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Abstract Strain localization during plastic deformation drastically reduces the shear band stability in metallic glasses, ultimately leading to catastrophic failure. Therefore, improving the plasticity of metallic glasses has been a long-standing goal for several decades. In this regard, nanoglass, a novel type of metallic glass, has been proposed to exhibit differences in short and medium range order at the interfacial regions, which could promote the formation of shear transformation zones. In the present work, by introducing heterogeneities at the nanoscale, both crystalline and amorphous, significant improvements in plasticity are realized in micro-compression tests. Both amorphous and crystalline dispersions resulted in smaller strain bursts during plastic deformation. The yield strength is found to increase significantly in Cu–Zr nanoglasses compared to the corresponding conventional metallic glasses. The reasons for the mechanical behavior and the importance of nanoscale dispersions to tailor the properties is discussed in detail. Graphic Abstract

Orientation microscopy (EBSD) has been used to investigate the structure of austenitic stainless steel containing 18% Cr and 9 wt % Ni after its long-term operation at high temperatures and neutron irradiation. The γ → α shear transformation has been implemented partially in the samples during deformation-free cutting. Austenite has decomposed due to isotropic stresses oriented normally to the surface under study. The precision of orientation relationships (ORs), such as Kurdjumov–Sachs, Nishiyama–Wassermann, Greninger–Troiano, and others during γ → α transformation has been comparatively analyzed. The Greninger–Troiano OR has been found to be the best possible OR describing the transformation in this case. The α phase has been shown to nucleate at coherent twin boundaries (Σ3 in the coincidence site lattice model) between austenite grains. This has determined the variants of the current ORs and the unambiguous crystallographic orientation of α-phase grains.

The elementary excitations in metallic glasses (MGs), i.e., β processes that involve hopping between nearby sub-basins, underlie many unusual properties of the amorphous alloys. A high-efficacy prediction of the propensity for those activated processes from solely the atomic positions, however, has remained a daunting challenge. Recently, employing well-designed site environment descriptors and machine learning (ML), notable progress has been made in predicting the propensity for stress-activated β processes (i.e., shear transformations) from the static structure. However, the complex tensorial stress field and direction-dependent activation could induce non-trivial noises in the data, limiting the accuracy of the structure-property mapping learned. Here, we focus on the thermally activated elementary excitations and generate high-quality data in several Cu-Zr MGs, allowing quantitative mapping of the potential energy landscape. After fingerprinting the atomic environment with short- and medium-range interstice distribution, ML can identify the atoms with strong resistance or high compliance to thermal activation, at a high accuracy over ML models for stress-driven activation events. Interestingly, a quantitative “between-task” transferring test reveals that our learnt model can also generalize to predict the propensity of shear transformation. Our dataset is potentially useful for benchmarking future ML models on structure-property relationships in MGs.

Shear transformation zones (STZs) are widely believed to be the fundamental flow defects that dictate the plastic deformation of amorphous alloys. However, it has been a long-term challenge to characterize STZs and their evolutions by experimental methods due to transient nature. Here we first introduced a consistent, automated, robust method to identify STZs by linear based machine learning outlier detection algorithms. We exemplify these algorithms to identify the atoms of STZs in Cu64Zr36 metallic glass system, and verify this data-driven model with a physical based model. It is revealed that the average STZ size slightly increases with decreasing cooling rate.

The mechanical relaxation behavior of metallic glasses (MGs) is composition sensitive. For example, in dynamic mechanical analysis, La70Ni15Al15 shows a pronounced secondary peak, termed β relaxation, of the normalized loss modulus at high frequency and/or low temperature, while La70Cu15Al15 only exhibits a shoulder. We have determined relaxation-time spectra at room temperature for these alloys over eleven orders of magnitude of time from quasi-static anelastic relaxation measurements. These are employed to characterize shear transformation zone (STZ) properties in both the α and β regimes. The pronounced β relaxation peak, observed for La70Ni15Al15, is a result of both larger volume fraction of fast and small potential STZs and smaller volume fraction of slow and large potential STZs as compared to La70Cu15Al15. Room-temperature tensile tests show increasing plasticity with decreasing strain rates, characteristic of thermally activated processes. La70Cu15Al15 exhibits greater plasticity than La70Ni15Al15, a negative correlation with the intensity of the β relaxation that is opposite to that previously suggested. The STZ spectra are used to explain the plasticity difference between the two alloys. Plasticity predictions from loss modulus measurements need to be revised, and require absolute measurements.

Lattice inhomogeneities, i.e. nitrogen interstitial-induced hexagonal-close-packed martensite (HCP-eN) and shear bands, can form in face-centred cubic nitrogen-expanded austenite (FCC-γN) synthesised on Fe-Cr-Mn and Fe-Cr-Ni austenitic stainless steel (ASS) using triode-plasma nitriding (TPN). Homogenous elemental distribution between HCP-eN and FCC-γN supports the displacive shear transformation mechanism proposed for a high-Mn, low stacking fault energy ASS under nitrogen interstitial-induced deformation. While being a product of transformation-induced plasticity effect, HCP-eN exhibits similar lattice expansion behaviour to the parent FCC-γN. However, inhomogeneous elemental distributions in the shear bands formed in γN layers on a 400°C TPN-treated high-Ni ASS indicate local migration of substitutional elements.

Metallic nanoglasses are non-crystalline solids with interfacial regions, typically characterized by a modified short-range order and compositional gradients. These interfaces can act as nucleation sites for the formation of shear transformation zones during mechanical deformation, which gives rise to a deformation behavior distinct from the bulk glass counterpart. While various studies have investigated nanoglasses experimentally (mostly Fe–Sc) and in computer simulations (typically Cu–Zr), there is hitherto no study comparing compositionally identical nanoglasses and conventional metallic glasses by experiments and simulations. In this contribution, we investigate Pd–Si as a model system and compare nanoglasses produced by inert gas condensation with melt-spun ribbons. Molecular dynamics simulations and atom probe tomography provide evidence that glass–glass interfaces are primarily topological and chemical defects in this particular system. Differential scanning calorimetry shows a decrease in the glass transition and crystallization temperature of the nanoglasses compared to melt-spun ribbons. Nanoindentation and micropillar tests on Pd–Si metallic nanoglasses, however, provide evidence for shear band formation in both sample types, the melt-spun ribbons and nanoglass. Shear bands in the nanoglass samples appear more diffuse as compared to melt-spun ribbons. This is also evident from the reduced strain localization in the nanoglass. It is concluded that the topological inhomogenieties induced by forming glass–glass interfaces significantly affect the mechanical properties of nanoglasses.

An amorphous/crystalline metallic composite (A/C-MC) integrates metallic glass with crystalline metals in one system. The amorphous-crystalline interface (ACI) in A/C-MCs under deformation absorbs dislocations and may fundamentally change the dilemma that the strength comes at the expense of the ductility of a material. However, the development of such materials is still at a trial and error stage due to the lack of a clear-cut understanding on how the amorphous component become instable when a dislocation-mediated plasticity flows into the glassy phases. To meet this need, here we focus on gaining the physical insights into the dislocation-ACI reaction in A/C-MCs through atomistic simulations. We have (i) digitally resembled an interface structure close to that in experiments by annealing melted metallic glasses at cooling rates as low as ∼ 104 K/s; (ii) correlated the dislocation absorption events with the activation of shear transformation zones (STZs) in A/C-MCs under a plastic shear; (iii) identified the mechanisms responsible for a continuous dislocation absorption-induced instability in glassy phases; (iv) calibrated a set of constitutive relations, kinetic rules, and model parameters that can be used in an effective temperature concept-based STZ theories at the continuum level; and (v) characterized the local stress states ahead of the instability band and lay the macroscopic-level glass instability criterion on a firm atomistic basis. Our major findings are: (a) there exists a nanoscale structure transition at the ACI when the cooling rate in the atomistic simulations is reduced to an experimentally-comparable level; (b) the number of atoms participating in the STZs exponentially increases with the number of dislocations arriving at the ACI at an early stage of the dislocation-ACI reaction, but is linearly proportional to the number of absorbed dislocations at a later stage; (c) the dislocation absorption-induced instability in metallic glasses occurs through a three-stage process, i.e., the activation of STZs in the region between icosahedral (ICO) clusters, the coalescence of newly formed STZs, and then the breakdown of ICOs; (d) the model parameters in the continuum-level constitutive relations and kinetic rules are found to be sensitive to cooling rates; and (e) the local stress states ahead of the instability band in glassy phases map surprisingly well with the Mohr-Coulomb criterion regardless of the applied stress at the macroscopic level. The gained knowledge may provide a pathway of connecting the atomistic deformation physics of an A/C-MC with its overall mechanical performance, which is currently difficult to achieve in laboratory experiments.

Unlike obviously topological defects in crystals, “defect” identification in metallic glasses (MGs) is still controversial and under investigation. Based on molecular simulations and analysis of MG samples, a structural parameter related to the Laplacian of local equivalent stiffness is proposed for prediction of localized shear deformation in MGs. It is found that local regions with the parameter of positive and relatively large value represent several particular modes of “stiffness valleys” in initial configuration which will strengthen local shear deformation and lead to the formation of shear transformation zones (STZs). More than 80% of the locations where STZs are formed in six types of MG samples under athermal quasi-static shear deformation match well with the regions predicted by the parameter calculated from initial configuration of the samples. The parameter not only reveals the relationship among local heterogeneity, nonaffine displacement, and shear localization, but also provides an efficient way for predicting the activation of STZs in MGs.

Interference between the grids of the camera sensor and the screen cause moire patterns to always appear on photographs captured from a screen, significantly affecting people’s ability to review images. We propose a novel method to remove such a screen moire pattern from a single image. We characterize the degraded image as a composition of two layers: the latent layer and the moire pattern layer. Because the screen moire pattern is global and content-independent, we regard it as a group of sublayers , and we find that each sublayer after the shear transformation has a low-rank property . Combined with the piecewise constant feature of the latent layer, a convex model is proposed to solve the demoireing problem. Experiments on synthetic and real data demonstrate its feasibility and efficiency.

The incipient plasticity of an amorphous solid represents the onset of shear deformation, which is a stochastic progress closely related to microstructure evolution. It is well known that the cooling rate plays a crucial role in the microstructure evolution of a glass. Nevertheless, how the cooling rate affects the incipient plasticity is still unclear. In this work, the incipient plastic deformation of the amorphous phase in Cu47.5Zr48Al4Nb0.5 bulk metallic glass composites (BMGCs) cast with different cooling rates is systematically studied. The incipient plasticity of the glassy matrix of the BMGCs is found to occur via a first displacement burst, the occurrence of which is more stochastic as the cooling rate decreases. According to the auto-correlation functions and cooperative shear model, the stochastic behavior is attributed to the effects of the cooling rate on the initial free volume and subsequent activated shear transformation zones (STZs). A higher content of free volume is present in the glassy matrix of the studied samples cooled at a faster rate, which facilitates the operation of STZs. Moreover, the larger incipient burst size is correlated with the higher content of free volume and larger STZs in the glassy matrix. The larger STZs result in more preferable propagation of multiple shear bands, leading to less stochastic deformation and more obvious plastic deformation. This study provides further understanding on the incipient plasticity of glassy matrix in BMGCs.

Aiming at the problem of irregular shape and low contrast of the scratches in the image of mobile phone screen, a method based on machine vision was proposed to detect the surface scratches of mobile phone screen. Firstly, the PatMax algorithm and affine transformation were adopted to preprocess the screen images of mobile phone. Then the shear transformation was used to decompose the image into two parts: low frequency and high frequency, the element shapes in four directions of 0°, 45°, 90° and 135° were constructed to perform gray-scale closing operation on the low frequency part, and the N × M median filter denoising operation was performed on the high frequency part, the enhanced image was generated by the inverse shear transformation. Finally, the improved Otsu double threshold method was used to extract the target. 450 pieces of mobile phone screen images were randomly selected for experiments, and the highest detection rate is 98.7%. The results show that this method can effectively enhance the detail information of the images, which greatly guarantees the integrity of the scratch defects.

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An anomaly in martensitic transformation (the effect of martensitic two-peak splitting in the temperature-dependent thermal expansion coefficient) in complex alloyed 12% chromium steels Fe-12%Cr-Ni-Mo-W-Nb-V-B (ChS-139), Fe-12%Cr-Mo-W-Si-Nb-V (EP-823) and Fe-12%Cr-2%W-V-Ta-B (EK-181) was investigated in this study. This effect is manifested in steels with a higher degree of alloying (ChS-139). During varying temperature regimes in dilatometric analysis, it was found that the splitting of the martensitic peak was associated with the superposition of two martensitic transformations of austenite depleted and enriched with alloying elements. The anomaly was subsequently eliminated by homogenization of the steel composition due to high-temperature aging in the γ-region. It was shown that if steel is heated to 900 °C, which lies in the (α + γ) phase region or slightly higher during cooling, then the decomposition of austenite proceeds in two stages: during the first stage, austenite is diffused into ferrite with carbides, during the second stage, shear transformation of austenite to martensite occurs.

Johari–Goldstein (JG) relaxation closely relates to the shear transformation zones (STZs) in the flow of metallic glasses (MGs). However, the actual role played by JG relaxation in the STZ-evoked plastic deformation of MGs remains unknown. In this work, by substituting the transition metal (TM) element in La(TM)Al MGs (TM = Ni, Co, Cu, CuNi) to tune the feature of JG relaxation, how JG relaxation alters the deformation behaviors of MGs is tentatively examined with nanoindentation. The results demonstrate that JG relaxation modulates the anelastic to plastic transition rate in the plastic deformation accommodation of MGs via a characteristic relaxation time.

A novel Cu–Zr nanoglass consisting of glassy nano-cells connected by oxide interfaces is proposed. Compared to conventional nanoglasses, the novel oxide-connected nanoglass presents ultrahigh tensile strength and superior tensile plasticity at ambient temperature. Subjected to tensile loading, the oxide interfaces are found to promote the nucleation of shear transformation zones (STZs) due to the existence of excess free volume. Meanwhile, the strong bonding between metallic and oxygen atoms in the oxide interface makes it difficult for STZs to propagate through. Thus, the STZs are effectively proliferated and confined inside the cell interior without any mature shear band (SB) formed. The results provide new ideas for toughening metallic glasses with a decent combination of plasticity and strength, thus making it possible to overcome the longstanding strength-ductility trade-off dilemma.

We report martensitic shear transformation of strongly segregated block copolymer micelles on face-centered cubic (FCC) lattices to hexagonally close-packed (HCP) structures elucidated by X-ray sca...

The plastic deformation of metallic glasses (MG) is well-known to occur via shear transformation zones (STZs) on the scale of atomic clusters, yet fracture of MG takes place via shear bands of the micron scale. So far, understanding on how the operation of STZs leads to shear localization and fracture remains limited. In this work, tensile tests on Cu/Zr-based MG micro-wires show that both the first-yield and fracture stress exhibit the Weibull distribution, and fractography reveals that shear localization in the form of intense shear bands leads to shear fracture. Molecular dynamics (MD) simulations show that shear bands form via the correlated emergence and operation of discrete STZs close to one another. To describe how the stochastic yet correlated occurrence of the discrete STZs leads to shear localization, a model is constructed to relate the probability of the successive operation of discrete STZs, to their nucleation density. The model predicts that, if nucleation density of the STZs grows along the strain path, as prior shear events triggers the emergence of new STZs, then successive occurrence of discrete shear events speeds up rapidly to an asymptotic state which is exactly the condition of shear localization and shear banding. Furthermore, the MD results suggest an exponential growth law for the occurrence of the STZs along the strain path, which also gives predictions in good agreement with the experimental Weibull distributions of the first-yield stress of Cu/Zr-based MGs.

Dual-phase crystalline/amorphous nanostructure model is an effective method to improve the mechanical properties of Mg alloys. The effects of amorphous thickness and crystal orientation on the plastic deformation mechanism of dual-phase crystalline/amorphous Mg/Mg-Al nanolaminates under tensile loading are investigated by using molecular dynamics simulation method. The results indicate that for the model in which the crystal phase orientation is [0 0 0 1] along tensile direction, with the increase of amorphous thickness, the deformation mechanism of samples changes from localized deformation dominated by generalized shear band (GSB) to the homogeneous plastic deformation. Here, the uniform plastic deformation is achieved by combining complete basal-prismatic (BP) transformation in crystal phase and uniformly distributed shear transformation zones in amorphous phase. The results also show that for the large amorphous thickness model, there is an obvious secondary hardening stage in the plastic deformation process, and the large amorphous phase is conducive to the formation of BP interface. However, when the crystal orientation is [ 1 - 0 1 0] along tensile direction, all samples undergo local plastic deformation dominated by GSB, which indicates that the plastic deformation mechanisms of dual-phase nanolaminates depend not only on the thickness of amorphous phase, but also on the orientation of crystalline phase.

Molecular dynamics (MD) simulations are conducted to investigate the influence of various critical structural aspects such as crystallographic direction, spatial distribution and size/volume fraction of nanoscale crystalline secondary phase on the mechanical behavior of dual-phase nanocrystal-metallic glass composites (NCMGCs). The results of MD simulations show that the ‘softer’ amorphous matrix and amorphous-crystal interfaces serve as the nucleation sites of the shear transformation zones, and eventually developing into mature shear bands (SBs). We find that the different crystallographic directions of the nanocrystals have great influence on elastic modulus of composites. Moreover, the spatial distribution of nanocrystals plays an important role in SBs propagation direction. In particular, by increasing the volume fraction of the crystalline phase, plastic co-deformation of the SBs and stacking faults is achieved for the NCMGCs with nanocrystals of [1 1 0] and [1 1 1] directions. Moreover, the presence of stacking faults releases most of the stress of nanocrystals and retards the formation of a mature SB. By systematically varying the characteristics of the B2 CuZr nanoscale crystalline phase one can design composites with improved mechanical properties.

Fe-based amorphous alloys with excellent soft magnetic properties always suffer catastrophic annealing embrittlement. The soft magnetic and mechanical properties of a series of Fe84.3-xCoxSi2B13Cu0.7 (x = 0, 2, 4, 6, 8) amorphous alloy ribbons were investigated. With appropriate substitution of Co for Fe, the BS of the alloys shows a slight increase and the HC remains at a low level. From two-point bending tests, a sharp transition from ductility to brittleness can be observed upon annealing. The embrittlement can be attributed to localized shear bands due to shear bands branching during deformation. It is found that the ductile-brittle transition temperature increases slightly by applying cryogenic thermal cycling treatment to annealed ribbons, indicating that the annealing embrittlement can be improved to some extent by cryogenic thermal cycling treatment. According to nanoindentation results, the increased shear transformation zone volume is responsible for the bending ductility increment. Ultimately, a ductile Fe80.3Co4Si2B13Cu0.7 amorphous alloy ribbons with a BS of 1.68 T and a HC of 4.8 A/m were obtained by cryogenic thermal cycling treatment after annealing.

The observation of negative strain rate sensitivity during nanoindentation is a common, yet poorly understood phenomenon in metallic glasses. In this study, a combination of experimental investigation and atomistic simulation has been employed to understand the mechanism behind this perplexing effect. The results suggest that the negative strain rate sensitivity arises out of the influence of a slow time-dependent relaxation process during the driven deformation at a controlled rate. By complementing the experimental outcome by simulation results, it is possible to show that this unification of the rate-driven and relaxation mechanisms is the consequence of their overlapping timescales. In addition, we demonstrate that by using the numerical results of simulated nanoindentation, it is possible to calculate the size and activation volume of the shear transformation zone, which is otherwise difficult using only experimental data in the regime of negative strain rate sensitivity.

cited By 1; Rate-dependent plastic deformation behavior of TiZrHfCuNiBe high entropy bulk metallic glass (HE-BMG) is investigated by the nanoindentation and quasi-static compression tests. The experimental results reveal that the pop-in sizes during nanoindentation and the serrations sizes under compression will reduce when the loading/strain increases. The strain rate sensitivity during nanoindentation creep is enhanced as loading rate increases, which represents more homogeneously deformation of TiZrHfCuNiBe HE-BMG at higher loading/strain rate. The average serrations sizes of TiZrHfCuNiBe HE-BMG are significantly smaller than that of traditional bulk metallic glasses. The plastic deformation behavior of the TiZrHfCuNiBe HE-BMG is discussed with respect to the self-organized critical (SOC) state behavior. The results demonstrated that the shear-band interactions of multiple shear bands could affect the SOC behavior and inhomogeneous deformation. Research suggests the shear transformation zone (STZ) sizes become smaller as the loading rate increases based on the statistical analysis. It is ascribed to have a larger shear band density at lower loading/strain rate. The current research is in coincidence with the shear-band patterns shown in microscopic micrographs of specimen surfaces. More shear-banding distributions at the lower loading/strain rate will result in more inhomogeneous deformation. © 2019 Elsevier B.V.

In the plastic deformation of amorphous materials, dilatation occurs universally with softening. However, the critical question that whether softening is caused by dilatation or not remains an ansatz and requires experimental examination. In this work, by examining the deformation behaviors of 3 metallic glasses (MGs) with distinct Johari-Goldstein (JG) relaxation characteristics before and after crystallization with nanoindentation, it is found that the origin of softening is probably not dilatation but the collective mode in the activation dynamics of shear transformation zones (STZs). Since the deformation in the creep stage of nanoindentation of the MGs originates from the “delayed plasticity” from the loading stage and depends on the softened deforming state of the MGs, the creep depth vs. time curves in the creep stage of nanoindentation of the MGs are examined and display similar loading rate dependent softening phenomena for both the glassy and crystallized MGs. The stretched exponent and relaxation time characterizing the deformation dynamics in the creep stage of nanoindentation are derived by fitting the creep depth vs. time curves with the Kohlrausch-Williams-Watts (KWW) equation. The stretched exponents indicate similar collective modes in the activation dynamics of the elementary deformation units (STZs in glassy MGs and dislocations in crystallized MGs). The relaxation times manifest similar softening effects in the deformation accommodation processes of both the glassy and crystallized MGs, except for a glassy La MG of which the relaxation time is extraordinary for its pronounced JG relaxation. The extraordinary relaxation time of the glassy La MG precludes the possibility of shear dilatation being the main cause for the softening of the glassy La MGs indicated by the loading rate dependent creep depth vs. time curves. The stretched exponent and the relaxation time indicate the homological softening dynamics in the plastic deformation of the glassy and crystallized MGs. For the distinct elementary deformation units, i.e., STZs in glassy MGs and dislocations in crystallized MGs, noting the absence of dilatation in dislocation movements, the softening phenomena in the plastic deformation of both the glassy and crystallized MGs is suggested to originate from the collective mode in the activation dynamics of the elementary deformation units, rather than from local properties of elementary deformation units, such as dilatation in STZs.

Nanolaminate composites consisting of alternate layers of Nanoglasses (NGs) and metallic glasses (MGs) have shown enhanced tensile ductility without great penalty on strength. Recent atomistic simulations on such NG-MG nanolaminate composites have revealed that peak stress attained in these materials do not follow rule of mixture. Also, a transition in deformation behaviour takes place when MG layer thickness is reduced below a threshold level which is correlated with average size of glassy grain in NG layer. However, the mechanistic reasons for this correlation is not well understood. Therefore, continuum simulations of tensile loading on NG-MG laminate composites are performed using thermodynamic consistent non-local plasticity model. Results show that interaction stress associated with flow defects such shear transformation zones (STZs) plays a pivotal role in the deformation response of laminate composites. Also, shear band width in these materials, scales with intrinsic material length associated with the interaction stress. Further, the material length with respect to MG layer thickness governs the transition in deformation behaviour. The present work may provide guidelines in developing highly ductile NG-MG laminate composites for practical engineering applications.

Plasticity improvement in metallic glasses resulting from cycling treatment between room and liquid nitrogen temperature has been reported and attributed to rejuvenation due to a non-uniform thermal expansion coefficient. However, the detailed microscopic effect is still unclear. The present study focuses on the microscopic effect of room-temperature ageing and cryogenic cycling. La70Cu15Al15 and La70Ni15Al15 metallic glasses were subjected to varying ageing times, after which some were also cryogenically cycled. Quasi-static anelastic relaxation measurements were then employed to characterize the time-constant spectra over seven orders of magnitude. The overall anelastic strain decreases with increasing ageing time, but is not noticeably affected by cryogenic cycling. On the other hand, while ageing also causes an increase in characteristic time constants, cycling reverses this effect. The new details shed light on the effect of structural relaxation and rejuvenation on the properties of shear transformation zones.

Shock loading causes complicated twinning processes in Ti and Ti alloys. In this work, two types of {10 1 ¯ 2} sequential twinning processes are for the first time reported according to electron backscatter diffraction (EBSD) characterization of titanium sheets that are subjected to shock loading. One is described as {11 2 ¯ 1} ⇒ P → {10 1 ¯ 2} ( T i I I ⇒ P → T j I ), i.e., {10 1 ¯ 2} sequential twinning is activated in the parent grain (P) along with {11 2 ¯ 1} twins. The other is described as {11 2 ¯ 2} ⇒ {11 2 ¯ 4} → {10 1 ¯ 2} ( C i I ⇒ C j I I → T k I ), i.e., {10 1 ¯ 2} secondary twinning is stimulated inside {11 2 ¯ 4} twin by co-zone {11 2 ¯ 2} twin. A statistical analysis according to EBSD characterization reveals the well-defined crystallographic relations between sequential {10 1 ¯ 2} twin variants and the primary/incoming twins, i.e., T i I I ⇒ P → T i I o r T i + 1 I and C i I ⇒ C i + 3 I I → T i I or T i + 1 I . We proposed and examined two sequential twinning mechanisms, (i) emissary twinning disconnections at steps along twin boundary for the first case and (ii) shear transformation into the primary twin for the second case, based on dislocation theory and the deformation accommodation ability of the sequential {10 1 ¯ 2} twinning to the shear deformation of the primary/incoming twin. Crystal plasticity modelling is performed to calculate the local stress field associated with the proposed twinning mechanisms. The results demonstrate that the preferred twin variant observed in experiments has the maximum resolved shear stress among the six twin variants. Our work suggests that complicated twinning processes under shock loading obey crystallographic relations according to deformation accommodation ability. The findings from this study can be implemented into meso-/macro-scale crystal plasticity models for predicting mechanical behaviors and texture evolution of polycrystalline aggregates of hexagonal materials.

Aluminum nitrides (AlNs) have many unique properties for broad applications. However, their mechanical behaviour has not been well understood. In this work, the notch effects on the deformation of wurtzite AlN (w-AlN) and amorphous AlN (a-AlN) under tension were investigated using molecular dynamics simulations. As compared to w-AlN, lower strength sensitivity to the notch and the improved fracture toughness are observed in a-AlN, which are attributed to the short-range ordered atomic arrangement, rupture, reconstruction and rotation of bonds during deformation. The introduction of notch leads to obviously reduced strength and ductility in the w-AlN and a-AlN, respectively. The deformation in intact a-AlN is dominated by the formation of shear bands, followed by void coalescence. On the other hand, the deformation in notched a-AlN starts from the development of shear transformation zone near to the notches, followed by void coalescence. These results are useful in design of AlN based systems and devices.

The effects of interfaces in crystalline Cu/amorphous Cu50Zr50 on shear banding dynamics are investigated using molecular dynamics simulations. The results show that the introduction of amorphous-crystalline interfaces can effectively promote the homogeneous distribution of shear transformation zones (STZs). We found that the high potential energy combined with the defects of the interfaces promote the nucleation of STZs. Further, the amorphous-crystalline interfaces are transition regions that mediate the transmission of dislocations in the crystallites into STZs in the metallic glasses. The accumulation of STZs and dislocations at the interfaces provide the sources for the enhanced plastic deformation in nanocomposites. These results allow us to determine the fundamental atomic structure of amorphous-crystalline interfaces in nanocomposites.

The structural evolutions of potential energy landscape (PEL) are investigated in a metallic glass modeling system with different cooling histories spanning more than five orders of magnitude. The local minima in the PEL are observed to be spatially more separated in the samples with lower fictive temperature Tfic than in the samples with higher Tfic. An Arrhenius scaling between the local minima density and Tfic is observed, which directly links the distribution of inherent structures in the PEL to the population of shear transformation zones (STZ) in amorphous solids. Moreover, very interestingly, the Arrhenius scaling breaks at 1.3–1.4 Tg, above which an invariant PEL structure with a saturated density of local minima is achieved. The hereby obtained critical temperature coincides with the experimentally observed dynamics crossover temperature, which suggests a profound connection between the PEL structure and dynamics in glassy system.

Amorphous/crystalline nanolaminate composites have aroused extensive research interest because of their high strength and good plasticity. In this paper, the nanoindentation behavior of Cu64Zr36/Cu amorphous/crystalline nanolaminates (ACNLs) is investigated by molecular dynamics (MD) simulation while giving special attention to the plastic processes occurring at the interface. The load–displacement curves of ACNLs reveal small fluctuations associated with shear transformation zone (STZ) activation in the amorphous layer, whereas larger fluctuations associated with dislocations emission occur in the crystalline layer. During loading, local STZ activation occurs and the number of STZs increases as the indentation depth in the amorphous layer increases. These STZs are mostly located around the indenter, which correlates to the high stresses concentrated around the indenter. When the indenter penetrates the crystalline layer, dislocations emit from the interface of amorphous/crystalline, and their number increases with increasing indentation depth. During unloading, the overall number of STZs and dislocations decreases, while other new STZs and dislocations become activated. These results are discussed in terms of stress distribution, residual stresses, indentation rate and indenter radius.

Structural heterogeneity of amorphous solids present difficult challenges that stymie the prediction of plastic events, which are intimately connected to their mechanical behavior. Based on a perturbation analysis of the potential energy landscape, we derive the atomic nonaffinity as an indicator with intrinsic orientation, which quantifies the contribution of an individual atom to the total nonaffine modulus of the system. We find that the atomic nonaffinity can efficiently characterize the locations of the shear transformation zones, with a predicative capacity comparable to the best indicators. More importantly, the atomic nonaffinity, combining the sign of third order derivative of energy with respect to coordinates, reveals an intrinsic softest shear orientation. By analyzing the angle between this orientation and the shear loading direction, it is possible to predict the protocol-dependent response of plastic events. Employing the new method, the distribution of orientations of shear transformation zones in a model two-dimensional amorphous solids can be measured. The resulting plastic events can be understood from a simple model of independent plastic events occurring at variously oriented shear transformation zones. These results shed light on the characterization and prediction of the mechanical response of amorphous solids., 3 figures

Plastic deformation in amorphous solids is known to be carried by stress-induced localized rearrangements of a few tens of particles, accompanied by the conversion of elastic energy to heat. Despite their central role in determining how glasses yield and break, the search for a simple and generally applicable definition of the precursors of those plastic rearrangements -- the so-called shear transformation zones (STZs) -- is still ongoing. Here we present a simple definition of STZs -- based solely on the harmonic approximation of a glass' energy. We explain why and demonstrate directly that our proposed definition of plasticity carriers in amorphous solids is more broadly applicable compared to anharmonic definitions put forward previously. Finally, we offer an open-source library that analyzes low-lying STZs in computer glasses and in laboratory materials such as dense colloidal suspensions for which the harmonic approximation is accessible. Our results constitute a physically motivated methodological advancement towards characterizing mechanical disorder in glasses, and understanding how they yield., Comment: 9 pages, 7 figures (added 2 new figures and discussion)

Minor alloying is widely used to control mechanical properties of metallic glasses (MGs). The present understanding of how a small amount of alloying element changes strength is that the additions lead to more efficient packing of atoms and increased local topological order, which then increases the barrier for shear transformations and the resistance to plastic deformation. Here, we discover that minor alloying can improve the strength of MGs by increasing the chemical bond strength alone and show that this strengthening is distinct from changes in topological order. The results were obtained using Al–Sm based MGs minor alloyed with transition metals (TMs). The addition of TMs led to an increase in the hardness of the MGs which, however, could not be explained based on changes in the topological ordering in the structure. Instead we found that it was the strong bonding between TM and Al atoms which led to a higher resistance to shear transformation that resulted in higher strength and hardness, while the topology around the TM atoms had no influence on their mechanical response. This finding demonstrates that the effects of topology and chemistry on mechanical properties of MGs are independent of each other and that they should be understood as separate, sometimes competing mechanisms of strengthening. This understanding lays a foundation for design of MGs with improved mechanical properties.

The nanoindentation results of Polymethyl Methacrylate (PMMA) after hygrothermal aging under different indentation strain rates are analyzed. The influences of hygrothermal aging on its indentation size effects (ISE) and microindentation measurements are discussed. The theory of shear transformation plasticity is utilized to analyze the ISE of PMMA after hygrothermal aging. The shear transformation zone (STz) sizes of PMMA under different conditions have been calculated and can be continuously described by aging time and strain rate. The characteristic deep, which represents the vanishment of ISE, is obtained and exhibits increases with strain rate and aging time. The objective measurements (i.e., elastic modulus and hardness) that represent the practical properties of the aged PMMA can be calculated: elastic modulus and hardness decrease with aging time. The effects of aging on the mechanical properties weaken with the increase with aging time, which results from the variation in the micro-mechanism. The prediction model can be constructed to explain the ISE of PMMA after hygrothermal aging through relating χ with aging time and strain rate. The proposed model agrees well with the experimental results.

A mesoscale numerical model based on shear transformation zone (STZ) theory is implemented in a commercial finite element software. The model is designed to predict the (visco)plastic deformation response of amorphous solids at the nano- and microscale. The theoretical framework relies on earlier models developed by Bulatov and Argon (1994a) and of Homer and Schuh (2009). We justify the potential of the computational model by conducting reference calculations for model metallic and polymeric glasses in plane strain compression. Emphasis is placed on the effect of time and space discretisation on the predicted macroscopic response. The dependence of the predicted yield strength upon the values of the fundamental model parameters is analysed via a mean-field approximation. The mean-field approximation is validated based on a series of simulations in model parameter space. We provide guidelines for a straightforward but consistent parameter identification method via the mean-field approximation while starting from experimental data.

We compare the macroscopic and the local plastic behavior of a model amorphous solid based on two radically different numerical descriptions. On the one hand, we simulate glass samples by atomistic simulations. On the other, we implement a mesoscale elasto-plastic model based on a solid-mechanics description. The latter is extended to consider the anisotropy of the yield surface via statistically distributed local and discrete weak planes on which shear transformations can be activated. To make the comparison as quantitative as possible, we consider the simple case of a quasistatically driven two-dimensional system in the stationary flow state and compare mechanical observables measured on both models over the same length scales. We show that the macroscale response, including its fluctuations, can be quantitatively recovered for a range of elasto-plastic mesoscale parameters. Using a newly developed method that makes it possible to probe the local yield stresses in atomistic simulations, we calibrate the local mechanical response of the elasto-plastic model at different coarse-graining scales. In this case, the calibration shows a qualitative agreement only for an optimized subset of mesoscale parameters and for sufficiently coarse probing length scales. This calibration allows us to establish a length scale for the mesoscopic elements that corresponds to an upper bound of the shear transformation size, a key physical parameter in elasto-plastic models. We find that certain properties naturally emerge from the elasto-plastic model. In particular, we show that the elasto-plastic model reproduces the Bauschinger effect, namely the plasticity-induced anisotropy in the stress-strain response. We discuss the successes and failures of our approach, the impact of different model ingredients and propose future research directions for quantitative multi-scale models of amorphous plasticity.

Dynamic mechanical relaxation is a fundamental tool to understand the mechanical and physical properties of viscoelastic materials like glasses. Mechanical spectroscopy shows that the high-entropy bulk metallic glass (La30Ce30Ni10Al20Co10) exhibits a distinct β-relaxation feature. In the present research, dynamic mechanical analysis and thermal creep were performed using this bulk metallic glass material at a temperature domain around the β relaxation. The components of total strain, including ideal elastic strain, anelastic strain, and viscous-plastic strain, were analyzed based on the model of shear transformation zones (STZs). The stochastic activation of STZ contributes to the anelastic strain. When the temperature or external stress is high enough or the timescale is long enough, the interaction between STZs induces viscous-plastic strain. When all the spectrum of STZs is activated, the quasi-steady-state creep is achieved.

A new connection between structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as $J_\sigma$, is obtained as a function of inherent-state elastic moduli and radial distribution function. The energy barrier from the current theory is compared to one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations., Comment: 11 pages, 6 figures, 1 table; final version submitted to the Journal of Chemical Physics

Journal of materials research 36(11), 2325 - 2336 (2021). doi:10.1557/s43578-021-00187-5, High strain rate micromechanical testing can assist researchers in elucidating complex deformation mechanisms in advanced material systems. In this work, the interactions of atomic-scale chemistry and strain rate in affecting the deformation response of a Zr-based metallic glass was studied by varying the concentration of oxygen dissolved into the local structure. Compression of micropillars over six decades of strain rate uncovered a remarkable reversal of the strain rate sensitivity from negative to positive above ~ 5 s$^{���1}$ due to a delocalisation of shear transformation events within the pre-yield linear regime for both samples, while a higher oxygen content was found to generally decrease the strain rate sensitivity effect. It was also identified that the shear band propagation speed increases with the actuation speed, leading to a transition in the deformation behaviour from serrated to apparent non-serrated plastic flow at ~ 5 s$^{���1}$., Published by Cambridge Univ. Press, Cambridge [u.a.]

The variations in local yield strength and plasticity of a Zr-based bulk metallic glass at different fictive temperatures (Tf) are studied. To probe the size and distribution of microscopic carriers of plasticity, spherical-tip nanoindentation and microindentation are employed. With nanoindentation, events signifying the departure from Hertzian elastic contact, which manifest as pop-ins in the load-displacement response and correspond to incipient plasticity, are recorded and analyzed. Results indicate that with increasing Tf, the incipient plastic event and the number of subsequent pop-ins increases. Using statistical analysis of the scatter in strength, the activation parameters for shear transformation zones (STZs) in all specimens are determined. By considering the linear accumulation of STZs to form a shear band, the increase in shear yield strength along with plasticity, with increasing Tf, is explained.

It has been accepted that low-frequency vibrational modes are causally correlated to fundamental plastic rearrangement events in amorphous solids, irrespective of the structural details. But the mode-event relationship is far from clear. In this work, we carry out case studies using atomistic simulations of a three-dimensional Cu50Zr50 model glass under athermal, quasistatic shear. We focus on the first four plastic events, and carefully trace the spatiotemporal evolution of the associated low-frequency normal modes with applied shear strain. We reveal that these low-frequency modes get highly entangled with each other, from which the critical mode emerges spontaneously to predict a shear transformation event. But the detailed emergence picture is event by event and shear-protocol dependent, even for the first plastic event. This demonstrates that the instability of a plastic event is a result of extremely complex multiple-path choice or competition, and there is a strong, elastic interaction among neighboring instability events. At last, the generality of the present findings is shown to be applicable to covalent-bonded glasses.

The influence of isothermal annealing on the strain rate sensitivity (SRS) of a Zr-based bulk metallic glass (BMG) was investigated by nanoindentation. A more positive SRS is observed with a decrease in the content of the free volume (FV) of the sample. Furthermore, the SRS becomes nearly constant with increasing annealing time when the FV is annealed out. By taking into consideration the FV-assisted activation and combination of the shear transformation zones (STZs), the underlying mechanism is well understood. The current work may offer useful insights into the correlation between the microstructure and mechanical properties of BMGs.

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypoelastoplastic mechanical model, and develop a projection method to enforce quasistatic equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and which imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.

© 2018 Elsevier Ltd The deformation behavior of polymer materials below their glass transition temperature involves a complex intermingling of elasticity, of viscoplastic yielding with softening and large strain hardening, and of significant rate, temperature and pressure dependency. During unloading, the response exhibits large non-linearity as well, combining forward and backward creep. Even though the nature of the atomistic underlying mechanisms is relatively well understood, a full picture of the interactions between the elementary distortion mechanisms and their collective organization capturing the complexity of the macroscopic behavior is still lacking. Here, we propose a mesoscale approach based on the heterogeneous activation of molecular level shear transformation zones and we show that it is rich enough to unravel the physical origin of most aspects of the macroscopic viscoplastic response. The study is based on a wide micro- and macro-mechanical test campaign on a thermoset material. In addition to providing a full characterization of all macroscopic properties, evidence of a complex rate reversal mechanism upon unloading is given. Other experiments provide insights about the characteristic length scales at play. Compared to existing continuum models involving typically more than 25 parameters, the present formalism is based on only 7 physical parameters while allowing quantitative predictions of all the experimental data. The present approach opens new avenues for the prediction of the mechanical response of a variety of polymer applications in confined state such as in composites or in adhesive joints. It also offers a new line of thought to address the mechanics of polymers at small and intermediate length scales.

Metallic glasses with pronounced high-frequency \ensuremath{\beta} relaxation in their dynamic-mechanical response have been observed to exhibit large plasticity. Due to their disordered atomic structure, it is challenging to identify the microscopic mechanisms of their relaxation behavior. Quasistatic anelastic relaxation measurements have been performed over 10 orders of magnitude of time on $\mathrm{L}{\mathrm{a}}_{55}\mathrm{N}{\mathrm{i}}_{20}\mathrm{A}{\mathrm{l}}_{25}$ metallic glass, which exhibits a strong \ensuremath{\beta} relaxation. The corresponding time-constant spectra were computed from the data---they contain a series of peaks corresponding to an atomically quantized hierarchy of shear transformation zones (STZs), where both the \ensuremath{\alpha} and \ensuremath{\beta} relaxations are consistent with the STZ model. Two different regimes of activation-volume increment between the peaks are observed, suggesting the involvement of different elements in STZs corresponding to \ensuremath{\alpha} vs \ensuremath{\beta} relaxations. Room-temperature structural relaxation significantly affects the former but not the latter.

Shearing granular materials induces non-affine displacements. Such non-affine displacements have been studied extensively, and are known to correlate with plasticity and other mechanical features of amorphous packings. A well known example is shear transformation zones as captured by the local deviation from affine deformation, $D^2_{min}$, and their relevance to failure and stress fluctuations. We analyze sheared frictional athermal disk packings and show that there exists at least one additional mesoscopic transport mechanism that superimposes itself on top of local diffusive motion. We evidence this second transport mechanism in a homogeneous system via a diffusion tensor analysis and show that the trace of the diffusion tensor equals the classic $D^2_{min}$ when this second mesoscopic transport is corrected for. The new transport mechanism is consistently observed over a wide range of volume fractions and even for particles with different friction coefficients and is consistently observed also upon shear reversal, hinting at its relevance for memory effects., 6 pages, 4 figures + supplemental materials

NPG Asia Materials 12(1), 1-59 (2020). doi:10.1038/s41427-020-00241-4, The design of ductile heterogeneous metallic glasses (MGs) with enhanced deformability by purposely controlling theshear-band dynamics via modulation of the atomic-scale structures and local stress states remains a significantchallenge. Here, we correlate the changes in the local atomic structure when cooling to cryogenic temperature withthe observed improved shear stability. The enhanced atomic-level structural and elastic heterogeneities related to thenonaffine thermal contraction of the short-range order (SRO) and medium-range order (MRO) change thecharacteristics of the activation process of the shear transformation zones (STZs). The experimental observationscorroborated by Eshelby inclusion analysis and molecular dynamics simulations disclose the correlation between thestructuralfluctuations and the change in the stressfield around the STZ. The variations in the inclination axes of theSTZs alter their percolation mechanism, affect the shear-band dynamics and kinetics, and consequently delay shearfailure. These results expand the understanding of the correlation between the atomic-level structure and elementaryplastic events in monolithic MGs and thereby pave the way for the design of new ductile metallic alloys., Published by Macmillan Publishers Limited, part of Springer Nature, Tokyo

A new concept of soft ferromagnetic bulk metallic glass (BMG) with self-healing ability is proposed. The specific [Fe36Co36B19.2Si4.8Nb4]100−x(Ga)x (x = 0, 0.5, 1 and1.5) BMGs prepared by copper mold casting were investigated as a function of Ga content. The Ga-containing BMGs still hold soft magnetic properties and exhibit large plastic strain of 1.53% in compression. Local melting during shearing produces molten droplets of several µm size throughout the fracture surface. This concept of local melting during shearing can be utilized to produce BMGs with self-healing ability. The molten regions play a vital role in deflecting shear transformation zones, thereby enhancing the mechanical properties., Materials, 13 (6), ISSN:1996-1944

The present work investigated systematically the glass forming ability, the mechanical properties and the shear deformation of the TiZrHfCuBe high entropy bulk metallic glass (HE-BMG) with minor Sn addition. The results revealed that the glass forming ability and the thermal stability are enhanced by minor Sn addition but within a rather limited composition range. A nanoindentation study of the mechanical response in the (TiZrHfCuBe)1-xSnx (x = 0, 1, 2 and 3 at. %) HE-BMGs showed that the structural heterogeneity caused by Sn addition resulted in higher hardness, larger number of shear bands and smaller size of shear transformation zone, ascribing to the positive enthalpy of mixing between the Sn and Cu/Be elements. A statistical analysis of the serrated flow revealed that the chemical heterogeneities promote a relatively large population of shear deformation units and lead to multiple nucleation of shear bands. The present work might has implications in establishing the link between minor element addition and structure heterogeneity, which is of critical importance for understanding of shear banding behaviors in BMGs.