Nonequilibrium Statistical Modeling of Fatigue Crack Growth Behaviour

In order to study the influence of microstructural texture on the growth of short fatigue cracks in metals, the nonequilibrium statistical theory of fatigue fracture correlating a microscopic mechanism with the macroscopic properties is modified to take into consideration the microstructural features of a material, thereby allowing a rationalisation of the experimental data of short fatigue crack growth and long fatigue crack growth. The nonequilibrium statistical theory thus developed relates the growth of cracks with a dislocation mechanism to simulate short fatigue crack growth with the long fatigue crack growth behaviour and predicts the fatigue crack growth rates throughout the fatigue lifetime. The results is finally compared with that of other fatigue theories.

Nonequilibrium Statistical Theory of Fracture

Nonequilibrium statistical theory of fracture is a theory of fracture that macromechanical quantities can be derived from the microscopic atomic mechanism of microcrack(or microvoid)evolution kinetcs by means of nonequilibrium statistical physical concepts and methods. The microcrack evolution equation is the central equation in the theory.The coefficents of the equation, the microcrack growth rate and the microcrack nucleation rate,come from microscopic atomic mechanism.The solution of the equation connects with macromechanical quantities by the model of the weakest chain. All the other formulas and quantities, for instance, distribution function,fracture probability, reliability, failure rate and macromechanical quantities such as strength, toughness, life etc. and their statistical distribution function and statistical fluctuation are derived in a unified fashion and expressed by a few physical parameters. This theory can be widely applied to various kinds of fracture, such as the brittle, fatigue, delayed and environmental fracture of metals and structural ceramics. The theoretical framework of this theory is given in this paper.

Effective diffusion of a tracer in active bath:A path-integral approach

We investigate the effective diffusion of a tracer immersed in an active particle bath consisting of self-propelled particles.Utilising the Dean's method developed for the equilibrium bath and extending it to the nonequilibrium situation,we derive a generalized Langevin equation(GLE)for the tracer particle.The complex interactions between the tracer and bath particles are shown as a memory kernel term and two colored noise terms.To obtain the effective diffusivity of the tracer,we use path integral technique to calculate all necessary correlation functions.Calculations show the effective diffusion decreases with the persistent time of active force,and has rich behavior with the number density of bath particles,depending on different activities.All theoretical results regarding the dependence of such diffusivity on bath parameters have been confirmed by direct computer simulation.

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochas- tic differential equation （SDE） into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the a-type interpretation for multi- dimensional systems. The potential landscape serves as a Hmniltonian-like function in nonequilibrimn processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel frame- work. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.

Phonon Excitation and Energy Redistribution in Phonon Space for Energy Dissipation and Transport in Lattice Structure with Nonlinear Dispersion

We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics （MD） simulations. Locally dominant phonon modes （k-space） are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k（x, t） are critical to the concept of the local thermodynamic equilibrium （LTE）. Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes （k-space）. This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution （or frequency content） of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems. Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode （k = O） is excited first and gradually expanding to the highest mode （km^（x,t））, where km^（x,t） can only asymptotically approach the maximum mode kB of the first Brillouin zone （kmax（x,t） --~ kB）. NO energy distributed into modes with k_max（x,t） 〈 k 〈 k^B demonstrates that the local thermodynamic equilibrium cannot be established in harmonic chain. Energy is shown to be uniformly distributed in all available phonon modes k ≤ _max（x, t） at any position with heat transfer along the harmonic chain. The energy flux along the chain is shown to be a constant with time and proportional to the sound speed （ballistic transport）. Comparison with the Fourier＇s law leads to a time-dependent thermal conductivity that diverges with time.