Micro-Structural Evolution and Size-Effects in Plastically Deformed Single Crystals: Strain Gradient Continuum Modeling (original) (raw)
Related papers
Plastic deformation of crystalline solids depends to a high degree on the mechanisms related to the dislocation network. In order to accommodate plastic deformation and to reduce the crystal's energy, new dislocations are nucleated and pile up near the grain or phase boundaries, thereby giving rise to material strengthening. The nucleation and motion of dislocations is hence an essential mechanism to explain plastic yielding, work hardening as well as size and hysteresis effects in crystal plasticity and needs embedding into the constitutive framework of modeling materials with microstructure. An important aspect of modeling dislocation microstructures by a continuum approach lies in a sensible representation of those effects stemming from the characteristics of the discrete crystal lattice which, in particular, prohibits high local dislocation concentrations. Such a saturation behavior gives rise to numerous experimentally observed effects. In particular, experimental investigations hint at an essential size-effect of many properties of elasto-plastic crystals (e.g., the size-dependence of the indentation force during nano-indentation experiments, the grain-size dependence of the yield stress of Hall-Petch or other type, etc.)
Scripta Materialia, 2003
The relations between mesoscopic plastic strain gradients, Ôgeometrically necessaryÕ dislocations (GND), and dislocation dynamics are discussed. It is argued that the connection between GND and size effects in crystal plasticity should be established on the basis of dislocation dynamics, taking into account the specific deformation conditions. It is demonstrated that dislocation dynamics based models for size effects lead to different phenomenological forms of gradient plasticity ÔlawsÕ proposed in the literature.
2009
Plastic deformation of crystalline solids depends to a high degree on the mechanisms related to the dislocation network. In order to accommodate plastic deformation and to reduce the crystal's energy, new dislocations are nucleated and pile up near the grain or phase boundaries, thereby giving rise to material strengthening. The nucleation and motion of dislocations is hence an essential mechanism to explain plastic yielding, work hardening as well as size and hysteresis effects in crystal plasticity and needs embedding into the constitutive framework of modeling materials with microstructure. An important aspect of modeling dislocation microstructures by a continuum approach lies in a sensible representation of those effects stemming from the characteristics of the discrete crystal lattice which, in particular, prohibits high local dislocation concentrations. Such a saturation behavior gives rise to numerous experimentally observed effects. In particular, experimental investigations hint at an essential size-effect of many properties of elasto-plastic crystals (e.g., the size-dependence of the indentation force during nano-indentation experiments, the grain-size dependence of the yield stress of Hall-Petch or other type, etc.)
Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis
Journal of The Mechanics and Physics of Solids, 2008
Mechanism-based discrete dislocation plasticity is used to investigate the effect of size on micron scale crystal plasticity under conditions of macroscopically homogeneous deformation. Long-range interactions among dislocations are naturally incorporated through elasticity. Constitutive rules are used which account for key short-range dislocation interactions. These include junction formation and dynamic source and obstacle creation. Two-dimensional calculations are carried out which can handle high dislocation densities and large strains up to 0.1. The focus is laid on the effect of dimensional constraints on plastic flow and hardening processes. Specimen dimensions ranging from hundreds of nanometers to tens of microns are considered. Our findings show a strong size-dependence of flow strength and work-hardening rate at the micron scale. Taylor-like hardening is shown to be insufficient as a rationale for the flow stress scaling with specimen dimensions. The predicted size effect is associated with the emergence, at sufficient resolution, of a signed dislocation density. Heuristic correlations between macroscopic flow stress and macroscopic measures of dislocation density are sought. Most accurate among those is a correlation based on two state variables: the total dislocation density and an effective, scale-dependent measure of signed density. r
A Dislocation Based Gradient Plasticity Theory With Applications to Size Effects
Applied Mechanics, 2005
The intent of this work is to derive a physically motivated mathematical form for the gradient plasticity that can be used to interpret the size effects observed experimentally. This paper addresses a possible, yet simple, link between the Taylor's model of dislocation hardening and the strain gradient plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and microtorsion tests of thin wires.
Modeling dislocation sources and size effects at initial yield in continuum plasticity
Journal of Mechanics of Materials and Structures, 2010
Size effects at initial yield (prior to stage II) of idealized micron-sized specimens are modeled within a continuum model of plasticity. Two different aspects are considered: specification of a density of dislocation sources that represent the emission of dislocation dipoles, and the presence of an initial, spatially inhomogeneous excess dislocation content. Discreteness of the source distribution appears to lead to a stochastic response in stress-strain curves, with the stochasticity diminishing as the number of sources increases. Variability in stress-strain response due to variations of source distribution is also shown. These size effects at initial yield are inferred to be due to physical length scales in dislocation mobility and the discrete description of sources that induce internal-stress-related effects, and not due to length-scale effects in the mean-field strain-hardening response (as represented through a constitutive equation).
Computational Methods for Microstructure-Property Relationships, 2010
Plasticity of crystalline solids is a dynamic phenomenon resulting from the motion under stress of linear crystal defects known as dislocations. Such a statement is grounded on numerous convincing observations, and it is widely accepted by the scientific community. Nevertheless, the conventional plasticity theories use macroscopic variables whose definition does not involve the notion of dislocation. This paradoxical situation arises from the enormous range covered by the length scales involved in the description of plasticity, from materials science to engineering. It may have seemed impossible to account for the astounding complexity of the (microscopic) dynamics of dislocation ensembles at the (macroscopic) scale of the mechanical properties of materials. Justifications offered for such a simplification usually reside in perfect disorder assumptions. Namely, plastic strain is regarded as resulting from a large number of randomly distributed elementary dislocation glide events, showing no order whatsoever at any intermediate length scale. Hence, deriving the mechanical properties from the interactions of dislocations with defects simply requires averaging on any space and time domain. The existence of grain boundaries in polycrystals is of course affecting this averaging
Philosophical Magazine, 2010
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