Fracture Mechanics Applied to Grinding, Polishing, Adhesion and Slitting
Microscopic deformation within a material determines if the solid is brittle or ductile on a macroscopic level. Crack tip shielding for the brittle-to-ductile transition on a microlevel was started at Rochester and is still studied as there is little understanding of this transition in mechanical behavior. Microstructural fracture mechanics is applied to ceramics, polymers, glasses and metals to achieve high fracture toughness. Adhesion mechanics for AFMs, nanoindenters, and macroscopic systems are analyzed for stability. Cutting and slitting mechanics are generally unstable and always give rough surfaces. Controlling cutting stability is a technological challenge for which some progress has been made.
The constitutive relationship between stress, temperature and strain-rate is called kinetics. Reaction kinetics near a glass transition temperature, Tg involve simultaneous deformation events on an atomic scale; these double events in turn control deformation. In materials that have amorphous or glassy structures, plastic flow and dimensional stability are achieved via non-newtonian kinetics. Kinetics near Tg, are investigated and measured in polymer films. Deformation kinetics are also used to study slow crack propagation.
Thermodynamic Energy Balances in Linear Systems
The assumption that a material is linear in stress vs. strain is widely used in elastic analysis; linear dielectric materials are also generally assumed in electrostatic and electrodynamic systems. These relations are generally isothermal and the elastic constants are temperature dependent. Similarly, the dielectric constants are also dependent on temperature. It has been shown that all isothermal linear materials have a higher order term if the processes follow adiabaticic equations of state. The adiabatic term comes from the temperature dependence of the linear relationship. In the case of a linear capacitor filled with water, the heat term is 40% larger than the electric field energy in the capacitor.
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