Creep Constitutive Equations for 1CrMoV Bolt Material

2002 ◽  
Author(s):  
Fred V. Ellis ◽  
Robert L. Zielke
Keyword(s):  
Creep Rate ◽  
Power Law ◽  
Constitutive Equations ◽  
Minimum Creep Rate ◽  
Good Description ◽  
Primary Creep ◽  
Primary Component ◽  
Creep Equation ◽  
Statistical Measures ◽  
Rational Polynomial

Creep constitutive equations were developed for 1CrMoV bolt material using the NRIM creep data at temperatures of 450°C, 500°C and 550°C. The creep constitutive equations were those used by the ANSYS FEM stress analysis program. Three types of creep equations were developed: (1) primary, (2) secondary, and (3) primary plus secondary. The primary creep equation had a power law in stress and time with an exponential inverse temperature dependence. The secondary models for log minimum creep rate had either log stress alone or stress and log stress terms. Two primary plus secondary models were used: (1) a power law primary and (2) the rational polynomial. For the rational polynomial, the constant p was estimated as nineteen over the time to the end of primary creep. The time to end of primary creep was defined by the attainment of a low value for the ratio of the primary creep rate to minimum creep rate. The primary creep rate was calculated using the power law primary component of the power law primary plus steady state creep equation. To evaluate the fits, comparisons of calculated and observed creep curves were made as well as plots of residual in log creep strain. Based on these comparisons and the statistical measures (R2 and standard deviation), the derived creep equations were judged to be a good description of the creep behavior.

Creep and Creep-rupture Behavior of 2124-T851 Aluminum Alloy

2013 ◽  
Vol 32 (6) ◽  
pp. 533-540 ◽  
Author(s):  
Yu-Qiang Jiang ◽  
Y.C. Lin ◽  
C. Phaniraj ◽  
Yu-Chi Xia ◽  
Hua-Min Zhou
Keyword(s):  
Aluminum Alloy ◽  
Creep Rate ◽  
Power Law ◽  
Minimum Creep Rate ◽  
Tensile Creep ◽  
Uniaxial Tensile ◽  
Secondary Creep ◽  
Creep Life ◽  
Creep Tests ◽  
Creep Equation

AbstractHigh temperature creep and useful creep life behavior of Al-Cu-Mg (2124-T851 aluminum) alloy was investigated by conducting constant stress uniaxial tensile creep tests at different temperatures (473–563 K) and at stresses ranging from 80 to 200 MPa. It was found that the stress and temperature dependence of minimum creep rate could be successfully described by the power-law creep equation. The power-law stress exponent, n = 5.2 and the activation energy for secondary creep, Q = 164 kJ mol−1, which is close to that observed for self diffusion of aluminum (~140 kJ mol−1). The observed values of n and Q suggest that the secondary creep of 2124-T851 aluminum alloy is governed by the lattice diffusion controlled dislocation climb process. A Monkman-Grant type relationship between minimum creep rate and time for reaching 1.5% creep strain is proposed and could be employed for predicting the useful creep life of 2124-T851 aluminum alloy.

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.

Creep During Power-Law Breakdown in Phosphorus Alloyed Copper

2007 ◽  
Author(s):  
Rolf Sandstro¨m ◽  
Henrik C. M. Andersson
Keyword(s):  
Creep Rate ◽  
Effective Stress ◽  
Power Law ◽  
Constitutive Equations ◽  
Pure Copper ◽  
Back Stress ◽  
Fe Modelling ◽  
Creep Ductility ◽  
First Case ◽  
Order Of Magnitude

Copper alloyed with 50 ppm phosphorus (Cu-OFP) is selected for canisters for nuclear waste packages to avoid a low creep ductility, which is sometimes present in pure copper. The operating temperatures of these canisters are in the range from 0 to 100°C. Creep readily takes place in copper even at room temperature. At temperatures below 100°C, creep is well inside the power-law breakdown regime. The creep exponent is in the range from 30 to 100. Since creep models for this situation are missing in the literature, a new model for the minimum creep rate based on fundamental principles for climb and glide has been derived. This model gives the correct order of magnitude for the creep rate in the temperature range from 20 to 400°C without the use of fitted parameters. Design against creep can either be based on the total applied stress or the effective stress. In the first case the constitutive equations can be directly obtained from the minimum experimental creep rates. A new approach is proposed to handle the effective stress case, which is based on the initial creep rates. The φ-model is used to relate the initial creep rate to the minimum one. It is shown how the constitutive equations for the creep rate and the back stress can be transferred to multiaxial stress states for use in FE-modelling.

Investigation of Tensile and Compressive Creep Behaviour of AA2050-T34 during Creep Age Forming Process

2016 ◽  
Vol 716 ◽  
pp. 323-330 ◽  
Author(s):  
Yong Li ◽  
Zhusheng Shi ◽  
Yo Lun Yang ◽  
Jian Guo Lin
Keyword(s):  
Power Law ◽  
Creep Behaviour ◽  
Primary Creep ◽  
Constitutive Modelling ◽  
Ageing Process ◽  
Forming Process ◽  
Creep Equation ◽  
Compressive Creep ◽  
Creep Stress ◽  
Creep Age Forming

The tensile and compressive creep behaviour of aluminium alloy 2050 with T34 initial temper (AA2050-T34) during creep-ageing process has been experimentally investigated and analysed in detail. Both tensile and compressive creep-ageing tests under various stress levels (ranging from 100 MPa to 187.5 MPa) have been carried out at a temperature of 155 °C for 18 hours. The results show that creep strains under tensile stresses are much larger than those under the same levels of compressive stresses and a new “double primary creep feature” with five-stage creep behaviour has been observed in the alloy during the creep-ageing tests. The conventional power-law creep equation was applied to analyse the new creep behaviour of the alloy at the steady-state creep stage. Furthermore, the power-law relationship between the applied stress and the corresponding creep strain rate was found to be effective in all creep-ageing stages of the alloy and was used for further analysis. These analyses indicate that the dislocation and diffusion mechanisms may both contribute to this new creep behaviour and may play different roles in different creep-ageing stages. Moreover, the evolution of the creep resistance or threshold creep stress of the alloy during the creep-ageing process was quantitatively investigated by the proposed relationship. These results help to not only understand the new creep behaviour of AA2050-T34 during the creep-ageing process, but also facilitate further constitutive modelling of this new creep behaviour for its creep age forming applications.

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.

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.

CREEP ANALYSIS FOR A WIDE STRESS RANGE BASED ON STRESS RELAXATION EXPERIMENTS

2008 ◽  
Vol 22 (31n32) ◽  
pp. 5413-5418 ◽  
Author(s):  
HOLM ALTENBACH ◽  
KONSTANTIN NAUMENKO ◽  
YEVGEN GORASH
Keyword(s):  
Experimental Data ◽  
Creep Rate ◽  
Stress Relaxation ◽  
Constitutive Model ◽  
Power Law ◽  
Creep Behavior ◽  
Minimum Creep Rate ◽  
High Stress ◽  
Stress Range ◽  
Power Law Creep

Many materials exhibit a stress range dependent creep behavior. The power-law creep observed for a certain stress range changes to the viscous type creep if the stress value decreases. Recently published experimental data for advanced heat resistant steels indicates that the high creep exponent (in the range 5-12 for the power-law behavior) may decrease to the low value of approximately 1 within the stress range relevant for engineering structures. The aim of this paper is to confirm the stress range dependence of creep behavior based on the experimental data of stress relaxation. An extended constitutive model for the minimum creep rate is introduced to consider both the linear and the power law creep ranges. To take into account the primary creep behavior a strain hardening function is introduced. The material constants are identified for published experimental data of creep and relaxation tests for a 12% Cr steel bolting material at 500°C. The data for the minimum creep rate are well-defined only for moderate and high stress levels. To reconstruct creep rates for the low stress range the data of the stress relaxation test are applied. The results show a gradual decrease of the creep exponent with the decreasing stress level. Furthermore, they illustrate that the proposed constitutive model well describes the creep rates for a wide stress range.

scholarly journals THE INITIAL CREEP OF COLUMNAR-GRAINED ICE: PART II. ANALYSIS

1965 ◽  
Vol 43 (8) ◽  
pp. 1423-1434 ◽  
Author(s):  
L. W. Gold
Keyword(s):  
Creep Rate ◽  
Creep Strain ◽  
Power Law ◽  
Creep Behavior ◽  
Minimum Creep Rate ◽  
Transient Creep ◽  
Time Dependent ◽  
Secondary Creep ◽  
Stress Dependence ◽  
Deflection Rate

Observations on the initial creep behavior of columnar-grained ice are analyzed by assuming that the creep strain at a given time has a power-law dependence on the applied constant compressive stress. The exponent for the stress was time-dependent during transient creep. For first load it started at a low value, increased to a maximum of about 2.23 approximately 75 minutes after the application of the load, and decreased thereafter. For reload it started at a high value and decreased continuously to a constant value of 1.46 by 100 minutes after the application of the load. Creep rates at a given time, calculated from the observed power-law dependence of the creep strain on stress, also had a power-law dependence on stress for time greater than about 25 minutes after the application of the load. The observations are shown to be in agreement with observations by Krausz (1963) on the deflection rate of ice beams and by Steine-mann (1954) and Glen (1958) on the stress-dependence of the minimum creep rate during secondary creep. The observations indicate that the creep rate during secondary creep varies approximately as t−0.5.

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