Study of size effects in thin films by means of a crystal plasticity theory based on DiFT

In a recent publication, we derived the mesoscale continuum theory of plasticity for multiple-slip systems of parallel edge dislocations, motivated by the statistical-based nonlocal continuum crystal plasticity theory for single-glide due to Yefimov et al. (2004b). In this dislocation field theory (DiFT) the transport equations for both the total dislocation densities and geometrically necessary dislocation densities on each slip system were obtained from the Peach-Koehler interactions through both single and pair dislocation correlations. The effect of pair correlation interactions manifested itself in the form of a back stress in addition to the external shear and the self-consistent internal stress. We here present the study of size effects in single crystalline thin films with symmetric double slip using the novel continuum theory. Two boundary value problems are analyzed: (1) stress relaxation in thin films on substrates subject to thermal loading, and (2) simple shear in constrained films. In these problems, earlier discrete dislocation simulations had shown that size effects are born out of layers of dislocations developing near constrained interfaces. These boundary layers depend on slip orientations and applied loading but are insensitive to the film thickness. We investigate stress response to changes in controlled parameters in both problems. Comparisons with previous discrete dislocation simulations are discussed.Comment: 20 pages, 11 figure

A fatigue crack initiation model incorporating discrete dislocation plasticity and surface roughness

Although a thorough understanding of fatigue crack initiation is lacking, experiments have shown that the evolution of distinct dislocation distributions and surface roughness are key ingredients. In the present study we introduce a computational framework that ties together dislocation dynamics, the fields due to crystallographic surface steps and cohesive surfaces to model near-atomic separation leading to fracture. Cyclic tension–compression simulations are carried out where a single plastically deforming grain at a free surface is surrounded by elastic material. While initially, the cycle-by-cycle maximum cohesive opening increases slowly, the growth rate at some instant increases rapidly, leading to fatigue crack initiation at the free surface and subsequent growth into the crystal. This study also sheds light on random local microstructural events which lead to premature fatigue crack initiation

Micromechanics of creep fracture: simulation of intergranular crack growth

A computational model is presented to analyze intergranular creep crack growth in a polycrystalline aggregate in a discrete manner and based directly on the underlying physical micromechanisms. A crack tip process zone is used in which grains and their grain boundaries are represented discretely, while the surrounding undamaged material is described as a continuum. The constitutive description of the grain boundaries accounts for the relevant physical mechanisms, i.e. viscous grain boundary sliding, the nucleation and growth of grain boundary cavities, and microcracking by the coalescence of cavities. Discrete propagation of the main crack occurs by linking up of neighbouring facet microcracks. Assuming small-scale damage conditions, the model is used to simulate the initial stages of crack growth under C* controlled, model I loading conditions. Initially sharp or blunted cracks are considered. The emphasis in this study is on the effect of the grain microstructure on crack growth.

Relaxation of thermal stress by dislocation motion in passivated metal interconnects

The development and relaxation of stress in metal interconnects strained by their surroundings (substrate and passivation layers) is predicted by a discrete dislocation analysis. The model is based on a two-dimensional plane strain formulation, with deformation fully constrained in the line direction. Plastic deformation occurs by glide of edge dislocations on three slip systems in the single crystal line. The substrate and passivation layers are treated as elastic materials, and therefore impenetrable for the dislocations. Results of the simulations show the dependence of the stress evolution and of the effectiveness of plastic relaxation on the geometry of the line. The dependence of stress development on line aspect ratio, line size, slip plane orientation, pitch length and passivation layer thickness are explored.

A continuum framework for grain boundary diffusion in thin film/substrate systems

A two-dimensional continuum model is developed for stress relaxation in thin films through grain boundary (GB) diffusion. When a thin film with columnar grains is subjected to thermal stress, stress gradients along the GBs are relaxed by diffusion of material from the film surface into the GBs. The transported material constitutes a wedge and becomes the source of stress inside the adjacent elastic grains that are perfectly bonded to the substrate. In the model, the coupling between diffusion and elasticity is obtained by numerically solving the governing equations in a staggered manner. A finite difference scheme is used to solve the diffusion equations, modified in order to implement realistic boundary conditions, while the elasticity problem is solved with the finite element method. The solutions reveal the existence of a universal power law scaling between the unrelaxed fraction of stress and the grain aspect ratio. For slender grains, the GB wedge attains a more uniform shape and relaxation is more effective. The kinetics of the process depends not only on the grain aspect ratio but also strongly on the thickness of the film. In case there is no adhesion between film and substrate, complete stress relaxation is attained albeit at a slightly slower rate. © 2010 American Institute of Physics