The authors have developed a finite-element program with constant-strain capabilities that can handle cyclic loading. The constitutive relation is considered to be elastic-viscoplastic incorporating the Bodner-Partom flow rule. Incalloy 718 is the alloy considered at a temperature of 670°C. The computer algorithms are discussed for consideration of crack closure and extension.
The program is applied to a single-edge-cracked specimen with an initial crack length of 25 μm acting under a load distribution of 90% of the yield stress for the material considered. A plane-stress finite element is used to evaluate the effect of an R-value equal to 0.1, considering frequencies of 0.01 and 1.0 Hz. The crack is allowed to grow to a final length of 46 μm. The plastic zone in front of the crack tip is approximately equal to the initial crack length, yielding conditions associated with short cracks.
The results indicate the effect viscoplasticity plays when considering and comparing two separate frequencies. A plastic wake, due to crack closure, develops behind the propagating crack and increases for the lower frequency. In order to realistically predict plasticity-induced closure, one must mathematically allow the crack to grow. Stress and strain fields in front of the crack show a noticeable change with time due to the viscoplastic effect.