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.

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.

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.

Strain and Damage-Based Analytical Methods to Determine the Kachanov–Rabotnov Tertiary Creep-Damage Constants

2011 ◽  
Vol 21 (8) ◽  
pp. 1186-1201 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Creep Behavior ◽  
Creep Deformation ◽  
Analytical Methods ◽  
Numerical Optimization ◽  
Creep Damage ◽  
Tertiary Creep ◽  
Nickel Base Superalloy ◽  
Trial And Error ◽  
Nickel Base ◽  
Base Superalloy

In the power generation industry, the goal of increased gas turbine efficiency has led to increased operating temperatures and pressures necessitating nickel-base superalloy components. Under these conditions, the tertiary creep regime can become the dominant form of creep deformation. In response, the classical Kachanov–Rabotnov coupled creep-damage constitutive model is often used to predict the creep deformation and damage of Ni-base superalloys. In this model, the secondary creep behavior can be determined through analytical methods while the tertiary creep behavior is often found using trial and error or numerical optimization. Trial and error may produce no constants. Numerical optimization can be computationally expensive. In this study, a strain-based and damage-based approach to determine the tertiary creep behavior of nickel-base superalloys has been developed. Analytically determined constants are found for a given nickel-base superalloy. Creep deformation and damage evolution curves are compared. Methods to deal with stress dependence are introduced and studied.

Investigations on Creep Behavior of P91-Type Steel Using Combined Creep Damage Model

2013 ◽  
Author(s):  
Fujun Liu ◽  
Ping Tang ◽  
Shuai Kong ◽  
Zhangwei Ling ◽  
Muling Zheng ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Creep Behavior ◽  
Power Plants ◽  
Damage Model ◽  
Creep Damage ◽  
Damage Function ◽  
Creep Model ◽  
Secondary Creep ◽  
Type Steel ◽  
Damage Theory

P91-type steel is widely used for the high-temperature pipe work components in advanced power plants. The creep behavior of the P91-type steel has been studied by many researchers during the past years. Since it is well known that the creep behavior of P91-type steel cannot be satisfactorily described by a simple, Arrhenius-type, power-law constitutive model. While Norton-Bailey creep is a deviatoric temperature-dependent creep model, furbished with a time-hardening creep model, which is the most common model for modeling primary and secondary creep together, and Kachanov-Rabotnov creep damage theory described with Norton creep model can be used to model tertiary creep. Both of them based on Norton creep constitutive equation. In this paper, based on the Norton-Bailey creep law and Kachanov-Rabotnov creep damage theory, a new combined constitutive model has been developed, in which the creep and damage function are both considered as nonlinear variables. The damage parameters in the model have clear physical meaning and can be determined from the benchmark experiment. The results indicated that this combined damage model was applicable to describe the full damage evolution for P91-type steel.

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.

Numerical Simulation of Stress Relaxation and Creep Response of X20 Steam Piping under Diverse Operating Conditions

2021 ◽  
Vol 57 ◽  
pp. 19-32
Author(s):  
Smith Salifu ◽  
Dawood A. Desai ◽  
Schalk Kok
Keyword(s):  
Steady State ◽  
Stress Relaxation ◽  
Damage Accumulation ◽  
Creep Behaviour ◽  
Creep Damage ◽  
Operating Conditions ◽  
Creep Model ◽  
Element Analysis ◽  
Peak Period ◽  
Creep Response

The creep response and stress relaxation of X20 CrMoV12-1 steam piping under diverse operating conditions were simulated using finite element analysis (FEA) code, Abaqus alongside fe-safe/Turbolife software. In the study, steady-state creep and creep analysis characterized by 24 hours daily cycle consisting of a total of 6 hours peak, 4 hours transient and 14 hours off-peak period was considered. Modified hyperbolic sine creep model used in the analysis was implemented in Abaqus via a special creep user-subroutine to compute the stress relaxation and creep behaviour, while the useful service life and creep damage was estimated using fe-safe/Turbolife. The optimum creep strain, stress, damage, and worst life were found at the intrados of the piping, with the steady-state analysis having a higher useful creep life and slower creep damage accumulation. Furthermore, slower stress relaxation with faster damage accumulation was observed in the analysis involving cycles. Finally, a good agreement was obtained between the analytical calculated and simulated rates of the piping.

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.

Long-term settlement of model rock-socketed piers

1989 ◽  
Vol 26 (3) ◽  
pp. 348-358 ◽  
Author(s):  
Robert G. Horvath ◽  
K-J. Chae
Keyword(s):  
Large Scale ◽  
Load Transfer ◽  
Creep Behaviour ◽  
Small Diameter ◽  
Soft Rock ◽  
Load Test ◽  
Creep Model ◽  
Secondary Creep ◽  
Initial Portion

Very little information is available concerning the long-term settlement behaviour of drilled pier foundations socketed into rock. This paper summarizes the results of laboratory investigations of the long-term settlement (creep) behaviour of model socketed pier foundations. The testing program included seven model piers constructed with different materials and different load-support conditions. The primary models were two small-diameter concrete piers constructed in soft shale. For all models tested the results indicated similarly shaped time–displacement curves, having two distinct regions. The initial portion of the curves represents a region of primary creep and the remaining portion represents a zone of secondary creep having a much lower rate of displacement. A comparison of short-term (1 day, which is a normal maximum duration of a full-scale load test) and long-term (200 days) settlements for the model piers showed an 84–245% increase in settlements. In addition, some information concerning load transfer with time in the model piers and available data from loading tests on large-scale socketed piers are included. Key words: socketed pier foundations, long-term settlement, creep model tests, soft rock.

scholarly journals Experimental and Theoretical Studies on the Creep Behavior of Bayer Red Mud

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Baoyun Zhao ◽  
Wei Huang ◽  
Zhile Shu ◽  
Mengmeng Han ◽  
Yanbo Feng
Keyword(s):  
Creep Strain ◽  
Creep Behavior ◽  
Red Mud ◽  
Damage Model ◽  
Creep Damage ◽  
Creep Model ◽  
Creep Tests ◽  
Accelerated Creep ◽  
Bayer Red Mud ◽  
Creep Damage Model

Long-term stability and safety of the Bayer red mud (BRM) disposal field is very important for the local residents’ life, which necessitates the knowledge of its creep behavior. In order to investigate the creep behavior of BRM, a series of triaxial drained creep tests were conducted by using an improved triaxial creep apparatus. The results indicate that the creep behavior of BRM is significant with confining and deviatoric stresses being critical factors. The creep strain is in a nonlinear relationship with stress and time, and a larger deviator stress will lead to a larger creep strain. The main failure mechanism of BRM is plastic shear, accompanied by a significant compression and ductile dilatancy. Based on the test results, two well-established creep models, the Burgers creep model and Singh–Mitchell creep model, were used to comparatively analyze the creep behavior of the Bayer red mud under a certain stress level. Then, an improved Burgers creep damage constitutive model with the addition of a damage variable was proposed, whose parameters were also analyzed in detail. The comparison of the calculated values of the creep model and the experimental values shows that the proposed creep damage model can better describe the instant elastic deformation, attenuation creep, steady-state creep, and accelerated creep stages of the Bayer red mud.

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.

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