The eigen equation of crack growth to metals

There is an assumption that crack growth is controlled by the high strain area at the very tip of a crack. Based upon the theory of the interaction energy between the inclusion and the applied stress, and the theory of the force acting on elastic singularity, the eigen equation of crack growth is proposed. According to the eigen equation the relation between fracture toughness K_Ic and tensile properties is researched. A general analytical expression for calculation of fatigue threshold values of common metals and alloys is also derived. The fracture toughness and fatigue threshold values for some materials are calculated by the results in this paper. It is found that the theoretical values are in good agreement with the experimental results. A new method predicting the eigen value is also proposed.