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 Calibration of CDM-Based Creep Constitutive Model Using Accelerated Creep Test (ACT) Data

2020 ◽  
Author(s):  
Md Abir Hossain ◽  
Robert Mach ◽  
Jacob Pellicotte ◽  
Calvin M. Stewart
Keyword(s):  
Constitutive Model ◽  
Creep Strain ◽  
Creep Deformation ◽  
Numerical Optimization ◽  
Creep Damage ◽  
Deformation Curve ◽  
Long Duration ◽  
Processing Procedure ◽  
Accelerated Creep ◽  
Damage Constitutive Model

Abstract In conventional creep testing (CCT) a specimen is subject to constant load and temperature for a long-duration until creep rupture occurs. Conventional testing can be costly when considering the number of experiments needed to characterize the creep response of a material over a range of stress and temperature. To predict long-term creep-rupture properties, the time-temperature-stress superposition principle (TTSSP) approach has been employed where stress and/or temperature is applied at an elevated level; the result of which are extrapolated down to low stress and/or temperature conditions. These methods have been successful in predicting minimum-creep-strain-rate (MCSR) and stress-rupture (SR) but suffer from an inability to predict the creep deformation curve or account for changes in deformation mechanisms or aging that occurs at long-duration. An accelerated technique, termed the Stepped isostress method (SSM) allows the accelerated testing of materials to determine their creep deformation response. Unlike TTSSP tests, the SSM test employs a single specimen where the stress is periodically step increased until rupture. The SSM creep deformation curve is processed (time and strain shifted) to produce an accelerated creep deformation curve that represent the creep deformation curve at the initial stress level in SSM. A processing procedure for metals has yet to be developed. The research objective of this study is to develop a processing procedure for SSM test data using a creep-damage constitutive model. Triplicate SSM tests were conducted on Ni-based superalloy Inconel 718 at 650°C with stress being periodically increased until rupture. Triplicate CCT tests were conducted at the initial stress level of the SSM tests. The Sine-hyperbolic (Sinh) creep-damage model was employed in this study. The Sinh creep-damage constitutive model is based on coupled creep strain rate and damage evolution equations; where both rates are dependent on the current state of damage. Calibration is two-step: analytical and numerical optimization. Each stepped creep deformation curve is tackled quasi-analytically to determine MCSR and SR related material constants and accumulated damage. The damage accumulated at the end of each step was then passed onto subsequent steps to calibrate the MCSR, rupture prediction, and damage evolution. Numerical optimization was applied to optimize model constants involved in the creep strain constitutive equations in order to generate best-fitted Sinh creep deformation curves. The Sinh model predictions were compared to the SSM and CCT data. The Sinh model satisfactorily predicts the SSM data and thus the calibrated material constants provides a good estimate of rupture found in the CCT data. Calibration using SSM data reduces the number of tests needed to calibrate a model; significantly reducing costs. A single SSM test replaces numerous creep tests at different stresses.

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.

A Multistage Creep Damage Constitutive Model for Isotropic and Transversely-Isotropic Materials With Elastic Damage

2011 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Constitutive Model ◽  
Creep Deformation ◽  
Constitutive Models ◽  
Creep Damage ◽  
Transversely Isotropic ◽  
Common Source ◽  
Isotropic Materials ◽  
Damage Constitutive Model ◽  
Transversely Isotropic Materials ◽  
Elastic Damage

In the pressure vessel and piping and power industries, creep deformation has continued to be an important design consideration. Directionally-solidified components have become commonplace. Creep deformation and damage is a common source of component failure. A considerable effort has gone into the study and development of constitutive models to account for such behavior. Creep deformation can be separated into three distinct regimes: primary, secondary, and tertiary. Most creep damage constitutive models are designed to model only one or two of these regimes. In this paper, a multistage creep damage constitutive model is developed and designed to model all three regimes of creep for isotropic materials. A rupture and critical damage prediction method follows. This constitutive model is then extended for transversely-isotropic materials. In all cases, the influence of creep damage on general elasticity (elastic damage) is included. Methods to determine material constants from experimental data are detailed. Finally, the isotropic material model is exercised on tough pitch copper tube and the anisotropic model on a Ni-base superalloy.

An anisotropic tertiary creep damage constitutive model for anisotropic materials

2011 ◽  
Vol 88 (8-9) ◽  
pp. 356-364 ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon ◽  
Young Wha Ma ◽  
Richard W. Neu
Keyword(s):  
Constitutive Model ◽  
Creep Damage ◽  
Anisotropic Materials ◽  
Tertiary Creep ◽  
Damage Constitutive Model

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 a Creep Damage Constitutive Model for the Rotor of a 1000 MW Ultra-Supercritical Steam Turbine

2015 ◽  
Author(s):  
Jishen Jiang ◽  
Weizhe Wang ◽  
Nailong Zhao ◽  
Peng Wang ◽  
Yingzheng Liu ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Steam Turbine ◽  
Axial Stress ◽  
Creep Damage ◽  
Turbine Rotor ◽  
Creep Analysis ◽  
Wide Range ◽  
Damage Constitutive Model ◽  
Creep Constitutive Model ◽  
Basic Features

A damage-based creep constitutive model for a wide stress range is applied to the creep analysis of a 1000 MW ultra-supercritical steam turbine, the inlet steam of which reaches 600°C and 35 MPa. In this model, the effect of complex multi-axial stress and the nonlinear evolution of damage are considered. To this end, the model was implemented into the commercial software ABAQUS using a user-defined material subroutine code. The temperature dependent material constants were identified from the experimental data of advanced heat resistant steels using curve fitting approaches. A comparison of the simulated and the measured results showed that they reached an acceptable agreement. The results of the creep analysis illustrated that the proposed approach explains the basic features of stress redistribution and the damage evolution in the steam turbine rotor over a wide range of stresses and temperatures.

Sign in / Sign up

Export Citation Format

Share Document