Research On Fuzzy Theory-Based Fatigue Damage Accumulation Model

Irreversible damage under cyclic loading mainly causes fatigue damage on material and component. The damage accumulation on material and component eventually makes them failure or damage. It is significant to build a reasonable model of damage accumulation by analyzing the causes of fatigue damage and resolving issues such as material's fatigue damage.Effect of the loading sequence and attenuation of fatigue limit on material's fatigue damage accumulation is analyzed. This paper presents the Box-Cox variable transformation fitting method to fit the three-parameter P-S-N curves because the logarithm fatigue life does not meet the normal linear regression Gauss-Markov assumptions under different stress level. The fuzzy fatigue damage theory is explained with the fuzzy mathematics. Then, modeling the sand pile fatigue damage cumulative model SPFDCM associated with the Miner linear rule and fuzzy theory. Furthermore, the heterogeneous sand pile fatigue damage cumulative model HSPFDCM is investigated on basis of SPFDCM.The main conclusion is given as follows: (1) Loading sequence and attenuation of material fatigue limit would effect on fatigue damage accumulation. Low stress would produce enhanced effect on the material's fatigue strength and defer damage development under low-high loading sequence. High stress would weaken crack closure effect under high-low loading sequence, and low stress would promote the development of damage in the expansion phase that crack has been formed.(2) Verification of experimental data shows that results of fitting the three parameters P-S-N curves are better by using the Box-Cox variable transformation fitting method than by using the least squares curve fitting method. The relative fitting error is only 1/4 to 1/2 of the least squares curve fitting method. Residuals of the transformed model reach to a minimum. This method can also improve the fitting accuracy on original data.(3) The fuzzy fatigue damage theory and its feasibility are described in according with the fuzzy phenomenon in fatigue analysis.(4) Adjoining damage is proposed to determine loading sequence on fatigue damage accumulation. The presentment of SPFDCM is on the basis of even damage that considers accumulation of fatigue damage as fatigue sand pile accumulating. Verification shows that errors of fatigue life prediction with the model are smaller.(5) Concept of fuzzy equivalent damage is depicted in this paper. HSPFDCM is built with heterogeneous damage that can well determine effect of loading sequence and attenuation of material fatigue limit on fatigue damage accumulation. Results show that the model is superior on prediction than SPFDCM and calculation is more close to the experimental value.