Shear Transformation Zone Dynamics Research Articles

The Strain Rate Sensitivity of Heterogeneous Thin Film Metallic Glasses: Interplay Between Nanoscale Heterogeneity and Dynamic Plasticity

The dynamic mechanical properties of metallic glasses (MGs) are crucial to capturing the deformation signatures as well as for structural and functional applications. In this work, we investigate the influence of nanoscale structural heterogeneity of MGs on dynamic plasticity, focusing on the variation in strain rate sensitivity and the transition of deformation mechanisms, using a combined experimental and simulation approach. The Cu50Zr50 thin-film MGs with different nanoscale heterogeneities are synthesized using magnetron sputtering and further characterized using dynamic force microscopy and nanoindentation. All the films exhibit a strain rate hardening effect, but a transition in strain rate sensitivity as the indentation rate increases has been found in the MG with a higher heterogeneity. To understand the underlying mechanisms, mesoscale shear transformation zone dynamics simulations are performed on model Cu50Zr50 MGs. The simulation results are able to capture the experimental trend. Notably, the transition in strain rate sensitivity for a heterogenous MG stems from a change in deformation mechanisms: from structure-dictated strain localization at a lower strain rate to stress-dictated strain percolation into a shear band at a higher strain rate. The observed strain rate sensitivity and the corresponding mechanisms are summarized in a deformation mechanism map where nanoscale structural heterogeneity and strain rate are varied. We envision our study not only providing insights into the structure and property relationship of MGs on the nanoscale but also will facilitate the design of heterogeneous MGs for dynamic applications.

Accelerating coupled finite element-kinetic Monte Carlo models: 200 $$\times $$ × speedup of shear transformation zone dynamics simulations

Shear transformation zone dynamics models of metallic glass deformation access experimentally-relevant time scales by using the kinetic Monte Carlo method to simulate small, fast, often discrete events, while the finite element method calculates macroscopic shape change and continuum-level interactions within samples. The most time-consuming portion of these models is the finite element method calculation on each step. However, in cases where the finite element mesh geometry and element elastic properties do not change from step to step, the finite element stiffness matrix (and its Cholesky factors) from previous steps can be reused. This strategy improves the asymptotic complexity of these models and in practice accelerates their execution by nearly 200 $$\times $$ . This enables simulation of larger samples in more reasonable time. A set of three-dimensional shear transformation zone dynamics simulations, with larger length scales than any currently in the literature, illustrates the utility of this approach.

Spatial correlation of elastic heterogeneity tunes the deformation behavior of metallic glasses

Metallic glasses (MGs) possess remarkably high strength but often display only minimal tensile ductility due to the formation of catastrophic shear bands. Purposely enhancing the inherent heterogeneity to promote distributed flow offers new possibilities in improving the ductility of monolithic MGs. Here, we report the effect of the spatial heterogeneity of elasticity, resulting from the inherently inhomogeneous amorphous structures, on the deformation behavior of MGs, specifically focusing on the ductility using multiscale modeling methods. A highly heterogeneous, Gaussian-type shear modulus distribution at the nanoscale is revealed by atomistic simulations in Cu64Zr36 MGs, in which the soft population of the distribution exhibits a marked propensity to undergo the inelastic shear transformation. By employing a mesoscale shear transformation zone dynamics model, we find that the organization of such nanometer-scale shear transformation events into shear-band patterns is dependent on the spatial heterogeneity of the local shear moduli. A critical spatial correlation length of elastic heterogeneity is identified for the simulated MGs to achieve the best tensile ductility, which is associated with a transition of shear-band formation mechanisms, from stress-dictated nucleation and growth to structure-dictated strain percolation, as well as a saturation of elastically soft sites participating in the plastic flow. This discovery is important for the fundamental understanding of the role of spatial heterogeneity in influencing the deformation behavior of MGs. We believe that this can facilitate the design and development of new ductile monolithic MGs by a process of tuning the inherent heterogeneity to achieve enhanced ductility in these high-strength metallic alloys.

Influence of nanoscale structural heterogeneity on shear banding in metallic glasses

Structural heterogeneity at the nanoscale such as medium-range order (MRO) in metallic glasses (MGs) has been suggested by theories and simulations for many years and recently been observed by experiments. However, its correlation with plastic deformation is still poorly understood and investigation into this correlation has just begun. In this study, we first propose a correlation between the properties of shear transformation zone (STZ) and the local structural information at the MRO length scale. As revealed by experiments, the MRO exhibits different types of atomic order and symmetry in MGs depending strongly on the processing history and service condition. We then carry out STZ dynamics simulations to document effects of volume fraction and symmetry of dissimilar STZs (derived from experimental characterization of the MRO) on shear banding dynamics and stress-strain behavior. In particular, a “precipitation-hardening” effect is observed and “strain frustration” is introduced to explain and better understand the influence of nanoscale structural heterogeneity on mechanical behavior of MGs. Our approach intends to provide new fundamental insights into the relationship between the mechanical properties of MGs and their MRO-level structural heterogeneities.

Constitutive modeling of large inelastic deformation of amorphous polymers: Free volume and shear transformation zone dynamics

Due to the lack of the long-range order in their molecular structure, amorphous polymers possess a considerable free volume content in their inter-molecular space. During finite deformation, these free volume holes serve as the potential sites for localized permanent plastic deformation inclusions which are called shear transformation zones (STZs). While the free volume content has been experimentally shown to increase during the course of plastic straining in glassy polymers, thermal analysis of stored energy due to the deformation shows that the STZ nucleation energy decreases at large plastic strains. The evolution of the free volume, and the STZs number density and nucleation energy during the finite straining are formulated in this paper in order to investigate the uniaxial post-yield softening-hardening behavior of the glassy polymers. This study shows that the reduction of the STZ nucleation energy, which is correlated with the free volume increase, brings about the post-yield primary softening of the amorphous polymers up to the steady-state strain value; and the secondary hardening is a result of the increased number density of the STZs, which is required for large plastic strains, while their nucleation energy is stabilized beyond the steady-state strain. The evolutions of the free volume content and STZ nucleation energy are also used to demonstrate the effect of the strain rate, temperature, and thermal history of the sample on its post-yield behavior. The obtained results from the model are compared with the experimental observations on poly(methyl methacrylate) which show a satisfactory consonance.

Microstructural factors of strain delocalization in model metallic glass matrix composites

Metallic glass matrix (MGM) composites demonstrate impressive plasticity over monolithic metallic glasses due to their ability to delocalize strain and inhibit shear band propagation. This work investigates various microstructural factors (volume fraction, length scale and yield strength) influencing strain delocalization in a model MGM composite. Shear transformation zone dynamics is utilized to model the amorphous phase while a local Taylor dislocation model is used for the crystalline phase. An N-factorial experiment examines replicates for various macro- and microscopic measures of strain delocalization and regression analysis is used to identify statistically significant trends in the data. The experiment shows that strain delocalization and the consequent ductility are most strongly influenced by a crystalline phase with a substantially lower yield stress than that of the amorphous matrix. It also shows that increased crystalline volume fraction alone is insufficient to promote strain delocalization in the case of a crystalline phase with high relative yield stress, and that a lower yield stress for the crystalline phase implies lower maximum stresses supported by the composite. Examination of shear band–inclusion interactions indicate that the nucleation and diffuse transmission of numerous shear bands is critical to the strain delocalization. The regression analysis provides continuous functional forms for the various relationships between properties that can be exploited to optimize the microstructure of MGM composites.

Effect of hydrogen on the yielding behavior and shear transformation zone volume in metallic glass ribbons

The effect of hydrogen (H) charging on the shear yield strength (τmax) and shear transformation zone volume (Ω) of Ni–Nb–Zr metallic glass ribbons, with varying Zr content, were studied through the first pop-in loads during nanoindentation. Weight gain measurements after H charging and desorption studies were utilized to identify how the total H absorbed during charging is partitioned into mobile and immobile (or trapped) parts. These, in turn, indicate the significant role of H mobility in the amorphous structure on the yielding behavior. In high-Zr alloys, τmax increases significantly whereas Ω decreases. In low-Zr alloys, a slight decrease in τmax and increase in Ω were noted. These experimental observations are rationalized in terms of the mobility of the absorbed H in the amorphous structure and the possible role of it in the shear transformation zone dynamics during deformation of the metallic glass.

Transient response in metallic glass deformation: A study based on shear transformation zone dynamics simulations

The transient response in metallic glass deformation is investigated via a mesoscale simulation by shear transformation zone dynamics. We directly connect the microscopic processes, i.e. shear transformation-induced free volume creation and diffusive rearrangement-induced free volume annihilation, to the macroscopic transient response. Notably, the dynamic competition between these processes gives rise to the signature stress overshoot in the homogeneous deformation regime at elevated temperatures; and the suppression of the annihilation process facilitates strain localization into a shear band at low temperatures.

Shear transformation zone dynamics model for metallic glasses incorporating free volume as a state variable

A mesoscale model, shear transformation zone dynamics (STZ dynamics), is employed to investigate the connections between the structure and deformation of metallic glasses. The present STZ dynamics model is adapted to incorporate a structure-related state variable, and evolves via two competing processes: STZ activation, which creates free volume, vs. diffusive rearrangement, which annihilates it. The dynamical competition between these two processes gives rise to an equilibrium excess free volume that can be connected to flow viscosity via the phenomenological Vogel–Fulcher–Tammann relation in relaxed structures near the glass transition temperature. On the other hand, the excess free volume allows glasses to deform at low temperatures via shear localization into shear bands, even in the presence of internal stress distributions that arise upon cooling after processing.

Nanoscale strength distribution in amorphous versus crystalline metals

Low-load nanoindentation can be used to assess not only the plastic yield point, but the distribution of yield points in a material. This paper reviews measurements of the so-called nanoscale strength distribution (NSD) on two classes of materials: crystals and metallic glasses. In each case, the yield point has a significant spread (10–50% of the mean normalized stress), but the origins of the distribution are shown to be very different in the two materials classes. In crystalline materials the NSD can arise from thermal fluctuations and is attended by significant rate and temperature dependence. In metallic glasses well below their glass-transition temperature, the NSD is reflective of fluctuations in the sampled structure and is not very sensitive to rate or temperature. Computer simulations using shear transformation zone dynamics are used to separate the effects of thermal and structural fluctuations in metallic glasses, and support the latter as dominating the NSD of those materials at low temperatures. Finally, the role of the NSD as a window on structural changes due to annealing or prior deformation is discussed as a direction for future research on metallic glasses in particular.

Three-dimensional shear transformation zone dynamics model for amorphous metals

A fully three-dimensional (3D) mesoscale modeling framework for the mechanical behavior of amorphous metals is proposed. The model considers the coarse-grained action of shear transformation zones (STZs) as the fundamental deformation event. The simulations are controlled through the kinetic Monte Carlo algorithm and the mechanical response of the system is captured through finite-element analysis, where STZs are mapped onto a 3D finite-element mesh and are allowed to shear in any direction in three dimensions. Implementation of the technique in uniaxial creep tests over a wide range of conditions validates the model's ability to capture the expected behaviors of an amorphous metal, including high temperature flow conforming to the expected constitutive law and low temperature localization in the form of a nascent shear band. The simulation results are combined to construct a deformation map that is comparable to experimental deformation maps. The flexibility of the modeling framework is illustrated by performing a contact test (simulated nanoindentation) in which the model deforms through STZ activity in the region experiencing the highest shear stress.

Cyclic hardening of metallic glasses under Hertzian contacts: Experiments and STZ dynamics simulations

A combined program of experiments and simulations is used to study the problem of cyclic indentation loading on metallic glasses. The experiments use a spherical nanoindenter tip to study shear band formation in three glasses (two based on Pd and one on Fe), after subjecting the glass to cycles of load in the nominal elastic range. In all three glasses, such elastic cycles lead to significant increases in the load required to subsequently trigger the first shear band. This cyclic hardening occurs progressively over several cycles, but eventually saturates. The effect requires cycles of sufficient amplitude and is not induced by sustained loading alone. The simulations employed a new shear transformation zone (STZ) dynamics code to reveal the local STZ operations that occur beneath an indenter during cycling. These results reveal a plausible mechanism for the observed cyclic hardening: local regions of confined microplasticity can develop progressively over several cycles, without being detectable in the global load–displacement response. It is inferred that significant structural change must attend such microplasticity, leading to hardening of the glass.

Nonequilibrium thermodynamics of driven amorphous materials. III. Shear-transformation-zone plasticity

We use the internal-variable, effective-temperature thermodynamics developed in two preceding papers to reformulate the shear-transformation-zone (STZ) theory of amorphous plasticity. As required by the preceding analysis, we make explicit approximations for the energy and entropy of the STZ internal degrees of freedom. We then show that the second law of thermodynamics constrains the STZ transition rates to have an Eyring form as a function of the effective temperature. Finally, we derive an equation of motion for the effective temperature for the case of STZ dynamics.

Mesoscale modeling of amorphous metals by shear transformation zone dynamics

A new mesoscale modeling technique for the thermo-mechanical behavior of metallic glasses is proposed. The modeling framework considers the shear transformation zone (STZ) as the fundamental unit of deformation, and coarse-grains an amorphous collection of atoms into an ensemble of STZs on a mesh. By employing finite element analysis and a kinetic Monte Carlo algorithm, the modeling technique is capable of simulating glass processing and deformation on time and length scales greater than those usually attainable by atomistic modeling. A thorough explanation of the framework is presented, along with a specific two-dimensional implementation for a model metallic glass. The model is shown to capture the basic behaviors of metallic glasses, including high-temperature homogeneous flow following the expected constitutive law, and low-temperature strain localization into shear bands. Details of the effects of processing and thermal history on the glass structure and properties are also discussed.

Shear-transformation-zone theory of plastic deformation near the glass transition

The shear-transformation-zone (STZ) theory of plastic deformation in glass-forming materials is reformulated in light of recent progress in understanding the roles played by the effective disorder temperature and entropy flow in nonequilibrium situations. A distinction between fast and slow internal-state variables reduces the theory to just two coupled equations of motion, one describing the plastic response to applied stresses and the other the dynamics of the effective temperature. The analysis leading to these equations contains, as a by-product, a fundamental reinterpretation of the dynamic yield stress in amorphous materials. In order to put all these concepts together in a realistic context, I conclude with a reexamination of the experimentally observed rheological behavior of a bulk metallic glass. That reexamination serves as a test of the STZ dynamics, confirming that system parameters obtained from steady-state properties such as the viscosity can be used to predict transient behaviors.