Twin Volume Research Articles

Deformation and microstructure radial gradient evolution of AZ31 magnesium alloy bar during three-roll skew rolling

AZ31 magnesium alloy bar with radial gradient microstructure was prepared by three-roll skew rolling process (TRS), and achieving an excellent combination of ductility and strength. To elucidate the formation mechanism of this gradient microstructure, the deformation behavior during rolling was analyzed through experiments and simulations. The simulation results indicated that the metal flow of the bar in a spatial helical trajectory during rolling, with the trajectory inclination angle gradually decreasing from the center to the surface, promoting dynamic recrystallization in the surface and near-surface regions. The radial equivalent strain decreased from 1.5 at the surface to 0.01 at the center, and the shear strain decreased from 0.051 at the surface to 0.00012 at the center. Experimental results showed that the grain size of the bars decreased from 49.77 µm at the center to 19.72 µm at the surface, and the tensile twin volume fraction decreased from 34.1 % to 19.4 %. Dynamic recrystallization predominantly occurred in the outer ring region of the bars, while significant {10−12} tensile twin activation was observed in the central region, with twin-induced dynamic recrystallization observed at the twin boundaries. Mechanical property tests demonstrated that the gradient structure endowed the bars with a favorable combination of strength and elongation, with hardness significantly increasing from 50 HV at the center to 90 HV at the surface. This indicates that the three-roll skew rolling technology effectively promotes dynamic recrystallization at the surface, and the resulting gradient microstructure achieves an excellent combination of strength and plasticity in magnesium alloy bars.

Experimental and crystal plasticity finite element study of dynamic shear behavior of CoCrNiSi0.3 medium-entropy alloy

Single-phase CrCoNi-based medium-entropy alloys (MEAs) have garnered considerable attention as a promising class of metallic materials. However, despite this growing interest, the dynamic mechanical response of CrCoNi-based MEAs at high strain rate remains controversial. The dynamic shear mechanical behavior of CoCrNiSi0.3 was characterized through Hopkinson-bar experiment utilizing hat-shaped specimen. In this study, a damage model based on the maximum shear strain of each slip system was chosen to describe the damage initiation and evolution. Combined with this micro-scale damage and dislocation density-based crystal plasticity theory, two constitutive models were proposed to perform predictions of the dynamic shear behavior of CoCrNiSi0.3. The strain rate effect, adiabatic temperature rising, damage evolution, and twin volume fraction during dynamic shear deformation were tracked by investigating the influence of resolved shear stress, dislocation density, texture evolution, and twinning systems shear strain. The presented model effectively predicts the deformation state of specimen, the formation and evolution of Adiabatic Shear Bands (ASBs), and the variations in strain rate and temperature at different locations within the shear region. Adiabatic Shear Bands and texture evolution are caused by the local dislocation density rising and misorientation distributions.

Deformation Behavior of AZ31 Magnesium Alloy with Pre-Twins under Biaxial Tension.

In the present study, the mechanical response and deformation behavior of a Mg AZ31 plate with different types of pre-twins was systematically investigated under biaxial tension along the normal direction (ND) and transverse direction (TD) with different stress ratios. The results show that significant hardening was observed under biaxial tension. The yield values in the direction of larger stress values were higher than those under uniaxial loading conditions, and the solute atom segregation at twin boundaries generates more obvious strengthening effect. Noting that, for TRH (with cross compression along the rolling direction (RD) and TD and annealing at 180 °C for about 0.5 h) sample, the strength effect of the RD yield stress σRD:σND = 2:1 was higher than that of the ND yield stress under stress ratio σRD:σND = 1:2. There is a complex competition between twinning and detwinning under biaxal tension along the ND and TD of the pre-twinned samples with the variation in the stress ratio along the TD and RD. The variation in the twin volume fractions for all samples under biaxial firstly decreases and then increases with a higher stress ratio along the ND. As for the TDH sample (precompression along the TD and annealing), the changes of the twin volume fraction were lower than that of the TR sample (cross compression along the TD and RD). However, the amplitude of variation in twin volume fraction of the TRH sample is higher than that of the TR sample. This is because the relative activity of detwinning decreases and that of twinning increases, as the ND stress mainly leads to the growth of pre-twins and the TD stress often promotes detwinning of primary twins. With a higher stress ratio along the ND, the activity of twinning deformation increases and that of detwinning decreases.

Study on anisotropic mechanical behavior of AZ31 magnesium alloys under free-end torsion

In this study, the mechanical behavior and microstructure of a hot-rolled AZ31 magnesium alloy sheet under free-end torsion with torsional axis along rolling direction (RD), normal direction (ND) and 45° in ND-RD plane, have been investigated both experimentally and numerically. The mechanical behavior under torsion, including stress-strain response, Swift effect and strain hardening rate, present obvious anisotropy. The Swift effect is sensitive to the direction of torsion axis and exhibits remarkable anisotropy with axial elongation in ND sample and axial shortening in RD and 45° samples. The axial elongation or shortening is determined by both slips and extension twin, with extension twin exerting a greater influence on the extent of the axial deformation. During shear straining, the dominant deformation mode transforms basal slip to prismatic slip with the axial direction deviating from ND to RD, while the second-order pyramidal ⟨c+a⟩ slip is nearly not activated during whole deformation attributed to its high critical resolved shear stress. Based on the effective Schmid factor (ESF) of deformation modes, the grains with favored orientation would get activation of {101‾2} extension twin due to the high ESF, resulting in the different twin volume fractions. Additionally, the activation of twin relative to basal slip has a connection with the increasing trend of normalized strain hardening rate.

Crystal plasticity finite element method investigation of normal tensile deformation anisotropy in rolled pure titanium sheet

Industrial pure titanium with hexagonal close-packed (HCP) crystal structure has a high degree of anisotropy at room temperature. On the mesoscopic scale, this is due to the rolling texture presented by its crystal orientation. Tensile tests were performed on smooth specimens with five angles in the first quadrant at room temperature, and the central deformation region and fracture region were characterized using EBSD and SEM, respectively. The modified Salem anisotropic hardening model is incorporated into the crystal plasticity finite element method (CPFEM) framework in the form of incremental hardening to describe the initial strength and hardening increment evolution of each deformation system of pure titanium. Both slip dislocation and twinning mechanisms are considered in the CPFEM simulation. Three models with different meshing strategies are used to simulate the tensile conditions to capture the evolution of macro and micro variables of pure titanium sheet. The results show that there are anisotropy in stress-strain, system activity, cumulative shear strain, crystal orientation, twin volume fraction, stress triaxiality and Lode parameter. The purpose of this paper is to explore the anisotropy of macro-meso variables in different directions before damage occurs, so as to provide reference for the subsequent construction of related damage models.

Mechanical responses and deformation mechanisms in the AZ31 magnesium alloy during cyclic bending

Cyclic loading behavior, such as cyclic bending, is unavoidably involved in various forming processes and the service of end products. Understanding the mechanical behavior of magnesium (Mg) alloys under cyclic bending is essential for promoting their application. Despite existing research, the microscopic mechanisms at play during cyclic bending, specifically the slip and twinning-de-twinning (TDT), warrant further exploration, which is the innovative focus of our study. To address this need, cyclic bending tests were performed on an extruded AZ31 Mg plate with the in-situ digital-image-correlation (DIC) technology. And the texture evolution was determined through electro backscattered diffraction (EBSD) measurements. Concurrently, the crystal-plasticity-based bending-specific approach, EVPSC-BEND, incorporating the TDT scheme, is utilized to interpret the mechanisms involved in cyclic bending. The impact at the macroscopic level is manifested in asymmetric cyclic moment-curvature curves, stress-strain distribution, and shifting of the neutral layer. The developed textures at different regions of the beam and the twin volume fraction distribution further directly illustrate twinning-de-twinning behaviors. Particularly, the upper and lower halves of the beam experience very distinct cyclic behaviors simultaneously. The upper half experiences a twinning, detwinning, and twinning cycle, while the lower half experiences a twin-free, twinning, and detwinning cycle. Additionally, through modeling the cyclic bending with different initial textures, the strong texture dependence has been revealed. The behaviors of magnesium alloy beam under cyclic bending discovered in this work can shed light on the application of Mg alloys, such as forming processes and service of end product.

Anisotropic strain hardening in an extruded lean Mg-Al-Ca-Mn alloy

Compared to commercial magnesium (Mg) alloys, recently the low-alloyed Mg alloys have attracted extensive research interest for their advantages in formability, corrosion resistance, and low cost. However, their strain hardening behavior is yet fully understood. In this work, the strain hardening of an extruded lean Mg-Al-Ca-Mn alloy is qualitatively and quantitatively analyzed. As compared to the dislocation-dominated deformation along the extrusion direction (ED), the hardening along the transverse direction (TD) is significantly improved due to the activation of twinning. We quantified the specific contributions of twinning and dislocations to the net hardening effect through cyclic stress relaxation and calculations. Interestingly, the dominant hardening mechanism is always related to dislocations, even though the twin volume faction reaches ∼40 %. This work furthers our understanding of the deformation behavior of lean Mg alloys and indicates that the strain hardening of Mg alloys can be improved if the twin morphology is properly controlled.

Anisotropic and heterogeneous acoustoplasticity of α-Ti during ultrasonic vibration assisted compression: Modeling and experiments

Introducing ultrasonic vibration (UV) into the plastic deformation process is a promising and efficient way to improve the formability of metallic materials. However, the acoustoplasticity of α-Ti with pronounced anisotropic behavior during UV-assisted deformation is still not well understood, and the underlying mechanisms associated with the ultrasonic effect on multiple slip/twinning systems remain ambiguous. In this research, the anisotropic and heterogeneous acoustoplasticity of α-Ti was investigated through modeling and experiments. A novel acoustic crystal plasticity model considering the anisotropic ultrasonic response of multiple slip/twinning systems was proposed, in which the ultrasonic softening is determined by the coupling effect of crystal orientation, mechanical threshold, and ultrasonic energy density. The proposed model was validated through the mechanical response of the UV-assisted compression and the twin volume fraction of α-Ti specimens along RD, TD, and ND directions. Full-field crystal plasticity simulations regarding UV-assisted compression were carried out. Then the mechanism of the acoustoplasticity of α-Ti was explored via the analysis of ultrasonic activation on multiple slip/twinning systems and the grain scale deformation behavior. A considerable anisotropic and heterogeneous ultrasonic softening effect of α-Ti was found, and the anisotropy as well as the magnitude of ultrasonic softening increase with the ultrasonic energy density. The ultrasonically activated deformation modes gradually change from prismatic slip and tensile twinning to basal slip and compressive twinning from RD, TD to ND specimens, which results in a higher average CRSS decrease and more pronounced ultrasonic softening macroscopically. The grain scale stress inhomogeneity of α-Ti is relieved under UV, and the local deformation and grain rotation are both enhanced. The dislocation motion and twinning behavior are both promoted by UV. The facilitated twinning behavior can be attributed to the enhanced dislocation assisted nucleation and propagation of deformation twins under UV. These findings provide a fundamental understanding of the anisotropic and heterogeneous acoustoplasticity of α-Ti during the UV-assisted deformation process.

A constitutive model incorporating the interplay of dynamic recrystallization and twinning during hot deformation of AZ31 magnesium alloy

Dynamic recrystallization (DRX) and deformation twinning play a pivotal role in stress partitioning during hot deformation of magnesium alloy. However, the influence of twinning on stress is diverse, and the interaction between DRX and twinning is intricate. Existing constitutive models cannot simultaneously describe the relationship between DRX and twinning, as well as their effects on stress. In this study, the hot compression tests were conducted to study the flow behavior and microstructure evolution of AZ31. The obtained flow curves and microstructure revealed that AZ31 alloy undergoes simultaneously DRX softening and twinning hardening during hot deformation. Furthermore, texture evolution was significantly influenced by both DRX and twinning behaviors. As a result of DRX behavior, there was a decrease in twin volume fraction in the later stages of deformation. Consequently, a twin volume fraction model that incorporates the inhibitory effect of DRX was proposed. According to the experimental results of high temperatures and low strain rates, a constitutive model incorporating work hardening, dynamic recovery (DRV), and DRX was established. Additionally, the influence of twinning on flow stress was incorporated into the model, resulting in a constitutive model that considers both DRX and twinning simultaneously. Finally, the proposed model's reliability was validated through the wedging spinning process, successfully predicting both macroscopic deformation and microstructure evolution of the spinning parts.

“Nothing’s Forever”: Destruction, Creation, Connection, and Miltonic Influence in Cormac McCarthy’s The Passenger and Stella Maris

ABSTRACT The article proposes that engagement with John Milton’s Paradise Lost in Cormac McCarthy’s The Passenger and Stella Maris furnishes a clue to comprehending the duology. These twin volumes present an extraordinary brother and sister, Bobby and Alicia Western, as a new Adam and Eve in a vitiated world. The narrative suggests that the Western siblings’ unconsummated love and the underlying theme of the absent child they never had make their circumstances a dark variation upon the Edenic story. McCarthy countervails his well-documented distrust of language by reinvigorating Milton’s haptic motif of Adam and Eve’s handclasp and offering an alternative form of human connection, lying beyond language, in interpersonal acts of care. McCarthy’s duology instructs his readers by negative example to be thankful for life’s most precious gifts by revering nature, loving another, nurturing a child, and showing kindness to those other passengers who travel with us in our shared lives.

Temperature-dependent behavior of CP-Ti interpreted via self-consistent crystal plasticity simulation

A commercially-pure titanium sample was investigated using an elasto-visco-plastic self-consistent polycrystal model. Temperature-dependent plastic deformation behavior was described by a dislocation density-based hardening model. The model reasonably reproduced various experimental behaviors, including stress vs. strain curves, diffraction lattice strains, twin volume fraction, and crystallographic texture. The temperature-dependent behavior was interpreted based on the dislocation evolution rules comprised of dislocation generation and recombination in accordance with the Kocks-Mecking rule. The modeling results successfully provided an in-depth interpretation of mechanical behavior of α-titanium under a wide range of temperatures.

Study on the deformation behavior of AZ31B-O magnesium alloy with the VPSC model

The mechanical anisotropy of the magnesium alloy AZ31B-O was investigated using the Viscoplastic-Self-Consistent (VPSC)-Twinning and Detwinning (TDT) model. The anisotropic behavior of the material under uniaxial strain was studied using five distinct sheet orientations. In order to investigate the mechanical behavior under uniaxial compression, four alternative specimen orientations were employed. The VPSC model with the TDT mechanism was used to simulate the uniaxial tension and compression experiments. For tensile strain, the magnesium alloy samples were mainly regulated by base slip and prismatic slip. In compression of magnesium alloy samples, it was dominated by basal slip and {10–12} twinning. In all compression specimens, the grain c-axes are parallel to the compression axis regardless of the initial orientation. The r-values under different uniaxial strain paths have been also predicted by using the VPSC-TDT model. The negative r-values under uniaxial compression along RD to TD were further explained. The contribution of {10–12} twinning to plastic strain and the extra hardening induced by {10–12} extension twinning were discussed in depth. This study confirms that the extra hardening induced by {10–12} extension twinning will perform an important function when the twin volume fraction reaches a degree of about 50% with the active pyramidal slip at the same time.

Microstructure evolutions and deformation mechanisms of a Ni-based GH3536 Superalloy during loading at 293 K and 77 K

In this study, tensile tests and interrupted experiments at different true strain levels were performed at 293 K and 77 K to reveal the deformation mechanisms of GH3536 superalloy during loading. The microstructure evolutions of the alloy with strain at both temperature were studied via Transmission electron microscopy (TEM), and dislocation densities were calculated by X-ray diffraction (XRD) for quantifying the forest hardening contribution to the flow stress. Deformation twins were rarely observed in the GH3536 superalloy specimens deformed at 293 K, where deformation occurred solely by dislocation slip. While twinning was initially found at a strain of ∼7% at 77 K, and the corresponding stress at which twinning occurs is 808 ± 46 MPa. The twin volume fractions, their widths and spacings were determined by electron backscatter diffraction (EBSD), which is used to investigate the twin evolution of GH3536 alloy at 77 K. The deformation mechanisms of GH3536 alloy, as well as its twinning behaviors, depend on the competition between the maximum flow stress and critical stress for twinning. The maximum flow stress is large enough to activate twinning at cryogenic temperature, resulting in the transition of deformation mechanisms for GH3536 alloy as SLIP (dislocation slip) at 293 K and TWIP+SLIP (deformation twinning and dislocation slip) at 77 K, and the improved combination of ductility and strength at 77 K compared to 293 K is derived from additional deformation mode provided by twinning during the process of deformation.

Embedding strain-rate sensitivities of multiple deformation mechanisms to predict the behavior of a precipitate-hardened WE43 alloy under a wide range of strain rates

A rare earth Mg alloy, WE43, exhibits high strength, good ductility, low anisotropy, and moderately high strain rate sensitivity. As such, the alloy is a viable candidate for high strain rate applications. In this work, a comprehensive set of mechanical and microstructure data recorded during quasi-static, high strain rate split Hopkinson bar (SHB), and impact tests on specimens of WE43 Mg alloy reported in (Savage et al., 2020b) is simulated and interpreted using an advanced Taylor-type crystal plasticity finite element (T-CPFE) model. The T-CPFE model is formulated physically to embed two sources of strain-rate sensitivities inherent to each slip and twinning mode in WE43, one that occurs under constant structure and another that affects structure evolution. The model parameters are established for the alloy by achieving agreement in the stress-strain response and microstructure evolution under quasi-static and SHB tests. Density functional theory calculations of anti-phase boundary (APB) energy are carried out to explain origins of the unusually large initial slip resistance for basal dislocations, which shear precipitates in the alloy. The initial slip resistances of the prismatic and pyramidal dislocations are, instead, rationalized by Orowan looping around precipitates. After calibration and validation, the model is shown to successfully predict WE43 response at much larger strain rates than those used for model calibration. Specifically, mechanical response, specimen geometry changes, twin volume fractions, and texture evolution are predicted for different orientations of the Taylor cylinders. Details of the modeling framework, comparison between simulation and experimental results, and insights from the results are presented and discussed.

Energy and morphology of martensite–twinned martensite interface in CuAlNi shape memory alloy: A phase-field study

Needle-like twins are observed experimentally within the transition layer at the martensite–twinned martensite interface. We utilize a phase-field approach to investigate this microstructure. Our goal is to simulate the morphology of the transition layer and to perform a detailed analysis to characterize its interfacial and elastic micro-strain energy. To illustrate the micromechanical framework developed for that purpose, sample computations are carried out for a CuAlNi shape memory alloy undergoing a cubic-to-orthorhombic martensitic transformation. A particular focus of the study is on size-dependent morphology through examining the impact of twin spacing. Additionally, our results reveal that certain twin volume fractions lead to the emergence of twin branching as a way to minimize the total free energy stored in the microstructure.

Strain-rate-dependent behaviors of CoCrNiSi0.2 medium-entropy alloy: Deformation mechanism and microstructural-based constitutive modeling

Abundant strengthening mechanisms in medium-entropy alloys (MEAs) endow them with excellent comprehensive properties, rendering them promising candidates for use in extreme service conditions, such as low/high temperatures and strong impact environment. Investigation of the mechanical behaviors and micro deformation mechanisms of MEAs under intermediate/high strain rate loadings should therefore help to explore their application potential in impact-resistant structures. In this study, the tensile mechanical properties of a single-phase face-centered cubic (FCC) CoCrNiSi0.2 MEA were tested over low, intermediate, and high strain rates, and the micro deformation mechanisms at different strain rates were analyzed systematically. Dislocation evolution, deformation twinning, and phase transformation (from single FCC to FCC + hexagonal close-packed (HCP)) were observed in the three groups of tensile specimens loaded at low, intermediate, and high strain rates. The dislocation densities and twin volume fractions in the three groups were comparable, while the volume fraction of phase transformation increased significantly with the increasing strain rate. Therefore, more HCP phases generated during high-strain-rate deformation should lead to a stronger precipitation-strengthening effect on the material, which made the strain-rate-strengthening effect more significant to the extent that it could not be ignored in constitutive modeling. Finally, the contribution of the phase transformation was introduced for the first time into a constitutive model in which dislocation slip and deformation twinning were also considered to describe the viscoplastic flow behavior of the CoCrNiSi0.2 MEA over a wide range of strain rates.

The hardening effect of deformation twinning based on visco-plastic self consistent model and a multi-scale grain refinement prediction model during machining of titanium alloy

Deformation twins act as one of the deformation characteristics of hexagonal close packed (HCP) materials and occur during machining of Ti–6Al–4V alloy. To clarify the hardening mechanisms of deformation twins in Ti–6Al–4V machined surface, work-hardening effects induced by grain refinement in meso scale as well as deformation twins in micro scale were investigated. A 2D cutting finite element (FE) model was established to predict grain refinement in multi-scales and its hardening behavior during machining of Ti–6Al–4V. A visco-plastic self consistent model (VPSC) coupled with predominant twin reorientation (PTR) scheme was also used to simulate stress variation with considering the activations of twin systems. The results show that different grain refinement degrees in meso scale are observed with the increasing of cutting speeds (100–500 m/min). {101¯1} compression nano twins generate at higher cutting speeds, and the twin volume fraction is relatively small (20%). The hardening behaviors of grain refinement in meso scale as well as nano twins predicted with FE model and VPSC model are similar, and the generation of nano twins cause inhomogeneous hardening in Ti–6Al–4V machined surface. Nano-indentation tests further prove the accuracy of the prediction results for the hardening effect induced by nano twins in Ti–6Al–4V machined surface. The results provide two explanations and quantitative evaluations for the hardening effects of deformation twins from the macroscopic stress and the microscopic deformation of slip and twinning modes.

Modelling mechanical behaviour of a gradient-microstructured material obtained by surface mechanical attrition treatment accounting for residual stresses

In this work, an austenitic 316 L steel was processed by surface mechanical attrition treatment (SMAT), and the induced gradient microstructure was highlighted by experimental measurements. A combined dislocation density-based and grain size-dependent constitutive model is developed to describe the mechanical behaviour of the gradient-microstructured material. In addition, this model also incorporates the grain size-dependent initial twin distribution and evolution of deformation twinning. Residual stress, initial dislocation density and twins are considered to reconstruct the depth-dependent residual fields induced by SMAT. Furthermore, the evolution of dislocation density and twin volume fraction is described during uniaxial tensile loading. Particular attention is devoted to investigate the effect of residual stress and deformation twinning on mechanical behaviour. Results of finite element simulation showed that the gradient microstructure enhances the yield strength, which is in agreement with previous experimental observations. It was revealed that residual stress significantly weakens the yield strength at the initial deformation stage, whereas it has little influence on the plastic behaviour at large deformation. The assumed grain size-dependent deformation twinning model allows describing the evolution of deformation twinning on gradient microstructure. The deformation twinning increases in relation to increased strain hardening during tensile loading. However, the evolution of twin volume fraction shows almost no twin and no variation of twinning within the nanocrystalline grain region.

On the cyclic torsion behavior of extruded AZ61A magnesium alloy tube

This work investigated the cyclic torsional behaviors of extruded AZ61A Mg alloy tubes through experiments and simulations. To capture the Bauschinger effect, the elastic viscoplastic self-consistent model with the twinning and detwinning scheme, together with a torsion-specific finite element approach was improved by adding a back-stress. A unique Swift effect with the “butterfly” shape was observed and reasonably reproduced by our model. Furthermore, the relative activities of deformation mechanisms, internal stress distributions, and twin volume fraction distributions under cyclic torsion were discussed. The findings could be beneficial to the design, manufacturing, and service of Mg alloys, particularly under cyclic torsion.

Finite element analysis using elasto-visco-plastic self-consistent polycrystal model for E-form Mg sheet subjected to bending

The mechanical behavior of a magnesium alloy E-form under bending was investigated using the elasto-visco-plastic polycrystal model (ΔEVPSC) and its finite element (FE) implementation (ΔEVPSC-FE) developed in Jeong et al. and Jeong and Tomé. The crystallographic orientation distribution (COD) obtained from X-ray diffraction was used to represent the initial texture, and the Voce hardening parameters were calibrated by fitting the uniaxial tension and the compression flow stress curves. A quasi-static FE analysis of a miniaturized V-bending operation was conducted using the ΔEVPSC-FE model. The bending induced an inhomogeneous stress response along the through-thickness and the lateral directions, which was well captured by the model. Moreover, the predictive capability of the model was validated by comparing with various experimental results such as (1) force vs. displacement curves; (2) the through-thickness variations in the twin volume fraction; and (3) the changes in crystallographic texture as a function of displacement. Additional bending simulation was performed using an isotropic texture, the result of which suggests that the potential improvement in bendability of the magnesium alloy is attainable by weakening the initial texture. Moreover, the simulation results imply that the crystallographic texture, which may affect the twin activation across the thickness direction, plays a significant role in the shifting direction of the neutral layer.