macrotexture is measured by x-ray diffraction. The discrepancies are discussed and further work to validate the modelling approach for simulation of texture evolution in the ASR process is briefly outlined.

A fully coupled void damage and Mohr–Coulomb based ductile fracture model in the framework of a Reduced Texture Methodology

This paper deals with the modeling of ductile fracture in the whole range of stress triaxiality. At high stress triaxiality, a classical void damage based model is used. At low stress triaxiality, the Mohr–Coulomb model at the slip system scale combines the resolved normal and shear stresses for each slip plane and direction. These two models are fully coupled in the framework of classical polycrystalline plasticity. A Reduced Texture Methodology (RTM) is used to provide the computational efficiency needed for numerical applications. The RTM approach involves a significant reduction of the number of representative crystallographic orientations. The model is applied to a 6260 thin-walled aluminum extrusion. With RTM, a special hybrid experimental–numerical procedure is used to identify all plasticity parameters (including texture) from mechanical experiments. The fracture parameters are calibrated with fracture experiments on a flat notched tensile specimen and the so-called butterfly shear specimen. Fractographic examinations show a combination of dimples and large smooth areas in the notched specimens (mixed fracture) and flat smooth areas only in the shear specimens. It highlights the need of combined fracture models. With the embedded new fracture model, finite element analyses of the notched specimen can model the through-the-thickness slant fracture propagating from the center towards the edges. Because of the very large strains in the shear specimen tests/analyses, small edge cracks first appear in the tensile areas before main shear cracks initiate and propagate along the width of the specimen. The experimental and numerical results are in good agreement with regard to fracture strains and locations, macroscopic and microscopic features.

Modeling of large strain multi-axial deformation of anisotropic metal sheets with strength-differential effect using a Reduced Texture Methodology

This paper works on the macroscopic modeling of the anisotropic plasticity of a 6260-T6 thin-walled aluminum extrusion with a focus on the large strain multi-axial deformation with Strength-Differential Effect (SDE). Based on the framework of the self-consistent polycrystalline plasticity, the recently developed Reduced Texture Methodology (RTM) (Rousselier et al., 2012) is employed to provide the computational efficiency needed for industrial applications while keeping the physically-based nature of the plasticity model. In particular, the new model features a novel hardening law at slip-system level to better capture large strain behaviors, as well as a generic method designed to describe the stress/strain history effect. All model parameters (including texture) are identified from mechanical experiments using a special optimization procedure. An extensive experimental program covering more than 30 distinct multi-axial stress states with both proportional and non-proportional loadings is used to calibrate and validate the present model. Both full- and reduced-thickness specimens are tested to capture the through-thickness heterogeneity of texture and grain size. It is shown that the present model predicts well the stress–strain responses in most of the multi-axial loading conditions which have been tested. Moreover, the model is able to capture various interesting behaviors of the present material during plastic deformation, including anisotropy, through-thickness heterogeneity, SDE of tension/compression or shear, and cross-hardening during non-proportional loadings. Furthermore, successful simulation of two structural level tests including a circular punch indentation and a three-point bending shows the applicability and potential of the new model in industrial practices.

A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms

Together with slip, deformation twinning and de-twinning are the plastic deformation mechanisms in hexagonal close packed (HCP) crystals, which strongly affect texture evolution and anisotropic response. As a consequence, several twinning models have been proposed and implemented in the existing polycrystalline plasticity models. De-twinning is an inverse process with respect to twinning, which is relevant to cycling, fatigue and complex loads but is rarely incorporated into polycrystalline plastic models. In this paper, we propose a physics-based twinning and de-twinning (TDT) model that has the capability of dealing with both mechanisms during plastic deformation. The TDT model is characterized by four deformation mechanisms corresponding to twin nucleation, twin growth, twin shrinkage and re-twinning. Twin nucleation and twin growth are associated with deformation twinning, and twin shrinkage and re-twinning are associated with de-twinning. The proposed TDT model is implemented in the Elasto-Visco-Plastic Self-Consistent (EVPSC) model. We demonstrate the validity and the capability of the TDT model by simulating cyclic loading of magnesium alloys AZ31B plate and AZ31 bar. Comparison with the measurements indicates that the TDT model is able to capture the key features observed in experiments, implying that the mechanical response in the simulated materials is mainly associated with twinning and de-twinning.

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.

A hybrid crystal plasticity and phase transformation model for high carbon steel

Presence of retained austenite in two-phase steels can have a significant effect on the response of the material. The current state-of-the-art in multi-phase modeling of polycrystalline plasticity has limits on scaling, explicit phase modeling, and tracking multiple plasticity types. To address these issues, a hybrid material model is developed for high-carbon steels. The model can account for crystal plasticity of martensite and stress-assisted transformation from austenite to martensite in dual-phase high-carbon steel. The parameters of the model are calibrated to experimental stress-strain and volumetric transformation strain data. The combination of scalability and multiple phase representation gives a useful tool for the investigation of two-phase high-carbon steel behavior.

Twinning and de-twinning in beryllium during strain path changes

Rolled beryllium samples in the form of rectangular parallelepipeds were deformed at strain rates of 0.001/s and 5/s through multiple strain paths. Samples were initially deformed in-plane nominally −0.22 in compression at a rate of 5/s to populate the microstructure with twins and then reoriented and deformed a second time either in the through-thickness direction or the other in-plane direction. The microstructure (texture and internal strain) were monitored through in-situ and ex-situ diffraction measurements using neutron diffraction on the HIPPO diffractometer at LANSCE, and high energy X-ray diffraction on the 1-ID-C beamline at the APS. Twin reversal is observed when the sample is reoriented and deformed a second time in the TT direction. The twin reversal is strain rate independent in contrast to the strong strain rate dependence observed during twinning in beryllium. Deformation twinning is also observed during secondary compression in the second in-plane direction, but from the current data set we cannot determine with certainty if these twins originate from the parent orientation or the twins formed during primary in-plane compression. As a whole, this data set creates a very demanding test for the development of polycrystalline plasticity models of deformation in hexagonal metals.

On the determination of single-crystal plasticity parameters by diffraction: optimization of a polycrystalline plasticity model using a genetic algorithm

A genetic algorithm was implemented in order to optimize the selection of parameters within a polycrystalline plasticity model. Previously collected experimental data from tests performed on textured Zircaloy-2, consisting of macroscopic flow curves, lattice strains and Lankford coefficients, all measured in both tension and compression in three principle directions of a plate, were reproduced by the model. The results obtained were found to be comparable to prior attempts to optimize the model parameters manually.

Hierarchical multi-scale modeling of texture induced plastic anisotropy in sheet forming

In this paper we present a Hierarchical Multi-Scale (HMS) model of coupled evolutions of crystallographic texture and plastic anisotropy in plastic forming of polycrystalline metallic alloys. The model exploits the Finite Element formulation to describe the macroscopic deformation of the material. Anisotropy of the plastic properties is derived from a physics-based polycrystalline plasticity micro-scale model by means of virtual experiments. The homogenized micro-scale stress response given by the micro-scale model is approximated by an analytical plastic potential function. The methods to reconstruct the plastic potential upon a sufficient change of the crystallographic texture are discussed. A dedicated stress integration scheme is elaborated to utilize the hierarchy of the models. Cup drawing from circular blanks is considered as an example of sheet forming process. The results from the HMS simulations with updating of texture and anisotropy are compared to the outcomes of the FE model assuming constant anisotropy. Experimental verification of the HMS model is provided for two steel grades and one aluminum alloy. An assessment of the texture evolution calculated by the HMS model reveals very high reliability of the predictions. Macroscopic cup profiles obtained by the HMS model show good agreement with the experiment. A substantial improvement of the predicted cup profile is found for one of the investigated steels. The origin of this enhancement is discussed in the context of evolving plastic anisotropy.

A regularized multi-laminate-like plasticity scheme for poly-crystals, applied to the FCC structure

Poly-crystalline plasticity has been formally modeled in [1], [2] using a globally Regularized Schmid Law at the aggregate scale. The description of multi-planar slip as a Multi-Laminate-like structure was shown likely to allow the simplifying use of the Transformation Field Analysis as homogenization framework. So far, numerical simulations of the relevancy of this model both for heterogeneous single crystals and for poly-crystals have only been reported for 2D situations of limited sets of pseudo crystals, each restricted to bi-planar slip at most. The present work reports a “full-size” application of this modeling for 3D aggregates of FCC crystalline domains which confirms that the modeling scheme provides a relevant estimate for the overall plastic behavior of poly-crystals.

Study on the effects of polycrystal grain orientations on indentation hardness

The effects of polycrystal grain orientations on the indentation hardness were studied by both the experimental investigation and numerical simulation. The surface grain orientations of the sample were measured using the electron back scatter diffraction (EBSD) technique, and are divided into three types of grains according to the characteristics of orientations. The indentation experiment was carried out on the surface grains with various orientations as the same direction of the indenter axis. According to the polycrystalline plastic forming theory, a new finite element method (FEM) model was established and the indentation processes on the grains with orientations of [111] and [100] were numerically simulated. By comparing the hardness from simulation results with those of experiments, the new FEM model considering grain orientations was validated. The forming mechanism of the contour during indentation on surface grains with different orientations is also discussed in the study.

Hybrid Micro‐Macro‐Modeling of Evolving Anisotropies and Length Scales in Finite Plasticity of Polycrystals

AbstractThe paper focuses on an efficient multiscale approach to the description of evolving anisotropies in polycrystals. The predictive description of complex overall effects needs multiscale methods, taking into account basic ingredients of the material microstructure by model‐inherent scale‐bridging techniques. Straightforward homogenization‐based multiscale methods, such as FEM2 type two‐scale bridgings, are too time consuming for the solution of real engineering problems. A computationally manageable approach is provided by hybrid micro‐macro‐modeling techniques, which combine a purely macroscopic modeling with selected microstructural bridging techniques. Of particular importance are crystal reorientation mechanisms, which cause texture‐based anisotropies at the macroscale. The coupling is realized by homogenization‐based definitions of macroscopic structural tensors, which account for the evolving orientation texture. A crucial aspect is the combination of this hybrid texture modeling with further anisotropy effects, caused by dislocation‐structures. They are mainly responsible for hardening effects related to changes of the strain path. Furthermore, a particular account is taken on size effects and length scales by embedding the hybrid modeling technique into an extended theory of gradient‐plasticity. This results in a computationally efficient hybrid two‐scale model for polycrystalline plasticity, whose capability is demonstrated by means of representative benchmarks. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Microstructure-sensitive extreme-value probabilities of high-cycle fatigue for surface vs. subsurface crack formation in duplex Ti–6Al–4V

The distributions of the extreme-value driving force(s) for surface vs. subsurface fatigue crack formation (nucleation and early growth) in high-cycle fatigue are evaluated for a microstructure variant of duplex Ti–6Al–4V. In polycrystalline metals, previous work has explored estimation of the driving force(s) for fatigue crack formation at the scale of the grains by computing non-local fatigue indicator parameters (FIPs) based on the cyclic plastic strain averaged over domains on the length scale of the grains. Instantiated statistical volume elements (SVEs), which sample the distributed microstructure attributes of interest for a given material system, can be simulated via the finite element method with embedded polycrystalline plasticity models to estimate the distributed plasticity and resulting FIPs. This strategy of simulating multiple SVEs is in contrast to the simulation of a single representative volume element which is typically untenably large for extreme-value distributions of microstructure attributes or response variables. In this work, multiple SVEs are instantiated with both traction-free (i.e. surface) boundary conditions and fully periodic (i.e. subsurface) boundary conditions. In addition to estimating the extreme-value distributions of the FIPs, newly introduced extreme-value marked correlation functions are applied to characterize the coupled crystallographic microstructure attributes (e.g. grain size, grain orientation, grain misorientation) that most influence the extreme-value distributions of the FIPs. It is shown that there is overlap in the distributions of the driving forces for surface vs. subsurface crack formation in the low to moderate range of failure probability based on FIPs; however, at higher failure probability levels, the driving forces are highest for surface crack formation. The overlap in the distributions of the driving forces for fatigue crack formation in the low to moderate probability range may assist in describing the competing surface vs. subsurface failure modes that are observed experimentally.

Macroscopic plasticity modeling of anisotropic aluminum extrusions using a Reduced Texture Methodology

This paper deals with the modeling of the plasticity of extruded aluminum 6260-T6 at the macroscopic level. The model is based on the framework of classical polycrystalline plasticity. A Reduced Texture Methodology (RTM) is used to provide the computational efficiency needed for industrial applications. The RTM approach involves a significant reduction of the number of representative crystallographic orientations. Furthermore, a special hybrid experimental–numerical procedure is used to identify all model parameters (including texture) from mechanical experiments. The experimental program includes uniaxial tensile experiments for different material orientations. Due to the heterogeneity in texture and grain size along the thickness direction of the 2mm thick extruded material, specimens of full- and reduced thickness are prepared. Uniaxial compression–tension experiments are completed with the help of an anti-buckling device. The mechanical response of full-thickness specimens is modeled using 12 crystallographic orientations. Only eight distinct grain orientations are required to obtain satisfactory predictions for the reduced-thickness specimens with the same set of hardening parameters. The models describe well the stress–strain curves and Lankford ratios for all directions. It is found that the computed reduced textures are in good agreement with EBSD measurements. The 8-grain model is also validated for non-proportional loading paths in the space of tension and shear. Simulations of punch experiments are performed to further validate the model and to demonstrate the computational efficiency of the RTM based polycrystalline plasticity model in structural applications.

The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity

The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity

The single-slip hypothesis revisited: Crystal-preferred orientations of sheared quartz aggregates with increasing strain in nature and numerical simulation

This study discusses the fabric development in naturally sheared quartz aggregates in comparison to results from texture modeling according to the polycrystalline plasticity theory with particular emphasis on the formation of a single c-axis maximum. The investigated natural shear zone samples were deformed at about 650 ± 50 °C with increasing strain up to γ ≈ 14 and show dynamic recrystallization microstructures of grain boundary migration recrystallization. Neutron diffraction texture analysis results in c-axis pole figures with a single maximum at the periphery of the pole figure. This maximum does not align with the shear plane normal towards higher strain, but rotates towards an inclined orientation in accordance with the sense of shear. Such a rotation is inconsistent with the single-slip hypothesis and suggests that the formation of this c-axis pattern is controlled by multi-slip on several slip systems. Based on the polycrystalline plasticity theory, this quartz fabric can develop if combined { 10 1 ¯ 1 } 〈 1 2 ¯ 10 〉 {r}<a>, { 1 ¯ 011 } 〈 1 2 ¯ 10 〉 {z}<a> and { 10 1 ¯ 1 } 〈 1 2 ¯ 10 〉 prism<a> slip dominates and must not be related to the commonly proposed ( 0001 ) 〈 1 2 ¯ 10 〉 basal<a> slip. The multi-slip texture development is in agreement with the shear sense interpretation from the asymmetry between well-defined quartz fabrics and the foliation. For dominant ( 0001 ) 〈 1 2 ¯ 10 〉 basal<a> slip in quartz and γ > 2, numerical simulations predict a single peripheral maximum perpendicular to the shear plane and two a-maxima with a ∼30°-inward position parallel to the shear plane. This simulation corresponds to naturally observed CPO patterns of quartz formed at different deformation conditions and it is in agreement with the single-slip hypothesis. Hence, our combined natural and numerical data suggest that the single-slip hypothesis is a possible explanation for a single c(0001)-maximum but not universally true.

Modeling texture evolution during rolling process of AZ31 magnesium alloy with elasto-plastic self consistent model

To gain a better understanding about texture evolution during rolling process of AZ31 alloy, polycrystalline plasticity model was implemented into the explicit FE package, ABAQUS/Explicit by writing a user subroutine VUMAT. For each individual grain in the polycrystalline aggregate, the rate dependent model was adopted to calculate the plastic shear strain increment in combination with the Voce hardening law to describe the hardening response, the lattice reorientation caused by slip and twinning were calculated separately due to their different mechanisms. The elasto-plastic self consistent (EPSC) model was employed to relate the response of individual grain to the response of the polycrystalline aggregate. Rolling processes of AZ31 sheet and as-cast AZ31 alloy were simulated respectively. The predicted texture distributions are in qualitative agreement with experimental results.