Crystal plasticity of sub-micron finite volumes is characterized by the flow of emergent dislocation defects, giving rise to size effects in mechanical properties and avalanche phenomena. In this chapter, we present a minimal model for discrete edge dislocations in a finite volume, that has been benchmarked against experimental data and displays known phenomenological trends. We discuss how this model can explain seemingly disconnected effects of rate, size and prior deformation on microcrystal plasticity. We demonstrate the statistical features of dislocation ensembles for both stress and displacement controlled loading conditions and explore in detail the connection between loading rate and displacement bursts. Finally, we present model studies of machine learning algorithms in microcrystal plasticity that both improve understanding and clarify the range of such methods' usefulness. In this way, we elucidate the role of prior deformation history on micro and nano-sized specimens and we use this understanding to predict the mechanical response of thin films through microstructural observations of pre-existing dislocation configurations.
Microcrystals deform very differently from their macroscopic counterparts, displaying a size-dependent yield stress and intermittent plastic strain bursts. Here we demonstrate that size effects and strain bursts may be just two different signatures of fundamental collective phenomena that govern the dynamics of dislocation systems on all scales. We confirm this conjecture by demonstrating agreement between the results of 2D and 3D dislocation dynamics simulations and experimental results on compressed micropillars. Our results indicate that many peculiarities of small-sample plasticity may ari…
Experimental investigations of plastic flow have demonstrated temporal intermittency as deformation proceeds in a series of intermittent bursts with scale-free size distribution. In the present investigation, a corresponding spatial intermittency is demonstrated for plastic flow of KCl single crystals. Deformation bursts lead to large surface steps with a height distribution that is consistent with the distribution of strain increments in deformation of micro-columns, and the energy distribution of acoustic emission bursts observed in deformation of macroscopic single crystal samples of a wide…
Despite decades of extensive research on mechanical properties of diamond, much remains to be understood in term of plastic deformation mechanisms due to the poor deformability at room temperature. In a recent work in Advanced Materials, it was claimed that room-temperature plasticity occurred in <001>-oriented single-crystal diamond nanopillars based on observation of unrecovered deformation inside scanning electron microscope. The plastic deformation was suggested to be mediated by a phase transition from sp3 carbon to an O8-carbon phase by molecular dynamics simulations. By comparison, our …
Voids can limit the life of engineering components. This motivates us to understand local plasticity around voids in a nickel base superalloy combining experiments and simulations. Single crystal samples were deformed in tension with in-situ high angular resolution electron back scatter diffraction to probe the heterogeneous local stress field under load; the reference stress is informed by crystal plasticity finite element simulations. This information is used to understand the activation of plastic deformation around the void. Our investigation indicates that while the resolved shear stress …
Intermittent plastic deformation in crystals with power-law behaviors has been reported in previous experimental studies. The power-law behavior is reminiscent of self-organized criticality, and mesoscopic models have been proposed that describe this behavior in crystals. In this letter, we show that intermittent plasticity in metals under tensile deformation can be observed in molecular dynamics models, using embedded atom method potentials for Ni, Cu, and Al. Power-law behaviors of stress drop and waiting time of plastic deformation events are observed. It is shown that power-law behavior is…
Stressed dislocation pattern formation in crystal plasticity at finite deformation is demonstrated for the first time. Size effects are also demonstrated within the same mathematical model. The model involves two extra material parameters beyond the requirements of standard classical crystal plasticity theory. The dislocation microstructures shown are decoupled from deformation microstructures, and emerge without any consideration of latent hardening or constitutive assumptions related to cross-slip. Crystal orientation effects on the pattern formation and mechanical response are also demonstr…
Crystal plasticity occurs by deformation bursts due to the avalanche-like motion of dislocations. Here we perform extensive numerical simulations of a three-dimensional dislocation dynamics model under quasistatic stress-controlled loading. Our results show that avalanches are power-law distributed, and display peculiar stress and sample size dependence: The average avalanche size grows exponentially with the applied stress, and the amount of slip increases with the system size. These results suggest that intermittent deformation processes in crystalline materials exhibit an extended critical-…
In order to efficiently explore the nearly infinite composition space in multicomponent solid solution alloys, it is important to establish predictive design strategies and use computation-aided methods. In the present work, we demonstrated the density functional theory calculations informed design routes for realizing transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) in Cr-Co-Ni medium entropy alloys (MEAs). We systematically studied the effects of magnetism and chemical composition on the generalized stacking fault energy surface (gamma-surface) and showed that …
The sequence of deformation bursts during plastic deformation exhibits scale-free features. In addition to the burst or avalanche sizes and the rate of avalanches the process is characterized by correlations in the series which become manifest in the resulting shape of the stress-strain curve. We analyze such features of plastic deformation with 2D and 3D simulations of discrete dislocation dynamics models and we show, that only with severe plastic deformation the ensuing memory effects become negligible. The role of past deformation history and dislocation pinning by disorder are studied. In …
The work considers the effect of deformation on the exhaustion of the plasticity resource of steel 45 after the drawing deformation. The results of theoretical and experimental studies of damage accumulation are listed. A possibility of employment of a scanning electron microscope to observe submicropores is demonstrated.
Using molecular-dynamics simulation and finite-element modelling, we simulate nanoindentation into the three principal surfaces -- the (100), (110) and (111) surface -- of Cu and Al. In the elastic regime, the simulation data agree fairly well with the linear elastic theory of indentation into an elastically anisotropic substrate. With increasing indentation, the effect of pressure hardening becomes visible. When the critical stress for dislocation nucleation is reached, even the elastically isotropic Al shows a strong dependence of the surface orientation on the force-displacement curves. Aft…
We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the local yield stresses. Using a finite element implementation of this simple model, we simulate the plane-strain deformation of long thin rods loaded in tension. The resulting strain patterns are statistically characterized in terms of their spatial correlation functions. Studies of the corresponding surface morphology reveal a non-trivial Hurst exponent of ap…
We present a framework which unifies classical phenomenological $J_2$ and crystal plasticity theories with quantitative dislocation mechanics. The theory allows the computation of stress fields of arbitrary dislocation distributions and, coupled with minimally modified classical ($J_2$ and crystal plasticity) models for the plastic strain rate of statistical dislocations, results in a versatile model of finite deformation mesoscale plasticity. We demonstrate some capabilities of the framework by solving two outstanding challenge problems in mesoscale plasticity: 1) recover the experimentally o…
There is growing interest in promoting deformation twinning for plasticity in advanced materials, as highly organized twin boundaries are beneficial to better strength-ductility combination in contrast to disordered grain boundaries. Twinning deformation typically involves the kinetics of stacking faults, its interaction with dislocations, and dislocation - twin boundary interactions. While the latter has been intensively investigated, the dynamics of stacking faults has been less known. In this work, we report several new insights on the stacking fault behavior in twin induced plasticity from…
Enabling plastic co-deformation of disparate phases in a laser rapid solidified Sr-modified Al-Si eutectic through partial-dislocation-mediated-plasticity in Si
Understanding deformation in polycrystalline metals is critical to use them in high-value high-risk applications. We present in-situ characterisation of plastic deformation of zirconium, a hexagonal closed packed (HCP), metal. Analysis of plastic deformation is performed using electron backscatter diffraction (EBSD) to reveal changes in lattice orientation. Through implementation of TrueEBSD, we can relate the lattice rotations back to the undeformed reference frame. This enables us to explore which slip systems are active and the degree of homogeneous (i.e. deformation with respect to the ext…
A numerical strategy to simulate plastic deformation in Mg alloys including dislocation slip and twin propagation is presented. Dislocation slip is included through a crystal plasticity model which is solved using the finite element method while twin propagation is taken into account by means of a phase field model which is solved using a fast Fourier transform algorithm. The coupled crystal plasticity and phase field equations were solved using different discretizations of the simulation domain using the same time step for both of them. The numerical strategy was used to simulate the deformat…
The investigation of the deformation behaviour of intermetallic phases is mostly limited to high temperatures due to their low ductility at ambient temperature. Therefore, within this study, nanoindentation experiments on the Al$_{2}$Cu phase were performed from ambient temperature up to 300°C in conjunction with TEM investigations of the deformed material. It was found that the Al$_{2}$Cu phase starts to soften from temperatures above 150°C. The low temperature deformation behaviour was dominated by serrated yielding and transitioned towards a smooth deformation behaviour above 150°C. No slip…
Plasticity modelling has long been based on phenomenological models based on ad-hoc assuption of constitutive relations, which are then fitted to limited data. Other work is based on the consideration of physical mechanisms which seek to establish a physical foundation of the observed plastic deformation behavior through identification of isolated defect processes ('mechanisms') which are observed either experimentally or in simulations and then serve to formulate so-called physically based models. Neither of these approaches is adequate to capture the complexity of plastic deformation which b…
The importance of accurate simulation of the plastic deformation of ductile metals to the design of structures and components is well-known. Many techniques exist that address the length scales relevant to deformation pro- cesses, including dislocation dynamics (DD), which models the interaction and evolution of discrete dislocation line segments, and crystal plasticity (CP), which incorporates the crystalline nature and restricted motion of dis- locations into a higher scale continuous field framework. While these two methods are conceptually related, there have been only nominal efforts focu…
Plastic deformations in body-centered-cubic (BCC) crystals have been of critical importance in diverse engineering and manufacturing contexts across length scales. Numerous experiments and atomistic simulations on BCC crystals reveal that classical crystal plasticity models with the Schmid law are not adequate to account for abnormal plastic deformations often found in these crystals. In this paper, we address a continuum mechanical treatment of anomalous plasticity in BCC crystals exhibiting non-Schmid effects, inspired from atomistic simulations recently reported. Specifically, anomalous fea…
This investigation extends earlier studies of a shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. My main purpose here is to explore the possibility that the configurational degrees of freedom of such systems fall out of thermodynamic equilibrium with the heat bath during persistent mechanical deformation, and that the resulting state of configurational disorder may be characterized by an effective temperature. The further assumption that the population of STZ's equilibrates with the effective temperature allows the theory to be compared directly with experimen…
Detailed microstructure characterisation and in-situ micropillar compression were coupled with crystal plasticity-based finite element modelling (CP-FEM) to study the micro-mechanisms of plastic anisotropy in lamellar TiAl alloys. The consideration of microstructure in both simulation and in-situ experiments enables in-depth understanding of micro-mechanisms responsible for the highly anisotropic deformation response of TiAl on the intra-lamella and inter-lamella scales. This study focuses on two specific configurations of γ/α_2 lamellar microstructure with the γ/α_2 interfaces being aligned {…
The plastic component of the deformation gradient plays a central role in finite kinematic models of plasticity. However, its characterization has been the source of extended debates in the literature and many important issues still remain unresolved. Some examples are the micromechanical understanding of F=FeFp with multiple active slip systems, the uniqueness of the decomposition, or the characterization of the plastic deformation without reference to the so-called intermediate configuration. In this paper, we shed some light to these issues via a two-dimensional kinematic analysis of the pl…
We have investigated the plastic deformation properties of non-equiatomic single phase Zr-Nb-Ti-Ta-Hf high-entropy alloys from room temperature up to 300 °C. Uniaxial deformation tests at a constant strain rate of 10$^{-4}$ s$^{-1}$ were performed including incremental tests such as stress-relaxations, strain-rate- and temperature changes in order to determine the thermodynamic activation parameters of the deformation process. The microstructure of deformed samples was characterized by transmission electron microscopy. The strength of the investigated Zr-Nb-Ti-Ta-Hf phase is not as high as the…
Plastic deformation of crystals proceeds through a sequence of intermittent slip avalanches with scale-free (power-law) size distribution. On macroscopic scales, however, plastic flow is known to be smooth and homogeneous. In the present letter we use a recently proposed continuum model of slip avalanches to systematically investigate the nature of the cut-off which truncates scale-free behavior at large avalanche sizes. The dependence of the cut-off on system size, geometry, and driving mode, but also on intrinsic parameters such as the strain hardening rate is established. Implications for t…
This work proposes a dislocation density-based strain gradient $J_2$ plasticity framework that models the strength contribution due to Geometrically Necessary Dislocations (GNDs) using a lower order, Taylor hardening backstress model. An anisotropy factor is introduced to phenomenologically represent the differential hardening between grains in this $J_2$ plasticity framework. An implicit numerical algorithm is implemented for the time integration of the finite deformation plasticity model. The framework is first used to predict directional hardening due to the GND-induced backstress during cy…
In this work we analyze the relation between the multiplicative decomposition $\mathbf F=\mathbf F^{e}\mathbf F^{p}$ of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations - total $ϕ$ and the inelastic $ϕ_{1}$. We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained fo…
A systematic study on the different roles of the governing components of a well-defined finite-deformation gradient crystal-plasticity model proposed by (Gurtin, 2008b) is carried out, in order to visualize the capability of the model in the prediction of a wide range of hardening behaviors as well as rate-dependent, scale-variation and Bauschinger-like responses in a single crystal. A function of accumulation rates of dislocations is employed and viewed as a measure of formation of short-range interactions which impede dislocation movements within a crystal. The model is first represented in …
Coarse-grained, metallic materials undergo microstructure refinement during tribological loading. This in turn results in changing tribological properties, so understanding deformation under tribological load is mandatory when designing tribological systems. Single-trace experiments were conducted to understand the initiation of deformation mechanisms acting in various tribological systems. The main scope of this work was to investigate the influence of normal and friction forces as well as crystal orientations on the dominating deformation mechanism in a face-centred cubic concentrated solid …
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic material with a stiff? elastic inclusion. Combinations of micro-hard and micro-free boundary conditions are used. The strengthening and hardening behavior is explored in relation to the dissipative and energetic length scales. There is a strong dependence on length scale with the imposition of micro-hard boundary conditions. For micro-free conditions there is…
Selective laser melting is receiving increasing interest as an additive manufacturing technique. Residual stresses induced by the large temperature gradients and inhomogeneous cooling process can favour the generation of cracks. In this work, a crystal plasticity finite element model is developed to simulate the formation of residual stresses and to understand the correlation between plastic deformation, grain orientation and residual stresses in the additive manufacturing process. The temperature profile and grain structure from thermal-fluid flow and grain growth simulations are implemented …
The mechanical properties of polycrystalline metals are governed by the interaction of defects that are generated by deformation within the 3D microstructure. In materials that deform by slip, the plasticity is usually highly heterogeneous within the microstructure. Many experimental tools can be used to observe the results of slip events at the free surface of a sample; however, there are only a few methods for imaging these events in the bulk. In this article, the imaging of bulk slip events within the 3D microstructure are enabled by the combined use of X-ray diffraction contrast tomography…
West Virginia University（西弗吉尼亚大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）
Digital image correlation (DIC) is a well-established, non-invasive technique for tracking and quantifying the deformation of mechanical samples under strain. While it provides an obvious way to observe incremental and aggregate displacement information, it seems likely that DIC data sets, which after all reflect the spatially-resolved response of a microstructure to loads, contain much richer information than has generally been extracted from them. In this paper, we demonstrate a machine-learning approach to quantifying the prior deformation history of a crystalline sample based on its respon…
The structure of the overall response of a metal polycrystal is analyzed under the assumption that activity on the slip systems of its constituents is governed by a generalized Schmid law. In the resulting macro-model of metal plasticity the overall rate of plastic deformation is related to the stress-gradient of the yield surface via a generalized, but still associated flow rule. While the overall rate of plastic deformation is no longer collinear with the stress-gradient of the yield surface, its deviation is characterized by an additional macro-variable, representative of the rate of the no…
In the preceding paper, we developed an athermal shear-transformation-zone (STZ) theory of amorphous plasticity. Here we use this theory in an analysis of numerical simulations of plasticity in amorphous silicon by Demkowicz and Argon (DA). In addition to bulk mechanical properties, those authors observed internal features of their deforming system that challenge our theory in important ways. We propose a quasithermodynamic interpretation of their observations in which the effective disorder temperature, generated by mechanical deformation well below the glass temperature, governs the behavior…
Wehrenberg et. al. [Nature 550 496 (2017)] used ultrafast in situ x-ray diffraction at the LCLS x-ray free-electron laser facility to measure large lattice rotations resulting from slip and deformation twinning in shock-compressed laser-driven [110] fibre textured tantalum polycrystal. We employ a crystal plasticity finite element method model, with slip kinetics based closely on the isotropic dislocation-based Livermore Multiscale Model [Barton et. al., J. Appl. Phys. 109 (2011)], to analyse this experiment. We elucidate the link between the degree of lattice rotation and the kinetics of plas…
Decoupling Strain-Rate Sensitivity and Deformation Length Scale Effects in Neutron-Irradiated Tungsten: A Coupled Nano-Indentation, HR-EBSD and Crystal Plasticity Study
Indian Institute of Science（印度科学学院）；University of Oxford（牛津大学）；UK Atomic Energy Authority（英国原子能管理局）
We use energetic considerations to deduce the form of a previously uncertain coupling term in the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. As in the earlier versions of the STZ theory, the onset of steady deformation at a yield stress appears here as an exchange of dynamic stability between jammed and plastically deforming states. We show how an especially simple ``quasilinear'' version of this theory accounts qualitatively for many features of plasticity such as yielding, strain softening, and strain recovery. We also show that this minimal version of…
Atomistic simulations are performed to probe the anisotropic deformation in the compressions of face-centred-cubic metallic nanoparticles. In the elastic regime, the compressive load-depth behaviors can be characterized by the classical Hertzian model or flat punch model, depending on the surface configuration beneath indenter. On the onset of plasticity, atomic-scale surface steps serve as the source of heterogeneous dislocation in nanoparticle, which is distinct from indenting bulk materials. Under [111] compression, the gliding of jogged dislocation takes over the dominant plastic deformati…
High-entropy alloys (HEAs) are solid solutions of multiple elements with equal atomic ratios which present an innovative pathway for de novo alloy engineering. While there exist extensive studies to ascertain the important structural aspects governing their mechanical behaviors, elucidating the underlying deformation mechanisms still remains a challenge. Using atomistic simulations, we probe the particle rearrangements in a yielding, model HEA system to understand the structural origin of its plasticity. We find the plastic deformation is initiated by irreversible topological fluctuations whic…
A microstructure-based model that accounts for the effect of grain size has been developed to study the effect of grain size on the fatigue life of Inconel 718 alloys. The fatigue behavior of two alloys with different grain size was determined by means of uniaxial cyclic deformation tests under fully-reversed deformation ($R_\varepsilon$ = -1) at 400$^\circ$C in the low cycle fatigue regime. The model was based in the determination of the fatigue indicator parameter (based on the local crystallographic strain energy dissipated per cycle) by means of computational homogenization of a representa…
In this paper we present a thermodynamically consistent material model which is capable of modelling ductile-to brittle failure mode transition in ductile material undergoing deformations at high strain rates, and demonstrate the performance of the model in a numerical study using a fully coupled thermal-structural finite element analysis of a notched aluminium alloy specimen loaded in cyclic tension. The model is based on an objective representation of the deformation and stress measures and on a rate type constitutive equations. It does not only complies with the principles of material model…
Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for micr…
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present significant challenges when formulating simulation models. In particular, no overall unified field framework exists to model concurrent viscoplastic deformation and recrystallization and grain growth in metal polycrystals. In this work a thermodynamically consistent diffuse interface framework incorporating crystal viscoplasticity and grain boundary migration is …
Grain structure plays a key role in the mechanical properties of alloy materials. Engineering the grain structure requires a comprehensive understanding of the evolution of grain boundaries (GBs) when a material is subjected to various manufacturing processes. To this end, we present a computationally efficient framework to describe the co-evolution of bulk plasticity and GBs. We represent GBs as diffused geometrically necessary dislocations, whose evolution describes GB plasticity. Under this representation, the evolution of GBs and bulk plasticity is described in unison using the evolution e…
The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatio-temporal correlations in the undeformed glass that may trigger plastic instability. In contrast, here we show that the topological defects which correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dis…
Small-scale mechanical behaviour shows significant departures from classical elastic-plastic theory. In a remarkable number of instances, the strength of a material appears to scale as the reciprocal square root of the smallest length scale. There are several recent experimental and modeling results in the literature that show an interaction between dimensional (extrinsic) size and microstructural (intrinsic) size effects. In this paper, we present a mechanical model that naturally produces the inverse square root strengthening and derive an expression for the effective length when both the ex…
On microscopic and mesoscopic scales, plastic flow of crystals is characterized by large intrinsic fluctuations. Deformation by crystallographic slip occurs in a sequence of intermittent bursts ('slip avalanches') with power-law size distribution. In the spatial domain, these avalanches produce characteristic deformation patterns in the form of slip lines and slip bands which exhibit long-range spatial correlations. We propose a generic continuum model which accounts for randomness in the local stress-strain relationships as well as for long-range internal stresses that arise from the ensuing …
Knowledge of the state of plastic deformation in metallic structures is vital to prevent failure. This is why non-destructive acoustic tests based on the measurement of first order elastic constants have been developed and intensively used. However, plastic deformations, which are usually heterogeneous in space, may be invisible to these methods if the variation of the elastic constants is too small. In recent years, digital image correlation techniques, based on measurements carried out at the surface of a sample, have been successfully used in conjunction with finite element modeling to gain…
Bonding between polymeric interfaces is encountered widely in several industrial applications. Many of these bonding processes rely on time-consuming and temperature-dependent classical mechanism of polymer interdiffusion via reptation in a melt state. Here, for the first time, we report a new mechanistic pathway for achieving solid-state polymer bonding by triggering rapid macromolecular acceleration through mechanical deformation. Large-scale molecular simulations reveal that active plastic deformation in glassy polymers, at temperatures well-below the bulk (and surface) glass transition tem…
Many engineering applications of Shape Memory Alloys (SMAs) involve passing back and forth through phase transformation many times. Repeated phase transformation develops permanent deformations originating from the significant distortion that phase transformation induces at the austenite-martensite interfaces and grain boundaries. This distortion drives dislocation activity resulting in an observable macroscopic Transformation-Induced Plastic (TRIP) deformation, which occurs at effective stress levels much lower than the plastic yield limit of the material. TRIP strains may accumulate up to 20…
