Showing papers by "David J. Srolovitz published in 1994"

Surface morphology evolution in stressed solids : surface diffusion controlled crack initiation

Abstract: We present a nonlinear analysis of the temporal evolution of the surface morphology of a stressed solid based on a general parametric description of the surface shape. We find that surfaces of elastic, defect-free solids are unstable against the nucleation and growth of cracks. The rate at which this surface instability occurs depends on the material transport kinetic mechanism. The surface instability creates a groove that sharpens as it grows deeper. The groove growth rate accelerates until the groove reaches a critical length (or time) where the growth rate diverges. Comparison of these results with predictions of linear elastic fracture mechanics shows that the critical length is in excellent agreement with the classical Griffith fracture criterion, with no adjustable parameters. The stress field ahead of the growing groove becomes increasingly singular as the groove grows. Once the critical groove length is achieved, the stress field ahead of the groove approaches the inverse square root dependence on distance from the tip, which is characteristic of a sharp crack. Therefore, the sub-critical groove is not simply a short crack.

Microstructural Mechanics Model of Anisotropic-Thermal-Expansion-Induced Microcracking

Abstract: Thermal-expansion-induced microcracking in single-phase ceramics has been simulated using a simple mechanics model based upon a regular lattice of brittle, elastic springs. Microcracks preferentially form at grain boundaries and propagate either into the bulk or along grain boundaries, depending on the toughness of the boundaries relative to the grain interiors. The present results show that anisotropic-thermal-expansion-induced microcracking can be more severe for either large or small grain size samples depending on the damage measure employed. At very small misfit strains, the large grain microstructure develops microcracks before the small grain microstructure. However, over most of the misfit strain regime examined, the total length/area of all cracks in a sample is larger when the grain size is small. This is manifested in a larger decrement of the elastic modulus in small grain size samples as compared with large grain size samples at the same misfit (AT). However, large grain sizes are more detrimental with regard to fracture properties. This is because the fracture stress scales as inversely with the crack length and large grain samples exhibit larger microcracks than small grain samples. Unlike in the unconstrained samples, when a sample is constrained during a temperature excursion, the stress created by the overall thermal expansion can directly lead to fracture of the entire sample. I. Introduction ANY ceramic materials are known to undergo spontaneM ous cracking when cooled from high processing temperatures. The presence of microcracks modifies several physical properties including thermal diffusivity, dielectric constant, acoustic transparency, and elastic moduli.' Microcracking can also lead to an increase in fracture toughness: presumably associated with the microcracking-induced dilatation and also partly due to the formation of a process zone ahead of a propagating rack.^,^ However, the contribution of microcracking to toughening is usually minor.' The tendency to form these cracks is known to increase with increasing temperature excursions and increasing grain size6 and is often attributable to residual stresses that develop from either thermal contraction anisotropy or non-shape-preserving phase transformations.' In multiphase

Metal / ceramic adhesion: a first principles study of MgO/Al and MgO/Ag

Abstract: The energetics of adhesion and the electronic structure are determined for MgO/Ag(100) and MgO/Al(100) interfaces via local density-functional calculations. At the interface, both Ag and Al atoms energetically favour the site directly above the O atom, which is consistent with recent high-resolution transmission electron microscopy experiments on MgO/Ag(100). For that site, electron density distributions in the metal surface regions are reminiscent of a charge array imaging only the surface Mg and O ions. This implies a substantial ionic component to the adhesive bond. The screening charge distributions appear smoother in the A1 case than in the Ag case, suggesting a direct role of the Ag d electrons in the screening. Despite the ionic contribution to the bonding, the adhesive energy versus interfacial separation curves obey the same, universal form originally discovered for bimetallic adhesion. This could be explained by a significant metallic and/or covalent contribution to the metal/ceramic bonds. Furt...

Elastic equilibrium of curved thin films.

Abstract: We present a unified theory of the bending of crystalline films that accounts for both elastic effects and crystal defects. Our theory predicts a transition from a bent coherent film with no dislocations to an incoherent, dislocated one as the film thickness or curvature is increased. The presence of the dislocations serves to renormalize the bending modulus of the system to smaller values. The degree to which the dislocations relax the elastic bending energy is found by calculating the equilibrium dislocation density and bending energy as a function of elastic constants, curvature, and film thickness. We demonstrate that at critical values of the curvature or thickness, there is a second-order phase transition between the undislocated and dislocated film. Generalizing these results to anisotropic elastic systems shows that weak bonding between crystal planes (such as in graphite) leads to a significant decrease in the critical curvature or thickness. An analysis of the case where the relaxation of the bending energy occurs by the formation of grain boundaries is also presented. We find that the introduction of grain boundaries can relieve the energy of the curved crystal more effectively than can the introduction of a uniform array of dislocations. Nonetheless, dislocation formation may be the dominant relaxation mechanism for very thin films (thin compared to the dislocation spacing in the grain boundary) and/or when dislocation migration kinetics are slow. Examples based upon nested fullerenes and bilayer surfactants are discussed.

Adhesion at a heterophase interface: First-principles study of Mo(001)/MoSi2(001)

Abstract: The bonding characteristics, interfacial energetics, and electronic structure associated with adhesion at the Mo-MoSi2(001) heterophase interface are investigated using the first-principles, self-consistent local orbital method. We found both the adhesive energy and peak interfacial strength for the interface to be 10%-15% smaller than the respective values for cleavage along the (001) planes in crystalline Mo and MoSi2. The equilibrium interlayer separation between Mo and MoSi2 is found to lie between the interplanar spacings of crystalline Mo and MoSi2. The interfacial adhesive bonding is attributable to the combination of a nearly uniform band of charge accumulation at the interface and directional charge accumulation between atoms across the interface. These first-principles calculations demonstrate that the universal-binding-energy relation can be extended to describe adhesion between dissimilar materials.

Shape of hollow dislocation cores

Abstract: Dislocations with large Burgers vectors have hollow dislocation cores in crystals with large elastic constants and low surface energies. We analyse the shape of the hollow core and find that it is influenced by anisotropy in both surface energy and elastic constants. Faceted shapes tend to be rotated relative to the Gibbs-Wulff shapes. Analogous results should apply for internal precipitates on dislocations.

Statistical mechanical-atomistic determination of vacancy formation free energies in Cu-Ni alloys

Abstract: Atomistic and statistical mechanical methods are combined to determine the vacancy formation free energy in binary solid solutions. The first-shell grey model is based on the assumption that all the atoms are effective or mean-field atoms, but with the concentration of the first shell different from the bulk. Comparison of the vacancy formation free energy and the average local concentration profile around the vacancy obtained from the first-shell grey model and the more accurate but much less computationally efficient first-shell black-white model (where the mean-field approximation is not used) suggest that only the composition of the first atomic shell adjacent to the vacancy must be determined. The temperature dependence of the vacancy formation free energy for a Cu-Ni system can be efficiently determined using the first-shell grey atom approximation. Our results show that the vacancy has a strong tendency to form in Cu-rich regions of the Cu-Ni alloy at low temperatures and low Cu bulk conce...

Simulation of Grain Growth During Directional Annealing

Abstract: A Monte Carlo simulation procedure is applied to simulate non-uniform grain growth during directional annealing. The assumed temperature profile consists of a small, finite size hot zone which blends smoothly into cold zones ahead and behind the hot zone. The hot zone is assumed to move with a constant velocity. The influence of the ratio of hot zone to cold zone temperatures and the velocity of the temperature field are investigated. The grain size is analyzed as a function of these variables. We find that very high aspect ratio grains (long axis parallel to the thermal field velocity vector) are possible within a restricted velocity window. These results are analyzed in terms of an analytic model based upon conventional grain growth laws.

The effect of surface relaxation and atomic vibration on the equilibrium shape of gold and copper crystallites

Abstract: The free energy of surfaces along the pole in gold and copper is determined to assess the effect of surface relaxation and atomic vibration on the equilibrium crystal shape of gold and copper. The Wulff construction is performed on the γ-plots to determine the equilibrium shape of gold and copper crystallites at different temperatures. It is shown that surface relaxation and atomic vibration do not have any discernible effect on the equilibrium shape of EAM gold or copper crystallites. The equilibrium shape of EAM gold crystallites is formed entirely from {111} and {100} facets, while that of EAM copper shows small {110} facets in addition to the {111} and {100} facets.

Simulation of dynamic fracture of an impact-loaded brittle solid

Abstract: A new model for simulating dynamic fracture in impact-loaded solids is presented. This model is based upon the traditional molecular dynamics procedure, but accounts for the irreversible nature of the fracture process by deleting the attractive part of the particle interaction potential when the bond between two particles is stretched beyond a critical length. This critical length is determined by comparison with Griffith theory. In the present paper, the model is applied to a two-dimensional homogeneous solid in the absence of microstructure (microstructural effects are treated in a subsequent publication). When the impact zone is much smaller man the size of the sample, or the impact zone is wide and the impact amplitude is large, the first crack forms a finite distance ahead of the impact zone. Static continuum elasticity theory shows that the position of this first crack occurs at the position of the maximum tensile stress. This crack then propagates back to the edges of the impact zone and forward into the sample, thereby creating an X-shaped crack pattern. The tips of the X-shaped crack propagate more slowly than the stress wave and hence strong deviations from this pattern are observed when the stress wave passes the crack tips. When the predominantly compressive stress wave reflects off the back free surface, a tensile wave propagates back into the sample creating even more damage. This damage occurs in bands parallel to and set back from the back surface.

Simulation of Segregation to Interfaces in Metal-Oxides

Abstract: Segregation of isovalent cation impurities to (001) and (011) free surfaces in (Co0.3Ni0.7)O and (Fe0.12Mn0.88)O was investigated using atomistic computer simulations. Impurity concentrations were represented by a mean-field approximation, and equilibrium distributions of impurities were calculated by minimization of the free energy. Surface energy effects were found to dominate segregation behavior, even when in competition with misfit strain energy effects. These Free Energy method predictions compared well with more accurate Monte Carlo simulations, suggesting that the mean-field representation of impurity concentration is satisfactory for this application.

Thermal Misfit and Thermal Fatigue Induced Damage in Brittle Composites

Abstract: We examine the conditions under which differences in thermal expansion between a particle and the matrix leads to crack growth within the matrix Using linear elastic fracture mechanics, we obtain closed-form, analytical results for the case of a penny shaped crack present in the matrix interacting with a spherical inclusion which is misfitting with respect to the matrix A simple and direct relationship is established between the strain energy release rate, the crack size, the crack orientation with respect to the inclusion, the crack/inclusion separation, the degree of thermal expansion mismatch and the elastic properties of the medium We also analyze the size to which these cracks can grow and find that for a given misfit strain and material properties, crack growth is inhibited beyond a certain critical crack size Finally, the preferred orientation of these cracks as a function of misfit strain is predicted The implication of these results for thermal cycling are analyzed

Effects of Impurities on Bonding: Application to the Mo/MoSi2 Interface

Abstract: The role of impurities in adhesion at a metal/intermetallic interface is determined from first principles. Electron density distributions, total energies, and forces as a function of interfacial spacing are reported for the Mo/MoSi2 interface. All impurities investigated at the monolayer level caused a decrease in adhesive energies. The decreases were substantial, being as large as a factor of 2 for S. On the other hand, C and O were found to substantially increase the peak interfacial strength. A linear relationship between interfacial spacing and impurity covalent radii was found. Impurity changes in bonding were mirrored by changes in electron density distributions.