Crystal Plasticity and Hardening: A Dislocation Dynamics Study (original) (raw)
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Acta Materialia 54 (2006) 2181
"We suggest a dislocation based constitutive model to incorporate the mechanical interaction between mobile dislocations and grain boundaries into a crystal plasticity finite element framework. The approach is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of grain boundaries. The energy barrier is derived by using a geometrical model for thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems and is formulated as a vectorial conservation law. The new model is applied to the case of 50% (frictionless) simple shear deformation of Al bicrystals with either a small, medium, or large angle grain boundary parallel to the shear plane. The simulations are in excellent agreement with the experiments in terms of the von Mises equivalent strain distributions and textures. The study reveals that the incorporation of the misorientation alone is not sufficient to describe the influence of grain boundaries on polycrystal micro-mechanics. We observe three mechanisms which jointly entail pronounced local hardening in front of grain boundaries (and other interfaces) beyond the classical kinematic hardening effect which is automatically included in all crystal plasticity finite element models owing to the change in the Schmid factor across grain boundaries. These are the accumulation of geometrically necessary dislocations (dynamic effect; see [Ma A, Roters F, Raabe D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 2006;58:2169–79]), the resistance against slip penetration (dynamic effect; this paper), and the change in the orientation spread (kinematic effect; this paper) in the vicinity of grain boundaries."
A dislocation density based constitutive model for the face centered cubic crystal structure has been implemented into a crystal-plasticity finite element framework and extended to consider the mechanical interaction between mobile dislocations and grain boundaries by the authors [Ma, A., Roters, F., Raabe, D., 2006a. A dislocation density based constitutive model for crystal-plasticity FEM including geometrically necessary dislocations. Acta Materialia 54, 2169–2179; Ma, A., Roters, F., Raabe, D., 2006b. On the consideration of interactions between dislocations and grain boundaries in crystalplasticity finite element modeling – theory, experiments, and simulations. Acta Materialia 54, 2181–2194]. The approach to model the grain boundary resistance against slip is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of internal interfaces. This energy barrier is derived from the assumption of thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems. In this study we focus on the influence of the one remaining model parameter which can be used to scale the obstacle strength of the grain boundary.
Dislocation Patterns and Work-Hardening in Crystalline Plasticity
Journal of Elasticity, 2004
We propose here a continuum model for the evolution of the total dislocation densities in fcc crystals, in the framework of rate-independent plasticity. The basic physical features which are taken into account are: (i) the role of dislocations in hardening; (ii) the relations between the slip velocity and dislocation mobility; (iii) the energetics of self and mutual interactions between dislocations; (iv) non local effects in the interaction between dislocations. A set of reactiondiffusion equations is obtained, with mobilities depending on the slip velocities, which is able to describe the formation of dislocation walls and cells. To this effect, the results of numerical simulations in two special cases are presented.
Discrete Dislocation Plasticity Analysis of Size Effects in Single Crystals
The effect of loading conditions on the tensile stress versus strain response of micron-sized planar crystals with a single active slip system is investigated via finite and small deformation discrete dislocation plasticity analyses. When rotation of the tensile axis is prevented, lattice curvature is induced in the crystal in both the small and finite strain analyses with the build-up of geometrically necessary dislocations resulting in a hardening response. The hardening rate is higher in the small strain analyses and this is attributed to the assumption of linear kinematics in that analysis. On the other hand, when rotation of the tensile axis is permitted, no lattice curvature is induced in the crystal in the small strain analysis resulting in an ideally plastic response. However, the change in the geometry of the crystal induces bending moments in the crystal in the finite strain analyses giving rise to a mildly hardening tensile stress versus strain response.
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.)
Dislocation Mean Free Paths and Strain Hardening of Crystals
Science, 2008
Predicting the strain hardening properties of crystals constitutes a long-standing challenge for dislocation theory. The main difficulty resides in the integration of dislocation processes through a wide range of time and length scales, up to macroscopic dimensions. In the present multiscale approach, dislocation dynamics simulations are used to establish a dislocation-based continuum model incorporating discrete and intermittent aspects of plastic flow. This is performed through the modeling of a key quantity, the mean free path of dislocations. The model is then integrated at the scale of bulk crystals, which allows for the detailed reproduction of the complex deformation curves of face-centered cubic crystals. Because of its predictive ability, the proposed framework has a large potential for further applications.
Dislocation density evolution and interactions in crystalline materials
Acta Materialia, 2011
Dislocation density-based evolution formulations that are related to a heterogeneous microstructure and are physically representative of different crystalline interactions have been developed. The balance between the generation and annihilation of dislocations, through glissile and forest interactions at the slip system level, is taken as the basis for the evolution of mobile and immobile dislocation densities. The evolution equations are coupled to a multiple slip crystal plasticity formulation, and a framework is established that relates it to a general class of crystallographies and deformation modes. Specialized finite element (FE) methodologies have then been used to investigate how certain dislocation density activities, such as dislocation density interactions and immobilization, are directly related to strain hardening and microstructure evolution. The predictions are validated with channel die compressed (CDC) experiments, and are consistent with inelastic deformation modes of fcc metals.
Density of grain boundaries and plasticity size effects: A discrete dislocation dynamics study
2009
Discrete dislocation dynamics simulations are carried out to systematically investigate the microstructural and geometrical size dependence of films under tension that have a varying number of grains through their thickness. By varying film thickness, grain size and aspect ratio, more insight is gained into the competition between grain boundary hardening and film thickness effects. This provides a seamless link between previous dislocation plasticity studies and qualitative agreement with experimental data. In the simulations, plasticity arises from the collective motion of discrete dislocations of edge character. Their dynamics is incorporated through constitutive rules for nucleation, glide, pinning and annihilation. Grain boundaries are treated as impenetrable to dislocation motion. The numerical results show that the grain size dependence of yield in thin films as well as in bulk polycrystals is controlled by the density of grain boundaries.