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Stress relaxation and its effect on tensile deformation of steels
Materials and Design 52 (2013) 284–288
Contents lists available at SciVerse ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Short Communication
Stress relaxation and its effect on tensile deformation of steels K. Hariharan, O. Majidi, C. Kim, M.G. Lee ⇑, F. Barlat Materials Mechanics Laboratory, Graduate Institute of Ferrous Technology, Postech University, San 31 Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Republic of Korea
a r t i c l e
i n f o
Article history: Received 25 March 2013 Accepted 27 May 2013 Available online 6 June 2013
a b s t r a c t The tensile deformation of metallic materials, when interrupted without unloading, exhibit relaxation of stress. The stress relaxation phenomenon can alter the mechanical behavior of the materials. Stress relaxation phenomenon during tensile test is studied in three steel grades with different microstructures. The influence of stress relaxation on uniform elongation has not been reported before. The uniform elongation varies with strain at which material relaxes and is found to increase upto 3.5%. Contradicting with the published results, the stress drop during stress relaxation varies with strain and the possible reasons are explained. The stress drop during relaxation is governed by strain hardening mechanism in low carbon steel and strain aging mechanism due to martensite in dual phase (DP) and transformation induced plasticity (TRIP) steels. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Stress relaxation tests under tension involve intermittent stopping of the cross-head at a fixed total strain. During relaxation, a portion of stored elastic energy is converted into plastic strain leading to a relaxation of the applied stress with time. The stress relaxation test has been used to characterize understand the deformation related metallurgical parameters such as internal stress and activation volume [1]. Gupta and Li [2,3] proposed a power law function to estimate the internal stress, assuming constant mobile dislocation density during stress relaxation. The internal stress estimated using the relation is validated for several materials [4,5]. The assumption of constant mobile dislocation density during stress relaxation is not valid as it decreases during stress relaxation [6]. The existing equations for determining internal stress can be modified to take the variation of mobile dislocation density into account for better prediction [7]. The activation volume required for thermal activation of plastic deformation at a particular temperature is related to effective stress [8]. Estimation of activation volume using stress relaxation tests accounting the variation of mobile dislocation density has been described in [1,6]. In the recent years, activation volume measurement using stress relaxation has been used to determine the deformation mechanism of nano-crystalline materials [9–12]. The stress versus strain rate data obtained during stress relaxation have also been utilized to develop phenomenological models for mechanical equation of state [13] and viscoplasticity [14]. Hart [15] proposed a phenomenological constitutive model using stress, plastic strain rate and an evolutionary state variable called hard⇑ Corresponding author. Tel.: +82 54 279 9034; fax: +82 54 279 9229. E-mail address: [email protected] (M.G. Lee). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.05.088
ness, independent of prior deformation path. The locus of all possible combinations of stress and strain rate state at a constant plastic strain gives a constant hardness curve. Lee and Hart [16] demonstrated that the stress relaxation test with a negligible change in plastic strain is the most suitable to generate the constant hardness curves. Similar phenomenological models using stress relaxation data are proposed by others [17]. Among the proposed models, Hart’s model is generally found to be acceptable for a wide range of materials and conditions [18–23]. During stress relaxation, the plastic strain rate decreases continuously [24], which is characteristic to viscoplastic materials. Krempl and coworkers [14,25] have extensively studied stress relaxation phenomenon using viscoplastic models on overstress. Accordingly, the flow stress consists of two components namely, equilibrium flow stress and overstress. The overstress is dependent on strain rate, similar to the effective stress discussed above. The stress relaxation phenomenon also alters the mechanical behavior of the materials. In spite of advances in stress relaxation testing, efforts in understanding its influence in mechanical behavior especially flow stress and elongation, remains insufficient. In a recent report [26], better formability of a deep drawn component with intermediate stops is attributed to the stress relaxation phenomenon. However, detailed analysis on the mechanism of ductility enhancement through structured experiments has not yet been reported. In the present work, stress relaxation phenomenon is studied experimentally in three alloys, a low carbon steel, a dual phase (DP) steel and a transformation induced plasticity (TRIP) steel, with specific focus on the ductility. The work involves three different microstructures, i.e fully ferritic, ferrite + martensite and ferrite + austenite. In the latter case, the volume fraction of austenite changes with strain, over a wide range of strain rates.
K. Hariharan et al. / Materials and Design 52 (2013) 284–288
2. Experiments Stress relaxation under monotonic tension in the three commercially available steels, a low carbon steel, a dual phase (DP 780) and a TRIP (TRIP 780) from POSCO was studied using a Zwick tensile testing machine. The specimens were prepared according to ASTM: E8 standard along the rolling direction. The stress relaxation test was carried out by interruption at pre-defined engineering strains. Preliminary tests showed that in the low carbon steel, the increase in elongation due to stress relaxation at a strain rate of 10 3 s 1 is negligible, whereas appreciable improvement was noted at strain rates of 10 2 s 1 and above. Henceforth the experiments in the present study were carried out at 10 2 s 1 and 10 1 s 1. The ductility improvement was found to be sensitive to the strain itself. Therefore, experiments were performed at around three different strains in the uniform elongation zone in the corresponding strain rate. At each selected strain location, relaxations were repeated for five times. A constant strain interval of 0.5% was maintained between successive steps. In all the test cases, the relaxation time was fixed to 60 s. Each test was repeated with at least three samples and the average values are reported. 3. Results and discussion Interrupted tests true stress- true strain data representative of the three steels are shown in Fig. 1. The elongation of the specimens subjected to stress relaxation was greater than that in the monotonic tensile tests. A closer examination reveals that the stress–strain curve follows that of the simple tension till relaxation
285
and deviates from the curve after relaxation. Thus the stress relaxation alters the flow stress of the material, in addition to ductility. The hardening mechanism therefore must be considered in order to understand the stress relaxation phenomenon. As a measure of ductility, the uniform elongation is used instead of total elongation, as the latter is known to be affected by the width-thickness aspect ratio of the specimen. For the case of low carbon steel and DP steel with constant phase fractions, the improvement in uniform elongation was marginal at low strains and increased significantly at strain near ultimate tensile strength (UTS) (Fig. 2a and b). At low strains, the beneficial effect of relaxation on elongation is competed by the strain hardening mechanism. Negligible strain hardening occurs after peak load (UTS) and hence the improvement on elongation is appreciable. However, in the case of TRIP steel, the elongation improvement was high at lower strains and tended to saturate at UTS (Fig. 2c) As the material deforms, the temperature increases due to plastic work and phase transformation [27]. The temperature increase is significant at high strains; a temperature rise of around 60 °C at uniform elongation is reported for TRIP 800 when deformed at a strain rate of 10 2 s 1, out of which around 5 °C is attributed to phase transformation [27]. This temperature increase affects the transformation kinetics as the stability of retained austenite (RA) is sensitive to temperature and strain rate[28], for example, it is reported that at 10% strain, the volume fraction decreased from 0.071 to 0.048 (by around 30%) when the testing temperature is reduced from 60 °C to 20 °C [29]. During stress relaxation, both temperature and strain rate decreases and phase transformation occurs at constant strain. How-
Fig. 1. Stress relaxation compared with monotonic tensile curve, (a) low carbon steel (b) DP steel and (c) TRIP Steel [34].
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Fig. 2. Influence of strain rate on the uniform elongation improvement due to stress relaxation, (a) low carbon steel (b) DP steel and (c) TRIP Steel [34].
ever, the transformation is sensitive to the strain at which relaxation experiments are performed. At low strains, the temperature increase due to plastic work and phase transformation is low, but the rate of phase transformation is high, and vice versa at higher strains. It may also be noted from Fig. 1c that the stress relaxation is followed by a distinct rise in stress. A similar stress increment after relaxation at room temperature in stainless steel is attributed to the Snoek type strain aging [30]. In the case of TRIP steel, this can be related to the interaction between martensite islands and dislocations. The exact mechanism is not well understood due to its complexity associated with phase transformation [31]. The transformation to martensite decreases with increase in strain rate in TRIP steel [32]. The stress increment after relaxation for TRIP steels in the present work decreases with increase in strain rate, which indicates that the stress relaxation behavior is influenced by the phase transformation. The transformation kinetics during stress relaxation has not been addressed so far. Experiments correlating the change in volume percentage of martensite during stress relaxation under different strain rate and plastic strain are under progress. The grain structure remains unaltered during stress relaxation [33] indicates that the mechanism is related to microstructural changes within the grains. However, the prior studies do not sufficiently explain the mechanism for increased elongation [34]. It is been verified that the stress relaxation phenomenon in metallic materials is related to reduction of mobile dislocation density [6]. It is necessary to measure the dislocation density prior to and immediately after relaxation to explain the underlying mechanism. Elastic unloading of the specimen can affect the dislocation density distribution due to microplastic deformation. Therefore, in-situ observation of dislocation density during relaxation is important. Diffraction based experiments are generally used for in-situ experiments. However, the rapid stress drop during relaxation in the first few seconds (Fig. 3) poses difficulty for experimental evalua-
tion of microstructural mechanism [35]. It is however possible to present a physically feasible explanation based on the general understanding of deformation behavior. The reduction in mobile dislocation density could be either by immobilization of the dislocation by barriers or by other rearrangement or exhaustion process. The immobilization mechanism will cause increased stress relaxation in materials with more barriers, however stress relaxation is found to decrease in heat treated and hardened alloys [36]. This indicates that the reduction in mobile dislocation density during stress relaxation could not be due to immobilization at barriers. The authors propose the following explanations, represented schematically in Fig. 4a and b. The failure by strain localization occurs when the dislocation density reaches an upper limit in the particular zone within the grain (Fig. 4a). As mentioned, the mobile dis-
Fig. 3. Stress drop with time –typical TRIP 780 steel at 10
2
s
1
.
K. Hariharan et al. / Materials and Design 52 (2013) 284–288
287
density after relaxation is re-distributed to non-critical regions within the grain so that the critical regions are less densely populated when compared to specimen without relaxation. This delays the localization (from B to C in Fig 4) or increase the elongation. The redistribution of dislocations allows further increase in dislocation density in the critical regions, which could be the reason for variation of flow stress or hardening behavior after relaxation.
3.1. Stress drop during relaxation
Fig. 4. Plausible explanation for ductility increase due to relaxation–schematic (a) without relaxation and (b) dislocation density rearrangement during relaxation.
location density decreases during stress relaxation (Al in Fig 4b). Upon reloading, the mobile dislocation density increases again to reach the previous strain hardened state. However the distribution of dislocation density with and without relaxation (A and All in Fig 4) is not same as the deformation path is different. The dislocation
The stress decrease in the specific time interval during the intermittent stops is referred to as ‘stress drop’. The difference between the true stress before and after relaxation is calculated from experimental data. In order to compare the trend of different material, the stress drop is plotted against the strain values normalized with the respective uniform elongation. This ratio of strain at relaxation to uniform elongation is designated as ‘strain ratio’. The strengthening mechanisms by thermomechanical treatment like precipitation hardening resists stress relaxation; the stress drop is lesser in strengthened materials [36]. The stress drop during relaxation is inversely related to rate of change of velocity as the average dislocation velocity reduces rapidly due to the resistance offered by obstacles. In the case of DP steels, the martensite islands resist the dislocation motion. As deformation proceeds, the volume fraction of martensite is unaltered whereas the dislocation density increases. The resistance offered by the martensite to dislocation movement decreases with strain and the velocity change is less rapid than at initial stages of plastic deformation. Therefore the stress drop during stress relaxation increases with strain (Fig. 5b). In the case of TRIP steel, additional resistance is provided by phase transformation. Therefore the increase in stress drop is not as rapid as DP steel (Fig. 5c); it may be noted that the slope of stress drop with strain ratio for TRIP is less than that of DP steel. For materials like low carbon steel with ferritic phase, resistance to dislocation motion is only through strain hardening. With deformation, strain hardening increases and the stress drop during stress relaxation decreases with strain (Fig 5a). The above results differ from the published information on 304 stainless steel, where the stress drop was unaffected by the strain
Fig. 5. Stress drop during relaxation (a) Low carbon (b) DP steel and (c) TRIP steel.
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[14]. It is possible that both aging and strain hardening mechanisms influence the stress relaxation behavior in stainless steel due to its high hardening rate and martensitic transformation.
4. Conclusion The stress relaxation behavior and their effects on the ductility of three steels were evaluated and the following conclusions are arrived at Stress relaxation phenomenon improves the uniform elongation by 0.1–3.5%, (1–15% improvement relatively) in the tested range of plastic strain and strain rate. A possible microstructural mechanism for the observed increase in ductility is discussed. The mechanism is complicated in TRIP steels involving phase transformation, for which further studies are under progress. The stress drop during relaxation is related to the relaxation mechanism of strain aging and strain hardening. The stress drop increases with strain in DP and TRIP steels and decreases with strain for low carbon steel.
Acknowledgements Authors appreciate the supports by Basic Science Research program (Grant #2011-0009801) and by the Ministry of Education, Science and Technology (NRF-2012R1A5A1048294). Authors would like to thank Mr. Seawoong Lee and Mr. Jae-Hyun Choi of GIFT, Postech university for their support during preliminary tests on low carbon steel. References [1] Martin JL, Kruml T. Characterizing thermally activated dislocation mobility. J Alloy Compd 2004;378(1–2):2–12. [2] Gupta I, Li JCM. Stress relaxation, internal stress, and work hardening in some Bcc metals and alloys. Metall Trans 1970;1(8):2323–30. [3] Li JCM. Dislocation dynamics in deformation and recovery. Can J Phys 1967;45(2):493–509. [4] Trojanová Z et al. Internal stress and thermally activated dislocation motion in an AZ63 magnesium alloy. Mater Chem Phys 2011;130(3):1146–50. [5] Li JCM, Chau CC. Internal stresses in plasticity, microplasticity and ductile fracture. Mater Sci Eng A 2006;421(1–2):103–8. [6] Spätig P, Bonneville J, Martin JL. A new method for activation volume measurements: application to Ni3(Al, Hf). Mater Sci Eng A 1993;167(1– 2):73–9. [7] Xiao L, Bai JL. Stress relaxation properties and microscopic deformation structure of H68 and QSn6.5–0.1 copper alloys at 353 K. Mater Sci Eng A 1998;244(2):250–6. [8] Kubát J, Rigdahl M. Activation volumes for flow processes in solids. Mater Sci Eng 1976;24(2):223–32.
[9] Han Kim J, Sang Byun TD, Hoelzer T. Stress relaxation behavior of nanoclusterstrengthened ferritic alloy at high temperatures. J Nucl Mater 2012;425(1– 3):147–55. [10] Lee S, Lee S-J, De Cooman BC. Work hardening behavior of ultrafine-grained Mn transformation-induced plasticity steel. Acta Mater 2011;59(20):7546–53. [11] Diologent F, Goodall R, Mortensen A. Activation volume in microcellular aluminium: Size effects in thermally activated plastic flow. Acta Mater 2011;59(18):6869–79. [12] Couteau O, Kruml T, Martin J-L. About the activation volume for cross-slip in Cu at high stresses. Acta Mater 2011;59:4207–15. [13] Hart EW. Constitutive relations for the Nonelastic deformation of metals. J Eng Mater Technol 1976;98(3):193–202. [14] Krempl E. Relaxation behavior and modeling. Int J Plast 2001;17(10):1419–36. [15] Hart EW. A phenomenological theory for plastic deformation of polycrystalline metals. Acta Metall 1970;18(6):599–610. [16] Lee D, Hart EW. Stress relaxation and mechanical behavior of metals. Metall Trans 1971;2(4):1245–8. [17] Swearengen JC, Rhode RW. Application of mechanical state relations at low and high homologous temperatures. Metall Trans A 1977;8(4):577–82. [18] Wire GL, Ellis FV, Che-Yu L. Work hardening and mechanical equation of state in some metals in monotonic loading. Acta Metall 1976;24(7):677–85. [19] Bocˇek M. Investigation of variables of state for plastic deformation of copper. Mater Sci Eng 1975;17(1):31–40. [20] Tanoue K, Matsuda H. Mechanical equation of state in molybdenum transactions of the Japan institute of metals 1982;23(5):234–42. [21] Tanoue K et al. Mechanical equation of state in metallic single crystals. Scripta Metall 1988;22(3):379–84. [22] Yamada H, Li C-Y. Stress relaxation and mechanical equation of state in b.c.c. metals in monotonic loading. Acta Metall 1974;22(2):249–53. [23] Lerner I, Chiang SW, Kohlstedt DL. Load relaxation studies of four alkali halides. Acta Metall 1979;27(7):1187–96. [24] Gibeling JC, TH A. Observations of plastic strain rate continuity in iron in and near the ‘‘athermal plateau’’. Acta Metall 1984;32(11):2069–76. [25] Krempl E, Khan F. Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers. Int J Plasticity 2003;19(7):1069–95. [26] Yamashita H et al. Technology to enhance deep-drawability by strain dispersion using stress relaxation phenomenon. Honda R&D Tech Rev 2012;24(1):142–8. [27] Rusinek A, Klepaczko JR. Experiments on heat generated during plastic deformation and stored energy for TRIP steels. Mater Des 2009;30(1):35–48. [28] Feng W. Effect of testing temperature on retained austenite stability of cold rolled cmnsi steels treated by quenching and partitioning process. Steel Res Int 2013;84(3):246–52. [29] Feng W. et al. Effect of testing temperature on retained austenite stability of Cold Rolled CMnSi steels treated by quenching and partitioning process. Steel Res Int; 2012: p. n/a–n/a. [30] Hannula SP, Korhonen MA, Li CY. Strain aging and load relaxation behavior of type 316 stainless steel at room temperature. Metall Mater Trans A 1986;17(10):1757–67. [31] Samek L et al. Static strain aging of microstructural constituents in transformation-induced-plasticity steel. Metall Mater Trans A 2008;39(11):2542–54. [32] Polat A. The effects of strain rate and temperature on the deformation behavior of cold-rolled TRIP800 steel. Steel Res Int 2012;83(8):775–82. [33] Rohde RW, Jones WB, Swearengen JC. Deformation modeling of aluminum: stress relaxation, transient behavior, and search for microstructural correlations. Acta Metall 1981;29(1):41–52. [34] Hariharan K et al. Stress relaxation for formability improvement. Key Eng Mater 2013;554–557:145–50. [35] Tomota Y et al. In situ neutron diffraction during tensile deformation of a ferrite-cementite steel. Acta Mater 2003;51(3):805–17. [36] Yong L, Jingchuan Z. Effects of triple heat treatment on stress relaxation resistance of BT20 alloy. Mech Mater 2008;40(10):792–5.
Contents lists available at SciVerse ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Short Communication
Stress relaxation and its effect on tensile deformation of steels K. Hariharan, O. Majidi, C. Kim, M.G. Lee ⇑, F. Barlat Materials Mechanics Laboratory, Graduate Institute of Ferrous Technology, Postech University, San 31 Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, Republic of Korea
a r t i c l e
i n f o
Article history: Received 25 March 2013 Accepted 27 May 2013 Available online 6 June 2013
a b s t r a c t The tensile deformation of metallic materials, when interrupted without unloading, exhibit relaxation of stress. The stress relaxation phenomenon can alter the mechanical behavior of the materials. Stress relaxation phenomenon during tensile test is studied in three steel grades with different microstructures. The influence of stress relaxation on uniform elongation has not been reported before. The uniform elongation varies with strain at which material relaxes and is found to increase upto 3.5%. Contradicting with the published results, the stress drop during stress relaxation varies with strain and the possible reasons are explained. The stress drop during relaxation is governed by strain hardening mechanism in low carbon steel and strain aging mechanism due to martensite in dual phase (DP) and transformation induced plasticity (TRIP) steels. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Stress relaxation tests under tension involve intermittent stopping of the cross-head at a fixed total strain. During relaxation, a portion of stored elastic energy is converted into plastic strain leading to a relaxation of the applied stress with time. The stress relaxation test has been used to characterize understand the deformation related metallurgical parameters such as internal stress and activation volume [1]. Gupta and Li [2,3] proposed a power law function to estimate the internal stress, assuming constant mobile dislocation density during stress relaxation. The internal stress estimated using the relation is validated for several materials [4,5]. The assumption of constant mobile dislocation density during stress relaxation is not valid as it decreases during stress relaxation [6]. The existing equations for determining internal stress can be modified to take the variation of mobile dislocation density into account for better prediction [7]. The activation volume required for thermal activation of plastic deformation at a particular temperature is related to effective stress [8]. Estimation of activation volume using stress relaxation tests accounting the variation of mobile dislocation density has been described in [1,6]. In the recent years, activation volume measurement using stress relaxation has been used to determine the deformation mechanism of nano-crystalline materials [9–12]. The stress versus strain rate data obtained during stress relaxation have also been utilized to develop phenomenological models for mechanical equation of state [13] and viscoplasticity [14]. Hart [15] proposed a phenomenological constitutive model using stress, plastic strain rate and an evolutionary state variable called hard⇑ Corresponding author. Tel.: +82 54 279 9034; fax: +82 54 279 9229. E-mail address: [email protected] (M.G. Lee). 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.05.088
ness, independent of prior deformation path. The locus of all possible combinations of stress and strain rate state at a constant plastic strain gives a constant hardness curve. Lee and Hart [16] demonstrated that the stress relaxation test with a negligible change in plastic strain is the most suitable to generate the constant hardness curves. Similar phenomenological models using stress relaxation data are proposed by others [17]. Among the proposed models, Hart’s model is generally found to be acceptable for a wide range of materials and conditions [18–23]. During stress relaxation, the plastic strain rate decreases continuously [24], which is characteristic to viscoplastic materials. Krempl and coworkers [14,25] have extensively studied stress relaxation phenomenon using viscoplastic models on overstress. Accordingly, the flow stress consists of two components namely, equilibrium flow stress and overstress. The overstress is dependent on strain rate, similar to the effective stress discussed above. The stress relaxation phenomenon also alters the mechanical behavior of the materials. In spite of advances in stress relaxation testing, efforts in understanding its influence in mechanical behavior especially flow stress and elongation, remains insufficient. In a recent report [26], better formability of a deep drawn component with intermediate stops is attributed to the stress relaxation phenomenon. However, detailed analysis on the mechanism of ductility enhancement through structured experiments has not yet been reported. In the present work, stress relaxation phenomenon is studied experimentally in three alloys, a low carbon steel, a dual phase (DP) steel and a transformation induced plasticity (TRIP) steel, with specific focus on the ductility. The work involves three different microstructures, i.e fully ferritic, ferrite + martensite and ferrite + austenite. In the latter case, the volume fraction of austenite changes with strain, over a wide range of strain rates.
K. Hariharan et al. / Materials and Design 52 (2013) 284–288
2. Experiments Stress relaxation under monotonic tension in the three commercially available steels, a low carbon steel, a dual phase (DP 780) and a TRIP (TRIP 780) from POSCO was studied using a Zwick tensile testing machine. The specimens were prepared according to ASTM: E8 standard along the rolling direction. The stress relaxation test was carried out by interruption at pre-defined engineering strains. Preliminary tests showed that in the low carbon steel, the increase in elongation due to stress relaxation at a strain rate of 10 3 s 1 is negligible, whereas appreciable improvement was noted at strain rates of 10 2 s 1 and above. Henceforth the experiments in the present study were carried out at 10 2 s 1 and 10 1 s 1. The ductility improvement was found to be sensitive to the strain itself. Therefore, experiments were performed at around three different strains in the uniform elongation zone in the corresponding strain rate. At each selected strain location, relaxations were repeated for five times. A constant strain interval of 0.5% was maintained between successive steps. In all the test cases, the relaxation time was fixed to 60 s. Each test was repeated with at least three samples and the average values are reported. 3. Results and discussion Interrupted tests true stress- true strain data representative of the three steels are shown in Fig. 1. The elongation of the specimens subjected to stress relaxation was greater than that in the monotonic tensile tests. A closer examination reveals that the stress–strain curve follows that of the simple tension till relaxation
285
and deviates from the curve after relaxation. Thus the stress relaxation alters the flow stress of the material, in addition to ductility. The hardening mechanism therefore must be considered in order to understand the stress relaxation phenomenon. As a measure of ductility, the uniform elongation is used instead of total elongation, as the latter is known to be affected by the width-thickness aspect ratio of the specimen. For the case of low carbon steel and DP steel with constant phase fractions, the improvement in uniform elongation was marginal at low strains and increased significantly at strain near ultimate tensile strength (UTS) (Fig. 2a and b). At low strains, the beneficial effect of relaxation on elongation is competed by the strain hardening mechanism. Negligible strain hardening occurs after peak load (UTS) and hence the improvement on elongation is appreciable. However, in the case of TRIP steel, the elongation improvement was high at lower strains and tended to saturate at UTS (Fig. 2c) As the material deforms, the temperature increases due to plastic work and phase transformation [27]. The temperature increase is significant at high strains; a temperature rise of around 60 °C at uniform elongation is reported for TRIP 800 when deformed at a strain rate of 10 2 s 1, out of which around 5 °C is attributed to phase transformation [27]. This temperature increase affects the transformation kinetics as the stability of retained austenite (RA) is sensitive to temperature and strain rate[28], for example, it is reported that at 10% strain, the volume fraction decreased from 0.071 to 0.048 (by around 30%) when the testing temperature is reduced from 60 °C to 20 °C [29]. During stress relaxation, both temperature and strain rate decreases and phase transformation occurs at constant strain. How-
Fig. 1. Stress relaxation compared with monotonic tensile curve, (a) low carbon steel (b) DP steel and (c) TRIP Steel [34].
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Fig. 2. Influence of strain rate on the uniform elongation improvement due to stress relaxation, (a) low carbon steel (b) DP steel and (c) TRIP Steel [34].
ever, the transformation is sensitive to the strain at which relaxation experiments are performed. At low strains, the temperature increase due to plastic work and phase transformation is low, but the rate of phase transformation is high, and vice versa at higher strains. It may also be noted from Fig. 1c that the stress relaxation is followed by a distinct rise in stress. A similar stress increment after relaxation at room temperature in stainless steel is attributed to the Snoek type strain aging [30]. In the case of TRIP steel, this can be related to the interaction between martensite islands and dislocations. The exact mechanism is not well understood due to its complexity associated with phase transformation [31]. The transformation to martensite decreases with increase in strain rate in TRIP steel [32]. The stress increment after relaxation for TRIP steels in the present work decreases with increase in strain rate, which indicates that the stress relaxation behavior is influenced by the phase transformation. The transformation kinetics during stress relaxation has not been addressed so far. Experiments correlating the change in volume percentage of martensite during stress relaxation under different strain rate and plastic strain are under progress. The grain structure remains unaltered during stress relaxation [33] indicates that the mechanism is related to microstructural changes within the grains. However, the prior studies do not sufficiently explain the mechanism for increased elongation [34]. It is been verified that the stress relaxation phenomenon in metallic materials is related to reduction of mobile dislocation density [6]. It is necessary to measure the dislocation density prior to and immediately after relaxation to explain the underlying mechanism. Elastic unloading of the specimen can affect the dislocation density distribution due to microplastic deformation. Therefore, in-situ observation of dislocation density during relaxation is important. Diffraction based experiments are generally used for in-situ experiments. However, the rapid stress drop during relaxation in the first few seconds (Fig. 3) poses difficulty for experimental evalua-
tion of microstructural mechanism [35]. It is however possible to present a physically feasible explanation based on the general understanding of deformation behavior. The reduction in mobile dislocation density could be either by immobilization of the dislocation by barriers or by other rearrangement or exhaustion process. The immobilization mechanism will cause increased stress relaxation in materials with more barriers, however stress relaxation is found to decrease in heat treated and hardened alloys [36]. This indicates that the reduction in mobile dislocation density during stress relaxation could not be due to immobilization at barriers. The authors propose the following explanations, represented schematically in Fig. 4a and b. The failure by strain localization occurs when the dislocation density reaches an upper limit in the particular zone within the grain (Fig. 4a). As mentioned, the mobile dis-
Fig. 3. Stress drop with time –typical TRIP 780 steel at 10
2
s
1
.
K. Hariharan et al. / Materials and Design 52 (2013) 284–288
287
density after relaxation is re-distributed to non-critical regions within the grain so that the critical regions are less densely populated when compared to specimen without relaxation. This delays the localization (from B to C in Fig 4) or increase the elongation. The redistribution of dislocations allows further increase in dislocation density in the critical regions, which could be the reason for variation of flow stress or hardening behavior after relaxation.
3.1. Stress drop during relaxation
Fig. 4. Plausible explanation for ductility increase due to relaxation–schematic (a) without relaxation and (b) dislocation density rearrangement during relaxation.
location density decreases during stress relaxation (Al in Fig 4b). Upon reloading, the mobile dislocation density increases again to reach the previous strain hardened state. However the distribution of dislocation density with and without relaxation (A and All in Fig 4) is not same as the deformation path is different. The dislocation
The stress decrease in the specific time interval during the intermittent stops is referred to as ‘stress drop’. The difference between the true stress before and after relaxation is calculated from experimental data. In order to compare the trend of different material, the stress drop is plotted against the strain values normalized with the respective uniform elongation. This ratio of strain at relaxation to uniform elongation is designated as ‘strain ratio’. The strengthening mechanisms by thermomechanical treatment like precipitation hardening resists stress relaxation; the stress drop is lesser in strengthened materials [36]. The stress drop during relaxation is inversely related to rate of change of velocity as the average dislocation velocity reduces rapidly due to the resistance offered by obstacles. In the case of DP steels, the martensite islands resist the dislocation motion. As deformation proceeds, the volume fraction of martensite is unaltered whereas the dislocation density increases. The resistance offered by the martensite to dislocation movement decreases with strain and the velocity change is less rapid than at initial stages of plastic deformation. Therefore the stress drop during stress relaxation increases with strain (Fig. 5b). In the case of TRIP steel, additional resistance is provided by phase transformation. Therefore the increase in stress drop is not as rapid as DP steel (Fig. 5c); it may be noted that the slope of stress drop with strain ratio for TRIP is less than that of DP steel. For materials like low carbon steel with ferritic phase, resistance to dislocation motion is only through strain hardening. With deformation, strain hardening increases and the stress drop during stress relaxation decreases with strain (Fig 5a). The above results differ from the published information on 304 stainless steel, where the stress drop was unaffected by the strain
Fig. 5. Stress drop during relaxation (a) Low carbon (b) DP steel and (c) TRIP steel.
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[14]. It is possible that both aging and strain hardening mechanisms influence the stress relaxation behavior in stainless steel due to its high hardening rate and martensitic transformation.
4. Conclusion The stress relaxation behavior and their effects on the ductility of three steels were evaluated and the following conclusions are arrived at Stress relaxation phenomenon improves the uniform elongation by 0.1–3.5%, (1–15% improvement relatively) in the tested range of plastic strain and strain rate. A possible microstructural mechanism for the observed increase in ductility is discussed. The mechanism is complicated in TRIP steels involving phase transformation, for which further studies are under progress. The stress drop during relaxation is related to the relaxation mechanism of strain aging and strain hardening. The stress drop increases with strain in DP and TRIP steels and decreases with strain for low carbon steel.
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