Modification of the MPC Omega Model to Predict Primary and Tertiary Creep

2019 ◽  
Author(s):  
Mohammad Shafinul Haque
Keyword(s):  
Creep Deformation ◽  
Work Hardening ◽  
Primary Creep ◽  
Deformation Curve ◽  
Tertiary Creep ◽  
Suitable Model ◽  
Hyperbolic Tangent ◽  
Natural Logarithm ◽  
Wide Range ◽  
Omega Model

Abstract The MPC Omega model has become popular in recent years for the prediction of creep deformation. Successful predictions of the tertiary creep for a wide range of materials are available. The Omega model relates the strain as a linear function of the natural logarithm of strain-rate. It is assumed that the primary creep is a short-lived phenomenon and can be neglected. The Omega model is unable to predict the primary creep deformation. Often primary creep is a long-lived phenomenon and cannot be neglected. A mathematical modification can be performed to incorporate the primary creep curve in the Omega model. A common approach is by adding a work hardening function to the original constitutive model. Approaches using power, or exponential, or logarithmic work-hardening function are available. However, it is difficult to discern which function is the best for accurate prediction. In this study, the Omega model is modified to predict the primary and tertiary creep deformation curve by adding a hyperbolic tangent work hardening function. A metamodel incorporating the four modified Omega sub-models (power, exponential, logarithmic and hyperbolic tangent) is developed. The metamodel enables the determination of the most suitable model for a given material and avoids the force fit of a preselected model. Short, medium, and long-term creep deformation data for alloy P91 (pipe) and G91 (plate) at two isotherms of 600°C and 650°C are used to calibrate the metamodel. The data include five stress levels ranging from 70 to 160 MPa including creep life from 233 to 1.1 × 105 hrs. A detail calibration process is provided. A numerical analysis is performed to compare the four submodels. It is observed that the selection of the most suitable function depends on the loading condition and material properties. Based on the analysis, a recommendation to select the suitable work-hardening function to predict the primary and tertiary creep deformation curve is presented.

A Modified Theta Projection Creep Model for a Nickel-Based Super-Alloy

2013 ◽  
Author(s):  
W. David Day ◽  
Ali P. Gordon
Keyword(s):  
Creep Rate ◽  
Creep Deformation ◽  
Primary Creep ◽  
Tertiary Creep ◽  
Creep Model ◽  
Creep Tests ◽  
Creep Equation ◽  
Physical Constraints ◽  
Primary Creep Strain ◽  
Super Alloy

Accurate prediction of creep deformation is critical to assuring the mechanical integrity of heavy-duty, industrial gas turbine (IGT) hardware. The classical description of the creep deformation curve consists of a brief primary, followed by a longer secondary, and then a brief tertiary creep phase. An examination of creep tests at four temperatures for a proprietary, nickel-based, equiaxed, super-alloy revealed many occasions where there is no clear transition from secondary to tertiary creep. This paper presents a new creep model for a Nickel-based super-alloy, with some similarities to the Theta Projection (TP) creep model by Evans and all [1]. The alternative creep equation presented here was developed using meaningful parameters, or θ’s, such as: the primary creep strain, time at primary creep strain, minimum (or secondary) creep rate, and time that tertiary creep begins. By plotting the first and second derivative of creep, the authors were able to develop a creep equation that accurately matches tests. This creep equation is identical to the primary creep portion of the theta projection model, but has a modified second term. An additional term is included to simulate tertiary creep. An overall scaling factor is used to satisfy physical constraints and ensure solution stability. The new model allows a constant creep rate phase to be maintained, captures tertiary creep, and satisfies physical constraints. The coefficients of the creep equations were developed using results from 27 creep tests performed at 4 temperatures. An automated routine was developed to directly fit the θ coefficients for each phase, resulting in a close overall fit for the material. The resultant constitutive creep model can be applied to components which are subjected to a wide range of temperatures and stresses. Useful information is provided to designers in the form of time to secondary and tertiary creep for a given stress and temperature. More accurate creep predictions allow PSM to improve the structural integrity of its turbine blades and vanes.

scholarly journals Microstructural evolution during high-temperature tensile creep at 1,500°C of a MoSiBTiC alloy

2020 ◽  
Vol 39 (1) ◽  
pp. 136-145 ◽  
Author(s):  
Sojiro Uemura ◽  
Shiho Yamamoto Kamata ◽  
Kyosuke Yoshimi ◽  
Sadahiro Tsurekawa
Keyword(s):  
Grain Size ◽  
Grain Boundaries ◽  
Microstructural Evolution ◽  
Grain Boundary Sliding ◽  
Primary Creep ◽  
Tensile Creep ◽  
Tertiary Creep ◽  
Continuous Dynamic Recrystallization ◽  
Continuous Dynamic ◽  
Creep Regime

AbstractMicrostructural evolution in the TiC-reinforced Mo–Si–B-based alloy during tensile creep deformation at 1,500°C and 137 MPa was investigated via scanning electron microscope-backscattered electron diffraction (SEM-EBSD) observations. The creep curve of this alloy displayed no clear steady state but was dominated by the tertiary creep regime. The grain size of the Moss phase increased in the primary creep regime. However, the grain size of the Moss phase was found to remarkably decrease to <10 µm with increasing creep strain in the tertiary creep regime. The EBSD observations revealed that the refinement of the Moss phase occurred by continuous dynamic recrystallization including the transformation of low-angle grain boundaries to high-angle grain boundaries. Accordingly, the deformation of this alloy is most likely to be governed by the grain boundary sliding and the rearrangement of Moss grains such as superplasticity in the tertiary creep regime. In addition, the refinement of the Moss grains surrounding large plate-like T2 grains caused the rotation of their surfaces parallel to the loading axis and consequently the cavitation preferentially occurred at the interphases between the end of the rotated T2 grains and the Moss grains.

Application of a Composite Model in the Analysis of Creep Deformation at Low and Intermediate Temperatures

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Xinjun Yang ◽  
Xiang Ling
Keyword(s):  
Projection Method ◽  
Power Law ◽  
Creep Deformation ◽  
Primary Creep ◽  
Composite Model ◽  
Intermediate Temperature ◽  
Model Parameters ◽  
Creep Life ◽  
Temperature Creep ◽  
Multiaxial Creep

The creep behaviors of TA2 and R60702 at low and intermediate temperature were presented and discussed in this paper. Experimental results indicated that an apparent threshold stress was exhibited in the creep deformation of R60702. Meanwhile, the primary creep phase was found as the main pattern in the room temperature creep behavior of TA2. Compared with the exponential law, the power law has been proved to be a proper constitutive model in the description of primary creep phase. It also showed that θ projection method had its significant advantage in the evaluation of accelerated creep stage. Thus, a composite model which combined power law with θ projection method was applied in the creep curves evaluation at low and intermediate temperature. Based on the multiaxial creep deformation results, the model was modified and discussed. A linear relationship existed between composite model parameters and applied load. Finally, the creep life of TA2 and R60702 could be accurately predicted by the composite model, and it is suitable for the application in low and intermediate temperature creep life analysis.

Evaluation of Creep Deformation Property of Grade 91 Steels

2015 ◽  
Author(s):  
Kazuhiro Kimura ◽  
Kota Sawada ◽  
Hideaki Kushima
Keyword(s):  
Creep Rate ◽  
Creep Deformation ◽  
Minimum Creep Rate ◽  
Deformation Property ◽  
Time Dependent ◽  
Tertiary Creep ◽  
Total Strain ◽  
Dominant Factor ◽  
Creep Equation ◽  
Time To Rupture

Creep deformation property of Grade T91 steels over a range of temperatures from 550 to 625°C was analyzed by means of the empirical creep equation reported in the previous study [1]. The creep equation consists of four time dependent terms and one constant and time to rupture is estimated as a time to total strain of 10%. Accuracy of the creep equation to represent creep curve and to predict time to rupture and minimum creep rate was indicated. Times to minimum creep rate, total strain of 1%, initiation of tertiary creep and rupture were evaluated by the creep equation. Stress dependence of strains at minimum creep rate and the initiation of tertiary creep were analyzed. Contribution of four time dependent terms to the strains at minimum creep rate, total strain of 1% and initiation of tertiary creep was investigated. Three parameters to determine a temperature and time-dependent stress intensity limit, St, were compared and a dominant factor of St was examined. Heat-to-heat variation of the creep deformation property was investigated on two heats of T91 steels contain low and high nickel concentrations.

Development of a Constitutive Backstress Model for the Prediction of Creep and Stress Relaxation in Gas Turbine Materials

2020 ◽  
Author(s):  
Andrew Moffat ◽  
Richard Green ◽  
Calum Ferguson ◽  
Brent Scaletta
Keyword(s):  
Stress Relaxation ◽  
Creep Deformation ◽  
Gas Turbines ◽  
Operating Conditions ◽  
Creep Model ◽  
Effect Of Temperature ◽  
Deformation Model ◽  
Corrosion Resistant ◽  
Single Temperature ◽  
Wide Range

Abstract There is a drive towards a broader range of fuels in industrial gas turbines, with higher levels of sulphur and potentially hydrogen. Due to these harsher environments, there is also a drive for corrosion resistant alloys and coatings. A number of key corrosion resistant superalloys, which are being employed to cope with these evolving conditions, exhibit primary creep. It is therefore imperative that fundamental material models, such as those for creep deformation, are developed to ensure they can accurately predict the material response to evolving operating conditions. The requirements for a creep model are complex. The model must be able to: predict forward creep deformation in regions dominated by primary loads (such as pressure); predict stress relaxation in regions dominated by secondary loads (such as differential thermal expansion); predict the effects of different creep hardening mechanisms. It is also clear that there is an interaction between fatigue and creep. With flexible operation, this interaction can be significant and should be catered for in lifing methods. A model that has the potential to account for the effect of plasticity on creep, and creep on plasticity is therefore desirable. In previous work the authors presented the concept for a backstress model to predict creep strain rates in superalloys. This model was fitted to a limited dataset at a single temperature. The approach was validated using simple creep-dwell tests at the same temperature. This paper expands on the previous work in several ways: 1) The creep model has been fitted over a wide range of temperatures. Including the effect of temperature in complex creep models presents a number of difficulties in model fitting and these are explored. 2) The model was fitted to constant load (forward creep) and constant strain (stress relaxation) tests since any creep model should be able to predict both forms of creep deformation. However, these are often considered separately due to the difficulty of fitting models to two different datasets. 3) The creep deformation model was validated on stress change tests to ensure the creep deformation response can cope with changes in response variables. 4) The approach was validated using creep-fatigue tests to show that the creep deformation model, in addition to our established fatigue models, can predict damage in materials under complex loading.

On the Interrupted Creep Test Under Low Stress Levels for the Power Law Parameter Extraction

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Bin Yang ◽  
Fu-Zhen Xuan ◽  
Wen-Chun Jiang
Keyword(s):  
Creep Strain ◽  
Stress Level ◽  
Creep Test ◽  
Creep Deformation ◽  
Parameter Extraction ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Creep Stage ◽  
Strain Data

Abstract Low stress interrupted creep test, as an interim compromise, can provide essential data for creep deformation design. However, there are no clear guidelines on the characterization of the terminating time for interrupted low-stress creep test. To obtain a suitable terminating time in terms of economy and effectiveness, long-term creep strain data of 9%Cr steels are collected from literatures and their creep deformation characterization is analyzed. First, the variations of normalized time and strain of each creep stage with the stress level are discussed. Then, the effect of the terminating time on final fitted results of Norton–Bailey equation is estimated. Third, the relationship between demarcation points at different creep stages and minimum/steady-state creep rate is analyzed. The results indicate that when the creep rupture life is considered as an important factor for creep design, the tertiary creep stage is of greatest significance due to the largest life fraction and creep strain fraction at low stress level. However, the primary and secondary creep stages are of great significance for design due to their larger contribution to 1% limited creep strain. And the long-term secondary creep data could be extrapolated by combining the primary creep strain data obtained from interrupted creep tests with the time to onset of tertiary creep derived from a similar Monkman–Grant relationship.

Creep Deformation Analyses for Grade 91 Steels Considering Heat-to-Heat Variation

2018 ◽  
Author(s):  
Haruhisa Shigeyama ◽  
Yukio Takahashi ◽  
John Siefert ◽  
Jonathan Parker
Keyword(s):  
Creep Strain ◽  
Creep Deformation ◽  
Deformation Behavior ◽  
Power Plants ◽  
Primary Creep ◽  
Heat Resistant ◽  
Large Heat ◽  
Reasonable Prediction ◽  
Materials Used ◽  
Grade 91

In order to evaluate creep life of heat-resistant materials used in power plants, it is important to estimate variation of stress distribution caused by creep deformation appropriately. For achieving this, creep strain equations which can express the creep deformation behavior with good accuracy are indispensable. Additionally, a lot of heat-resistant steels show large heat-to-heat variations in creep properties. Therefore, it is also important to take into account of the heat-to-heat variations in the creep analyses. In this study, existing creep strain equations for Grade 91 steel were applied to six heats with a variety of creep strength and creep deformation behavior. Furthermore, some modification was made in order to obtain better agreement with test data in primary creep stage. It was found that reasonable agreements were obtained between the measured creep deformation behavior and predictions obtained by these equations only by changing creep rupture property depending on the particular heats. This suggests that reasonable prediction for creep deformation can be made even for the materials lacking the information of creep deformation as long as their rupture properties are known.

A Model for the Coupled Lift and Drag on a Circular Cylinder

2003 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Farouk Owis ◽  
Muhammad R. Hajj
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Quadratic Function ◽  
Phase Relations ◽  
Suitable Model ◽  
Van Der Pol ◽  
Spectral Moments ◽  
Drag Coefficients ◽  
Wide Range ◽  
Lift And Drag

The time-varying coupled lift and drag coefficients acting on a circular cylinder are modeled. Data used for the model are obtained by numerically solving the unsteady Reynolds-Averaged Navier Stokes equations over a wide range of Reynolds numbers. Using spectral moments, we determine the frequency components in the lift and drag coefficients and their phase relations. Using a perturbation technique, we obtain approximate solutions of both the van der Pol and Rayleigh equations. By fitting the amplitude and phase relations, we find that the van der Pol equation is the suitable model for the lift. The Rayleigh equation fails to give the correct phase relation. Because the major frequency in the drag component is twice that of the lift, the drag component is modeled as a quadratic function of the lift. Through analysis with higher-order spectral moments, the correct quadratic relation of the lift that yields the drag is determined. The model and results presented here are a first step in the development of a reduced-order model for vortex-induced vibrations, which includes the motions of the cylinder.

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