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

Abstract

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.

A novel damage constitutive model for creep deformation and damage evolution prediction

“…Penny also proposed a probabilistic K‐R model, and Monte Carto simulation method was adopted to deal with the randomness of material and geometrical parameters 48 . Recently, Hossain and Stewart have made a lot of efforts to simulate the uncertainty of creep deformation and damage evolution predicted by Sinh model where the randomness of material constants are achieved using Monte Carlo method and probability distribution function 45,49–51 . In the aerospace field, reliability greater than 99.74% is usually required.…”

“…48 Recently, Hossain and Stewart have made a lot of efforts to simulate the uncertainty of creep deformation and damage evolution predicted by Sinh model where the randomness of material constants are achieved using Monte Carlo method and probability distribution function. 45,[49][50][51] In the aerospace field, reliability greater than 99.74% is usually required. Therefore, it will be further work to introduce probability theory into TTC CDMbased model and carry out probabilistic life evaluation.…”

Probabilistic creep with the Wilshire–Cano–Stewart model

“…13,18 The WCS model is advantageous because of an explicit description of temperature dependency from Wilshire and the ability to model secondary and tertiary creep and creep damage given by Sinh. 13,18,43,44 Deterministically, the model has been calibrated and validated for alloy P91 13 and applied to model the accelerated creep test data of Inconel 718. 43 The WCS model was applied for rupture prediction of alloy P91 and exhibited superior accuracy compared to Larson-Miller (LM) model.…”

“…More details on the ω 0 calibration have been published elsewhere. 19,57 The uncertainty of material constants arises from intrinsic features of the microstructure such as grain structure (grains/boundaries), phases, precipitates, and carbides. The morphology and distribution of these features changes from specimen to specimen.…”

Modeling the creep deformation and damage evolution of superalloy GH4169: Application of a novel damage constitutive model based on continuum damage mechanics

“…Penny also proposed a probabilistic K-R model, and Monte Carto simulation method was adopted to deal with the randomness of material and geometrical parameters 54 . Recently, Hossain and Steward have made a lot of efforts to simulate the uncertainty of creep deformation and damage evolution predicted by Sinh model where the randomness of material constants are achieved using Monte Carlo method and probability distribution function [55][56][57][58] . 6.…”