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.

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.

An Integrated Creep Model Based on Internal Stress Evolution

2014 ◽  
Author(s):  
Nicola Bonora ◽  
Luca Esposito
Keyword(s):  
Creep Rate ◽  
Internal Stress ◽  
Effective Stress ◽  
Secondary Phase ◽  
Primary Creep ◽  
Chromium Steel ◽  
Tertiary Creep ◽  
Creep Model ◽  
Secondary Creep ◽  
Modeling Framework

In creep design, not only secondary creep but also primary and tertiary creep regimes become important for an accurate creep life prediction and need to be accounted for in more sophisticated models. Mechanism-based theories showed a better potential since they usually leads to more accurate prediction over wider range of stress and temperature. It has long been recognized that the mechanics and kinetics of the deformation and recovery processes occurring at the microscale are determined by, amongst other things, the local effective stress while, at macroscopic level, it may still possible to discern an effective stress, which is different from the applied stress that drives the creep strain accumulation, [1]. Recently, the authors proposed an internal stress based model for primary creep, which is independent on the creep rate formulation at the steady state, ensuring the continuity of the creep curve at the transition between primary and secondary creep stages, [2]. In this work, in order to account for all creep stages, this modeling framework is extended further. In particular, for tertiary creep stage, it is assumed that the occurrence of microstructural modifications (such as fine particle dissolution, secondary phase precipitations, etc.) is the process responsible for the reduction of the internal stress and consequent increase of the creep rate as result of the increment of the effective stress. The possibility to derive the internal stress decay function from tertiary creep data is discussed. The proposed model has been applied to P91 high chromium steel and preliminary results are presented in this work.

Creep Behavior and Microstructural Stability of Lamellar γ-T1AI (Cr, Mo, Si, B) with Extremely Fine Lamellar Spacing

2000 ◽  
Vol 646 ◽  
Author(s):  
Wolfram Schillinger ◽  
Dezhi Zhang ◽  
Gerhard Dehm ◽  
Arno Bartels ◽  
Helmut Clemens
Keyword(s):  
Creep Rate ◽  
Creep Behavior ◽  
Lamellar Microstructure ◽  
Lamellar Spacing ◽  
Primary Creep ◽  
Vacuum Arc ◽  
Internal Stresses ◽  
Microstructural Stability ◽  
Thermodynamical Equilibrium ◽  
Creep Tests

ABSTRACTγ-T1AI (Cr, Mo, Si, B) specimens with two different fine lamellar microstructures were produced by vacuum arc melting followed by a two-stage heat treatment. The average lamellar spacing was determined to be 200 nm and 25–50 nm, respectively. Creep tests at 700°C showed a very strong primary creep for both samples. After annealing for 24 hours at 1000 °C the primary creep for both materials is significantly decreased. The steady-state creep for the specimens with the wider lamellar spacing appears to be similar to the creep behavior prior to annealing while the creep rate of the material with the previously smaller lamellar spacing is significantly higher. Optical microscopy and TEM-studies show that the microstructure of the specimens with the wider lamellar specing is nearly unchanged, whereas the previously finer material was completely recrystallized to a globular microstructure with a low creep resistance. The dissolution of the fine lamellar microstructure was also observed during creep tests at 800 °C as manifested in an acceleration of the creep rate. It is concluded that extremely fine lamellar microstructures come along with a very high dislocation density and internal stresses which causes the observed high primary creep. The microstructure has a composition far away from the thermodynamical equilibrium which leads to a dissolution of the structure even at relatively low temperatures close to the intended operating temperature of γ-T1AI structural parts. As a consequence this limits the benefit of fine lamellar microstructures on the creep behavior.

Investigation on Creep Behavior of Grade 91 Heat-Resistant Steel at 923K

2016 ◽  
Vol 853 ◽  
pp. 163-167
Author(s):  
Fa Cai Ren ◽  
Xiao Ying Tang
Keyword(s):  
Creep Rate ◽  
Creep Behavior ◽  
Creep Deformation ◽  
Deformation Behavior ◽  
Minimum Creep Rate ◽  
Resistant Steel ◽  
Creep Tests ◽  
Heat Resistant Steel ◽  
Heat Resistant ◽  
Grade 91

Creep deformation behavior of SA387Gr91Cl2 heat-resistant steel used for steam cooler has been investigated. Creep tests were carried out using flat creep specimens machined from the normalized and tempered plate at 973K with stresses of 100, 125 and 150MPa. The minimum creep rate and rupture time dependence on applied stress was analyzed. The analysis showed that the heat-resistant steel obey Monkman-Grant and modified Monkman-Grant relationships.

Change in Creep Deformation of PST Crystals with Different Stress Axes

2006 ◽  
Vol 980 ◽  
Author(s):  
Xiaohua Min ◽  
Eisaku Sakurada ◽  
Masao Takeyama ◽  
Takashi Matsuo
Keyword(s):  
Creep Rate ◽  
Slip System ◽  
Initial Stress ◽  
Creep Deformation ◽  
Strain Curve ◽  
Stage I ◽  
Stress Axis ◽  
Creep Tests ◽  
Transient Stage ◽  
Stereographic Triangle

AbstractBased on our analysis of a lot of creep rate-strain curves of PST crystals with the different angles between the lamellar plate and the stress axis, designated as ø, it was confirmed that the creep rate and the creep deformation manner strongly depend on the ø. It was supposed that the predominant creep deformation using γ plate during the transient stage is derived by the fully suppression of the operation of another slip systems not parallel to γ plate through α2 plate. It was also confirmed that the initial stress axes of the PST crystals within the standard stereographic triangle move for the [001]-[111] line, and then turn their directions for [111] pole during the transient stage. This moving manner of the stress axis indicated that the first slip system of [101](111) continues to the area near the [001]-[111] line in the standard stereographic triangle, and then, the second slip system of [110](111) operates. By comparing this moving manner to the creep rate-strain curve, it is suggested that the first slip system of [101](111) operates during the Stage I where the light decrease in the creep rate remains, after that, the second slip system of [110](111) appears and leads to steep decrease in the creep rate. This stage was designated as the Stage II. According to this conception, it is supposed that the strain at the end of the Stage I is directly correlated with the angle from the initial stress axis to the [001]-[111] line in the standard stereographic triangle. In this study, this supposition was confirmed by conducting the creep tests at 1148 K/68.6 MPa using two PST crystals with ø of 31° and 34°. The initial stress axis of the PST crystal with ø of 31° locates nearer to the [001]-[-111] line than that of the PST crystal with ø of 34°. The strain at the end of the Stage I of the PST crystal with ø of 31° is half that of the PST crystal with ø of 34°. By analyzing the inverse pole figures of the creep interrupted PST crystals, it was confirmed that the angle from the initial stress axis to the [001]-[111] line is correlated with the strain of the transient stage.

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.

Life Fraction Hardening Applied to a Modified Theta Projection Creep Model for a Nickel-Based Super-Alloy

2014 ◽  
Author(s):  
W. David Day ◽  
Ali P. Gordon
Keyword(s):  
Strain Hardening ◽  
Analytical Calculation ◽  
Tertiary Creep ◽  
Creep Model ◽  
Integration Scheme ◽  
Hardening Rule ◽  
Creep Models ◽  
Computationally Intensive ◽  
Super Alloy ◽  
Life Fraction

This paper presents the application of a life fraction hardening rule to the analytical calculation of creep in hot section components. Accurate prediction of creep is critical to assuring the mechanical integrity of heavy-duty, industrial gas turbine (IGT) hardware. The accuracy of such predictions depend upon both the creep models assumed and how those models are implemented in a finite element solution. A modified theta projection creep model for a nickel-based super alloy was presented in a previous paper as an accurate simulation of creep behavior [1]. Application of such a user defined creep law depends upon definition of a hardening rule in the form of either an explicit or an implicit integration scheme in order to calculate incremental strains during any time increment. Time hardening is the simplest and least computationally intensive of the two most common hardening rules, but does not correctly show the effect of changing stresses or temperatures. Strain hardening may provide the most accurate solution, but the creep models are too complex to invert, which results in highly iterative and computationally intensive solutions. A life fraction hardening rule has been presented in other works [2] as a compromise between time hardening and strain hardening. Life fraction hardening is presented here as a highly efficient and accurate means of calculating incremental creep strain when applied to a modified theta projection creep model. A user creep subroutine was defined using a state variable to represent the strain life fraction at any time. By using the time to tertiary creep as the denominator for the life fraction, no new material constants are needed to relate to creep failure. The start of tertiary creep is effectively considered to be a failure. Additional design insight can be provided through the inclusion of other state variables to calculate temperature margins at current conditions. Material testing with changing stress levels will be used to help validate the technique. A simplified example of the technique is presented in the paper. More accurate creep predictions allow our company to improve the structural integrity of its turbine blades and vanes.

An Investigation of the Creep of Ni3Al(B, Hf) Single Crystals at Intermediate Temperatures

1988 ◽  
Vol 133 ◽  
Author(s):  
K. J. Hemker ◽  
W. D. Nix
Keyword(s):  
Creep Deformation ◽  
Temperature Drop ◽  
Primary Creep ◽  
Constant Stress ◽  
Octahedral Plane ◽  
Creep Tests ◽  
Creep Properties ◽  
Yielding Behavior ◽  
Octahedral Slip ◽  
Inverse Creep

ABSTRACTThis study was undertaken to characterize the intermediate temperature creep properties of Ni3Al. Itfocuses on the mechanisms controlling creep deformation and their relationship to the anomalous yielding behavior of this alloy. Constant stress creep tests were conducted for temperatures between 713–973 K, and the following observations were made. The creep curves exhibited two distinct regions. Primary creep was followed by inverse creep. Specimens cooled under constant stress strained an additional 20% during cooling. Temperature drop experiments indicate that Ni3Al is weakened by the addition of creep deformation.Glide on the primary octahedral plane appears to be exhausted during primary creep. Slip trace and TEM studies indicate that inverse creep is controlled by slip on the cube cross slip plane and a secondary octahedral plane. Primary octahedral slip is observed in the specimens that are cooled and deformed under constant stress.

High Temperature Creep of Alpha-2 Ti-34mo1%Al Polycrystals

1994 ◽  
Vol 364 ◽  
Author(s):  
Hiroshi Oikawa ◽  
Toshihiko Fukuda ◽  
Makoto Ohtsuka
Keyword(s):  
Creep Rate ◽  
Minimum Creep Rate ◽  
Single Phase ◽  
Creep Condition ◽  
Primary Creep ◽  
High Temperature Creep ◽  
Creep Tests ◽  
Creep Stage ◽  
Fine Grained ◽  
Equiaxed Grains

AbstractConstant-stress compressive creep tests were carried out on an Al-rich a2 single-phase material, which had equiaxed-grains of 60μim in grain size, at 1050∼1250 K under 100∼500MPa. The type of the primary creep stage and the microstructures developed during creep depend greatly on the creep condition. The minimum creep-rate, however, can be represented by one set of parameters over the whole range of experimental condition. The stress exponent is 5.0±0.2 and the (modulus-compensated) activation energy is 360 ± 10kJ/mol. The Dorn-type plot of the minimum creep rate reveals that the normalized creep strength of fine-grained Ti-34mol%Al is not greatly different from that of disordered solid-solution hardened alloys.

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