A predictive discrete-continuum multiscale model of plasticity with quantified uncertainty (original) (raw)
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Plastic deformation of micro- and nanoscale samples differs from macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size, and (ii) the scatter of plastic deformation behavior increases significantly. In this work, we focus on the scatter of plastic behavior. We statistically characterize the deformation process of micropillars using results from discrete dislocation dynamics (DDD) simulations. We then propose a stochastic microplasticity model that uses the extracted information to make statistical predictions regarding the micropillar stress-strain curves. This model aims to map the complex dynamics of interacting dislocations onto stochastic processes involving the continuum variables of stress and strain. Therefore, it combines a classical continuum description of the elastic-plastic problem with a stochastic description of plastic flow. We compare the model predictions with the underlying DDD simulations and outline potential future app...
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Materials Science and Engineering: A, 2011
Size effects and strain bursts that are observed in compression experiments of single crystalline micropillars are interpreted using a gradient plasticity model that can capture the process of sequential slip and heterogeneous yielding of thin material layers. According to in situ experiments during compression subgrains and significant strain gradients develop, while deformation occurs through slip layers in the gauge region. In the multilayer strain gradient model, the higher order stress is discontinuous across the interface between a plastic layer and an elastic layer, but it becomes continuous across the interface between two plastic layers. Strain bursts occur when two neighboring layers yield. Based on this hypothesis the experimental stress-strain curves with strain bursts observed in micropillars can be fitted by properly selecting the number of layers that yield and the ratio of the internal length over the specimen size; the modulus and the yield stress are obtained from the experimental curves while the hardening modulus evolves during deformation based on the dislocation mechanisms.
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The effect of taper on the plastic response of micropillars with a relatively high density of dislocation sources (1.5 × 10 14 m −2) is analyzed. The large number of dislocation sources and dislocations in the simulations rule out many of the mechanisms that govern size effects in pillars with a low dislocation source density. The mechanical response of compressed pillars with mean widths of W = 0.4, 0.8, 1.6, 3.2 µm and taper angles of 0 • , 2 • and 5 • is analyzed using 2.5D discrete dislocation plasticity. For all taper angles, large scatter is found in the stress strain response for the submicron, W = 0.4 and 0.8 µm pillars, and relatively little scatter for the larger pillars. Taper leads to an increased average hardening rate for the submicron pillars, although this increase is within the scatter band of the stress strain response. Little sensitivity of the plastic response to taper is found for the larger pillars. The effect of size and taper on the stress strain response stems from the build up of geometrically necessary dislocations (GNDs). The reduced number of dislocation sources in the submicron pillars is identified as the origin of the large scatter in the predicted mechanical response.
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A new numerical model has been developed in order to study the plastic deformation of mesoscopic crystalline samples under complex boundary conditions. The model is based on the coupling of two types of simulations, a dislocation dynamics and a finite element code. The former accounts for the dislocation-based plastic properties of the material, thus replacing the usual constitutive form, while the latter treats the boundary value problem and cares of the mechanical equilibrium. In order to test the hybrid simulation and examine its accuracy, the self-stress fields of straight dislocations have been computed in a single crystal of finite size and compared with the predictions of the isotropic elasticity theory. The excellent agreement obtained emphasizes the enormous potential of such hybrid methods for a rigorous treatment of meso-macro problems in plasticity.
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Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.
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Polycrystalline materials, with nanosized grains (<100 nm), exhibit superior strength exceeding those of their coarse-grained counterparts. With such small grains, the deformation mechanisms taking place at grain boundaries (GBs) become dominant compared to the intragranular crystal plasticity. Recent studies have revealed that the deformation mechanisms are influenced by the GB network. For instance, a high yield stress in nanostructured metals can be obtained by choosing the relevant grain boundary character distribution (GBCD). In this paper we present an original numerical multiscale approach to predict the mechanical behavior of nanostructured metals according to their GBCD composed of either high angle (HA) GBs (HAB) or low angle (LA) GBs (LAB). Molecular simulations using the quasicontinuum method (QC) are performed to obtain the mechanical response at the nanoscale of GB undergoing simple shear (GB sliding behavior) and tensile loads (GB opening behavior). To simulate the grain behavior, a mechanical model of dislocation motions through a forest dislocation is calibrated using a nanoindentation simulation performed with QC. These QC results are then used in a finite element code (direct numerical simulation-DNS) as a GB constitutive model and as a grain constitutive model. This two-scale framework does not suffer from length scale limitations conventionally encountered when considering the two scales separately.
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A parallel discrete dislocation dynamics tool is employed to study the size dependent plasticity of small metallic structures. The tool has been parallelised using OpenMP. An excellent overall scaling is observed for different loading scenarios. The size dependency of the plastic flow is confirmed by the performed simulations for uniaxial loading and micro-bending tests. The microstructural origin of the size effect is analysed. A strong influence of the initial microstructure on the statistics of the deformation behaviour is observed, for both the uniaxial and bending scenario.
Procedia IUTAM, 2012
Gradient plasticity theory formulates a constitutive framework on the continuum level that bridges the gap between the micromechanical plasticity and classical continuum plasticity by incorporating the material length scale. A micromechanical-based model of variable material intrinsic length scale is developed in the present work which allows for variations in temperature and strain rate and its dependence on the grain size and accumulated plastic strain. The material constants of the proposed model are calibrated using the size effect encounter in nanohardness experiments. In this regard, two different physically based models for Temperature and Rate Indentation Size Effects (TRISE) are also developed in this work for single and polycrystalline metals by considering different expressions of the geometrical necessary dislocation (GND) density. The results of indentation experiments performed on various single-and polycrystalline materials are then used here to implement the aforementioned framework in order to predict simultaneously the TRISE and variable length scale at different temperatures, strain rates and various grain sizes.
Le Journal de Physique IV, 2001
A two-dimensional nonlocal version of continuum crystal plasticity theory is proposed, which is based on a statistical-mechanics description of the collective behavior of dislocations coupled to standard small-strain crystal continuum kinematics for single slip. It involves a set of transport equations for the total dislocation density ÿeld and for the net-Burgers vector density ÿeld, which include a slip system back stress associated to the gradient of the net-Burgers vector density. The theory is applied to the problem of shearing of a two-dimensional composite material with elastic reinforcements in a crystalline matrix. The results are compared to those of discrete dislocation simulations of the same problem. The continuum theory is shown to be able to pick up the distinct dependence on the size of the reinforcing particles for one of the morphologies being studied. Also, its predictions are consistent with the discrete dislocation results during unloading, showing a pronounced Bauschinger e ect. None of these features are captured by standard local plasticity theories. ?