Prediction of Fatigue Crack Initiation Using Continuum Damage Mechanics
Dr. Baidurya Bhattacharya
Advanced Analysis Department
American Bureau of Shipping
Houston, Texas
Sponsored by: the Department of Engineering Mechanics and the College of Engineering and Technology
Date: Tuesday, December 15, 1998
Time: 3:30 p.m.
Place: W128 Nebraska Hall
The crack initiation period in an originally defect-free component can be a significant portion of its total fatigue life. The initiation phase is generally believed to constitute the nucleation and growth of short cracks, but the threshold crack length at which initiation occurs lacks uniform definition. Moreover, available methods for predicting fatigue damage growth usually require an existing flaw (e.g., Paris law) and are difficult to apply to the initiation phase.
This talk presents a continuum damage mechanics (CDM)-based approach that estimates cumulative fatigue damage, and predicts crack initiation from fundamental principles of thermodynamics and mechanics, independent of ambiguous crack sizes. CDM defines damage in a rational manner and provides a direct link between the damage variable and the state of the material microstructure. When the damage variable attains its critical value, the damage growth process localizes and a macroscopic defect is formed. Assuming that fatigue damage prior to localization occurs close to a state of thermodynamic equilibrium, a differential equation of isotropic damage growth under uniaxial loading is derived that is amendable to closed-form solution. Damage, as a function of the number of cycles, is computed in a recursive manner using readily available material parameters. Estimates of initiation life are compared with available experimental data, and commonly observed phenomena like mean stress effect, load sequencing effect are demonstrated using the proposed method.
Finally, the method is extended into the stochastic domain to analyze randomness in fatigue crack initiation. A stochastic differential equation of damage increment is derived, statistics of cumulative fatigue damage are obtained, and predicted probabilities of crack initiation are compared with available experimental results.
