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.

四十多年前，几位研究人员提出了一个假设，即疲劳裂纹的前端必须以一定（临界）角与自由表面相交，以确保在末端（顶点）具有有限的能量通量。自从提出以来，这一假说在许多研究中都受到了审查，这些研究利用了各种材料，循环加载条件和不同的样品几何形状。这些研究的结果非常分歧：从对该假设的压倒性确认到完全放弃。在本文中，我们首先讨论会影响自由表面附近裂纹前沿形状的条件。此外，我们证明，当塑性（或过程）区域远小于3D顶点奇异性控制的区域的大小时，临界角假设似乎是有效的。如许多过去的数值研究所证明的，该尺寸与裂纹和试样的几何形状有关，例如与裂纹的前沿长度有关。过去的实验研究还表明，疲劳裂纹前沿在稳态生长时倾向于以临界角与自由表面相交，而不是当裂纹扩展导致裂纹前沿发生变化或演变时，例如在疲劳裂纹扩展过程中。圆棒。