Does the front of fatigue crack intersect free surface at critical angle?

• The critical angle hypothesis has been suggested more than forty years ago. • More than a dozen of past experimental studies have been analysed. • Experimental evidences are controversial. • The hypothesis is valid for a steady state crack propagation and sufficiently small plastic zone size. More than forty years ago, several researchers suggested a hypothesis that the front of a fatigue crack must intersect the free surfaces at a certain (critical) angle to ensure the finite energy flux at the terminal (vertex) point(s). Since its formulation, this hypothesis was under scrutiny in many studies, which utilised various materials, cyclic loading conditions and different specimen geometries. The outcomes of these studies were very divisive: from overwhelming confirmation of this hypothesis to total abjuration. In this paper, we first discuss the conditions, which can affect the shape of the crack front near free surfaces. Further, we demonstrate that the critical angle hypothesis seems to be valid when the plastic (or process) zone is much smaller than the size of the region controlled by 3D vertex singularity. As demonstrated in a number of past numerical studies, this size is related to the crack and specimen geometry, e.g., to the crack front length. Past experimental studies also indicate that fatigue crack fronts tend to intersect the free surface at the critical angle at the steady-state growth rather than when the crack propagation leads to the changes or evolution of the crack front, e.g., during propagation of fatigue cracks in round bars. [ABSTRACT FROM AUTHOR]