scholarly journals Constitutive Equation for Flow Stress in Superalloy 718 by Inverse Analysis under Hot Forming in a Region of Precipitation

Crystals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 811
Author(s):  
Hyung-Won Park ◽  
Sosei Kakiuchi ◽  
Kyunghyun Kim ◽  
Akira Yanagida ◽  
Jun Yanagimoto
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Inverse Analysis ◽  
Rate Sensitivity ◽  
Turbine Engines ◽  
Strain Rates ◽  
Gas Turbine Engines ◽  
Dynamic Precipitation ◽  
Compression Tests ◽  
Plastic Modulus

The purpose of this study is to obtain a constitutive equation of high-accuracy flow stress in superalloy 718, which allows fabrication of highly reliable disks for gas turbine engines. Hot compression tests using superalloy 718 at deformation temperatures from 850 to 1100 °C, a 67% height reduction, and strain rates of 1, 10, and 25 s−1 were performed to investigate the flow stress behavior, which excludes environmental effects during hot working by inverse analysis. The effects of dynamic recrystallization and strain-induced dynamic precipitation on the flow stress were also investigated. The dynamically precipitated δ phases deformed at 1050 °C and γ″ phases deformed at 950 °C might affect the increase in the plastic modulus F1 and the decrease in the critical strain εc, deteriorating the accuracy of regression in terms of, for example, the strain rate sensitivity m and the temperature sensitivity A. A constitutive equation for a generalized flow curve for superalloy 718 is proposed by considering these effects.

Constitutive Equation of an Al-12.7Si-0.7Mg Alloy in Superplastic Deformation

2011 ◽  
Vol 415-417 ◽  
pp. 1147-1152 ◽  
Author(s):  
Yin Ben Han ◽  
Zhuo Liang Li ◽  
Ge Zhou ◽  
Fu Rong Cao ◽  
Hua Ding ◽  
...  
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Hot Deformation ◽  
Testing Machine ◽  
Rate Sensitivity ◽  
Strain Rates ◽  
Deformation Parameters ◽  
Deformation Activation Energy ◽  
Deformation Features

The hot deformation characteristics of Al-12.7Si-0.7Mg alloy were investigated on an Instron5500 electronic universal testing machine at strain rates ranging from 1.67×10-4 s-1 to 1.67×10-3 s-1 and testing temperatures ranging from 460 °C to 520 °C. The results show that strain rate had a great effect on the flow stress. The flow stress increased with increasing the strain rate. The true stress-strain curves of the Al-12.7Si-0.7Mg alloy were obtained, and the strain rate sensitivity and hot deformation parameters of deformation activation energy were calculated. The hot deformation constitutive equation with hyperbolic sine form was also obtained. The test calculations demonstrate that the constitutive equation describes the deformation features of the Al-12.7Si-0.7Mg alloy well.

Hot Deformation Behavior and Constitutive Equation of Mg-4Al-3Ca -1.5Zn-1Nd-0.2Mn Magnesium Alloy As-Extruded

2014 ◽  
Vol 900 ◽  
pp. 588-591
Author(s):  
Gang Chen ◽  
Wei Chen ◽  
Guo Wei Zhang ◽  
Jing Zhai ◽  
Li Ma ◽  
...  
Keyword(s):  
Activation Energy ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Constitutive Equation ◽  
Constitutive Equations ◽  
Hot Deformation ◽  
Deformation Behavior ◽  
Strain Rates ◽  
Compression Tests ◽  
Hot Deformation Behavior

The deformation behavior and constitutive equation of Mg-4Al-3Ca-1.5Zn-1Nd-0.2Mn alloy were investigated using hot compression tests at the temperatures range of 200, 250, 300, and 350°C with the constant strain rates of 0.001, 0.01, 0.1 And1 s-1. The influence of strain was also incorporated in the constitutive equation by considering the effects of strain on material constants which are consist of A, α, β, n and activation energy Q. The predicted flow stress curves using the proposed constitutive equations well agree with the experimental results of the flow stress for experimental Alloy.

Construction of Flow Stress Constitutive Equation for 3Cr1Mo0.25V Steel

2012 ◽  
Vol 567 ◽  
pp. 244-249
Author(s):  
Yu Hua Zhang ◽  
Guang Yu Tan ◽  
Shu Cai Yang
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Dynamic Recovery ◽  
Rate Variation ◽  
Strain Rates ◽  
Compression Tests ◽  
Temperature Range ◽  
Softening Mechanism ◽  
Dynamic Softening ◽  
Increasing Temperature

The flow stress change of 3Cr1Mo0.25V steel was researched in this paper through hot compression tests performed in a temperature range from 800 to 900oC and with a strain rate variation from 0.01 to 10s-1. Flow stress constitutive equation was constructed according to true stress-strain curves of 3Cr1Mo0.25V steel. Results indicate that the dynamic recovery is the dynamic softening mechanism of 3Cr1Mo0.25V steel. The flow stress increases with increasing strain rates and decreases with increasing temperature. The rheological behavior of 3Cr1Mo0.25V steel can be characterized by the parameter of Zener-Hollomon in a high temperature range. As for 3Cr1Mo0.25V steel, the activation energy of Q evaluated by the linear regression is about 142.9 kJ/mol.

Characterization of High Temperature Deformation Behavior of BFe10-1-2 Cupronickel Alloy Using Orthogonal Analysis

2017 ◽  
Vol 36 (7) ◽  
pp. 701-710
Author(s):  
Jun Cai ◽  
Kuaishe Wang ◽  
Xiaolu Zhang ◽  
Wen Wang
Keyword(s):  
High Temperature ◽  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Deformation Behavior ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Compression Tests ◽  
Statistical Parameters ◽  
Orthogonal Analysis

AbstractHigh temperature deformation behavior of BFe10-1-2 cupronickel alloy was investigated by means of isothermal compression tests in the temperature range of 1,023~1,273 K and strain rate range of 0.001~10 s–1. Based on orthogonal experiment and variance analysis, the significance of the effects of strain, strain rate and deformation temperature on the flow stress was evaluated. Thereafter, a constitutive equation was developed on the basis of the orthogonal analysis conclusions. Subsequently, standard statistical parameters were introduced to verify the validity of developed constitutive equation. The results indicated that the predicted flow stress values from the constitutive equation could track the experimental data of BFe10-1-2 cupronickel alloy under most deformation conditions.

Thermal Deformation Behavior and Processing Map of Al-Mg-Er Alloy

2018 ◽  
Vol 913 ◽  
pp. 30-36
Author(s):  
Ran Liu ◽  
Hui Huang ◽  
Ya Liu ◽  
Li Rong
Keyword(s):  
Flow Stress ◽  
Deformation Behavior ◽  
Deformation Temperature ◽  
Material Model ◽  
Instability Criterion ◽  
Strain Rates ◽  
Processing Maps ◽  
Hot Workability ◽  
Compression Tests ◽  
Dynamic Material Model

To study the hot deformation behavior of Al-Mg-Er alloy, hot compression tests were conducted on a Gleeble-1500D thermal simulator at the temperature range of 200-500°C with the strain rates from 0.001 to 10s-1. With the increase in the deformation temperature and the decrease in strain rates, the flow stress of the Al-Mg-Er alloy decreased. Processing maps were constructed to study on hot workability characteristics. The results showed that the flow stress curves exhibited the typical dynamic recrystallization characteristics and the stress decreased with the increase of deformation temperature and the decrease of strain rate. Moreover, the processing maps were established on the basis of dynamic material model and Prasad’s instability criterion.

Prediction of High Temperature Flow Stress for AISI 4120 Steel during Hot Compression

2012 ◽  
Vol 233 ◽  
pp. 339-342 ◽  
Author(s):  
Ming Ping Zou ◽  
Wu Jiao Xu ◽  
Peng Cheng Wang
Keyword(s):  
High Temperature ◽  
Flow Stress ◽  
Constitutive Equation ◽  
Constitutive Equations ◽  
Good Prediction ◽  
Compression Tests ◽  
Absolute Relative Error ◽  
Constitutive Analysis ◽  
Average Absolute Relative Error ◽  
Deformation Behaviors

To investigate the hot deformation behaviors of AISI 4120 steel, isothermal compression tests were conducted using Gleeble-1500 thermal-mechanical simulator in the temperature range of 1073-1373K with the strain rate of 0.01-10s-1. The hyperbolic sine law in Arrhenius type is used in the constitutive modeling for AISI 4120. The influence of strain is incorporated in constitutive analysis by considering the effect of strain on material constants α, n, Q and ln A. The flow stress values predicted by the developed constitutive equations show a good agreement with experimental results, which reveals that the developed constitutive equations could give an accurate and precise prediction for the high temperature flow behaviors of AISI 4120 steel. The predictability of developed constitutive equation was further quantified in terms of correlation coefficient (R) and average absolute relative error (AARE). The R and AARE were found to be 0.9847 and 8.0372% respectively, which reflects the good prediction capabilities of the developed constitutive equation.

Prediction of Microstructure During High Temperature Forming of Ti-6Al-4V Alloy

2004 ◽  
Vol 449-452 ◽  
pp. 189-192 ◽  
Author(s):  
You Hwan Lee ◽  
T.J. Shin ◽  
Jong Taek Yeom ◽  
Nho Kwang Park ◽  
S.S. Hong ◽  
...  
Keyword(s):  
Activation Energy ◽  
Finite Element Analysis ◽  
Finite Element ◽  
High Temperature ◽  
Flow Stress ◽  
Rate Sensitivity ◽  
Strain Rates ◽  
Element Analysis ◽  
Strain Data ◽  
Final Microstructure

Prediction of final microstructures after high temperature forming of Ti-6Al-4V alloy was´attempted in this study. Using two typical microstructures, i.e., equiaxed and Widmanstätten microstructures, compression test was carried out up to the strain level of 0.6 at various temperatures (700 ~ 1100°C) and strain rates (10-4 ~ 102/s). From the flow stress-strain data, parameters such as strain rate sensitivity (m) and activation energy (Q) were calculated and used to establish constitutive equations for both microstructures. Then, finite element analysis was performed to predict the final microstructure of the deformed body, which was well accorded with the experimental results.

Using Split Hopkinson Pressure Bars to Perform Large Strain Compression Tests on Neoprene at Intermediate and High Strain Rates

2013 ◽  
Vol 631-632 ◽  
pp. 458-462 ◽  
Author(s):  
Peng Duo Zhao ◽  
Yu Wang ◽  
Jian Ye Du ◽  
Lei Zhang ◽  
Zhi Peng Du ◽  
...  
Keyword(s):  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Large Strain ◽  
Rate Sensitivity ◽  
Strain Rates ◽  
Compression Tests ◽  
Hopkinson Pressure Bar ◽  
High Strain Rates ◽  
Split Hopkinson ◽  
Pressure Bar

The strain rate sensitivity of neoprene is characterized using a modified split Hopkinson pressure bar (SHPB) system at intermediate (50 s-1, 100 s-1) and high (500 s-1, 1000 s-1) strain rates. We used two quartz piezoelectric force transducers that were sandwiched between the specimen and experimental bars respectively to directly measure the weak wave signals. A laser gap gage was employed to monitor the deformation of the sample directly. Three kinds of neoprene rubbers (Shore hardness: SHA60, SHA65, and SHA70) were tested using the modified split Hopkinson pressure bar. Experimental results show that the modified apparatus is effective and reliable for determining the compressive stress-strain responses of neoprene at intermediate and high strain rates.

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.

Dynamic Recrystallization of Zircaloy-4 during Working within the Upper α-Range

2004 ◽  
Vol 467-470 ◽  
pp. 1151-1156 ◽  
Author(s):  
Cédric Chauvy ◽  
Pierre Barbéris ◽  
Frank Montheillet
Keyword(s):  
Dynamic Recrystallization ◽  
Large Strain ◽  
Large Angle ◽  
Rate Sensitivity ◽  
Large Strains ◽  
Strain Rates ◽  
Compression Tests ◽  
Continuous Dynamic Recrystallization ◽  
Ebsd Technique ◽  
Continuous Dynamic

Compression tests were used to simulate simple deformation paths within the upper a-range of Zircaloy-4 (i.e. 500°C-750°C). The mechanical behaviour reveals two different domains : at low temperatures and large strain rates, strain hardening takes place before flow softening, whereas this first stage disappears at lower flow stress levels. Strain rate sensitivity and activation energy were determined for both domains. Dynamic recrystallization was investigated using the Electron BackScattering Diffraction (EBSD) technique. It appears that the mechanism involved here is continuous dynamic recrystallization (CDRX), based on the increasing misorientation of subgrain boundaries and their progressive transformation into large angle boundaries. At low strains (e £ 0.3), CDRX kinetics are similar whatever the deformation conditions, while higher temperatures and lower strain rates promote recrystallization at large strains.

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