Three‐dimensional effects on fatigue crack closure in the small‐scale yielding regime – a finite element study

Abstract

Plasticity induced closure often strongly influences the behaviour of fatigue cracks at engineering scales in metallic materials. Current predictive models generally adopt the effective stress‐intensity factor (ΔΚeff = Κmax–Κop) in a Paris law type relationship to quantify crack growth rates. This work describes a 3D finite element study of mode I fatigue crack growth in the small‐scale yielding (SSY) regime under a constant amplitude cyclic loading with zero T‐stress and a ratio Κmin/Κmax = 0. The material behaviour follows a purely kinematic hardening constitutive model with constant hardening modulus. Dimensional analysis suggests, and the computational results confirm, that the normalized remote opening load value, Κop/Κmax, at each location along the crack front remains unchanged when the peak load (Κmax), thickness (B) and material flow stress (σ0) all vary to maintain a fixed value of . Through parametric computations at various K levels, the results illustrate the effects of normalized peak loads on the through‐thickness opening–closing behaviour and the effects of σ0/E, where E denotes material elastic modulus. The examination of deformation fields along the fatigue crack front provides additional insight into the 3D closure process.

Effect of T-stress on fatigue crack closure in 3-D small-scale yielding

“…Each crack front location thus has a computed value of opening stress intensity factor K op . This work defines K op at a crack front location when the second node behind the current crack tip loses contact with the symmetry plane upon reloading (see Roychowdhury and Dodds, 2003a,b for short discussions on this issue). A steadily rising K op with crack extension marks the initial transitory phase as the crack passes through the forward plastic zone created by the first excursion to peak load.…”

“…Eq. (5) indicates that the normalized opening stress intensity factor has no functional dependence on r 0 =E (Roychowdhury and Dodds, 2003a). However, material hardening characteristics, represented through the ratio E T =E, do influence the opening behavior.…”

“…For SSY configurations, Roychowdhury and Dodds (2003a) demonstrate the existence of a similarity scaling relationship that couples in a unique way the effective stress intensity factor, DK eff ¼ K max À K op , to the peak load in each cycle, the specimen thickness and the material flow properties. In particular, we show through numerical computations that for fatigue loading at a constant K min =K max ¼ R ¼ 0 and zero Tstress, the K op =K max value at each location along the crack front remains unchanged when K max , thickness (B) and material flow stress (r 0 ) all vary to maintain a fixed value of K ¼ K max =r 0 ffiffiffi B p .…”

“…In real structures and specimens, deformations evolve in more complex patterns than the ones envisaged in these limiting cases. To study the effects of thickness and material flow properties on PICC, Roychowdhury and Dodds (2003a) simulate fatigue crack growth under 3-D small-scale yielding (SSY) conditions using a boundary layer representation. Such conditions represent thin metallic components and test specimens subjected to moderate-to-high cycle fatigue loading.…”

Implementation of a plastically dissipated energy criterion for three dimensional modeling of fatigue crack growth

“…Due to constraint from the bulk at the interior section, the plastic zones are smaller at the mid-plane than near the free surface. Based on recommendations in the literature [31,32], the mesh refinement is chosen such that the reverse plastic zone at the mid-plane is resolved with at least 3-4 elements. Conse quently, the elements near the crack tip have a length of h e = 5 X 10 -4 B.…”