A Probabilistic Model for Forging Flaw Crack Nucleation Processes

Abstract

A probabilistic model for quantifying the number of load cycles for nucleation of forging flaws into a crack has been developed. The model correlates low cycle fatigue (LCF) data, ultrasonic testing (UT) indication data, flaw morphology and type with the nucleation process. The nucleation model is based on a probabilistic LCF model applied to finite element analyses (FEA) of flaw geometries. The model includes statistical size and notch effects. In order to calibrate the model, we conducted experiments involving specimens that include forging flaws. The specimens were machined out from heavy duty steel rotor disks for the energy sector. The large disks, including ultrasonic indications on the millimeter scale, were cut into smaller segments in order to efficiently machine specimens including manufacturing related forging flaws. We conducted cyclic loading experiments at a variety of temperatures and high stresses in order to capture realistic engine operating conditions for flaws as they occur in service. This newly developed model can be incorporated into an existing probabilistic fracture mechanics framework and enables a reliable risk quantification allowing to support customer needs for more flexible operational profiles due to the emergence of renewable energy sources.

Crack nucleation at forging flaws studied by non-local peridynamics simulations

“…We applied fatigue loading vertically using the same load-controlled simulation technique described in section 2, but with a different stress level of 800 MPa. In our 2D simulation cell this is resulting in plane strain comparable loading conditions, which is also comparable to the condition present in specimen-based tests [5,23], as well as in large rotor forgings including small flaws or cracks. Here, we considered aluminum oxide as discontinuous inclusions.…”

“…Here, N is the number of cycles and i, j are two corresponding cycles where crack length a is measured. DK is calculated using equations ( 28) and (29), A 2 is calculated using only equation (23). A series of A 2 values are calculated, with their values varying due to the discretization of peridynamics by material point description (coefficient of variation is 0.812).…”

“…Material properties used in this model for inclusions and rotor steel matrix are shown in Table 3 for temperatures of 20, 350 and 450°C. Details on the inclusions and rotor steel can be found in Varfolomeev et al [5] and Radaelli et al [23]. [27] 1.89 0.2 8000…”

“…We categorize these densities as low, medium, and high inclusion density. The inclusion density is calculated by measuring the sum of the total inclusion area over total flaw area [23]:…”

“…Both S-N curves and Paris law parameters were investigated at 20, 350 and 450°C temperatures. These temperatures were chosen as they represent relevant gas turbine rotor conditions and were investigated in the experimental study with which we are comparing our results [2, 23]. The nucleation phase parameters are calibrated using S-N curves as shown in Figure 4.…”