Probabilistic Creep Modeling of 304 Stainless Steel Using a Modified Wilshire Creep-Damage Model

Pressure vessel components subject to high temperature and pressure are susceptible to life-limiting creep and/or creep-induced failure. Traditional continuum damage mechanics (CDM) based creep-damage model are used extensively for the prediction and design against creep in these components. Conventional creep experiments show considerable uncertainty in the creep response of materials where scatter can span decades of creep life. The objective of this paper is to introduce the probabilistic methods into a deterministic creep-damage model in order to predict experimental uncertainty. In this study, a modified Wilshire model capable of creep deformation, damage, and rupture prediction is selected. Creep deformation data for 304 stainless steel is collected from the literature consisting of quintuplicate (five) tests at 600°C with varying stress levels. It is hypothesized that the scatter in creep data is due to: test condition (temperature fluctuations and eccentric loading), initial damage (pre-existing surface and sub-surface defects), and metallurgical (local variation in microstructure) uncertainties. Probability distribution functions (pdfs) and Monte Carlo simulations are applied to introduce the uncertainties into the modified Wilshire equations. The domain of each source of uncertainty must be defined. A systematic calibration approach is followed where the material constant for each creep curve (in the quintuple) are obtained and statistical analysis is performed on the material properties to assess the random distribution associated with each uncertain material parameter. The probabilistic calibration begins with the introduction of test condition randomness (±2°C and ±3.2% MPa of nominal temperature/stress) in accordance with the ASTM standards. Cross calibration of temperature-stress variability proceeds the approximation of initial damage uncertainty which captures the remaining scatter in the data. Deterministic calibration unveils the range of variabilities associated with the material properties. The best-fitted pdfs are assigned to each uncertain parameter and subsequently, the deterministic model is converted into a probabilistic model where reliability is a tunable factor. A large number of Monte Carlo simulation are conducted to generate probabilistic creep deformation, minimum-creep-strain-rate (MCSR), and stress-rupture (SR) predictions. It is demonstrated that the probabilistic model produces quantitatively and qualitatively good fits when compared with experimental data. Future work will be directed towards the inclusion of service condition related uncertainty (power plant, turbine blade, Gen IV nuclear reactor application) into the probabilistic framework where the uncertainties are more robust.