Optimization and verification of creep equations for heat resistant steels

A direct creep curve assessment of multi-heat creep data delivers condensed creep curve bands of a steel type for a limited number of stress groups. The mean creep curves of these stress groups are the basis for an examination and if necessary optimization of a creep equation which was originally based on a time temperature parameter assessment. This procedure is demonstrated for creep equations of steel types 10 CrMo 9 10 and X 21 CrMoV 12 1. The creep equations are available in the form of a subroutine Kara FW which serves as a user subroutine for finite element programmes. The scatter band covered by such a creep equation can be described by strain factors for initial plastic strain and for creep strain. A critical strain was developed to indicate creep rupture or local crack initiation. This critical strain is the uniform elongation which appears at rupture. It can be determined by finite element analyses of the specimens tested. Further, the optimized creep equations are verified by the recalculation of different service type tests using the programme Abaqus and the subroutine Kara FW.     

Direct creep curve assessment and optimization of creep equations for high temperature alloys

The conventional use of a time temperature parameter method for the basic assessment of a multi-heat creep data set facilitates the establishment of a creep equation for a material type. However, the parameter can introduce some distortion to the creep data and hence the creep equation. To avoid this disadvantage, a new method for the direct creep curve assessment of multi-heat data was developed. Systematic deviations in creep behaviour of individual test materials in respect to the mean behaviour of the multi-heat data set are reduced and the creep curves for individual stresses are transformed to mid creep curves of a limited number of stress classes. With this method large multi-heat creep data sets of Alloy 100 and Alloy 738 LC could be reduced to mean creep curves. On this basis, existing parameter based creep equations were examined and optimized, if necessary. Further, the confidence limits of these equations were determined. With a stress modification the creep behaviour of a material similar in structure can be described. In finite element analyses some verification experiments which simulate typical loading conditions of components could be successfully recalculated with the optimized creep equations.     

Creep equations for high temperature alloys on the basis of a parametric assessment of multi-heat data

For the design of high temperature components creep equations are necessary. These describe the deformation behaviour of the material type used over its whole application range. The method of developing such an equation is demonstrated for the example of alloy G-NiCo 15 Cr 10 Al 6 TiMo (Alloy 100). As a basic requirement, a multi-heat assessment of time to specific strain is performed with the aid of a time temperature parameter procedure. In this way optimum correlated master curves are generated for the whole range of permanent strain and rupture. From these curves mean creep curves for the material type can be determined by minimal further smoothing. On the basis of these creep curves a modified Garofalo equation with initial plastic strain as well as primary, secondary and tertiary strain can be established to describe the creep behaviour of Alloy 100. Additionally, an equation for the time temperature dependent contraction of this alloy can be developed. These equations form a useful tool for the calculation of high temperature components with the finite element method.     

Predictive capabilities of the dislocation-network theory of Harper-Dorn creep

The dislocation-network theory of Harper-Dorn (H-D) creep is reformulated using a new equation for the kinetics of growth of individual dislocation links in the network. The new kinetic equation has no impact on the scaled differential equation derived previously, which predicts the distribution of link lengths. However, the new theory predicts slightly different behavior for the kinetics of static recovery and leads to a new equation for the strain rate, which is expressed in terms of parameters that can be evaluated independently. This equation is valid not only for steady-state H-D creep, but is also valid for primary creep, provided the instantaneous value of the dislocation density is known. Using data on the variation of dislocation density with time, calculated values of the creep rates for Al deformed in the H-D regime agree with experimentally measured values to within a factor of 2. Creep curves for Al are calculated with the same degree of accuracy. These calculations involve no adjustable parameters. Steady-state creep rates for many materials presumably deformed in the H-D creep regime are compared with the predictions of the new equation for the strain rate. The calculated values agree with experimentally measured data to within a factor of about 150, which compares well with the predictions of other equations proposed in the literature. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in San Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy.     

Hot Deformation Behavior of GCr15 Steel

 Hot deformation behavior of GCr15 (ASTM 52100) steel was investigated using single-hit compression tests on Gleeble-1500 simulator at the temperature range of 850-1100 ℃ and strain rate range of 0. 1-10 s-1. The flow stress constitutive equation of GCr15 steel during hot deformation was determined by stress-strain curves analysis on the basis of the hyperbolic sine equation. And the models of dynamic recrystallization fraction and dynamic recrystallization grain size of GCr15 steel were established by the measured curves and microstructure observation in different experimental conditions. The mean activation energy and the time exponent of dynamic recrystallization kinetics equation in the range of experimental conditions were determined to be 356. 2 kJ/mol and 2. 12, respectively. Meanwhile, the flow stress model was also established by the method of allocating flow stress curve with three main stress values, the saturation stress, the steady state stress and the stress when strain is 0. 1. The flow stress curves predicted by the developed models under different deformation conditions are in good agreements with the measured ones.     

Transient creep in mild steel and copper at room temperature

Transient creep curves were obtained from mild steel and copper specimens which had been work hardened by cycling. Results are presented in terms of an “overstress” model in which strain rates are related to differences between the actual stress and the corresponding stress-strain point on a quasi-static stress-strain curve. It is further shown that a semi-empirical equation used to describe steady state plastic deformation can be adapted to describe transient behaviour when re-written in terms of the ‘overstress’ rather than the actual stress.     

New model describing creep of metallic materials under variable temperatures

A creep function using only three fitting parameters is presented hereafter. The function is derived from a more general physical - phe-nomenoiogical model representing metallic materials creep behaviour and describes all three stages of creep. The dependence of the fitting parameters upon the temperature are investigated and simple analytical relations are provided for that purpose. Those relations already incorporate the effect of stress. At the outcome, ten material constants are derived which are neither dependent on the stress nor on the temperature. On the basis of the derived constitutive relations a prediction is carried out for creep strain of three metallic materials and particularly steels, at different temperatures and under constant stress. The derived curves agree with the experiments, not only the ones carried out in the laboratory but also the ones taken from literature.     

High Temperature Deformation Behavior of 4340 Steel: Activation Energy Calculation and Modeling of Flow Response

The 4340 steel is extensively utilized in several industries including automotive and aerospace for manufacturing a large number of structural components. Due to the importance of thermo-mechanical processing in the production of steels, the dynamic recrystallization (DRX) characteristics of 4340 steel were investigated. Namely, hot compression tests on 4340 steel have been performed in a temperature range of 900–1200 °C and a strain rate range of 0. 01–1 s^?1 and the strain of up to 0. 9. The resulting flow stress curves show the occurrence of dynamic recrystallization. The flow stress values decrease with the increase of deformation temperature and the decrease of strain rate. The microstructure of 4340 steel after deformation has been studied and it is suggested that the evolution of DRX grain structures can be accompanied by considerable migration of grain boundaries. The constitutive equations were developed to model the hot deformation behavior. Finally based on the classical stress-dislocation relations and the kinematics of the dynamic recrystallization; the flow stress constitutive equations for the dynamic recovery period and dynamic recrystallization period were derived for 4340 steel, respectively. The validity of the model was demonstrated by demonstrating the experimental data with the numerical results with reasonable agreement.     

Finite element modelling of the creep deformation of T91 steel weldments at 600°C

Finite element modelling of the creep deformation of T91 steel weldments, welded using the manual metal arc (MMA) and submerged arc (SA) welding processes, was carried out to predict creep curves for both of the weldments under different stresses and compared with the experimental data. The stress and strain redistribution across the length of the transverse-weld specimens has also been predicted. Data of creep tests at 600°C at stresses between 90-130 MPa for the base metal, the MMA and SA weld metals, and the simulated heat-affected zone were used to determine Garofalo's equation for creep strain. Finite element meshes for both of the weldments were constructed after calculating the HAZ locations using Rosenthal's heat flow equation.     

9Cr低活化马氏体钢高温变形行为

采用Gleeble-1500D热模拟试验机研究了9Cr低活化马氏体钢在950~1200℃、应变速率为10^-2~10s^-1变形条件下的热压缩变形行为,并用金相显微镜观察了相应显微组织的变化.回归分析得出在0.15~0.8真应变量范围内变形激活能和材料常数随真应变量变化的关系式,并得出双曲正弦本构方程;利用数学方法直接从真应力-真应变曲线获得动态再结晶的峰值应力、临界应力、峰值应变和临界应变;回归得出了峰值应力、临界应力、峰值应变、临界应变和动态再结晶晶粒大小与Zener-Hollomon参数的关系式.     

Determination of parameters for thermally activated glide from stress- strain curves at different temperatures and strain rates

Material parameters describing both steady state and primary creep deformation by thermally activated dislocation glide were investigated as a function of temperature for polycrystalline copper by determining stress-strain curves at different rates. Dynamic rather than static testing had to be used to eliminate effects due to other deformation mechanisms at the higher temperatures. Activation energies and 0 K flow stresses involved in both steady state and primary creep equations were independent of temperature. The flow stress terms defining ’equilibrium’ stress-strain curves required for the primary creep formulation were linear functions of temperature. This indicates that primary creep due to thermally activated glide at different temperatures may be estimated from tests at a single temperature.     

Constitutive Equations for Flow Behavior of Powder-forged Fe-0.5C-2Cu Steel under Hot Compression

To investigate the hot deformation behavior of powder-forged(P/F)Fe-0.5C-2Cu steel,the hot compression tests were conducted at temperatures ranging from 900to 1 000 ℃ and strain rates from 0.1to 10s-1 using Gleeble-1500thermal simulator.The true stress-true strain curves at different temperatures and strain rates of P/F steel were obtained.It is found that dynamic recovery only occurs as strain rate is 10s-1 at 900℃,and the dynamic recrystallization is the main softening mechanism.The flow stress increases with decreasing temperature and increasing strain rate.The experimental data are employed to develop constitutive equations on the basis of the Arrheniustype equation by introducing the strain with nonlinear fitting.The flow stresses predicted by the proposed constitutive equations are in good agreement with the experimental values,and the correlation coefficient(R2)and the average absolute relative error(AARE)are 0.995 25and 3.07%respectively.These results indicate the proposed constitutive equations can effectively describe the hot deformation behavior of the material.     

高铌微合金钢高温变形流变应力预测模型

 以流变应力曲线的唯象特征和本构方程的传统理论为基础,针对高铌微合金钢开发出一种新的描述高温变形应力 应变曲线的数学模型。该模型包括两个基本方程,确立了应力与应变、温度、变形速率的数学关系,预测了加工硬化和动态再结晶各阶段流变应力的变化,预测结果与实验结果吻合良好。     

Creep mechanism in Fe-1.8 At. Pct Mo alloy at high temperatures

High temperature creep of Fe-1.8Mo alloy, the stress exponent,n, of which is about 4, has been studied to check whether then value can be a good indication of the creep mechanism or not. Creep tests were carried out at 1124 K under 5.9 to 39.2 MPa. After sudden stress increments during the steady-state creep, inverse-type transient creep curves were obtained with no instantaneous permanent strain. Mean internal stresses were determined by stress-transient dip-tests using a back extrapolation technique. The mean internal stress was obviously smaller than the applied stress. These results indicate that creep deformation of Fe-1.8Mo alloy under the present conditions is controlled by the viscous glide motion of dislocations, thoughn is not close to 3. Steady-state creep rates as well as the value ofn calculated from the Orowan-type equation using experimentally obtained values for every parameter, are in reasonable agreement with the observed ones. These findings suggest that classification of creep behavior according to then value is not appropriate in some cases for discussing mechanisms of high temperature creep. Formerly was a Graduate Student, Tohoku University.     

14Cr-ODS铁素体钢的热变形行为及热加工图

利用Gleeble-1500D热模拟实验机研究机械合金化法制备的14Cr-ODS铁素体钢在变形温度为1 050~1 200℃、应变速率为0.001~0.3 s 1条件下的高温变形行为,测定其真应力真应变曲线,分析流变应力随应变速率以及变形温度的变化关系。应用MATLAB软件计算最佳的应力水平参数,通过线性回归分析得出材料的变形激活能、材料常数和材料的双曲线本构方程,构造14Cr-ODS铁素体钢的热加工图。结果表明:14Cr-ODS铁素体钢的流变应力随温度升高而减小,随应变速率增加而增大;其变形激活能为501.11 kJ/mol,最佳应力水平参数为0.007,应力指数为4.08;加工失稳温度区域为1 050~1 100℃,应变速率区域为0.1~0.3 s 1;适合加工的条件是变形温度为1 150℃,应变速率为0.1 s 1。     

Constitutive Equation Models of Hot-Compressed T122 Heat Resistant Steel

 Based on dislocation reaction theory and Avrami equation, a constitutive equation model was developed to describe dynamic recovery and dynamic recrystallization during hot deformation of T122 heat resistant steel, which have taken the effect of dynamic strain aging into account. Uniaxial hot compression test had been carried out over a wide range of strain rate (001 to 10 s-1) and temperature (900 to 1200 ℃) with the help of Gleeble 3500. Obtained experimental data was applied to determine the material parameters in proposed constitutive equations of T122 steel, by using the non-linear least square regress optimization method. The calculated constitutive equations are quantitatively in good agreement with experimentally measured curves and microstructure observation. It shows that propose constitutive equation T122 steel is able to be used to predict flow stress of T122 steel during hot deformation in austenite temperature scope.     

Dynamic strain aging during creep of α-Zr

In the temperature range 723 to 823 K (450° to 550°C) annealed, crystal bar α-Zr exhibits anomalous behavior with respect to both single stress and incrementally stressed creep tests. The nature and extent of the anomalous behavior depends on temperature, stress, and impurity content. Specimens with low oxygen content exhibit: 1) normal, three-stage creep behavior during single stress tests, and 2) normal transients during incremental stress and temperature tests. Specimens with higher oxygen contents exhibit: 1) multi-stage creep curves whose shapes depend on temperature and stress, 2) inverse transients following stress and temperature increments, and 3) peaks in activation energy-tempera-ture curves. The nature of the anomalous behavior is consistent with a model for strain aging in which the possibility of localized depletion of the strain aging species exists. In the material being studied oxygen is probably responsible for the observed effects. R. D. WARDA, formerly of Department of Metallurgy, University of British Columbia     

316L不锈钢动态再结晶行为

在Gleeble-1500热模拟试验机上,通过高温压缩实验对316L不锈钢的动态再结晶行为进行了系统研究.结果表明:316L不锈钢热变形加工硬化倾向性较大,在真应力应变曲线上没有出现明显的应力峰值σ_p;316L不锈钢在热变形过程中发生了动态再结晶,但只是在局部区域观察到了动态再结晶晶粒.对动态再结晶的实验数据进行拟合,得到316L不锈钢的热激活能和热变形方程,并给出了发生动态再结晶的临界应变和临界应力以及Zener-Hollomon参数和稳态应力的关系.