Twin Propagation Research Articles

Discrete twin evolution in Mg alloys using a novel crystal plasticity finite element model

This paper implements the image-based crystal plasticity FE model with explicit twin evolution, developed in [1, 2], to study mechanisms of deformation and twinning in polycrystalline microstructures of the Mg alloy AZ31. The physics of twin nucleation, propagation and interaction with slip systems are represented in the constitutive formulation and implemented in a FE code. Image-based simulations are conducted for statistically equivalent representative volume elements, for which the morphological and crystallographic parameters are statistically equivalent to those observed in EBSD data of experimental samples. Validation studies show satisfactory agreement of the stress-strain response with experiments. Analyses of deformation in AZ31 reveal various deformation mechanisms captured by the model. An important contribution of this paper is in the exploration of various twin-related local phenomenon and deformation mechanisms using tricrystalline and polycrystalline models. Several underlying mechanisms are revealed through these simulations.

A study on the combined effect of in-situ (TiC-TiB2) reinforcement and aging treatment on the yield asymmetry of magnesium matrix composite

The present work aims to study the individual as well as the combined effect of in-situ particles and precipitates on the tension-compression asymmetricity of AZ91 magnesium (Mg) alloy and AZ91 + TiC-TiB2 Mg matrix composites. Investigations have been done on four different material conditions: (a) alloy without particles or precipitates, (b) alloy with precipitates, (c) composite with particles, (d) composites with both particles and precipitates. Both the particle and precipitate significantly contribute towards lowering of tension to compression yield asymmetry. These particles/precipitates increase the critical stress for twinning by exerting a back stress which hinders the twin propagation. Due to decrease in the twinning propensity, the tension to compression asymmetry reduces from 1.30 (at base condition) to 1.04 (peak aged condition of the composite). This phenomenon has been experimentally validated by means of tension and compression tests and the results have been correlated with the pre and post-deformation microstructures.

Crystallographic characters of {11¯22} twin-twin junctions in titanium

contraction twins that are commonly activated in α-titanium interact to each other and form three types of twin–twin junctions (, , TTJs) corresponding to the crystallography of six twin variants (i = 1,2, … , 6). We detected 243 TTJs in rolled pure α-titanium sheets. Electron backscatter diffraction analysis reveals that TTJs are profuse, 79.8% among three types while and TTJs take up 17.7 and 2.5%. Twin transmission does not occur. Consequently, boundaries associated with twin–twin interactions block twin propagation and influence twin growth. We explain structural features of TTJs according to the Schmid factor analysis and the reaction mechanism of twinning dislocations. The knowledge regarding TTJs provides insight for improving the predictive capability of meso/macro-scale crystal plasticity models for hexagonal metals.

Twin-interface interactions in nanostructured Cu/Ag: Molecular dynamics study

The interaction of deformation twins with interfaces in nanostructured Cu/Ag is studied using molecular dynamics simulations. The influence of the interface structure on twin nucleation, propagation and thickening is analysed, and the role of the misfit interfacial dislocations mesh is detailed. In particular, we show that the interface can induce, directly or indirectly via Lomer dislocations, the nucleation of twinning dislocations. A thorough description of the involved mechanisms is given. Through this atomic scale approach, our study offers some useful understanding of the mechanical twinning process in nanolamellar composites, where twinning appears to be a common plasticity mechanism.

Anomalous hardening in magnesium driven by a size-dependent transition in deformation modes

Here, we report a comprehensive study that combines in situ scanning electron microscopy experiments and atomistic simulations to quantify the effect of crystal size on the transformation in deformation modes in a-axis oriented Mg single crystals at room temperature. The experimental results indicate that the deformation is dominated by the nucleation and propagation of tensile twins. The stress required for twin propagation was found to increase with decreasing sample size, showing a typical “smaller is stronger” behavior. Furthermore, an anomalous increase in strain hardening is first reported for microcrystals having diameters larger than ∼18 μm, which is induced by twin-twin and dislocation-twin interactions. The hardening rate gradually decreases toward the bulk response as the microcrystal size increases. Below 18 μm, deformation is dominated by the nucleation and propagation of a single tensile twin followed by basal slip activity in the twinned crystal, leading to no apparent hardening. In addition, molecular dynamics simulations indicate a transition from twinning mediated plasticity to dislocation mediated plasticity for crystal sizes below a few hundred nanometers in size. A deformation mechanism map for twin oriented Mg single crystals, ranging from the nano-scale to bulk scale is proposed based on the current simulations and experiments. The current predicted size-affected deformation mechanism of twin oriented Mg single crystals can lead to better understanding of the competition between dislocations plasticity and twinning plasticity.

A dislocation density based model for twinning induced softening of TWIP steel

Twinning induced softening (i.e. stress drop) is a non-negligible deformation characteristic related to twin nucleation, propagation and growth (TNPG) of twinning-induced plasticity (TWIP) steel single crystals. However, the mesoscale physical-based TNPG models considering the softening effect are applied at the crystal level and cannot provide insight into the dislocation activity within grain or at grain boundary. In this paper, a dislocation-density-based constitutive model was proposed to describe the evolution of the TNPG process based on dislocation theory integrating the twin-energy pathway. Then the model was employed to reflect the deformation mechanisms of TWIP steel single crystal in plastic deformation processes. The results show the twinning induced softening was caused by different critical shear stress for twinning (CSST) nucleation and growth, and the twin nucleation and growth were conducted by partial dislocation emission from an inner source and a surface source, respectively. The CSST for nucleation was larger than that for growth since no additional faulting energy had been introduced in twin growth. Furthermore, different leading partial dislocations were obtained under tension and compression even with the same orientation, which resulted in the tension-compression asymmetry in twinning nucleation.

Prediction of deformation twinning statistics in zirconium using the Taylor, ALAMEL and binary tree models and a classical twinning criterion

The classical Chin-Hosford-Mendorf (CHM) criterion for deformation twinning is used widely in polycrystal plasticity computer simulations. It assumes that twin nuclei are abundant, and that twin propagation and growth control the realisation of deformation twins. However, recent experimental studies reported in the literature have found that nominally unfavourable twin systems are activated in grains. This has been attributed to twin nucleation in some of the unfavourable twinning systems with low Schmid factors, and its suppression in some of the nominally more favourable ones. Presently, this explanation is quantitatively examined. Full and relaxed constraint versions of the Taylor, ALAMEL, and binary tree based models, all implementing the CHM criterion are used to simulate uniaxial compression of a zirconium billet. Model predictions are compared with experimentally measured twinning statistics reported in the literature for a Zr polycrystal. The ALAMEL and binary tree models, which explicitly represent intergranular interactions, are found to capture the twinning statistics well. These observations suggest that the CHM criterion is adequate to capture twinning in Zr, provided intergranular interactions are represented in the model used to interpret the experiments.

Twinning and detwinning mechanisms in a BCC Ti Mo-Fe multilayered alloy

We have investigated {332}<113> twinning and detwinning mechanisms in a multilayered Ti-10Mo-xFe (x =1−3) alloy fabricated by multi-pass hot rolling. A strong influence of the Fe-graded structure on both phenomena is observed. The propagation of twins that are nucleated in Fe-lean regions (∼1 wt.% Fe) is interrupted in the grain interiors at about 2 wt% Fe. We ascribe this effect to the role of the Fe content on the stress for twin propagation. The unusual twin structure determines the subsequent detwinning process upon thermal annealing. This process consists of two independent detwinning events that occur at two different microstructural regions, namely at twin tips located at grain interiors and at grain boundaries. Both detwinning modes can be explained from a thermodynamic standpoint whereby the boundary dissociation processes minimize the boundary free energy.

Effect of initial orientation on twinning in commercially pure titanium

The effect of initial orientation on twinning micro-mechanisms during tensile deformation of commercially pure titanium has been studied using micro focus X-ray diffraction and electron back scatter diffraction (EBSD) in a scanning electron microscope. Three orientations A, B and C obtained from a rolled and annealed block of commercially pure titanium were deformed in uniaxial tension till failure and the tested specimens were characterised with regard to bulk texture, microstructure and crystal orientation mapping using EBSD. Orientation B along the transverse direction in ND-TD plane exhibits higher strength and lower strain hardening compared to orientations A and C along the rolling direction in TD-RD and ND-RD plane, respectively. This is attributed to different texture of sample B compared to samples A and C leading to dissimilar twinning micro-mechanisms and characteristic variation in nature of twinning. It is observed that limited twin nucleation and prominent lateral growth plays a dominant role in orientation B while multiple twin nucleation with significant non-Schmid behaviour is dominant for the other two orientations. It is proposed from this study that conventional factors associated with twin formation like Schmid factor play a main role in twin nucleation and propagation, however, growth or lateral thickening of the twins is explained by elastic stiffness variation across twins and their parent grains.

Crystal plasticity finite element modeling of discrete twin evolution in polycrystalline magnesium

This paper develops an advanced, image-based crystal plasticity finite element (CPFE) model, for predicting explicit twin formation and associated heterogeneous deformation in single crystal and polycrystalline microstructures of hexagonal close-packed or hcp materials, such as magnesium. Twin formation is responsible for premature failure of many hcp materials. The physics of nucleation, propagation and growth of explicit twins are considered in the CPFE formulation. The twin nucleation model is based on dissociation of sessile dislocations into stable twin loops, while propagation is assumed by atoms shearing on twin planes and shuffling to reduce the thermal activation energy barrier. The explicit twin evolution model however has intrinsic issues of low computational efficiency. Very fine simulation time steps with enormous computation costs are required to simulate the fast propagating twin bands and associated strain localization. To improve the computational efficiency, a multi-time scale subcycling algorithm is developed. It decomposes the computational domain into sub-domains of localized twins requiring very fine time-steps and complementary domains of relatively low resolution. Each sub-domain updates the stress and the deformation-dependent variables in different rates, followed by a coupling at the end of every coarse time step to satisfy global equilibrium. A 6-fold increase in computing speed is obtained for a polycrystalline Mg microstructure simulation in this paper. CPFE simulations of high purity Mg microstructures are compared with experiments with very good agreement in stress-strain response as well as heterogeneous twin formation with strain localization.

Effect of CH4/SiCl4 ratio on the composition and microstructure of 〈110〉-oriented β-SiC bulks by halide CVD

Halide chemical vapor deposition process was carried out for fast fabricating oriented stoichiometric β-SiC through controlling flow rate of precursors (SiCl4 and CH4). The effects of molar ratio of C and Si precursors (RC/Si) on composition, preferred orientation, microstructure and deposition rate (Rdep) were investigated. The deposits transformed from silicon-rich to stoichiometric β-SiC to carbon-rich with increasing RC/Si. 〈110〉-oriented stoichiometric β-SiC with lower density of defects were obtained at RC/Si in the range of 0.86–1.00, where the maximum Rdep was 883μm/h at RC/Si=1.00, leading to a thickness of 1.7mm in 2h deposition. Formation of ridge-like morphology has been discussed based on a twin plane propagation model.

Modeling of twin formation, propagation and growth in a Mg single crystal based on crystal plasticity finite element method

A crystal plasticity finite element method (CPFEM) with a stress relaxation effect for twinning in the constitutive description is employed to simulate twin formation, propagation and growth in Mg single crystals subjected to plane-strain compression along the direction perpendicular to the c-axis of its HCP lattice. Tensile twinning dominates the early stage of plastic deformation and numerical results explicitly show the twinning process including twin formation, propagation and growth. After a twin band (or a narrow twin) is formed, a large gradient of effective stress is found across the band front. Also, the resolved shear stress (RSS) on the twin plane along the twin direction is highly non-homogeneous across the band front. It has been demonstrated that softening facilitates the formation of a twin band and work hardening is contributive to the growth of the twin band. In addition, numerical results indicate that softening plays an important role in the propagation of a twin across a grain boundary with a large misorientation.

Insights into twinning in Mg AZ31: A combined EBSD and machine learning study

To explore the driving forces behind deformation twinning in Mg AZ31, a machine learning framework is utilized to mine data obtained from electron backscatter diffraction (EBSD) scans in order to extract correlations in physical characteristics that cause twinning. The results are intended to inform physics-based models of twin nucleation and growth. A decision tree learning environment is selected to capture the relationships between microstructure and twin formation; this type of model effectively highlights the more influential characteristics of the local microstructure. Trees are assembled to analyze both twin nucleation in a given grain, and twin propagation across grain boundaries. Each model reveals a unique combination of crystallographic attributes that affect twinning in the Mg. Twin nucleation is found to be mostly controlled by a combination of grain size, basal Schmid factor, and bulk dislocation density while twin propagation is affected most by grain boundary length, basal Schmid factor, angle from grain boundary plane to the RD plane, and grain boundary misorientation. The machine learning framework can be readily adapted to investigate other relationships between microstructure and material response.

Comparative study regarding the effect of Al, Zn, and Gd on the microstructure and mechanical properties of Mg alloy Mg-Sn-Li

The effect of Al, Zn, and Gd respectively on the microstructure and mechanical properties of Mg alloy Mg-Sn-Li (the base alloy) is performed. Our results reveal that with Al addition (Al-modified alloy) or Zn addition (Zn-modified alloy), the secondary dendrite arm spacing of the primary α-Mg phase is refined and no new phase is formed. Gd addition (Gd-modified alloy) results in the formation of needle-like or particle-like GdMgSn phase. The extruded base alloy has a low tension-compression yield asymmetry (about 1.00). Addition of Al or Gd yields a slight increase in value of tension-compression yield asymmetry, while Zn a notable reduce. Under tension along the extrusion direction, the yield strength and ultimate tensile strength of Al-modified and Zn-modified alloy other than Gd-modified alloy are enhanced when compared with the base alloy. This is attributed to solute strengthening, the reduced volume fraction of tin-containing metallic compounds and the existence of many needle-like GdMgSn phases in α-Mg matrix. The yield strength of the Gd-modified alloy under tension is the lowest whereas not under compression. This associates with the fact that GdMgSn phases distributed mainly in the interior of grains would offer resistance to twin propagation and growth.

Deformation twinning in hexagonal materials

Abstract

Theoretical study on the [formula omitted] deformation twinning and cracking in coarse-grained magnesium alloys

This paper theoretically and systematically investigates: (1) the effect of local transformed strains within deformation twinning on twin intersection; (2) the fracture mode based on type I co-zone tensile twin intersection in coarse-grained magnesium alloys, as well as the impacts of twin intersection and grain diameter on interfacial crack nucleation along twin boundaries; and (3) the influence of the local stresses arising from the encountered twin bands on crack growth. A novel dislocation-based strain nucleus model and a Green's function method, which are applicable to any material with local transformations in which elastic properties are reasonably approximated as isotropic, are specifically employed to model the concentrated transformed strain and calculate the local stress field resulting from deformation twinning and the stress intensity factors at crack tips in the magnesium alloys, respectively. In addition, an electron backscatter diffraction (EBSD) measurement is provided for crack nucleation originating from Type I co-zone tensile twin intersection. The theoretical modeling indicates: (i) the local strains within barrier twins strongly dictate the growth of incident twins and enhance the twin propagation stress; (ii) larger grains favor brittle fracture. More specifically, the dislocation reactions and pile-ups at the junctions between tensile twins can result in interfacial crack nucleation and growth along the twin boundaries, which is a brittle fracture mode based on lower twinning stress and stress concentration in the coarse-grained magnesium alloys; and (iii) the direction of crack propagation is easily changed by high-density twin bands and twin intersections owing to the local strains.

Deformation behavior of Mg-8.5wt.%Al alloy under reverse loading investigated by in-situ neutron diffraction and elastic viscoplastic self-consistent modeling

The EVPSC-TDT model for polycrystal plasticity and in-situ neutron diffraction have been used to investigate the behavior of a Mg-8.5wt.%Al alloy with two starting textures: 1) a typical extrusion texture in which a majority of the grains are oriented favorably for extension twinning via compression perpendicular to the basal pole, and 2) a modified texture in which extension twinning can be activated via tension parallel to the basal pole in a majority of the grains. Using a small number of adjustable parameters, and only two macroscopic tensile stress–strain curves for calibration, the model is able to capture, quantitatively, the trends in multiple data sets, including grain-level elastic lattice strains, and diffraction peak intensity changes due to lattice re-orientation associated with twinning. For twinning, the model assumes a polar critical resolved shear stress activation criterion and assigns the stress and hardening of the parent crystal to a newly formed twin. The model allows twinning to be driven either by the stress in the parent crystal (matrix reduction), in which case all of the twin transformation strain is assigned to the matrix, or by the stress in the twin (twin propagation), in which case all of the twin transformation strain is assigned to the twin. A detailed comparison between the model predictions and the neutron diffraction data reveals that assigning all of the twin transformation strain either to the matrix or to the twin is too one-sided, leading to excessive relaxation and hardening effects. A more equitable partitioning of the twin transformation strain is necessary. It is suggested that the stress and hardening assigned to a newly formed twin is of less importance to the performance of the model than the partitioning of the twin transformation strain.

Study of {332} twinning in a multilayered Ti-10Mo-xFe (x = 1–3) alloy by ECCI and EBSD

We have investigated the propagation of {332}<113> twins in a multilayered Ti-10Mo-xFe (x = 1–3) alloy fabricated by multi-pass hot rolling. The material contains a macroscopic Fe-graded structure (about 130 μm width) between 1 and 3 wt% Fe in the direction perpendicular to rolling. We observe strong influence of the Fe-graded structure in the twin propagation behavior. The propagation of {332}<113> twins that are nucleated in Fe-lean regions (~1 wt% Fe) is interrupted in the grain interiors at a specific Fe content, namely, about 2 wt% Fe. We ascribe this effect to the role of Fe content in solid solution on the stress for twin propagation. The interruption of twins in the grain interiors results in the development of characteristic dislocation configurations such as highly dense dislocation walls (HDDWs) associated to strain localization phenomena. The nucleation and propagation of these dislocation configurations is ascribed to the underlying plastic accommodation mechanisms of the stress field at the twin tips. We find that the crystallographic alignment of HDDWs is determined by the stress field at the twin tips and the deformation texture. The excellent plastic accommodation at the interrupted twin tips allows attaining the good ductility of the present material (total elongation of 28%).

Evolution of the Annealing Twin Density during δ-Supersolvus Grain Growth in the Nickel-Based Superalloy Inconel™ 718

Grain growth experiments were performed on Inconel™ 718 to investigate the possible correlation of the annealing twin density with grain size and with annealing temperature. Those experiments were conducted at different temperatures in the δ supersolvus domain and under such conditions that only capillarity forces were involved in the grain boundary migration process. In the investigated range, there is a strong inverse correlation of the twin density with the average grain size. On the other hand, the twin density at a given average grain size is not sensitive to annealing temperature. Consistent with previous results for pure nickel, the twin density evolution in Inconel™ 718 is likely to be mainly controlled by the propagation of the pre-existing twins of the growing grains; i.e., the largest ones of the initial microstructure. Almost no new twin boundaries are created during the grain growth process itself. Therefore, the twin density at a given average grain size is mainly dependent on the twin density in the largest grains of the initial microstructure and independent of the temperature at which grains grow. Based on the observations, a mean field model is proposed to predict annealing twin density as a function of grain size during grain growth.

Study of twinning behaviors of rolled AZ31 magnesium alloy by interrupted in situ compressive tests

In this paper rolled AZ31 magnesium alloy was deformed by interrupted in situ compressive tests. Compressive and re-compressive tests were conducted along rolling direction (RD). It is discovered that the yield strength of re-compression is enhanced due to grain refinement by {10–12} tensile twins. Twinning activation and evolution are evidenced by electron backscatter diffraction. Correlations with grain orientation and boundary misorientation are observed in the region of twins that arise at grain boundaries. The distributions of grain boundary misorientation associated with twin nucleation are mapped. It is found that nucleation of twin is mainly controlled by the initial texture, and is more easy at low misorientation grain boundaries. The growth of twins depend on two modes: the thickening of the existing twin lamellae and new twins is nucleated at grain boundary. With increasing compressive strain, the growth and coalescence of twins eventually encompassed the whole grain. Meanwhile, the basal texture is weaker after compression due to the propagation and coalescence of tensile twins.