Statistical and geometrical size effects in notched members based on weakest-link and short-crack modelling

Abstract

Cracks originate at defects of numerous kinds spread in the material. The fatigue life is – besides many other factors – governed by the large defects in the highly stressed area. The statistical size effect may be taken into account by identifying the highly stressed surface of a structure. The geometrical size effect is strictly interpreted from the viewpoint of fracture mechanics. Endurance limit stresses are correlated with thresholds of fatigue crack growth. For short cracks the increase of the threshold with crack length may be steeper than the increase of the applied stress intensity factor. In terms of applied local stresses this phenomenon of non propagating cracks can be expressed as a support factor. Additionally, some metals may show stable cyclic plastic deformation at the endurance limit. If proofs of the fatigue strength are based on the Theory of Elasticity a hypothetical stress state in accordance with the theory must be found which corresponds with the real stresses and strains at the critical locations of components. Neuber’s formula is used to supply this correlation expressed as a macro support factor. The paper describes a multiplicative ansatz for considering these combined effects in a design environment. A validation of the system of factors against experimental evidence is provided.