Solutions And Applications Of The Macro/Micro Trans-scale Fatigue Crack Propagation Unified Model

With the development of the microscopic technique, the size of some engineering components becomes smaller and smaller. When the mechanical behaviors of the components are analyzed, some material characteristic parameters that depict the macroscopic properties are not valid any more. A large number of fatigue fracture experiments show that the material microscopic structures have a large influence on the macroscopic fatigue fracture behaviors.Therefore, how to describe the material damage process from microscopic defects to macroscopic crack has been a focus in the mechanics. The main work in this paper is as follows:(1) A restraining stress zone is applied to describe the state of the material damage.Considering the linear distributed restraining stresses, a restraining stress zone crack model is established. At macro-scale, the microscopic crack tip zone is not considered. The model can be solved by application of the complex function approach. An analytical solution of the stress intensity factor is obtained. Numerical calculations are performed. The influence of the remote applied stresses, restraining stress radio and crack size on the stress intensity factor and crack opening displacement has been investigated.(2) Another restraining stress zone crack model, containing a microscopic crack tip zone,is analytically solved by application of the Muskhelishivili approach at both the micro-scale and macro-scale. Analytical solutions of stress intensity factors and crack opening displacements are obtained. Numerical calculations are performed. The influences of the macroscopic and microscopic quantities on the stress intensity factors and crack opening displacements are investigated.(3) The results at both the micro-scale and macro-scale are coupled by adopting the continuity condition of crack opening displacement from micro-scale to macro-scale. The analytical solution of trans-scale strain energy density factor is obtained. By taking the variation of trans-scale strain energy density factor per cycle as the controlling physical quantity for the fatigue crack growth, a formulation for the whole fatigue failure process from micro-scale to macro-scale is completed.(4) Take LC4 aluminum alloy smooth plate specimens for instance. The S-N curves forthe LC4 aluminum alloy smooth plate specimens are accurately re-produced by the present model. Thus, the accuracy of this trans-scale model has been verified. Numerical calculations are performed. The influences of the size of initial microscopic defects and evolution modes of normalized parameters on the fatigue crack propagation behavior are investigated.Moreover, when the microscopic effects are taken into account, the scatter feature of the fatigue test data can also be reflected.