A numerical investigation of 3-D small-scale yielding fatigue crack growth

The 3-D small-scale yielding (SSY) model provides a computational framework to study fatigue crack growth in thin, metallic components (and test specimens) containing an initially sharp, straight-through crack. This work describes a finite element study of plasticity-induced crack closure in the 3-D SSY model under mode I, constant amplitude cyclic loading with a ratio R=Kmin/Kmax. A purely kinematic hardening model with constant modulus represents the material constitutive behavior. This paper first addresses key computational issues and proposes modeling guidelines leading to 3-D numerical results for fatigue crack growth in SSY that exhibit convergence with mesh refinement. Specifically, computed crack opening loads show an independence of finite element mesh refinement when (a) the plastic zone at peak load encloses more than 10 eight-noded brick elements (b) the reverse plastic zone encloses at least two elements, and (c) the half-thickness has at least five element layers. The paper also describes stress and deformation fields at the crack front for a growing fatigue crack and provides an understanding of localized 3-D effects on the normalized remote opening load value Kop/Kmax. In addition, the computational studies demonstrate that the similarity scaling relationship established for R=0 [Roychowdhury and Dodds, Fatigue Fract. Engng. Mater. Struct. (accepted for publication)] also holds for the non-zero ratio R=0.1––a value commonly adopted in experimental programs. In particular, Kop/Kmax, at each location along the crack front remains unchanged when the peak load (Kmax), thickness (B) and material flow stress (σ0) all vary to maintain a fixed value of K=Kmax/σ0B.