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In this work, we study the deformation behavior in amorphous/crystalline metallic composites (A/C-MCs) through nanoindentation experiments and molecular dynamic (MD) simulations. The atomic deformation processes in both crystalline (C-) and amorphous (A-) phases near the amorphous-crystalline interface (ACI) are investigated and correlated with the material’s overall constitutive behavior at the microscale. Our major findings are (i) the ACIs enable a co-deformation of the A- and C-phases through “stiffening” the soft phases but “softening” the stiff phases in A/C-MCs through different micro-mechanisms; (ii) there exists an ACI-induced transition zone with a thickness of ~ 10 nm; (iii) the strong coupling between shear transformation zones (STZs) and dislocations can be quantified through carefully designed indentation experiments and simulations; and (iv) the nanoscale MD-simulation-predicted mechanisms can be mapped to the “pop-in” or “excursion” events on the force–indentation depth curves extracted from microscale experiments, although there is a length-scale gap in between.

The study on the structure and mechanical properties of Zr55Al10Ni5Cu29Y1 bulk metallic glasses (BMGs) indicates that deep cryogenic cycling treatment (DCT) is an effective method to improve room-temperature plasticity of BMGs containing trace rare earth elements. DCT not only increases the volume and size of STZs in BMGs, promotes the generation of multiple shear bands, but also reduces the maximum shear stress that occurs in pop-in events. Due to the internal stress generated during DCT, rejuvenation causes the larger volume and size of the shear deformation zone, which can promote the shear bands formation and generate multiple shear bands to accommodate plastic deformation. In different BMGs systems, the volume of STZs tends to decrease as v increases. STZ is more sensitive to the composition, and changes in trace elements can cause changes of the volume of STZs.

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.

Using molecular dynamics simulations, we provide an atomistic description of the shear band multiplication mechanisms in a heterogeneous metallic glass consisting of two distinct amorphous regions with different amounts of free volume and degrees of short-range order. The structural differences and elastic fluctuations encountered by the developing shear band while crossing the interface between the two regions alter the autocatalytic activation of the shear transformation zones (STZs) and, subsequently, lead to shear band branching. The two-unit STZ-vortex mechanism sheds light on the correlation between the strain distribution during tensile deformation and the directional characteristics of the STZ activation process.

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.

Most images have lots of linear information, which plays an important role in the tasks of image processing and pattern recognition. However, due to the interference of complex background in the images, the multiple directional characteristics of the linear information, and the problems of directional limitations in traditional methods, all these lead to the incomplete and discontinuities existed in the extracted linear information. To solve these problems, this paper puts forward a general model for improving the performance of the linear information extraction methods (LIEM) by utilizing the shear transformation. In this model, the shear transformation can transform an object (a filter or an image) in multiple directions, which directly or indirectly increases the directional characteristics of the traditional LIEM, and improves their performances to extract directional linear information and weak linear information. This paper elaborates on the basic principles of the model and its two implementations for the specific tasks. Furthermore, a variety of experiments are made to verify the versatility and effectiveness of the proposed model.

In this work, we have synthesized dual-phase high entropy alloys (DP-HEAs) multilayers with a tunable layer thickness through a bottom-up approach. The DP-HEAs' multilayers reach the maximum hardness of 13.3 GPa at a critical thickness of 10 nm. The main strengthening mechanism is that dislocation movement is locked by both interior columnar grain boundaries and heterogeneous interfaces. A crystalline-to-amorphous transition occurs when layer thickness is below the critical thickness. The formation of amorphous DP-HEAs deformed by shear transformation zones with collective atomic rearrangement is responsible for the softening behavior.

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.

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.

The effects of loading rate on creep behavior and shear transformation zone (STZ) in magnetron sputtered La-Co-Al and Zr-Cu-Ni-Al amorphous alloy thin films were characterized through instrumented nanoindentation with a spherical indenter. It was revealed that with an increase in loading rate, both thin films became harder with a narrower distribution of mechanical response, and exhibited more pronounced creep displacement with higher creep strain rate. Based on cooperative shear model, both STZ volume and activation energy were calculated by measuring the strain rate sensitivity during creep, showing an increasing tendency with loading rate. However, the strain rate sensitivity was found to decrease with loading rate. Furthermore, structural heterogeneity density, estimated by analyzing the stressed volume at yielding, decreased with loading rate. Therefore, with increasing loading rate, the STZ event can only be activated at detectable structural heterogeneities with relatively larger volume, and the number of available fertile sites was decreased, resulting in postponed shear band formation and suppressed deformation mode transition.

The shear transformation zone (STZ) and ductility of Zr-based bulk metallic glass with varying hydrogen content were analyzed using serrated flow in nanoindentation, with each serration representing the formation and expansion of one or more shear bands. An exponential model was employed to extract the serrations and obtain a certain range of shear stress, and STZ size was estimated via thorough statistical data analysis. The experimental results demonstrated a striking decrease in the serration number and width of the load-displacement curve after hydrogenation, which is similar to the effects of the nanoindentation loading rate. The calculated STZ volume and atomic number were in good agreement with those reported in the literature. The STZ volume, size, activation energy, and activation volume also increased with the increased hydrogen content, leading to shear band formation and proliferation as well as increased shear band density, plastic zone, and plasticity. At the microscopic level, the hydrogen addition accelerated free volume formation and enhanced flow ability between the atoms, as characterized by the improvement of plasticity. At the macroscopic level, hydrogen addition promoted shear band nucleation and multiplication and increased shear band density, plastic zones, and plasticity. The metallic glass plasticity was greatly improved after hydrogenation as assessed via compression tests at room temperature, confirming the rationale of the experimental results.

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.

In the work reported in this paper, high-pressure torsion (HPT) was conducted on Ti-22Al-25Nb alloy under the applied pressure of 6 GPa at ambient temperature in 1, 5, and 10 turns. Investigation of the microstructural characteristics and microhardness evolution of the HPT-processed Ti-22Al-25Nb alloy showed that the lamella B2-phase could be transformed to O-phase at ambient temperature. This was due to severe shear transformation of the B2 lattice caused by the high density of dislocations generated during HPT. Significant grain refinement was achieved, from grain size of ~67 μm in the initial annealed specimen to ~53 nm after 10 turns in the HPT process. In addition to dislocations, nanotwins played an important role in the grain refining process. With increasing accumulation of equivalent strain, the microhardness value of this alloy increased and reached a saturated value of about ~600 HV when the equivalent strain reached ~20. This is higher than that obtained by conventional processes. The hardening mechanisms were primarily attributed to pronounced grain refinement and the high density of dislocations induced by the HPT process.

To uncover the physical correlation between intrinsic structural heterogeneity and mechanical properties of metallic glasses, we performed high-pressure torsion (HPT) to tailor their microstructure with a rejuvenated state. Nanoindentation results show that the change of mechanical properties results from the convolution of the intrinsic thermal activation process and the structural inhomogeneity in the glassy phase. The spatial heterogeneity induced by severe plastic deformation can markedly operate to reduce the energy barrier for shear transformation zone (STZ) activation and increase the number of STZ events during tensile testing to accommodate the plastic strain, leading to a brittle-to-ductile transition. We highlight that by properly controlling the distribution of structural heterogeneities, one can purposely tune the mechanical performance of metallic glasses.

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.

To investigate the intrinsic effect of the pre-stress (σpre) on the onset of yielding, nanoindentation experiments are performed on two metallic glasses (MGs) which are elastically-bent and constrained within a home-made apparatus. Statistical calculations for the first pop-ins are made and noticeable decrease in maximum shear stress (τmax) is observed under tensile pre-stress, but only slight increase under compressive one, without considering the pre-stress effect on the ratio (0.29) of τmax to the maximum contact pressure (p0). This asymmetry phenomenon is related to the anharmonic and asymmetric nature of the interatomic interaction potential caused by the applied pre-stress. Moreover, finite-element analysis is conducted to obtain the elastic stress field of the pre-stressed region upon indentation, which becomes anisotropy and quarter-symmetric. τmax for the specimen is defined as 0.29p0 + 0.50σpre for the tensile-stressed region and 0.29p0 for the compressive-stressed region within elastic strain limit of MGs, which requires the correction for the intrinsic τmax with tensile σpre, but not for compressive σpre. The corrected τmax and activation energy barrier of shear transformation zone are found to be independent on σpre, suggesting that the intrinsic shear stress is a constant and the yielding of MGs obeys the maximum shear stress criterion.

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 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.

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)

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.

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.]

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

A Zr-based bulk metallic glass produced using selective laser melting (SLM) was compared to the same alloy fabricated using traditional suction-casting. Analysis of the fracture toughness through single edge notched beam bending experiments showed a significantly reduced damage tolerance for the laser-processed material (KQ ~ 138.0 ± 13.1 → 28.7 ± 3.7 MPa √m), even though X-ray diffraction and microhardness responses were identical. Using uniaxial quasistatic micro-pillar compression, it was found that as-cast samples more readily underwent shear transformations (evidenced through discrete load drops) below the nominal 0.2% yield stress, which was connected to the higher macroscopic toughness. Differential scanning calorimetry demonstrated that the increased barrier to shear transformation for the SLM material could not be explained by the relative relaxation states. Rather, it was attributed to the greater dissolved oxygen concentration in the laser-processed material, which is postulated to decrease atomic mobility in the structure and thereby increase the activation energy required to initiate shear transformations.

The annealing effect below glass transition temperature (Tg) on nanoindentation hardness and shear transformation zone (STZ) volume was studied in a Ni Nb metallic glassy thin film. The indentation size effect (ISE) and loading rate effect on hardness were systematically investigated. It was found that ISE was less pronounced and strain rate sensitivity (SRS) was higher in the sample suffered longer annealing time. As annealing time reached a critical value, hardness value, ISE and SRS changed quite limited which could be due to full structure relaxation in samples. The hardness spatial distribution was more scattered with increasing annealing time, indicating a more pronounced mechanical heterogeneity at microscale. Based on SRS values and cumulative probability distribution of hardness, STZ volumes were estimated upon two distinct methods, respectively. A tight correlation between STZ volume and structure state was revealed. As increasing annealing time, STZ volume was continuously decreased and approached down to a stable value.

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.

A number of studies have found that the formation of double twins in low symmetry metals can lead to the onset of strain localizations, leading further to void nucleation and ultimately fracture. This work extends a recently developed three-dimensional crystal plasticity finite element framework [1] to explicitly model kinematics and kinetics of nucleation/formation, propagation, and thickening/growth of a discrete double twin lamella ( { 10 1 ¯ 1 } − { 10 1 ¯ 2 } ) in a magnesium alloy AZ31. With this approach, morphological and crystallographic reorientations as well as the shear transformation strains associated with strain accommodation by the double twinning sequence are modeled during simple compression and tension. The simulations predict that the distribution of local stress-strain fields during formation and growth of primary contraction twin creates the driving force for the formation of a secondary extension twin variant, which is consistent with experimental observations in both compression and tension. In particular, the contraction twin variant ( 0 1 ¯ 11 ) [ 0 1 ¯ 1 2 ¯ ] is predicted to form an internal extension twin variant ( 01 1 ¯ 2 ) [ 0 1 ¯ 11 ] . Furthermore, the prediction of the underlining crystallographic slip deformation mechanism reveals a substantial activity of basal slip within the contraction portion of the double twin, causing strain localization in its vicinity. Finally, the simulations reveal a gradient in the traction force field across twin-parent interface, suggesting that contraction twin-parent boundaries are weak links in the microstructure where voids can nucleate.

Nanoindentation experiments on disordered nanoparticle packings performed both in an atomic force microscope and in situ in a transmission electron microscope are used to investigate the mechanics of plastic deformation. Under an applied load, these highly porous films exhibit load drops, the magnitudes of which are consistent with an exponential population distribution. These load drops are attributed to local rearrangements of a small number of particles, which bear similarities to shear transformation zones and to the T1 process, both of which have been previously predicted for disordered packings. An increase in the relative humidity results in an increase in the number of observed load drops, indicating that the strength of the particle interactions has a significant effect on the modes of plastic deformation. These results suggest how disordered nanoparticle packings may be expected to behave in devices operating under varying environments.

Microcompressive tests were performed to investigate the intrinsic modulation effect and extrinsic diameter effect on strength and deformation behaviors of nanolaminated Cu/Cu-Zr crystalline/amorphous micropillars within a diameter D range from 300 to 1500 nm as well as a modulation ratio η range from 0.1 to 3.0. Experimental results revealed a transition of D-dependent deformation mode from homogeneous-like to shear localization at large η, while D-independent homogeneous extrusion of Cu at small η. Furthermore, the flow strength increased with raising D at small η, but decreased at large η, exhibiting a D-insensitive strength at a critical η* ~ 0.5. These unusual results were rationalized in terms of a coupling effect of dislocation actions and shear transformation zone mediated operations.

In this work, we have developed a multiscale shear-transformation-zone (STZ) model to simulate inelastic deformations in amorphous materials at macroscale without using phenomenological constitutive modeling. The main novelties of the multiscale method are two: (1) the multiscale method employs an atomistic-based representative sampling cell (RS-cell) that is embedded in every quadrature points of macroscale finite elements, and it generically contains potential shear-transformation-zones. Thus the evolution of RS-cells can naturally allow molecular clusters having irreversible microstructure rearrangements at microscale in response to applied loads, and subsequently translate the effects of the irreversible rearrangements of molecular clusters in each RS-cell to inelastic responses at the continuum scale, i.e. delineating the defect-mediated amorphous plasticity, and (2) the method uses a Parrinello-Rahman molecular mechanics based the Cauchy-Born rule to construct an atomistically-informed constitutive model at continuum level, which is able to quantitatively measure amorphous plasticity behaviors, including plastic flow stress, inelastic hysteresis loops under cyclic loading, and strain localizations at macroscale. By doing so, we have successfully simulated plastic deformation in the Lennard-Jones binary glass (LJBG) at macroscale level. Moreover, we have shown that the multiscale shear-transformation-zone can capture cyclic plasticity and the shear band formations in LJBG material.

We report density fluctuations spanning from nano-to micrometer scale in the three-dimensional (3D) space in metallic glasses (MGs) detected with synchrotron X-ray nano-computed tomography, which decouple with the chemical homogeneity. The MG quenched from fragile supercooled liquid exhibits a more heterogeneous microstructure with a gradient density fluctuation. Severe inhomogeneous deformation rejuvenates the microstructure of the MG with the creation of a large amount of low-density regions, which percolate into shear-band-like layers. Ramified 2.5-dimensional fractal low-density regions exist in all the MGs with the correlation length increasing with microstructural heterogeneity. The formation of the density fluctuations with fractal order in the MGs is discussed based on the percolation of low-density regions and shear transformation zones during the glass transition and deformation processes. Our results directly demonstrate the existence of fractal low-density entropic droplets in MGs affected by fragilities and thermomechanical histories, which could be significant for understanding and controlling the disordered structure of amorphous solids.

The deformation behavior of crystalline-amorphous nanolaminates is controlled by a confluence of mechanisms involving dislocation and grain boundary (GB) plasticity in the crystalline phase, shear transformation zone (STZ) plasticity and its localization into shear bands in the amorphous phase, and their coupling across the amorphous-crystalline interface. Leveraging molecular dynamics simulations, the influence of microstructural length scales on the mechanical behavior is quantified using deformation mechanism maps, which provide mechanistic insights into the scaling of mechanical properties with layer thickness ratio and grain size. We find that flow stress primarily scales with the relative phase fraction as deformation shifts toward STZ dominated plasticity with increasing amorphous layer thickness while the onset of plasticity is also influenced by grain size due to the role of GB plasticity in yielding. Toughness limiting mechanisms involve void formation at GBs and shear localization in the amorphous layer, where the former is attributed to dislocation-GB interactions during mixed mode deformation and the latter to dislocation slip bands biasing the process of shear localization. An Ashby plot representation combining flow stress with void and shear band localization factors demonstrates that configurations with microstructural length scales promoting cooperative strain accommodation through the coupling of dislocation, GB, and STZ plasticity exhibited limited strain localization while retaining a high flow stress, thus providing a mechanistic basis for microstructural design of crystalline-amorphous nanolaminates.

Although phase-separated metallic glass has been reported in the literature, its plastic deformation mechanism is still open to debate. In this paper, molecular dynamics simulations were performed to explore the plastic deformation mechanism of phase-separated Cu50Ag50 metallic glass during compression deformation. Our findings indicate that homogeneous atom pairs show stronger interaction than heterogeneous atom pairs in the Cu50Ag50 glass, which also shows higher plastic deformation ability demonstrated by stress–strain curves. The degree of phase separation increases with increasing deformation. Ag atoms show higher Voronoi volume and potential energies than Cu atoms. The Ag-rich regions, which yield preferentially, also exhibit larger local shear strain than the Cu-rich regions. Voronoi volume and potential energy of Ag atoms remain nearly unchanged during plastic deformation because of the atom arrangement and release of elastic energy; on the other hand, the same parameters of Cu atoms increase because of their resistance to shear transformation.

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an adaptive stochastic simulation-based methodology is introduced that refines the probability space based on Grassmann manifold variations. The proposed method has a multi-element character discretizing the probability space into simplex elements using a Delaunay triangulation. For every simplex, the high-dimensional solutions corresponding to its vertices (sample points) are projected onto the Grassmann manifold. The pairwise distances between these points are calculated using appropriately defined metrics and the elements with large total distance are sub-sampled and refined. As a result, regions of the probability space that produce significant changes in the full-field solution are accurately resolved. An added benefit is that an approximation of the solution within each element can be obtained by interpolation on the Grassmann manifold without the need to develop a mathematical surrogate model. The method is applied to study the probability of shear band formation in a bulk metallic glass using the shear transformation zone theory.

Based on the free volume, shear transformation zone and percolation theory, a new percolation model has been established to investigate the ductile-brittle transition in amorphous alloys. Taking the binary Cu25Zr75 amorphous alloy for example, the influence of the free volume concentration and flow unit dispersity on its percolation threshold value was analyzed. The results show that the concentration of flow units reach a critical value when the ductile-brittle transition occurs in the Cu25Zr75 amorphous alloy, and this critical value is independent of the concentration of the free volume but dependent on the dispersity of flow units. Furthermore, the percolation threshold values of La-, Zr-, Cu-, Pd-, Fe-, Sr- and Tm-based amorphous alloys were also calculated, a percolation threshold value of ~0.516 for ductile-brittle transition in these amorphous alloys was obtained. Therefore, our analysis results suggest that ~0.516 appears to be a universal percolation threshold value for ductile-brittle transition in amorphous alloys.

Discrete stress relaxations (slip avalanches) in a model metallic glass under uniaxial compression are studied using a metadynamics algorithm for molecular simulation at experimental strain rates. The onset of yielding is observed at the first major stress drop, accompanied, upon analysis, by the formation of a single localized shear band region spanning the entire system. During the elastic response prior to yielding, low concentrations of shear transformation deformation events appear intermittently and spatially uncorrelated. During serrated flow following yielding, small stress drops occur interspersed between large drops. The simulation results point to a threshold value of stress dissipation as a characteristic feature separating major and minor avalanches consistent with mean-field modeling analysis and mechanical testing experiments. We further interpret this behavior to be a consequence of a nonlinear interplay of two prevailing mechanisms of amorphous plasticity, thermally activated atomic diffusion and stress-induced shear transformations, originally proposed by Spaepen and Argon, respectively. Probing the atomistic processes at widely separate strain rates gives insight to different modes of shear band formation: percolation of shear transformations versus crack-like propagation. Additionally a focus on crossover avalanche size has implications for nanomechanical modeling of spatially and temporally heterogeneous dynamics.