Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

A theoretical analysis on stochastic behaviour of short cracks and fatigue damage of metals

In this paper, the closed form of solution to the stochastic differential equation for a fatigue crack evolution system is derived. and the relationship between metal fatigue damage and crack stochastic behaviour is investigated. It is found that the damage extent of metals is independent of crack stochastic behaviour ii the stochastic deviation of the crack growth rate is directly proportional to its mean value. The evolution of stochastic deviation of metal fatigue damage in the stage close to the transition point between short and long crack regimes is also discussed.

A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

Study on growth mechanism of low-temperature prepared microcrystalline Si thin films

Microcrystalline silicon thin films at different growth stages were prepared by hot wire chemical vapor deposition. Atomic force microscopy has been applied to investigate the evolution of surface topography of these films. According to the fractal analysis I it was found that, the growth of Si film deposited on glass substrate is the zero-diffused stochastic deposition; while for the film on Si substrate, it is the finite diffused deposition on the initial growth stage, and transforms to the zero-diffused stochastic deposition when the film thickness reaches a certain value. The film thickness dependence of island density shows that a maximum of island density appears at the critical film thickness for both substrates. The data of Raman spectra approve that, on the glass substrate, the a-Si: H/mu c-Si:H transition is related to the critical film thickness. Different substrate materials directly affect the surface diffusion ability of radicals, resulting in the difference of growth modes on the earlier growth stage.