Twin Propagation Research Articles

Coupled crystal plasticity-phase field simulation of twin-twin interaction in magnesium

Twin-twin interactions significantly influence the mechanical properties of magnesium and its alloys. A thorough understanding of the underlying mechanisms governing these interactions is essential for designing Mg alloys with enhanced strength and toughness. In this work, a crystal plasticity-twin coupled phase field (CP-TPF) model incorporating multiple extension twin variants and considering the role of dislocation slipping is proposed to investigate the interactions between/among the same twin variants and those between co-zone twin variants in Mg single crystals. The model incorporates an additional energy term to represent the interaction among different twin variants and couples the CP and TPF models through order parameters and stress tensor. The simulated results show that the interaction between the same twin variants can either promote or inhibit the twin propagation, and multiple twins tend to generate concurrently in Mg single crystal to minimize the free energy associated with the accumulation of elastic strain. During co-zone twin-twin interaction, localized thickening of the recipient twin occurs due to the concentrated stresses induced by the intrusion twin, and the mutual extrusion of the two twins leads to blunting of the intrusion twin tip. Both the coalescence of the same twin variants and the formation of twin-twin boundaries between the co-zone twin variants contribute to the effective mechanism of twinning-induced hardening. Moreover, local dislocation accommodation plays a crucial role in twin-twin interactions. It relaxes the stress concentration near the twin tips and twin-twin boundaries and significantly contributes to the uneven migration of the twin boundary.

Study of Tensile and Compressive Behavior of ECO-Mg97Gd2Zn1 Alloys Containing Long-Period Stacking Ordered Phase with Lamellar Structure

A suitable heat treatment in the Mg97Gd2Zn1 (at.%) alloy in the as-cast condition results, after extrusion at high temperature, in a two-phase lamellar microstructure consisting of magnesium grains with thin lamellar shape precipitates and long fibers of the 14H-Long-Period Stacking Ordered (LPSO) phase elongated in the extrusion direction. The magnesium matrix is not fully recrystallized and highly oriented coarse non-dynamically recrystallized (non-DRXed) grains (17% volume fraction) elongated along the extrusion direction remain in the material. The deformation mechanisms of the extruded alloy have been studied measuring the evolution of the internal strains during in situ tension and compression tests using synchrotron diffraction radiation. The data demonstrate that the macroscopic yield stress is governed by the activation of the basal slip system in the randomly oriented equiaxed dynamic recrystallized (DRXed) grains. Non-DRXed grains, due to their strong texture, are favored oriented for the activation of tensile twinning. However, the presence of lamellar-shape precipitates strongly delays the propagation of lenticular thin twins through these highly oriented grains and they have no effect on the onset of the plastic deformation. Therefore, the tension–compression asymmetry is low since the plasticity mechanism is independent of the stress mode.

Study of low-temperature impact deformation behavior of Ti–6Al–4V alloy

The impact behavior of the Ti–6Al–4V alloy has been investigated at varying temperatures (298 K, 223 K, 77 K) in this study. The results reveal a decrease in toughness with reduced temperature, with notable changes in energy distribution between crack initiation and propagation. The {101¯2}α twins formed in the studied sample under impact loading at 298 K and 223 K, and were absent at 77 K. The formation and propagation of twins contribute to the higher toughness of the 298 K and 223 K samples. These findings would provide valuable guidance to optimize the Ti–6Al–4V alloy toughness in low-temperature environments.

A unique {332} twin to α″ martensite transition during twin propagation in a Ti-12wt.% Mo alloy with micro-segregation

In this study, the propagation behavior of {332}<113>β twins was investigated in a Ti-12Mo (wt.%) alloy with micro-segregation bands (Mo content ranging from 10 to 13 wt.%). A unique transition from {332}<113>β twins to α"-martensite was observed when those twins propagated across the Mo-lean bands inside the grain. A deflection angle of ∼18° was found between the twin boundary and the α"-martensite plate. This transition was more frequently found at relatively higher stresses. Thermodynamic analysis revealed that the Mo content together with the applied stress govern the required mechanical work for triggering α" martensitic phase transformation. The stress-induced α" martensitic phase transformation was easier to trigger in the Mo-lean bands, with a spontaneous interruption of the {332}<113>β twin propagation. The present chemically segregated microstructure provides a novel approach to comprehensively characterize the variable deformation modes in metastable β titanium alloys.

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.

Dependence of deformation mechanisms on micro-pores in the fourth-generation single crystal superalloy during out-of-phase thermal-mechanical fatigue

The high-temperature and long-term solution heat treatments of fourth-generation single crystal (SX) superalloys have sparked an increasing number of homogenization pores in the alloy. Out-of-phase (OP) thermal–mechanical fatigue (TMF) experiments were conducted to elucidate the effect of pores on the fatigue behaviors and deformation mechanisms. The results showed that the plastic deformation was mainly concentrated upon γ matrix in regions away from pores, more specifically, intrinsic stacking fault (ISF) and extrinsic stacking fault (ESF) as well as dislocation cross-slipping were detected. In areas near micro-pores, however, the γ/γ′-structure was subjected to severe twinning shearing. High-resolution observation illustrated that the amount of ESF and a/6 〈112〉 twinning dislocations had remarkably increased. Besides, the partial dislocations were more prone to move in different slipping systems at these regions with considerable stress concentration. These factors collectively enabled the formation of deformation twins from the edge of micro-pores. Moreover, the twinning nucleation could occur near both H-pores and S-pores, while the increasing pore size would enhance the nucleation and propagation of pore-induced twins by a large margin. These findings reported have provided important guidance for the future application of the fourth-generation SX superalloys.

Strain Rate Dependence of Twinning Behavior in AZ31 Mg Alloys

This study investigates the impact of strain rate on the twinning process (i.e., twin nucleation, twin propagation, and twin growth) and associated mechanical behavior during compression along the normal direction (ND) and transverse direction (TD) of a rolled AZ31 Mg plate at a range of strain rates from 0.00005 s−1 to 2500 s−1. The findings reveal that the yield strength is insensitive to strain rates below 0.05 s−1 during both ND and TD compression tests, while at higher strain rates of 2500 s−1, the yield strength increases under both loading conditions. Interestingly, the TD-compressed sample exhibits a larger yield plateau at a strain rate of 2500 s−1, attributed to an increased activation of {101¯2} twins. Further examination of the microstructure reveals that the twinning process is highly dependent on the strain rate. As the strain rate increases, twin nucleation is promoted, leading to a higher twin boundary density. In contrast, at lower strain rates, twin nucleation is restrained, and the external strain is mainly accommodated by twin growth, which results in higher area fractions of twinned regions.

Understanding the interaction of {10–12} twins and Mg17Al12 precipitates in magnesium alloys via high-resolution electron microscopy

The interactions between {10 1‾ 2} twins and basal precipitates in the Mg–8Al-0.5Zn alloys have been investigated using high-resolution transmission electron microscopy. The underlying interaction mechanisms at different twinning processes were analyzed in detail. In the process of twin propagation, the twin tip can traverse across multiple basal precipitates in the form of nucleation of new twins on the opposite side of the precipitates and continuously expand in the grain. Such re-nucleation events are suggested to be driven by the local stress concentration arising from the twin impinging upon the precipitate. During twin thickening, the precipitates undergo a small elastic deflection rather than plastic shearing when the twin engulf them. Furthermore, a large number of I1 stacking faults are activated at the twin-precipitate interface to accommodate the twinning shear. The orientation relationship (OR) of the precipitates inside the twin is changed from Burgers to [2 1‾1‾ 0]α//[11 1‾]β, (0 1‾ 10)α//(011)β, (0001)α//(2‾ 11‾)β when they are engulfed by twin.

Assessing the predictive capabilities of precipitation strengthening models for deformation twinning in Mg alloys using phase-field simulations

Precipitation strengthening is a key strategy for improving the overall mechanical properties of Mg alloys. In Mg-Al alloys, basal precipitates are known to strengthen against twinning, resulting in an increase in the critical resolved shear stress (CRSS) necessary for continued deformation. Although several models have been proposed to quantify the influence of precipitate shape, size, and distribution on the CRSS, the accuracy, scope, and applicability of these models has not been fully assessed. Accordingly, the objectives of this study are: (i) to analyze the accuracy of analytical models proposed in the literature for precipitation strengthening against twin thickening and propagation (in Mg-Al alloys) using phase-field (PF) simulations, (ii) to propose modifications to these model forms to better capture the observed trends in the PF data, and (iii) to subsequently test the predictiveness of the extended models in extrapolating to experimental strengthening data. First, using an atomistically-informed phase-field method, the interactions between migrating twin boundaries (during the propagation and thickening stages) and basal plates are simulated for different precipitate sizes and arrangements. In general, comparison of the increase in CRSS determined from the PF simulations and the predictions from four precipitation strengthening models reveals that modifications are necessary to the model forms to extend their applicability to precipitation strengthening against both twin thickening and propagation. A subsequent comparison between predictions from the extended models and experimental strengthening data for peak age-hardened samples reveals that the (extended) single dislocation and dislocation wall models provide reasonably accurate values of the increase in CRSS. Ultimately, the results presented here help elucidate the fidelity and applicability of the various hardening models in predicting precipitation strenghtening effects in technologically important alloys.

Fabrication, microstructure and mechanical properties of TiAl matrix composite reinforced by submicro/nano-Ti2AlC

In the present work, using pre-alloyed Ti-48Al-2Cr-2Nb powders and graphene nanosheets as raw materials, the TiAl matrix composite reinforced by submicro/nano-Ti2AlC was fabricated via spark plasma sintering and subsequent heat-treatment. The microstructure characterization results have indicated that submicro-Ti2AlC and nano-Ti2AlC exhibit the coherent atomic correspondence with the full lamellar TiAl matrix. Furthermore, The Ti2AlC/TiAl composite has excellent balance relationship of room-temperature compression strength (∼2171 ± 3 MPa) and fracture strain (∼31 ± 1%). The submicro-Ti2AlC could effectively hinder the twin propagation and inhibit the dislocations motion, which is benefit to improve the strength of the Ti2AlC/TiAl composite. In addition, the nano-Ti2AlC could not only cause the dislocation multiplication in γ-TiAl by the activation of pyramidal dislocations, but also induce the formation of deformation twins in γ-TiAl by the basal-plane slip, resulting in the improvement of plastic deformation capacity in the Ti2AlC/TiAl composite.

Multi-domain ubiquitous digital twin model for information management of complex infrastructure systems

Digital twin is a comprehensive digital equivalent of an object or an activity, reflecting the semantic and geometric properties and behaviors through virtual models and data. Digital twin and related information technologies are widely used in the construction, operation and maintenance of infrastructure and facility. Transdisciplinary stakeholders are always involved in the long-term and cross-scene management of IoT and digital twin-enabled smart infrastructures and facilities. The intensive interactions among stakeholders often cause conflicts due to the variations in experience, knowledge, and interests. Moreover, with the change propagation of digital twins, cyber-physical resources can’t be efficiently and consistently established, connected, and utilized with multi-domain information through selective simplification and structured methods. This paper proposes a Ubiquitous Digital Twin model for the information management of complex infrastructure systems based on Domain-Driven Design. To achieve the unified and structured description, six domains are deployed in the proposed model with sequential or parallel tuples for shared understanding of overall system framework or specific functional modules. Three cases of one smart nuclear plant management scenario are hierarchically instantiated to evaluate the proposed model.

The influence of gadolinium concentration on the twin propagation rate in magnesium alloys

Ultra-high-speed camera (UHSC) imaging was used for the study of the influence of gadolinium (Gd) content on the longitudinal growth of twins in Mg-Gd binary alloys. The results clearly indicate that the twin propagation rate is of the order of 101 m/s and slows down with increasing Gd concentration. Concurrent molecular dynamics (MD) simulations reveal that the presence of Gd atoms enhances the formation of stacking faults (SFs), which hinder twin propagation as effectively as twin boundary pinning by Gd solutes. As a result, the twin tip exhibits intermittent motion at the microscopic level.

Simulation of dislocation slip and twin propagation in Mg through coupling crystal plasticity and phase field models

A numerical strategy to simulate plastic deformation in Mg alloys including dislocation slip and twin propagation is presented. Dislocation slip is included through a crystal plasticity model which is solved using the finite element method while twin propagation is taken into account by means of a phase field model which is solved using a fast Fourier transform algorithm. The coupled crystal plasticity and phase field equations were solved using different discretizations of the simulation domain using the same time step for both of them. The numerical strategy was used to simulate the deformation in compression of a Mg micro-pillar along the [101̄0] direction. The stress–strain curve predicted by the model as well as the dominant deformation mechanisms were in agreement with the experimental data in the literature and demonstrate the viability of the strategy to take explicitly into account twin propagation during the simulation of plastic deformation of Mg alloys. Finally, an example of slip/twin interaction in polycrystals was simulated to show the capabilities of the model.

Twin suppression by atomic scale engineering of precipitate-matrix interfaces

This work aims to investigate the influence of solute segregation at particle-matrix interfaces on the twin activity of aged Mg alloys. With that purpose a binary Mg-8Al alloy (wt%) and two ternary Mg-8Al-1 Zn and Mg-8Al-1Ag alloys (wt%) were first homogenized and then aged in order to obtain comparable precipitate distributions. Particle-matrix interfaces in the binary alloy were observed to be clean, while Zn and Ag atomic segregation was clearly present at the interfaces of the ternary alloys. Room temperature micropillar compression tests were carried out in grains with favorable orientations for tensile twinning in the homogenized and the aged conditions for the three materials under investigation. The activation of twinning and slip was then characterized by electron microscopy. This study shows that while in the binary alloy precipitation did not lead to any major changes in the twinning activity and, in particular, it did not prevent the formation of thick twin lamellae encompassing the entire width of the tested micropillars, a drastic reduction of the twin activity took place in the aged ternary alloys. In the latter, straining led to the formation of narrow twin lamellae belonging to a single variant, and occasionally arrested at the interior of the micropillars. We propose that the drastic reduction of the twin volume fraction in the aged ternary alloys may be attributed to the decrease of the particle-matrix interface energy due to Zn and Ag segregation, which would hinder re-nucleation at such interfaces, thus suppressing twin propagation.

Three-dimensional crystal plasticity and HR-EBSD analysis of the local stress-strain fields induced during twin propagation and thickening in magnesium alloys

Present work focuses on analysis of the stress and strain fields inside and around the individual {10–12} twin in magnesium alloy. The 3D crystal plasticity model represents twin as an ellipsoidal inclusion surrounded by the matrix. Five different twin thicknesses and three different lateral twin lengths are used for stress/strain analysis. The simulations are complemented with experimental observations using high-resolution electron backscattered diffraction. The simulations and experiments show a similar distribution of the shear stress and the spatial activity of individual slip systems (basal, prismatic, pyramidal). Plasticity induced inside the twin is dominantly caused by the prismatic dislocations slip and does not influence twin back stress which is identical to pure elastic twin. The twin with larger lateral dimension requires lower equilibrium stress which suggests anisotropic twin propagation and increased thickness of such twins. The lateral twin propagation is mostly influenced by prismatic and pyramidal slip in the twin vicinity. The twin thickness can reach a maximal level that is driven by the critical resolved shear stress values for dislocation slip with the significant influence of basal slip.

Mg-3Al-1Zn alloy deformed along different strain paths: Role of latent hardening

The mechanical properties of magnesium alloy AZ31 were investigated experimentally with visco-plastic self-consistent modeling. Tension, compression and plane strain compression (PSC) tests were performed along 3 directions of a hot rolled plate, and the material parameters input in the model were fitted with the uniaxial stress-strain curves. The critical resolved shear stress (CRSS) for tension twinning was modeled with a modified Voce hardening law first decreasing, and then increasing with strain, that could reproduce better the flow stress for twin-predominant deformation. Such CRSS evolution may better model twin nucleation, propagation and growth. Firstly simulations were carried out assuming latent hardening coefficients for slip by other slip systems equal to self-hardening. Then different heterogeneous latent hardening were used, whose values were based on dislocation dynamics simulations from the literature. This study shows that equal self and latent hardening can reproduce the stress strain curves and plastic anisotropy as well as heterogeneous mode on mode latent hardening. Discrepancies between simulations and experimental results from PSC are explained by an under-estimation of twinning for some PSC strain paths.

Microstructure and deformation behavior of MoReW in the temperature range from 25°C to 1500°C

Refractory alloys which retain high strength above 1000 °C and, at the same time, have excellent malleability, are in high demand for high temperature structural applications. Here we report the microstructure and mechanical properties of an equiatomic MoReW alloy, which has demanding combination of strength and ductility in the temperature range of 25 °C to 1500 °C. The alloy was prepared by arc melting followed by hot isostatic pressing at 1400 °C, 207 MPa for 5 h and it has a single-phase BCC structure with the average grain size of ∼170 μm. The alloy yield stress is relatively low (555 MPa) at 25 °C, but it has weak temperature dependence resulting in remarkably good yield stress values at high temperatures, e.g. 402 MPa at 1000 °C and 247 MPa at 1400 °C. The alloy shows strong strain hardening at 25–1000 °C, with the true flow stress tripled at 25 °C and doubled at 1000 °C after true strain of 0.4. The microstructural analysis of the deformed specimens reveals extensive deformation twinning activity at the beginning of deformation and activation of other deformation modes at later deformation stages in this temperature range. This is unusual behavior as generally activation of twinning occurs at high stresses, after extensive dislocation activity, and deformation twinning in refractory alloys has never been reported above 400 °C. To understand and explain the observed behaviors of the alloy, a detailed analysis of strengthening mechanisms associated with screw and edge dislocation glide, as well as with twin nucleation and propagation, has been conducted and reasonable qualitative models of yielding, strain hardening and ductility of the studied MoReW alloy have been proposed.

Influence of lowering basal stacking fault energy on twinning behaviours

Deformation twinning plays a crucial role in the strong anisotropic strength, poor deformability, and texture and microstructure evolutions of hexagonal metals. Modifying twinning behaviour thus may tailor mechanical behaviour of hexagonal metals. Since propagation and growth of deformation twins inevitably interact with other plastic deformation carriers, such as dislocations, stacking faults and phase transformation bands if they can be activated simultaneously, we hypothesize that lowering basal stacking faults energy (SFE) may promote the activity of partial dislocations, thus generating basal stacking faults (BSFs) and even face centred cubic (fcc) phase. Based on first-principles density functional theory calculations, Al solutes can reduce basal SFE and the cohesive energy difference between hexagonal close packed (hcp) and fcc phases of Ti alloys. Microscopy characterizations of deformed Ti-10at.%Al alloy demonstrated that lowering basal SFE actually promotes the formation of profuse BSFs and fcc nanobands in hcp-phase Ti-10at.%Al alloy during mechanical deformation. Consequently, these defects constrain the propagation and growth of {101¯2} deformation twins. More importantly, BSFs and fcc nanobands are activated from twin boundaries during twinning, pinning deformation twins. As a result, deformation twins in Ti-10at.%Al alloy have an average thickness of ∼130 nm, much thinner than twins in pure Ti and other Ti alloys with the similar grain size and under similar strains. In addition, BSFs and fcc nanobands are activated during twin-twin interactions, releasing local stress/strain concentration. Using topological model and atomistic simulations, we further explored interaction mechanisms between deformation twinning and BSFs or fcc nanobands that formed prior to twinning, and the mechanisms of the emission of BSFs and fcc nanobands from twin boundaries during twinning. This work provides insights into understanding the influence of lowering basal SFE on twinning behaviours in hexagonal metals.

Finite strain crystal plasticity-phase field modeling of twin, dislocation, and grain boundary interaction in hexagonal materials

Twin, dislocation, and grain boundary interaction in hexagonal materials, such as Mg, Ti, and Zr, has critical influence on the materials’ mechanical properties. The development of a microstructure-sensitive constitutive model for these deformation mechanisms is the key to the design of high-strength and ductile alloys. In this work, we have developed a mechanical formulation within the finite strain framework for modeling dislocation slip- and deformation twinning-induced plasticity. A dislocation density-based crystal plasticity model was employed to describe the dislocation activities, and the stress and strain distributions. The model was coupled with a multi-phase-field model to predict twin formation and twin-twin interactions. The coupled model was then employed to study twin, dislocation, and grain boundary interactions in Mg single- and polycrystals during monotonic and cyclic deformation. The results show that twin-twin interactions can enhance the strength by impeding twin propagation and growth. The role of dislocation accommodation on twin-twin interactions was twofold. Dislocation slip diminished twin-twin hardening by relieving the development of back-stresses, while it effectively relaxed the stress concentration near twin-twin intersections and thus may alleviate crack nucleation. The plastic anisotropy in each grain and the constraints imposed by the local boundary conditions resulted in stress variations among grains. This stress heterogeneity was responsible for the observed anomalous twinning behaviour. That is, low Schmid factor twins were activated to relax local stresses and accommodate the strain incompatibility, whereas the absence of high Schmid factor twins was associated with slip band-induced stress relaxation.

Swap motion-directed twinning of nanocrystals.

Twinning frequently occurs in nanocrystals during various thermal, chemical, or mechanical processes. However, the nucleation and propagation mechanisms of twinning in nanocrystals remain poorly understood. Through in situ atomic resolution transmission electron microscopy observation at millisecond temporal resolution, we show the twinning in Pb individual nanocrystals via a double-layer swap motion where two adjacent atomic layers shift relative to one another. The swap motion results in twin nucleation, and it also serves as a basic unit of movement for twin propagation. Our calculations reveal that the swap motion is a phonon eigenmode of the face-centered cubic crystal structure of Pb, and it is enhanced by the quantum size effect of nanocrystals.