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In recent years, the use of dual-phase (DP) steels by the automotive industry has been growing rapidly, motivated by government policies prompting the production of fuel-efficient vehicles. While it is of high interest for the transportation industry to design and discover different grades of DP steels exhibiting desirable mechanical properties, this requires exploring a large number of DP steel microstructure combinations. Expensive trial-and-error-based experimentations and multiscale materials simulations are two conventional approaches that have been widely adopted in the field of materials design and discovery. Yet, it is challenging to use such approaches for fast materials design and discovery when considering the computational and cost limitations, as it is computationally infeasible and intractable to use multiscale materials models to characterize the mechanical properties of millions of different microstructures. To address this major limitation in material design, a Gaussian process is developed to accelerate the discovery of the mechanical properties of different DP steels by evolving the microstructure parameters using a limited number of numerical simulations (using a multiscale materials model). A Gaussian process is a machine learning technique that is trained to find nontrivial correlations between a set of inputs (microstructure properties) to predict a desired output (mechanical property). The proposed Gaussian process not only accelerates the prediction of the desired mechanical properties of millions of multiscale materials simulations but also offers uncertainty quantification around its predictions. These merits make the Gaussian process a very reliable, robust, and practical solution for material design exploration. The proposed framework combining multiscale simulations and the Gaussian process is used to discover the microstructural design of DP steel with maximum tensile toughness. The results showed the effectiveness and robustness of the proposed method in comparison to benchmark methods.

The arching phenomenon is intrinsic to granular materials and is a manifestation of the effects of their discrete microstructure. The fundamental mechanism of arching is the ability of dis...

This study presents an irradiation-dependent internal state variable (ISV) elastoviscoplasticity-damage constitutive model that accounts for nuclear irradiation hardening and embrittlement of the irradiated polycrystalline materials. The irradiation effects were added to the coupled plasticity-damage kinetics with consideration of the structure–property relationships. The present irradiation-dependent elastoviscoplasticity-damage model was compared with the lab deformation experimental data of irradiated oxygen-free high conductivity (OFHC) copper, modified 9Cr-1Mo steel, and Ti-5Al-2.5Sn. The results show excellent agreement over the entire stress–strain curves at various irradiation doses. Because the ISV model, before the irradiation plasticity-damage addition, had been used on over 80 different metal alloys, it is anticipated that this nuclear irradiation supplement will also allow for application to many more irradiated metal alloys.

Radiation-induced embrittlement of reactor pressure vessel (RPV) steels can potentially limit the operating life of nuclear power plants. Over extended exposure to radiation doses, these body-centered cubic (BCC) irons demonstrate irradiation damage. Here, we present a continuum dislocation density (CDD) crystal plasticity model to capture the interaction among dislocations and self-interstitial atom (SIA) loops in α-iron. We demonstrate the importance of modeling cross slip using a combined stochastic Monte Carlo approach and the role of slip system strength anisotropy in capturing stochastic cross slip interactions. Through these captured interactions, the CDD crystal plasticity model can capture both the stress response and the physical evolution of dislocations on different slip system planes. Single-crystal verification experiments are used to calibrate the CDD crystal plasticity model, and a set of simplified polycrystalline simulations demonstrates the model’s ability to capture the stress response from tensile experiments on α-iron.

In this work, a viscoplastic fast Fourier transform (FFT)-based code is combined with a continuum dislocation dynamics (CDD) framework to analyze the mechanical behavior of polycrystalline MgAZ31 material under unidirectional tensile test. A crystal plasticity formulation including the size effects through a stress/strain gradient theory, dislocation density flux among neighboring grains and grain boundary back stress field is implemented into the CDD and coupled with VPFFT for this purpose. Then, an electron backscatter diffraction-based orientation image microscopy of a sample microstructure is applied as an input to the code. The model predicts, among other things, distributions of stress, strain, mobile dislocation density, geometrically necessary dislocation and stress–strain behavior. The numerical findings are compared with experimental results, and the micromechanical behavior of the polycrystal is discussed regarding dislocation density evaluation in different stages of strain hardening.

This paper studies the effects of high-pressure torsion (HPT) at ambient temperature on microstructural evolution and mechanical properties enhancement in pure copper. The aim is to introduce gradient microstructure, with various statistical distributions of grain size and grain orientations to examine their effect on strength and ductility. To this end, extruded cylindrical pure copper subjected to HPT for 1, 2, and 3-turns resulted in grain refinement down to the grain size of 500 nm. Combination of microhardness test and EBSD scans through the radial direction confirm the creation of a heterogeneous structure through the thickness and radial directions. The results demonstrate that increasing the shear strain leads to (1) ultra-fine grain (UFG) generation at deformed coarse-grain boundaries, (2) an increase in the fraction of recrystallized grains and high angle grain boundaries, and (3) a homogenous structure in the last step. A unique mixture has been obtained due to the particular shape of the anvils. The mixture included a chain of UFGs and coarse grains contain dislocations and subgrains. The highest level of gradient structure through the thickness was observed after 1-turn, which leads to the best combination of strength and ductility.

Clay minerals are platelike particles that play a critical role in problems involving swelling, deformation, and failure. Fundamental understanding of these phenomena and the parameters tha...

Molecular dynamics simulations were performed to identify the underlying deformation mechanisms controlling the plastic behavior of nanoindented nanoscale multilayered Ti/TiN. MD simulations were conducted on pure Ti and pure TiN as well as on four different layer-thickness ratios of Ti/TiN multilayers, Ti:TiN = 1, 2.5, 4, and 7.5. The Ti layer thickness varied from 2 nm to 15 nm while the TiN layer thickness is kept constant of 2 nm. The plastic deformation of nanoindented pure Ti was dominated by the formation of dislocation loops resulting from basal partial dislocations, while very few perfect dislocations that tie dislocation loops together were observed. The plastic deformation of nanoindented pure TiN was controlled by the activation of perfect dislocation propagation along the ( 1 1 1 ) plane that dissociates into two partials. Depending on the thickness ratio, either dislocation pile-up or single dislocation crossing through the interface was the controlling plastic deformation mechanism of nanoindented Ti/TiN multilayers. For metal layer thicknesses above 5 nm, significant dislocation pile-ups were observed at the interface of the multi-layered samples. The Ti/TiN multilayer with a thickness ratio of 1:1 with individual layer thickness of 2 nm exhibited the highest strain-hardening rate. At this length scale, the activation of dislocation sources requires very high stresses, and the single dislocation crossing process is the most dominant deformation mechanism. The initiation of plasticity in the TiN layer occurs at a high level of stress since there is no dislocation pile-up at the interface.

This paper develops a continuum model of deformation of X70 steel coated with Cu/Nb–nanolaminate metallic systems (NMSs). The developed model is based on an elastic/viscoplastic framework that includes the effects of dislocation density, size effect, and strain hardening on the plastic deformation. The X70 steel is modeled according to a modified Taylor equation that considers the effects of statistically stored and geometrically necessary stored dislocation densities. NMSs obey two different mechanisms, the confined layer slip (CLS) and dislocation nucleation (Nu), during plastic deformation. NMSs are modeled according to the CLS mechanism when the individual lamina thickness is between 100 nm and 5 nm and the Nu mechanism when the individual lamina thickness is 5 nm or below. The model is implemented in a subroutine of a commercial finite element analysis code. Simulating a tensile test is the benchmark to generate flow curves of the model that agree with experimental data found in the literature.

Although metallic materials with gradient microstructure exhibit notable performance in harsh environmental conditions, they can also exhibit unusual mechanical behaviour. This is attributed to bot...

We present an entirely new method of bottoms-up fabrication of polycrystalline micropillars using direct printing and sintering of nanoparticles in 3D and study their behavior under compression for different microstructures. The pillars showed brittle behavior with higher effective modulus for small grain sizes with high porosity, while highly ductile behavior with a lower effective modulus and larger grain sizes but low porosity. These unusual trends are explained by a porosity model. The results point to a novel method of fabricating micropillars with different microstructures to study fundamental materials science of polycrystalline materials at micro to meso-length scales.

The increase in use of dual-phase (DP) steel grades by vehicle manufacturers to enhance crash resistance and reduce body car weight requires the development of a clear understanding of the effect of various microstructural parameters on the energy absorption in these materials. Accordingly, DP steelmakers are interested in predicting the effect of various microscopic factors as well as optimizing microstructural properties for application in crash-relevant components of vehicle bodies. This study presents a microstructure-based approach using a multiscale material and structure model. In this approach, Digimat and LS-DYNA software were coupled and employed to provide a full micro–macro multiscale material model, which is then used to simulate tensile tests. Microstructures with varied ferrite grain sizes, martensite volume fractions, and carbon content in DP steels were studied. The impact of these microstructural features at different strain rates on energy absorption characteristics of DP steels is investigated numerically using an elasto-viscoplastic constitutive model. The model is implemented in a multiscale finite-element framework. A comprehensive statistical parametric study using response surface methodology is performed to determine the optimum microstructural features for a required tensile toughness at different strain rates. The simulation results are validated using experimental data found in the literature. The developed methodology proved to be effective for investigating the influence and interaction of key microscopic properties on the energy absorption characteristics of DP steels. Furthermore, it is shown that this method can be used to identify optimum microstructural conditions at different strain-rate conditions.

Mechanical properties that are considered to be deterministic in the macro-scale have been shown to be stochastic in the sub-micron length scale. The origin of such stochastic responses is not well understood. This work examines the potential influence of grain boundaries and grain orientations on the stochastic nature of pop-in and hardness measurement in annealed high purity polycrystalline Cu samples during low load nanoindentation. Statistical analysis on pop-in load and hardness showed that variations of these measurements depend on crystal orientations and is influenced by the indenter probe size. Analysis on the pop-in load statistics showed that pop-ins are likely initiate from an atomic sized precursor that leads to dislocation generation or expansion. Variation in hardness measurements near an arbitrary chosen grain boundary and the apparent grain boundary hardening effect observed may be related to the higher density of dislocations at and near the grain boundary.

Cu/Ni/Nb tri-layer and CuNi/Nb alloy multilayer films were annealed to examine the microstructural evolution and mechanical properties of three component laminated metallic nanostructures. Scanning transmission electron microscopy showed Ni x Nb y compounds forming on either side of the Nb layer in both tri-layer and alloy films. Post annealing nanoindentation showed all annealing conditions resulted in increased hardness, indicative of the Ni x Nb y intermetallic phase increasing the hardness of the films. The hardness of both films achieves a maximum hardness after annealing for 3 h at 300 °C. The hardness increase as the annealing temperature increases corresponds to a thicker Ni x Nb y layer at the incoherent boundary. This strengthening technique could be implemented in a variety of different multilayer systems to achieve age-hardenable multilayer metallic nanostructures.

In this work, the mechanical behaviour and texture evolution of AZ31B magnesium alloy under uniaxial tensile testing are investigated at different strain rates and temperatures. A crystal plasticity model is developed and calibrated to predict the mechanical response of the AZ31B at different temperatures and strain rates. The model results show that the relative activity of the pyramidal slip increases with increasing temperature, reaching a maximum activity at 200 °C. In order to achieve the continuous increase in the relative activity of the pyramidal slip as reported in the literature, a grain boundary sliding mechanism is implemented in the crystal plasticity framework. The incorporation of the grain boundary sliding at elevated temperatures results in considerable improvement in the model’s capabilities for prediction of yielding, hardening and texture evolution.

Since the introduction of the term “nanolaminate” in the mid-1990s, considerable research activities on metallic/ceramic nanolaminates (MCN) have been conducted. Incorporating ceramics with high hardness and high melting point together with high ductile metals can improve their thermomechanical behavior in corrosive environments. A great number of researchers have reported that MCNs exhibit outstanding thermomechanical properties compared with the constituent layers and bulk material, which is attributed to the atomic structure and high density of the interfaces. This article provides a review of recent advances in modeling of the mechanical behavior of MCN composites, with focus on Nb/NbC and Ti/TiN multilayer composites. The main strengthening mechanisms of MCNs, based on the layer thickness, the interface structure, and the interaction of threading dislocations with the interface as well as dislocations nucleation from the interface, are reviewed, and recently, obtained results from molecular dynamics simulations, along with these findings, are presented. Moreover, MD-based flow surfaces for use in large-scale continuum models are reviewed in connection with results from MD of MCNs under various mechanical loading conditions, including uniaxial and biaxial loadings.

Dual-phase (DP) steels have received widespread attention for their low density and high strength. This low density is of value to the automotive industry for the weight reduction it offers and the attendant fuel savings and emission reductions. Recent studies on developing DP steels showed that the combination of strength/ductility could be significantly improved when changing the volume fraction and grain size of phases in the microstructure depending on microstructure properties. Consequently, DP steel manufacturers are interested in predicting microstructure properties and in optimizing microstructure design. In this work, a microstructure-based approach using representative volume elements (RVEs) was developed. The approach examined the flow behavior of DP steels using virtual tension tests with an RVE to identify specific mechanical properties. Microstructures with varied martensite and ferrite grain sizes, martensite volume fractions, carbon content, and morphologies were studied in 3D RVE approaches. The effect of these microstructure parameters on a combination of strength/ductility of DP steels was examined numerically using the finite element method by implementing a dislocation density-based elastic-plastic constitutive model, and a Response surface methodology to determine the optimum conditions for a required combination of strength/ductility. The results from the numerical simulations are compared with experimental results found in the literature. The developed methodology proves to be a powerful tool for studying the effect and interaction of key microstructural parameters on strength and ductility and thus can be used to identify optimum microstructural conditions.

Pre-existing dislocations (PED) are ubiquitous inside crystalline lattices which in turn affect the yield stress and the process of plastic deformation. Hence, understanding the onset of dislocations motion and interaction is critical in modifying or designing new materials with advanced properties so that their mechanical behavior approach realistic conditions. One such family of new materials is the ceramic/metallic nanolaminates. In this work, we have investigated the effect of pre-existing dislocations on the mechanical behavior of NbC/Nb nanolaminates using molecular dynamics simulations. Upon unloading at different strains from stress-strain curve of 3 nm NbC/7 nm Nb sample, we were able to generate structures with various pre-existing dislocation densities inside the layers. Uniaxial loadings parallel to the interface at two different temperatures (10 K and 300 K) were performed on each structure. Also, the yield locus was determined at 300 K by applying biaxial in-plane loading and fitted with a general flow potential to be used in macroscale analysis. Finally, the tension-compression asymmetry (TCA) was investigated for the structures with pre-existing dislocations along two different in-plane loading directions.

Traditionally, modeling the effect of grain size on the mechanical behavior of crystalline materials is based on assuming an equivalent homogenous microstructure with strength being dependent on the average grain size, for example the well-known Hall-Petch relation. However, assuming an equivalent homogenized microstructure for a highly heterogeneous microstructure can lead to inaccurate prediction of strength and ductility, especially when the gradients in the spatial heterogeneity are severe. In this work, we employ a multiscale dislocation-based model combined with a strain/stress-gradient theory to investigate the effect of spatial heterogeneity of the microstructure on strength and ductility. We concentrate on understanding the effect of various grain size spatial distributions on the mechanical properties of interstitial free (IF)-steel. The results show that by controlling some parameters in the spatial distribution of the microstructure with regions composed of micro-grains and nano-grains one can achieve improved strength and ductility. Based on these results, it is suggested that the mechanical properties of gradient materials can be described by phenomenological relations that include two structural parameters, grain size and grain-size gradient, in contrast to Hall-Petch relation for homogenous materials where only grains size appears in the equation.

Metal-ceramic multilayers have been reported to show high strength, measurable plasticity, and a high strain-hardening rate when the crystallographic layers are a few nanometers thick. In this work, large-scale molecular dynamics simulations are carried out in order to understand the deformation mechanisms of the Ti/TiN multilayer subjected to multiaxial loading. The yield behavior of the Ti/TiN multilayer is thoroughly explored by constructing the yield surface in the interface plane. The strong dependency of the yielding stresses on the loading direction highlights the anisotropic behavior of the structure. The Ti/TiN multilayer structure shows high strength and ductility under uniform compression loading. However, low strength and ductility are observed under tensile loading, which favors crack initiation and propagation. Unlike typical metal stress-strain curves, metal/ceramic multilayers show two main yield points. Furthermore, the Ti/TiN multilayer structure shows three distinctive peak points for compressive loading normal and parallel to the interface. Different slip planes are activated depending on loading directions. Two main mechanisms are found to control the plasticity of the Ti/TiN multilayer: (1) interface strengthening, in which, when the metal-ceramic multilayers are under compressive loading, the interface acts as a barrier and induces repulsive forces against the slip transmission from the Ti layer into the TiN layer; (2) interface softening, in which, when applying tensile loading on the metal-ceramic multilayer structure, the interfacial misfit dislocations act as sources for the emission of dislocations into the TiN layer or promote slip transmission from the Ti to the TiN layer.

Exceptional mechanical and physical properties of transition metal carbides and nitrides make them good coating-material candidates for extreme corrosive environments such as oil and natural gas wells. However, existence of small pores, pinholes and columnar structures of these ceramics significantly affect their resistance to corrosion, as pore sites would accelerate the diffusion of corrosive media into the substrate. In this research, molecular dynamics atomistic simulations are employed to investigate the effects of the isolated vacancies and the columnar structure on the diffusion rate of H atoms in NbC single crystal at various temperatures. Diffusion coefficient (D) of H atoms in NbC increased with C vacancy concentration. At elevated temperatures, the trapping effect of Nb vacancies is less effective when C vacancies are also present, as H atoms gain enough energy to jump back and forth between the C vacancies. Atomistic simulations also showed a jump in diffusion coefficient for cylindrical pore size of larger than 3 A radius. Furthermore, D increased monotonically with temperature up to 1000 K in the presence of cylindrical pores. Further increase in temperature resulted in a drop in the diffusion coefficient for small pores while the large pores only showed a lower increasing trend in diffusion coefficient with the temperature.

Additive manufacturing (AM) methods such as Aerosol Jet (AJ) printing allow the fabrication of structures via sintering of micro and/or nanoparticles, leading to microstructures that consist of various combinations of pore and grain sizes. It has been reported that AJ printed and sintered silver micropillars show an unusual behavior of high stiffness and high strain-to-failure for structures with high porosity and vice versa (Saleh et al. 2018 [1]). This behavior, however, is accompanied by the stiffer structures having smaller grain sizes and softer structures having larger grain sizes. To explain the physics of this behavior where a trade-off between hardening caused by size effects (grain refinement and gradients) and softening caused by porosity is expected to play a critical role, a multi-scale modeling approach is proposed in this paper. The model formulation consists of a continuum dislocation dynamics (CDD) framework, coupled with continuum plasticity and finite element analysis. The dislocation dynamics formulation is introduced into a user material subroutine and coupled with a finite element commercial solver, in this case, LS-DYNA, to solve the model in three-dimensional scale with the same size as the AM micropillars. The results from the model capture the general trends observed in compression tests of AM micropillars. In particular, it is shown that the grain size and dislocation density have a disproportionately higher influence over the mechanical deformation of metallic structures when compared to the porosity. These results show that the behavior of AM structures in the plastic regime is dominated by grain size effects rather than porosity. Some limitations of the model and possible future refinements are discussed. The paper provides an important analytical framework to model the mechanical behavior of AM structures with internal porosity in the plastic regime.

The promising mechanical, physical and chemical properties of nano-scale metal/ceramic multilayers (MCMs) are of high interest for extreme environment applications. Understanding the plastic deformation mechanisms and the variables affecting those properties is therefore essential. The interface characteristics and the plastic deformation mechanisms under compressive loading in a Ti/TiN multilayer with a semi-coherent interface are numerically investigated. The interface structure of the Ti/TiN interface and the interface misfit dislocation were characterized using molecular dynamic simulations combined with atomically informed Frank-Bilby method. Three possible atomic stacking interface structures are identified according to the crystallographic analysis of the interface. Upon relaxation, large interface areas are occupied with the energetically stable configuration. Furthermore, the higher energy stacking are transformed into misfit dislocations or dislocation nodes. The molecular dynamic compressive stress strain response of the Ti/TiN multilayers exhibited three distinctive peaks. The first peak was generated by the dislocation dissociation of perfect dislocation into pairs of partials dislocation around extended nodes region at the interface. Upon further compression the second peak, identified as the first yielding, resulted from the activation of pyramidal slip planes in the Ti layer. Finally, a third peak identified as the second yielding, occurred when dislocation nucleated/transmitted in/into the TiN layer.

The heterogeneous microstructure has a predominant effect on the mechanical behavior of polycrystalline material. In most instances, a homogenized parameter such as mean grain size is used to describe and to represent the microstructure. However, these models do not account for a measure of heterogeneity in the grain size and grain shape distributions. In this work, we introduce the grain size distribution into a multi-scale stress–strain-gradient model using a controlled Poisson Voronoi tessellation. The correlation between grain size distribution and strength is studied with various cases of grain size distribution with a fixed grid area and mean grain size. In addition, the effect of the spatial distribution of second phases and grain size on the material strength and ductility is also investigated. The results show that introducing heterogeneity into the microstructure can enhance the strength and ductility of the material compared with its equivalent homogeneous microstructure. In addition, different spatial distributions of phases can also lead to different mechanical responses.

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile c...

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield st...

A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

Nano-scale multilayer composite thin films are potential candidates for coating applications at harsh environments due to their promising mechanical and thermal properties. In this study, a viscoplasticity continuum model based on the plastic flow potential of metal/ceramic nanolayer composites, obtained from molecular dynamics (MD) simulations, is developed to build up a multiscale model bridges atomistic simulation with continuum models for the thin film composites. The model adopts a power law hardening considering confined layer slip (CLS) mechanism and accounts for the evolution of dislocation density based on the statistically stored dislocations and geometrically necessary dislocations. It is then implemented into a finite element code (ls-dyna) to investigate the deformation behavior of nanolayer composites at the macroscale. The deformation behavior of a high strength steel coated with Nb/NbC multilayer is also examined.

This chapter, outlines a multiscale dislocation-based plasticity framework coupling discrete dislocation dynamics (DDD) with continuum dislocation-based plasticity. In this framework, and guided by DDD, a continuum dislocation dynamics (CDD) plasticity model involving a set of spatio-temporal evolution equations for dislocation densities representing mobile and immobile species is developed. The evolution laws consist of a set of components each corresponding to a physical mechanism that can be explicitly evaluated and quantified from DDD analyses. In this framework, stochastic events such as cross-slip of screw dislocations and uncertainties associated with initial microstructural conditions are explicitly incorporated in the continuum theory based on probability distribution functions defined by activation energy and activation volumes. The result is a multiscale dislocation-based plasticity model which can predict not only the macroscopic material mechanical behavior but also the corresponding microscale deformation and the evolution of dislocation patterns, size and gradient-dependent deformation phenomena, and related material instabilities at various length and time scales.

Recent studies on developing dual phase (DP) steels showed that the combination of strength/ductility could be significantly improved when changing the volume fraction and grain size of phases in the microstructure depending on microstructure properties. Consequently, DP steel manufacturers are interested in predicting microstructure properties as well as optimizing microstructure design at different strain rate conditions. In this work, a microstructure-based approach using a multiscale material and structure model was developed. The approach examined the mechanical behavior of DP steels using virtual tensile tests with a full micro-macro multiscale material model to identify specific mechanical properties. Microstructures with varied ferrite grain sizes, martensite volume fractions, and carbon content in DP steels were also studied. The influence of these microscopic parameters at different strain rates on the mechanical properties of DP steels was examined numerically using a full micro-macro multiscale finite element method. An elasto-viscoplastic constitutive model and a response surface methodology (RSM) were used to determine the optimum microstructure parameters for a required combination of strength/ductility at different strain rates. The results from the numerical simulations were compared with experimental results found in the literature. The developed methodology proved to be a powerful tool for studying the effect and interaction of key strain rate sensitivity and microstructure parameters on mechanical behavior and thus can be used to identify optimum microstructural conditions at different strain rates.

In strain-gradient plasticity, the length scale controlling size effect has been attributed to so-called geometrically necessary dislocations. This size dependency in plasticity can also be attributed to dislocation pileups in source-obstacle configurations. This has led to the development of stress-gradient plasticity models in the presence of stress gradients. In this work, we re-examine this pileup problem by investigating the double pileup of dislocations emitted from two sources in an inhomogeneous state of stress using both discrete dislocation dynamics and a continuum method. We developed a generalized solution for dislocation distribution with higher-order stress gradients, based on a continuum method using the Hilbert transform. We qualitatively verified the analytical solution for the spatial distribution of dislocations using the discrete dislocation dynamic. Based on these results, we developed a dislocation-based stress-gradient plasticity model, leading to an explicit expression for flow stress. Findings show that this expression depends on obstacle spacing, as in the Hall–Petch effect, as well as higher-order stress gradients. Finally, we compared the model with recently developed models and experimental results in the literature to assess the utility of this method.

In this work, we investigate the mechanical behavior of multi-phase steels using a continuum dislocation dynamic model (CDD) coupled with a viscoplastic self-consistent (VPSC) model that accounts for both the effect of dislocations evolution inside the grain as well as grain–grain interactions. Because the conventional viscoplasticity theory does not capture the grain size effect, we introduce an intrinsic length scale within the concepts of geometrically necessary dislocations (GND) by means of the Nye's dislocation tensor. The effect of the GND density is implemented into the model for the mean free path of dislocations and is shown to contribute to strain hardening. As a validation of this multiscale model, we investigate the mechanical behavior of various dual phase steels. The stress-strain response obtained from this approach is compared to experimental data found in the literature and reveal good agreement between experimental results and predictions. The model also predicts the evolution of dislocation densities in each phase and suggests the connection between underlying deformation mechanisms and macroscopic material hardening. The relation between flow stress and grain size is also investigated. The model predictions follow the Hall–Petch relation of strength versus grain size for grains larger than one micron meter but deviates from this relation for grains in the order of tens of nanometers.

In this paper we investigate the stochastic behavior in the mechanical response of polycrystalline materials consisting of few grains to hundreds of grains at micron size scales. We study the transition from stochastic (at small scale) to deterministic (at large scale) deformation behavior in polycrystalline samples using both simulation and nanoindentation experiments. Specifically, we develop a stochastic crystal plasticity model combining a Monte Carlo method with a polycrystal continuum dislocation dynamics model in a self-consistent viscoplasticity framework. Using this framework, we numerically calculate the mechanical properties of the polycrystal and gather randomized sampling data of the flow stress. The numerical results are compared to nanoindentation experimental data from three samples with ultra-fine grain structures manufactured via the severe plastic deformation method. The controlling mechanisms of the observed stochastic yield behavior of polycrystals are then discussed using simulations and experimental results. Our results suggest that it is the combination of stochastic plasticity at small scales (where the strength may vary from grain to grain) coupled with the effects of microstructural features such as grain size distribution and crystallite orientations that govern the uncertainty in the mechanical response of the polycrystalline materials. The extent of the uncertainty is correlated to the “effective cell size” in the sampling procedure of the simulations and experiments. The simulations and experimental results demonstrate similar quantitative behavior in terms of coefficient of variation within the same effective cell size.

Molecular dynamics (MD) simulations were performed to explore the effect of interface structure on the inception of plastic deformation in Nb/NbC nanolayered composites. Using the atomistically informed Frank–Bilby method and disregistry analysis, we characterized the structure of the Nb/NbC interface, including misfit dislocations, dislocation nodes and three coherent interface structures. According to the crystallographic analysis of the interface, four possible coherent interface structures were identified. However, study of the interface energy showed that only three of these are energetically stable. After the relaxation of the interface, the unstable coherent region, which features Nb atoms in the Nb layer on the top of the Nb atoms in the NbC layer, evolves into a condensed interface dislocation node. Three stable coherent interface regions are retained in association with the formation, glide and reaction of interface misfit dislocation loops. Disregistry analysis of the Nb/NbC interface revealed that (i) all misfit dislocations are edge type, and (ii) misfit dislocations enclosing the coherent extended nodes have Burgers vectors along 〈1 1 0〉 Nb . The role of the interface structure in the plastic deformation of Nb/NbC nanolayered composites was studied under two loading conditions, i.e. uniform compression and nanoindentation. Under uniform compression, lattice dislocations primarily nucleate from the condensed nodal regions where the local strains are the highest. Dislocations propagate in two {1 1 0} slip planes with the same Schmid factors. Under nanoindentation, by proper positioning of the indenter, lattice dislocations nucleate from the segments of the misfit dislocations and propagate in {1 1 2} slip planes. MD simulations also show cross-slip of lattice dislocations from {1 1 2} planes into {1 1 0} planes and the formation of vacancies as a result of climb of dislocation jogs.

Strain-hardening in tri-component nano-scale metallic multilayers was investigated using nanoindentation and micro-pillar compression. Cu/Ni/Nb films were made in tri-layer structures as well as bi-layers consisting of an alloy of Cu–Ni/Nb. Strain-hardening increases as the layer thickness decreases, with 5 nm layers exhibiting higher strengths and hardening coefficients than 30 nm layers. The experimental evidence is described in light of the confined layer slip model, and supports the hypothesis that coherent interfaces with a modulus mismatch in the tri-layer system are responsible for additional deformation mechanisms that can lead to hardening in excess of that found in bi-layer systems.

In this study, a dislocation density-based model is introduced to analyze slip transmission across grain boundaries in polycrystalline materials. The method applies a combination of the misorientation of neighboring grains and resolved shear stress on relative slip planes. This model is implemented into a continuum dislocation dynamics framework and extended to consider the physical interaction between mobile dislocations and grain boundaries. The model takes full account of the geometry of the grain boundary, the normal and direction of incoming and outgoing slip systems, and the extended stress field of the boundary and dislocation pileups at the boundary. The model predicts that slip transmission is easier across grain boundaries when the misorientation angle between the grains is small. The modeling results are verified with experimental nanoindentation results for polycrystalline copper samples.

A tri-layer nano-scale metallic multilayer (Cu/Ni/Nb) system with a mixture of incoherent and coherent interfaces was investigated to determine the effect of elevated temperature conditions on the strength at temperature and after annealing. Elevated temperature nanoindentation showed a reduction in the temperature sensitivity of hardness as individual layer thickness decreases (i.e. thinner layers retain strength better at elevated temperatures). This is explained using the confined layer slip model which suggests the drop in stress is due to both changes in the shear modulus of the film as well as dislocation/interface interactions. Molecular dynamic simulations of Cu/Nb bi-layers are presented in support of the concept that dislocation interactions at incoherent interfaces are less temperature sensitive than dislocation–dislocation interactions within the layers, supporting the experimental results.

Self-healing glass, a recent advancement in the class of smart sealing materials, has attracted great attention from both research and industrial communities because of its unique capability of repairing itself at elevated temperatures. However, further development and optimization of this material rely on a more fundamental and thorough understanding of its essential thermo-mechanical response characteristics, which is also pivotal in predicting the coupling and interactions between the nonlinear stress and temperature dependent damage and healing behaviors. In the current study, a continuum three-dimensional thermo-inelastic damage–healing constitutive framework has been developed for the compliant self-healing glass material with different damage mechanisms, i.e. micro-cracks and micro-pores, taken into account. The important feature of the present model is that different physically-driven evolution kinetics have been unified to represent the distinct inelastic, damage, and healing behaviors associated with the mechanical degradation processes. Coupled with the micro-crack and micro-void models reported in the literature, a continuum description of the healing behavior has been established based on the lower-length scale kinetic Monte Carlo simulations to characterize the local thermal–diffusional bond re-formation process across the fracture interface. The proposed formulations are implemented into finite element analyses and the effects of various loading conditions and material properties on the material’s mechanical resistance are investigated.

The viscoplastic behaviour of magnesium alloys at high temperatures leads to highly temperature-dependent mechanical properties. While at high strain rates a notable strain hardening response is observed, at low strain rates the material shows a smooth plastic response with negligible amount of hardening. This complicated behaviour is due to different deformation mechanisms that are active at different strain rate regimes, resulting in different strain rate sensitivity parameters. In this study we show, by utilizing both numerical simulations and experiments, that this behaviour can be predicted by a model that combines two deformation mechanisms, grain boundary sliding mechanism and dislocation glide mechanism. We discuss the importance of each deformation mechanism at different strain rate regimes based on the findings of modelling and experimental results for AZ3 magnesium alloy. By developing a model that includes the above-mentioned two deformation mechanism, the prediction of flow properties is expa...

Metal/ceramic multilayers combine high hardness of the ceramic layer and the high ductility of the metallic layer, enabling the design of novel composite coatings with high hardness and measurable ductility when the layer thickness reduces to a few nanometers. In this article, we review recent work with a focus on plastic deformation of metal/ceramic nanolayered composites from three aspects: experiment, theory, and atomistic modeling, and we propose several research directions in this topic.

Experimental studies show that metal–ceramic multilayers can have high strength, high strain hardening and measurable plasticity when the ceramic layer is a few nanometers thick. Using molecular dynamics simulations we studied deformation mechanisms in metal–ceramic multilayers and the role of interface structure and layer thickness on mechanical behavior. NbC/Nb multilayers were investigated numerically using the molecular dynamics (MD) method with empirical interatomic potentials. The interface dislocation structure was characterized by combining MD simulations and atomically informed Frank–Bilby theory. Two sets of pure edge misfit dislocations have been identified. Plastic deformation in NbC/Nb multilayers commences first in the metal layers by nucleation and glide of lattice dislocations initiating from interface misfit dislocations. These dislocations glide in the Nb layer and are deposited at the interface. The deposited dislocations facilitate slip transmission from the Nb layer to the NbC layer. The critical strain corresponding to dislocation nucleation is insensitive to layer thickness but depends on interface dislocation structure. The strain hardening and the peak flow strength of NbC/Nb multilayers are associated with the slip transmission from Nb to NbC, and are correlated to the interfacial dislocations, Nb layer thickness, and NbC layer thickness. The flow strength decreases with increasing Nb layer thickness and decreasing the NbC layer thickness.

Nanoindentation was used to evaluate the effect of three surface preparation techniques—mechanical polishing, electropolishing, and ion polishing—on experimental measurements of incipient plasticity in commercially pure Ni 200. Surface preparation techniques are linked to defect densities, estimated with image quality (IQ) and kernel average misorientation (KAM) data obtained from electron backscatter diffraction patterns and the Taylor relation. Minimum yield pressures are insensitive to surface preparation, while mean yield pressure depends on dislocation density, and the maximum yield pressure is likely influenced by defects other than dislocations. KAM coupled with IQ may be a useful non-destructive parameter to relate surface defect density to the resulting changes in the spatial variability of incipient plasticity during a nanoindentation experiment. This analysis makes the assumption that geometrically necessary dislocation density is proportional to total dislocation density; in cases where this condition is not satisfied, the KAM analysis may not be valid.

Deformation twinning, a common and important plastic deformation mechanism, is the key contributor to the excellent combination of strength and ductility in twinning-induced plasticity (TWIP) steel. In the open literature, a significant amount of research has been reported on the microstructural characteristics of deformation twinning and its influence on the overall deformation behavior of TWIP steel. In this study, we examine the feasibility of a mechanism-based crystal plasticity model in simulating the microstructural level deformation characteristics of TWIP steel. To this end, a model considering both double-slip and double-twin is developed to investigate the stress–strain behavior and local microstructural features related to the formation and growth of micro-twins in low stacking fault energy (SFE) TWIP steel. The twin systems are described as pseudo-slips that can be activated when their resolved shear stress reaches the corresponding critical value. A hardening law that accounts for the interaction among the slip and twin systems is also developed. Numerical simulations for different mesh sizes and single crystal patch tests under different loading modes are carried out to verify the modeling procedure. Our simulation results reveal that, despite its simple nature, the double-slip/double-twin model can capture the key deformation features of TWIP steel, including twin volume fraction evolution, continuous strain hardening, and the final fracture in the form of strain localization.

We developed a plane-strain crystal plasticity finite element (CPFE) numerical model to predict the tensile behavior of twinning-induced plasticity (TWIP) steel with both slip and mechanical twinning as the main deformation modes. Our CPFE model may not only predict well the tensile stress versus strain (S-S) curve but also capture the variation in the volume fraction of twins with a reasonable accuracy. The nucleation of mechanical twin is obviously controlled by the stress concentration. At the same time, the growth of twin may either lead to a stress relaxation in the matrix or cause a local stress concentration around twin, which depends on the deformation condition.

Precipitation strengthening in nanostructured metallic multilayer (NMM) films of Cr/Cu–Cr was studied using nanoindentation and electron microscopy. Magnetron-sputtered NMM films having layer thicknesses of 10, 20 and 30 nm were prepared at room temperature (RT) and 100 °C. Some of the RT-deposited films were annealed at 100 °C for 30 min. Cr was introduced in the Cu–Cr layers by using a Cu–Cr target (95 at.% – 5 at.%) target. A significant increase in nanoindentation hardness was observed in the Cr/Cu–Cr. A reduction of hardness dependence on layer thickness was also observed in the Cr/Cu–Cr, such that sample having a layer thickness of 30 nm provides the equivalent strength of a 10/10 nm Cr/Cu. Uniformly distributed Cr particles in the Cu–Cr layers are key strengthening features in these new Cr/Cu–Cr NMM films. A single dislocation-based model was used to correlate the observed mechanical behaviours and microstructure. The model predicts similar trend observed from the experimental results, suggesting t...

Nanoscale metallic multilayer (NMM) composites represent a class of advanced engineering materials that are shown to exhibit high structural stability, mechanical strength, high ductility, toughness and resistance to fracture and fatigue. This paper addresses the question of the effect of the interface imperfections on the strengthening of NMMs with incoherent interfaces, by performing molecular dynamics simulations. Two types of interfaces are considered, a perfect one, and one with discontinuities (steps and ledges). Our simulations demonstrate that the result of the interaction between dislocations and interfaces is the creation of interfacial disconnections made of a dislocation that spreads within the interface, and a step entrapped at the interface. The energy calculations show that these steps increase the total energy of the system and enhance the strengthening effect of the interface by adding extra barriers to slip transmission, thus improving the mechanical properties of the structure.

The mechanical behavior of Cu–Ni–Nb- based nanoscale metallic multilayers (NMM) under high strain rate loadings is investigated in this work using molecular dynamics simulations. The simulations of NMMs with various individual layer thicknesses under uniaxial tensile strains at two different controlled strain rates (109/s and 1010/s) are performed. This type of loading condition generates a stress state necessary for void nucleation commonly observed under shock loading. The mechanisms for void nucleation in the NMMs are examined and identified; the void nucleation strengths (VNS) of the NMMs and their variations with respect to increasing individual layer thickness as well as available nucleation sites (affected by addition of interfacial disconnections) are obtained and explained. It is discovered that the void always nucleate from within the Cu layers, where the partial dislocations intersect with each other or with existing stacking faults. The void nucleation strength of the NMMs is closely related to the density of available sites for void nucleation. By introducing interfacial steps into the incoherent interfaces of the NMMs the abundance of dislocation sources is changed, thus more (less) sites for void nucleation are produced which decrease (increase) the void nucleation strength of the NMMs.