| The present dissertation summarizes the results of research and development for elastic-plastic deformation of metals by nonlinear stress waves. The focus of the present work is the development of a new theoretical and numerical framework to simulate nonlinear stress waves in solids. The application of the new method focuses on modeling the plateau stage of a novel ultrasound welding process. Superimposed by ultrasonic vibrations, metal specimens under static loading experience remarkable transitory softening, which has been called the Blaha effect or the Acousto-Plastic Effect (APE). Previous microscopy studies showed that the metals experience significant plastic deformation and the morphology resembles the Kelvin-Helmholtz instability waves in the presence of shear stresses. The present research addresses the need to understand the APE beyond phenomenological descriptions in the literature. Theoretical and numerical studies have been performed to understand the unusual metal deformation induced by ultrasonic vibrations.;A comprehensive continuum mechanics model for macroscopic description of nonlinear stress waves in solids has been developed, including conservation laws of mass, momentum, and energy in the Eulerian frame, in conjunction with a set of transport equations for stress components, which have been derived based on the elastic-plastic constitutive relation employed. The present approach aims to directly address the dynamic nature of the processes rather than treating transitory metal softening by proposing "effective constitutive relations" to relate the nominal "static stress" to the nominal "static strain." A hierarchy of theoretical model equations have been systematic developed, including (i) one-dimensional isothermal elastic model for longitudinal extensional waves in a thin rod, (ii) one-dimensional isothermal elastic model for longitudinal plane waves in a bulk material, (iii) one-dimensional isothermal elastic model for shear waves in a bulk material, (iv) one-dimensional elastic-plastic model for longitudinal plane waves in a bulk material with and without considering the thermal effect, and (v) two-dimensional elastic-plastic model for coplanar waves in solids with and without considering the thermal effect. Various forms of the governing equations have been systematically derived, including the conservation form, the non-conservative form, and the characteristic form. The eigensystem of each set of model equations has been analyzed in details with clear presentation of the analytical forms of eigenvalues and the associated eigenvector matrices. As a part of the eigenvalues, the speed of sound for various wave phenomena can be clearly discerned. (Abstract shortened by UMI.)... |
