Using the lattice Green’s function approach and LCAO (linear combination of atomic orbitals) electron theory, we investigate the atomistic configuration and lattice trapping of cracks in Si. The LCAO electron theory coupled to second order perturbation theory (SOP) has been used to derive explicit expressions for the bond breaking nonlinear forces between Si atoms. We calculate the cracked lattice Green’s functions for a crack on the (111) plane and lying in the (110) direction. With the nonlinear forces acting in a cohesive region near the crack tips, the crack structure is then calculated. The calculated structure possesses a crack opening at the Griffith load which should allow penetration of typical external molecules to the crack tip at the Griffith loading. Other consequences for chemical reactions at the crack tip are discussed in the light of these results. The lattice trapping is low, only a few percent of the Griffith load.

An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.

This article is this second of a pair on a theory of chemically assisted fracture. In it a simple bond orbital model of the force laws to be used in fracture is developed. In the bond orbital model, only a few of the atoms in the vicinity of the bond to be broken are considered and do not include interactions with the rest of the system, which is assumed to be Newtonian. Numerical accuracy is not required, but qualitative features of the force laws are believed to be valid. The silica bond is shown to rise quickly to a high peak, after which it develops a relatively long tail. When the bond is attacked by water, modeling by the same technique indicates that the bond has a “snapping” characteristic that is important in the theory developed in the first article. For bonds with smooth “back sides” the barriers to crack motion are shown to be low, but barriers are expected to be observable when the bond snaps. A tight binding treatment of a one-dimensional chain has been included in order to investigate the effect of including band effects in the force law. These effects are found to be small compared to the simple bond breaking of the bond orbital calculation.

In this paper, we address some fundamental questions regarding the response of a crack to externally generated dislocations. We note that since dislocations that formed at external sources in the material must be in the form of loops or dipoles, the theory must be couched in terms of crack shielding in a plastically polarizable medium. There are strong analogies to dielectric theory. We prove two general theorems: (1) Dipoles formed in the emission geometry relative to a crack tip always antishield the crack and (2) when dipoles are induced during uniform motion of a crack through a uniformly plastically polarizable material, then the net shielding is always positive. We illustrate these general theorems with a number of special cases for fixed and polarizable sources. Finally, we simulate the self consistent time dependent response of a crack to a polarizable source as the crack moves past it. The results show that the crack is initially antishielded, but that positive shielding always dominates during later stages of configuration evolution. The crack may be arrested by the source, or it may break away from it, depending upon the various parameters (source strength and geometry, dislocation mobility, Griffith condition for the crack, etc.). The results indicate that the time dependence of crack shielding in the presence of a nonuniform density of sources will be very important in practical cases of brittle transitions in materials.

This article is the first of a pair on a theory of chemically assisted fracture. It includes the Green’s function analysis for a three-dimensional crack with a kink on it. Equations are developed for the activation energy for the motion and nucleation of such kinks using information to be found in the second article regarding the force laws appropriate for water attack of silica. The most general conclusion is that lattice trapping barriers to crack motion (including chemical effects) are associated with a narrow core region of the crack, which is in turn connected to the nature of the interatomic force laws of the material (including the modifications of these force laws induced by chemical reactions). Further, it is found that the force law must have a severely “snapping” characteristic in order to assure a narrow core, a feature not to be expected except under certain types of external chemical attack of the crack. Additional results are that the energy to nucleate a kink pair in silica under water attack is in the neighborhood of 2 eV and that the motion energy is of order 0.1 eV. Motion energies are expected to be considerably smaller than formation energies in general.

Theories of toughness of materials depend on an understanding of the characteristic instabilities of the crack tip, and their possible interactions. In this paper we examine the effect of dislocation emission on subsequent cleavage of a crack and on further dislocation emission. The work is an extension of the previously published Lattice Greens Function methodology[1, 2, 3]. We have developed a Cavity Greens Function describing a blunt crack and used it to study the effect of crack blunting under a range of different force laws. As the crack is blunted, we find a small but noticeable increase in the crack loading needed to propagate the crack. This effect may be of importance in materials where a dislocation source near the crack tip in a brittle material causes the crack to absorb anti-shielding dislocations, and thus cause a blunting of the crack. It is obviously also relevant to cracks in more ductile materials where the crack itself may emit dislocations.

We develop a form of nonequilibrium statistical mechanics designed to be applicable to the evolution of dislocation structure (or patterning) during metal deformation. The formalism can be applied both to time independent relaxed dislocation systems as well as to the time dependent relaxation itself. One specific application is to a simplified version of the "equilibrium" relaxed state, where we show that an effective temperature can be defined in terms of the noise in the system (back stress fluctuations). As the noise is decreased, varying degrees of order appear. In a second application to a simple two-dimensional (2D) dislocation computer model, we show how to obtain an effective time dependent free energy and temperature from the ensemble driving forces developed in earlier work. In this model, too, the underlying physics relates to a competition between the noise and energy. And, finally, we show that the behavior of the Boltzmann H function for the same 2D computer model can be tied to the rather complex physics of the evolving time dependent structure.

R. LeSar ∗,1 M. Koslowski, 2 Robb Thomson, 3 and J. M. Rickman 4† 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA 2Department of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 USA 3(Retired) 250 E. Alameda, Apt 515, Santa Fe, NM 87501 USA 4Department of Materials Science and Engineering and Department of Physics, Lehigh University, Bethlehem, PA 18015 USA E-mail:lesar@lanl.gov

We explore the underlying physics of dislocation ordering in deforming metals, where we focus on the competing role of energy relaxation and the fluctuations (noise) in the local stress field. We investigate the competition by employing a simple two-dimensional model that exhibits the essential physics, while avoiding extraneous mechanisms that might cloud the issues. We show that noise and energetics are equally important in determining the final state of the system. Quantitative functions for the energetic driving force for ordering and the resistive force owing to the noise are developed that balance one another at the relaxed state. These features follow from the system being scale invariant, with power law dependencies of the macrovariables on the number of relaxing dislocations.

A major goal in dislocation theory is the development of a coarse-grained method that would enable predictions of dislocation response without resolving the degrees of freedom of all the dislocations.While a number of possible coarse-grained theories have been proposed, all of these need information about structures at scales smaller than the coarse-graining volume.Here we present results from dislocation simulations that yield scaling relations with the hope that they can provide a framework for modeling the sub-scale dislocation structures and dynamics.For example, we show that dislocations have a self-similar (fractal) structure over wide range of stress/strain; dislocations move by means of avalanches that have power-law (self-organized critical) behavior; and the energy, order and noise all scale as powers of the density, with a welldefined balance between noise and order.

A dislocations-based model is presented for predicting the flow stress of a pre-deformed metal single crystal. The model is based upon a combination of basic dislocation physics, the distribution of dislocation segment lengths in cell walls and percolation theory. With only the magnitude of the Burgers vector and the elastic shear modulus as inputs, and with no adjustable parameters, the model correctly predicts the formation of slip lines and slip bands, the linear behavior of the stress–strain curve in stage II hardening, the Voce behavior in stage III and the magnitude of the flow stress for deformed Al single crystals.

The competition between energy and noise in the patterning transition in deformation is explored by employing a two-dimensional model of parallel straight edge dislocations. We define a generalized force for ordering and show that at mechanical equilibrium, the ordering force is equal to the average back stress noise on the slip plane.

We present results from phase-field simulations of a two-dimensional model of dislocation microstructure development under increasing strain that incorporates the effects of the full, three-dimensional, microstructure in an approximate way. Despite its simplicity, the model yields quantitative predictions of both the deformation properties of face-centered cubic metals as well as key descriptors of the evolving microstructure over a wide range of stress and strain. The present results have important implications for how we interpret and describe the deformation properties of fcc materials.

Plastic deformation of crystalline materials is a complex nonhomogeneous process characterized by avalanches in the motion of dislocations. We study the evolution of dislocation loops using an analytically solvable phase-field model of dislocations for ductile single crystals during monotonic loading. The distribution of dislocation loop sizes is given by P(A) approximately A-sigma, with sigma=1.8+/-0.1. The exponent is in agreement with those found in acoustic emission experiments. This model also predicts a range of macroscopic behaviors in agreement with observation, including hardening with monotonic loading, and a maximum in the acoustic emission signal at the onset of yielding.

We introduce a simple stochastic model that describes the dynamics of the recovery of dislocations in dislocation cell walls in stage III deformation in fcc metals. The stage II/III transition is identified as a break between walls with well-defined populations and those with power law distributions.

In this paper, we present a recent advance in theoretical understanding of a deforming metal, using a strain percolation model which possibly explains spasmodic, fine slip line burst events occurring in the metal. The model addresses how the additional strain nucleated in a cell propagates through a dislocation cell structure, and predicts that near the critical point, the system exhibits critical power-law behavior. It is found that although the model displays long-transient behavior associated with the initial strain in the model, asymptotically critical behavior observed in the system is well explained by standard percolation theory. The long-transient behavior suggests that finite-size effects could be an important factor for the stress-strain relation in the metal. A detailed study reveals that the universal aspects of the model, i.e., the evolution into an initial condition- independent, critical state, arise from collective behavior of a huge number of self- organizing critical cells that develop the minimum or at least marginally stable strain