A phenomenological model utilizing Voce’s strain-hardening model describing high strain rate behavior of alloy 800H during hot working

2020 ◽  
Vol 55 (7-8) ◽  
pp. 271-276
Author(s):  
M Heydarian ◽  
E Shafiei ◽  
F Ostovan
Keyword(s):  
Mathematical Model ◽  
Strain Rate ◽  
Strain Hardening ◽  
High Strain ◽  
Material Constant ◽  
Correlation Factor ◽  
Strain Rates ◽  
Alloy 800H ◽  
Stress Strain ◽  
Strain Hardening Rate

In this study, a simple mathematical model is introduced to predict the stress–strain curves under the occurrence of minor dynamic recrystallization. In this regard, first, with the assumption of nonlinear variation of strain-hardening rate versus strain, a mathematical equation was derived to obtain the strain-hardening rate. Then, using the Voce’s equation, a new mathematical model was developed to predict the hot deformation behavior of metallic alloys at high strain rates. The most important feature of the proposed model is its simplicity so that the only constant of the stress–strain equation can easily be interpolated at different temperatures and strain rates. Accordingly, it was found that the defined material constant varies linearly and exponentially with strain rate and temperature, respectively. The high correlation factors (average correlation factor, r2 = 0.85) obtained from regression analysis showed that the model can provide a precise estimation of flow stress curves for the defined deformation conditions.

Dynamic Compression Behavior and Numerical Modeling of Ti-6246 Alloy at Different Temperatures

2012 ◽  
Vol 527 ◽  
pp. 159-164 ◽  
Author(s):  
Dmitri Gomon ◽  
Mikko Hokka ◽  
Veli Tapani Kuokkala
Keyword(s):  
Numerical Modeling ◽  
Strain Rate ◽  
Strain Hardening ◽  
High Strain ◽  
Material Behavior ◽  
Materials Testing ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Strain Hardening Rate

The current research concentrates on the characterization of the mechanical behavior of Ti-6Al-2Sn-4Zr-6Mo alloy. The material was studied in compression using the Split Hopkinson Pressure Bar (SHPB) equipment at high strain rates and conventional servohydraulic materials testing devices at low strain rates. The tests were performed at temperatures ranging from room temperature up to 600 °C. According to the results of the compression tests, the strain hardening rate of the studied material decreases strongly with increasing strain rate. The observed strong decrease in the strain hardening rate with increasing strain rate is a consequence of the extremely strong adiabatic heating of the material due to its high strength and low thermal conductivity. In this study, the Johnson-Cook material model parameters were obtained from isothermal stress-strain curves that were calculated from the experimental (adiabatic) stress-strain data. In this paper, the results of the mechanical testing at high strain rates and the numerical modeling of the material behavior are presented and discussed in details.

Tensile Behavior of Ti-5Al-2.5Sn Alloy at Low Temperatures and High Strain Rates

2019 ◽  
Vol 794 ◽  
pp. 135-141
Author(s):  
Bin Zhang ◽  
Yang Wang
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Low Temperatures ◽  
High Strain ◽  
Testing Temperature ◽  
Tensile Behavior ◽  
Experimental Results ◽  
Strain Rates ◽  
Increasing Temperature ◽  
Strain Hardening Rate

The mechanical responses of Ti-5Al-2.5Sn alloy at low temperatures were investigated under quasi-static and dynamic tensile loads using MTS system and SHTB system, respectively. Tensile stress-strain curves were obtained over the temperature range of 153 to 298K and the rate range of 0.001 to 1050 s-1. Experimental results indicate that the tensile behavior of Ti-5Al-2.5Sn alloy is dependent on strain rate and temperature. Yield stress and flow stress increase with increasing strain rate and decrease with increasing temperature. Results also indicate that strain hardening rate of Ti-5Al-2.5Sn alloy is lower at high strain rate, while strain hardening rate varies little with testing temperature. The Khan-Huang-Liang constitutive model was chosen to characterize the tensile responses of Ti-5Al-2.5Sn alloy at low temperatures and different strain rates. The model results coincide well with the experimental results within the tested temperature and rate ranges.

A Dynamic Mechanical Analysis of T2 Copper at High Strain Rates

2019 ◽  
Vol 812 ◽  
pp. 38-44
Author(s):  
Shuai Chen ◽  
Wen Bin Li ◽  
Xiao Ming Wang ◽  
Wen Jin Yao
Keyword(s):  
Yield Strength ◽  
Strain Rate ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Pure Copper ◽  
Dislocation Slip ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Shpb Test

This work compares the pure copper (T2 copper)’s stress-strain relationship at different strain rates in the uni-axial tension test and Split Hopkinson Pressure Bar (SHPB) test. Small samples were utilized in the high strain rate SHPB test in which the accuracy was modified by numerical simulation. The experimental results showed that the T2 copper’s yield strength at high strain rates largely outweighed the quasi static yield strength. The flow stress in the stress-strain curves at different strain rates appeared to be divergent and increased with the increase in strain rates, showing great strain strengthening and strain rate hardening effects. Metallographic observation showed that the microstructure of T2 copper changed from equiaxed grains to twins and the interaction between the dislocation slip zone grain boundary and twins promoted the super plasticity distortion in T2 copper.

High Strain-Rate Compressive Behavior and Constitutive Modeling of Selected Polymers Using Modified Ramberg-Osgood Equation

2014 ◽  
Vol 566 ◽  
pp. 80-85
Author(s):  
Kenji Nakai ◽  
Takashi Yokoyama
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Compressive Stress ◽  
Constitutive Modeling ◽  
High Strain ◽  
Strain Rates ◽  
Stress Strain ◽  
Strain Behavior ◽  
Least Squares Fit ◽  
Wide Range

The present paper is concerned with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10-3 to 103/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves up to strains of nearly 0.08 for four different commercially available extruded polymers were determined on the standard split Hopkinson pressure bar (SHPB). The low and intermediate strain-rate compressive stress-strain relations were measured in an Instron testing machine. Six parameters in the modified Ramberg-Osgood equation were determined by fitting to the experimental stress-strain data using a least-squares fit. It was shown that the monotonic compressive stress-strain behavior over a wide range of strain rates can successfully be described by the modified Ramberg-Osgood constitutive model. The limitations of the model were discussed.

High Strain Rate Mechanical Properties of SAC-Q Between -65°C and +200°C After Exposure to Isothermal Aging

2020 ◽  
Author(s):  
Pradeep Lall ◽  
Vishal Mehta ◽  
Jeff Suhling ◽  
Ken Blecker
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Isothermal Aging ◽  
High Strain ◽  
Strain Rates ◽  
Solder Alloys ◽  
Stress Strain ◽  
Wide Range ◽  
Operating Temperatures ◽  
Electronic Parts

Abstract In many industries, such as automotive, oil and gas, aerospace, medical technologies, electronic parts can often be exposed to high strain loads during shocks, vibrations and drop-impact conditions. Such electronic parts can often be subjected to extreme low and high temperatures ranging from −65°C to 200°C. Also, these electronic devices can be subjected to strain rates of 1 to 100 per second in the critical environment. Recently, many doped SAC solder alloys are being introduced in the electronic component including SAC-Q, SAC-R, Innolot. SAC-Q is made with addition of Bi in Sn-Ag-Cu composition. Mechanical characteristic results and data for lead-free solder alloys are extremely important for optimizing electronic package reliability, at high temperature storage and elevated strain rates. Furthermore, the mechanical properties of solder alloys can be changed significantly due to a thermal aging, which is causing modification of microstructure. Data for the SAC-Q solder alloy with a high temp aging and testing at extreme low to high operating temperatures are not available. SAC-Q material was tested and analyzed for this study at range of operating temperatures of −65°C to 200°C and at a strain rate up to 75 per second. After the specimens were manufactured and reflowed, specimens were stored at 100°C for the isothermal aging for up to 90 days, before tensile tests were carried out at different operating temperatures. For the wide range of strain rates and test temperatures, stress-strain curves are established. In addition, the measured experimental results and data were fitted to the Anand viscoplasticity model and the Anand constants were calculated by estimating the stress-strain behavior measured in the wide range of operating temperatures and strain rates.

scholarly journals Strain-Rate-Dependent Tensile Response of Ti–5Al–2.5Sn Alloy

Materials ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 659 ◽  
Author(s):  
Bin Zhang ◽  
Jin Wang ◽  
Yang Wang ◽  
Yu Wang ◽  
Ziran Li
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Uniaxial Tension ◽  
Temperature Rise ◽  
High Strain ◽  
Adiabatic Temperature ◽  
High Rate ◽  
Strain Rates ◽  
High Strain Rates ◽  
Adiabatic Temperature Rise

This study is an experimental investigation on the tensile responses of Ti–5Al–2.5Sn alloy over a wide range of strain rates. Uniaxial tension tests within the rate range of 10−3–101 s−1 are performed using a hydraulic driven MTS810 machine and a moderate strain-rate testing system. The high-rate uniaxial tension and tension recovery tests are conducted using a split-Hopkinson tension bar to obtain the adiabatic and isothermal stress–strain responses of the alloy under dynamic loading conditions. The experimental results show that the value of the initial yield stress increases with the increasing strain rate, while the strain rate sensitivity is greater at high strain rates. The isothermal strain-hardening behavior changes little with the strain rate, and the adiabatic temperature rise is the main reason for the reduction of the strain-hardening rate during high strain-rate tension. The electron backscatter diffraction (EBSD) analysis of the post-deformed samples indicates that there are deformation twins under quasi-static and high-rate tensile loadings. Scanning electron microscope (SEM) micrographs of the fracture surfaces of the post-deformed samples show dimple-like features. The Zerilli–Armstrong model is modified to incorporate the thermal-softening effect of the adiabatic temperature rise at high strain rates and describe the tension responses of Ti–5Al–2.5Sn alloy over strain rates from quasi-static to 1050 s−1.

Establishment of Flow Stress Model of EW75 Alloy

2013 ◽  
Vol 423-426 ◽  
pp. 241-246
Author(s):  
Ming Long Ma ◽  
Kui Zhang
Keyword(s):  
Mathematical Model ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Strain Rate ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Stress Strain ◽  
Deformation Degree ◽  
Maximum Deformation ◽  
The Mathematical Model

The behavior evolvement of Mg-7.22Gd-4.84Y-1.26Nd-0.58Zr (EW75) magnesium alloy during the hot deformation process was discussed. The flow stress behavior of magnesium alloy over the strain rate range 0.002s-1to 2s-1and the temperature range 623K to 773K had been researched on Gleeble-1500D hot simulator under the maximum deformation degree 60%. A mathematical model was established to predict the stress-strain curves of this alloy during deformation. The experimental results showed that the stress-strain curves were obviously affected by the strain rates and deformation temperatures. The mathematical model could predict the stress-strain curves when the strain rates were under 0.2-1, but there was significant error in some of stress-strain curves when the strain-rate was 2-1by the reason of deformation temperature rising.

Dynamic Testing at High Strain Rates of AZ31 Magnesium Alloys on SHPB Equipment

2013 ◽  
Vol 303-306 ◽  
pp. 2648-2651
Author(s):  
Xu Qing Chang ◽  
Tie Hua Ma
Keyword(s):  
Strain Rate ◽  
Optical Microscopy ◽  
Strain Hardening ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Mg Alloy ◽  
Strain Rates ◽  
Hopkinson Pressure Bar ◽  
High Strain Rates ◽  
Az31 Mg Alloy

The mechanical behaviour of as-cast AZ31 Mg alloy has been investigated at strain rates up to 2.0×103s-1. Dynamic tests were carried out at room temperature using a Split Hopkinson Pressure Bar (SHPB) apparatus. Microstructural characteristic were analysed by Image MAT A1 optical microscopy. The results demonstrated that AZ31 Mg alloy exhibited obvious yield phenomena and strain hardening behaviour at high strain rates. The basically same curvature of stress-strain curves exhibited an similar strain hardening rate. The dynamic yield strength changes little and the peak stress increases with the strain rates. An examination by optical microscopy after high strain rate deformation reveals the occurrence of twinning and twin area percentage increases with the strain rate increasing.

scholarly journals Hot Deformation Behavior and Constitutive Modeling of H13-Mod Steel

Metals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 846 ◽  
Author(s):  
Changmin Li ◽  
Yuan Liu ◽  
Yuanbiao Tan ◽  
Fei Zhao
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Hot Deformation ◽  
Deformation Behavior ◽  
High Strain ◽  
Flow Behavior ◽  
Peak Stress ◽  
Strain Rates ◽  
Hot Deformation Behavior ◽  
Stress Strain

The H13-mod steel optimized by composition and heat treatment has reached the performance index of the shield machine hob. The hot deformation behavior of the H13-mod steel was investigated by compression tests in the temperature range from 900 to 1150 °C and the strain rate range from 0.01 to 10 s−1. The true stress-strain curve showed that the rising stress at the beginning of deformation was mainly caused by work hardening. After the peak stress was attained, the curve drop and the flow softening phenomenon became more obvious at low strain rates. The flow behavior of the H13-mod steel was predicted by a strain-compensated Arrhenius-type constitutive equation. The relationship between the material constant in the Arrhenius-type constitutive equation and the true strain was established by a sixth-order polynomial. The correlation coefficient between the experimental value and the predicted value reached 0.987, which indicated that the constitutive equation can accurately estimate the flow stress during the deformation process. A good linear correlation was achieved between the peak stress (strain), critical stress (strain) and the Zener‒Hollomon parameters. The processing maps of the H13-mod steel under different strains were established. The instability region was mainly concentrated in the high-strain-rate region; however, the microstructure did not show any evidence of instability at high temperatures and high strain rates. Combined with the microstructure and electron backscattered diffraction (EBSD) test results under different deformations, the optimum hot working parameters were concluded to be 998–1026 °C and 0.01–0.02 s−1 and 1140–1150 °C and 0.01–0.057 s−1.

Measurement of Mechanical Properties of St 37 Material at High Strain Rates Using a Split Hopkinson Pressure Bar

2014 ◽  
Vol 660 ◽  
pp. 562-566 ◽  
Author(s):  
Akbar Afdhal ◽  
Leonardo Gunawan ◽  
Sigit P. Santosa ◽  
Ichsan Setya Putra ◽  
Hoon Huh
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Test Specimen ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Strain Rates ◽  
Hopkinson Pressure Bar ◽  
Stress Strain ◽  
Split Hopkinson ◽  
Pressure Bar

The dynamic mechanical properties of a material are important keys to investigate the impact characteristic of a structure such as a crash box. For some materials, the stress-strain relationships at high strain rate loadings are different than that at the static condition. These mechanical properties depend on the strain rate of the loadings, and hence an appropriate testing technique is required to measure them. To measure the mechanical properties of a material at high strain rates, ranging from 500 s-1 to 10000 s-1, a Split Hopkinson Pressure Bar is commonly used. In the measurements, strain pulses are generated in the bars system, and pulses being reflected and transmitted by a test specimen in the bar system are measured. The stress-strain curves as the material properties of the test specimen are obtained by processing the measured reflected and transmitted pulses. This paper presents the measurements of the mechanical properties of St 37 mild steel at several strain rates using a Split Hopkinson Pressure Bar. The stress-strain curves obtained in the measurement were curve fitted using the Power Law. The results show that the strength of St 37 material increases as the strain rate increases.

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