Estimating fatigue damage model constants with maximum likelihood method

Obtaining fatigue damage model constants for different damage models have long been of interest to many scientists and researchers interested in evaluating the reliability of materials. The conventional technique is to test the material for many numbers of cycles and fit the model to the stress-number of cycles to failure (S-N) curve. This manuscript proposes a new methodology to statistically obtain the fatigue model constants using Weibull based maximum likelihood (ML) function. Maximum likelihood theory for different stress levels is introduced. The ML function is then elaborated using the Weibull distribution as underlying distribution. Weibull based ML function is used to obtain the damage model constants. The proposed approach is then tested Coffin-Manson model using the data obtained from a thermo-mechanical fatigue test conducted for BGA solder joints. The model constants obtained using this approach is compared with available model constants and showed a good correlation.