Development Of Shear Bands Research Articles

Coordinate transformation methodology for simulating quasistatic elastoplastic solids

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.

Role of plastic deformation mechanisms during the microstructural evolution and intermetallics formation in dissimilar friction stir weld

During dissimilar Friction Stir Welding (FSW) of titanium (Ti) to aluminum (Al), particles of titanium are inhomogeneously distributed in the aluminum matrix, in the weld nugget. The Al/Ti interfaces are the potential zones for intermetallic formation. The inhomogeneous distribution of Ti particles and intermetallic particles can have a negative impact on the mechanical properties of the weld. The objective of the present investigation is to highlight the mechanism of such inhomogeneity in the distribution and formation of intermetallics within the weld. In the present investigation, FSW of Al to Ti was carried out in butt-weld configuration and microstructure across the weld was characterized using Scanning Electron Microscopy (SEM) and X-ray Tomography (XCT). Results from the weld nugget showed three regions of Ti particle distribution, variation in their fragmentation and chemical composition across the Al/Ti interfaces when investigated from top to bottom of the weld. Such variations were correlated with conventional strain rate and temperature variation in the weld nugget. Detailed analysis of microstructure in the weld nugget illustrated that both titanium and aluminum undergo dynamic recrystallization. However, the mechanisms leading to such microstructural evolution were different. Recrystallization in titanium occurred due to low-temperature deformation and evolution of adiabatic shear bands whereas dynamic recrystallization in aluminum was attributed to its high stacking fault energy. The present results and mechanism can be useful in further development of the weld nugget in dissimilar FSW and development of composite by friction stir processing with homogeneous microstructure and superior mechanical properties.

Microstructure and Mechanical Properties Evolution in HfNbTaTiZr Refractory High‐Entropy Alloy During Cold Rolling

The effect of cold rolling on the structure and mechanical properties of the HfNbTaTiZr refractory high‐entropy alloy with a single body‐centered cubic (BCC) phase structure is studied. The microhardness evolution during cold rolling to the thickness strain εth = 80% shows three distinct stages: an increase till εth ≈ 15%, a plato in the interval ≈15–40%, and again some increase at εth ≥ 40%. This behavior is found to be associated with an increase in dislocation density at the first stage, the formation of kink bands at the second stage, and the development of shear bands with fine lamellar internal substructure at the third stage. After cold rolling to 80%, the alloy demonstrates the yield strength of 1220 MPa, peak strength 1320 MPa, and elongation to fracture 3.4%. A short steady‐state flow stage is observed on the engineering stress–strain curve that can also be associated with kinking.

A damage and elastic-viscoplastic constitutive model of frozen soil under uniaxial impact loading and its numerical implementation

We analyzed the uniaxial impact compression due to different strain rates on frozen soil specimens at different temperatures using split-Hopkinson pressure bar (SHPB) and obtained the dynamic stress–strain curves under the corresponding conditions. The experimental results showed that the dynamic mechanical behavior of frozen soil under impact loading shows an obvious strain-rate effect and temperature effect, as well as obvious elastic-viscoplastic deformation characteristics. Furthermore, the dynamic stress–strain curves of frozen soil showed instability with the evolution of internal micro-cracks, micro-voids, and shear bands in frozen soil. The dynamic mechanical behavior of frozen soil was described by introducing an advanced rate-dependent continuous damage evolution model and an elastic-viscoplastic constitutive model based on the Chaboche unified viscoplastic constitutive theory and using the Drucker–Prager yield criterion. To obtain a numerical solution of the elastic-viscoplastic constitutive equation, the constitutive equation was discretized into an incremental form by Euler's method, and the closest point projection algorithm was used as the numerical integral to update the stress state during the deformation process of frozen soil. The constitutive model was numerically solved, and the theoretically calculated curves agreed well with the experimentally measured curves. Thus, we verified the rationality and applicability of the uniaxial dynamic constitutive model constructed for this study and developed its numerical integral algorithm.

A thermo-elastic-plastic phase-field model for simulating the evolution and transition of adiabatic shear band. Part I. Theory and model calibration

Adiabatic shear band (ASB) is an important failure mode of solid materials, especially for metal materials under high strain rate loading. In this study, a thermo-elastic-plastic phase-field model, which considers both damage softening and thermal softening, is established to simulate the formation of multiple ASBs and the transition from ASB to the fracture. How to select and calibrate the material parameters in the phase-field model is seldom clearly discussed in the current phase-field model when dealing with ASB. In this paper, the damage parameters in the phase-field method are calibrated using data from pure shear specimens, taking into account both the overall response of the structure and the local response in the ASB. As an application, the calibrated model is used to numerically study the evolution of the ASB of the hat specimen and the process of its transition to the fracture. The simulation results successfully explain the typical phenomena such as transient “hot spots” and double softening in the experiment. The numerical model we developed provides a reliable quantitative description for the evolution and width calculation of ASBs and lays a foundation for the further study of ASB.

Numerical Study on the Fatigue Limit of Metallic Glasses under Cyclic Tension-Compression Loading.

Numerical study was performed to determine the fatigue limit of metallic glass under tension-compression cyclic loading. A revised free-volume theory which considers the hydrostatic stress was utilized to make the predictions. Systematical simulations showed that a higher strain amplitude is prone to making the sample completely damaged earlier. However, lower strain fluctuations could result in a longer fatigue life. Shear banding evolution history described by free-volume localization could reasonably explain the mechanical responses of different samples. In addition, compressive loading could give rise to a higher stress than that under tensile loading because of hydrostatic stress contribution. In the end, a correlation between fatigue life and applied strain amplitude was plotted which could supply a guidance for designing the engineering application of metallic glass under periodic loading.

A thermo-elastic-plastic phase-field model for simulating the evolution and transition of adiabatic shear band. Part II. Dynamic collapse of thick-walled cylinder

In Part I, a thermo-elastic-plastic phase-field model is established for describing the adiabatic shear band (ASB) in metal materials. In this Part II, the developed model is used to simulate the classical thick-walled cylinder (TWC) experiment to investigate the self-organizing behavior of multiple ASBs. For the first time, the formation process of self-organized ASBs in the TWC experiment is reproduced by the phase-field method and the underlying physical mechanism is analyzed in detail. The simulation results show that the number and spacing of ASBs are related to loading rate and material properties. A higher loading rate leads to more intensive ASBs. For typical engineering materials such as 304L stainless steel (Ss304L) and titanium alloy (Ti6Al4V), the contribution of thermal softening to the formation of ASBs is far less than that of damage softening. However, thermal softening is very important to induce initial ASBs. In addition, we also find that defects, especially large ones, play a dominant role in the initiation and evolution of ASBs, leading to complex patterns of ASBs in the TWC experiments.

Shear band multiplication induced strong strain delocalization and high tensile ductility in amorphous thin films by metallic substrates

Metallic glass usually ruptures at a small strain by forming single dominant shear band under tension at room temperature. Experiments have shown that multiple shear bands can be induced in metallic glass film by a ductile metallic substrate, and the ductility of the film can be elevated significantly. However, the mechanism behind remains unsolved. Here we established a computational model to investigate the effect of a Ni substrate on the deformation of a Ni-P amorphous film. The shear band evolution in the film was described by a free volume-based constitutive theory, while the deformation of the Ni substrate was simulated by a dislocation density-based model. The film/substrate interface was modeled by a cohesive zone law. In the simulations, the shear band evolution and the stress in the film can be measured directly, which is difficult to achieve in experiments. Our simulations show that multiple shear bands have been formed in the substrate-supported metallic glass film if the film thickness hf is less than 10 µm. The thinner the film is, the more the shear bands the film has. The number of shear bands can reach as high as 16 as hf is refined down to 2.5 µm. The generation of the multiple shear bands alleviated the strong strain-softening as observed in free standing film, as clearly shown in the stress-strain response of the thin film in the film/substrate system. The suppressed strain-softening induces significantly enhanced tensile ductility in the amorphous film. The tensile ductility of the 2.5 µm-thick film on the Ni substrate can reach as high as 13.3%, which is much higher than that of the corresponding freestanding film, i.e., 3.1%. The proposed computational model has been validated by the coincident stress-strain responses between simulations and experiments. The findings revealed that the enhanced tensile ductility originates from the shear band multiplication-induced strain delocalization in the amorphous film due to the constraint of the metallic substrate.

Numerical study on deformation behavior of bulk metallic glass composites via modified free-volume theory

A modified free-volume theory accounting for tensile and compressive strength asymmetry of bulk metallic glass (BMG) is implemented into finite element code as a user material subroutine. By means of representative volume element, systematical simulations are carried out to investigate the mechanical response as well as shear band evolution of BMG composites (BMGCs) under both tensile and compressive loadings. Comparison between experiments and simulations proves that this modified free volume model could yield acceptable prediction for both BMG matrix and BMGCs. Furthermore, free-volume is utilized to characterize the shear banding process of BMGCs, which is found to be dependent on volume fraction, shapes, orientation as well as yielding strength of particle materials. The present model could provide a computational tool to analyzing deformation behavior of BMGCs as well as designing new composites with high strength and plasticity.

Layer thickness effects on the strengthening and toughening mechanisms in metallic glass-graphene nanolaminates

Experiments have proved that one solution to improve the ductility of metallic glasses lies in introducing graphene and synthesizing metallic glass (MG) nanolaminates. In this work, molecular dynamic simulations are conducted to investigate layer thickness effects on the tensile behaviors of Cu50Zr50 metallic glass-graphene nanolaminates (MGGNLs). The increase in MG layer thickness leads to the decrease in the ultimate strength of MGGNL and helps to the development of shear bands. Meanwhile, plastic deformation mode transits from homogeneous flow to shear localization. The critical layer thickness related to such a transition can be predicted by the strain energy theory. Once the dissipated energy in MG matrix during shear bands formation exceeds the stored strain energy in graphene, shear localization dominates plastic deformation mode. Besides, fracture strain decreases with increasing MG layer thickness. There also exists a kink for the linear decline in fracture strain, corresponding to the plastic deformation transition. Finally, the equivalent model for layer thickness is proposed to better describe the Hall-Petch effect on the yield strength of MGGNLs. Our study provides the guidance to the synthesis of novel metallic glass nanocomposites.

In situ analysis of shear bands and boundary layer formation in metals.

Shear banding is a plastic instability in large deformation of solids where the flow becomes concentrated in narrow layers, with broad implications in materials processing applications and dynamic failure of metals. Given the extremely small length and time scales involved, several challenges persist in studying the development of shear bands. Here, we present a new approach to study shear bands at low speeds using low melting point alloys. We use in situ imaging to directly capture the essential features of shear banding, including transition from homogeneous to shear banded flow, band nucleation and propagation dynamics, and temporal evolution of the flow around a developing band. High-resolution, time-resolved measurements of the local displacement and velocity profiles during shear band growth are presented. The experiments are complemented by an analysis of the shear band growth as a Bingham fluid flow. It is shown that shear banding occurs only beyond a critical shear stress and is accompanied by a sharp drop in the viscosity by several orders of magnitude, analogous to the yielding transition in yield-stress fluids. Likewise, the displacement field around a nucleated band evolves in a manner that resembles boundary layer formation, with the band thickness scaling with time as a power law.

DEM study of the shear behavior and formation of shear band in biaxial test

This paper aims to study the shear behavior of granular matter by DEM simulations. Granular samples are prepared by automatic clump generation algorithm to create particles of irregular shapes. Simulations of the biaxial test with membrane boundary condition are used to test the shear behavior of samples. A new method for computing sample volume in membrane boundary condition is proposed. Deviatoric stress and volumetric strain curves are plotted to describe contracting-dilatancy of granular materials during the shearing stage. Formation of the shear band is studied from particle rotation and particle displacement fields. The influence of confining pressure, initial porosity, and friction coefficient on the development of shear band are studied. Lower confining pressure, higher initial porosity can be resulted in later formation of shear bands.

Semi-Implicit Numerical Strategy for Implementing a Nonlocal Finite-Deformation Gurson Model for Glassy Polymer Using Finite Element Analysis

Post-peak strain softening for some thermoplastic resins often leads to localized deformation with plastic flow instability, spurious energy dissipation, and numerical solutions with mesh dependency using finite element analysis (FEA) due to the lack of a length scale. This paper introduces the nonlocal integral theory with a length scale into the Gurson model to capture objective void evolution and shear bands for glassy polymer under quasi-static loading. Nonlocal numerical technique using the finite-deformation Gurson model is developed, where the nonlocal implicit stress return algorithm and the nonlocal consistent tangent stiffness are presented in the corotational configuration by performing nonlocal averaging on the void volume fraction in a semi-implicit way. The numerical strategy is implemented by combining the finite element software ABAQUS-UMAT, USDFLD, and UEXTERNALDB subroutines. For plane tension problem, the developed nonlocal numerical technique circumvents mesh dependency well by studying the void growth, the evolution of shear bands, and the load responses.

On the microstructural evolution pattern toward nano-scale of an AISI 304 stainless steel during high strain rate surface deformation

In the present investigation, an austenitic AISI 304 stainless steel was subjected to high strain rate surface deformation by Pipe Inner-Surface Grinding (PISG) technique. The depth-dependent deformation parameters (strain, strain rate and strain gradient) were evaluated and the microstructures were systematically characterized. Microstructural evolution from millimeter- to nano-scale was explored, with special attention paid to the localized deformation. Microstructural evolution begins with the formation of planar dislocation arrays and the twin-matrix lamellae, which is followed by the localized deformation characterized by the initiation and the development of shear bands. A twinning-dominated process that was supplemented with dislocation slip-dominated one governed the microstructural evolution inside shear bands. The twin-matrix lamellae transform into extended/lamellar structure and finally the nano-sized grains. Austenitic grains were substantially refined and martensitic transformation was effectively suppressed, of which the underlying mechanisms were analyzed.

The influence of pipeline–trenchbed interaction intensity on lateral soil resistance and failure mechanisms

ABSTRACT Buried offshore pipelines may be subjected to large lateral displacements caused by ground movements, landslides, etc. A proper estimation of lateral soil resistance against the moving pipeline requires a deep understanding of pipeline–backfill–trench interaction mechanisms. Recent studies show that pipeline–trenchbed interaction can significantly affect the failure mechanisms and the resultant lateral soil resistance, an important aspect that is currently neglected by pipeline design codes. In this paper, the effect of pipeline–trenchbed interaction intensity on lateral soil resistance was investigated by performing centrifuge tests. The soil deformations and failure mechanisms were obtained by Particle Image Velocimetry (PIV) analysis. Two experiments with horizontal and downward inclined pulling directions were conducted to simulate different intensities of bed interaction. It was observed that increasing the intensity of pipeline–trenchbed interaction results in a faster and full development of shear bands in the trench wall and reduction of the mobilized lateral soil resistance.

Revisiting the effect of aspect ratio on shear band evolution by hydrostatic-stress embedded free-volume theory

The shear band evolution process induced by different aspect ratios was investigated by experiments and hydrostatic-stress embedded free-volume theory. It was found that specimen with lower aspect ratio displayed a higher compressive plasticity since the shear band propagation was confined by the machine head in a way of preventing the sample from fracturing along one major shear band. Hydrostatic-stress embedded free-volume theory was incorporated into ABAQUS as a user material subroutine UMAT. Numerical method was performed to reveal the shear band evolution caused by different aspect ratios. There was a good agreement between experiments and simulations. Furthermore, simulations demonstrated that sample with smaller aspect ratios yielded a relatively lower strain localization level, leading to a correspondingly stable plastic deformation process. Compared with the viscoelastic model, it showed that the current model could better describe shear band evolution history.

Deformation nanotwins suppress shear banding during impact test of CrCoNi medium-entropy alloy

We report deformation bands ahead of the crack tip in a CrCoNi alloy under impact loading, and analyze the effects of deformation twinning on strain localization in the form of shear banding. Due to low stacking fault energy, upon high-strain-rate deformation this medium-entropy alloy forms twins with thickness and spacing of only a few nanometers. These nano-twins are embedded dynamically not only ahead of any developing shear band to retard its advance, but also in its interior to work harden. This dual effect helps to suppress runaway shear banding instability that instigates failure and contributes to the energy absorption as recorded in instrumented Charpy tests.

The toughening mechanism and spatial–temporal evolution of shear bands at different strain rates in Vit-1 metallic glass

Shear banding behavior plays an essential role in exploring the toughening mechanisms of bulk metallic glasses (BMGs). However, due to the instability in time and inhomogeneity in space, it is difficult to investigate the formation, extension, intersection and other spatial–temporal evolution of shear bands via the previous ex-situ method. In this work, uniaxial compressions for Zr41.2Ti13.8Ni10Cu12.5Be22.5 (Vit-1) BMGs are conducted at the strain rates of 3 × 10−5/s, 3 × 10−4/s, and 3 × 10−3/s. Multi-surface in-situ Digital Image Correlation (DIC) measurement is used to capture the spatial–temporal evolution of multiple shear bands, presenting results that cannot be found by the previous ex-situ method. The stick–slip behavior between multiple shear bands is directly observed. Based on the free volume theory, a quantitative calculating method coupled with stress and strain rate for local viscosity of metallic glass is proposed. The inhibiting mechanisms of shear band intersections on their further evolutions are discussed. Besides, the intersection of shear bands may not be the cause of toughening metallic glasses, which even make them more brittle when different atomic clusters are shearing in the same plane.

The morphology evolution of the shear band in slope: insights from physical modelling using transparent soil

Shear band propagation is the internal cause of the deformation and failure of landslides and is associated with much of the damage and loss of life. Understanding how the shear band develops will affect the process of slope deformation is thus of great interest. However, little investigation has been conducted studying the correlation between the slope deformation and the shear band propagation due to the inability to see through the shear band in traditional soil materials. By using transparent soil as a surrogate of natural cement soil, we achieve the visualization of the shear band in a laboratory slope model test, in which the failure was deliberately triggered by top-loading. The temporal evolution of the shear band length and the slope deformation are measured by tracking the tip of shear band and the feature points on slope surface using a commercial software After Effects. The spatial distribution of the shear band thickness and spatial deformation of the slope surface are separately measured based on the image measurement technology in OpenCV and PIVlab, respectively. The results suggest that the geometry of the shear band has a significant influence on the slope deformation. In particular, the velocity of the slope deformation changes synchronously with the speed of the shear band evolution. The spatial differentiation of the slope deformation exhibits a high correlation with the shear band thickness. This is the first time observing that the slope deformation at different locations can be combined to assess the slope stability more precisely by revealing the evolution of shear band geometry.

Atomic-scale origin of shear band multiplication in heterogeneous metallic glasses

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.