Crack tip stress study for elastic-perfectly plastic materials with some applications

The problems of plasticity and non-linear fracture mechanics have been generally recognized as the most difficult problems of solid mechanics. The present dissertation is devoted to some problems on the intersection of both plasticity and non-linear fracture mechanics. The crack tip is responsible for the crack growth and therefore is the focus of fracture science. The problem of crack has been studied by an army of outstanding scholars and engineers in this century, but has not, as yet, been solved for many important practical situations. The aim of this investigation is to provide an analytical solution to the problem of plasticity at the crack tip for elastic-perfectly plastic materials and to apply the solution to a classical problem of the mechanics of composite materials.^ In this work, the stresses inside the plastic region near the crack tip in a composite material made of two different elastic-perfectly plastic materials are studied. The problems of an interface crack, a crack impinging an interface at the right angle and at arbitrary angles are examined. The constituent materials are assumed to obey the Huber-Mises yielding condition criterion. The theory of slip lines for plane strain is utilized. For the particular homogeneous case these problems have two solutions: the continuous solution found earlier by Prandtl and modified by Hill and Sokolovsky, and the discontinuous solution found later by Cherepanov. The same type of solutions were discovered in the inhomogeneous problems of the present study. Some reasons to prefer the discontinuous solution are provided. The method is also applied to the analysis of a contact problem and a push-in/pull-out problem to determine the critical load for plasticity in these classical problems of the mechanics of composite materials.^ The results of this dissertation published in three journal articles (two of which are under revision) will also be presented in the Invited Lecture at the 7$\rm\sp{th}$ International Conference on Plasticity (Cancun, Mexico, January 1999). ^

The study of thermal stresses in a single long elastic fiber embedded in an infinite matrix

This work considered the micro-mechanical behavior of a long fiber embedded in an infinite matrix. Using the theory of elasticity, the idea of boundary layer and some simplifying assumptions, an approximate analytical solution was obtained for the normal and shear stresses along the fiber. The analytical solution to the problem was found for the case when the length of the embedded fiber is much greater than its radius, and the Young's modulus of the matrix was much less than that of the fiber. The analytical solution was then compared with a numerical solution based on Finite Element Analysis (FEA) using ANSYS. The numerical results showed the same qualitative behavior of the analytical solution, serving as a validation tool against lack of experimental results. In general this work provides a simple method to determine the thermal stresses along the fiber embedded in a matrix, which is the foundation for a better understanding of the interaction between the fiber and matrix in the case of the classical problem of thermal-stresses.

Optimization of three-dimensional branching networks of microchannels for thermal management of microelectronics

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. A conjugate heat transfer analysis software package and an automatic 3D microchannel network generator were developed and coupled with a modified version of a particle-swarm optimization algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow passages. Numerical algorithms in the conjugate heat transfer solution package include a quasi-ID thermo-fluid solver and a steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. Pareto-optimal solutions demonstrate that thermal loads of up to 500 W/cm2 can be managed with 3D microchannel networks, with pumping power requirements up to 50% lower with respect to currently used high-performance cooling technologies.