Continuum modeling of dislocation plasticity: Theory, numerical implementation, and validation by discrete dislocation simulations (original) (raw)
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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.)
Philosophical Magazine, 2010
Crystal plasticity is governed by the motion of lattice dislocations. Although continuum theories of static dislocation assemblies date back to the 1950's, the line-like character of these defects posed serious problems for the development of a continuum theory of plasticity which is based on the averaged dynamics of dislocation systems. Only recently the geometrical problem of performing meaningful averages over systems of moving, oriented lines has been solved. Such averaging leads to the definition of a dislocation density tensor of second order along with its evolution equation. This tensor can be envisaged as the analogue of the classical dislocation density tensor in an extended space which includes the line orientation as an independent variable. In the current work we discuss the numerical implementation of a continuum theory of dislocation evolution that is based on this dislocation density measure and apply this to some simple benchmark problems as well as to plane-strain microbending.
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.)
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).
Discrete dislocation plasticity: a simple planar model
Modelling and Simulation in Materials Science and Engineering, 1995
A method for solving small-stnin plasticity problem with plastic flow represented by the collective motion of a large number of discrete dislocations is presented. The dislocations are modelled as line defects in a h e a r elastic medium. At each instant, superposition is used to represent the solution in terms of the infinitemedium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions on the finite body. The complementary solution is nonsingular and is obtained from a finite-element solution of a linear elastic boundary value problem The lattice resistance to dislocation motion, dislocation nuclealion and annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-swain boundary value problem are solved for a solid having edge dislocaUons on parallel slip planes. Monophase and compasite materials subject to simple shear p d i e l to the slip plme are analysed. Typically, a peak in the shear stress versus shear strain C U N~ is found, &er which the svess falls to a plateau at which the material deforms steadily. The plateau is associated with the localization of dislocation activity on more or less isalated systems. The results for composite malerials are compared with solutions for a phenomenological continuum slip characterivtion of plastic flow.
Discrete Dislocation Plasticity
Handbook of Materials Modeling, 2005
Plastic deformation of crystalline solids is of both scientific and technological interest. Over a wide temperature range, the principal mechanism of plastic deformation in crystalline solids involves the glide of large numbers of dislocations. As a consequence, since the 1930s, when dislocations were identified as carriers of plastic deformation in crystalline solids, there has been considerable interest in elucidating the physics of individual dislocations and of dislocation structures. Major effort has also been devoted to developing tools to solve boundary value problems based on phenomenological continuum descriptions in order to predict the plastic deformations that result in structures and components from some imposed loading. Since the 1980s these two approaches have grown toward each other, driven by, for instance, miniaturization and the need for more accurate models in engineering design. The approaches meet at a scale where the collective behavior of individual dislocations controls phenomena. This encounter, together with continuously increasing computing power, has fostered the development of an approach where boundary value problems are solved with plastic flow modeled in terms of the collective motion of discrete dislocations represented as line defects in a linear elastic continuum . This is the field of discrete dislocation plasticity.
MRS Proceedings, 2009
The advancing miniaturisation of e.g. microelectronic devices leads to an increasing interest in physically motivated continuum theories of plasticity in small volumes. Such theories need to be based on the averaged dynamics of dislocations. Preserving the line-like character of these defects, however, posed serious problems for the development of dislocation-based continuum theories, while continuum theories based on scalar dislocation densities necessarily stay on a phenomenological level. Within this work we apply a dislocation-based continuum theory, which is based on a physically meaningful averaging of dislocation lines, to the benchmark problem of bending of a free-standing thin film.
High Performance Computing in Science and Engineering '08
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.
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
Computational Materials Science, 2009
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