Modeling dislocation density evolution in continuum crystal plasticity

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.Includes bibliographical references (p. 221-229).Dislocations are the singly most important material defects in crystal plasticity, and although dislocation mechanics has long been understood as the underlying physical basis for continuum crystal plasticity formulations, explicit consideration of crystallo- graphic dislocation mechanics has been largely absent in working constitutive models. In light of recent theoretical developments in dislocation dynamics, and the introduc- tion of geometrically necessary dislocation (GND) density in continuum formulations through plastic strain gradients, a single crystal plasticity model based on dislocation density state variables is developed. The density state variables evolve from initial conditions according to equations based on fundamental concepts in dislocation me- chanics such as the conservation of Burgers vector in multiplication and annihilation processes. Along with those processes that account for bulk statistical dislocation evolution, the evolving polarity due to dislocation species flux divergences may be in- cluded to detail the length-scale dependence of mechanical properties on the micron level. The full dislocation density description of plasticity allows a simple evaluation of the role of GND density in non-homogeneously deforming bodies. A local version of the constitutive model, which captures the bulk processes of dislocation multiplication and annihilation during plastic deformation, is implemented within a finite element framework to investigate the poly-slip behavior of aluminum single crystals under tension.(cont.) A non-local version of the constitutive model using an idealized planar double slip system geometry is implemented within a finite element framework to investigate the length-scale dependence observed in the bending of thin single crystal beams. The results not only capture the mechanical stress/strain response of the material, but also detail the development of underlying dislocation structure responsible_ fr: the plistic behavior of the crystal.by Athanasios Arsenlis.Ph.D

Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.Comment: 11 pages, 1 figure, accepted for publication in J. Non-Newtonian Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium thermodynamics, GENERIC, Lie groups, Reference state

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part I: interactions with screw dislocations

We present a comprehensive dislocation dynamics (DD) study of the strength of stacking fault tetrahedra (SFT) to screw dislocation glide in fcc Cu. Our methodology explicitly accounts for partial dislocation reactions in fcc crystals, which allows us to provide more detailed insights into the dislocation– SFT processes than previous DD studies. The resistance due to stacking fault surfaces to dislocation cutting has been computed using atomistic simulations and added in the form of a point stress to our DD methodology. We obtain a value of 1658.9 MPa, which translates into an extra force resolved on the glide plane that dislocations must overcome before they can penetrate SFTs. In fact, we see they do not, leading to two well differentiated regimes: (i) partial dislocation reactions, resulting in partial SFT damage, and (ii) impenetrable SFT resulting in the creation of Orowan loops. We obtain SFT strength maps as a function of dislocation glide plane-SFT intersection height, interaction orientation, and dislocation line length. In general SFTs are weaker obstacles the smaller the encountered triangular area is, which has allowed us to derive simple scaling laws with the slipped area as the only variable. These laws suffice to explain all strength curves and are used to derive a simple model of dislocation–SFT strength. The stresses required to break through obstacles in the 2.5–4.8-nm size range have been computed to be 100–300 MPa, in good agreement with some experimental estimations and molecular dynamics calculations

Atomistically informed dislocation dynamics in fcc crystals

We develop a nodal dislocation dynamics (DD) model to simulate plastic processes in fcc crystals. The model explicitly accounts for all slip systems and Burgers vectors observed in fcc systems, including stacking faults and partial dislocations. We derive simple conservation rules that describe all partial dislocation interactions rigorously and allow us to model and quantify cross-slip processes, the structure and strength of dislocation junctions, and the formation of fcc-specific structures such as stacking fault tetrahedra. The DD framework is built upon isotropic non-singular linear elasticity and supports itself on information transmitted from the atomistic scale. In this fashion, connection between the meso and micro scales is attained self-consistently, with all material parameters fitted to atomistic data. We perform a series of targeted simulations to demonstrate the capabilities of the model, including dislocation reactions and dissociations and dislocation junction strength. Additionally we map the four-dimensional stress space relevant for cross-slip and relate our findings to the plastic behavior of monocrystalline fcc metal

Development of a process simulation capability for the formation of titanium nitride diffusion barriers

Titanium nitride (TiN) films deposited by chemical vapor deposition (CVD) techniques are of interest for a wide range of commercial applications. In this report, the authors describe a mechanism that predicts Tin film growth rates from TiCl{sub 4}/NH{sub 3} mixtures as a function of process parameters, including inlet reactant concentrations, substrate temperatures, reactor pressures, and total gas flow rates. Model predictions were verified by comparison with the results of TiN deposition experiments in the literature and with measurements made in a new stagnation-flow reactor developed for the purpose of testing deposition mechanisms such as this. In addition, they describe ab initio calculations that predict thermodynamic properties for titanium-containing compounds. The results of calculations using Moeller-Plesset perturbation theory, density functional theory, and coupled cluster theory are encouraging and suggest that these methods can be used to estimate thermodynamic data that are essential for the development of CVD models involving transition-metal compounds. Finally, measurements of the adsorption and desorption kinetics of NH{sub 3} on TiN films using temperature-programmed desorption are described and their relevance to TiN CVD and mechanism development are discussed

Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations

We use a physically-based crystal plasticity model to predict the yield strength of body-centered cubic (bcc) tungsten single crystals subjected to uniaxial loading. Our model captures the thermally-activated character of screw dislocation motion and full non-Schmid effects, both of which are known to play a critical role in bcc plasticity. The model uses atomistic calculations as the sole source of constitutive information, with no parameter fitting of any kind to experimental data. Our results are in excellent agreement with experimental measurements of the yield stress as a function of temperature for a number of loading orientations. The validated methodology is then employed to calculate the temperature and strain-rate dependence of the yield strength for 231 crystallographic orientations within the standard stereographic triangle. We extract the strain-rate sensitivity of W crystals at different temperatures, and finish with the calculation of yield surfaces under biaxial loading conditions that can be used to define effective yield criteria for engineering design models

Interfacial diffusion in high-temperature deformation of composites: A discrete dislocation plasticity investigation

© 2016 Elsevier Ltd We present a discrete dislocation plasticity (DDP) framework to analyse the high temperature deformation of multi-phase materials (composites) comprising a matrix and inclusions. Deformation of the phases is by climb-assisted glide of the dislocations while the particles can also deform due to stress-driven interfacial diffusion. The general framework is used to analyse the uniaxial tensile deformation of a composite comprising elastic particles with dislocation plasticity only present in the matrix phase. When dislocation motion is restricted to only glide within the matrix a strong size effect of the composite strength is predicted with the strength increasing with decreasing unit cell size due to dislocations forming pile-ups against the matrix/particle interface. Interfacial diffusion decreases the composite strength as it enhances the elongation of the elastic particles along the loading direction. When dislocation motion occurs by climb-assisted glide within the matrix the size effect of the strength is reduced as dislocations no longer arrange high energy pile-up structures but rather form lower energy dislocation cell networks. While interfacial diffusion again reduces the composite strength, in contrast to continuum plasticity predictions, the elongation of the particles is almost independent of the interfacial diffusion constant. Rather, in DDP the reduction in composite strength due to interfacial diffusion is a result of changes in the dislocation structures within the matrix and the associated enhanced dislocation climb rates in the matrix.Support from ONR under grant number N62909-14-1N242 on Multi-scale methods for creep resistant alloys (program manager Dr. David Shifler) is gratefully acknowledged