Formulation of gradient multiaxial fatigue criteria

• Formulation of gradient fatigue criteria to capture gradient and loading effects.
• Gradients of the shear stress amplitude and hydrostatic stress are simultaneously introduced.
• Gradient versions of Crossland and Dang Van criteria are provided.
• Experimental observations of gradient and loading effects are reproduced.

A formulation of gradient fatigue criteria is proposed in the context of multiaxial high-cycle fatigue (HCF) of metallic materials. The notable dependence of fatigue limit on some common factors not taken into account in classical fatigue criteria, is analyzed and modeled. Three interconnected factors, the size, stress gradient and loading effects, are here investigated. A new class of fatigue criteria extended from classical ones with stress gradient terms introduced not only in the normal stress but also in the shear stress components, is formulated. Such a formulation allows to capture gradient effects and related “size” effects, as well as to cover a wide range of loading mode, then can model both phenomena “Smaller is Stronger” and “Higher Gradient is Stronger”. Gradient versions of some classical fatigue criteria such as Crossland and Dang Van are provided as illustrations.