Stress Phase Angle Research Articles

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery.

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.

Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks

New domain integrals for extracting mixed-mode stress intensity factors along curved, three-dimensional bimaterial interface cracks are derived. In the derivation, the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front. The general crack-tip interaction integral (a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip) is then expressed in domain form which is more suitable for numerical computation. A consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium, and the auxiliary strain fields do not satisfy compatibility. The terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack-tip interaction integral or to affect its path independence; however, these terms become important when domain integral representations are introduced, because they involve fields which are not asymptotically close to the crack tip. In order to compute the pointwise stress intensity factors along the crack front, the domain integrals are evaluated as a post-processing step in the finite element method. In the numerical results, it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields, especially in regions where the local crack front curvature is high. In the paper, we present two numerical examples. As a benchmark, we first consider the problem of a penny-shaped interface crack embedded in a cylinder. The results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution. The problem of an elliptical crack embedded between two dissimilar isotropic materials is also considered, and the results are discussed.

Finite element analysis of a thermally loaded interface crack in a ceramic coating

The finite element method is used to model the thermally induced stresses in an interface crack between a ceramic coating and a metallic substrate. This analysis uses finite heat transfer across the crack flanks, and the results indicate that modeling of the heat transfer across the crack faces is important to the evaluation of stresses near the crack tip. The complex stress intensity factor magnitude and phase angle were determined using several techniques, including the local collocation technique, all of which were found to be in reasonable agreement. The results show that the local collocation technique can be used successfully in the evaluation of stress intensity factors of bimaterial interface cracks.

A Combined Analysis of Moisture Diffusion with Interface Fracture Mechanics on the Interface Delamination in the Plastic IC Packages During Reflow Soldering

ABSTRACTThe popcorn cracking phenomenon of plastic IC packages during the reflow soldering was investigated by conducting the stress analysis of heat transfer and moisture diffusion. Vapor pressures at delaminated interfaces between the die pad and EMC(Epoxy molding compound) were calculated and mechanistic parameters such as energy release rate, stress intensity factor and phase angle were derived under various loading conditions; thermal, crack face vapor pressure and mixed loadings. It was shown that thermal loading was the main driving force for crack propagation for small cracks lengths, but vapor pressure loading played more significant role as the crack extended.

A crack at the interface between a Kane-Mindlin plate and a rigid substrate

The interface fracture of an elastic plate bonded to a rigid substrate is studied using Kane and Mindlin's kinematic assumptions for the quasi-three-dimensional (3-D) deformations of plates deformed in stretching. The stresses and deformations are computed for a semi-infinite plate perfectly bonded to a rigid substrate and subjected to uniform in-plane normal tractions at infinity. These agree well with those obtained from the 3-D elasticity theory when the latter are averaged over the plate thickness. The Kane-Mindlin theory predicts a boundary layer adherent to the interface between the plate and the substrate and its thickness approximately equals the plate thickness. An interface crack between the elastic plate and the rigid substrate is investigated. The crack front average stress fields consist of a plane strain (not plane stress) oscillatory singular field and an antiplane shear inverse-square-root singular field, and the three fracture modes are coupled. These agree with the existing 3-D finite element results. The effect of the plate thickness on stress intensity factors and phase angles is studied. The antiplane shear stress intensity factor approaches zero for a vanishingly thin plate, but cannot be ignored otherwise. A path-independent integral including the thickness effects is deduced and is used to establish a fracture criterion for thin plates. Finally, the interface fracture criterion is discussed within the framework of the Kane-Mindlin theory.