Modeling of plane strain fatigue crack closure

Mechanisms and models proposed for plane strain fatigue crack closure are evaluated. A mechanism based on out-of-plane plastic strain component, ε(lunate)^p_z, in plane strain is shown not to be adequate in explaining closure over a wide range of applied load levels. In the second model, partial relief of compressive stresses in front of the crack tip upon crack advance is forwarded as responsible for crack closure in plane strain. It is argued that this model would hold only if the crack advanced into a compressive stress zone which is highly improbable. A third model based on compressive strain accumulation in the x-direction, ε(lunate)^p_x, (transverse or crack growth direction) is studied. Material ahead of the crack tip contracts in the transverse direction and this mechanism provides residual material for crack surfaces as the crack advances. Stress-strain history and material displacements as crack advances are presented for plane strain conditions that lend further support to the third model. The results are obtained with a specialized finite element analysis with provisions for crack advance and crack closure. The crack opening load corresponding to relief of compressive residual stresses behind the crack tip is determined for plane stress and plane strain cases under R= -1, 0 and 0.3 loading. The load at which stresses ahead of the crack tip become tensile, P_t, is also determined for plane stress and plane strain conditions and is found to exceed the crack opening load in all cases. The relevance of this parameter on fatigue crack growth behavior is discussed.