A probabilistic method of determining fatigue life of a structural component using the paris formuła and the probability density function of time of exceeding the boundary condition - an outline

An attempt has been made to present a probabilistic method to determine fatigue life of an aeronautical structure's component by means of a density function of time a growing crack needs to reach the boundary condition. It has been assumed that in a component of a structure given consideration there is a small crack that grows due to fatigue load affecting it. After having reached the boundary value the component in question loses its usability. Time of the crack growth up to the boundary value is termed a fatigue life of the component. From the aspect of physics, the propagation of a crack within the component, if approached in a deterministic way, is described with the Paris 's relationship for m = 2. To model the fatigue crack growth a difference equation has been applied, from which the Fokker-Planck equation has been derived to be then followed with a density Junction of the growing crack. The in this way found density function of the crack length has been applied to find density Junction of time of reaching the boundary condition. This function has been used in the present paper to determine the randomly approached fatigue life of a component of a structure. The present paper has been prepared for the case there is coefficient m = 2 in the Paris formula. With the in the paper presented scheme, one can find fatigue life of the structure's component for the case m not equal to 2.