AN ANALYTICAL MODEL OF FATIGUE CRACK-GROWTH BASED ON THE CRACK-TIP PLASTICITY

In the present study, an analytical model of fatigue crack growth based on the plastic-blunting mechanism is developed. Both the plastic and reversed plastic flow during the process of cycling are considered. In each loading cycle, the size of the plastic and reversed plastic zone, the crack-tip opening displacement, and the stress intensity factor at crack-closure are determined. With an assumption of a crack-extension law, the crack-growth behavior under arbitrary load history is traced by making a step-by-step analysis. For the crack growing under constant-amplitude loading, the analysis of the steady-state crack-growth behavior is carried out with a simplified formulation. Regarding the crack-growth behavior near the fatigue threshold, although all of the near-threshold mechanisms are not incorporated into the model, the promoted crack-closure due to corrosion debris and surface roughness is introduced in terms of a material parameter CTOD*. Under constant-amplitude loading, the results from the step-by-step analysis demonstrate that the closure level of the stress intensity considerably increases during the growth process due to accumulation of the residual strains. This may in part provide an explanation for the arrest a crack at a distance far from the root of a sharp notch, which is frequently observed in experiments. After a sufficiently large number of cycles, the crack-growth behavior from the step-by-step analysis reaches the steady state, and the results agree with the ones from the steady-state analysis. The crack growth law of second power is derived as a consequence of the assumed linear relation between DELTA-a and DELTA-CTOD. The crack growth curves from the analysis agree with the ones obtained from experiments for A1 2024-T3 and A1 7075-T6. the ratio of DELTA-a to DELTA-CTOD chosen for the calculation is in agreement with the direct, experimental measurement of DELTA-a and DELTA-CTOD. With the presence of CTOD*, the results show that the crack-growth behavior at low load changes drastically, and for each value of CTOD* a threshold exists below which no crack growth occurs at all. It is shown that under the action of variable-amplitude loading, the crack-growth behavior from the model exhibits a transient behavior upon altering the loading condition. The study shows that the residual plastic deformation in the wake of an advancing crack has a large influence on the crack-growth behavior. The results also lend a theoretical support to the existence of the controversial plasticity-induced crack-closure under plane-strain conditions.