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Role of strain-induced martensitic phase transformation in mechanical response of 304L steel at different strain-rates and temperatures
Journal of Materials Processing Tech. 280 (2020) 116613
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Role of strain-induced martensitic phase transformation in mechanical response of 304L steel at different strain-rates and temperatures
T
Zihao Qin, Yong Xia* State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China
A R T I C LE I N FO
A B S T R A C T
Associate Editor: Z Cui
The strain-rate and temperature dependencies of the strain-induced martensitic phase transformation (MPT) of AISI 304 L are experimentally investigated. Firstly, the tensile tests of 304 L at room temperature are conducted at the strain-rates ranges from 6.67 × 10−4 s-1 to 80 s-1. The stress-strain curves indicate a significant strain-rate effect of the strain-induced MPT, which is closely relevant to extent of the adiabatic heating. The second batch of tensile tests are conducted at several representative strain-rates and at different temperatures ranging from 0 °C to 100 °C. The martensitic volume fractions at different plastic deformation stages are measured by X-ray diffraction to trace the evolution of martensitic phase in the tests. The test results indicate that the environmental temperature and the strain-rate exert coupling influence on the stress-strain behavior. Variations in strength and ductility of 304 L in the tests are explained with a competition mechanism between strain-induced MPT, thermal softening and strain-rate strengthening. A kinetic model of MPT is modified to take the strain-rate, initial temperature and temperature rise into account.
Keywords: Martensitic phase transformation (MPT) Strain-rate Environmental temperature Mechanical behavior
1. Introduction Because of the excellent corrosion resistance, weldability and mechanical properties, Austenitic stainless steels (ASS) are widely applied in engineering structures. Activated by plastic deformation, some grades of ASS tend to transform from face-centered-cubic (FCC) austenite (γ) to body-centered-cubic (BCC) martensite (α'), known as straininduced martensitic phase transformation (MPT). The transformation usually results in: (1) a higher strength as martensite is stronger than austenite, and (2) a higher ductility and the delay of necking onset if the transformation takes place quickly and closely prior to severely localized deformation. As a consequence, the MPT has a significant effect on the mechanical behavior of the steels and is attractive to engineering applications. Over the past a couple of decades, the influential factors of straininduced MPT, such as temperature, strain rate, chemical composition and stress state, has been studied deeply by different research teams. In the present study, we mainly concern about the influence of temperature and strain rate to the MPT. Hecker et al. (1982) measured the martensitic volume fraction vs. true strain curve of AISI 304 under the temperature ranging from -188 °C to 50 °C. The volume fraction of martensite decreases with an increase in temperature under a given true strain. Huang et al. (1989) conducted the uniaxial tensile test of AISI
⁎
304 under the temperature ranging from -80 °C to 160 °C and concluded that the plastic hardening behavior results from the competition of strain-induced MPT and dislocation interactions during deformation. Along with the temperature rise, the dislocation slip dominates, and the proportion of MPT decreases. Moser et al. (2014) studied MPT of AISI 304 in conventional and isothermal tension. Besides the findings similar to the above, they adopted isothermal tests to determine Md, above which temperature the transformation behavior is totally inhibited. By performing uniaxial tensile test of AISI 304 and AISI 301 L N under strain-rate ranging from 3 × 10−4 s-1 to 200 s-1 and room temperature, Talonen et al. (2005) studied the relation between strain-rate and MPT as well as material tensile properties, finding that the transformation behavior is suppressed under high strain-rate. The suppression finally affects the ultimate tensile strength and uniform elongation of the material. Lichtenfeld et al. (2006) chose two grades of ASS for testing, i.e. Alloy 309 which is stable so as to provide the property response of pure austenite and Alloy 304 L which is susceptible to the strain-induced MPT. Tensile Tests were conducted at room temperature and under strain-rate ranging from 1.25 × 10−4 s-1 to 400 s-1. It indicated that the martensitic volume fraction is highly correlated with adiabatic heating and the stress-strain curve of Alloy 304 L exhibits apparent secondary hardening. With room temperature tensile tests below 0.1 s-1, Kundu and Chakraborti (2010) revealed that, for solution
Corresponding author. E-mail address: [email protected] (Y. Xia).
https://doi.org/10.1016/j.jmatprotec.2020.116613 Received 3 October 2019; Received in revised form 14 January 2020; Accepted 20 January 2020 Available online 21 January 2020 0924-0136/ © 2020 Elsevier B.V. All rights reserved.
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
annealed 304 stainless steel, yield strength increases and tensile strength decreases with increase of strain rate. They observed the threestage work hardening behavior at all the investigated strain rates, and attributed the highest hardening exponent at Stage 3 to the strain-induced MPT. Both Talonen et al. (2005) and Lichtenfeld et al. (2006) characterized the strain-induced MPT using a kinetic model proposed by Olson and Cohen (1975). In Olson and Cohen’s study, by the comparison of kinetics model and experiment data, they correlated MPT with temperature sensitivity and stacking-fault energy (SFE). The stability of austenite and SFE increase as temperature rises, limiting the MPT. Based on this, they proposed a kinetics model containing two temperature dependent parameters to quantitatively characterize the MPT. Peng et al. (2015) chose 304 stainless steel as research object and conducted the room temperature tests at strain rates ranging from 1 × 10-3 s-1 to 0.1 s-1. They incorporated the effect of strain rate to Olson and Cohen model, and applied the improved model to characterize the change of stress-strain response at the strain rates below 0.1 s-1. In the previous publications, most of the investigation on straininduced MPT concentrated on the environmental temperature effect (under quasi-static) or the strain-rate effect (at room temperature) separately. Regarding the practical engineering application, the ASS materials are usually employed in more complicated work scenarios, where the MPT could be affected by environmental temperature and strain-rate simultaneously. In the present study, focusing on the mechanical behavior of a susceptible ASS alloy 304 L, we investigate the coupling effect of environmental temperature and strain-rate on the strain-induced MPT. Firstly, the uniaxial tension tests at room temperature are conducted at different strain-rates. Effect of strain-rate on the tensile performance is analyzed. Secondly, the tensile tests at three representative strain-rates are performed at different temperatures ranging from 0 °C to 100 °C. By measuring the martensitic volume fraction in the various cases, the MPT is correlated with the tensile mechanical behavior at different temperatures and strain-rates. A kinetic model is then proposed on the basis of the Olson-Cohen model to characterize the strain-induced MPT by taking into account the effect of both strain-rate and environmental temperature.
Table 2 Processing parameters of electrolytic etching.
Si
C
P
S
base
18.61
8.00
1.20
0.688
0.0275
0.0304
0.0269
Time (min)
55 % phosphoric acid + 25 % sulfuric acid + 20 % distilled water
50-60
0.2
6-8
2
2.2.1. Quasi-static tension Quasi-static tension was carried out using a universal material test machine (Zwick 20 kN AllroundLine Table-Top). The signal of force was recorded by a built-in load sensor. The deformation was captured by a CCD camera and then processed by Digital Image Correlation (DIC) method. The universal test machine was equipped with an environmental chamber (Fig. 2a) capable of controlling the temperature for testing ranging from -80 °C to 250 °C. 2.2.2. Dynamic tension A customized intermediate strain-rate test machine was employed to perform the dynamic tests (Fig. 2b). The machine operates with open-loop and the hydraulic bar moves with a free stroke to reach the predefined speed before stretching the specimen. Deformation of the specimen was captured by a high-speed digital camera, and also DIC method was used for data processing. With respect to the dynamic force measurement, as demonstrated by Xia et al. (2015,2016) and Qin et al. (2016,2017), the force signal measured by the built-in load sensor often suffers from severe oscillation, attributed to the system ringing. To overcome this problem, Xia et al. (2016) designed a lightweight load sensor combining the function of gripper and sensor, with which the oscillation of force was significantly attenuated. In order to assure the data accuracy, this lightweight load sensor was adopted in the current study. To fulfill the dynamic tests at different temperatures, we used a thermoplastic gun and liquid nitrogen, respectively, to locally heat or cool the specimen mounted on the test machine. The temperature of the specimen was changed by adjusting the distance from the thermoplastic gun or the nozzle of liquid nitrogen container to the specimen. For the purpose of maintaining the temperature uniformity in the specimen, after reaching the target temperature, we kept heating or cooling the specimen for another 10 min before the test. The stress-strain curves of 80 s−1 strain-rate at temperatures ranging from 0 °C to 100 °C and the corresponding device for heating or cooling are plotted in Fig. 3, and the good repeatability of the test results validates this method. Specified
Table 1 Chemical composition of the austenitic stainless steel 304 L (Mass percent: %). Mn
Voltage (V)
In this study, we performed two groups of tensile tests. In the first test group, uniaxial tension tests under different strain-rates (from 6.67 × 10−4 s-1 to 80 s-1) were conducted at room temperature (25 °C). In the second test group, we chose three representative strain-rates and performed the uniaxial tension tests at different temperatures (from 0 °C to 100 °C). For the purpose of analyzing the ductility of the material, the dimensions of the specimen for quasi-static and dynamic tensile tests were identical (Fig. 1).
The austenitic stainless steel 304 L, which was 1.8 mm thick coldrolled sheet and heat-treated, was tested in this study. The chemical composition of the material was detected by an X-ray fluorescence spectrometer as listed in Table 1. To correctly measure the volume fraction of martensite, we applied electrolytic etching to thin the 304 L sheet with the processing parameters as shown in Table 2, and then examined the processed sample with X-ray diffraction (see details of the measurement procedure described in Section 2.4). In this way, a surface layer of approximately 0.2 mm thick was removed, and the measured volume fraction of martensite in the as-received sheet was within the range of 0-0.01. For comparison, another examination of X-ray diffraction was directly made on the 304 L sheet without surface processing, indicating that the volume fraction of martensite was approximate 0.13, much higher than the measurement with surface processing. It demonstrates that the martensite mainly exists in a very thin surface layer of the asreceived sheet, which is actually attributed to the temper rolling
Ni
Current (A)
2.2. Tensile tests
2.1. As-received material
Cr
Temperature (oC)
processing. The surface layer will disturb the measurement when we analyze the martensitic transformation inside the material induced by external loading. Therefore, it is preferred to remove the surface layer for an appropriate measurement. Another fact that has been demonstrated is, mechanically removing the surface material is unsuitable because it introduces extra mechanical damage and motivates the strain-induced transformation. Concerning the above observations, prior to measurement of the martensitic volume fraction, all the specimens were subjected to the same electrolytic etching.
2. Description of experiments
Fe
Composition of etching liquid
2
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 1. Dimensions of the tensile test specimen (unit: mm).
under lowest strain-rate has the highest flow stress. Besides, the stressstrain curves of low strain-rate display a sigmoidal shape, having an obvious secondary hardening. In contrast, the stress-strain curves of high strain-rate are more parabolic. We use work hardening rate (WHR, numerical differential of true stress-true strain curve, dσ dε ) as a parameter to further investigate this phenomenon. Fig. 6 shows the curve of WHR versus strain under each strain-rate. The WHR under low strain-rate firstly decreases at low strain levels. Then, around the strain of 0.12, it starts to increase, presenting the secondary hardening. After reaching a peak at a relatively large strain, the WHR goes down again until fracture. On the contrary, the WHR under high strain-rate decreases monotonously.
for the present study, the room temperature is 25 °C, the low temperature condition corresponds to 0 °C fulfilled by liquid nitrogen cooling, while the high temperature conditions include 50, 75 and 100 °C fulfilled by thermoplastic gun heating (as shown in Fig. 3). 2.3. Temperature measurement The real-time temperature of the specimen was recorded with a ktype thermocouple, capable of measuring temperature ranging from -50 °C to 200 °C with a sensitivity of 0.5 °C. The thermocouple was glued to the specimen, almost covering the entire surface of the gauge section. In this way, it recorded the average temperature of the gauge section. The stress-strain curves of the specimen glued with thermocouple are identical with those without thermocouple, demonstrating that the thermocouple has no influence on the material property.
3.2. Transition from isothermal to adiabatic condition To identify the critical strain-rate at which the specimen in tension becomes subjected to adiabatic condition, we recorded the temperature rise of the specimen in each test at room temperature but different strain-rate (Test Group 1). If the adiabatic condition is satisfied, the temperature rise can be theoretically estimated as
2.4. Measurement of martensitic volume fraction A 6 mm × 6 mm block was cut from the gauge section of the specimen using electric discharging machining (EDM). After polished and cleaned with acetone, the specimens were electrolytic etched to remove the surface material. A Rigaku D/max 2500H X-ray diffractometer using Cu Kα radiation was employed to quantitatively measure the martensitic volume fraction. Software THCLXPD was adopted to analyze the diffraction peaks. Diffraction spectrums of as-received material and that processed by electrolytic etching are shown in Fig. 4. The martensitic diffraction peaks of as-received material disappear after electrolytic etching.
p
ΔT = β
ε¯ ∫0 f σdε¯ p
ρcp
(1)
where ε¯fp is the final plastic strain, σ is the flow stress, ρ is the material mass density, cρ is the material specific heat, and β is a conversion coefficient and assumed as 0.95 in the present study. The actual measurement was then compared with the theoretical estimate. Fig. 7 presents the actually measured temperature rise of the specimen at each strain-rate and the theoretical estimate. At 6.67 × 10−4 s-1, the maximum temperature rise of the specimen is around 8 °C, much lower than the adiabatic estimate, as shown in Fig. 7a, implying that almost all the internal energy due to plastic deformation is dissipated to the surroundings in the form of thermal conduction, and a nearly isothermal condition achieves. When the strain-rate becomes higher, the actual temperature rise becomes larger (Fig. 7b and c) and finally approaches the adiabatic
3. Experimental results and discussions 3.1. Tensile behaviors at room temperature but different strain-rates Fig. 5 shows the stress-strain curves of 304 L, covering strain-rate from 6.67 × 10−4 s-1 to 80 s-1 at room temperature. At low strain, with the increase of strain-rate, the flow stress presents an apparent strengthening effect. However, at higher strain, the stress-strain curve
Fig. 2. Test machines: (a) universal test machine, and (b) hydraulic medium-speed test machine. 3
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 3. Stress-strain curves of 304 L at the strain-rate of 80 s−1 and different temperatures.
estimation (Fig. 7c). At 6.67 × 10−3 s-1, the maximum temperature rise of the specimen is about 45 °C, apparently higher than the value at 6.67 × 10-4 s-1. This indicates that in the tests of 6.67 × 10−3 s-1, a sufficient heat convection to environment is difficult to achieve, making the deformed sample deviate from the ideal isothermal state. At 0.133 s1 , the two curves almost superpose upon each other, which means the internal energy is almost fully converted into the heat in the material, and an adiabatic condition achieves. According to this observation, the uniaxial tension at a strain-rate higher than 0.133 s-1 is regarded as the test under adiabatic condition, and the strain-rate level of 0.133 s-1 is approximately identified as the critical strain-rate corresponding to the transition from non-adiabatic to adiabatic condition for the investigated 304 L steel. On account of the fact that heating condition of the specimen is closely related to the mechanical behavior of 304 L steel, estimation of the critical strain-rate corresponding to the transition from non-adiabatic to adiabatic condition is helpful for us to understand the mechanical behavior at room temperature but different strain-rates. Fig. 5. Stress-strain curves of 304 L at 25 °C but different strain-rates.
3.3. Discussion on change of mechanical properties test due to the heat accumulation, while it is extensively triggered in low strain-rate test, as demonstrated by X-ray diffractometer detection results provided in Section 3.5. The formation of martensite at large strain can be characterized with the secondary hardening of the stressstrain behavior. Apparently, the tendency of secondary hardening becomes weak when the strain-rate becomes high.
At higher strain-rate, more heat converted from the internal energy accumulates inside the specimen instead of dissipating to surroundings. In addition, the internal energy induced by plastic deformation at high strain-rate is larger than that at low strain-rate due to relatively high flow stress at the same deformation. At large deformation (above the true stain of 0.25), strain-induced MPT is inhibited in high strain-rate
Fig. 4. Diffraction spectrum of (a) as-received material, and (b) electrolytic etched material. 4
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 8. Strain-rate dependence of the yield strength, the ultimate tensile strength, and the uniform elongation. Fig. 6. Variation of WHR with true strain at 25 °C but different strain-rates.
the critical strain-rate is adiabatic and most of the internal energy is converted into heat. Because of the additional heating, the strain-induced MPT is suppressed at higher strain-rate (as demonstrated in Section 3.5). Therefore, above the critical strain-rate the second strengthening mechanism dominates. The variation trend of the UEL is similar with that of UTS. At beginning, the UEL decreases from the maximum until the critical strainrate. The major reason is that the MPT slightly prior to severe strain localization enhances the ductility of steels. Hence, less formation of martensite along with the strain-rate increase corresponds to lower UEL and ductility. Beyond the critical strain-rate, the strain-induced MPT has been suppressed, UEL exhibits a moderate increase. Fig. 9 shows the logarithm stress vs. logarithm strain-rate curve of 304 L at seven strain levels between 0.05 and 0.35. At the low strain levels (below 0.20), only small amount of strain-induced martensite forms which does not affect the macroscale behavior. Therefore, mechanical property of 304 L mainly presents a positive rate sensitivity (indicated by the overall slope of the curves). At the high strain levels (above 0.20), the rate sensitivity varies in a non-monotonous way from
At small deformation (below strain of 0.15), no apparent effect of MPT is observed from the material mechanical behavior at either low or high strain-rate. The major reason is that very few shear band intersections for nucleation of martensite can form at small deformation, as demonstrated by Lichtenfeld et al. (2006). Relationships between the yield strength (YS), the ultimate tensile strength (UTS), the uniform elongation (the true strain value corresponding to the dispersed necking, UEL) of 304 L and the strain-rate are depicted in Fig. 8. It can be seen that YS becomes larger when strainrate increases, identical with the positive rate sensitivity at the entire small deformation stage. 304 L has the highest UTS at the lowest strain-rate. The UTS reaches the minimum at around 0.333 s−1 which is the critical strain-rate of transition from non-adiabatic to adiabatic condition. Above the critical strain-rate, the UTS increases moderately along with the strain rate. In essence, the strengthening of ASS during deformation has two mechanisms, strain-induced MPT and dislocation interactions. Test beyond
Fig. 7. The measured temperature rise in the tensile specimen and the theoretical adiabatic estimate at strain-rate of (a) 6.67 × 10−4 s-1, (b) 6.67 × 10-3 s-1, and (c) 0.133 s-1. 5
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
sigmoidal to parabolic. We also calculated the WHR to further characterize this change, as depicted in Fig. 11. For the tests at 6.67 × 10−4 s-1 (Fig. 11a), the WHRs at different temperatures are similar when the strain is smaller than 0.1, while at larger strains the WHR becomes dramatically large when the temperature becomes low. The test results at 0 °C and 25 °C show remarkable secondary hardening. The variation of WHR with temperature at 0.333 s-1 (Fig. 11b) is similar to that at 6.67 × 10−4 s-1. The only difference is that the secondary hardening behavior at 0 °C and 25 °C attenuates. For the test at 80 s-1 (Fig. 11c), only the stress-strain curve at 0 °C presents apparent secondary hardening. Under the same strain-rate, two mechanisms, i.e. thermal softening and strain-induced MPT, impose opposite effect on the work hardening rate. Thermal softening reduces the WHR while formation of the martensite increases the WHR. Competition between the two mechanisms leads to the different change tendencies of WHR at different temperatures. For example, at a higher temperature, the thermal softening and the less amount of strain-induced martensite together result in the decrease of WHR as well as flow stress. YS, UTS and UEL versus temperature at the three representative strain-rates are shown in Fig. 12. YS yields a decrease along with the temperature rising under the three representative strain-rates, which is the result of thermal softening. Three mechanisms, i.e. strain-induced MPT, thermal softening and strain-rate strengthening effect, play together to affect the hardening behavior of 304 L at different temperatures and different strain-rates. At 0 °C and 25 °C, the MPT is almost unhindered because both austenite stability and SFE are low. However, due to adiabatic condition at higher strain-rates (0.333 and 80 s−1), less martensite forms, resulting in lower UTS than that at 6.67 × 10-4 s−1. Furthermore, UTS at 80 s−1 is higher than that at 0.333 s−1, clearly presenting strain-rate strengthening effect. At 50 °C, UTS at 80 s−1 is approximate to that at 6.67 × 10-4 s−1. The MPT is inhibited to a certain extent due to the rise of temperature. However, the strain-rate strengthening effect still works at high strainrate. Combination of these two tendencies leads to reduction of the difference of UTS between strain-rates of 6.67 × 10-4 s−1 and 80 s−1. As for higher temperature, such as 75 °C and 100 °C, even under isothermal condition, the amount of martensite is small (demonstrated in
Fig. 9. Log stress vs. log strain-rate curve of 304 L under different strain levels.
low to high strain-rate, similar to that of UTS or UEL, which is also related to the increasing inhibition of MPT under higher strain-rate. 3.4. Tensile behavior at different temperatures In Test Group 2, we chose three representative strain-rates, 6.67 × 10−4 s-1, 0.333 s-1 and 80 s-1. The first strain-rate corresponds to an isothermal condition, the second corresponds to an adiabatic condition and is close to the critical strain-rate, and the third corresponds to an adiabatic condition. Under each representative strain-rate, we conducted uniaxial tension tests at different temperatures to learn the coupling effect of strain-rate and temperature on the strain-induced MPT. Stress-strain curves of Test Group 2 are plotted in Fig. 10. The variation tendency along with the temperature is similar. Along with the temperature increasing, the flow stress decreases, which is more remarkable at large deformation, and the curve shape changes from
Fig. 10. Stress-strain curves of 304 L at different temperatures under strain-rate of (a) 6.67 × 10−4 s-1, (b) 0.333 s-1, and (c) 80 s-1. 6
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 11. WHR vs. strain at different temperatures under strain-rate of (a) 6.67 × 10−4 s-1, (b) 0.333 s-1, and (c) 80 s-1.
Fig. 12. Change of material properties: (a) yield strength (b) ultimate tensile strength, and (c) uniform elongation along with temperature at three strain-rates.
The MPT can effectively increase the ductility of the steel if it can occur rapidly before the severe strain localization, which can be exactly achieved around Tmax. At temperature lower than Tmax, the MPT takes place at low strains, but the transformation rate is low before the severe strain localization (as evidenced in Section 3.5), which is not much favorable to the material ductility. At temperature higher than Tmax, the MPT is inhibited when the transformation rate has not reached its peak. Less martensite has formed during the deformation process. For higher
Section 3.5), and the strain-rate strengthening effect becomes dominant. That is why UTS at 80 s−1 is higher than that at 6.67 × 10-4 s−1. For the test at 0.333 s−1, the strain-rate strengthening effect cannot counteract the thermal softening caused by adiabatic heating. Therefore, in such a temperature range UTS at 0.333 s−1 is still lower than that at 6.67 × 10-4 s−1. UEL at each strain-rate shows a peak (corresponding to a temperature Tmax) which shifts to lower temperature when strain-rate increases. 7
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 13. Martensite volume fraction vs. strain under different strain-rates and at (a) 0 °C, (b) 25 °C, and (c) 50 °C.
form proposed by Peng et al. (2015), as shown in Eqs. (3) and (4),
strain-rate, lower temperature is beneficial to the MPT, so the peak shifts to the lower temperature, corresponding to the result shown in Fig. 12c. At the investigated temperature range, UEL under 6.67 × 10−4 s-1 is always higher than those under 0.333 s-1 and 80 s-1. This is mainly because the MPT is inhibited at higher strain-rate.
α = (α 0 (T0) + q1 ΔT )(ε˙/ ε˙0 )q2
(3)
β = β0 (T0)(ε˙/ ε˙0 )q3
(4)
where T0 is the initial environmental temperature and ΔT is the temperature rise during the test. Substituting Eqs. (3) and (4) into (2), the integrated MPT model is shown in Eq. (5),
3.5. Variation of martensitic volume fraction under various loading conditions
q
f α′ = 1 − exp { −β [1 − exp (−αε )]n }
n
q
ε˙ 3 ε˙ 2 ⎫ ⎧ f α′ = 1 − exp −β0 (T0) ⎛ ⎞ ⎡ 1 − exp ⎛⎜−(α 0 (T0) + q1 ΔT ) ⎛ ⎞ ε ⎞⎟ ⎤ ⎢ ⎥ ⎨ ˙ ε ε ⎝ 0⎠ ⎣ ⎝ ˙0 ⎠ ⎠ ⎦ ⎬ ⎝ ⎭ ⎩ (5)
Aiming to quantitatively measure the volume fraction of martensite, the specimen is loaded at a specific temperature and strain-rate until a designated force-level which corresponds to a target true strain, and then unloaded. A 6 mm × 6 mm block is cut from the gauge section of the specimen, electrolytic etched to remove the surface material, and detected by X-ray diffractometer. Volume fraction of martensite versus strain curves at three different temperatures and three strain-rates are shown in Fig. 13. Test results at 75 °C and 100 °C are not included (the volume fraction of martensite is nearly zero at these two high temperatures). The results indicate that martensite volume fraction increases with plastic deformation. Either the increase of strain-rate at the same environmental temperature or the increase of environmental temperature at the same strain-rate leads to the reduction of martensite volume fraction. Furthermore, the transformation rate drops before the severe strain localization. All of the characteristics confirm the analysis in Section 3.4. According to the test results described in Fig. 13, we modify the Olson-Cohen model proposed by Olson and Cohen (1975) to characterize the transformation kinetics under plastic deformation. The original Olson-Cohen model is given as Eq. (2),
⎜
⎟
⎜
⎟
The parameters in Eq. (5) are calibrated using the test results in Fig. 13, as listed in Table 3. As the initial temperature dependent parameters, both α 0 and β0 decrease with increase of the initial temperature. The other three parameters, q1 to q3 keep consistent. It can be noted that this modified model extends the scope of characterizing the strain-induced MPT to both strain rate ranging from quasi-static to about 100 s−1 and temperature ranging from 0 °C to 75 °C. The calibration results are plotted in Fig. 13, where it can be seen that under the three environmental temperatures, the changes of martensite volume fraction induced by plastic deformation at different strain-rates are correctly described by the modified Olson-Cohen model. 4. Conclusions In the present paper, we investigated the influence of temperature and strain-rate on strain-induced MPT (martensitic phase
(2)
Table 3 Calibrated parameters of the modified Olson-Cohen model.
α′
where f is martensite volume fraction, ε is the effective plastic strain, n is equal to 4.5 which was determined by Olson and Cohen, α is the shear-band forming rate and β reflects the probability that a shear-band intersection forms an embryo of transformation. To explicitly characterize the strain-rate and temperature dependence of MPT with the Olson-Cohen model, we enrich the expressions of α and β based on the
0 °C 25 °C 50 °C
8
α0
β0
q1
q2
q3
4.12 3.43 1.81
11.53 4.34 3.26
−0.0138 −0.0138 −0.0138
0.0210 0.0210 0.0210
−0.154 −0.154 −0.154
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
CRediT authorship contribution statement
transformation) of 304 L. We conducted tensile tests of 304 L at different temperatures and strain-rates, which result in different evolutions of the MPT, in turn exhibiting the variety of apparent mechanical behaviors. With these tests and observations, conclusions are drawn as follows.
Zihao Qin: Investigation, Formal analysis, Validation, Software, Data curation, Writing - original draft, Visualization. Yong Xia: Conceptualization, Methodology, Resources, Investigation, Writing review & editing, Visualization, Supervision, Project administration, Funding acquisition.
(1) Strain-rate affects the mechanical performance of 304 L significantly at the room temperature. The loading of high strain-rates meets the adiabatic condition, which suppresses the MPT. A critical strain-rate corresponding to the transition from non-adiabatic to adiabatic condition can be experimentally identified. At low strainrate, the strain-induced MPT is gradually reduced along with the increase of strain-rate. UTS (Ultimate Tensile Strength) decreases and then reaches its minimum at the critical strain-rate. UTS increases above the critical strain-rate, mainly attributed to dislocation interaction. A similar tendency is found for UEL (Uniform Elongation). (2) At low strain-rate, the sigmoidal shape of the stress-strain curve, i.e. the obvious secondary work hardening, characterizes the significant strain-induced MPT. At high strain-rate, the parabolic shape of the stress-strain curve, i.e. the monotonous decrease of work hardening rate, implies suppression of the transformation. (3) Environmental temperature influences the tensile performance of 304 L significantly. The strain-induced MPT is gradually suppressed when the temperature rises, and as a result, UTS decreases. UEL (i.e. the ductility) reaches the peak value at a characteristic temperature when the severe strain localization of the material takes place very close to the moment of the maximum martensitic transformation rate. (4) Temperature and strain-rate have coupling effect on the hardening behavior of 304 L with three mechanisms: the strain-induced MPT, the thermal softening and the strain-rate strengthening. UTS achieves the maximum at the lowest temperature and strain-rate which motivate the largest amount of strain-induced martensite, whilst it achieves the minimum at the highest temperature and the critical strain-rate that corresponds to the transition from nonadiabatic to adiabatic condition. UEL achieves the maximum at the lowest strain-rate and the characteristic temperature, while it achieves the minimum at the highest temperature and strain-rate. Characteristic temperature shifts towards the lower end of the temperature range when the strain-rate becomes higher. (5) A kinetic model correlating the martensite volume fraction with environmental temperature, strain-rate and effective plastic strain is proposed based on the Olson-Cohen formula, which is capable of correctly characterizing the MPT evolution and the dependence on temperature and strain-rate.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The presented work is sponsored by the Ministry of Science and Technology of China under Contract No. 2016YFB0101606. References Hecker, S.S., Stout, M.G., Staudhammer, K.P., Smith, J.L., 1982. Effects of strain state and strain rate on deformation-induced transformation in 304 stainless steel: part I. Magnetic measurements and mechanical behavior. Metall. Trans. A 13, 619–626. Huang, G.L., Matlock, D.K., Krauss, G., 1989. Martensite formation, strain rate sensitivity, and deformation behavior of type 304 stainless steel sheet. Metall. Mater. Trans. A 20, 1239–1246. Kundu, A., Chakraborti, P.C., 2010. Effect of strain rate on quasistatic tensile flow behaviour of solution annealed 304 austenitic stainless steel at room temperature. J. Mater. Sci. 45, 5482–5489. Lichtenfeld, J.A., Van Tyne, C.J., Mataya, M.C., 2006. Effect of strain rate on stress-strain behavior of alloy 309 and 304L austenitic stainless steel. Metall. Mater. Trans. A 37 (1), 147–161. Moser, N.H., Gross, T.S., Korkolis, Y.P., 2014. Martensite formation in conventional and isothermal tension of 304 austenitic stainless steel measured by X-ray diffraction. Metall. Mater. Trans. A 45, 4891–4896. Olson, G.B., Cohen, M., 1975. Kinetics of strain-induced martensitic nucleation. Metall. Mater. Trans. A 6 (4), 791–795. Peng, F., Dong, X.H., Liu, K., Xie, H.Y., 2015. Effects of strain rate and plastic work on martensitic transformation kinetics of austenitic stainless steel 304. J. Iron Steel Res. Int. 22 (10), 931–936. Qin, Z., Li, W., Zhu, J., Xia, Y., 2016. Experimental and numerical analysis of the system ringing in intermediate strain rate tests. ASME International Mechanical Engineering Congress and Exposition, ASME-IMECE 2016. Qin, Z., Zhu, J., Li, W., Xia, Y., Zhou, Q., 2017. System ringing in impact test triggered by upper-and-lower yield points of materials. Int. J. Impact Eng. 108, 295–302. Talonen, J., Hänninen, H., Nenonen, P., Pape, G., 2005. Effect of strain rate on the straininduced γ → α′-martensite transformation and mechanical properties of austenitic stainless steels. Metall. Mater. Trans. A 36, 421–432. Xia, Y., Zhu, J., Zhou, Q., 2015. Verification of a multiple-machine program for material testing from quasi-static to high strain-rate. Int. J. Impact Eng. 86, 284–294. Xia, Y., Zhu, J., Wang, K., Zhou, Q., 2016. Design and verification of a strain gauge based load sensor for medium-speed dynamic tests with a hydraulic test machine. Int. J. Impact Eng. 88, 139–152.
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Journal of Materials Processing Tech. journal homepage: www.elsevier.com/locate/jmatprotec
Role of strain-induced martensitic phase transformation in mechanical response of 304L steel at different strain-rates and temperatures
T
Zihao Qin, Yong Xia* State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China
A R T I C LE I N FO
A B S T R A C T
Associate Editor: Z Cui
The strain-rate and temperature dependencies of the strain-induced martensitic phase transformation (MPT) of AISI 304 L are experimentally investigated. Firstly, the tensile tests of 304 L at room temperature are conducted at the strain-rates ranges from 6.67 × 10−4 s-1 to 80 s-1. The stress-strain curves indicate a significant strain-rate effect of the strain-induced MPT, which is closely relevant to extent of the adiabatic heating. The second batch of tensile tests are conducted at several representative strain-rates and at different temperatures ranging from 0 °C to 100 °C. The martensitic volume fractions at different plastic deformation stages are measured by X-ray diffraction to trace the evolution of martensitic phase in the tests. The test results indicate that the environmental temperature and the strain-rate exert coupling influence on the stress-strain behavior. Variations in strength and ductility of 304 L in the tests are explained with a competition mechanism between strain-induced MPT, thermal softening and strain-rate strengthening. A kinetic model of MPT is modified to take the strain-rate, initial temperature and temperature rise into account.
Keywords: Martensitic phase transformation (MPT) Strain-rate Environmental temperature Mechanical behavior
1. Introduction Because of the excellent corrosion resistance, weldability and mechanical properties, Austenitic stainless steels (ASS) are widely applied in engineering structures. Activated by plastic deformation, some grades of ASS tend to transform from face-centered-cubic (FCC) austenite (γ) to body-centered-cubic (BCC) martensite (α'), known as straininduced martensitic phase transformation (MPT). The transformation usually results in: (1) a higher strength as martensite is stronger than austenite, and (2) a higher ductility and the delay of necking onset if the transformation takes place quickly and closely prior to severely localized deformation. As a consequence, the MPT has a significant effect on the mechanical behavior of the steels and is attractive to engineering applications. Over the past a couple of decades, the influential factors of straininduced MPT, such as temperature, strain rate, chemical composition and stress state, has been studied deeply by different research teams. In the present study, we mainly concern about the influence of temperature and strain rate to the MPT. Hecker et al. (1982) measured the martensitic volume fraction vs. true strain curve of AISI 304 under the temperature ranging from -188 °C to 50 °C. The volume fraction of martensite decreases with an increase in temperature under a given true strain. Huang et al. (1989) conducted the uniaxial tensile test of AISI
⁎
304 under the temperature ranging from -80 °C to 160 °C and concluded that the plastic hardening behavior results from the competition of strain-induced MPT and dislocation interactions during deformation. Along with the temperature rise, the dislocation slip dominates, and the proportion of MPT decreases. Moser et al. (2014) studied MPT of AISI 304 in conventional and isothermal tension. Besides the findings similar to the above, they adopted isothermal tests to determine Md, above which temperature the transformation behavior is totally inhibited. By performing uniaxial tensile test of AISI 304 and AISI 301 L N under strain-rate ranging from 3 × 10−4 s-1 to 200 s-1 and room temperature, Talonen et al. (2005) studied the relation between strain-rate and MPT as well as material tensile properties, finding that the transformation behavior is suppressed under high strain-rate. The suppression finally affects the ultimate tensile strength and uniform elongation of the material. Lichtenfeld et al. (2006) chose two grades of ASS for testing, i.e. Alloy 309 which is stable so as to provide the property response of pure austenite and Alloy 304 L which is susceptible to the strain-induced MPT. Tensile Tests were conducted at room temperature and under strain-rate ranging from 1.25 × 10−4 s-1 to 400 s-1. It indicated that the martensitic volume fraction is highly correlated with adiabatic heating and the stress-strain curve of Alloy 304 L exhibits apparent secondary hardening. With room temperature tensile tests below 0.1 s-1, Kundu and Chakraborti (2010) revealed that, for solution
Corresponding author. E-mail address: [email protected] (Y. Xia).
https://doi.org/10.1016/j.jmatprotec.2020.116613 Received 3 October 2019; Received in revised form 14 January 2020; Accepted 20 January 2020 Available online 21 January 2020 0924-0136/ © 2020 Elsevier B.V. All rights reserved.
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
annealed 304 stainless steel, yield strength increases and tensile strength decreases with increase of strain rate. They observed the threestage work hardening behavior at all the investigated strain rates, and attributed the highest hardening exponent at Stage 3 to the strain-induced MPT. Both Talonen et al. (2005) and Lichtenfeld et al. (2006) characterized the strain-induced MPT using a kinetic model proposed by Olson and Cohen (1975). In Olson and Cohen’s study, by the comparison of kinetics model and experiment data, they correlated MPT with temperature sensitivity and stacking-fault energy (SFE). The stability of austenite and SFE increase as temperature rises, limiting the MPT. Based on this, they proposed a kinetics model containing two temperature dependent parameters to quantitatively characterize the MPT. Peng et al. (2015) chose 304 stainless steel as research object and conducted the room temperature tests at strain rates ranging from 1 × 10-3 s-1 to 0.1 s-1. They incorporated the effect of strain rate to Olson and Cohen model, and applied the improved model to characterize the change of stress-strain response at the strain rates below 0.1 s-1. In the previous publications, most of the investigation on straininduced MPT concentrated on the environmental temperature effect (under quasi-static) or the strain-rate effect (at room temperature) separately. Regarding the practical engineering application, the ASS materials are usually employed in more complicated work scenarios, where the MPT could be affected by environmental temperature and strain-rate simultaneously. In the present study, focusing on the mechanical behavior of a susceptible ASS alloy 304 L, we investigate the coupling effect of environmental temperature and strain-rate on the strain-induced MPT. Firstly, the uniaxial tension tests at room temperature are conducted at different strain-rates. Effect of strain-rate on the tensile performance is analyzed. Secondly, the tensile tests at three representative strain-rates are performed at different temperatures ranging from 0 °C to 100 °C. By measuring the martensitic volume fraction in the various cases, the MPT is correlated with the tensile mechanical behavior at different temperatures and strain-rates. A kinetic model is then proposed on the basis of the Olson-Cohen model to characterize the strain-induced MPT by taking into account the effect of both strain-rate and environmental temperature.
Table 2 Processing parameters of electrolytic etching.
Si
C
P
S
base
18.61
8.00
1.20
0.688
0.0275
0.0304
0.0269
Time (min)
55 % phosphoric acid + 25 % sulfuric acid + 20 % distilled water
50-60
0.2
6-8
2
2.2.1. Quasi-static tension Quasi-static tension was carried out using a universal material test machine (Zwick 20 kN AllroundLine Table-Top). The signal of force was recorded by a built-in load sensor. The deformation was captured by a CCD camera and then processed by Digital Image Correlation (DIC) method. The universal test machine was equipped with an environmental chamber (Fig. 2a) capable of controlling the temperature for testing ranging from -80 °C to 250 °C. 2.2.2. Dynamic tension A customized intermediate strain-rate test machine was employed to perform the dynamic tests (Fig. 2b). The machine operates with open-loop and the hydraulic bar moves with a free stroke to reach the predefined speed before stretching the specimen. Deformation of the specimen was captured by a high-speed digital camera, and also DIC method was used for data processing. With respect to the dynamic force measurement, as demonstrated by Xia et al. (2015,2016) and Qin et al. (2016,2017), the force signal measured by the built-in load sensor often suffers from severe oscillation, attributed to the system ringing. To overcome this problem, Xia et al. (2016) designed a lightweight load sensor combining the function of gripper and sensor, with which the oscillation of force was significantly attenuated. In order to assure the data accuracy, this lightweight load sensor was adopted in the current study. To fulfill the dynamic tests at different temperatures, we used a thermoplastic gun and liquid nitrogen, respectively, to locally heat or cool the specimen mounted on the test machine. The temperature of the specimen was changed by adjusting the distance from the thermoplastic gun or the nozzle of liquid nitrogen container to the specimen. For the purpose of maintaining the temperature uniformity in the specimen, after reaching the target temperature, we kept heating or cooling the specimen for another 10 min before the test. The stress-strain curves of 80 s−1 strain-rate at temperatures ranging from 0 °C to 100 °C and the corresponding device for heating or cooling are plotted in Fig. 3, and the good repeatability of the test results validates this method. Specified
Table 1 Chemical composition of the austenitic stainless steel 304 L (Mass percent: %). Mn
Voltage (V)
In this study, we performed two groups of tensile tests. In the first test group, uniaxial tension tests under different strain-rates (from 6.67 × 10−4 s-1 to 80 s-1) were conducted at room temperature (25 °C). In the second test group, we chose three representative strain-rates and performed the uniaxial tension tests at different temperatures (from 0 °C to 100 °C). For the purpose of analyzing the ductility of the material, the dimensions of the specimen for quasi-static and dynamic tensile tests were identical (Fig. 1).
The austenitic stainless steel 304 L, which was 1.8 mm thick coldrolled sheet and heat-treated, was tested in this study. The chemical composition of the material was detected by an X-ray fluorescence spectrometer as listed in Table 1. To correctly measure the volume fraction of martensite, we applied electrolytic etching to thin the 304 L sheet with the processing parameters as shown in Table 2, and then examined the processed sample with X-ray diffraction (see details of the measurement procedure described in Section 2.4). In this way, a surface layer of approximately 0.2 mm thick was removed, and the measured volume fraction of martensite in the as-received sheet was within the range of 0-0.01. For comparison, another examination of X-ray diffraction was directly made on the 304 L sheet without surface processing, indicating that the volume fraction of martensite was approximate 0.13, much higher than the measurement with surface processing. It demonstrates that the martensite mainly exists in a very thin surface layer of the asreceived sheet, which is actually attributed to the temper rolling
Ni
Current (A)
2.2. Tensile tests
2.1. As-received material
Cr
Temperature (oC)
processing. The surface layer will disturb the measurement when we analyze the martensitic transformation inside the material induced by external loading. Therefore, it is preferred to remove the surface layer for an appropriate measurement. Another fact that has been demonstrated is, mechanically removing the surface material is unsuitable because it introduces extra mechanical damage and motivates the strain-induced transformation. Concerning the above observations, prior to measurement of the martensitic volume fraction, all the specimens were subjected to the same electrolytic etching.
2. Description of experiments
Fe
Composition of etching liquid
2
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 1. Dimensions of the tensile test specimen (unit: mm).
under lowest strain-rate has the highest flow stress. Besides, the stressstrain curves of low strain-rate display a sigmoidal shape, having an obvious secondary hardening. In contrast, the stress-strain curves of high strain-rate are more parabolic. We use work hardening rate (WHR, numerical differential of true stress-true strain curve, dσ dε ) as a parameter to further investigate this phenomenon. Fig. 6 shows the curve of WHR versus strain under each strain-rate. The WHR under low strain-rate firstly decreases at low strain levels. Then, around the strain of 0.12, it starts to increase, presenting the secondary hardening. After reaching a peak at a relatively large strain, the WHR goes down again until fracture. On the contrary, the WHR under high strain-rate decreases monotonously.
for the present study, the room temperature is 25 °C, the low temperature condition corresponds to 0 °C fulfilled by liquid nitrogen cooling, while the high temperature conditions include 50, 75 and 100 °C fulfilled by thermoplastic gun heating (as shown in Fig. 3). 2.3. Temperature measurement The real-time temperature of the specimen was recorded with a ktype thermocouple, capable of measuring temperature ranging from -50 °C to 200 °C with a sensitivity of 0.5 °C. The thermocouple was glued to the specimen, almost covering the entire surface of the gauge section. In this way, it recorded the average temperature of the gauge section. The stress-strain curves of the specimen glued with thermocouple are identical with those without thermocouple, demonstrating that the thermocouple has no influence on the material property.
3.2. Transition from isothermal to adiabatic condition To identify the critical strain-rate at which the specimen in tension becomes subjected to adiabatic condition, we recorded the temperature rise of the specimen in each test at room temperature but different strain-rate (Test Group 1). If the adiabatic condition is satisfied, the temperature rise can be theoretically estimated as
2.4. Measurement of martensitic volume fraction A 6 mm × 6 mm block was cut from the gauge section of the specimen using electric discharging machining (EDM). After polished and cleaned with acetone, the specimens were electrolytic etched to remove the surface material. A Rigaku D/max 2500H X-ray diffractometer using Cu Kα radiation was employed to quantitatively measure the martensitic volume fraction. Software THCLXPD was adopted to analyze the diffraction peaks. Diffraction spectrums of as-received material and that processed by electrolytic etching are shown in Fig. 4. The martensitic diffraction peaks of as-received material disappear after electrolytic etching.
p
ΔT = β
ε¯ ∫0 f σdε¯ p
ρcp
(1)
where ε¯fp is the final plastic strain, σ is the flow stress, ρ is the material mass density, cρ is the material specific heat, and β is a conversion coefficient and assumed as 0.95 in the present study. The actual measurement was then compared with the theoretical estimate. Fig. 7 presents the actually measured temperature rise of the specimen at each strain-rate and the theoretical estimate. At 6.67 × 10−4 s-1, the maximum temperature rise of the specimen is around 8 °C, much lower than the adiabatic estimate, as shown in Fig. 7a, implying that almost all the internal energy due to plastic deformation is dissipated to the surroundings in the form of thermal conduction, and a nearly isothermal condition achieves. When the strain-rate becomes higher, the actual temperature rise becomes larger (Fig. 7b and c) and finally approaches the adiabatic
3. Experimental results and discussions 3.1. Tensile behaviors at room temperature but different strain-rates Fig. 5 shows the stress-strain curves of 304 L, covering strain-rate from 6.67 × 10−4 s-1 to 80 s-1 at room temperature. At low strain, with the increase of strain-rate, the flow stress presents an apparent strengthening effect. However, at higher strain, the stress-strain curve
Fig. 2. Test machines: (a) universal test machine, and (b) hydraulic medium-speed test machine. 3
Journal of Materials Processing Tech. 280 (2020) 116613
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Fig. 3. Stress-strain curves of 304 L at the strain-rate of 80 s−1 and different temperatures.
estimation (Fig. 7c). At 6.67 × 10−3 s-1, the maximum temperature rise of the specimen is about 45 °C, apparently higher than the value at 6.67 × 10-4 s-1. This indicates that in the tests of 6.67 × 10−3 s-1, a sufficient heat convection to environment is difficult to achieve, making the deformed sample deviate from the ideal isothermal state. At 0.133 s1 , the two curves almost superpose upon each other, which means the internal energy is almost fully converted into the heat in the material, and an adiabatic condition achieves. According to this observation, the uniaxial tension at a strain-rate higher than 0.133 s-1 is regarded as the test under adiabatic condition, and the strain-rate level of 0.133 s-1 is approximately identified as the critical strain-rate corresponding to the transition from non-adiabatic to adiabatic condition for the investigated 304 L steel. On account of the fact that heating condition of the specimen is closely related to the mechanical behavior of 304 L steel, estimation of the critical strain-rate corresponding to the transition from non-adiabatic to adiabatic condition is helpful for us to understand the mechanical behavior at room temperature but different strain-rates. Fig. 5. Stress-strain curves of 304 L at 25 °C but different strain-rates.
3.3. Discussion on change of mechanical properties test due to the heat accumulation, while it is extensively triggered in low strain-rate test, as demonstrated by X-ray diffractometer detection results provided in Section 3.5. The formation of martensite at large strain can be characterized with the secondary hardening of the stressstrain behavior. Apparently, the tendency of secondary hardening becomes weak when the strain-rate becomes high.
At higher strain-rate, more heat converted from the internal energy accumulates inside the specimen instead of dissipating to surroundings. In addition, the internal energy induced by plastic deformation at high strain-rate is larger than that at low strain-rate due to relatively high flow stress at the same deformation. At large deformation (above the true stain of 0.25), strain-induced MPT is inhibited in high strain-rate
Fig. 4. Diffraction spectrum of (a) as-received material, and (b) electrolytic etched material. 4
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
Fig. 8. Strain-rate dependence of the yield strength, the ultimate tensile strength, and the uniform elongation. Fig. 6. Variation of WHR with true strain at 25 °C but different strain-rates.
the critical strain-rate is adiabatic and most of the internal energy is converted into heat. Because of the additional heating, the strain-induced MPT is suppressed at higher strain-rate (as demonstrated in Section 3.5). Therefore, above the critical strain-rate the second strengthening mechanism dominates. The variation trend of the UEL is similar with that of UTS. At beginning, the UEL decreases from the maximum until the critical strainrate. The major reason is that the MPT slightly prior to severe strain localization enhances the ductility of steels. Hence, less formation of martensite along with the strain-rate increase corresponds to lower UEL and ductility. Beyond the critical strain-rate, the strain-induced MPT has been suppressed, UEL exhibits a moderate increase. Fig. 9 shows the logarithm stress vs. logarithm strain-rate curve of 304 L at seven strain levels between 0.05 and 0.35. At the low strain levels (below 0.20), only small amount of strain-induced martensite forms which does not affect the macroscale behavior. Therefore, mechanical property of 304 L mainly presents a positive rate sensitivity (indicated by the overall slope of the curves). At the high strain levels (above 0.20), the rate sensitivity varies in a non-monotonous way from
At small deformation (below strain of 0.15), no apparent effect of MPT is observed from the material mechanical behavior at either low or high strain-rate. The major reason is that very few shear band intersections for nucleation of martensite can form at small deformation, as demonstrated by Lichtenfeld et al. (2006). Relationships between the yield strength (YS), the ultimate tensile strength (UTS), the uniform elongation (the true strain value corresponding to the dispersed necking, UEL) of 304 L and the strain-rate are depicted in Fig. 8. It can be seen that YS becomes larger when strainrate increases, identical with the positive rate sensitivity at the entire small deformation stage. 304 L has the highest UTS at the lowest strain-rate. The UTS reaches the minimum at around 0.333 s−1 which is the critical strain-rate of transition from non-adiabatic to adiabatic condition. Above the critical strain-rate, the UTS increases moderately along with the strain rate. In essence, the strengthening of ASS during deformation has two mechanisms, strain-induced MPT and dislocation interactions. Test beyond
Fig. 7. The measured temperature rise in the tensile specimen and the theoretical adiabatic estimate at strain-rate of (a) 6.67 × 10−4 s-1, (b) 6.67 × 10-3 s-1, and (c) 0.133 s-1. 5
Journal of Materials Processing Tech. 280 (2020) 116613
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sigmoidal to parabolic. We also calculated the WHR to further characterize this change, as depicted in Fig. 11. For the tests at 6.67 × 10−4 s-1 (Fig. 11a), the WHRs at different temperatures are similar when the strain is smaller than 0.1, while at larger strains the WHR becomes dramatically large when the temperature becomes low. The test results at 0 °C and 25 °C show remarkable secondary hardening. The variation of WHR with temperature at 0.333 s-1 (Fig. 11b) is similar to that at 6.67 × 10−4 s-1. The only difference is that the secondary hardening behavior at 0 °C and 25 °C attenuates. For the test at 80 s-1 (Fig. 11c), only the stress-strain curve at 0 °C presents apparent secondary hardening. Under the same strain-rate, two mechanisms, i.e. thermal softening and strain-induced MPT, impose opposite effect on the work hardening rate. Thermal softening reduces the WHR while formation of the martensite increases the WHR. Competition between the two mechanisms leads to the different change tendencies of WHR at different temperatures. For example, at a higher temperature, the thermal softening and the less amount of strain-induced martensite together result in the decrease of WHR as well as flow stress. YS, UTS and UEL versus temperature at the three representative strain-rates are shown in Fig. 12. YS yields a decrease along with the temperature rising under the three representative strain-rates, which is the result of thermal softening. Three mechanisms, i.e. strain-induced MPT, thermal softening and strain-rate strengthening effect, play together to affect the hardening behavior of 304 L at different temperatures and different strain-rates. At 0 °C and 25 °C, the MPT is almost unhindered because both austenite stability and SFE are low. However, due to adiabatic condition at higher strain-rates (0.333 and 80 s−1), less martensite forms, resulting in lower UTS than that at 6.67 × 10-4 s−1. Furthermore, UTS at 80 s−1 is higher than that at 0.333 s−1, clearly presenting strain-rate strengthening effect. At 50 °C, UTS at 80 s−1 is approximate to that at 6.67 × 10-4 s−1. The MPT is inhibited to a certain extent due to the rise of temperature. However, the strain-rate strengthening effect still works at high strainrate. Combination of these two tendencies leads to reduction of the difference of UTS between strain-rates of 6.67 × 10-4 s−1 and 80 s−1. As for higher temperature, such as 75 °C and 100 °C, even under isothermal condition, the amount of martensite is small (demonstrated in
Fig. 9. Log stress vs. log strain-rate curve of 304 L under different strain levels.
low to high strain-rate, similar to that of UTS or UEL, which is also related to the increasing inhibition of MPT under higher strain-rate. 3.4. Tensile behavior at different temperatures In Test Group 2, we chose three representative strain-rates, 6.67 × 10−4 s-1, 0.333 s-1 and 80 s-1. The first strain-rate corresponds to an isothermal condition, the second corresponds to an adiabatic condition and is close to the critical strain-rate, and the third corresponds to an adiabatic condition. Under each representative strain-rate, we conducted uniaxial tension tests at different temperatures to learn the coupling effect of strain-rate and temperature on the strain-induced MPT. Stress-strain curves of Test Group 2 are plotted in Fig. 10. The variation tendency along with the temperature is similar. Along with the temperature increasing, the flow stress decreases, which is more remarkable at large deformation, and the curve shape changes from
Fig. 10. Stress-strain curves of 304 L at different temperatures under strain-rate of (a) 6.67 × 10−4 s-1, (b) 0.333 s-1, and (c) 80 s-1. 6
Journal of Materials Processing Tech. 280 (2020) 116613
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Fig. 11. WHR vs. strain at different temperatures under strain-rate of (a) 6.67 × 10−4 s-1, (b) 0.333 s-1, and (c) 80 s-1.
Fig. 12. Change of material properties: (a) yield strength (b) ultimate tensile strength, and (c) uniform elongation along with temperature at three strain-rates.
The MPT can effectively increase the ductility of the steel if it can occur rapidly before the severe strain localization, which can be exactly achieved around Tmax. At temperature lower than Tmax, the MPT takes place at low strains, but the transformation rate is low before the severe strain localization (as evidenced in Section 3.5), which is not much favorable to the material ductility. At temperature higher than Tmax, the MPT is inhibited when the transformation rate has not reached its peak. Less martensite has formed during the deformation process. For higher
Section 3.5), and the strain-rate strengthening effect becomes dominant. That is why UTS at 80 s−1 is higher than that at 6.67 × 10-4 s−1. For the test at 0.333 s−1, the strain-rate strengthening effect cannot counteract the thermal softening caused by adiabatic heating. Therefore, in such a temperature range UTS at 0.333 s−1 is still lower than that at 6.67 × 10-4 s−1. UEL at each strain-rate shows a peak (corresponding to a temperature Tmax) which shifts to lower temperature when strain-rate increases. 7
Journal of Materials Processing Tech. 280 (2020) 116613
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Fig. 13. Martensite volume fraction vs. strain under different strain-rates and at (a) 0 °C, (b) 25 °C, and (c) 50 °C.
form proposed by Peng et al. (2015), as shown in Eqs. (3) and (4),
strain-rate, lower temperature is beneficial to the MPT, so the peak shifts to the lower temperature, corresponding to the result shown in Fig. 12c. At the investigated temperature range, UEL under 6.67 × 10−4 s-1 is always higher than those under 0.333 s-1 and 80 s-1. This is mainly because the MPT is inhibited at higher strain-rate.
α = (α 0 (T0) + q1 ΔT )(ε˙/ ε˙0 )q2
(3)
β = β0 (T0)(ε˙/ ε˙0 )q3
(4)
where T0 is the initial environmental temperature and ΔT is the temperature rise during the test. Substituting Eqs. (3) and (4) into (2), the integrated MPT model is shown in Eq. (5),
3.5. Variation of martensitic volume fraction under various loading conditions
q
f α′ = 1 − exp { −β [1 − exp (−αε )]n }
n
q
ε˙ 3 ε˙ 2 ⎫ ⎧ f α′ = 1 − exp −β0 (T0) ⎛ ⎞ ⎡ 1 − exp ⎛⎜−(α 0 (T0) + q1 ΔT ) ⎛ ⎞ ε ⎞⎟ ⎤ ⎢ ⎥ ⎨ ˙ ε ε ⎝ 0⎠ ⎣ ⎝ ˙0 ⎠ ⎠ ⎦ ⎬ ⎝ ⎭ ⎩ (5)
Aiming to quantitatively measure the volume fraction of martensite, the specimen is loaded at a specific temperature and strain-rate until a designated force-level which corresponds to a target true strain, and then unloaded. A 6 mm × 6 mm block is cut from the gauge section of the specimen, electrolytic etched to remove the surface material, and detected by X-ray diffractometer. Volume fraction of martensite versus strain curves at three different temperatures and three strain-rates are shown in Fig. 13. Test results at 75 °C and 100 °C are not included (the volume fraction of martensite is nearly zero at these two high temperatures). The results indicate that martensite volume fraction increases with plastic deformation. Either the increase of strain-rate at the same environmental temperature or the increase of environmental temperature at the same strain-rate leads to the reduction of martensite volume fraction. Furthermore, the transformation rate drops before the severe strain localization. All of the characteristics confirm the analysis in Section 3.4. According to the test results described in Fig. 13, we modify the Olson-Cohen model proposed by Olson and Cohen (1975) to characterize the transformation kinetics under plastic deformation. The original Olson-Cohen model is given as Eq. (2),
⎜
⎟
⎜
⎟
The parameters in Eq. (5) are calibrated using the test results in Fig. 13, as listed in Table 3. As the initial temperature dependent parameters, both α 0 and β0 decrease with increase of the initial temperature. The other three parameters, q1 to q3 keep consistent. It can be noted that this modified model extends the scope of characterizing the strain-induced MPT to both strain rate ranging from quasi-static to about 100 s−1 and temperature ranging from 0 °C to 75 °C. The calibration results are plotted in Fig. 13, where it can be seen that under the three environmental temperatures, the changes of martensite volume fraction induced by plastic deformation at different strain-rates are correctly described by the modified Olson-Cohen model. 4. Conclusions In the present paper, we investigated the influence of temperature and strain-rate on strain-induced MPT (martensitic phase
(2)
Table 3 Calibrated parameters of the modified Olson-Cohen model.
α′
where f is martensite volume fraction, ε is the effective plastic strain, n is equal to 4.5 which was determined by Olson and Cohen, α is the shear-band forming rate and β reflects the probability that a shear-band intersection forms an embryo of transformation. To explicitly characterize the strain-rate and temperature dependence of MPT with the Olson-Cohen model, we enrich the expressions of α and β based on the
0 °C 25 °C 50 °C
8
α0
β0
q1
q2
q3
4.12 3.43 1.81
11.53 4.34 3.26
−0.0138 −0.0138 −0.0138
0.0210 0.0210 0.0210
−0.154 −0.154 −0.154
Journal of Materials Processing Tech. 280 (2020) 116613
Z. Qin and Y. Xia
CRediT authorship contribution statement
transformation) of 304 L. We conducted tensile tests of 304 L at different temperatures and strain-rates, which result in different evolutions of the MPT, in turn exhibiting the variety of apparent mechanical behaviors. With these tests and observations, conclusions are drawn as follows.
Zihao Qin: Investigation, Formal analysis, Validation, Software, Data curation, Writing - original draft, Visualization. Yong Xia: Conceptualization, Methodology, Resources, Investigation, Writing review & editing, Visualization, Supervision, Project administration, Funding acquisition.
(1) Strain-rate affects the mechanical performance of 304 L significantly at the room temperature. The loading of high strain-rates meets the adiabatic condition, which suppresses the MPT. A critical strain-rate corresponding to the transition from non-adiabatic to adiabatic condition can be experimentally identified. At low strainrate, the strain-induced MPT is gradually reduced along with the increase of strain-rate. UTS (Ultimate Tensile Strength) decreases and then reaches its minimum at the critical strain-rate. UTS increases above the critical strain-rate, mainly attributed to dislocation interaction. A similar tendency is found for UEL (Uniform Elongation). (2) At low strain-rate, the sigmoidal shape of the stress-strain curve, i.e. the obvious secondary work hardening, characterizes the significant strain-induced MPT. At high strain-rate, the parabolic shape of the stress-strain curve, i.e. the monotonous decrease of work hardening rate, implies suppression of the transformation. (3) Environmental temperature influences the tensile performance of 304 L significantly. The strain-induced MPT is gradually suppressed when the temperature rises, and as a result, UTS decreases. UEL (i.e. the ductility) reaches the peak value at a characteristic temperature when the severe strain localization of the material takes place very close to the moment of the maximum martensitic transformation rate. (4) Temperature and strain-rate have coupling effect on the hardening behavior of 304 L with three mechanisms: the strain-induced MPT, the thermal softening and the strain-rate strengthening. UTS achieves the maximum at the lowest temperature and strain-rate which motivate the largest amount of strain-induced martensite, whilst it achieves the minimum at the highest temperature and the critical strain-rate that corresponds to the transition from nonadiabatic to adiabatic condition. UEL achieves the maximum at the lowest strain-rate and the characteristic temperature, while it achieves the minimum at the highest temperature and strain-rate. Characteristic temperature shifts towards the lower end of the temperature range when the strain-rate becomes higher. (5) A kinetic model correlating the martensite volume fraction with environmental temperature, strain-rate and effective plastic strain is proposed based on the Olson-Cohen formula, which is capable of correctly characterizing the MPT evolution and the dependence on temperature and strain-rate.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The presented work is sponsored by the Ministry of Science and Technology of China under Contract No. 2016YFB0101606. References Hecker, S.S., Stout, M.G., Staudhammer, K.P., Smith, J.L., 1982. Effects of strain state and strain rate on deformation-induced transformation in 304 stainless steel: part I. Magnetic measurements and mechanical behavior. Metall. Trans. A 13, 619–626. Huang, G.L., Matlock, D.K., Krauss, G., 1989. Martensite formation, strain rate sensitivity, and deformation behavior of type 304 stainless steel sheet. Metall. Mater. Trans. A 20, 1239–1246. Kundu, A., Chakraborti, P.C., 2010. Effect of strain rate on quasistatic tensile flow behaviour of solution annealed 304 austenitic stainless steel at room temperature. J. Mater. Sci. 45, 5482–5489. Lichtenfeld, J.A., Van Tyne, C.J., Mataya, M.C., 2006. Effect of strain rate on stress-strain behavior of alloy 309 and 304L austenitic stainless steel. Metall. Mater. Trans. A 37 (1), 147–161. Moser, N.H., Gross, T.S., Korkolis, Y.P., 2014. Martensite formation in conventional and isothermal tension of 304 austenitic stainless steel measured by X-ray diffraction. Metall. Mater. Trans. A 45, 4891–4896. Olson, G.B., Cohen, M., 1975. Kinetics of strain-induced martensitic nucleation. Metall. Mater. Trans. A 6 (4), 791–795. Peng, F., Dong, X.H., Liu, K., Xie, H.Y., 2015. Effects of strain rate and plastic work on martensitic transformation kinetics of austenitic stainless steel 304. J. Iron Steel Res. Int. 22 (10), 931–936. Qin, Z., Li, W., Zhu, J., Xia, Y., 2016. Experimental and numerical analysis of the system ringing in intermediate strain rate tests. ASME International Mechanical Engineering Congress and Exposition, ASME-IMECE 2016. Qin, Z., Zhu, J., Li, W., Xia, Y., Zhou, Q., 2017. System ringing in impact test triggered by upper-and-lower yield points of materials. Int. J. Impact Eng. 108, 295–302. Talonen, J., Hänninen, H., Nenonen, P., Pape, G., 2005. Effect of strain rate on the straininduced γ → α′-martensite transformation and mechanical properties of austenitic stainless steels. Metall. Mater. Trans. A 36, 421–432. Xia, Y., Zhu, J., Zhou, Q., 2015. Verification of a multiple-machine program for material testing from quasi-static to high strain-rate. Int. J. Impact Eng. 86, 284–294. Xia, Y., Zhu, J., Wang, K., Zhou, Q., 2016. Design and verification of a strain gauge based load sensor for medium-speed dynamic tests with a hydraulic test machine. Int. J. Impact Eng. 88, 139–152.
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