- Open Access
Dynamic mechanical response and a constitutive model of Fe-based high temperature alloy at high temperatures and strain rates
© Su et al. 2016
- Received: 3 November 2015
- Accepted: 14 April 2016
- Published: 23 April 2016
The effects of strain rate and temperature on the dynamic behavior of Fe-based high temperature alloy was studied. The strain rates were 0.001–12,000 s−1, at temperatures ranging from room temperature to 800 °C. A phenomenological constitutive model (Power-Law constitutive model) was proposed considering adiabatic temperature rise and accurate material thermal physical properties. During which, the effects of the specific heat capacity on the adiabatic temperature rise was studied. The constitutive model was verified to be accurate by comparison between predicted and experimental results.
- Dynamic mechanical response
- Constitutive model
- Adiabatic temperature rise
- Stainless steel
Steel alloys are used in a wide range of structural, naval, nuclear, and aerospace applications (Zaera et al. 2012), which have been widely investigated in machining process. Martensitic stainless steels demonstrate a high capability of energy absorption, making it suitable for military applications, where impacts and explosions are often involved (Abed et al. 2014). When it comes to the manufacturing of steam turbine important components, the Fe-based high temperature alloy shows excellent properties under extreme working conditions. The performance of steel alloys under high temperature should be carefully considered during the design and manufacturing process.
High-speed cutting is used for manufacturing steam turbine rotor blades for ultra-supercritical unit. The high cutting temperature generated during the cutting evidently influences tool wear, tool life, surface integrity, and chip formation. The high temperature also leads to the thermal deformation of the cutting tool, which is considered as the major source of error in the machining process (Abukhshim et al. 2006; Takeuchi et al. 1982; List et al. 2012; Özel and Altan 2000).
Power-Law model is controlled by the synergistic effects of temperature, strain and strain rate. During the last decades, many researchers used the experimental stress–strain data from isothermal hot compression tests over a wide range of temperatures (1073–1473 K), but comparatively low strain rates (0.001–1 s−1) (Samantaray et al. 2009). Some researchers conducted quasi-static and high strain rate (up to 4500 s−1) experiments, whereas the high temperature environment was not considered (Pereira et al. 2001). Recently, a few investigations have been done to study the modeling process fully considering a wide range of strain rates and temperatures (Hor et al. 2013a, b; Lee et al. 2011; Hernandez et al. 2011; Wang et al. 2009).
Chemical composition of the Fe-based high temperature alloy (wt%)
Basic mechanical properties of the Fe-based high temperature alloy
Tensile yield stress (MPa)
Tensile strength (MPa)
Reduction of area
Rockwell hardness (HB)
Charpy V impact energy (J)
Quasi-static loading experiments
Dynamic loading experiments
The dynamic compression experiments were performed by the modified Split Hopkinson Pressure Bar with synchronically assembled heating system. The experimental parameters variables were the temperatures and the strain rates: experiments with strain rate of 9000 s−1 at temperatures ranging from 20 to 800 °C, and experiments with strain rates ranging from 4000 to 12,000 s−1 at room temperature.
Each experiment condition is performed at least three times in order to ensure the reliability of the experimental results. Only the results with good repeatability or less scatter can be accepted.
As shown in Fig. 6, the specific heat capacity increases with temperature ranging from 20 to 700 °C, on the contrary while the temperature is above 700 °C.
As analyzed before, the flow stress decreases with the increase of temperature. However, the flow stress is balanced by work hardening and adiabatic thermal softening, which could be well exhibited in Power-Law model (Ranc et al. 2008).
Determination of the constants
Material constants of constitutive model
−6.0764e − 3
3.4791e − 5
−8.9607e − 8
9.9440e − 11
−3.9930e − 14
Verification of the constitutive model
It can be seen from Fig. 9a that predicted results well correlate with the experimental results. The errors under high strain rates and high true stain are <5 %. The errors between predicted results and experimental results at strain rate 9000 s−1 with temperature ranging from room temperature to 800 °C are larger than that at room temperature with high strain rates, as is shown in Fig. 9b. But the errors are <10 %. So, the Power-Law constitutive model proposed in this study is accurate enough to describe the dynamic mechanical response of the steel under high strain rate and high temperature conditions.
In order to explain the practicability and accuracy, orthogonal metal cutting process was carried out by both experiments and the finite element method (FEM). The main cutting forces were taken as the research object.
Orthogonal metal cutting experiment
Design of experiments by the orthogonal array
The work length of the insert is 1 mm in keeping with the settings of simulation. Kistler dynamometer typed 9257B was used to collect the cutting force. Nine groups of experiments were carried out, and the parameters are shown in Table 4. By this way, the workload was reduced and experimental effect was guaranteed.
Numerical study of metal cutting process
The simulation of orthogonal metal cutting process was performed using commercial finite element software Third Wave AdvantEdge 6.4, which is widely adopted in the machining industry to facilitate the automation of production. The constitutive model obtained in “Constitutive model” section was input into the software as the costumer materials. The other thermal and mechanical properties of work piece are set as temperature-dependent thermal property. For example, Fig. 6 and Eq. (8) show the specific heat capacity of material. The thermal conductivity and thermal expansion are also temperature-dependent thermal properties, which were tested accurately. The Young’s modulus was set as 211 GPa, and the Poisson’s ratio was 0.33. The properties of cutting tool and coating were offered by the material library in the software. By some trial simulations, the friction coefficient between cutting tool and work piece was set as 0.5.
Result and discussions
The values of simulation results are smaller than the experiment ones. The average error of cutting forces is 7.86 %, which indicates good data reproducibility, and the error is clearly labeled in Fig. 10. The simulated results are consistent with the experimental results, confirming that the model of simulation can provide an accurate prediction of the main cutting force. In other words, the constitutive model obtained in this study is practicable and accurate.
This paper investigated the dynamic mechanical response of the Fe-based high temperature alloy. The work hardening and temperature softening are significant at high strain rates and temperatures, and the results coincided with the actual machining process. The effects of the specific heat capacity on the adiabatic temperature rise was studied, it can be seen that the specific heat capacity affect the adiabatic temperature rise obviously, especially at high temperature (200–800 °C).
A Power-Law constitutive model considering accurate adiabatic temperature rise is obtained through regression analysis of the experimental data gathered from a modified Split Hopkinson Pressure Bar technique with synchronically assembled heating system. The constitutive model was verified to be accurate by comparison between predicted and experimental results. The main cutting forces obtained from the experiments and simulations were compared, of which the average error of cutting forces is 7.86 %, which indicates that the constitutive model obtained in this study is practicable and accurate.
All authors read and approved the final manuscript.
The work has been financially supported by National Science and Technology Major Project of the Ministry of Science and Technology of China (No. 2013ZX04009-022) and Beijing Natural Science Foundation Project (3152013).
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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