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.

Modelling of Tertiary Creep In Copper at 215 and 250°C

2020 ◽  
pp. 1-31
Author(s):  
Rolf Sandström ◽  
Fangfei Sui
Keyword(s):  
Dislocation Structure ◽  
Creep Damage ◽  
Empirical Models ◽  
Tertiary Creep ◽  
Creep Tests ◽  
Tertiary Stage ◽  
Creep Curves ◽  
Long Time ◽  
Lower Temperature

Abstract For a long time, only empirical models existed for creep curves in the tertiary stage. To understand the role of creep damage, including changes in the dislocation structure, cavitation and necking, basic models that do not involve adjustable parameters have however, recently been developed. These models were used to predict tertiary creep for copper at 75°C. In the present paper, these models are applied to creep tests at higher temperatures (215 and 250°C). These results demonstrate again that tertiary creep in copper is primarily controlled accelerated recovery of the dislocation structure and not by cavitation. The modelling results suggest that the role of cavitation is modest also in other creep exposed ductile alloys, which should be of importance to consider in the formulation of models for creep damage. Necking was only found to be of significance very close to rupture again in agreement with results at lower temperature.

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.

Creep Buckling of Ovalized Tubes Under External Pressure

1996 ◽  
Vol 118 (4) ◽  
pp. 460-463 ◽  
Author(s):  
V. Koundy ◽  
T. Forgeron ◽  
J. Hivroz
Keyword(s):  
Analytical Approach ◽  
External Pressure ◽  
The Finite Element Method ◽  
Creep Tests ◽  
Circular Tubes ◽  
Geometrical Characteristics ◽  
Calculation Results ◽  
Numerical Program ◽  
Good Agreement

In order to get a better understanding of the role of various parameters on the creep collapse phenomenon of long circular tubes, an experimental and numerical program has been undertaken. It mainly aims at studying the influence of the behavior of the material composing the circular tubes and their geometrical characteristics on the flattening time. This paper presents the results of numerical simulations performed with a specific computer program using an analytical approach. They have been compared with the data obtained from creep tests performed in various conditions on preovalized tubes as well as with the solutions obtained from the finite element method. It is shown that a good agreement is achieved between experimental results and calculation results.

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.

Creep Deformation of Ta Modified Gamma Prime Single Crystals

1986 ◽  
Vol 81 ◽  
Author(s):  
D.L. Anton ◽  
D.D. Pearson ◽  
D.B. Snow
Keyword(s):  
Single Crystals ◽  
Single Phase ◽  
High Ratio ◽  
Tertiary Creep ◽  
Creep Tests ◽  
Two Phase ◽  
Surface Stability ◽  
Substitutional Element ◽  
Gamma Prime

AbstractThe role of substitutional element alloying of single phase γ' has become of primary interest to alloy designers who would like to exploit its low density and excellent oxidation resistance. Current γ' alloys have not shown sufficient strength to be useful in a creep limited environment. In order to maximize the potential of single phase γ' alloys and to more fully understand the creep strengthening mechanisms in two phase Ni-base superalloys, it has become necessary to clarify the role of Al-substitution elements. Ta is a potent strengthening element in γ' as well as imparting beneficial surface stability to superalloys; its effect on the creep properties of Ni3Al is the subject of this paper. The 1300°C isotherm of the Ni-Al-Ta system was determined in order to establish the γ' single phase field. Comrpositions were fabricated having chemistries which systematically varied both the Al:Ta ratio at Ni=75% and Ni:(AI+Ta) ratio at Ta=6%. Creep tests were conducted on <001> oriented single crystals at 760, 871 and 982°C. Electron microscopy was used to characterize the nature of slip deformation, confirm phase purity and to determine the existence of tetragonal distortions in these crystals. In this manner the strengthening due to Ta was examined in the absence of grain boundary effects. These γ' mono—crystals did not display classical creep response. Incubation creep was observed in all of the specimens tested. Surprisingly, the maximum incubation time was found to occur in the high ratio Ni:(Al+Ta) compounds, where less than 0.5% creep strain was obtained after 200 hours at stress. After incubation, either tertiary creep leading to failure, or apparently classic primary, secondary and tertiary creep ensued. In addition extremely long elongations, to 85%, were measured.

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.

An Improved Anisotropic Tertiary Creep Damage Formulation

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Calvin M. Stewart ◽  
Ali P. Gordon ◽  
Young Wha Ma ◽  
Richard W. Neu
Keyword(s):  
Damage Model ◽  
Creep Damage ◽  
Cyclic Fatigue ◽  
Grain Structure ◽  
Tertiary Creep ◽  
Secondary Creep ◽  
Directionally Solidified ◽  
Stress Concentrations ◽  
Element Analysis ◽  
Damage Formulation

Directionally solidified (DS) Ni-base superalloys are commonly used as gas turbine materials to primarily extend the operational lives of components under high load and temperature. The nature of DS superalloy grain structure facilitates an elongated grain orientation, which exhibits enhanced impact strength, high temperature creep and fatigue resistance, and improved corrosion resistance compared with off-axis orientations. Of concern to turbine designers are the effects of cyclic fatigue, thermal gradients, and potential stress concentrations when dealing with orientation-dependent materials. When coupled with a creep environment, accurate prediction of crack initiation and propagation becomes highly dependent on the quality of the constitutive damage model implemented. This paper describes the development of an improved anisotropic tertiary creep damage model implemented in a general-purpose finite element analysis software. The creep damage formulation is a tensorial extension of a variation in the Kachanov–Rabotnov isotropic tertiary creep damage formulation. The net/effective stress arises from the use of the Rabotnov second-rank symmetric damage tensor. The Hill anisotropic behavior analogy is used to model secondary creep and tertiary creep damage behaviors. Using available experimental data for a directionally solidified Ni-base superalloy, the improved formulation is found to accurately model intermediate oriented specimen.

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.

The Problem of Identifying and Modeling the Relationship between Monetary Factor and Inflation in the Russian Economy

2008 ◽  
pp. 61-76
Author(s):  
A. Porshakov ◽  
A. Ponomarenko
Keyword(s):  
Money Supply ◽  
Money Demand ◽  
Russian Economy ◽  
Long Run ◽  
Complex Approach ◽  
Wide Range ◽  
Long Time ◽  
The Relationship ◽  
Supply Side Factors

The role of monetary factor in generating inflationary processes in Russia has stimulated various debates in social and scientific circles for a relatively long time. The authors show that identification of the specificity of relationship between money and inflation requires a complex approach based on statistical modeling and involving a wide range of indicators relevant for the price changes in the economy. As a result a model of inflation for Russia implying the decomposition of inflation dynamics into demand-side and supply-side factors is suggested. The main conclusion drawn is that during the recent years the volume of inflationary pressures in the Russian economy has been determined by the deviation of money supply from money demand, rather than by money supply alone. At the same time, monetary factor has a long-run spread over time impact on inflation.

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