The macroscopic elastic-plastic response of a metal polycrystal is analyzed here by homogenizing the response of a representative volume element. With this purpose, the theory developed in Hill(1967)(The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids, 15, 79-95) is extended so that the structural changes caused by plastic deformation are taken into account. It is found that the type of evolution assigned to the slip systems of a constituent crystal influences significantly the structure of the constitutive system characterizing the overall response. In particular, the classical normality structure is obtained only if slip systems are assumed to convect with the crystal lattice. Any other type of slip system evolution induces a deviation of the macro-rate of plastic deformation from the exterior normal to the yield surface. This provides a physical explanation and also a rigorous definition for the much debated concept of plastic spin.
Prior to macroscopic yielding, most materials undergo a regime of plastic activity that cannot be resolved in conventional bulk deformation experiments. In this pre-yield, or micro-plastic regime, it is the initial three dimensional defect network that is probed and the intermittently evolving microstructure admits small increments in plastic strain. By reducing the sample size, this intermittent activity becomes increasingly apparent and can be routinely observed through small-scale mechanical testing. In some cases, the intermittent activity was shown to exhibit aspects of scale-free behavio…
Ice plasticity has been thoroughly studied, owing to its importance in glaciers and ice sheets dynamics. In particular, its anisotropy (easy basal slip) has been suspected for a long time, then fully characterized 40 years ago. More recently emerged the interest of ice as a model material to study some fundamental aspects of crystalline plasticity. An example is the nature of plastic fluctuations and collective dislocation dynamics. 20 years ago, acoustic emission measurements performed during the deformation of ice single crystals revealed that plastic flow proceeds through intermittent dislo…
This work presents a detailed experimental-numerical analysis of a low-carbon dual-phase steel microstructure, revealing evidence of significant anisotropic plastic deformation in lath martensite. A careful determination of the habit plane orientations in the present martensitic variants demonstrates that the observed traces of plastic slip coincide with the directions of the corresponding habit planes. To study the local lath martensite plastic activity, a dedicated substructure-enriched crystal plasticity based model is exploited. Compared with conventional bcc crystal plasticity, the model …
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 …
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.
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 statistics and origin of the first discrete plastic event in a one dislocation dynamics simulation are studied. This is done via a linear stability analysis of the evolving dislocation configuration up to the onset of irreversible plasticity. It is found, via a fold catastrophe, the dislocation configuration prior to loading directly determines the stress at which the plastic event occurs and that between one and two trigger dislocations are involved. The resulting irreversible plastic strain arising from the instability is found to be highly correlated with these triggering dislocations.
A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse concrete structures subjected to dynamic loading. The aim is to obtain a model, which requires input parameters with clear physical meanings. The model should describe the important characteristics of concrete subjected to multiaxial and rate-depending loading. This is achieved by combining an effective stress based plasticity model with an isotropic damage model based on plastic and elastic strain measures. The model response in tension, uni-, bi- and tri-axial compression is compared to e…
The mode I crack tip asymptotic response of a solid characterised by strain gradient plasticity is investigated. It is found that elastic strains dominate plastic strains near the crack tip, and thus the Cauchy stress and the strain state are given asymptotically by the elastic K-field. This crack tip elastic zone is embedded within an annular elasto-plastic zone. This feature is predicted by both a crack tip asymptotic analysis and a finite element computation. When small scale yielding applies, three distinct regimes exist: an outer elastic K field, an intermediate elasto-plastic field, and …
The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient plasticity with linear softening is used, and the ensuing jump conditions and boundary conditions are discussed. Three cases with different regularity of the stress distribution are considered, and the problem is converted to a dimensionless form. Relations linking the load level, size of the plastic zone, distribution of plastic strain and plastic elongation of …
Uncertainty quantification (UQ) plays a major role in verification and validation of computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive exp…
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 …
There is a long standing technological problem in which a stress dwell during cyclic loading at room temperature in Ti causes a significant fatigue life reduction. It is thought that localised time dependent plasticity in soft grains oriented for easy plastic slip leads to load shedding and an increase in stress within a neighbouring hard grain poorly oriented for easy slip. Quantifying this time dependent plasticity process is key to successfully predicting the complex cold dwell fatigue problem. This work uses a novel approach of in situ synchrotron X-ray diffraction during stress relaxation…
A constitutive model based on the combination of damage mechanics and plasticity is developed to analyse the failure of concrete structures. The aim is to obtain a model, which describes the important characteristics of the failure process of concrete subjected to multiaxial loading. This is achieved by combining an effective stress based plasticity model with a damage model based on plastic and elastic strain measures. The model response in tension, uni-, bi- and triaxial compression is compared to experimental results. The model describes well the increase in strength and displacement capaci…
The first plastic event occurring in discrete intermittent plasticity, as for example a pop-in seen in nano-indentation, is evaluated with extreme value statistics. It is found that when the same deformation is repeated many times, the average of the stress at this first event is related to the deforming volume via an exponentially truncated power-law. The present work demonstrates this trend and the expected Weibull fluctuation around it. The statistical formalism is shown to apply to the nano-indentation data of Morris {\em et al}, Phys. Rev. Lett. 106, 165502 (2011), as well as to dislocati…
In this work the relation of plastic and rheological material models is analysed in the framework of non-equilibrium thermodynamics. After a short summary of the basic notions of classical elasticity and plasticity the traditional thermodynamic treatment of plasticity by Ziegler is introduced, where the plastic deformation is an internal variable, leading to the reduction of thermostatic stress. Then a simple thermodynamic treatment of static and dynamic friction follows, because the continuum generalization of these phenomena leads to viscosity and plasticity in our interpretation. Finally, p…
The residual resistivity $ρ$ in metals caused by wedge disclination dipoles is studied in the framework of the Drude formula. It is shown that $ρ\sim L^{-p}$ with $p=3$ for biaxial and $p=2$ for uniaxial dipoles ($L$ is a size of dipole arm)
Along with high strength, plasticity is what makes metals so widely usable in our material world. Both strength and plasticity properties of a metal are defined by the motion of dislocations - line defects in the crystal lattice that divide areas of atomic planes displaced relative to each other by an interatomic distance. Here we present first fully dynamic atomistic simulations of single crystal plasticity in metal tantalum predicting that above certain maximum rate of straining - the ultimate limit - the dislocations can no longer relieve mechanical loads and another mechanism, twinning, co…
Power law fluctuations and scale free spatial patterns are known to characterize steady state plastic flow in crystalline materials. In this Letter we study the emergence of correlations in a simple Frenkel-Kontorova (FK) type model of 2D plasticity which is largely free of arbitrariness, amenable to analytical study and is capable of generating critical exponents matching experiments. Our main observation concerns the possibility to reduce continuum plasticity to an integer valued automaton revealing inherent discreteness of the plastic flow.
Elastoplastic lattice models for the response of solids to deformation typically incorporate structure only implicitly via a local yield strain that is assigned to each site. However, the local yield strain can change in response to a nearby or even distant plastic event in the system. This interplay is key to understanding phenomena such as avalanches in which one plastic event can trigger another, leading to a cascade of events, but typically is neglected in elastoplastic models. To include the interplay one could calculate the local yield strain for a given particulate system and follow its…
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…
We use considerations of energy balance and dissipation to derive a self-consistent version of the shear-transformation-zone (STZ) theory of plastic deformation in amorphous solids. The theory is generalized to include arbitrary spatial orientations of STZs. Continuum equations for elasto-plastic material and their energy balance properties are discussed.
In this work, distortion gradient plasticity is used to gain insight into material deformation ahead of a crack tip. This also constitutes the first fracture mechanics analysis of gradient plasticity theories adopting Nye's tensor as primal kinematic variable. First, the asymptotic nature of crack tip fields is analytically investigated. We show that an inner elastic region exists, adjacent to the crack tip, where elastic strains dominate plastic strains and Cauchy stresses follow the linear elastic stress singularity. This finding is verified by detailed finite element analyses using a new nu…
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradien…
A mechanism of perfect plasticity under low homological temperatures has been suggested. According to this mechanism, the phenomenon under study is of critical nature. It connects with percolation transition in the net of grain boundaries and with nonlocal interaction of fragments uniquely under simple shear mode. The mechanism is justified by general reasoning, mainly of geometrical character, and also by employing computational modeling and well-known experimental results.
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…
We present a thermodynamic description of crystal plasticity. Our formulation is based on the Langer-Bouchbinder-Lookman thermodynamic dislocation theory (TDT), which asserts the fundamental importance of an effective temperature that describes the state of configurational disorder and therefore the dislocation density of the crystalline material. We extend the TDT description from isotropic plasticity to crystal plasticity with many slip systems. Finite-element simulations show favourable comparison with experiments on polycrystal fcc copper under uniaxial compression, tension, and simple she…
Crystal plasticity is mediated through dislocations, which form knotted configurations in a complex energy landscape. Once they disentangle and move, they may also be impeded by permanent obstacles with finite energy barriers or frustrating long-range interactions. The outcome of such complexity is the emergence of dislocation avalanches as the basic mechanism of plastic flow in solids at the nanoscale. While the deformation behavior of bulk materials appears smooth, a predictive model should clearly be based upon the character of these dislocation avalanches and their associated strain bursts…
