Size effects under homogeneous deformation of single crystals: A discrete dislocation analysis (original) (raw)
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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.)
Modelling and Simulation in Materials Science and Engineering, 2006
The effect of specimen size on the uniaxial deformation response of planar single crystals and polycrystals is investigated using discrete dislocation plasticity. The dislocations are all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. Two types of polycrystalline materials are considered: one that only has grains with a single orientation while the other has a checker-board arrangement of two types of grains which are rotated 90 • with respect to each other. The single crystals display a strong size dependence with the flow strength increasing with decreasing specimen size. In sufficiently small single crystal specimens, the nucleation rate of the dislocations is approximately equal to the rate at which the dislocations exit the specimens so that below a critical specimen size the flow strength is set by the strength of the initially present Frank-Read sources. On the other hand, grain boundaries acting as barriers to plastic deformation in polycrystalline specimens of the same size lead to a more diffuse deformation pattern and to a nearly size-independent response.
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.)
Continuum Dislocation Theory and Related Size Effects in Crystal Plasticity
2010
This Chapter discusses the continuum dislocation theory and its applications in crystal plasticity. We aim at studying the dislocation nucleation and accumulation, the resulting work hardening and the influence of the resistance to dislocation motion. Among boundary-value problems we consider plane constrained shear, plane strain uniaxial extension and their combination for single and bi-crystals, which admit analytical solutions. The interesting features of these solutions are the energetic and dissipative thresholds for dislocation nucleation, the Bauschinger translational work hardening, and the size effects.
Dislocation pattern formation in finite deformation crystal plasticity
International Journal of Solids and Structures
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 crossslip. Crystal orientation effects on the pattern formation and mechanical response are also demonstrated. The manifest irrelevance of the necessity of a multiplicative decomposition of the deformation gradient, a plastic distortion tensor, and the choice of a reference configuration in our model to describe the micromechanics of plasticity as it arises from the existence and motion of dislocations is worthy of note.
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.
Crystal Plasticity and Hardening: A Dislocation Dynamics Study
Procedia Engineering, 2009
Following the publication of several seminal studies, discrete dislocation dynamics has become well-established as a means of analysing the response of ductile crystals and polycrystals to mechanical loading. Developments undertaken by different authors have followed two principal directions: (i) the use of simple 2D formulations that do not seek to capture correctly the details of slip geometry, but allow some insight to be developed into the trends and relationships, and (ii) large scale 3D simulations seeking to represent correctly the geometry of dislocation segments, and their spatial distribution and interaction. The former is computationally inexpensive and fast, but fails to capture the effects of grain orientation. The latter is associated with large overheads in terms of the computational effort. The purpose of the present study is to propose and develop an intermediate level approach, whereby the geometry of the crystal slip is captured to a greater degree, while computational difficulty is kept to a minimum. The results are analysed in terms of the dependence of yield stress and cyclic hardening on the crystal orientation and dislocation interaction with each other and with the grain boundaries.
Acta Materialia, 2009
Realistic dislocation network topologies were generated by relaxing an initially pinning point free dislocation loop structure using three-dimensional discrete dislocation dynamics simulations. Traction-free finite-sized samples were used. Subsequently, these equilibrated structures were subjected to tensile loading and their mechanical behavior was investigated with respect to the initial configuration. A strong mechanical size effect was found. The flow stress at 0.2% plastic deformation scales with specimen size with an exponent between À0.6 and À0.9, depending on the initial structure and size regime. During relaxation, a mechanism, also favored by cross-slip, is identified which leads to rather stable pinning points. These pinning points are comparable to those of the isolated Frank-Read sources often used as a starting configuration in previous discrete dislocation dynamics simulations. These nodes act as quite stable dislocation sources, which can be activated multiple times. The influence of this source mechanism on the mechanical properties of small-scale specimens is discussed.
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.