An implicit gradient application to fatigue of complex structures

This paper presents a procedure to evaluate the stress gradient effect on the fatigue strength of steel welded joints and notched components. An effective stress is calculated by solving a second-order differential equation over all the component (the implicit gradient approach) independently of its geometric shape. The solution is obtained by assuming the isotropic linear elastic constitutive law for the material and the maximum principal stress as equivalent stress. The fatigue behaviour of geometrically complex steel welded joints is analysed and compared with previous fatigue scatter bands obtained for two-dimensional joints. In complex details, the actual critical point is derived from the analysis and is not assumed a priori. Implicit gradient analysis is also used to investigate high-cycle fatigue behaviour in the case of notches. In addition, it is shown that critical distance approaches can be obtained from the non-local theory by proper choice of the weight function