Rapid determination of temperature-dependent parameters for the crystal viscoplasticity model
Smith, Daniel J.
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Thermomechanical fatigue life prediction is important in the design of Ni-base superalloy components in gas turbine engines and requires a stress-strain analysis for accurate results. Crystal viscoplasticity models are an ideal tool for this stress-strain analysis of Ni-base superalloys as they can capture not only the anomalous yielding behavior, but also the non-Schmid effect, the strain rate dependence, and the temperature dependence of typically large grained directionally-solidified and single crystal alloys. However, the model is difficult to calibrate even for isothermal conditions because of the interdependencies between parameters meant to capture different but similar phenomena at different length scales, many tied to a particular slip system. The need for the capacity to predict the material response over a large temperature range, which is critical for the simulation of hot section gas turbine components, causes the determination of parameters to be even more difficult since some parameters are highly temperature dependent. Rapid parameter determination techniques are therefore needed for temperature-dependent parameterizations so that the effort needed to calibrate the model is reduced to a reasonable level. Specific parameter determination protocols are established for a crystal viscoplasticity model implemented in ABAQUS through a user material subroutine. Parameters are grouped to reduce interdependencies and a hierarchical path through the groups and the parameters within each group is established. This dual level hierarchy creates a logical path for parameter determination which further reduces the interdependencies between parameters, allowing for rapid parameter determination. Next, experiments and protocols are established to rapidly provide data for calibration of the temperature-dependencies of the viscoplasticity. The amount of data needed to calibrate the crystal viscoplasticity model over a wide temperature range is excessively large due to the number of parameters that it contains which causes the amount of time spent in the experimentation phase of parameter determination to be excessively large. To avoid this lengthy experimentation phase each experiment is designed to contain as much relevant data as possible. This is accomplished through the inclusion of multiple strain rates in each experiment with strain ranges sufficiently large to clearly capture the inelastic response. The experimental and parameter determination protocols were exercised by calibrating the model to the directionally-solidified Ni-bas superalloy DS-CM247LC. The resulting calibration describes the material's behavior in multiple loading orientations and over a wide temperature range of 20 °C to 1050 °C. Several parametric studies illustrate the utility of the calibrated model.