Description of crack propagation – theoretical approach and fitting accuracy to measurement results

Abstract

An energy criterion of fatigue crack propagation in the isotropic body has been formulated. It is based on the first principle of thermodynamics as a balance between energy variation rates (work of external forces, energy of body deformation, fracture energy, heat energy of the body) and the surface change due to fatigue crack under a cyclic loading. Finally, a kinetic equation of fatigue fracture as an analytical relation between the rate of fatigue crack surface propagation and the dissipation energy of plastic deformation in the precracked zone has been obtained. The method of an approximate solution of such an equation and determination of the period of precritical crack growth has been suggested. This method is based on the assumption that kinetics of the surface variation of the crack studied is close to the variation of a round crack with the same surface, but the solution for a round crack is given in a closed form. The validity of this method has been confirmed in the case of an elliptical crack. A new method of constructing kinetic fatigue fracture diagrams (KFFD) has been presented on the basis of measurement results of hysteresis loop area for the isotropic body with an internal flat crack under cyclic loading. For the experimental verification, the results of fatigue crack propagation studies for 18G2A and 40H steels have been utilized. In contradistinction to the force factor Kmax, the energetic parameter ΔH describes synonymously the propagation rate of the fatigue crack independently of a cycle asymmetry R. The linear dependence of crack propagation rate da/dN on energy dissipation of plastic deformation before the crack tip for one loading cycle has been discussed with taking into consideration the consequences for fitting models in double logarithmic axes.