This project comprises three parts. In Part 1, the objective is to develop a group-theoretic method by which explicit expressions that delineate the effects of crystallographic texture on material tensors of weakly-textured polycrystalline materials can be derived systematically. A representation theorem is proved that reduces the problem to that of finding irreducible tensor bases of the rotation group. A method is developed to generate irreducible tensor bases for a given tensor space. The method delivers representation formulas at once applicable to all texture and crystal symmetries. Specific instances important for applications in acoustoelasticity and plasticity are fully worked out. Part 2 concerns nondestructive inspection of subsurface residual stress by ultrasonic measurements. The material body in question is modeled as a vertically heterogeneous, prestressed, anisotropic half-space. An extension of the Stroh formalism is developed to relate the dispersion of the Rayleigh wave to the vertical heterogeneity of stress and/or texture. In Part 3 a phenomenological theory is developed for the interpretation of resonance shifts and line shapes in ultrasound resonance spectroscopy of sheet metals. The sheet metal in question is modeled as a textured, largely elastic material with a small power-law viscosity. An attempt is made to draw information on resonance shifts, line shapes, and frequency dependence of attenuation through analysis of the basic initial-boundary-value problem.
The crystal grains that constitute polycrystalline materials (e.g., wrought and cast metallic alloys) often carry preferred orientations (or crystallographic texture) that strongly affect mechanical behavior of the aggregate material (e.g., the formability of sheet metals). Part 1 of this project delivers formulas that describe quantitatively how crystallographic texture affects the behavior of a polycrystalline material in elastic and plastic deformations. Part 2 arises from the industrial need for a nondestructive measurement technique that allows monitoring of the retention of subsurface residual stress induced by surface conditioning treatments on metal parts for lifetime enhancement against fatigue failure and stress corrosion cracking. The availability of such nondestructive technique also allows emerging surface-enhancement technologies (e.g., laser-peening, low plasticity burnishing) to be more cost effective and improves quality control of surface conditioning processes. Part 3 helps lay the mathematical foundations for the development of an ultrasonic technique for monitoring of texture and material microstructures in sheet metals (and hence of their formability) on the production line.
