Modeling Creep Deformation and Damage Behavior of Tempered Martensitic Steel in the Framework of Additive Creep Rate Formulation

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
J. Christopher ◽  
B. K. Choudhary
Keyword(s):  
Creep Rate ◽  
Internal Stress ◽  
Creep Strain ◽  
Creep Deformation ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Time Behavior ◽  
Secondary Creep ◽  
Modeling Creep ◽  
Applied Stresses

Additive creep rate model has been developed to predict creep strain-time behavior of materials important to engineering creep design of components for high temperature applications. The model has two additive formulations: the first one is related to sine hyperbolic rate equation describing primary and secondary creep deformation based on the evolution of internal stress with strain/time, and the second defines the tertiary creep rate as a function of tertiary creep strain. In order to describe creep data accurately, tertiary creep rate relation based on MPC-Omega methodology has been appropriately modified. The applicability of the model has been demonstrated for tempered martensitic plain 9Cr-1Mo steel for different applied stresses at 873 K. Based on the observations, a power law relationship between internal stress and applied stress has been established for the steel. Further, a higher creep damage accumulation with increasing life fraction has been observed at low stresses than those obtained at high stresses.

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.

Application of the Monkman-Grant Relationship for Ultrafine-Grained Metallic Materials

2013 ◽  
Vol 577-578 ◽  
pp. 137-140
Author(s):  
Marie Kvapilová ◽  
Jiří Dvořák ◽  
Petr Král ◽  
Milan Svoboda ◽  
Vàclav Sklenička
Keyword(s):  
Creep Deformation ◽  
Damage Tolerance ◽  
Creep Damage ◽  
Tolerance Factor ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Metallic Materials ◽  
Ultrafine Grained ◽  
Ultrafine Grained Materials ◽  
The Relationship

The applicability of the Monkman-Grant relationship was analyzed and validated for ultrafine-grained metallic materials under investigation. A special attention has been given to the creep damage tolerance factor which is defined as the ratio of the strain to fracture to the Monkman-Grant ductility and which describes the coupling between creep deformation and damage based on continuum creep damage approach. It was found, that ultrafine-grained materials generally obey the Monkman-Grant relationship, however, the relationship is especially suitable for materials exhibiting short secondary creep and long tertiary creep stages when dislocation-controlled creep is dominant.

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.

Analytical Method to Determine the Tertiary Creep Damage Constants of the Kachanov-Rabotnov Constitutive Model

2010 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Constitutive Model ◽  
Creep Deformation ◽  
Analytical Method ◽  
Numerical Optimization ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Computational Time ◽  
Secondary Creep ◽  
Damage Constitutive Model ◽  
High Temperature Components

The classic Kachanov-Rabotnov isotropic creep damage constitutive model has been used in many situations to predict the creep deformation of high temperature components. Typically, the secondary creep behavior is determined by analytical methods; however, the tertiary creep damage constants are found using a mixture of trial and error and numerical optimization. These methods require substantial hand calculations and computational time to determine the tertiary creep damage constants. In this paper, a novel analytical method is developed to determine the tertiary creep damage constants. Comparisons between numerical optimized constants and those found using the analytical method are given for a Ni-based superalloy. Creep deformation, damage evolution, and rupture time predictions are compared. A detailed discussion of the analytical method is given.

scholarly journals Curve Fitting for Damage Evolution through Regression Analysis for the Kachanov–Rabotnov Model to the Norton–Bailey Creep Law of SS-316 Material

Materials ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 5518
Author(s):  
Mohsin Sattar ◽  
Abdul Rahim Othman ◽  
Maaz Akhtar ◽  
Shahrul Kamaruddin ◽  
Rashid Khan ◽  
...  
Keyword(s):  
Creep Behavior ◽  
Creep Deformation ◽  
Curve Fitting ◽  
Elevated Temperatures ◽  
Creep Behaviour ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Creep Model ◽  
Secondary Creep ◽  
Dog Bone

In a number of circumstances, the Kachanov–Rabotnov isotropic creep damage constitutive model has been utilized to assess the creep deformation of high-temperature components. Secondary creep behavior is usually studied using analytical methods, whereas tertiary creep damage constants are determined by the combination of experiments and numerical optimization. To obtain the tertiary creep damage constants, these methods necessitate extensive computational effort and time to determine the tertiary creep damage constants. In this study, a curve-fitting technique was proposed for applying the Kachanov–Rabotnov model into the built-in Norton–Bailey model in Abaqus. It extrapolates the creep behaviour by fitting the Kachanov–Rabotnov model to the limited creep data obtained from the Omega-Norton–Bailey regression model and then simulates beyond the available data points. Through the Omega creep model, several creep strain rates for SS-316 were calculated using API-579/ASME FFS-1 standards. These are dependent on the type of the material, the flow stress, and the temperature. In the present work, FEA creep assessment was carried out on the SS-316 dog bone specimen, which was used as a material coupon to forecast time-dependent permanent plastic deformation as well as creep behavior at elevated temperatures and under uniform stress. The model was validated with the help of published experimental creep test data, and data optimization for sensitivity study was conducted by applying response surface methodology (RSM) and ANOVA techniques. The results showed that the specimen underwent secondary creep deformation for most of the analysis period. Hence, the method is useful in predicting the complete creep behavior of the material and in generating a creep curve.

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.

A Metallographic Technique for High Temperature Creep Damage Assessment in Single Crystal Alloys

1998 ◽  
Author(s):  
Pamela Henderson ◽  
Jacek Komenda
Keyword(s):  
High Temperature ◽  
Single Crystal ◽  
Creep Strain ◽  
Creep Deformation ◽  
Damage Assessment ◽  
Creep Damage ◽  
High Temperature Creep ◽  
Gamma Prime ◽  
Aspect Ratios ◽  
Metallographic Technique

The use of single crystal (SX) nickel-base superalloys will increase in the future with the introduction of SX blades into large gas turbines for base-load electricity production. Prolonged periods of use at high temperatures may cause creep deformation and the assessment of damage can give large financial savings. A number of techniques can be applied for life assessment, e.g. calculations based on operational data, non-destructive testing or material interrogation, but because of the uncertainties involved the techniques are often used in combination. This paper describes a material interrogation (metallographic) technique for creep strain assessment in SX alloys. Creep tests have been performed at 950°C on the SX alloy CMSX-4 and quantitative microstructural studies performed on specimens interrupted at various levels of strain. It was found that the strengthening γ′-particles, initially cuboidal in shape, coalesced to form large plates or rafts normal to the applied stress. The γ-matrix phase also formed plates. CMSX-4 contains ∼ 70 vol % γ′-particles and after creep deformation the microstructure turned itself inside out, i.e. the gamma “matrix” became the isolated phase surrounded by the γ′-“particles”. This can cause problems for computerised image analysis, which in this case, were overcome with the choice of a suitable measurement parameter. The rafts reached their maximum length before 2% strain, but continued to thicken with increasing strain. Although of different dimensions, the aspect ratios (length/thickness ratio) of the gamma-prime rafts and the gamma plates were similar at similar levels of strain, increasing from ∼1 at zero strain to a maximum of ∼3 at about 1–2 % strain. Analysis of microstructural measurements from rafting studies on SX alloys presented in the literature showed that the aspect ratios of the γ- and γ′-phases were similar and that at a temperature of 950–1000°C a maximum length/thickness ratio of about 2.5–3.5 is reached at 1 to 2% creep strain. Measurement of gamma-prime raft or (or gamma plate) dimensions on longitudinal sections of blades is thus a suitable method for high temperature creep damage assessment of SX alloys. This gives a considerable advantage over conventional Ni-base superalloys whose microstructures are usually very stable with respect to increasing creep strain.

Modeling the Temperature-Dependence of Tertiary Creep Damage of a Directionally Solidified Ni-Base Superalloy

2009 ◽  
Author(s):  
Calvin M. Stewart ◽  
Erik A. Hogan ◽  
Ali P. Gordon
Keyword(s):  
Experimental Data ◽  
Gas Turbine ◽  
Creep Damage ◽  
Time Estimation ◽  
General Purpose ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Directionally Solidified ◽  
Estimation Model ◽  
Element Analysis

Directionally solidified (DS) Ni-base superalloys have become a commonly used material in gas turbine components. Controlled solidification during the material manufacturing process leads to a special alignment of the grain boundaries within the material. This alignment results in different material properties dependent on the orientation of the material. When used in gas turbine applications the direction of the first principle stress experienced by a component is aligned with the enhanced grain orientation leading to enhanced impact strength, high temperature creep and fatigue resistance, and improve corrosion resistance compared to off axis orientations. Of particular importance is the creep response of these DS materials. In the current study, the classical Kachanov-Rabotnov model for tertiary creep damage is implemented in a general-purpose finite element analysis (FEA) software. Creep deformation and rupture experiments are conducted on samples from a representative DS Ni-base superalloys tested at temperatures between 649 and 982°C and two orientations (longitudinally- and transversely-oriented). The secondary creep constants are analytically determined from available experimental data in literature. The simulated annealing optimization routine is utilized to determine the tertiary creep constants. Using regression analysis the creep constants are characterized for temperature and stress-dependence. A rupture time estimation model derived from the Kachanov-Rabotnov model is then parametrically exercised and compared with available experimental data.

Modeling the Temperature Dependence of Tertiary Creep Damage of a Ni-Based Alloy

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Temperature Dependence ◽  
Creep Deformation ◽  
Mechanical Response ◽  
Axial Stress ◽  
Nauk Sssr ◽  
Damage Model ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Continuum Damage ◽  
Over Time

To capture the mechanical response of Ni-based materials, creep deformation and rupture experiments are typically performed. Long term tests, mimicking service conditions at 10,000 h or more, are generally avoided due to expense. Phenomenological models such as the classical Kachanov–Rabotnov (Rabotnov, 1969, Creep Problems in Structural Members, North-Holland, Amsterdam; Kachanov, 1958, “Time to Rupture Process Under Creep Conditions,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Mekh. Mashin., 8, pp. 26–31) model can accurately estimate tertiary creep damage over extended histories. Creep deformation and rupture experiments are conducted on IN617 a polycrystalline Ni-based alloy over a range of temperatures and applied stresses. The continuum damage model is extended to account for temperature dependence. This allows the modeling of creep deformation at temperatures between available creep rupture data and the design of full-scale parts containing temperature distributions. Implementation of the Hayhurst (1983, “On the Role of Continuum Damage on Structural Mechanics,” in Engineering Approaches to High Temperature Design, Pineridge, Swansea, pp. 85–176) (tri-axial) stress formulation introduces tensile/compressive asymmetry to the model. This allows compressive loading to be considered for compression loaded gas turbine components such as transition pieces. A new dominant deformation approach is provided to predict the dominant creep mode over time. This leads to development of a new methodology for determining the creep stage and strain of parametric stress and temperature simulations over time.

Fundamental Modelling of Mechanisms Contributing to Tertiary Creep in Copper at 215 and 250°C

2018 ◽  
Author(s):  
Fangfei Sui ◽  
Rolf Sandström
Keyword(s):  
Spent Nuclear Fuel ◽  
Creep Damage ◽  
Back Stress ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Creep Tests ◽  
Long Time ◽  
Higher Temperature ◽  
Good Agreement

Extensive creep tests have been performed on oxygen free copper with 50 ppm phosphorus at both low and high temperatures. It is the candidate material for storage of spent nuclear fuel in Sweden. Basic models without fitting parameters have been formulated to reproduce primary and secondary creep. For a long time, only empirical models existed for fitting of tertiary creep. To understand the role of creep damage, including recovery, cavitation and necking, basic models that do not involve adjustable parameters are in urgent demand. Only recently, basic models taking the relevant mechanisms into account have been developed. These models were used to predict the tertiary creep for copper at 75°C. The modelled results were compared with experimental creep curves and good agreement has been found. In the present paper, the models are applied to creep tests at higher temperatures (215 and 250°C). A similar representation with good accuracy is obtained. This demonstrates that the fundamental model for back stress is applicable for the higher temperature tests as well.

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