Reliability Prediction of 304 Stainless Steel Using Sine-Hyperbolic Creep-Damage Model With Monte Carlo Simulation Method

2019 ◽  
Author(s):  
Md Abir Hossain ◽  
Calvin Maurice Stewart
Keyword(s):  
Stainless Steel ◽  
Monte Carlo ◽  
Strain Rate ◽  
Creep Strain ◽  
Creep Deformation ◽  
Stress Rupture ◽  
Material Constant ◽  
Creep Strain Rate ◽  
304 Stainless Steel ◽  
Material Constants

Abstract Typically continuum damage mechanics (CDM) based constitutive models are applied deterministically where the uncertainty of experiments is not considered. This is also true for the Sine-hyperbolic (Sinh) CDM-based constitutive model where the model is calibrated to represent 50% reliability of creep data. There is a need to implement Sinh in a more stochastic manner. The objectives of this study is to incorporate the probabilistic feature in the Sinh creep damage model to reliably predict the minimum-creep-strain-rate, creep-rupture and creep deformation. This will be achieved using Monte-Carlo methods. Creep deformation data for 304 Stainless Steel is collected from literature consisting of tests conducted at 300 and 320 MPa at 600°C with five replicates. The replicate tests exhibited substantial scatter in the minimum-creep-strain-rate, stress-rupture, and overall creep deformation. Subsequently, upon calibration using the Sinh model, the material constants among the replicates varied. The trends of uncertainty carried by each material constant are studied. The interdependence of the material constants is evaluated to determine if the uncertainty carried by each material constant can be regressed using a co-dependence function. The Monte Carlo method was applied to determine the extent that the creep deformation curve varies taking into consideration the variability of the material constants. Monte Carlo simulations show that the predicted creep deformation persists within the bounds of the experimental data. A large number of Monte Carlo simulations using the Sinh model enabled the creation of credible reliability bands for the minimum-creep-strain-rate, stress-rupture, and creep deformation of 304 Stainless Steel. In future work, this statistical method will be applied to the variability of service conditions, pre-existing defects, and material constants to quantitatively establish the reliability of the Sinh model in simulating component-level creep deformation to rupture.

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

2020 ◽  
Author(s):  
Md. Abir Hossain ◽  
Jaime A. Cano ◽  
Calvin M. Stewart
Keyword(s):  
Stainless Steel ◽  
Monte Carlo ◽  
Temperature Stress ◽  
Creep Deformation ◽  
Material Properties ◽  
Probabilistic Model ◽  
Damage Model ◽  
Creep Damage ◽  
304 Stainless Steel ◽  
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.

Development and Application of Minimum Creep Strain Rate Metamodeling

2019 ◽  
Author(s):  
Ricardo Vega ◽  
Calvin Stewart
Keyword(s):  
Strain Rate ◽  
Creep Strain ◽  
Creep Strain Rate ◽  
Heaviside Function ◽  
Final Model ◽  
Material Constants ◽  
Rate Laws ◽  
Calibration Algorithm ◽  
Best Fit ◽  
Mcr Model

Abstract Numerous minimum-creep-strain-rate laws exist, creating a challenge in determining which is best for a given material database. The objective of this study is to validate the applicability of a “metamodel” and its ability to model the minimum creep strain rate (MCR). A metamodel is a model that can combine and regress into different base models, in this case, seven established MCR models. The metamodel can be exploited using a calibration algorithm to rapidly calibrate the base models. The metamodel contains ten terms and eight material constants (one is a constraint, and another is stress as an input variable). Using the metamodel and calibration software, the user can determine the best MCR model for a given material database. Using the software, the metamodel is calibrated in two approaches: constrained and pseudo-constrained. The constrained approach restricts the metamodel to regress directly into one of the base models, allowing for the base models to be equally calibrated and compared alongside each other. The pseudo-constrained approach freely optimizes all eight of the metamodel material constants; however, the metamodel is modified to include 5 Heaviside function constants that turn on/off sections of the metamodel to increase the statistical-dependencies of the final model. This pseudo-constrained approach has the potential to identify novel MCR models that exist at the interface between the seven base models. Alloy data for 9Cr-1Mo-V-Nb (ASTM P91) was used with a total of 89 points which extended over a total of three isotherms: 600°C, 625°C, and 650°C. The MCR model that best fit the data was the Johnson-Henderson-Kahn model.

Application of the Wilshire Stress-Rupture and Minimum-Creep-Strain-Rate Prediction Models for Alloy P91 in Tube, Plate and Pipe Form

2019 ◽  
Author(s):  
Jaime A. Cano ◽  
Calvin M. Stewart
Keyword(s):  
Strain Rate ◽  
Creep Strain ◽  
Stress Rupture ◽  
Creep Strain Rate ◽  
Tube Plate ◽  
Short Term ◽  
Design Life ◽  
Term Creep ◽  
Term Data

Abstract There exists a challenge in predicting the long-term creep of materials (3 105 hours) where 11+ years of continuous testing is required to physically collect creep data. As an alternative to physical testing, constitutive models are calibrated to short-term data (< 104 hours) and employed to extrapolate the long-term creep behavior. The Wilshire model was introduced to predict the stress-rupture and minimum-creep-strain-rate behavior of materials and the model is well-accepted due to the explicit description of stress- and temperature-dependence allowing predictions across isotherms and stress levels. There is an ongoing effort to determine how alloy form affects the long-term creep predictions of the Wilshire model. In this study, stress-rupture and minimum-creep-strain-rate predictions are generated for alloy P91 in tube, plate, and pipe form. Data is gathered from the National Institute of Materials Science (NIMS) material database for alloy P91 at multiple isotherms. Following the establish calibration method for the Wilshire model, post-audit validation is performed using short-term data from NIMS to vet the extrapolations accuracy of each form at different isotherms. The Wilshire model demonstrates successful extrapolative techniques for the stress-rupture and minimum-creep-strain-rate of tube, plate, and pipe forms across multiple isotherms. Overall the form with the highest extrapolative accuracy for both stress-rupture and minimum-creep-strain-rate is the plate and the lowest one is the pipe. Stress-rupture design maps are provided where stress and temperature are axes and rupture-time is in contour. The design maps can be applied to: (a) given the boundary conditions, determine the design life (b) given the design life, determine the acceptable range of a boundary conditions. The latter is more useful in turbomachinery design.

Development of “Material Specific” Creep Continuum Damage Mechanics-Based Constitutive Equations

2020 ◽  
Author(s):  
Ricardo Vega ◽  
Jaime A. Cano ◽  
Calvin M. Stewart
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Creep Strain ◽  
Creep Deformation ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Constitutive Models ◽  
Continuum Damage Mechanics ◽  
Creep Strain Rate ◽  
Continuum Damage

Abstract The objective of this study is to introduce a method for creating “material specific” creep continuum damage mechanics-based constitutive models. Herein, material specific is defined as a constitutive model based on the mechanism-informed minimum creep strain rate (MCSR) equations found in deformation mechanism maps and calibrated to available material data. The material specific models are created by finding the best MCSR model for a dataset. Once the best MCSR model is found, the Monkman Grant inverse relationship between the MCSR and rupture time is employed to derive a rupture equation. The equations are substituted into continuum damage mechanics-based creep strain rate and damage evolution equations to furnish predictions of creep deformation and damage. Material specific modeling allows for the derivation of creep constitutive models that can better the material behavior specific to the available data of a material. The material specific framework is also advantageous since it has a systematic framework that moves from finding the best MCSR model, to rupture time, to damage evolution and, creep strain rate. Data for Alloy P91 was evaluated and a material specific constitutive model derived. The material specific model was able to accurately predict the MCSR, creep deformation, damage, and rupture of alloy P91.

scholarly journals Accelerated Creep Test (ACT) Qualification of Creep-Resistance Using the WCS Constitutive Model and Stepped Isostress Method (SSM)

2021 ◽  
Author(s):  
Jaime A. Cano ◽  
Calvin M. Stewart
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Creep Strain ◽  
Creep Deformation ◽  
Inconel 718 ◽  
Creep Resistance ◽  
Stress Rupture ◽  
Creep Testing ◽  
Accelerated Creep

Abstract In this study, a qualification of accelerated creep-resistance of Inconel 718 is assessed using the novel Wilshire-Cano-Stewart (WCS) model and the stepped isostress method (SSM) and predictions are made to conventional creep data. Conventional creep testing (CCT) is a long-term continuous process, in fact, the ASME B&PV III requires that 10,000+ hours of experiments must be conducted to each heat for materials employed in boilers and/or pressure vessel components. This process is costly and not feasible for rapid development of new materials. As an alternative, accelerated creep testing techniques have been developed to reduce the time needed to characterize the creep resistance of materials. Most techniques are based upon the time-temperature-stress superposition principle (TTSSP) that predicts minimum-creep-strain-rate (MCSR) and stress-rupture behaviors but lack the ability to predict creep deformation and consider deformation mechanisms that occur for experiments of longer duration. The stepped isostress method (SSM) has been developed which enables the prediction of creep deformation response as well as reduce the time needed for qualification of materials. The SSM approach has been successful for polymer, polymeric composites, and recently has been introduced for metals. In this study, the WCS constitutive model, calibrated to SSM test data, qualifies the creep resistance of Inconel 718 at 750°C and predictions are compared to CCT data. The WCS model has proven to make long-term predictions for stress-rupture, minimum-creep-strain-rate (MCSR), creep deformation, and damage in metallic materials. The SSM varies stress levels after time interval adding damage to the material, which can be tracked by the WCS model. The SSM data is calibrated into the model and the WCS model generates realistic predictions of stress-rupture, MSCR, damage, and creep deformation. The calibrated material constants are used to generate predictions of stress-rupture and are post-audit validated using the National Institute of Material Science (NIMS) database. Similarly, the MCSR predictions are compared from previous studies. Finally the creep deformation predictions are compared with real data and is determined that the results are well in between the expected boundaries. Material characterization and mechanical properties can be determined at a faster rate and with a more cost-effective method. This is beneficial for multiple applications such as in additive manufacturing, composites, spacecraft, and Industrial Gas Turbines (IGT).

Determination of Material Constants for Creep Damage Models Using Small Two-Bar and Notched Specimens

2014 ◽  
Author(s):  
Balhassn S. M. Ali ◽  
Thomas H. Hyde ◽  
Wei Sun
Keyword(s):  
Strain Rate ◽  
Creep Strain ◽  
Creep Test ◽  
Creep Damage ◽  
Creep Strain Rate ◽  
Creep Testing ◽  
Small Specimen ◽  
Material Constants ◽  
Damage Models ◽  
Testing Techniques

The work presented in this paper forms part of the research related to the development of small specimen creep testing techniques, which can be used when only small volumes of materials are available. Commonly used small creep test specimen types such as the impression and small ring creep tests can be only used to determine the minimum creep strain rate data. In this paper, two novel small-sized creep test specimens are described: (i) the recently developed small two-bar specimen, which is suitable for use in obtaining both uniaxial creep strain rate and creep rupture life data, and (ii) the newly developed small notched specimen, which can be used to determine the multiaxial stress state parameter. The two specimen types have been used to determine a full set of material constants for Norton model, Kachanov and Liu-Murakami creep damage models. Conversion relationships have been obtained based on the reference stress method in conjunction with the finite elements analyses and have been used to convert the two-bar specimen data to the corresponding uniaxial data. Two P91 power plant steels have been used to assess the accuracy of the two testing methods, (i) a weak P91 (Bar-257) steel at 650°C and (ii) a normal P91 (as received) steel at 600°C. The correlation between the data obtained from the two small specimens testing techniques and the corresponding uniaxial and Bridgeman specimens tests is excellent. The major advantages of the two novel small specimens testing techniques, over some existing small specimen creep testing techniques, are also highlighted in this paper.

Probabilistic Minimum-Creep-Strain-Rate and Stress-Rupture Prediction for the Long-Term Assessment of IGT Components

2020 ◽  
Author(s):  
Md Abir Hossain ◽  
Calvin M. Stewart
Keyword(s):  
Strain Rate ◽  
Creep Strain ◽  
Probabilistic Model ◽  
Stress Rupture ◽  
Service Condition ◽  
Creep Strain Rate ◽  
Experimental Uncertainty ◽  
Initial Damage ◽  
Long Duration

Abstract Time-dependent creep induced failure is a major concern for structural components (i.e. IGT components, Gen IV nuclear reactor components) operating at elevated temperature. The likelihood of a failure is aggravated by randomness in several sources of uncertainty. Creep rupture data shows expanding scatter bands for long-duration creep tests where uncertainty can span multiple logarithmic decades of life. This experimental uncertainty is exacerbated by the uncertainties that exist during service. The continuum damage mechanics (CDM) based creep-damage model readily available in literature does not consider the uncertainty effect while predicting the long-term reliability of the components; rather the problem is tackled deterministically. Introduction of probabilistic phenomena into the existing model to predict the minimum-creep-strain-rate (MCSR) and stress-rupture (SR) would present a pathway for estimation of effect of uncertainty ensuing high reliability in the assessment. The objective of this paper is to develop a probabilistic model for MCSR and SR that is capable of predicting experimental uncertainty and extrapolating the expanded scatter bands observed in long-duration creep data. The Sine-hyperbolic (Sinh) CDM model is selected. Multi-isotherm MCSR and SR data for 304 (18Cr-8Ni) and 316 (18Cr-12Ni-Mo) stainless steel are gathered from the NIMS material database. A deterministic calibration is performed where the optimal material constants are obtained with no initial damage and perfect loading conditions. Probabilistic calibration begins with adding ASTM-specified temperature and stress tolerances (± X°C, ±Y% MPa) to capture a portion of the experimental uncertainty. The initial damage tolerances is then calibrated to capture the remaining uncertainty in the data. Probability distribution functions (pdfs) are assigned to each uncertainty parameter. Monte Carlo simulations are performed over a range of stress and temperature. The probabilistic Sinh model is shown to predict the expanding scatter band observed in long-term MCSR and SR data. Parametric simulations are performed where service condition uncertainty is added to the probabilistic model. It is determined that service condition uncertainties further degrade the creep resistance of a material.

Modeling the Creep Deformation, Damage, and Rupture of Hastelloy X Using MPC Omega, Theta, and Sin-Hyperbolic Models

2016 ◽  
Author(s):  
Mohammad Shafinul Haque ◽  
Calvin M. Stewart
Keyword(s):  
Experimental Data ◽  
Strain Rate ◽  
Creep Strain ◽  
Creep Deformation ◽  
Rupture Life ◽  
Creep Strain Rate ◽  
Projection Model ◽  
Hastelloy X ◽  
Omega Model ◽  
Evolution With Time

Combined cycle power plants components such as steam pipe work, pressure vessels, boilers, heat exchangers, and gas turbine disks, etc. are exposed to elevated temperature and pressure operation conditions for longer durations. Components may fail within the elastic limit due to a time dependent deformation and damage mechanism called creep. Creep prediction models are used to determine the state of these components and to schedule optimum inspection, maintenance, and replacement intervals. In this study, the deformation, damage, and life of Hastelloy X is characterized using three recently developed models; the Omega, Theta projection, and Sin-hyperbolic models. An analysis is performed to compare the models in terms of accuracy, assumptions, constant identification techniques, flexibility in use, and limitations. The influence that final creep strain has on Theta and Omega model is discussed. Sixteen tests were performed at four different configurations of stress (2.1–36.5 ksi) and temperature (1200–1800°F). In the experimental data, Hastelloy X does not exhibit the primary stage. In this study, the secondary and tertiary creep stages are modeled. Creep deformation and rupture life data is used to optimize the constants for the three models. Predictions using these models are compared with experimental data. It is found that the novel Sin-hyperbolic model better fits the experimental data, and is easier to apply. The Omega model predicts longer life than the Sinh and the Theta Projection model. The rupture life prediction of the Theta projection model is the worst due to dependence on the critical creep strain rate. It is observed that the Hastelloy X final creep strain depends on stress and temperature; this leads to a less accurate critical creep strain rate prediction resulting in inaccurate rupture life predictions for the Theta projection model. The analytical damage of the Omega model exhibits a linear evolution with time while the Sinh model show a more realistic elliptical creep damage evolution with time. A process to determine the constants of all the models is clearly described. The dependence of the trajectory of the creep curves with respect to the constants is discussed in detail. An analytical derivation of each model is provided. Predictions of these three models show that the Sinh model produces a better creep deformation curve by normalizing the experimental creep strain rate data. It is found that overall the Sinh model offers more flexibility, prediction accuracy, and is easier to apply.

An Investigation of Transient Creep by Means of Endochronic Viscoplasticity and Experiment

1995 ◽  
Vol 117 (3) ◽  
pp. 260-268 ◽  
Author(s):  
Han C. Wu ◽  
Chin C. Ho
Keyword(s):  
Stainless Steel ◽  
Strain Rate ◽  
Creep Strain ◽  
Constant Strain Rate ◽  
Transient Creep ◽  
Constant Stress ◽  
Stress Rate ◽  
304 Stainless Steel ◽  
Unified Approach ◽  
Creep Tests

Creep of metals has been investigated by means of the endochronic constitutive equation. This is a unified approach. Transient creep tests have been conducted on 304 stainless-steel specimens with carefully monitored precreep loading stage, either loaded at a prescribed constant strain-rate or at a constant stress-rate. It has been found that, for the same hold stress, the creep strain is larger for test with a constant stress-rate preloading than that for a constant strain-rate preloading. This is an effect of plasticity-creep interaction. In all cases, the initial creep strain rate is a continuation of the preloading strain rate. The theory satisfactorily describes the experimental results.

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