Stability analysis of a nanopatterned bimaterial interface

In the article it is shown that the nanopatterned interface of bimaterial is unstable due to the diffusion atom flux along the interface. The main goal of the research is to analyze the conditions of interface stability. The authors developed a model coupling thermodynamics and solid mechanics frameworks. In accordance with the Gurtin—Murdoch theory of surface/interface elasticity, the interphase between two materials is considered as a negligibly thin layer with the elastic properties differing from those of the bulk materials. The growth rate of interface roughness depends on the variation of the chemical potential at the curved interface, which is a function of interface and bulk stresses. The stress distribution along the interface is found from the solution of plane elasticity problem taking into account plane strain conditions. Following this, the linearized evolution equation is derived, which describes the amplitude change of interface perturbation with time.

Analytical Solution for the Circular Orifice Problem with Four-Cracks

Using the method of complex analysis, the paper investigates the plane elasticity problem of circular orifices with four-cracks through conformal mapping, and provides an exact analytical solution for the crack-tip stress intensity factor (SIF). From this we have simulated circular orifices with three-cracks, symmetrical four-cracks, asymmetrical collinear double-cracks, and symmetrical collinear double-cracks; as well as the crack problems of asymmetrical cross-shaped cracks, symmetrical cross-shaped cracks, and T-shaped cracks.

An Exact Analytical Solution for Star-Shaped Cracks

Using the method of complex analysis and by constructing conformal mapping, the study investigates the plane elasticity problem of star-shaped cracks and provides an analytical solution for the stress intensity factor (SIF) of crack-tip type I and II. Problems of the classic Griffith crack, the cross-shaped crack, concurrent uniformly distributed three-cracks and symmetrical eight-cracks are also simulated.