Hysteresis and Fatigue

Abstract

Fatigue in materials is the result of cumulative damage processes that are usually induced be repeated loading cycles. Since the energy dissipation associated with damage is irreversible, and the loading cycles are accompanied by the evolution of heat, the corresponding relation between stress and strain is not single-valued; but rather exhibits a memory dependence, or hysteresis. Conversely, sustained hysteresis is a necessary condition for fatigue and is related to the rate of damage accumulation. Engineering design and safety standards for estimating fatigue life are based in part on the Manson-Coffin relations between the width of stress-strain hysteresis loops and the number of loading cycles required to produce failure in test pieces. Experimental and theoretical results show that this relation can be extended into a simple phenomenological description of fatigue that directly links total hysteresis energy dissipation, the cumulation of material damage, and the average number of loading cycles leading to failure. Detailed features of the hysteresis can be understood with the help of analogies between the incremental collapse of structures and the inception and organization of damage in materials. In particular, scanning tunneling microscope measurements of the threshold of mechanical irreversibility and acoustic emission patterns may be used to check on the evolution of hysteresis at the microscopic level.