Theoretical study on Manson-Coffin equation for physically short cracks and lifetime prediction

The Manson-Coffin equation has been widely applied to the prediction of fatigue lifetime. But this equation does not explicitly express the relation between the fatigue lifetime and the crack length. The present paper proposes that the grain size can be replaced by the maximum non-damaging crack length. Thus, the growth rate will decrease to zero when the crack reaches this size. Combining with the theory of the fatigue short crack propagation, we derived the relations between physically short crack’s initiation-propagation rates and material’s mechanical properties, as well as crack length, stress and strain. With the derived relations, fatigue lifetime of short cracks can be successfully predicted by basic mechanical properties. Similar to the format of Manson-Coffin equation, our relations uncover the essence of Manson-Coffin equation which may reveal the short crack’s initiation-propagation mechanism. Predictions of fatigue lifetime using our relations were compared with the results of well-known experiments. Good agreement is found in many aspects, such as coefficients, exponents, as well as fatigue lifetimes, especially for short cracks around 10 micrometers. Predictions on the short crack propagation rates are also compared for 16 types of carbon steels. Satisfactory consistency shows that our relations have wide applicability.