Simulation of Fatigue Crack Propagation in Ductile Metals by Blunting and Re-sharpening

Rainer Sievert,Vladislav Levkovitch,Bob Svendsen

doi:10.1007/s10704-005-6024-y

Abstract

Laird and Smith [(1962). Philosophical Magazine 8, 847–857] proposed a plastic sliding-off mechanism for the stage II fatigue crack growth via striation formation. In their view, the fatigue crack extension results solely from the changing character of deformation at the crack tip during loading and unloading. In particular, the crack tip blunts during the loading stage and folds into a double notch during the unloading stage, resulting in striation formation. In order to verify Laird’s plastic blunting mechanism for ductile polycrystals as well as for ductile fcc single crystals, FE calculations were performed for a rectangular plate with an initially sharp crack under plane strain conditions. The plate was subjected to a fully reversed tension-to-pressure cyclic load perpendicular to the crack plane (Mode 1). In the single crystal case the crack propagation simulations were carried out for cracks with crack plane (001) for two different crack growth orientations [110] and [100]. No initial radius for the crack tip was assumed. The actual shape of the crack tip followed from an initially sharp crack by repeated remeshing. To model the constitutive behavior typical for polycrystalline ductile metals, J2 hypo-elasto-plasticity model with Armstrong–Frederick kinematic hardening was used. To model the constitutive behavior typical for ductile fcc single crystals, a geometrically nonlinear version of Cailletaud’s model based on the multiplicative elasto-plastic decomposition of the deformation gradient was implemented into the FE program ABAQUS. For simplicity, only octahedral slip systems were considered. Using repeated remeshing for severely distorted elements at the advancing crack tip, deformation patterns in the sense of Laird’s mechanism for fatigue crack propagation with striation formation were obtained in the case of the polycrystal simulation as well as in the case of the single crystal simulation for [110] crack growth direction. The simulation for [100] crack growth direction with the same stress level as for [110] direction also yielded crack extension by progressive large deformations but without striation formation. The dependence of the fatigue striation formation on the crack growth direction as predicted by the simulation of crack propagation in single crystals is verified by the experimental results of Neumann [(1974). Acta Metallurgica 22, 1155–1165] on pure copper single crystals.

Highlights

1 INTRODUCTION While the statement that a fatigue crack advances by an increment ∆a in each cycle, except at very low growth rates in the near-threshold region, is generally accepted, there is a lack of agreement as to which mechanism controls the crack growth process
The slidingoff mechanism associates crack extension with blunting of the crack tip during loading followed by re-sharpening upon unloading. This approach, which is usually used to explain fatigue crack growth via a mechanism of striation formation, was fist proposed by Laird and Smith [1] for smooth blunting, and later by Neumann [2] and Pelloux [3] for blunting via alternating shear
For cyclic loads in the Paris regime of fatigue crack advance, it has been found that the spacing between adjacent striations correlates with the experimentally measured average crack growth rate per cycle

Summary

Introduction

While the statement that a fatigue crack advances by an increment ∆a in each cycle, except at very low growth rates in the near-threshold region, is generally accepted, there is a lack of agreement as to which mechanism controls the crack growth process. The slidingoff mechanism associates crack extension with blunting of the crack tip during loading followed by re-sharpening upon unloading. Fatigue striations are ripples on the fracture surface, and are often observed as a result of subcritical crack growth in ductile materials during cyclic loading.

Results

Conclusion