Giacomo Po

Controlling strain bursts and avalanches at the nano- to micrometer scale

We demonstrate, through three-dimensional discrete dislocation dynamics simulations, that the complex dynamical response of nano- and microcrystals to external constraints can be tuned. Under load rate control, strain bursts are shown to exhibit scale-free avalanche statistics, similar to critical phenomena in many physical systems. For the other extreme of displacement rate control, strain burst response transitions to quasiperiodic oscillations, similar to stick-slip earthquakes. External load mode control is shown to enable a qualitative transition in the complex collective dynamics of dislocations from self-organized criticality to quasiperiodic oscillations.

Microstructural comparison of the kinematics of discrete and continuum dislocations models

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.

The atomistic representation of first strain-gradient elastic tensors

We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy–Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.

The influence of laser-induced nanosecond rise-time stress waves on the microstructure and surface chemical activity of single crystal Cu nanopillars

An apparatus and test procedure for fabrication and loading of single crystal metal nanopillars under extremely high pressures (>1 GPa) and strain rates (>107 s-1), using laser-generated stress waves, are presented. Single-crystalline Cu pillars (∼1.20 μm in tall and ∼0.45 μm in diameter) prepared via focused ion beam milling of Cu(001) substrates are shock-loaded using this approach with the dilatational stress waves propagating along the [001] axis of the pillars. Transmission electron microscopy observations of shock-loaded pillars show that dislocation density decreases and that their orientation changes with increasing stress wave amplitude, indicative of dislocation motion. The shock-loaded pillars exhibit enhanced chemical reactivity when submerged in oil and isopropyl alcohol solutions, due likely to the exposure of clean surfaces via surface spallation and formation of surface steps and nanoscale facets through dislocation motion to the surface of the pillars, resulting in growth of thin oxide films on the surfaces of the pillars.

Atomistically enabled nonsingular anisotropic elastic representation of near-core dislocation stress fields in a-iron

The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the approximation of an effective core radius, inside which ad hoc regularizations are implemented, such approximations lead to a compromise in the accuracy of the calculations. In this work, an anisotropic non-singular elastic representation of dislocation fields is developed to accurately represent the near-core stresses of dislocations in

The solid angle and the Burgers formula in the theory of gradient elasticity: Line integral representation

\alpha

Shock-induced plasticity and the Hugoniot elastic limit in copper nano films and rods

-iron. The regularized stress field is enabled through the use of a non-singular Greens tensor function of Helmholtz-type gradient anisotropic elasticity, which requires only a single characteristic length parameter in addition to the materials elastic constants. Using a novel magnetic bond-order potential to model atomic interactions in iron, molecular statics calculations are performed, and an optimization procedure is developed to extract the required length parameter. Results show the method can accurately replicate the magnitude and decay of the near-core dislocation stresses even for atoms belonging to the core itself. Comparisons with the singular isotropic and anisotropic theories show the non-singular anisotropic theory leads to a substantially more accurate representation of the stresses of both screw and edge dislocations near the core, in some cases showing improvements in accuracy of up to an order of magnitude. The spatial extent of the region in which the singular and non-singular stress differ substantially is also discussed. The general procedure we describe may in principle be applied to accurately model the near-core dislocation stresses of any arbitrarily shaped dislocation in anisotropic cubic media.

Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations

Abstract A representation of the solid angle and the Burgers formula as line integral is derived in the framework of the theory of gradient elasticity of Helmholtz type. The gradient version of the Eshelby–deWit representation of the Burgers formula of a closed dislocation loop is given. Such a form is suitable for the numerical implementation in 3D dislocation dynamics (DD).

Atomistic Activation Energy Criteria for Multi-Scale Modeling of Dislocation Nucleation in FCC Metals

Shock deformation of copper nano-films and nano-rods is examined with Molecular Dynamics (MD) simulations. The influence of the small system size on the onset of plasticity, its origin resulting from the nucleation of dislocation loops, and its reversible nature are determined. While simulations of large systems with periodic boundary conditions indicate that tremendous axial stresses are needed to induce plastic deformation in perfect copper crystals, the present results suggest that the stress levels needed to initiate irreversible plasticity in nano-rods are more than one order of magnitude smaller than what has been reported for bulk single crystals. MD studies of nano-films show that shock waves are purely elastic up until the Hugoniot elastic limit of PHEL ≈ 30–40 GPa, at which point Shockley partial dislocations are internally nucleated at the shock front. However, our recent experiments on shocked nano-rods show that plasticity is evident at much lower axial stress levels, on the order of 1–2 GPa....

Dependence of hardening and saturation stress in persistent slip bands on strain amplitude during cyclic fatigue loading

The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X,t)=FL(X,t)FP(X,t), an initial stress-free polycrystal is constructed by imposing FL to be a piecewise constant rotation field R0(X), and FP=R0(X)T, thereby having F(X,0)=I, and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.