Inhomogeneous deformation in metallic glasses

The present study provides a theoretical framework for the inhomogeneous deformation in metallic glasses. The free volume concentration is adopted as the order parameter, which is a function of position and time. The three processes that can change the local free volume concentration are diffusion, annihilation, and stress-driven creation. The rate functions for free volume generation and plastic flow depend on the underlying microscopic model, but the framework is generally valid for different models. A simple shear problem is solved as an example. A linear stability analysis is performed on the basis of the homogeneous solution. An inhomogeneous solution is obtained with a finite amplitude disturbance to the initial free volume distribution. Numerical simulation shows the development of the inhomogeneous deformation and strain localization.     

Large strain deformation of polycrystalline metals at low homologous temperatures

Large strain compression data (true strains to about ?3.0) are presented for polycrystalline α U and α Fe at room temperature. The results, together with other published data at low homologous temperatures (≈0.2 T_m), where T_m is the absolute melting temperature, suggest that a steady-state flow stress σ_s is approached after extensive strain-hardening, α U exhibits a very high strain-hardening rate, with σ_s ≈ 2900 MPa (420 ksi) indicating that cold-working is a very potent method of strengthening this metal. All the data evaluated can be fit by the stress-strain relation σ = σ_s? exp (?(Nε)^p)(σ_s? σ_y), where σ_y is the yield stess, p is a constant equal to a for the metals analyzed, N is a constant associated with the strain-hardening characteristics of a material, σ is true stress, and ε is true strain.     

Effects of microscopic boundary conditions on the deformation behavior of small-volume metallic glasses

Although large-volume metallic glasses (MGs) are susceptible to shear localization due to their intrinsically strain-softening response, recent experiments and molecular dynamics simulations have shown that small-volume MGs samples are able to exhibit work hardening response. Here, we seek to address two issues regarding the mechanical response of small-volume MGs at low homologous temperatures from a continuum-based modeling perspective: (1) are MGs capable of exhibiting a work hardening response, and (2) what is the physical mechanism which causes its work hardening response?Along with implementing a recently-developed finite-deformation, strain gradient plasticity-based constitutive model for MGs into a self-developed finite-element code, we study the tensile response of small-volume MG samples of various sizes through finite-element simulations. Our simulations show that small-volume MG samples are capable of exhibiting a work hardening response provided the following conditions are met: (a) the sample size is small enough, and (b) the appropriate microscopic boundary conditions for the free volume are imposed on the sample.     

Simulation of crack propagation in fiber-reinforced bulk metallic glasses

Based on a phase-field model for deformation in bulk metallic glasses (BMGs), shear band formation and crack propagation in the fiber-reinforced BMG are investigated. Ideal unbroken fibers embedded in the BMG matrix are found to significantly influence the shear banding and crack propagation in the matrix. The crack propagation affected by fibers’ length and orientation is quantitatively characterized and is described by micromechanics models for composite materials. Furthermore, fractures in some practical fiber-reinforced BMG composites such as tungsten-reinforced Zr-based BMG are simulated. The relation between the enhanced fracture toughness and the mechanical properties of fiber reinforcements is determined. Different fracture modes of BMG-matrix composites are identified from the systematic simulation studies, which are found to be consistent with experiments. The simulation results suggest that the phase-field modeling approach could be a useful tool to assist the fabrication and design of BMG composites with high fracture toughness and ductility.     

金属非晶的强度和变形特性

金属非晶发展至今已有多种体系并可实现厘米量级的块体制备,其各种性能也都有了广泛的研究。本文主要介绍金属非晶的单轴拉伸、单轴压缩、微柱压缩、薄板弯曲、拉伸-扭转等物理力学特性及关于其变形的理论分析。文章涵盖了金属非晶的以下一些力学特性：金属非晶的弹性模量和其溶剂金属的相近性―金属非晶通常具有2% 左右的弹性应变极限,对应着GPa量级的高失效强度;金属非晶单轴拉伸、压缩时的宏观塑性特征及塑性变形的典型机制;金属非晶微观上的短程与中程原子团簇结构特点及其与非晶塑性的关联;金属非晶塑性屈服与静水压力的相关性,拉扭组合时呈现的螺旋断口特征,以及Mohr-Coulomb本构模型对这些屈服特征的适用性。最后,作者也介绍了金属非晶塑性变形的微观物理模型及连续介质力学本构,以及金属非晶的断裂与疲劳特性。     

Origin of anomalous inverse notch effect in bulk metallic glasses

Understanding notch-related failure is crucial for the design of reliable engineering structures. However, substantial controversies exist in the literature on the notch effect in bulk metallic glasses (BMGs), and the underlying physical mechanism responsible for the apparent confusion is still poorly understood. Here we investigate the physical origin of an inverse notch effect in a Zr-based metallic glass, where the tensile strength of the material is dramatically enhanced, rather than decreased (as expected from the stress concentration point of view), by introduction of a notch. Our experiments and molecular dynamics simulations show that the seemingly anomalous inverse notch effect is in fact caused by a transition in failure mechanism from shear banding at the notch tip to cavitation and void coalescence. Based on our theoretical analysis, the transition occurs as the stress triaxiality in the notched sample exceeds a material-dependent threshold value. Our results fill the gap in the current understanding of BMG strength and failure mechanism by resolving the conflicts on notch effects and may inspire re-interpretation of previous reports on BMG fracture toughness where pre-existing notches were routinely adopted.     

Measurement and modeling of back stress at intermediate to high homologous temperatures

Unified creep-plasticity models often require a number of internal state variables to accurately capture the path dependence of rate- and temperature-dependent alloys especially at intermediate to high homologous temperatures. However, it is impossible to fully measure the internal state variables directly. Consequently, assumptions on the relative importance of the various state variables must be made when determining the material parameters and their evolution must be inferred. Any enhancements designed to better capture the evolution of the state variables are dependent on these assumptions and are generally limited. The strain transient dip test and the rapid load/unload test are two indirect experimental methods used to obtain an approximate measure of the evolutionary nature of the back stress in 60Sn–40Pb, a common rate- and temperature-dependent solder alloy. The rapid load/unload test gives a better measure of back stress because there is less time for the internal state to evolve during data acquisition. Modifications to the back stress evolution equations in the McDowell unified creep-plasticity model are proposed using these new measurements as guidance. The modified model can better capture the transients under cyclic loading and following strain-rate jumps.     

Evolution of shear bands in bulk metallic glasses under dynamic loading

Shear band spacing in Zr-based bulk metallic glasses (BMGs) under dynamic loads is found to vary with position and local strain rate in the indented region. To investigate the dependence of shear band evolution characteristics on local strain rate and normal stress, a micromechanical model based on momentum diffusion is proposed. The thermo-mechanical model takes into account the normal stress dependence of yield stress, the free volume theory and the associated viscosity change within the shear band region. Temperature rise is obtained from the balance between the heat diffusion to the adjacent regions from a shear band and the heat generation due to the accumulated plastic work in a shear band. The parametric study has revealed that thermal effects play a minor role when the critical shear displacement is below 10 nm (as in nanoindentation) but become significant when the shear displacement accumulated in a shear band is of the order of hundreds of nanometers (as in uniaxial compression and in dynamic indentations). Finally, it is found that the normal stress plays a crucial role in the deformation behavior of BMGs by not only decreasing the time for shear band formation but also increasing the temperature rise significantly.     

On the fluorescent behavior of ketones at high temperatures

Results are presented of the effect of elevated temparature and pressure on the laser-induced fluorescence of ketone molecules. The fluorescent yield of ketones was found to decrease with temperature but was unaffected by pressure for a 266 nm excitation and broadband collection.Support for this work was provided by the Department of Energy, (Grant DE-FG04-90AL65006), the Ford Motor Co., and Cummins Engine Co.     

Consistency of the free-volume approach to the homogeneous deformation of metallic glasses

One of the most widely used approaches to model metallic-glasses high-temperature homogeneous deformation is the free-volume theory, developed by Cohen and Turnbull and extended by Spaepen. A simple elastoviscoplastic formulation has been proposed that allows one to determine various parameters of such a model. This approach is applied here to the results obtained by de Hey et al. on a Pd-based metallic glass. In their study, de Hey et al. were able to determine some of the parameters used in the elastoviscoplastic formulation through DSC modeling coupled with mechanical tests, and the consistency of the two viewpoints was assessed.     

Mode II fracture behavior of a Zr-based bulk metallic glass

Shear band formation and fracture are characterized during mode II loading of a Zr-based bulk metallic glass. The measured mode II fracture toughness, K_IIc=75±4 MPa√m, exceeds the reported mode I fracture toughness by ∼4 times, suggesting that normal or mean stresses play a significant role in the deformation process at the crack tip. This effect is explained in light of a mean stress modified free volume model for shear localization in metallic glasses. Thermal imaging of deformation at the mode II crack tip further reveals that shear bands initiate, arrest, and reactivate along the same path, indicating that flow in the shear band leads to permanent changes in the glass structure that retain a memory of the shear band path. The measured temperature increase within the shear band is a fraction of a degree. However, heat dissipation models indicate that the temperature could have exceeded the glass transition temperature for less than 1 ms immediately after the shear band formed. It is shown that this time scale is sufficient for mechanical relaxation slightly above the glass transition temperature.     

Uniaxial deformation behavior of different polypropylene cast films at temperatures near the melting point

A new apparatus for stretching polypropylenes at elevated temperatures below the melting point at high deformation speeds (up to 750 mm/s) is described. In the temperature range of 140-160 °C the tensile behavior of polypropylene undergoes a shift from the ductile to the quasi-rubber-like deformation behavior. Furthermore, the deformation behavior is strongly affected by the strain rate. The homogeneity of sample deformation increases with the deformation rate. Furthermore, the influence of the cast film morphology on the uniaxial deformation behavior is investigated and discussed in terms of the degree of crystallinity and crystallite size. The degree of the residual crystallinity plays a decisive role for the deformation behavior. At similar degree of crystallinity, the yield stress is significantly influenced by the crystallite size in a way that the larger the crystallite size the higher the yield stress.     

The ionization-rate constant at high temperatures high electron concentrations

The electron distribution function and the rate constant for ionization of atoms by electron impacts have been calculated as they apply to the conditions that are characteristic of a shock wave — namely, the energy distribution of the electrons and the ionization-rate constants are determined as functions of the temperature of the heavy particles. The energy dependence of the effective cross section for the excitation of an atom by electron impact is assumed to be linear. Equations of the Fokker-Planck type are used in the solution of the problem, and the range of temperatures and concentrations in which the deviation of the distribution from Maxwellian leads to a substantial change of the ionization-rate constant is determined.Translated from Zhurnal Prikladnoi Mekhaniki i Tecknicheskoi Fiziki, No. 2, pp. 32–40, March–April, 1971.     

Duplex model for homogenized elastic-viscoplastic behavior of plate-fin structures at high temperatures

In this study, a duplex model is developed as a constitutive model for the homogenized elastic-viscoplastic behavior of a class of plate-fin structures operating at high temperatures. This model consists of plate and fin layers, which are individually ruled by different macro-constitutive models. An anisotropic, compressible power-law equation that was derived in a recent study by the present authors is used to describe the homogenized viscoplastic behavior of the fin layer. On the other hand, an isotropic, incompressible power-law equation is used as the macro-constitutive equation of the plate layer. The duplex model developed is applied to an ultra-fine plate-fin structure made of Hastelloy X. It is shown that the duplex model is more successful under multiaxial loading than the corresponding simplex model in which plates and fins are non-separately homogenized.     

A technique for measuring the dynamic behavior of materials at high temperatures

A new experimental technique has been developed for the performance of high temperature, high-strain-rate experiments in the compression Kolsky bar (split-Hopkinson pressure bar or SHPB). The new technique (referred to as the High-Temperature Compression Kolsky Bar or HTCKB) uses an infra-red spot-heater to rapidly heat the specimen to the desired temperature, a!nd an electropneumatic actuation system to minimize the development of temperature gradients in the sample. The technique is cheap and relatively easy to implement and yet provides accurate, repeatable results. As an illustration of the application of the technique, we have examined the high-temperature response of the BCC metal vanadium at high-strain rates. Stress–strain curves are obtained for the material at strain rates of 4 × 10³ s⁻¹ and at temperatures ranging from 300 to 1100 K (27–800°C). Quasistatic (10⁻³ s⁻¹) experiments have also been performed on vanadium over a slightly smaller range of temperatures, and the results are compared with the new high-temperature, high-strain-rate data. It is observed that the rate of thermal softening is a function of the strain rate. These results illustrate the importance of including the coupling between temperature and strain r!ate in thermoviscoplastic constitutive models.     

Effects of size on the strength and deformation mechanism in Zr-based metallic glasses

We report results of uniaxial compression tests on Zr₃₅Ti₃₀Co₆Be₂₉ metallic glass nano-pillars with diameters ranging from ∼1.6 μm to ∼100 nm. The tested pillars have nearly vertical sidewalls, with the tapering angle lower than ∼1° (diameter >200 nm) or ∼2° (diameter ∼100 nm), and with a flat pillar top to minimize the artifacts due to imperfect geometry. We report that highly-localized-to-homogeneous deformation mode change occurs at 100 nm diameter, without any change in the yield strength. We also find that yield strength depends on size only down to 800 nm, below which it remains at its maximum value of 2.6 GPa. Quantitative Weibull analysis suggests that the increase in strength cannot be solely attributed to the lower probability of having weak flaws in small samples - most likely there is an additional influence of the sample size on the plastic deformation mechanism.     

Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones, notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode II component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.