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Effect of Prestrain and Stress Rate on Bauschinger Effect of Monotonically and Cyclically Deformed OFHC Copper
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 74 (2014) 368 – 375
XVII International Colloquium on Mechanical Fatigue of Metals (ICMFM17)
Effect of prestrain and stress rate on Bauschinger effect of monotonically and cyclically deformed OFHC copper Jayanta Kumar Mahatoa, Partha Sarathi Dea, Abhijnan Sarkara, Amrita Kundua,b Pravash Chandra Chakrabortia,b * b
a Centre of Exceelence on Phase Transformation and Product Characterisation Metallurgical and Material Engineering Department, Jadavpur University, Kolkata – 700032, West Bengal, India
Abstract The effect of monotonic and cyclic deformation on the evolution of back stress vis-à-vis Bauschinger effect due to different amounts of unidirectional plastic deformation in annealed OFHC copper has been investigated. It is observed that for the same amount of prestrain the back stress evolution and the corresponding Bauschinger phenomenon depend upon the mode of deformation. It is found that higher back stress develops in case of monotonic deformation as compared to ratcheting deformation for same amount of unidirectional prestrain. It is also found that the effect of stress rate on the change of Bauschinger parameters is comparatively less than the effect of increasing prestrain in both types of deformation.
© 2014 The Elsevier Ltd.Published Open access under CC BY-NC-ND license. © 2014 Authors. by Elsevier Ltd. Selection and peer-review underresponsibility responsibility Politecnico di Milano, Dipartimento di Meccanica Selection and peer-review under ofof thethe Politecnico di Milano, Dipartimento di Meccanica. Keywords: Bauschinger effect; back stress; tensile; ratcheting; stress rate.
1.
Introduction
During monotonic or cyclic plastic deformation dislocations are piled up against different kinds of barriers. As a result, back stress is generated, which reduces the yield stress of a material when the direction of deformation is reversed. Such reduction of yield stress in the reverse loading direction due to prior forward loading in the plastic regime is known as Bauschinger effect. There are two kinds of mechanisms behind the Bauschinger effect. In one
* Corresponding author. Tel.: +913324146940; fax: +913324137121. E-mail address: [email protected]
1877-7058 © 2014 Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the Politecnico di Milano, Dipartimento di Meccanica doi:10.1016/j.proeng.2014.06.281
Jayanta Kumar Mahato et al. / Procedia Engineering 74 (2014) 368 – 375
mechanism, during plastic deformation dislocations accumulate at barriers and produce both long range and short range interactions and pileups. As a result back stress is developed in the material, which assists the movement of dislocation in the reverse loading direction. In the second mechanism, when the loading direction is reversed, dislocations of opposite sign are produced from the same source, attract each other and annihilation of dislocations occur. Since strain hardening is related to dislocation density, reducing the number of dislocations reduces the strength. The net result is that the yield strength in reverse loading direction becomes lower than what is observed in case of forward loading direction. According to the back stress theory of Bauschinger effect the increase of dislocation density with increases in amount of prestrain results in more and more dislocation pile-ups which develop more back stress and consequently the Bauschinger parameters are influenced [1-5]. But once a dislocation becomes immobile by interaction, it does no longer contribute to back stress in a dislocation pileup. With increase in prestrain the number of mobile dislocation may be decreased due to more and more dislocation interaction and possible formation of more stable dislocation structure. Therefore increasing the amount of prestrain the back stress increases upto a certain level of prestrain and then decreases or saturates depending upon the number of mobile dislocation present in the material [2, 3, 6]. Several investigators reported that mobile dislocation density and dislocation velocity are proportionally related to the strain rate or stress rate of deformation. With increase of the stress rate/strain rate yield strength and flow stress of the material increase due to higher mobile dislocation density and dislocation velocity [7-12] and thus resulting in more dislocation pile-ups. In this context it would be expected that increasing the stress rate of deformation higher back stress will be developed and consequently the Bauschinger parameters of the material is influenced when the change in stress rate is sufficient to significantly alter the work hardening behavior of that material [1, 13-18]. The Bauschinger behaviour of a material is commonly studied by tension loading to certain percentage of unidirectional strain, followed by reversal of loading direction and comparing the flow behaviour of the material in the reversed loading direction with that of forward loading direction. But, the effect of asymmetric cyclic plastic deformation (ratcheting), which also produces unidirectional permanent strain, on the Bauschinger behaviour has not been received any attention. The objective of the present investigation is to make a comparative study of the effect deformation mode, monotonic and cyclic, and the rate of deformation on the Bauschinger behaviour of annealed OFHC copper. Specifically, the effect of different amounts of unidirectional prestrain under monotonic and ratcheting deformation and stress rate on Bauschinger behaviour have been investigated. Nomenclature EV Eh EH E( VP Vy1 Vy2 HP Hr EP Es Vb Vef V* VP
Bauschinger stress parameter Bauschinger hardening parameter Bauschinger strain parameter Bauschinger energy parameter Maximum pre stress 0.2% offset yield stress Yield stress in the direction of reverse strain (0.05% strain) Pre-strain Bauschinger strain, the strain in the reverse direction corresponding to the point of reverse stress equal to the maximum pre stress (VP) Energy spent during pre-strain Energy saved during reverse straining due to the Bauschinger effect Back stress Effective stress Thermal part of effective stress Athermal part of effective stress
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Jayanta Kumar Mahato et al. / Procedia Engineering 74 (2014) 368 – 375
2.
Experimental Procedure
The material used in the present investigation was commercially pure (99.97%) polycrystalline OFHC copper received in the form of 12 mm diameter rod. Cylindrical specimen blanks of 12 mm diameter and 120 mm length were annealed at 520 0C for one hour and then quenched in water. One of the annealed specimens was used to observe the microstructure following usual metallographic polishing and etching with ferric chloride solution. Microstructure was observed under in an inverted optical microscope. Linear intercept method was used to measure the two-dimensional average grain using an automatic image analyser. Specimens of cylindrical geometry for tension test, and to investigate the Bauschinger behaviour, both under prior monotonic and cyclic (ratcheting) deformation, were fabricated from the annealed specimen blanks. Before the tests all the specimens were polished with fine emery paper for better surface finish. Tension test was done under strain-control mode at a strain rate of 10-3 per sec at room temperature (~ 27oC) in a servohydraulic universal testing machine, Instron 8501 of +/- 100 KN load capacity. Buaschinger phenomenon has been studied both after monotonic cyclic (ratcheting) deformation to five different prefixed amounts of forward strain (+ 7, 10, 12, 15 and 18 %) at a stress rate of 200 MPa/s. In case of cyclic deformation the specimens were subjected to asymmetric cyclic plastic deformation within 100 and 150 MPa stress limits (mean stress = 25 MPa) for accumulation of the above prefixed amount of positive strains. In all cases after uniaxial deformation (+ve) the loading direction was reversed and deformation was continued to 2.5 pct in the compressive direction. In a separate set of experiments stress rate was varied from 50 to 500 MPa/s both for monotonic and ratcheting deformation to 15-pct strain and then loading direction was reversed and deformation was continued again to 2.5 pct. The maximum stress and accumulated strain in every cycle were considered for plotting true stress-strain curves to find out the Bauschinger parameters in case of prior uniaxial ratcheting deformation. 3.
Evolution of magnitude of Bauschinger effect parameters
There are mainly four types established parameters, which are used to quantify the Bauschinger phenomenon: the stress, hardness, strain and energy parameter. The Bauschinger parameters are calculated from the following expressions
i. Bauschinger stress parameter (EV This describes the relative decrease in yield stress from forward to reverse deformation. EV VPVy2)/VP
(1)
ii. Bauschinger hardening parameter (Eh This parameter describes the relative decrease in yield stress due to the back stress effect. Eh Vy1Vy2)/(VPVy2)
(2)
iii. Bauschinger strain parameter (EH This parameter describes the amount of deformation in the reverse direction needed to reach the prestress level of stress. EH Hr/HP
(3)
iv. Bauschinger energy parameter E( This parameter describes the amount of energy needed during the reverse deformation to reach the pre stress level of stress. EE Es/EP
4.
(4)
Back stress development during monotonic and cyclic deformation
During monotonic deformation of single-phase polycrystalline materials into plastic regime, dislocations interact and piled up at grain boundaries preventing their further propagation. As a result back stress develops around the contact point resisting further progress of similarly signed dislocations. When the direction of deformations is
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reversed the back stress acts to assist the movement of dislocation from grain boundaries. As a result the reverse yielding occurs at a low stress. According to back stress theory dislocation interactions and pilling up increases with increase of dislocation density. This leads to the development of more back stress and consequently influences the Bauschinger behaviour. But during cyclic deformation, two dislocations of opposite sign encounter with each other on slip plane. This causes annihilation of dislocations and thereby influences the development of the back stress in every cycle [6, 19-20]. Due to dislocation annihilation during cyclic deformation the collinear dislocation density should greater for monotonic deformation as compared to cyclic deformation resulting in different back stress development for a given plastic strain. The back stress is associated with long-range interaction of mobile dislocations and effective stress is associated with short-range interaction of mobile dislocations were previously discussed [21-25]. The back stress can be calculated from the following equations. Back stress (Vb VPVef)
(5)
Where, Vef = ((VPVy2)/2) + (V*/2) 5. Results and discussion 5.1 Microstrcture and tensile properties Figure 1(a) shows the optical micrograph of the solution annealed OFHC copper. It is found that the microstructure consists of polyhedral grains with annealing twins interspersed in some grains. The two-dimensional average grain size measured using linear intercept method is 36 microns.
Fig. 1. Figure showing (a) optical micrograph and (b) engineering stress-strain curve of OFHC copper annealed at 5200 C
5.2 Bauschinger test To evaluate the Bauschinger parameters deformed under monotonic deformation, all the engineering stressstrain curves were converted to true stress-strain curves. During cyclic deformation, maximum stress and accumulated strain in every cycle were considered for plotting true stress-strain curves. After reaching a certain amount of accumulated strain, the direction of deformation was immediately reversed and continued to 2.5 pct reversed strain. Figure 2(a) shows the effect of accumulated prestrain on the flow behaviour for a constant deformation rate of 200MPa/s for both monotonically and cyclically deformed specimens. Figure 2(b) shows the effect of stress rate on the flow behaviour for both 15 pct monotonically and cyclically deformed specimens.
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Fig. 2. (a) True stress-strain curves showing (a) forward prestrain effect at constant stress rate 200 MPa sec-1 and (b) stress rate effect for 15 pct monotonically and cyclically deformed specimens.
5.3 Bauschinger parameters When comparing and discussing the Bauschinger effect behavior, it is often useful to have some method of quantifying the response using a scalar measurement. The purpose of these values is to highlight the Bauschinger features for both monotonically and cyclically deformed OFHC copper. Before quantifying the Bauschinger effect parameters it is more important to evaluate the back stress in each case. The back stress is developed due to dislocation interaction and pilling up of dislocations at grain boundaries in single-phase polycrystalline materials. According to back stress theory of Bauschinger phenomenon dislocation interactions and pilling up increases with increase of dislocation density; this leads to the development of more back stress and consequently influences the Bauschinger behaviour. Figure 3 shows that increasing the amount of forward prestrain (at constant stress rate 200MPa/s) back stress increases [1-5]. But the developed back stress is different for monotonic and cyclic deformation due to dislocations interaction/pilling up and annihilation is different during monotonic and cyclic deformation. Result shows that the back stress developed during monotonic deformation is higher compared to the cyclic deformation for certain level of prestrain. Development of lower back stress for cyclic deformation can be related with the dislocation annihilation reaction in case of cyclic deformation [6, 19-20]. As a result collinear dislocation density is higher for monotonic deformation compared to cyclic deformation. Thus higher back stress is developed in case of monotonic deformation for a certain level of prestrain (constant stress rate) as well as at certain stress rate (for constant pre strain), Figure 3. Higher Bauschinger effect means lower yield strength during a reverse loading.
Fig. 3. Prestrain and stress rate effect on back stress developed during monotonic and cyclic (ratcheting) deformation.
Jayanta Kumar Mahato et al. / Procedia Engineering 74 (2014) 368 – 375
The Bauschinger stress parameter describes the relative decrease in yield stress from forward to reverse direction. It is highly associated with the dislocation pilling ups and annihilation process, which influence the development of back stress. As back stress increases, the reverse yield strength decreases and consequently the Bauschinger stress parameter is increased (Equation 1). From the back stress variation shown in Figure 3 it is observed that for a given forward prestrain levels, the back stress developed is higher for monotonic deformation compared to cyclic deformation. Hence higher Bauschinger stress parameter is obtained in case when deformation in forward direction is carried out monotonically as compared to the cyclically deformed condition, Figure 4(a).
Fig. 4. Variation of Bauschinger stress and hardening parameter with (a) prestrain at constant stress rate (200MPa sec1) and (b) stress rate at constant prestrain (15pct) of both modes of deformation (monotonic and cyclic).
The Bauschinger hardening parameter describes the relative decrease in yield stress due to back stress effect. As discussed above, increasing the amount of prestrain, dislocation pilling up increases upto a certain level of prestrain resulting in an increase of back stress. When the direction of deformation is reversed, the back stress assists the movement of dislocations in the reverse direction resulting in the drop of yield stress drop which gradually decreases with increasing the prestrain. This type of reverse yielding asymmetry is common in most classes of materials. As a result Bauschinger hardening parameter decreases with increasing the prestrain as shown in Figure 4(a). Figure 4(a) also shows that Bauschinger hardening parameter is higher for monotonic deformation compared to cyclic deformation for a certain amount of prestrain, whereas the effect of prestrain on Bauschinger hardening parameter is much higher in case of prior monotonic deformation in the forward direction due to more and more dislocation pilling up and lower rate of dislocation annihilation compared to cyclically deformed conditions. It has been studied by several investigators that increasing the stress rate the flow stress of the material increases by increasing mobile dislocation density and velocity [8-12] and hence resulting in more dislocation pile ups. This type of relationship is dependent on stress rate sensitivity of the materials. Our result shows that in the present annealed OFHC copper the stress rate has no significant effect in Bauschinger stress and hardening parameters, (Figure 4(b)). The very low effect of stress rate is believed to be related with the stacking fault energy of copper. Since the back stress developed in the material causes the difference in the reverse yield stress it is also important to quantify the transient period observed after the load reversal. The Bauschinger strain parameter describes the amount of deformation in the reverse direction needed to reach the unloading stress during forward deformation. This parameter also highly associated with the dislocation pilling up and annihilation processes. With increase of accumulated prestrain more and more dislocations are piled up against different barriers with development of back stress assisting the reverse flow behaviour in the opposite loading direction. Therefore increasing the prestrain Bauschinger strain parameter decreases for both monotonically and cyclically deformed materials following power relationship (Figure 5). Bauschinger strain parameters for cyclically deformed materials decreases more as compared to monotonic deformation due to dislocation annihilation in every cycle. This parameter is also highly related to the back stress development for a certain amount of prestrain. Due to higher back stress effect during monotonic deformation, higher EHparameter is observed for fixed prestrain as compared to cyclic deformation.
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Fig. 5. Variation of Bauschinger strain and energy parameter with prestrain of both modes of deformed (monotonic and cyclic) materials.
The Bauschinger energy parameter describes the energy needed during the reverse deformation to reach the stress level for forward loading direction. It is found that with increase of prestrain the Bauschinger energy parameter continuously decreases (Figure 5). This type of phenomenon occurs due to the more and more dislocation pilling up at higher level of prestrain which aids the dislocation motion during reverse loading. Due to enhancement of dislocation motion in the reverse loading direction because of the development of back stress the relative energy required to reach the unloading stress in the reverse loading direction is lower when the amount of prestrain is higher. Figure 5 also indicates that Bauschinger energy parameter is higher for monotonic deformation compared to cyclic deformation at a certain prestrain level. This occurs due to higher back stress developed in case of monotonic deformation compare to cyclic deformation at a certain prestrain level. Conclusions The effect of forward strain and stress rate on Bauschinger effect parameters by monotonically and cyclically deformed OFHC copper has been studied at room temperature. The evolution of Bauschinger stress, hardening, strain and energy parameters assess that how long lasting the Bauschinger effect is and thus support the long range work hardening/softening approach. The conclusions are as follows
x
x
x
The Bauschinger parameters are highly related to the prestrain of deformation. Bauschinger stress parameter is in increasing nature with pre strain for both mode of deformation i.e. monotonic and cyclic. Where as Bauschinger hardening parameter is in decreasing nature with pre strain for both mode of deformation. Similarly the Bauschinger strain and energy parameters are in decreasing nature with pre strain for both mode of deformation. In comparison to monotonically and cyclically (ratcheting) deformation upto a certain value of forward prestrain, the Bauschinger parameters are more higher for monotonic deformation compare to cyclic deformation. This type of behavior observed due to more back stress development during monotonic deformation compare to cyclic deformation for same amount of pre strain. The stress rate change shows that no significant change in Bauschinger parameters are observed for both mode of deformation. This may be due to that the limited change in stress rate for both mode of deformation are not sufficient to significantly alter the work hardening behavior of the material if the stress rate sensitivity of the material is significant.
Acknowledgements The authors would like to thank Council of Scientific and Industrial Research (New Delhi) and Jadavpur University for providing funding and facilities respectively for carrying out the research work.
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References [1] K. Han, C. J. Vantyne, B.S. Levy, Effect of strain and strain rate on Bauschinger effect response of three different steels, Met. Mat. Trans. A, 36A (2005) 2379-2384. [2] S.S. Sohn, S.Y. Han, S.Y. Shin, J.H. Bae, S. Lee, Effect of microstructure and pre-strain on Bauschinger effect in API X70 and X80 line pipe steel, Met. Mater. Int. 19 (2013) 423-431. [3] S.Y. Han, S.S. Sohn, S.Y. Shin, J.H. Bae, H. S.Kim, S. Lee, Effect of microstructure and yield ratio on strain hardening and Bauschinger effect in two API X80 linepipe steels, Mat. Sci. Engg. A 551 (2012) 192-199. [4] M. G. Stout, A. D. Rollett, Large-strain effect in FCC metals and alloy, Mat. Trans. A. 21A (1990) 3201. [5] E. Hemmerich, B. Rolfe, P. D. Hodgson, M. Weiss, The effect of pre-strain on the material behaviour and the Bauschinger effect in the bending of hot rolled aged steel, Mat. Sci Engg A 528 (2011) 3302-3309. [6] P. S. De, A. Kundu, P. C. Chakraborti, Effect of prestrain on tensile properties and ratcheting behavior of Ti-stabilised interstitial free steel, Mat. Design (2013) 87-97. [7] A. Kundu, P. C. Chakraborti, Effect of strain rate on quasistatic tensile flow behavior of solution annealed 304 austenitic stainless steel at room temperature, J. Mat. Sci. 45 (2010) 5482-5489. [8] G. Filacchioni, E. Casagrande, U. De Angelis, G. D. Santis, D. Ferrara, Effect of strain rate on tensile properties of TZM and Mo-5% Re, J. Nuclear Mat., 307-311 (2002) 705-709. [9] G. T. Gray II, T.C. Lowe, C. M. Cady, R. Z. Valiev, I. V. Aleksandrov, Influence of strain rate and temperature on the mechanical response of ultra-fined grained Cu, Ni, ans Al-4Cu-0.5Zr, Nano Str. Mat., 9 (1997) 477-780. [10] D. H. Sastry, Y. V. R. K. Prasad, S. C. Devi, Influence of temperature and strain rate on the flow stress of an FeAl alloy, Mat. Sci. Engg. A 299 (2001) 157-163. [11] B. Zhang, V. P. W. Shim, Effect of strain rate on microstructure of polycrystalline oxygen free high conductivity copper severely deformed at liquid nitrogen temperature, Acta Materialia, 58 (2010) 6810-6827. [12] J. L. Jordon, C. R. Sivious, Strain rate dependent mechanical properties of OFHC copper, J. Mat. Sci. 48 (2013) 7134-7141. [13] A. Thakur, K. S. Vecchio, S. Nemat-Nasser, Bauschinger effect in hhynes 230 alloy, Met. Mat. Trans. A 27A (1996) 1739. [14] G. T Gray III, W. R. Bhimenthal, C. P. Trujilo, R. W. Carpenter II, Influence of temperature and strain rate on the mechanical behavior of Adiprene L-100, J. Phys. IV (France) Colloq. C-3 (1997) 523-528. [15] D. J. A. Senden, J. A. W. Van Dom Molen, L.E., Gorvert, Strain hardening and its relation to Bauschinger effect in oriented polymers, J. Poly. Sci., Part B, 48 (2010) 1483-1494. [16] J. Peirs, P. Verleysen, K. Verbeken, F. Coghe, J. Degrieek, High strain rate torsion and Bauschinger tests on Ti6Al4V, Mat. Sci. Forum, 706709 (2012) 774-779. [17] K. Watanabe, K. Natori, T. Tanaka, Y. Imaida, Study on the Bauschinger effect with increasing of tensile strength in dual phase steel sheets, High Per. Str. Mat. V (2010) 120-131. [18] M. S. Pham, S. R. Holdsworth, Evolution of dislocation microstructures and internal stresses of AISI 316L during cyclicloading at 293 and 573K, Met. Mat. Trans. A 45 (2014) 738-751. [19] H. Mughrabi, Dislocation clustering and long-range internal stresses in monotonically and cyclically deformed metal crystals, Revue. Phys. Appl. 23 (1988) 367-379. [20] A. M. Eleiche, J. D. Campbell, Strain-rate effect during reverse torsional shear, Exp. Mech. (1976) 281-290. [21] X. Feaugas, H. Haddou, Grain-size effects on tensile behavior of Nickel and AISI 316L Stainless Steel, Met. Mat. Trans. A 34A (2003) 2329-2340. [22] C. Gaudin, C. Guillemer, X. Feaugas, Stacking fault energy (s.t.e.) and grain size effects (d) on the tensile bahaviour of F.C.C. polycrystalline alloys at 300 K: back stress and effective stress evolutions, J. Phys. IV France, 11 (2001) Pr4 283-291. [23] H. Haddoua, M. Risbet, G. Marichal, X. Feaugas, The effect of grain size on cyclic deformation behavior of polycrystalline nickel, Mat. Sci. Engg. A 379 (2004) 102-111. [24] C. Gaudin, X. Feaugas, Cyclic creep process in AISI 316L stainless steel in terms of dislocation patterns and internal stresses, Acta Materialia, 52 (2004) 3097-3110. [25] X. Feaugas, C. Gaudin, Ratcheting process in the stainless steel AISI 316L at 300K: an experimental investigation, Int. J. Plasticity 20 (2004) 643–662.
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ScienceDirect Procedia Engineering 74 (2014) 368 – 375
XVII International Colloquium on Mechanical Fatigue of Metals (ICMFM17)
Effect of prestrain and stress rate on Bauschinger effect of monotonically and cyclically deformed OFHC copper Jayanta Kumar Mahatoa, Partha Sarathi Dea, Abhijnan Sarkara, Amrita Kundua,b Pravash Chandra Chakrabortia,b * b
a Centre of Exceelence on Phase Transformation and Product Characterisation Metallurgical and Material Engineering Department, Jadavpur University, Kolkata – 700032, West Bengal, India
Abstract The effect of monotonic and cyclic deformation on the evolution of back stress vis-à-vis Bauschinger effect due to different amounts of unidirectional plastic deformation in annealed OFHC copper has been investigated. It is observed that for the same amount of prestrain the back stress evolution and the corresponding Bauschinger phenomenon depend upon the mode of deformation. It is found that higher back stress develops in case of monotonic deformation as compared to ratcheting deformation for same amount of unidirectional prestrain. It is also found that the effect of stress rate on the change of Bauschinger parameters is comparatively less than the effect of increasing prestrain in both types of deformation.
© 2014 The Elsevier Ltd.Published Open access under CC BY-NC-ND license. © 2014 Authors. by Elsevier Ltd. Selection and peer-review underresponsibility responsibility Politecnico di Milano, Dipartimento di Meccanica Selection and peer-review under ofof thethe Politecnico di Milano, Dipartimento di Meccanica. Keywords: Bauschinger effect; back stress; tensile; ratcheting; stress rate.
1.
Introduction
During monotonic or cyclic plastic deformation dislocations are piled up against different kinds of barriers. As a result, back stress is generated, which reduces the yield stress of a material when the direction of deformation is reversed. Such reduction of yield stress in the reverse loading direction due to prior forward loading in the plastic regime is known as Bauschinger effect. There are two kinds of mechanisms behind the Bauschinger effect. In one
* Corresponding author. Tel.: +913324146940; fax: +913324137121. E-mail address: [email protected]
1877-7058 © 2014 Elsevier Ltd. Open access under CC BY-NC-ND license. Selection and peer-review under responsibility of the Politecnico di Milano, Dipartimento di Meccanica doi:10.1016/j.proeng.2014.06.281
Jayanta Kumar Mahato et al. / Procedia Engineering 74 (2014) 368 – 375
mechanism, during plastic deformation dislocations accumulate at barriers and produce both long range and short range interactions and pileups. As a result back stress is developed in the material, which assists the movement of dislocation in the reverse loading direction. In the second mechanism, when the loading direction is reversed, dislocations of opposite sign are produced from the same source, attract each other and annihilation of dislocations occur. Since strain hardening is related to dislocation density, reducing the number of dislocations reduces the strength. The net result is that the yield strength in reverse loading direction becomes lower than what is observed in case of forward loading direction. According to the back stress theory of Bauschinger effect the increase of dislocation density with increases in amount of prestrain results in more and more dislocation pile-ups which develop more back stress and consequently the Bauschinger parameters are influenced [1-5]. But once a dislocation becomes immobile by interaction, it does no longer contribute to back stress in a dislocation pileup. With increase in prestrain the number of mobile dislocation may be decreased due to more and more dislocation interaction and possible formation of more stable dislocation structure. Therefore increasing the amount of prestrain the back stress increases upto a certain level of prestrain and then decreases or saturates depending upon the number of mobile dislocation present in the material [2, 3, 6]. Several investigators reported that mobile dislocation density and dislocation velocity are proportionally related to the strain rate or stress rate of deformation. With increase of the stress rate/strain rate yield strength and flow stress of the material increase due to higher mobile dislocation density and dislocation velocity [7-12] and thus resulting in more dislocation pile-ups. In this context it would be expected that increasing the stress rate of deformation higher back stress will be developed and consequently the Bauschinger parameters of the material is influenced when the change in stress rate is sufficient to significantly alter the work hardening behavior of that material [1, 13-18]. The Bauschinger behaviour of a material is commonly studied by tension loading to certain percentage of unidirectional strain, followed by reversal of loading direction and comparing the flow behaviour of the material in the reversed loading direction with that of forward loading direction. But, the effect of asymmetric cyclic plastic deformation (ratcheting), which also produces unidirectional permanent strain, on the Bauschinger behaviour has not been received any attention. The objective of the present investigation is to make a comparative study of the effect deformation mode, monotonic and cyclic, and the rate of deformation on the Bauschinger behaviour of annealed OFHC copper. Specifically, the effect of different amounts of unidirectional prestrain under monotonic and ratcheting deformation and stress rate on Bauschinger behaviour have been investigated. Nomenclature EV Eh EH E( VP Vy1 Vy2 HP Hr EP Es Vb Vef V* VP
Bauschinger stress parameter Bauschinger hardening parameter Bauschinger strain parameter Bauschinger energy parameter Maximum pre stress 0.2% offset yield stress Yield stress in the direction of reverse strain (0.05% strain) Pre-strain Bauschinger strain, the strain in the reverse direction corresponding to the point of reverse stress equal to the maximum pre stress (VP) Energy spent during pre-strain Energy saved during reverse straining due to the Bauschinger effect Back stress Effective stress Thermal part of effective stress Athermal part of effective stress
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2.
Experimental Procedure
The material used in the present investigation was commercially pure (99.97%) polycrystalline OFHC copper received in the form of 12 mm diameter rod. Cylindrical specimen blanks of 12 mm diameter and 120 mm length were annealed at 520 0C for one hour and then quenched in water. One of the annealed specimens was used to observe the microstructure following usual metallographic polishing and etching with ferric chloride solution. Microstructure was observed under in an inverted optical microscope. Linear intercept method was used to measure the two-dimensional average grain using an automatic image analyser. Specimens of cylindrical geometry for tension test, and to investigate the Bauschinger behaviour, both under prior monotonic and cyclic (ratcheting) deformation, were fabricated from the annealed specimen blanks. Before the tests all the specimens were polished with fine emery paper for better surface finish. Tension test was done under strain-control mode at a strain rate of 10-3 per sec at room temperature (~ 27oC) in a servohydraulic universal testing machine, Instron 8501 of +/- 100 KN load capacity. Buaschinger phenomenon has been studied both after monotonic cyclic (ratcheting) deformation to five different prefixed amounts of forward strain (+ 7, 10, 12, 15 and 18 %) at a stress rate of 200 MPa/s. In case of cyclic deformation the specimens were subjected to asymmetric cyclic plastic deformation within 100 and 150 MPa stress limits (mean stress = 25 MPa) for accumulation of the above prefixed amount of positive strains. In all cases after uniaxial deformation (+ve) the loading direction was reversed and deformation was continued to 2.5 pct in the compressive direction. In a separate set of experiments stress rate was varied from 50 to 500 MPa/s both for monotonic and ratcheting deformation to 15-pct strain and then loading direction was reversed and deformation was continued again to 2.5 pct. The maximum stress and accumulated strain in every cycle were considered for plotting true stress-strain curves to find out the Bauschinger parameters in case of prior uniaxial ratcheting deformation. 3.
Evolution of magnitude of Bauschinger effect parameters
There are mainly four types established parameters, which are used to quantify the Bauschinger phenomenon: the stress, hardness, strain and energy parameter. The Bauschinger parameters are calculated from the following expressions
i. Bauschinger stress parameter (EV This describes the relative decrease in yield stress from forward to reverse deformation. EV VPVy2)/VP
(1)
ii. Bauschinger hardening parameter (Eh This parameter describes the relative decrease in yield stress due to the back stress effect. Eh Vy1Vy2)/(VPVy2)
(2)
iii. Bauschinger strain parameter (EH This parameter describes the amount of deformation in the reverse direction needed to reach the prestress level of stress. EH Hr/HP
(3)
iv. Bauschinger energy parameter E( This parameter describes the amount of energy needed during the reverse deformation to reach the pre stress level of stress. EE Es/EP
4.
(4)
Back stress development during monotonic and cyclic deformation
During monotonic deformation of single-phase polycrystalline materials into plastic regime, dislocations interact and piled up at grain boundaries preventing their further propagation. As a result back stress develops around the contact point resisting further progress of similarly signed dislocations. When the direction of deformations is
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reversed the back stress acts to assist the movement of dislocation from grain boundaries. As a result the reverse yielding occurs at a low stress. According to back stress theory dislocation interactions and pilling up increases with increase of dislocation density. This leads to the development of more back stress and consequently influences the Bauschinger behaviour. But during cyclic deformation, two dislocations of opposite sign encounter with each other on slip plane. This causes annihilation of dislocations and thereby influences the development of the back stress in every cycle [6, 19-20]. Due to dislocation annihilation during cyclic deformation the collinear dislocation density should greater for monotonic deformation as compared to cyclic deformation resulting in different back stress development for a given plastic strain. The back stress is associated with long-range interaction of mobile dislocations and effective stress is associated with short-range interaction of mobile dislocations were previously discussed [21-25]. The back stress can be calculated from the following equations. Back stress (Vb VPVef)
(5)
Where, Vef = ((VPVy2)/2) + (V*/2) 5. Results and discussion 5.1 Microstrcture and tensile properties Figure 1(a) shows the optical micrograph of the solution annealed OFHC copper. It is found that the microstructure consists of polyhedral grains with annealing twins interspersed in some grains. The two-dimensional average grain size measured using linear intercept method is 36 microns.
Fig. 1. Figure showing (a) optical micrograph and (b) engineering stress-strain curve of OFHC copper annealed at 5200 C
5.2 Bauschinger test To evaluate the Bauschinger parameters deformed under monotonic deformation, all the engineering stressstrain curves were converted to true stress-strain curves. During cyclic deformation, maximum stress and accumulated strain in every cycle were considered for plotting true stress-strain curves. After reaching a certain amount of accumulated strain, the direction of deformation was immediately reversed and continued to 2.5 pct reversed strain. Figure 2(a) shows the effect of accumulated prestrain on the flow behaviour for a constant deformation rate of 200MPa/s for both monotonically and cyclically deformed specimens. Figure 2(b) shows the effect of stress rate on the flow behaviour for both 15 pct monotonically and cyclically deformed specimens.
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Fig. 2. (a) True stress-strain curves showing (a) forward prestrain effect at constant stress rate 200 MPa sec-1 and (b) stress rate effect for 15 pct monotonically and cyclically deformed specimens.
5.3 Bauschinger parameters When comparing and discussing the Bauschinger effect behavior, it is often useful to have some method of quantifying the response using a scalar measurement. The purpose of these values is to highlight the Bauschinger features for both monotonically and cyclically deformed OFHC copper. Before quantifying the Bauschinger effect parameters it is more important to evaluate the back stress in each case. The back stress is developed due to dislocation interaction and pilling up of dislocations at grain boundaries in single-phase polycrystalline materials. According to back stress theory of Bauschinger phenomenon dislocation interactions and pilling up increases with increase of dislocation density; this leads to the development of more back stress and consequently influences the Bauschinger behaviour. Figure 3 shows that increasing the amount of forward prestrain (at constant stress rate 200MPa/s) back stress increases [1-5]. But the developed back stress is different for monotonic and cyclic deformation due to dislocations interaction/pilling up and annihilation is different during monotonic and cyclic deformation. Result shows that the back stress developed during monotonic deformation is higher compared to the cyclic deformation for certain level of prestrain. Development of lower back stress for cyclic deformation can be related with the dislocation annihilation reaction in case of cyclic deformation [6, 19-20]. As a result collinear dislocation density is higher for monotonic deformation compared to cyclic deformation. Thus higher back stress is developed in case of monotonic deformation for a certain level of prestrain (constant stress rate) as well as at certain stress rate (for constant pre strain), Figure 3. Higher Bauschinger effect means lower yield strength during a reverse loading.
Fig. 3. Prestrain and stress rate effect on back stress developed during monotonic and cyclic (ratcheting) deformation.
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The Bauschinger stress parameter describes the relative decrease in yield stress from forward to reverse direction. It is highly associated with the dislocation pilling ups and annihilation process, which influence the development of back stress. As back stress increases, the reverse yield strength decreases and consequently the Bauschinger stress parameter is increased (Equation 1). From the back stress variation shown in Figure 3 it is observed that for a given forward prestrain levels, the back stress developed is higher for monotonic deformation compared to cyclic deformation. Hence higher Bauschinger stress parameter is obtained in case when deformation in forward direction is carried out monotonically as compared to the cyclically deformed condition, Figure 4(a).
Fig. 4. Variation of Bauschinger stress and hardening parameter with (a) prestrain at constant stress rate (200MPa sec1) and (b) stress rate at constant prestrain (15pct) of both modes of deformation (monotonic and cyclic).
The Bauschinger hardening parameter describes the relative decrease in yield stress due to back stress effect. As discussed above, increasing the amount of prestrain, dislocation pilling up increases upto a certain level of prestrain resulting in an increase of back stress. When the direction of deformation is reversed, the back stress assists the movement of dislocations in the reverse direction resulting in the drop of yield stress drop which gradually decreases with increasing the prestrain. This type of reverse yielding asymmetry is common in most classes of materials. As a result Bauschinger hardening parameter decreases with increasing the prestrain as shown in Figure 4(a). Figure 4(a) also shows that Bauschinger hardening parameter is higher for monotonic deformation compared to cyclic deformation for a certain amount of prestrain, whereas the effect of prestrain on Bauschinger hardening parameter is much higher in case of prior monotonic deformation in the forward direction due to more and more dislocation pilling up and lower rate of dislocation annihilation compared to cyclically deformed conditions. It has been studied by several investigators that increasing the stress rate the flow stress of the material increases by increasing mobile dislocation density and velocity [8-12] and hence resulting in more dislocation pile ups. This type of relationship is dependent on stress rate sensitivity of the materials. Our result shows that in the present annealed OFHC copper the stress rate has no significant effect in Bauschinger stress and hardening parameters, (Figure 4(b)). The very low effect of stress rate is believed to be related with the stacking fault energy of copper. Since the back stress developed in the material causes the difference in the reverse yield stress it is also important to quantify the transient period observed after the load reversal. The Bauschinger strain parameter describes the amount of deformation in the reverse direction needed to reach the unloading stress during forward deformation. This parameter also highly associated with the dislocation pilling up and annihilation processes. With increase of accumulated prestrain more and more dislocations are piled up against different barriers with development of back stress assisting the reverse flow behaviour in the opposite loading direction. Therefore increasing the prestrain Bauschinger strain parameter decreases for both monotonically and cyclically deformed materials following power relationship (Figure 5). Bauschinger strain parameters for cyclically deformed materials decreases more as compared to monotonic deformation due to dislocation annihilation in every cycle. This parameter is also highly related to the back stress development for a certain amount of prestrain. Due to higher back stress effect during monotonic deformation, higher EHparameter is observed for fixed prestrain as compared to cyclic deformation.
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Fig. 5. Variation of Bauschinger strain and energy parameter with prestrain of both modes of deformed (monotonic and cyclic) materials.
The Bauschinger energy parameter describes the energy needed during the reverse deformation to reach the stress level for forward loading direction. It is found that with increase of prestrain the Bauschinger energy parameter continuously decreases (Figure 5). This type of phenomenon occurs due to the more and more dislocation pilling up at higher level of prestrain which aids the dislocation motion during reverse loading. Due to enhancement of dislocation motion in the reverse loading direction because of the development of back stress the relative energy required to reach the unloading stress in the reverse loading direction is lower when the amount of prestrain is higher. Figure 5 also indicates that Bauschinger energy parameter is higher for monotonic deformation compared to cyclic deformation at a certain prestrain level. This occurs due to higher back stress developed in case of monotonic deformation compare to cyclic deformation at a certain prestrain level. Conclusions The effect of forward strain and stress rate on Bauschinger effect parameters by monotonically and cyclically deformed OFHC copper has been studied at room temperature. The evolution of Bauschinger stress, hardening, strain and energy parameters assess that how long lasting the Bauschinger effect is and thus support the long range work hardening/softening approach. The conclusions are as follows
x
x
x
The Bauschinger parameters are highly related to the prestrain of deformation. Bauschinger stress parameter is in increasing nature with pre strain for both mode of deformation i.e. monotonic and cyclic. Where as Bauschinger hardening parameter is in decreasing nature with pre strain for both mode of deformation. Similarly the Bauschinger strain and energy parameters are in decreasing nature with pre strain for both mode of deformation. In comparison to monotonically and cyclically (ratcheting) deformation upto a certain value of forward prestrain, the Bauschinger parameters are more higher for monotonic deformation compare to cyclic deformation. This type of behavior observed due to more back stress development during monotonic deformation compare to cyclic deformation for same amount of pre strain. The stress rate change shows that no significant change in Bauschinger parameters are observed for both mode of deformation. This may be due to that the limited change in stress rate for both mode of deformation are not sufficient to significantly alter the work hardening behavior of the material if the stress rate sensitivity of the material is significant.
Acknowledgements The authors would like to thank Council of Scientific and Industrial Research (New Delhi) and Jadavpur University for providing funding and facilities respectively for carrying out the research work.
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