Simulation Of Texture Evolution Research Articles

Phase‐Field Simulation of Texture Evolution in Magmatic Rocks

AbstractThe tool of phase‐field modeling for the prediction of chemical as well as microstructural evolution during crystallization from a melt in a mineralogical system has been developed in this work. We provide a compact theoretical background and introduce new aspects such as the treatment of anisotropic surface energies that are essential for modeling mineralogical systems. These are then applied to two simple model systems—the binary olivine‐melt and plagioclase‐melt systems ‐ to illustrate the application of the developed tools. In one case crystallization is modeled at a constant temperature and undercooling while in the other the process of crystallization is tracked for a constant cooling rate. These two examples serve to illustrate the capabilities of the modeling tool. The results are analyzed in terms of crystal size distributions (CSD) and with a view toward applications in diffusion chronometry; future possibilities are discussed. The modeling results demonstrate that growth at constant rates may be expected only for limited extents of crystallization, that breaks in slopes of CSD‐plots should be common, and that the lifetime of a given crystal of a phase is different from the lifetime of this phase in a magmatic system. The last aspect imposes an inherent limit to timescales that may be accessed by diffusion chronometry. Most significantly, this tool provides a bridge between CSD analysis and diffusion chronometry—two common tools that are used to study timescales of magmatic processes.

Modeling the role of local crystallographic correlations in microstructures of Ti-6Al-4V using a correlated structure visco-plastic self-consistent polycrystal plasticity formulation

This paper presents a multi-level crystal plasticity-based simulation framework for modeling mechanical response and microstructure evolution of Ti-6Al-4V with α-lath/lamellar microstructures. The model is a correlated structure visco-plastic self-consistent (CS-VPSC) formulation linking three scales: a single crystals micro-scale, a lath/lamellar colony meso-scale, and a lath/lamellar aggregate macro-scale. A selected hardening law for the evolution of critical resolved shear stress per slip system used in CS-VPSC is phenomenological. However, it adjusts the resistances of basal and prismatic slip systems based on the geometry of slip transfer between adjacent lamellae. Consistent with experimental evidences, the resolved shear stress on the pyramidal slip planes is dependent not only on the stress in the direction of slip but also on the two orthogonal shear stress components and the three normal stress components (non-Schmid effects). Electron backscatter diffraction (EBSD) data in conjunction with a procedure relying on α→β phase transformation is used to construct paired variants of α-laths/lamellae satisfying their local crystallographic correlations. The procedure fits volume fractions of individual laths/lamellae with the experimental EBSD data and selects a distribution of habit planes between adjacent variants with respect to the loading direction. The simulation framework is applied to interpret the deformation behavior in tension and compression along two sample directions of Ti-6Al-4V fabricated via laser powder bed fusion. Moreover, the model is used to simulate texture evolution during rolling of the material to large strains. It is demonstrated that the model is capable of predicting plastic anisotropy/asymmetry and the concomitant texture evolution. While the model reveals a significant effect of habit plane inclination with respect to the loading direction on yield stress, the comparison of the data and model predictions shows that a random distribution of habit planes fits the flow response. It is further inferred that the tension-compression asymmetry arises from the non-Schmid effects.

Modeling of Crystallographic Texture in Plastic Flow Machining

Plastic flow machining (PFM) is proposed as a new severe plastic deformation (SPD) technique capable of producing ultrafine‐grained sheet metal from bulk sample. Herein, a model is proposed for the three strain paths that the material follows during the PFM extrusion process. The proposed strain paths are justified by modeling the texture evolution in good agreement with the experiments in the three deformation zones. Two polycrystal models are used to simulate texture evolution: the viscoplastic self‐consistent (VPSC) polycrystal approach and the Taylor‐type lattice curvature‐based grain fragmentation (GR) model. The simulations reproduce faithfully all three textures observed experimentally within the sheet. The experimental texture in the zone carrying the smallest strain is obtained with the VPSC approach, whereas in the higher strain region, the GR model reproduced the texture. The two main results of this modeling are as follows: 1) an example is presented for the successful identification of the deformation mode in a new SPD process with the help of the crystallographic texture. 2) At large strains, the VPSC model fails; it is the Taylor deformation‐based GR approach which is able to reproduce the experimental texture evolution.

Simulation of Texture Evolution during Uniaxial Deformation of Commercially Pure Titanium

The evolution of texture in commercially pure (CP) titanium during uniaxial tension and compression through VPSC (Visco-plastic self-consistent) simulation is reported in the present study. CP-titanium was subjected to both uniaxial tension and compression upto 35% deformation. During uniaxial tension, tensile twin of type and compressive twin of type were observed in the samples. However, only tensile twin of type and compressive twin of type was observed in the samples during uniaxial compression. Volume fractions of the twins were increased linearly as a function of percentage deformation during uniaxial tension. Whereas, during uniaxial compression the twinning volume fraction was increased up to 20% deformation and then decreased rapidly on further increasing the percentage deformation. During uniaxial tension, the general t-type textures were observed in the samples irrespective of the percentage deformation. The initial non-basal texture was oriented to split basal texture during uniaxial compression of the sample. VPSC formulation was used for simulating the texture development in the material. Different hardening parameters were estimated through correlating the simulated stress-strain curve with the experimental stress-strain data. It was observed that, prismatic slip operated as the primary deformation mode during uniaxial tension whereas basal slip acquired the leading role during deformation through uniaxial compression. It was also revealed that active deformation modes were fully depending on percentage deformation, loading direction, and orientation of grains.

Evolution of the texture and microstructure in a nickel based superalloy during thermo-mechanical fatigue (TMF), using a modified integrated model and experimental results

Microstructure & texture evolutions in Hastelloy X superalloy during thermo-mechanical fatigue (TMF) were investigated in this research. For this purpose TMF tests were performed in two different ways using linear elastic fracture mechanics (LEFM) and elastic plastic fracture mechanics (EPFM). These methods can produce small and large scale yielding in plane stress mode, respectively. On the base of data obtained in these tests a modified integrated model for prediction and simulation of texture evolution has been proposed. This model consists of a mechanical and a thermal part relating variations of stress and temperature occur during TMF tests. For the mechanical part of the model, a modified Taylor method based on strain partitioning in the grains orientations was used; and for the thermal part of the model, an integrated phased field and Monte Carlo models with harmonic Fourier approach for orientations distribution function (ODF) was used. The effects of Twin boundaries and dispersed secondary phase particles were also considered in the model. The validation tests show a good correlation between experimental results and the proposed model for texture development during TMF. To predict the initiation of unstable crack growth up to failure of the specimen during TMF, a new parameter in the form of reduced critical ODF value has also been introduced in this research.

Evaluation of crystallographic changes and plastic strain ratio in Al alloys

Over the past several decades, extensive research endeavours in the field of crystal plasticity (CP) have led to the development of various Taylor-type homogenisation models enabling simulation of texture evolution during plastic deformation. This contribution provides a brief summary on the quality of deformation texture modelling under various boundary conditions. The crystallographic evolutionary patterns are discussed on the basis of grain interaction phenomena incorporated in the CP calculations. The annealing textures are successfully simulated by considering strain heterogeneities in the particle affected zone and by employing orientation selection during both nucleation and growth stages of recrystallisation. It is shown that the Lankford value profiles can be accurately reproduced by CP calculations on condition of reliable grain statistics.This paper is part of a Themed Issue on Aluminium-based materials: processing, microstructure, properties, and recycling.

Modelling and experimentation of the evolution of texture in an Al-Mg alloy during earing cupping test

Earing and thinning are often the major manufacturing problems occur during deep drawing processes. Thinning occurs when a section of a part undergoes localised deformation, and earing is the formation of wavy edges at the open end of a drawn part that must be trimmed at final stage leading to higher manufacturing costs. The anisotropic mechanical behavior of the initial sheet metal is the predominant source of thinning and earing problems. This work aims to establish a relationship between the properties of a sheet blank and thinning and earing issues during deep drawing by studying the evolution of crystallographic texture throughout the sheet forming process using crystal plasticity simulation modelling and experimental measurements. Firstly, to understand the impact of individual texture components on the mechanical properties of the material, Lankford coefficients for FCC crystal structure during uni-axial tensile loading were analysed using Visco-Plastic Self Consistent (VPSC) model. Subsequently, Finite Element (FE) analyses were carried out to study the effect of initial state of the material on earing and thinning issues occurred during deep drawing. It was observed that the existing Cube and Goss texture components evolved during annealing heat treatments were responsible for the generation of troughs along 45° to the rolling direction (RD) and peaks along the transverse direction (TD), respectively. Optical 3D scanning of a manufactured part confirmed that earing is less prominent in the case of as-rolled and shear-formed condition due to weakening of Cube and Goss texture components. Furthermore, a combination of FE simulation and the VPSC model has been used to simulate texture evolution during a standard earing cupping test at various points of interest. The results of texture evolution simulations were compared to those measured experimentally by electron backscatter diffraction (EBSD), and a good qualitative agreement is achieved.

A miniature physical simulator for pilgering

Pilgering is a complex incremental manufacturing process for seamless tubes. In this work, a miniature physical simulator for pilgering was designed and fabricated. This miniature simulator employs a grooved roll-die and a mandrel and can impose controlled reductions in both tube diameter and wall thickness. Pilgering deformation over a range of ratios of reductions in wall thickness and in tube diameter, known as the Q-factor, was imposed on hemi-cylindrical zirconium alloy specimens. The influence of the Q-factor on the microstructure and deformation texture of the deformed specimens was quantified. A polycrystal plasticity calculation based on the binary tree model was used to simulate texture evolution during the simulated pilgering process. The computer model quantitatively captured the variation with Q of the Kearns factors, as measured in the physically simulated specimen. The small differences noticed between the predicted and experimental final textures point to unaccounted transverse components of the flow field. These observations suggest that physical and/or computer simulations can form the basis of a rapid methodology for tool selection to realize prescribed post-pilgering textures.

Simulation of texture evolution and deformation mechanism in Mg-3Al-1Zn alloy during uniaxial compression

The effects of starting texture on he flow curves, and microstructure and texture evolutions of AZ31 (Mg-3Al-1Zn-0.3Mn in wt.%) alloy during uniaxial compression at room temperature have been investigated by experiments and simulations. Two kinds of cylindrical compression samples were cut from the AZ31 extruded rod: one was cut with the compression direction parallel to the extruded direction (ED), and the other was cut with the compression axis perpendicular to the ED. The samples were termed as C//ED sample and C⊥ED sample, respectively. The results indicate that the general characteristics of flow curves and texture evolutions in both C⊥ED and C//ED samples during compression can be well explained by the relative activities of deformation mechanisms, which show a strong orientation dependence on the initial textures and the current texture. A significant yield behavior can be induced by {10-12} twinning at the starting deformation, and the lower yield stress in C⊥ED sample can be enhanced by the high activity of basal slip. The work hardening behavior is related to the activities of basal slip, pyramidal slip, {10-12} twinning, as well as {10-11} twinning. However, the activity of prismatic slip is insensitive to the starting texture, and mostly negligible in all samples.

Simulation of texture evolution in magnesium alloy: Comparisons of different polycrystal plasticity modeling approaches

Three polycrystal plasticity modeling approaches: Taylor model, self-consistent (SC) model, and crystal plasticity based finite element method (CPFEM) have been mainly applied to simulate texture evolution of magnesium alloy. To examine the influence of different approaches on simulated results, comparisons between material point simulation based on Taylor model and that based on elastic–plastic self consistent (EPSC) model are conducted. Furthermore, comparisons between CPFEM based on single crystal scheme and that based on polycrystal scheme are also carried out. In addition, all the formulations are validated by comparing the predicted textures with experimental results during uniaxial compression for AZ31 magnesium alloy.

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.

Simulation of texture evolution during plastic deformation of FCC, BCC and HCP structured crystals with crystal plasticity based finite element method

Two alternative formulations of single crystal plasticity model were introduced respectively and two schemes were implemented in the explicit FE code with software ABAQUS/Explicit by writing the user subroutine VUMAT. Meshes containing material data were created with solid elements. Each element represented an individual grain, and the grain orientations were explicitly stored and updated at each increment. Tangential modulus method was employed to calculate the plastic shear strain increment of deformation systems in combination with a hardening law to describe the hardening responses. Both two developed subroutines were applied to simulate the texture evolution during the uniaxial tension of copper (FCC), cold rolling of IF steel (BCC) and uniaxial compression of AZ31 magnesium alloy (HCP). The predicted texture distributions are in qualitative agreement with the experimental results.

Simulation of texture evolution and macroscopic properties in Mg alloys using the crystal plasticity finite element method

A crystal plasticity finite element method (CPFEM), considering both crystallographic slip and deformation twinning, was used to simulate texture evolution and macroscopic properties of AZ31 Mg alloys. To capture grain reorientation due to deformation twinning in twin-dominated deformation, a predominant twin reorientation (PTR) model was considered. The validity of the proposed theoretical framework was demonstrated through comparison of simulated results, such as texture evolution and macroscopic properties, with the experimental results and measurements. The simulation of texture evolution and macroscopic properties of AZ31 Mg alloys was shown to be in good agreement with the corresponding experimental results.

Simulation of strain-softening behaviors in an AZ31 Mg alloy showing distinct twin-induced reorientation before a peak stress

To investigate strain-softening behavior during plastic deformation of an AZ31 Mg alloy, cylindrical specimens were compressed in a rolling direction at 300 °C. Experimental evidence revealed that an inhomogeneous microstructure evolved due to the softening behavior associated with deformation at elevated temperatures. The large grains that reoriented as a result of deformation twinning were free of dynamic recrystallization (DRX). Fine grains nucleated at grain boundaries of grains were deformed by a slip-dominated mechanism, which accommodated the external strain. A visco-plastic self-consistent (VPSC) polycrystal model was used to simulate softening of the flow stress curve and texture evolution during uniaxial compression. A softening scheme was implemented in the polycrystal model to predict the softening phenomenon and texture evolution after the peak stress. The original VPSC model was modified to simulate texture evolution in an AZ31 Mg alloy that exhibited twin-dominated deformation before the peak stress.

Three-dimensional numerical simulations of multi-pass equal-channel angular pressing by a variation difference method and comparison with experiment

A variation-difference method (VDM) of solving continuum mechanics equations has been implemented for simulation of the equal-channel angular pressing (ECAP) process. Application of the developed DRAKON code (VNIIEF, Russia) for numerical study of multi-pass ECAP allowed processes of severe plastic deformation to be described in three-dimensional (3D) continuum approximation in the field of low strain rates and high-pressure levels in terms of contact interaction. The influence of ECAP processing parameters on stress–strain field distribution over the ECAP sample's cross-section is studied in 3D formulation. The model validation is performed by comparison of simulation results with various experimental data. Deformation histories provided by DRAKON were used together with a polycrystal plasticity model (viscoplastic self-consistent model) allowing simulation of texture evolution during ECAP with account to macro-parameters of the process. It is shown that the VDM-based model possesses good predictive capabilities for 3D simulation of severe plastic deformation processes involving strain-path changes.

Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations

We present a detailed description of the numerical implementation, within the widely used viscoplastic self-consistent (VPSC) code, of a rigorous second-order (SO) homogenization procedure for non-linear polycrystals. The method is based on a linearization scheme, making explicit use of the covariance of the fluctuations of the local fields in a certain linear comparison material, whose properties are, in turn, determined by means of a suitably designed variational principle. We discuss the differences between this second-order approach and several first-order self-consistent (SC) formulations (secant, tangent and affine approximations) by comparing their predictions with exact full-field solutions. We do so for crystals with different symmetries, as a function of anisotropy, number of independent slip systems and degree of non-linearity. In this comparison, the second-order estimates show the best overall agreement with the full-field solutions. Finally, the different SC approaches are applied to simulate texture evolution in two strongly heterogeneous systems and, in both cases, the SO formulation yields results in better agreement with experimental evidence than the first-order approximations. In the case of cold-rolling of low-SFE fcc polycrystals, the SO formulation predicts the formation of a texture with most of the characteristic features of a brass-type texture. In the case of polycrystalline ice, deforming in uniaxial compression to large strain, the SO predicts a substantial and persistent accommodation of deformation by basal slip, even when the basal poles become strongly aligned with the compression direction.

Simulation of Texture Evolution during Hot Rolling Deformation in FCC Materials

The evolution of hot rolling texture in FCC materials has been simulated numerically using a visco-plastic self-consistent (VPSC) polycrystal model. A finite element (FE) analysis with ABAQUS/StandardTM was conducted to evaluate the deformation gradients during hot rolling deformation. In order to capture crystallographic rotation during hot rolling deformation, an octahedral slip system was considered in a microscopic hardening model. The FE analysis with the VPSC polycrystal simulations successfully predicted the inhomogeneous texture development through the thickness direction in the hot-rolled Al-5wt%Mg alloy sheets.

Simulation of deformation twins and deformation texture in an AZ31 Mg alloy under uniaxial compression

To investigate deformation twins and the evolution of deformation texture during plastic deformation, uniaxial compression tests on a hot-rolled AZ31 Mg alloy were carried out at 200 °C. Cylindrical specimens were then compressed in both the rolling and the normal directions. The findings revealed that texture evolution, work hardening and macroscopic anisotropy are strongly dependent on the loading direction. Electron backscattered diffraction analysis was used to examine the orientation of parent grains and twin bands in the AZ31 Mg alloy under uniaxial compression. A viscoplastic self-consistent model (VPSC) was theoretically employed to calculate the relative activities of slip and twin systems in polycrystalline hexagonal aggregates under uniaxial compression. Each deformed grain exhibited an independent number and type of twin variants under uniaxial compression. Neutron diffraction was used to measure the macroscopic texture of the AZ31 Mg alloy. The VPSC model was used to simulate texture evolution, work hardening and macroscopic anisotropy during the uniaxial compression. A modified predominant twin reorientation (PTR) scheme was suggested to explain the gradual increase in twin volume in deformed grains.

Homogenization estimates for texture evolution in halite

In this work, the recently developed “second-order” self-consistent method [Liu, Y., Ponte Castañeda, P., 2004a. Second-order estimates for the effective behavior and field fluctuations in viscoplastic polycrystals. J. Mech. Phys. Solids 52 467–495] is used to simulate texture evolution in halite polycrystals. This method makes use of a suitably optimized linear comparison polycrystal and has the distinguishing property of being exact to second order in the heterogeneity contrast. The second-order model takes into consideration the effects of hardening and of the evolution of both crystallographic and morphological texture to yield reliable predictions for the macroscopic behavior of the polycrystal. Comparisons of these predictions with full-field numerical simulations [Lebensohn, R.A., Dawson, P.R., Kern, H.M., Wenk, H.R., 2003. Heterogeneous deformation and texture development in halite polycrystals: comparison of different modeling approaches and experimental data. Tectonophysics 370 287–311], as well as with predictions resulting from the earlier “variational” and “tangent” self-consistent models, included here for comparison purposes, provide insight into how the underlying assumptions of the various models affect slip in the grains, and therefore the texture predictions in highly anisotropic and nonlinear polycrystalline materials. The “second-order” self-consistent method, while giving a softer stress-strain response than the corresponding full-field results, predicts a pattern of texture evolution that is not captured by the other homogenization models and that agrees reasonably well with the full-field predictions and with the experimental measures.

Modeling Texture Evolution during Rolling of Magnesium Alloy AZ31

Due to crystallographic texture rolled magnesium sheets exhibit strongly anisotropic and asymmetric plastic behavior. Therefore the simulation of texture evolution during manufacturing is a prerequisite for the prediction of the material properties. For this purpose we coupled the viscoplastic self-consistent (VPSC) model with the commercial finite element code ABAQUS/Explicit®. As magnesium sheets are usually produced by hot rolling the VPSC model was supplemented with a simple model for recrystallization. This model is able to describe the softening behavior of the magnesium alloy AZ31 during hot compression and allows us to simulate the development of the typical basal texture during hot rolling of this alloy.