Computational modelling of single crystals

The physical basis of computationally tractable models of crystalline plasticity is reviewed. A statistical mechanical model of dislocation motion through forest dislocations is formulated. Following Franciosi and co-workers (1980-88) the strength of the short-range obstacles introduced by the forest dislocations is allowed to depend on the mode of interaction. The kinetic equations governing dislocation motion are solved in closed form for monotonic loading, with transients in the density of forest dislocations accounted for. This solution, coupled with suitable equations of evolution for the dislocation densities, provides a complete description of the hardening of crystals under monotonic loading. Detailed comparisons with experiment demonstrate the predictive capabilities of the theory. An adaptive finite element formulation for the analysis of ductile single crystals is also developed. Calculations of the near-tip fields in Cu single crystals illustrate the versatility of the method

Multiscale modelling of hardening in BCC crystal plasticity

The mechanical behavior of polycrystalline metals can be successfully modeled by macroscopic theories, such as Von Mises plasticity. On the other hand, numerous studies can be performed on the atomic scale, either by atomistic or dislocation dynamics models. The proposed model attempts to bridge those two scales by deriving constitutive relations between slip strains, dislocation densities and resolved shear stresses on crystallographic planes, from mechanisms of deformation playing at the level of the dislocation line. The resulting "mesoscopic" hardening relations are controlled by dislocation self energies and junctions strengths. Temperature and strain rate dependence result from the presence of thermally activated mechanisms such as Peierls barriers or pair annihilation by cross slip. A set of material parameters is identified for Tantalum by fitting the numerical stress strain curves from these tests with experimental results gathered in the literature. These parameters prove to be in very good agreement with the values which can be derived from molecular dynamics computations

Mixed Atomistic–Continuum Models of Material Behavior: The Art of Transcending Atomistics and Informing Continua

The recent development of microscopes that allow for the examination of defects at the atomic scale has made possible a more direct connection between the defects and the macroscopic response they engender (see, e.g., the December 1999 issue of MRS Bulletin)

A multiscale approach for modeling crystalline solids

In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate

Two-phase densification of cohesive granular aggregates

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that particle rearrangement is a spatially heterogeneous phenomenon, which occurs in the form of a phase transformation between two configurational phases of the granular aggregate. We then show that the energy landscape associated with particle rearrangement is consistent with our interpretation of the experimental results. Besides affording insight into the physics of the granular state, our conclusions are relevant to many engineering processes and natural phenomena.Comment: 7 pages, 3 figure

A new approach for developing continuous age-depth models from dispersed chronologic data: applications to the Miocene Santa Cruz formation, Argentina

Traditional methods (linear regression, spline fitting) of age-depth modeling generate overly optimistic confidence intervals. Originally developed for C, Bayesian models (use of observations independent of chronology) allow the incorporation of prior information about superposition of dated horizons, stratigraphic position of undated points, and variations in sedimentology and sedimentation rate into model fitting. We modified the methodology of two Bayesian age depth models, Bchron (Haslett and Parnell, 2008) and OxCal (Ramsey, 2008) for use with U-Pb dates. Some practical implications of this approach include: a) model age uncertainties increase in intervals that lack closely spaced age constraints; b) models do not assume normal distributions, allowing for the non-symmetric uncertainties of sometimes complex crystal age probability functions in volcanic tuffs; c) superpositional constraints can objectively reject some cases of zircon inheritance and mitigate apparent age complexities. We use this model to produce an age-depth model with continuous and realistic uncertainties, for the early Miocene Santa Cruz Formation (SCF), Argentina.Facultad de Ciencias Naturales y Muse

A new approach for developing continuous age-depth models from dispersed chronologic data: applications to the Miocene Santa Cruz formation, Argentina

Traditional methods (linear regression, spline fitting) of age-depth modeling generate overly optimistic confidence intervals. Originally developed for C, Bayesian models (use of observations independent of chronology) allow the incorporation of prior information about superposition of dated horizons, stratigraphic position of undated points, and variations in sedimentology and sedimentation rate into model fitting. We modified the methodology of two Bayesian age depth models, Bchron (Haslett and Parnell, 2008) and OxCal (Ramsey, 2008) for use with U-Pb dates. Some practical implications of this approach include: a) model age uncertainties increase in intervals that lack closely spaced age constraints; b) models do not assume normal distributions, allowing for the non-symmetric uncertainties of sometimes complex crystal age probability functions in volcanic tuffs; c) superpositional constraints can objectively reject some cases of zircon inheritance and mitigate apparent age complexities. We use this model to produce an age-depth model with continuous and realistic uncertainties, for the early Miocene Santa Cruz Formation (SCF), Argentina.Facultad de Ciencias Naturales y Muse

A multiscale approach for modeling crystalline solids

In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate

A new approach for developing continuous age-depth models from dispersed chronologic data: applications to the Miocene Santa Cruz formation, Argentina

Traditional methods (linear regression, spline fitting) of age-depth modeling generate overly optimistic confidence intervals. Originally developed for C, Bayesian models (use of observations independent of chronology) allow the incorporation of prior information about superposition of dated horizons, stratigraphic position of undated points, and variations in sedimentology and sedimentation rate into model fitting. We modified the methodology of two Bayesian age depth models, Bchron (Haslett and Parnell, 2008) and OxCal (Ramsey, 2008) for use with U-Pb dates. Some practical implications of this approach include: a) model age uncertainties increase in intervals that lack closely spaced age constraints; b) models do not assume normal distributions, allowing for the non-symmetric uncertainties of sometimes complex crystal age probability functions in volcanic tuffs; c) superpositional constraints can objectively reject some cases of zircon inheritance and mitigate apparent age complexities. We use this model to produce an age-depth model with continuous and realistic uncertainties, for the early Miocene Santa Cruz Formation (SCF), Argentina.Facultad de Ciencias Naturales y Muse