Twins In Magnesium Research Articles

Uncovering avalanche sources via acceleration measurements

Avalanche sources describe rapid and local events that govern deformation processes in various materials. The fundamental differences between an avalanche source and its associated measured acoustic emission (AE) signal are encoded in the acoustic transfer function, which undesirably modifies the properties of the source. Consequently, information about the physical characteristics of avalanche sources is scarce and its exposure poses a great challenge. We introduce a novel experimental method based on acceleration measurements, which eliminates the effect of the transfer function and distills the avalanche source. Applying this method to deformation twinning in magnesium shows that the amplitudes and characteristic times of avalanche sources are unrelated by a clear physical law. Conversely, the amplitudes and durations of AE signals are related by a power law, which is attributed to the transfer function. Using our method, we identify and compute a new feature of avalanche sources, which is directly linked to the growth rate of the twinned volume. This feature displays a power-law distribution, implying an unpredicted behavior at dynamic criticality. Simultaneously, the characteristic times of avalanche sources possess an intrinsic upper bound, indicating a predicted limit that relates to the underlying physical process of twinning.

Theoretical models of double twinning in magnesium

Theoretical models of double twinning in magnesium

On the interaction of migrating {112¯6} twin boundary with nucleus of {101¯2} twin in Mg at T → 0 K

Interaction between migrating {112¯6} twin boundary and nucleus of {101¯2} twin in magnesium is studied in a framework of computer simulations. It is demonstrated that {112¯6} boundary can be split into basal-prismatic interfaces during interaction. These basal-prismatic interfaces form new nucleus of {101¯2} twin, which coalesces with a pre-existed nucleus. Subsequent migration of {112¯6} boundary leads to reverse conversion of {101¯2} nucleus into {112¯6} boundary. This process leads to “consumption” of pre-existed {101¯2} twin nucleus by growing of {112¯6} twin.

Energetic contributions to deformation twinning in magnesium

Modeling deformation twin nucleation in magnesium has proven to be a challenging task. In particular, the absence of a heterogeneous twin nucleation model which provides accurate energetic descriptions for twin-related structures indicates a need to more deeply understand twin energetics. To address this problem, molecular dynamics simulations are performed to follow the energetic evolution of tension twin embryos nucleating from an asymmetrically-tilted grain boundary. The line, surface and volumetric terms associated with twin nucleation are identified. A micromechanical model is proposed where the stress field around the twin nucleus is estimated using the Eshelby formalism, and the contributions of the various twin-related structures to the total energy of the twin are evaluated. The reduction in the grain boundary energy arising from the change in character of the prior grain boundary is found to be able to offset the energy costs of creating the other interfaces. The defect structures bounding the stacking faults that form inside the twin are also found to possibly have significant energetic contributions. These results suggest that both of these effects could be critical considerations when predicting twin nucleation sites in magnesium.

Embryo-to-lamella transition of grain boundary twins in magnesium

A combined experimental and computational analysis is performed to investigate the less commonly studied embryo-to-lamella transition of deformation twins in magnesium. This work aims to understand the structural variables controlling the embryo-to-lamella transition from grain boundaries. Statistical analysis of hundreds of early-stage twins in the lightly deformed microstructure reveals a prevailing wedge shape, with a much thicker base along the grain boundary (GB) where they originate and a thinner tip terminating in the crystal. The analysis also shows that the GB base is super thick and identifies a minimum GB twin thickness among all early-stage twins that is about one micron. A crystal plasticity-based full-field model is employed to calculate the driving forces to migrate the boundary of a three-dimensional GB twin embryo. The stress analysis, considering a full range of embryo shapes and neighboring grain orientations, indicate that the twin embryo is most likely going to form a wedge shape when it first propagates. The calculations predict that the thickness of the embryo at the GB needs to be significantly larger than its length into the crystal in order to propagate into the crystal. The analysis finds that the more aligned the twin embryo variant is with basal slip in the neighboring grain, the thinner the twin embryo needed for propagation.

Atomistic simulations of twin facets associated with three-dimensional {[formula omitted]} twins in magnesium

Twinning is a deformation mechanism that creates three-dimensional (3D) twin domains through the migration of twin facets. This occurs via the nucleation and glide of twinning disconnections (TDs), which can pile up to create twin facets. A comprehensive understanding of twin facets associated with 3D twins, including their atomic structures and energies, is crucial for understanding deformation twinning. In this study, we propose a molecular statics/dynamics (MS/MD) approach to determine characteristic twin facets enclosing 3D non-equilibrium/equilibrium {1¯011} twin domains, which has been much less studied than the counterpart {1¯012} twin domains. The stability of different TD pile-up arrangement with varying line senses informs the morphology of 3D non-equilibrium twins, which are bounded by {101¯0}T||{1¯013}M, {101¯1}T||{0002}M and {101¯3}T||{101¯3}M coherent facets associated with pile-up of edge TDs, and discrete non-edge TDs aligned along CTBs with their line senses parallel to <45¯13>, <11¯01>, <54¯1¯6> <21¯1¯3>or <101¯2> axes. Formation of semi-coherent facets of equilibrium twins is accompanied by rearrangement of TDs around misfit dislocations. 3D equilibrium {1¯011} twins may comprise {101¯1}T||{0002}M, {145¯7}T||{34¯19}M, {1¯65¯7}T||{56¯17}M, {1¯43¯3}T||{34¯13}M, {011¯0}T||{011¯1}M and {02¯21}T||{02¯21}M semi-coherent facets in <12¯10>, <45¯13>, <11¯01>, <54¯1¯6>, <21¯1¯3> and <101¯2> axes, respectively.

Three-dimensional shape and stress field of a deformation twin in magnesium

While the three-dimensional (3D) shape and stress field of a twin in hexagonal close-packed (HCP) metals have attracted considerable interest in recent years due to their substantial impact on internal stress and mechanical properties, a detailed understanding of their variation with twin size is still lacking. An analytical model that is not restricted by spatial scale is developed in this work by considering the effects of anisotropic twin boundary energy, elastic strain energy and plastic relaxation to predict the 3D shape with the minimum energy, and the stress field, of an isolated ellipsoidal twin of different sizes. The model is applied to Mg with a focus on the {101¯2} twin type. The analytical calculation results show that the nucleation of the nano-sized twin embryos is facilitated by the stress field near structural defects such as dislocations. During the expansion of this nano-sized twin embryo, the interplay between the elastic strain energy and interfacial energy changes the length of the twin along the twin shear (forward) direction from being shorter to longer than that along the lateral direction. In contrast to the current understandings, the maximum shear stress on the twin plane along the twin shear direction occurs at the lateral, rather than the forward, side of the twin. At the forward side, the maximum shear stress occurs at a distance ahead of the twin tip and this distance increases with increasing twin thickness.

Manufacturing Strategies to Mitigate Deformation Twinning in Magnesium

Abstract Magnesium (Mg) alloys exhibit poor room temperature ductility, which prohibits forming operations in cost-effective industrial settings and the use of these alloys in critical safety components. Profuse twinning in Mg alloys is widely associated with high strain path anisotropy and low material ductility. Twinning typically propagates across the grains through the autocatalysis phenomena in typical texture conditions. Twin–twin and twin–slip interactions often lead to high strain incompatibilities and eventually failure. One way to avoid such premature failure is to prevent the early nucleation of twins. This research tests a hypothesis that a strong yet ductile phase surrounding each individual grain in traditional polycrystals could inhibit twin accommodation effects and thus twin nucleation and autocatalysis mechanisms at grain boundaries. As a proof-of-concept for testing this hypothesis, sharply textured magnesium sheets plated with different materials were subjected to four-point bending to assess the potential of a surface/grain boundary barrier in limiting twinning extent. The results showed that Mg AZ31 alloy plated with zinc alleviated twin nucleation while improving the strength of the alloy.

Micromechanical Fields Associated with Irregular Deformation Twins in Magnesium

Understanding and controlling the development of deformation twins is paramount for engineering strong and stable hexagonal close-packed (HCP) Mg alloys. Actual twins are often irregular in boundary morphology and twin crystallography, deviating from the classical picture commonly used in theory and simulation. In this work, the elastic strains and stresses around irregular twins are examined both experimentally and computationally to gain insight into how twins develop and the microstructural features that influence their development. A nanoprecession electron diffraction (N-PED) technique is used to measure the elastic strains within and around a left{ {10overline{1}2} right} tensile twin in AZ31B Mg alloy with nm scale resolution. A full-field elasto-viscoplastic fast Fourier transform (EVP-FFT) crystal plasticity model of the same sub-grain and irregular twin structure is employed to understand and interpret the measured elastic strain fields. The calculations predict spatially resolved elastic strain fields in good agreement with the measurement, as well as all the stress components and the dislocation density fields generated by the twin, which are not easily obtainable from the experiment. The model calculations find that neighboring twins, several twin thicknesses apart, have little influence on the twin-tip micromechanical fields. Furthermore, this work reveals that irregularity in the twin-tip shape has a negligible effect on the development of the elastic strains around and inside the twin. Importantly, the major contributor to these micromechanical fields is the alignment of the twinning shear direction with the twin boundary.

In Situ Characterization of Deformation Twinning in Magnesium During Cyclic Loading via Electron Backscatter Diffraction

In Situ Characterization of Deformation Twinning in Magnesium During Cyclic Loading via Electron Backscatter Diffraction

The cross-transition of deformation twinning in magnesium

Deformation twinning operates via twinning dislocations gliding on a specific twinning plane and along a specific twinning direction. As a consequence, a twin variant is supposed to retain its identity and unable to transform into other variants. However, we demonstrated that for the {101¯2} deformation twinning in magnesium, one twin variant can transform towards its conjugated variant in response to the external applied loading via the participation of prismatic-basal interface migration. We term such transformation as cross-transition of deformation twinning, which is expected to broaden the understanding of twinning mechanism.

Formation and annihilation of stressed deformation twins in magnesium

The mechanical response of polycrystalline materials to an externally applied load and their in-service performance depend on the local load partitioning among the constituent crystals. In hexagonal close-packed polycrystals such load partitioning is significantly affected by deformation twinning. Here we report in-situ compression-tension experiments conducted on magnesium specimens to measure the evolution of grain resolved tensorial stresses and formation and annihilation of twins. More than 13000 grains and 1300 twin-parent pairs are studied individually using three-dimensional synchrotron X-ray diffraction. It is shown that at the early stages of plasticity, the axial stress in twins is higher than that of parents, yet twins relax with further loading. While a sign reversal is observed for the resolved shear stress (RSS) acting on the twin habit plane in the parent, the sign of RSS within the majority of twins stays unchanged until twin annihilation during the load reversal. The variations of measured average stresses across parents and twins are also investigated.

Phase-field model of deformation twin-grain boundary interactions in hexagonal systems

A phase-field model for describing dynamic interactions between deformation twins and grain boundaries in a hexagonal close packed (HCP) metal is established. It is applied to simulating the coupled evolution mechanisms of grains and twins in magnesium (Mg) by probing the transmission of {101¯2}deformation twins across grain boundaries. We analyze the effect of the strain relaxation near a grain boundary, which is related to the geometric compatibility arising from the misorientation angle between adjoining grains. Phase-field simulations demonstrate that twin transmission across a grain boundary into a neighboring grain leads to grain boundary migration towards the neighboring grain with a reduced grain boundary width. The preferred nucleation site of new twin variant in the neighboring grain is related to the elastic interaction energy distribution. These predicted transmission behaviors agree well with existing experimental observations and molecular dynamics simulations. By analyzing set of systematic phase-field simulation results, we establish a rotation-angle-related twin variant selection rule for analyzing the transmission of {101¯2}deformation twins across grain boundaries in Mg and its alloys.

Nucleation of {1012} Twins in Magnesium through Reversible Martensitic Phase Transformation

We report the discovery of a rigorous nucleation mechanism for {101¯2} twins in hexagonal close-packed (hcp) magnesium through reversible hcp-tetragonal-hcp martensitic phase transformations with a metastable tetragonal phase as the intermediate state. Specifically, the parent hcp phase first transforms to a metastable tetragonal phase, which subsequently transforms to a twinned hcp phase. The evanescent nature of the tetragonal phase severely hinders its direct observation, while our carefully designed molecular dynamics simulations rigorously reveal the critical role of this metastable phase in the nucleation of {101¯2} twins in magnesium. Moreover, we prove that the reversible hcp-tetragonal-hcp phase transformations involved in the twinning process follow strict orientation relations between the parent hcp, intermediate tetragonal, and twin hcp phases. This phase transformation-mediated twinning mechanism is naturally compatible with the ultrafast twin growth speed. This work will be important for a better understanding of the twinning mechanism and thus the development of novel strategies for enhancing the ductility of magnesium alloys.

Characteristic boundaries associated with three-dimensional twins in hexagonal metals.

Twinning is a critically important deformation mode in hexagonal close-packed metals. Twins are three-dimensional (3D) domains, whose growth is mediated by the motion of facets bounding the 3D twin domains and influences work hardening in metals. An understanding of twin transformations therefore necessitates that the atomic-scale structure and intrinsic mobilities of facets be known and characterized. The present work addresses the former point by systematically characterizing the boundary structures of 3D twins in magnesium using high-resolution transmission electron microscopy (HRTEM). Eight characteristic facets associated with twin boundaries are reported, five of which have never been experimentally observed before. Further, molecular dynamics simulations suggest that the formation and motion of these facets is associated with the accumulation of twinning dislocations. This work provides insights into understanding the structural character of 3D twins and serves to develop strategies for modulating twin kinetics by modifying twin boundaries, such as solute segregation.

Phase-Field Model of Deformation Twin - Grain Boundary Interactions in Polycrystalline Hexagonal Systems

A phase-field model for describing dynamic interactions between deformation twins and grain boundaries in a hexagonal close packed (HCP) metal is established. It is applied to simulating the coupled evolution mechanisms of grains and twins in magnesium (Mg) by probing the transmission of {101 2} deformation twins across grain boundaries. We analyze the effect of the strain relaxation near a grain boundary, which is related to the geometric compatibility arising from the misorientation angle between adjoining grains. Phase-field simulations demonstrate that twin transmission across a grain boundary into a neighboring grain leads to grain boundary migration towards the neighboring grain with a reduced grain boundary width. The preferred nucleation site of new twin variant in the neighboring grain is related to the elastic interaction energy distribution. These predicted transmission behaviors agree well with existing experimental observations and molecular dynamics simulations. By analyzing set of systematic phase-field simulation results, we establish a rotation-angle-related twin variant selection rule for analyzing the transmission of {101 2} deformation twins across grain boundaries in Mg and its alloys.

Finite strain phase-field microelasticity theory for modeling microstructural evolution

Implementing the phase-field model at finite strains is usually considered unattainable through the spectral method, largely because of the nonlinearity in the transformation-induced microelasticity. Here we present a phase-field microelasticity (PFM) theory at finite strains with a representation in the reference configuration, allowing the spectral method to be readily incorporated. Following the spirit of Khachaturyan’s PFM theory at small strains, the elastic energy is formulated as a functional of microstructure (order parameters) solely, which should automatically satisfy the mechanical equilibrium. Thermodynamic consistency of the current theory under multiplicative decomposition of the total deformation gradient (into elastic and inelastic parts) and in conjunction with hyperelasticity and the time-dependent Ginzburg-Landau equation is shown rigorously. The new theory is first applied to the classical Eshelby’s inclusion problem, where shear-dilation coupling due to geometric nonlinearity is shown and a convergence study between small strain and finite strain theories is also carried out. The effects of geometric nonlinearity on the co-evolution of micromechanics and microstructure is further studied through modeling the growth of {101¯2}〈1¯011〉 deformation twins in magnesium. The simulation results suggest significant differences in terms of the shape of and the stress field around the deformation twin. In particular, the current finite strain PFM theory predicts a deviation of the twin boundary plane from the theoretical K1 plane, which is not captured in the small strain theory nor in the crystallographic theory. A parametric study further reveals that the observed deviation is caused by the tip effect of the finite-sized twin plate when the aspect ratio is relatively small. The symmetry of the stress field distribution around the twin tip is also found to be drastically different between the small strain and finite strain based phase-field modeling. The sharp twin tip observed in experiments is also shown to be likely related to the anisotropy in twin/matrix interface mobility.

The strengthening effects of basal stacking faults on {10–12} twin in magnesium: A molecular dynamics study

{10–12} twin is one of the softest deformation modes in magnesium. And basal stacking fault is one of the most abundant planar defects in magnesium. In this work, we studied the strengthening effects of basal stacking faults on {10–12} twin, using molecular dynamics method. The results suggest that both stacking faults I1 and I2 show great strengthening potentials on {10–12} twin. Moreover, the strengthening effects of stacking fault I1 is stronger than that of I2. As byproducts, the morphologies of dislocations on the {10–12} twin boundary and BP interface were characterized. A formation mechanism of BP interface was also proposed.

Dislocation ↔ twin transmutations during interaction between prismatic slip and [formula omitted] twin in magnesium

Very unusual and interesting interaction between matrix prismatic dislocations and {101¯1} twin boundaries (TBs) in Magnesium (Mg) was observed in atomistic simulations. When the first prismatic dislocation impinged on the TB, the incoming dislocation was transmuted into a thin layer of {112¯1} twin inside the {101¯1} twin. When successive prismatic dislocations on the same slip plane impinged on the same location at the {101¯1} TB, the {112¯1} twin kept growing toward the opposite {101¯1} TB. Eventually, the {112¯1} twin reached the opposite TB and was then transmuted back to prismatic dislocations that exited the {101¯1} twin and glided into the matrix. Hence, the matrix prismatic dislocations temporarily lose their dislocation identity during twin-slip interaction and then resume their dislocation identity after the interaction is complete. The net effect of these interactions is that the matrix prismatic dislocations transmit across the {101¯1} twin. Lattice correspondence analysis for {101¯1} twinning was performed to understand the mechanism of the interactions. The results show that, the prismatic slip plane is exactly the corresponding plane of {112¯1} twinning. Such a correspondence is consistent with the crystallographic calculations based on classical twinning theory.

Non-diffusional growth mechanism of I1 basal stacking-faults inside twins in hcp metals

Deformation twins in magnesium exhibit considerable densities of I1 basal-plane stacking-faults. Since these faults generally transect their host twin, they presumably lengthen concommitantly with boundary migration during twin growth. We investigate this process using atomic-scale simulation for 101¯2 and 101¯1 twinning. It is demonstrated first that the intersection of a stacking-fault with a stationary twin boundary is delineated by a sessile imperfect disconnection. Subsequently, by applying a shear strain, we stimulate twin growth by the passage of twinning disconnections along twin boundaries, and show that these are able to propagate through such pre-existing imperfect disconnections in a conservative manner.