Theory of fatigue based on statistical distribution of grain size

A theory of fatigue behavior is developed based on the failure of the grains as the basic structural components of a metal. Briefly, the failure is described to initiate at the larger or weaker grains in which disruption by slip occurs. With further repeated loading, microscopic cracks nucleating at the disrupted grains and propagating throughout the member are presented as the mechanism of fatigue failure. Slip and subsequent microscopic crack initiation is based on Bragg’s Hypothesis which expresses the elastic strength of a grain as an inverse function of the mean free path for slip. Confining the analysis to a single-phase metal, the mean free path for slip is taken equal to the grain size, for the grain boundaries inhibit slip. Using a log-normal distribution of grain size and the mean free path for slip equal to the grain size, a mathematical correlation between the strength of the metal and its structure is established. Assuming as a first approximation that the fatigue life varies inversely with the number of microscopic cracks initiated, the role of microscopic crack initiation in influencing the fatigue life is determined. The influence of rate of propagation of the microscopic cracks on the fatigue life is expressed empirically from past experimental data by assuming a linear relationship between the relative stress level and the logarithm of the number of cycles from microscopic crack initiation to final failure. The interaction of crack initiation and rate of crack propagation is then given mathematical expression as an equation for the fatigue life. According to the theory developed, the fatigue strength and fatigue life of a single-phase metal is increased by: (a) decreasing the mean grain size, (b) making the material more uniform in grain size distribution, and (c) decreasing the volume of material subjected to stresses above a given reference stress. Finally, scatter of fatigue life and size-effect in fatigue specimens are explained qualitatively on the basis on the basis of the heterogeneity of the material that results in a wide variation in microscopic cracks initiating on the planes of failure.Office of Naval Research, U. S. Navy, Contract N6-ori-71, Task Order IV; Project NR-031-00