A physically based phenomenological model for deformation twinning in magnesium alloy

A partial differential equation is developed that captures the evolution of key characteristics of tensile twinning in magnesium base alloys. The objective is to provide a framework for ascertaining the effects of hardening – due to grain refinement, precipitation and dislocation substructure – on twin volume fraction, thickness and length. The model is developed with the help of observations made on alloy AZ31. It is shown that it is necessary to consider the nucleation of twins at locations where neighbouring twins impinge on the grain boundary. The model provides a reasonable approximation for the role of grain size on twinning. It predicts a period of low apparent work hardening following yielding and shows that this should be more extensive for finer grain sizes, in agreement with experiment. Finally, some predictions are made on the effect of changing the resistance to twinning.

Grain boundary segregation in Fe-Mn-C twinning-induced plasticity steels studied by correlative electron backscatter diffraction and atom probe tomography

We report on the characterization of grain boundary (GB) segregation in an Fe-28Mn-0.3C (wt.%) twinning-induced plasticity (TWIP) steel. After recrystallization of this steel for 24 h at 700 °C, ∼50% general grain boundaries (GBs) and ∼35% Σ3 annealing twin boundaries were observed (others were high-order Σ and low-angle GBs). The segregation of B, C and P and traces of Si and Cu were detected at the general GB by atom probe tomography (APT) and quantified using ladder diagrams. In the case of the Σ3 coherent annealing twin, it was necessary to first locate the position of the boundary by density analysis of the atom probe data, then small amounts of B, Si and P segregation and, surprisingly, depletion of C were detected. The concentration of Mn was constant across the interface for both boundary types. The depletion of C at the annealing twin is explained by a local change in the stacking sequence at the boundary, creating a local hexagonal close-packed structure with low C solubility. This finding raises the question of whether segregation/depletion also occurs at Σ3 deformation twin boundaries in high-Mn TWIP steels. Consequently, a previously published APT dataset of the Fe-22Mn-0.6C alloy system, containing a high density of deformation twins due to 30% tensile deformation at room temperature, was reinvestigated using the same analysis routine as for the annealing twin. Although crystallographically identical to the annealing twin, no evidence of segregation or depletion was found at the deformation twins, owing to the lack of mobility of solutes during twin formation at room temperature.

A constitutive model of the deformation behaviour of twinning induced plasticity (TWIP) steel at different temperatures

The mechanical behaviour of Fe-18Mn-0.6C-1Al (wt%) TWIP steel was modelled in the temperature range from room temperature to 400°C. The proposed constitutive model was based on the Kocks-Mecking-Estrin (KME) model. The model parameters were determined using extensive experimental measurements of the physical parameters such as the dislocation mean free path and the volume fraction of twinned grains. More than 100 grains with a total area of ~300μm2 were examined at different strain levels over the entire stress-strain curve. Uniaxial tensile deformation of the TWIP steel was modelled for different deformation temperatures using a modelling approach which considers two distinct populations of grains: twinned and twin-free ones. A key point of the work was a meticulous experimental determination of the evolution of the volume fraction of twinned grains during uniaxial tensile deformation. This information was implemented in a phase-mixture model that yielded a very good agreement with the experimental tensile behaviour for the tested range of deformation temperatures. © 2014 Elsevier B.V.

Contribution of twinning to low strain deformation in a Mg alloy

Deformation twinning plays an important role in the yielding of extruded magnesium alloys, especially when loaded in compression along the extrusion axis. The magnitude of this contribution is not accurately known. The present study employs electron backscatter diffraction to reveal the influence of grain orientation on twin-volume fraction for alloy AZ31 tested in compression to strains between 0.008 and 0.015. For these strains, it is seen that approximately 45 pct of the deformation can be attributed to "tensile" twinning. The variation of twin-volume fraction over different orientation classes correlates closely with the maximum Schmid factors for both tensile twinning and basal slip. These effects are readily explained quantitatively using a mean field crystal plasticity model without recourse to stochastic effects. Encouraged by this, we introduce an analytical approximation based on the uniformity of (axial) work. © 2013 The Minerals, Metals & Materials Society and ASM International.

Surface wrinkling of the twinning induced plasticity steel during the tensile and torsion tests

'Heterogeneous twinning' is defined as plastic deformation due to the formation and progress of twins resulting in surface wrinkles on the deforming part when the initial grain size is relatively large compared to the typical size of the part. In the case of a Twinning Induced Plasticity (TWIP) steel with an initial grain size of ~160. m, the heterogeneous twinning generated visible wrinkles, an orange peel effect, under medium uni-axial strains. The heterogeneous twinning did not occur in the material subjected to high shear strains. The complications resulting from this phenomenon on strain hardening characterization of the TWIP steels using two commonly used mechanical tests, tensile and torsion are discussed along with some experimental aspects of heterogeneous twinning. © 2014.

The correlation between stacking fault energy and the work hardening behaviour of high-mn twinning induced plasticity steel tested at various temperatures

High-Mn Twinning Induced Plasticity (TWIP) steels have superior mechanical properties, which make them promising materials in automotive industry to improve the passenger safety and the fuel consumption. The TWIP steels are characterized by high work hardening rates due to continuous mechanical twin formation during the deformation. Mechanical twinning is a unique deformation mode, which is highly governed by the stacking fault energy (SFE). The composition of steel alloy was Fe-18Mn-0.6C-1Al (wt.%) with SFE of about 25-30 mJ/m2 at room temperature. The SFE ensures the mechanical twinning to be the main deformation mechanism at room temperature. The microstructure, mechanical properties, work hardening behaviour and SFE of the steel was studied at the temperature range of ambient ≤T[°C]≤ 400°C. The mechanical properties were determined using Instron tensile testing machine with 30kN load cell and strain rate of 10-3s-1 and the work hardening behaviour curves were generated using true stress and true strain data. The microstructure after deformation at different temperatures was examined using Zeiss Supra 55VP SEM. It was found that an increase in the deformation temperature raised the SFE resulting in the deterioration of the mechanical twinning that led to decrease not only in the strength but also in the total strain of the steel. A correlation between the temperature, the SFE, the mechanical twinning, the mechanical properties and the work hardening rate was also found. © (2014) Trans Tech Publications, Switzerland.

A double inclusion homogenization scheme for polycrystals with hierarchal topologies: Application to twinning in Mg alloys

The present work introduces a double inclusion elasto-plastic self-consistent (DI-EPSC) scheme for topologies in which crystals can contain subdomains (i.e. twins, etc.). The approach yields a direct coupling between the mechanical response of grains and their subdomains via a concentration relationship on mean fields derived from both the Eshelby and the Tanaka-Mori properties. The latent effect caused by twinning on the mechanical response is observed on both initially extruded and non-textured Mg alloys. For twinned grains, it is shown that deformation system activities and plastic strain distributions within twins drastically depend on the interaction with parent domains. Moreover, a quantitative study on the coupled influence of secondary slip activities on the material response is proposed. © 2014 Published by Elsevier Ltd.

Time and spatial resolution of slip and twinning in a grain embedded within a magnesium polycrystal

Plastic yielding in magnesium alloys frequently involves the initiation of both slip and twinning events. A proper understanding of the phenomenon at the grain level requires knowledge of how these two mechanisms progress and interact over both time and space and what the local resolved stresses are. To date, simultaneous collection of such information has not been achievable. To address this shortfall, we have developed a modified Laue based in situ micro X-ray diffraction technique with an unprecedented combination of time and spatial resolution. A ten-fold reduction in data collection times is realized by the refinement of rapid polychromatic Laue "single-shot" mapping. From single Laue patterns, we extract grain depth information, detect onset of yielding and achieve 2 × 10-4 lattice strain resolution. The technique is employed to examine yielding and twinning in a magnesium grain embedded ∼200 μm below the sample surface. We examine 13 time steps and reveal the following behaviour: initial onset of basal slip, subsequent onset of twinning, development of further accommodation slip and evolution of twin shape and size; along with the corresponding values of local resolved shear stresses. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The effect of high yttrium solute concentration on the twinning behaviour of magnesium alloys

The deformation behaviour of two single phase binary alloys, Mg-5Y and Mg-10Y, have been examined. In compression, two twin types were observed, the common {101¯2} twin as well as the less common {112¯1} extension twin. It is shown that the {112¯1} twin is much less sensitive to solute concentration than the {101¯2} twin, and it is suggested that the simple atomic shuffle of the {112¯1} twin reduces the solute strengthening imparted by Y additions. The common {101¯2} twin showed significant hardening as a result of alloying with Y. An analysis of solute behaviour has indicated that of the four chemical parameters investigated, i.e. atomic size, shear modulus, electronegativity and solute distribution, it appears to be the larger atomic radius of Y compared to Mg that increases the stress required to activate the {101¯2} twin. It is suggested that the large atomic radius inhibits the atomic shuffling process which accompanies the twinning shear in this twin type.

The effect of deformation twinning on stress localization in a three dimensional TWIP steel microstructure

We present an investigation of the effect of deformation twinning on the visco-plastic response and stress localization in a low stacking fault energy twinning-induced plasticity (TWIP) steel under uniaxial tension loading. The three-dimensional full field response was simulated using the fast Fourier transform method. The initial microstructure was obtained from a three dimensional serial sectionusing electron backscatter diffraction. Twin volume fraction evolution upon strain was measured so the hardening parameters of the simple Voce model could be identified to fit both the stress-strain behavior and twinning activity. General trends of texture evolution were acceptably predicted including the typical sharpening and balance between the 1 1 1 fiber and the 1 0 0 fiber. Twinning was found to nucleate preferentially at grain boundaries although the predominant twin reorientation scheme did not allow spatial propagation to be captured. Hot spots in stress correlated with the boundaries of twinned voxel domains, which either impeded or enhanced twinning based on which deformation modes were active locally.

A microstructure based analytical model for tensile twinning in a rod textured Mg alloy

Abstract A model for tensile twinning during the compression of rod textured magnesium is developed based on the idea that these twins nucleate at grain boundaries and that when the twin number density per grain is low these twins readily give rise to the formation of other 'interaction' twins in adjacent grains. Experimental observations of twin aspect ratios measured at a single grain size and twin number densities measured over four grain sizes were used to determine model material parameters. Using these, the model provides reasonable predictions for the observed magnitudes and trends for the following observations:Effect of grain size and stress on twin volume fraction, fractional twin length and the fraction of twin contact.Effect of grain size on the yield stress.Effect of grain size on the general shape of the stress-strain curve at low strains. A parametric study shows the model to be quite robust but that it is particularly sensitive to the value of the exponent assumed for the twin nucleation rate law. It is seen that preventing the formation of interaction twins provides an important avenue for hardening and that the flow stress is also particularly sensitive to the relaxation of the twin back stresses. The model shows the importance of taking microstructure into account when modelling twinning.

Distinguishing between slip and twinning events during nanoindentation of magnesium alloy AZ31

Nanoindentation was performed in selected grain orientations close to [. 112-0] and [. 101-0] in magnesium alloy Mg-3Al-1Zn. The atomic force microscopy (AFM) and electron backscatter diffraction (EBSD) were used to examine the nanoindentation imprint. Two critical events, yielding and pop-in were observed in the depth-load curves. Slip trace analysis suggests that basal slip is responsible for yielding. The following pop-in events at higher loads are associated with the appearance {. 101-2} twins on the surface. The critical resolved shear stress (CRSS) was estimated to be in the range of 220-400. MPa for the initiation of basal slip.