Foundation of a Mechano-Chemical Fatigue Theory (MCFT)

摘要

A theory which identifies the chemical reaction between a broken molecule and its neighbor as the main micro-scale source of fatigue failure is developed. By applying statistical laws, the macro-behavior of the material is revealed. Three types of macro damage accumulation functions emerge, as a direct result of different values of the micro-scale parameters. The reference type shows secondary and tertiary stages, the second type includes an additional primary stage, and the third type, leading to a material with a specific endurance limit, has only a primary stage. An empirical power-law relationship between the stress level and the number of cycles to failure is obtained analytically by the theory for the reference type of damage, when a Weibull strength distribution function for the molecules is used. Three microscopic material parameters control the macro-behavior: (1) a statistical shape parameter, describing the strength distribution of the molecular chains; (2) a stress concentration factor, which describes the amount of weakening a broken chain can cause to its neighbor; and (3) a probability function for a chemical reaction to occur. The micro-scale roots of the theory enables the use of physical internal variables for the damage evolution equations. Thus, a clear interpretation of the macro-fatigue response, including the existence of an endurance limit is achieved. Experimental correlations with available fatigue data for different materials, including metals, plastics and composites, show the general validity of the theory, not only for polymeric interfaces. This is due to the mechano-chemical mechanism, on which the theory is based. The mathematical similarity of the basic equations to the ones found in chaotic theories is demonstrated and discussed briefly.