Shear Transformation Research Articles

Non-Equal Contributions of Different Elements and Atomic Bonds to the Strength and Deformability of a Multicomponent Metallic Glass Zr47Cu46Al7

Multicomponent metallic glasses (MGs) are a fascinating class of advanced alloys known for their exceptional properties such as limit-approaching strength, high hardness and corrosion resistance, and near-net-shape castability. One important question regarding these materials that remains unanswered is how the different elements and atomic bonds within them control their strength and deformability. Here, we present a detailed visual and statistical analysis of the behaviors of various elements and atomic bonds in the Zr47Cu46Al7 (at%) MG during a uniaxial tensile test (in the z-direction) simulated using molecular dynamics. Specifically, we investigate the identities of atoms undergoing significant shear strain, and the averaged bond lengths, projected z-lengths, and z-angles (angles with respect to the z-direction) of all the atomic bonds as functions of increasing strain. We show that, prior to yielding, the Zr element and the intermediate (Zr-Zr, Cu-Al) and stronger (Zr-Al, Zr-Cu) bonds dominate the elastic deformation and strength, while the Cu and Al elements and the weaker Al-Al and Cu-Cu bonds contribute more to the highly localized shear transformation. The significant reconstruction, as signified by the cessation of bond-length increment and bond-angle decrement, of the intermediate and the stronger bonds triggers yielding of the material. After yielding, all the elements and bonds participate in the plastic deformation while the stronger bonds contribute more to the residual strength and the ultimate (fracture) strain. The results provide new insights into the atomic mechanisms underlying the mechanical behavior of multicomponent MGs, and may assist in the future design of MG compositions towards better combination of strength and deformability.

Structural origin of relaxation in dense colloidal suspensions

Amorphous solids relax via slow molecular rearrangement induced by thermal fluctuations or applied stress. Microscopic structural signatures predicting these structural relaxations have been long searched for but have so far only been found in dynamic quantities such as vibrational quasi-localized soft modes or with structurally trained neural networks. A physically meaningful structural quantity remains elusive. Here, we introduce a structural order parameter derived from the mean-field caging potential experienced by the particles due to their neighbors, which reliably predicts the occurrence of structural relaxations. The structural parameter, derived from density functional theory, provides a measure of susceptibility to particle rearrangements that can effectively identify weak or defect-like regions in disordered systems. Using experiments on dense colloidal suspensions, we demonstrate a strong correlation between this order parameter and the structural relaxations of the amorphous solid. In quiescent suspensions, this correlation increases with density, when particle rearrangements become rarer and more localized. In sheared suspensions, the order parameter reliably pinpoints shear transformations; the applied shear weakens the caging potential due to shear-induced structural distortions, causing the proliferation of plastic deformation at structurally weak regions. Our work paves the way to a structural understanding of the relaxation of a wide range of amorphous solids, from suspensions to metallic glasses.

Inertia effect of deformation in amorphous solids: A dynamic mesoscale model

Shear transformation (ST), as the fundamental event of plastic deformation of amorphous solids, is commonly considered as transient in time and thus assumed to be an equilibrium process without inertia. Such an approximation however poses a major challenge when the deformation becomes non-equilibrium, e.g., under the dynamic and even shock loadings. To overcome the challenge, this paper proposes a dynamic mesoscale model for amorphous solids that connects microscopically inertial STs with macroscopically elastoplastic deformation. By defining two dimensionless parameters: strain increment and intrinsic Deborah number, the model predicts a phase diagram for describing the inertia effect on deformation of amorphous solids. It is found that with increasing strain rate or decreasing ST activation time, the significant inertia effect facilitates the activation and interaction of STs, resulting in the earlier yield of plasticity and lower steady-state flow stress. We also observe that the externally-applied shock wave can directly drive the activation of STs far below the global yield and then propagation along the wave-front. These behaviors are very different from shear banding in the quasi-static treatment without considering the inertia effect of STs. The present study highlights the non-equilibrium nature of plastic events, and increases the understanding of dynamic or shock deformation of amorphous solids at mesoscale.

Nanoindentation-induced serrated flow behavior and deformation mechanism in metallic glass: A combined experiments and molecular dynamics simulation

In this study, the deformation behaviors of bulk metallic glass (BMG) during the nanoindentation are presented via the experiments and molecular dynamics (MD). The relationship between shear transformation zone (STZ) formation and serrated flow dynamics are developed to explain the deformation characterization evolution of BMG. It is found that as the peak load increases, the hardness and elastic modulus significantly decrease. Creep behavior at room temperature was also revealed by analyzing the creep displacement curve and the stress index under different peak loads.The accumulation of free volume during the deformation process promotes more uniform creep deformation. Furthermore, the serrated flow behaviors were analyzed innovatively using the shear stress drops further statistically. At lower loads, the occurrence of serrated retention is due to energy exceeding the potential barrier required for flow unit activation, ultimately released in the form of kinetic energy. At higher loads, the transition from intermittent curve to smooth curve exhibits a typical self-organized critical (SOC) state dynamic characteristics, and ISE phenomenon is also observed. The results also suggested that the shear deformation of the spherical indenter is more pronounced, with the shear band forming at a 45° angle to the direction of the downward pressure. And based on the Cooperative shear model (CSM) theory, the STZ size was estimated and verify that the increment of STZ makes it easier to generate stronger plastic strain to dissipate STZ, ultimately leading to complete plastic deformation. Combining five fold symmetry and gradient atoms, the majority of atoms with five fold symmetry (LFFS>0.5) have stronger resistance to plastic deformation when the load rate is low.

Deformation behavior of thermally rejuvenated Zr-Cu-Al-(Ti) bulk metallic glass

The deformation behavior of metallic glasses has been shown in prior studies to be often dependent on its structural state, namely higher energy “rejuvenated” state versus lower energy “relaxed” state. Here, the deformation behavior of thermally rejuvenated Zr-Cu-Al-(Ti) bulk metallic glasses (BMGs) was evaluated. Rejuvenation was achieved by cryogenic thermal cycling with increase of free volume measured in terms of enthalpy of relaxation. Hardness, stiffness, and yield strength of the BMGs were all found to decrease while plasticity increased after rejuvenation. More free volume in the rejuvenated BMG resulted in homogeneous plastic deformation as was evident from the high strain rate sensitivity and more pronounced shear band multiplication during uniaxial compression. Shear transformation zone (STZ) volume was calculated by cooperative shear model and correlated well with the change in structural state after rejuvenation. The enhanced plasticity with the addition of 1 at. % Ti as well as after cryogenic thermal cycling was explained by lower activation energy for shear flow initiation due to increased heterogeneity induced in the system. Molecular dynamics simulation demonstrated that the variation in plastic deformation behavior is correlated with local atomic structure changes.

Mechanical performance of amorphous diamond-like carbon nanowires

Amorphous carbon nanowires (NW) are a fundamental piece in the study of novel nanoarchitectures with unexpected mechanical properties. However, the failure mechanism of amorphous carbon NW is still missing. In this study, classical molecular dynamics was employed to conduct stress-strain tests to address the mechanical response of amorphous carbons NW with different radii. This research characterizes the mechanical properties of aC NW with different sp3 contents, including Youngs modulus and ultimate tensile stress. Our study reveals that plastic deformation is mediated by chemical modifications in carbon bonding, leading to transitions from sp2 to sp3 and vice versa. We observed that denser amorphous carbon materials undergo a transition from sp3 to sp2 bonding prior to failure, facilitated by the recombination of sp2 clusters. Additionally, plastic deformation in amorphous carbon NW is facilitated by the formation of shear transformation zones and nanovoids, with the deformation mechanism strongly dependent on the average coordination of carbon atoms. These insights provide valuable information for designing nanomaterials with tailored mechanical properties.

The key to high-quality metallic glass casting: Interfacial reaction associated with vacuum induction melting process procedures

Even though vacuum induction melting (VIM) is widely employed in the industrial production of bulk metallic glasses (BMGs), the effect and mechanism of the interfacial reaction between the melt and the oxide ceramic crucible on BMG formations are not yet fully understood. Here, the influences and mechanisms of the interfacial reaction on a Zr-based BMG (Vit 105) subjected to various melting temperatures and holding times are revealed by employing experiments and theoretical calculations. We find that the degree of interfacial reaction is intriguingly correlated with the process parameters during VIM processing, leading to an increase in the oxygen content of the alloy and the reaction layer thickness. Besides, the increase of oxygen content also induces variations in the ordering and shear transformation zone (STZ) size of the BMGs, thus resulting in the precipitation of a nanoscale fcc phase and affecting the mechanical properties and reliability under deformation of the alloy. Furthermore, thermodynamic and kinetic parameters involved in the interfacial reaction, such as the molar Gibbs free energy of each element, the apparent activation energy, etc., are obtained, providing a comprehensive understanding of the transport processes at play. Our findings provide new insights into the preparation of BMGs by VIM and may be expanded to other melting techniques to accelerate the commercial application of metallic glasses.

Salkowski curves and spherical epicycloids

The relationship between Salkowski curves, a family of slant helices with constant curvature and non-constant torsion, and the family of spherical epicycloid curves is studied. It is shown that, for some values of the parameter defining the Salkowski curve, the curve is the image by a shear transformation along the z-axis of a spherical epicycle. Therefore, the projection of both curves on the xy-plane is the same. This result can be extended to the whole family of Salkowski curves if some parameter defining the spherical epicycle is allowed to be a complex imaginary number.

Nanostructured amorphous Al2O3-ZrO2 (La2O3) ceramics with plastic deformation via interface inducing hierarchical shear bands

Ionic-bonded ceramics are featured by their thermal stability, corrosion resistance, hardness and strength, but their applications are limited by the inherent brittleness. Ceramics are composed of strong chemical bonding and intricate crystal structures, making plastic deformation by dislocation slip highly challenging. A nanostructured amorphous Al2O3-ZrO2 ceramic comprising nanoscale amorphous particles and amorphous interfaces between particles was achieved in practice, where the amorphous interface is in scale of approximately 2.34 nm and amorphous particles is in width of approximately 6.75 nm. Based on nano-indentation tests, the shear transformation zone (STZ) volumes of nanostructured amorphous ceramics hot-pressed under various conditions are calculated, suggesting attenuation of free volume with the increase in pressure and temperature. The medium-temperature compression test of the samples exhibits a permanent plastic deformation of 14.6 %, with the presence of hierarchical shear bands in the deformed samples. The main shear bands (MSBs) in width of 0.84–9.15 μm are generated by the stress concentration in crystal-amorphous interface, and the small shear bands (SSBs) of 31–428 nm are related to abundant free volumes in the interface between amorphous particles.

Crystallographic Features of Shear Transformation in Martensitic and Martensitic–Ferritic Stainless Steels

Crystallographic Features of Shear Transformation in Martensitic and Martensitic–Ferritic Stainless Steels

Nucleation mechanisms of shear bands in amorphous alumina

The origin of the plastic deformation in amorphous solids is a challenging issue unlike that of the plasticity in crystals. Plasticity in amorphous systems can occur by the nucleation and propagation of shear bands (SBs). In this work, we investigate the mechanical response of an amorphous alumina sample subjected to shear deformation via extensive molecular dynamics simulations. We find SBs form only within a certain range of parameter values, e.g., low quenching rates, low temperatures and high strain rates. In our proposed atomic-scale model shear transformation zones (STZs) first nucleate and act as precursors of SBs due to their high stress concentration. The results showed that STZs generate an anti-symmetric stress that is responsible for the vortex-like motion of atoms that facilitate the percolation of STZs, finally forming an SB. These results provide insight into the mechanisms of plastic deformation of similar amorphous solids.

Effects of highly-textured and untextured polycrystalline layers on deformation mechanisms in amorphous submicron-layered materials

Amorphous alloys have high strength, but softening can lead to room temperature brittleness, limiting their applications. Typically, soft means low hardness and yield strength, and the lower the yield stress, the higher the fracture toughness. Two amorphous/crystalline multilayer samples with submicron single layer thickness were prepared. The crystalline layer of one sample is composed of highly-textured (111) nanocrystalline grains, and the other sample is untextured. Indentation experiments proved that the samples were plastically deformed, while the amorphous layer did not form shear bands with decreased layer thickness. The thickness reduction of the amorphous layer in the sample with highly-textured crystalline layers is greater than in the sample with untextured crystalline layers. The strain-hardening ability of the textured crystalline layer is higher, while the corresponding amorphous layer is deformed more severely with free volume annihilation and greater flow with more compact atoms. The amorphous layer corresponding to the untextured crystalline layer absorbs dislocations, and activates shear transformation zones (STZs), increasing the free volume near the interface. The annihilation of the free volume is less than the sample with highly-textured crystalline layers.

Atomistically informed mesoscale modelling of deformation behavior of bulk metallic glasses

Both atomistic and mesoscale simulation techniques have been extensively employed to gain fundamental understanding of the structures, deformation mechanisms, and structure-property relationships in bulk metallic glasses (BMGs), each with its unique strengths and limitations. Nevertheless, there is a limited degree of synergistic integration between the two approaches. In this study, we extract key properties of shear transformation zones (STZs) directly from the atomistic simulations, including their size, number of shear modes, eigenstrain, and most importantly, the activation energy barrier spectrum as a function of cooling history and strain rate. We then incorporate these STZ properties into a heterogeneously randomized STZ dynamic model implemented in a kinetic Monte Carlo algorithm to study parametrically the deformation microstructure, shear band formation and stress-strain behavior of BMGs. Two important characteristics of STZ activation that dictate the strength and ductility of a glass are identified. One is the average of the activation energy barrier spectrum (approximated by a Gaussian distribution), determined by the glass composition and processing history such as the cooling rate. The other is the amount of shift of the Gaussian distribution towards smaller activation energy barrier values during deformation, which is determined by the initial structural states and strain rate during deformation, and exhibits a saturation value. These findings have allowed us to gain important fundamental insights into the correlation between the degree of shear-induced softening and the general deformation behavior of BMGs, leading to a better understanding of the correlation between the processing history/loading condition and the mechanical behavior.

Topological characterization of rearrangements in amorphous solids.

In amorphous materials, plasticity is localized and occurs as shear transformations. It was recently shown by Wu etal. that these shear transformations can be predicted by applying topological defect concepts developed for liquid crystals to an analysis of vibrational eigenmodes [Z. W. Wu et al., Nat. Commun. 14, 2955 (2023)10.1038/s41467-023-38547-w]. This study relates the -1 topological defects to the displacement fields expected of an Eshelby inclusion, which are characterized by an orientation and the magnitude of the eigenstrain. A corresponding orientation and magnitude can be defined for each defect using the local displacement field around each defect. These parameters characterize the plastic stress relaxation associated with the local structural rearrangement and can be extracted using the fit to either the global displacement field or the local field. Both methods provide a reasonable estimation of the molecular-dynamics-measured stress drop, confirming the localized nature of the displacements that control both long-range deformation and stress relaxation.

Nanoindentation and relaxation behavior of nitrogen doped zirconium based bulk metallic glass

In this paper, the effect of nitrogen doping on the mechanical properties of Zr-based bulk metallic glasses (BMGs) was studied by nano indentation experiment, and the correlation mechanism between microstructure evolution and mechanical properties was analyzed. The results show that the serrations events exhibited by metallic glasses during nanoindentation are related to the loading rates. With the decreasing loading rate, more obvious serrations events occur in the loading segment, which is attributed to the sufficient time for shear bands to multiply and propagate at low rates. The addition of nitrogen will induce the generation of more flow defects. Compared with BMGs without nitrogen, the nitrogen-doped Zr-based BMGs exhibit more serration events due to introducing more flow defects to form the shear transformation zones (STZs) and subsequently facilitating the shear bands to multiply. The possible relationships between the structural evolution, shear band initiation and propagation, and relaxation behavior of nitrogen doped and non doped metallic glasses were discussed.

Long-term elasto-static compressive loading drives rejuvenation of a metallic glass

The current work focuses on the impact of mechanical protocol which can lead to either rejuvenation or relaxation of metallic glasses (MGs) through elasto-static compressive loading (ECL) treatment. Here we demonstrate that, even after imposing a long-term ECL process, the Zr52.5Cu17.9Ni14.6Al10Ti5 MG subjected to an elasto-static stress of 85% of the yield stress at room temperature shows varying degrees of rejuvenation without any relaxation. The MG undergoes an increasing trend in structural rejuvenation with an increased stored energy and a more disordered structure. Nanoindentation results reveal that the variation of mechanical responses emerges from the complementary effects of the thermal activation process and the structural heterogeneity of glassy phase. The spital heterogeneities can effectively reduce the activation barriers of the shear transformation zones (STZs) and widen their distributions, which will perturb the shear-banding processes from single motion to collective movements, leading to shear band multiplication/branching and an increase in the elastic energy density cut-off. As a result, the plasticity is significantly enhanced and the yield strength is decreased. These findings shed light on that ECL process is an effective way to enhance the structural heterogeneity and the level of rejuvenation of a monolithic MG, which may allow the design of MGs with desirable mechanical properties.

Tensile deformation of metallic glass and shape memory alloy nanolaminates

Mechanical deformation of Cu50Zr50 metallic glasses (MGs) with CuZr B2 layers was explored using tensile tests under iso-strain and iso-stress conditions using molecular dynamics simulations. Atomic structure identification was conducted through machine learning techniques, enabling a distinct examination of the deformation exhibited by each phase. Our results revealed early-stage plasticity driven primarily by shear transformation zones at the amorphous/crystalline interface, rather than shear band formation and propagation observed in the monolithic MG, leading to nanolaminates with enhanced strength. Furthermore, under iso-strain deformation, B2 layers underwent martensitic transformation promoted by the nucleation of voids. However, void growth quickly supersedes these effects under both iso-strain and iso-stress conditions, culminating in sample fracture. In summary, this work advances our understanding of amorphous/crystalline nanolaminates, providing valuable insights into their mechanical complexities.

Thermal cycling-induced evolution of structure and local mechanical properties in metallic glass

The influence of thermal treatment on the long-term mechanical properties of two different kinds of metallic glasses was investigated in this study. As model systems, bulk metallic glasses (BMGs) with the composition of Pd43Cu27Ni10P20 cycled 60, 200, and 500 times between 77 K and room temperature and Zr44Ti11Cu10Ni10Be25 cycled 300, 500, and 700 times have been employed. To ensure that meaningful steady-state properties have been reached, experiments have been performed three years after sample preparation. It was found that the thermal cycling of the Pd-based BMGs had induced rejuvenation when compared to the non-cycled sample, including a higher relaxation enthalpy, lower modulus, hardness, activation volume, and shear transformation zone volume. However, for Zr-BMGs, a rejuvenation to relaxation behavior is observed. Also, while Zr-BMGs showed significantly changes in yielding behavior upon thermal cycling, fluctuations in Pd-BMGs were negligible. We speculate that the observed substantial differences between these two samples might originate because Pd-BMG has a denser structure and higher fragility, making it more difficult to induce excess free volumes.

Mechanism of chip segmentation transition from shear slip to shear fracture of Zirconium-based bulk metallic glass in mechanical machining

An in-depth understanding of material cutting deformation forms the foundation for manufacturing Zirconium-based bulk metallic glass (Zr-based BMG) parts. This study explores the transition in chip segmentation mode from shear slip to shear fracture in Zr-based BMG during mechanical machining. The investigation covers chip micromorphology, cyclic cutting force, machined surface quality, and the themo-mechanical properties under various chip segmentation modes linked to cutting conditions. A size-dependent transition in chip segmentation has been observed in the cutting of Zr-based BMG. At a specific cutting speed, a smaller uncut chip thickness favors chip formation via shear slip, resulting in a smooth primary shear zone (PSZ). Conversely, a larger uncut chip thickness leads to chip shear fracture, with the PSZ displaying fishbone-like and dimple patterns. The integration of the modified cutting kinematic model with the free volume-dependent shear transformation zone (STZ) model suggests that the transition from shear slip to fracture is due to an increase in uncut chip thickness, which causes a greater STZ volume in the PSZ. When the STZ volume surpasses a threshold, the intrinsic structural recovery of material from shearing cannot fully compensate for the free volume softening, leading to excessive free volume that ultimately triggers shear fracture. During the chip shear fracture process, the evolution from fishbone-like patterns to dimples in the PSZ is attributed to faster crack propagation at greater uncut chip thickness or higher cutting speeds. In practical applications, it is advisable to avoid chip shear fracture during machining to maintain high-quality machined surface quality.

Reversing relaxation-induced embrittlement by high-temperature thermal cyclic annealing in Zr-based metallic glass

Annealing usually induces structural relaxation and reduction of liquid-like regions, leading to embrittlement in bulk metallic glasses (BMGs). Here, we find that the short-term high-temperature thermal cycling (HTC) annealed Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vit1) BMG shows an improved plasticity without sacrificing their yield strength. And only relaxation behavior with increased hardness is observed after HTC, which is different from the rejuvenation effect usually observed in cryogenic thermal cycling (CTC). We revealed that this embrittlement reversal is attributed to enhanced fluctuations of full width at half maximum (FWHM) of the hardness’ distribution at micrometer and larger scales induced by short-term HTC. The enhanced fluctuations of mechanical heterogeneities across the diameter on a cross-section of the short-term HTC sample may increase the number and decrease the size of shear transformation zones (STZs) activated at high stress and promote the deflection of shear bands (SBs) during their propagation to form multiple SBs. The enhanced plasticity after HTC induced relaxation contradicts the common sense that relaxation accompanying with annihilation of free volume or liquid-like region usually causes embrittlement. Present results indicate that short-term HTC could be a powerful mean to tune the mechanical performance, shedding new lights on the interplay among relaxation, mechanical/structural heterogeneity, and plasticity of MGs.