Hydrostatic stress

About: Hydrostatic stress is a research topic. Over the lifetime, 1568 publications have been published within this topic receiving 37773 citations.

Simple Shearing of Incompressible and Slightly Compressible Isotropic Nonlinearly Elastic Materials

Abstract: The classical problem of simple shear in nonlinear elasticity has played an important role as a basic pilot problem involving a homogeneous deformation that is rich enough to illustrate several key features of the nonlinear theory, most notably the presence of normal stress effects. Here our focus is on certain ambiguities in the formulation of simple shear arising from the determination of the arbitrary hydrostatic pressure term in the normal stresses for the case of an incompressible isotropic hyperelastic material. A new formulation in terms of the principal stretches is given. An alternative approach to the determination of the hydrostatic pressure is proposed here: it will be required that the stress distribution for a perfectly incompressible material be the same as that for a slightly compressible counterpart. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. For the particular case of a neo-Hookean material, the different stress distributions are compared and contrasted.

Numerical simulation of the effects of residual stress on the concentration of hydrogen around a crack tip

Abstract: For this study we used finite element analysis to show how the residual stress affects the hydrogen concentration around a crack tip in a plastically deformable material after a fatigue process. Following a 9 cycle fatigue process, hydrogen diffusion analysis was carried out at the highest applied fatigue stress. This showed hydrogen invading the crack surface and diffusing into the material. The concentration of hydrogen was higher close to the crack tip and its behavior was largely affected by the residual stress in the material. Tensile residual stress accelerated the hydrogen invasion and increased its concentration, while compressive residual stress simulated as the stress induced by peening clearly suppressed them. This is due to the affect the residual stress has on the hydrostatic stress around the crack tip which is a dominant factor in the hydrogen diffusion behavior. Peening, which is a surface treatment used to introduce compressive residual stress to enhance the mechanical properties of a material, such as its resistance to stress corrosion cracking and its fatigue strength, may, therefore, suppress the embrittlement caused by hydrogen.

The effects of stress and fluid pressure on the anisotropy of interconnected cracks

Abstract: SUMMARY The cracks in a porous matrix that is subjected to a change in the applied stress or fluid pressure will undergo a distortion related to their orientation relative to the principal directions of the applied stress. Both the crack distribution and the fluid-flow properties of the aggregate will be altered as a consequence, of a change in either the applied stress or fluid pressure, resulting in a change in the effective elastic parameters of the material. An effective medium theory, based on the method of smoothing and incorporating a transfer of fluid between connected cracks via non-compliant pores, is used to derive an expression for the effective elastic parameters of the material, to first order in the crack density � . This expression involves a dependence on both the applied stress and the fluid pressure, and is used to determine the effects on the anisotropy of the effective medium of the applied stress and the fluid pressure. A number of azimuthally symmetric compressive stresses are applied to an isotropic crack distribution to determine the material properties of the resulting transversely isotropic effective medium, as a function of the excess in compressive stress over fluid pressure. As a result of competing processes, the theory predicts that, for a non-hydrostatic stress, there is a pressure at which the anisotropy reaches a maximum value before the properties of the effective medium decay, under increasing stress, to those of the uncracked matrix. The theory does not, however, account for the material failure that will occur at large compressive stresses. Finally, the theory predicts that S waves are more sensitive to changes in the applied stress or fluid pressure than P waves.

Numerical simulation of stress evolution during electromigration in IC interconnect lines

Abstract: A finite element simulation of stress evolution in thin metal film during electromigration is reported in this paper. The electromigration process is modeled by a coupled diffusion- mechanical partial differential equations (PDEs). The PDEs are implemented with a plane strain formulation and numerically solved with the finite element (FE) method. The evolutions of hydrostatic stress, each component of the deviatoric stress tensor, and Von Mises' stress were simulated for several cases with different line lengths and current densities. Two types of displacement boundary conditions are considered. The simulation results are compared with Korhonen's analytical model and Black and Blech's experimentalesults.