Thermoviscoplastic Analysis of First Walls Subjected to Fusion Power Transients

1983 ◽  
Vol 105 (1) ◽  
pp. 42-51 ◽  
Author(s):  
H. L. Schreyer ◽  
J. M. Kennedy ◽  
D. F. Schoeberle
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Thermal Stresses ◽  
Large Deformations ◽  
Computer Code ◽  
Thermal Softening ◽  
Fusion Reactors ◽  
Fusion Power ◽  
Wide Range ◽  
Safety Features

Abrupt thermal fluxes on the first walls of fusion reactors represent a loading environment that requires advanced analytical capabilities. Solutions are needed to a wide range of postulated conditions to provide guidance for safety features and design modifications. A brief outline is given of a computer code that provides an integrated procedure for handling thermal stresses and large deformations under dynamic conditions. The code includes a new thermoviscoplastic constitutive equation that incorporates thermal softening, failure and strain rate. Solutions to several verification and illustrative problems are given.

scholarly journals A Modified Eyring Equation for Modeling Yield and Flow Stresses of Metals at Strain Rates Ranging from 10−5to 5 × 104 s−1

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Ramzi Othman
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Large Strain ◽  
Rate Sensitivity ◽  
Industrial Applications ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Wide Range ◽  
Large Strain Rate

In several industrial applications, metallic structures are facing impact loads. Therefore, there is an important need for developing constitutive equations which take into account the strain rate sensitivity of their mechanical properties. The Johnson-Cook equation was widely used to model the strain rate sensitivity of metals. However, it implies that the yield and flow stresses are linearly increasing in terms of the logarithm of strain rate. This is only true up to a threshold strain rate. In this work, a three-constant constitutive equation, assuming an apparent activation volume which decreases as the strain rate increases, is applied here for some metals. It is shown that this equation fits well the experimental yield and flow stresses for a very wide range of strain rates, including quasi-static, high, and very high strain rates (from 10−5to 5 × 104 s−1). This is the first time that a constitutive equation is showed to be able to fit the yield stress over a so large strain rate range while using only three material constants.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

2018 ◽  
Vol 37 (1) ◽  
pp. 75-87
Author(s):  
Jun Cai ◽  
Kuaishe Wang ◽  
Jiamin Shi ◽  
Wen Wang ◽  
Yingying Liu
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Nonlinear Regression ◽  
Flow Behavior ◽  
Strain Rate Range ◽  
Compression Tests ◽  
Constitutive Analysis ◽  
Average Absolute Relative Error ◽  
Wide Range

AbstractConstitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress–strain data from isothermal hot compression tests, in a wide range of temperature of 1,023~1,273 K, and strain rate range of 0.001~10 s–1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

A Thermo-Viscoplastic Constitutive Equation Based on Hyperbolic-Shape Thermo-Activated Barriers

1984 ◽  
Vol 106 (4) ◽  
pp. 331-336 ◽  
Author(s):  
Li-Lih Wang
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Present Model ◽  
Strain Rate Effects ◽  
Bcc Metals ◽  
Special Cases ◽  
Wide Range ◽  
Rate Effects ◽  
Simple Parameter ◽  
Good Agreement

A thermo-viscoplastic constitutive equation is proposed on the basis of thermoactivated mechanism with a spectrum of hyperbolic-shape barriers, suitable for a wide range of strain rate and temperature. Relations with other existing models or rate theories, which may be regarded a special cases of present model, are examined. Good agreement with experimental data for both fcc and bcc metals is shown. The activation volume is found dependent on temperature according to an exponential law. A simple parameter, which describes the equivalence between strain rate effects and temperature effects on flow stress, is suggested similar to Zener-Hollomon parameters

Modeling Temperature and Strain Rate Dependent Large Deformations of Metals

1990 ◽  
Vol 43 (5S) ◽  
pp. S312-S319 ◽  
Author(s):  
Douglas J. Bammann
Keyword(s):  
Strain Rate ◽  
Large Deformations ◽  
Uniaxial Stress ◽  
Thermal Softening ◽  
Plasticity Model ◽  
Anisotropic Hardening ◽  
Temperature Dependent ◽  
History Effects ◽  
Rate Dependent ◽  
Comparison With Experimental Data

We review the development of a strain rate and temperature dependent plasticity model for finite deformation. In particular we address both the method of determining the parameters of the model and the engineering meaning of the parameters in terms of uniaxial stress-strain curves. The ability of the model to predict some aspects of anisotropic hardening, strain rate history effects, and thermal softening are then illustrated by comparison with experimental data.

Prediction of Flow Stress for Superplastic Tension Deformation

2014 ◽  
Vol 941-944 ◽  
pp. 1501-1504
Author(s):  
Zhi Ping Guan ◽  
Ming Wen Ren ◽  
Pin Kui Ma ◽  
Po Zhao
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Flow Behavior ◽  
High Accuracy ◽  
Superplastic Flow ◽  
Al Alloy ◽  
Strain Rates ◽  
Good Reliability ◽  
Wide Range

With the development of numerical calculation and precision forming, constitutive equations are required to possess high accuracy and good reliability, rather than simplicity of mathematical form. Due to simple algorithm and constant parameters, the conventional constitutive models can not be suited to describing superplastic flow behavior which represents complex responses with a large strain. In this study, through surface fitting on experimental data from tension tests performed over a wide range of strain rates, tensile velocities and loads, an empirical approach was proposed to establish constitutive equation for complex superplastic behavior of Zn-5%Al alloy at 340 °C. The empirical constitutive equation not only represents the strain dependence and the strain rate dependence of stress, but also reflects the coupling effects of strain and strain rate on stress, which can not be achieved by traditional models. A comparison between the predicted flow stresses and the experimental data verified that the empirical constitutive equation has high accuracy and good reliability on modeling superplastic flow behavior of Zn-5%Al alloy at 340 °C in a wide range of strains 0~2.5 and strain rates 7.0×10-5~8.0×10-2s-1.

scholarly journals Tensile Behavior of Polyetheretherketone over a Wide Range of Strain Rates

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Zakaria El-Qoubaa ◽  
Ramzi Othman
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Volume Change ◽  
Axial Strain ◽  
Rate Sensitivity ◽  
Tensile Behavior ◽  
Image Correlation ◽  
Strain Rates ◽  
Wide Range ◽  
The Impact

Polyetheretherketone (PEEK) is used in several engineering applications where it has to bear impact loads. Nevertheless, the tensile behavior has only been studied in the quasi-static range of loading rates. To address the lack of data in the impact strain rate range, the tensile mechanical behavior of PEEK is investigated at room temperature over a large range of strain rates (from 0.001 to 1000/s). The macroscopic volume change is studied under uniaxial tension using digital image correlation (DIC) method, showing a significant dilatation that reaches 16% at a logarithmic axial strain of 40%. The true stress-strain behavior is therefore established based on the measured volume change. Elsewhere, the yield stress shows a significant sensitivity to strain rate. Besides, a new constitutive equation is proposed to take into account the increase in strain rate sensitivity at high strain rates. It assumes an apparent activation volume which decreases as the strain rate increases. The new constitutive equation gives similar results when compared to the Ree-Eyring equation. However, only three material constants are to be identified and are physically interpreted.

Constitutive Modeling for Superplastic Flow Behavior of H62 Alloy

2014 ◽  
Vol 941-944 ◽  
pp. 1488-1491
Author(s):  
Zhi Ping Guan ◽  
Hong Jie Jia ◽  
Ming Wen Ren ◽  
Dong Lai Wei
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Flow Behavior ◽  
Constant Strain Rate ◽  
Superplastic Flow ◽  
Strain Rates ◽  
Good Ability ◽  
Wide Range ◽  
Comprehensive Reliability

In order to precisely describe superplastic flow behavior of H62 alloy, a empirical constitutive equation was established based on the experimental data, which were obtained from the constant strain rate tensions (2.0×10-4~4.0×10-2s-1) at 720 °C. Through verification of the constitutive equation with the experimental data in constant strain rate tensions and constant velocity tensions, it was indicated that the empirical constitutive equation has high accuracy and comprehensive reliability in a wide range of strain rates (2.0×10-4~2.0×10-2s-1) and strains (0~1.8). In addition, the empirical constitutive equation has a good ability to model the superplastic flow behavior of H62 alloy at 720 °C under other deformation conditions besides constant strain rate tension.

The Constitutive Behavior of Al 7075 Aluminium Alloy under Hot Compression Test

2013 ◽  
Vol 752 ◽  
pp. 69-74 ◽  
Author(s):  
Tareg S. Ben Naser ◽  
György Krállics
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Interpolation Method ◽  
Strain Curve ◽  
Equivalent Strain ◽  
Absolute Relative Error ◽  
Average Absolute Relative Error ◽  
Wide Range ◽  
Al 7075 ◽  
Calculated Average

The constitutive equation in hot working for Al 7075 aluminum alloy was obtained employing experimental data of stress-strain curve, in a wide range of temperature (250-450°C) and strain rate (0.002-2 s-1). The influence of temperature and strain rate on the deformation behavior is represented by the equation proposed by Sellar and McTegart, all material parameters are considered as function of equivalent strain. The force-height data was corrected with interpolation method in the way to eliminate the error at the measurement. To verify the constitutive equation two parameter were calculated average absolute relative error (AARE=6.42) and correlation coefficient (R=0.998), for the same purpose the measuring and calculated flow curve are plotted together, the results shows that the constitutive equation obtained is good describing the behavior of the material.

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