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Slip behaviour and energy storage process during uniaxial tensile deformation of austenitic steel
Materials Science and Engineering A234&236 (1997) 1122-l 125
Slip behaviour
and energy storage process during uniaxial deformation of austenitic steel
tensile
Wiera Oliferuk a,*, Andrzej Korbel b, Maciej W. Grabski c a Institute ‘Department
of Fundamental Technological Research, Polish Academy of Science, iwietokrzyska b University of Mining and Metallurgy, Mickiewicza 20, 30-059 Krakdw, of Maierials Science and Engineering, Warsaw University of Technology, Narbutta
21, 00-049 Warsaw, Poland Poland 85, 02-524 Warsaw, Poland
Received 28 March 1997; received in revised form 14 April 1997
Abstract The mechanism of slip and its consequence in the process of energy storage during uniaxial tension of austenitic steel were studied. Interpretation of the energy storage process in terms of slip development and microscopic shear band formation is presented. 0 1997 Elsevier Science S.A. Keywords:
Austenitic steel; Energy storage; Polycrystalline metals
1. Introduction
When metals are cold worked, some mechanical energy e, expended in plastic deformation is converted into heat. The residual part of the energy, known as the stored energy e,, is retained in the metal. The energy conversion at a given instant is characterised by the instantaneous rate de,/de, of energy storage [1,2]. Since the beginning of this century, the process of energy storage has been investigated in numerous studies, reviewed by Bever et al. [l]. Recent studies [2-81 have shown that a polycrystalline metal stores much more energy than a single crystal. The process of energy storage during tensile test of austenitic steel has been investigated previously [2-41. The stored energy, e,, as a function energy expanded, e,, in plastic deformation and as a function strain Ewas measured using E = ln(l/l,)), where I is the instantaneous gauge length of the sample and 1, is the initial length. It has been shown experimentally that, in the initial stage of plastic deformation during uniaxial tensile tests of austenitic steel dependence, de,lde, versus E has a maximum (Fig. 1). These results have been interpreted in terms of the evolution of low-energy dislocation structure. The consequences of slip evolution in * Corresponding author. Tel.: +48 22 261281 ext. 177; fax: +48 22 269815.
0921-5093/97/$17.00 Q 1997 Elsevier Science S.A. All rights reserved. PIISO921-5093(97)00354-7
energy conversion have not been taken into consideration. The present work fills this gap. Slip within an individual grain in polycrystalline metal meets several constraints from the neighbouring grains. Incompatible deformations of neighbouring grains must be accommodated by the elastic or elastoplastic deformation in order to ensure the continuity of the deformed material [lo]. In both cases, additional energy must be provided.
0.50 A
: z
0.40
-
0.30
-
0.20
-
f
0.10 0.00 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,‘T”‘,,,,,I,, 0.05 0.10 True
0.15 Strain,
0.20
0.
5
E
Fig. 1. Dependence of de,/de, on strain obtained during uniaxial tension of austenitic steel for fine-grained (curve A, average grain diameter 8 pm) and coarse-grained (curve B, average grain diameter 80 pm) samples. Strain rate 0.12 min- ‘. The bars represent the mean square deviation [4].
W. Oliferuk
et al. /Materials
Science
and Engineering
A decrease of the rate of accumulation of dislocations is commonly attributed to the strain intensified recovery processes. However, it is known that homogeneous multisystem slip evolves into transsubstructural coarse slip and finally into shear banding [9]. The first stage of this evolution results in an increase of the free path of dislocations, i, which according to the Orowan relationship, y = bpl, affects the density of necessary dislocations, p, where y is the homogeneous shear strain. A much stronger effect may be caused by the replacement of multisystem slip by shear banding. It may be expected, therefore, that the change from a homogeneous multisystem slip into micro shear banding is manifested by a maximum on the de,/de, versus E curve. The aim of the present work is a verification of the possible correlation between the mode of slip and the energy storage rate during the tensile deformation of a polycrystalline metal.
2. Method of determination
A234-236
Fig. 2. Optical 0.0042.
ew -
qd
r r(h) dh s0
qd = 4 -
ete
sample
1123
surface
after
strain
of
r(tJ dt, -:
Jo
T,z PO
A unique feature of the method is the possibility of determining the stored energy at any given instant without interrupting the tensile tests and without using a calorimeter [3].
(1)
The energy e, is found from the load versus elongation curve. The heat qd is determined by simulating the process of sample heating during deformation by means of controlled supply of electrical power u(tJ in such a way that the temperature increase with time t, during the simulation is identical to that measured during tensile testing. When the straining and the simulation are conducted under identical conditions, then the heat q that would have been transferred to the surroundings if the temperature of the unloaded sample had returned to the initial temperature is the same in both cases and is equal to: q=
125
of the
f
e, = e, -
es =
micrograph
1122--l
where c( is the coefficient of linear thermal expansion, To is the initial absolute temperature, z is the Cauchy stress tensor and p. the density of tested metal. From Eqs. (l)-(4) the stored energy is obtained as:
of the stored energy
As in our previous reports [2-41, the method employed is based on the first law of thermodynamics. The stored energy, e,, is determined as the difference between the energy e, expended during plastic deformation and energy qd dispersed in the form of heat, i.e.:
(1997)
3. Experimental The optical microscope observation of the surface of samples after various degrees of deformation were performed under Nomarsky contrast conditions. The samples had a flat and well-polished surface before the tension. Photomicrographs are shown in Figs. 2-4. The samples were prepared from stainless austenitic steel. They had the homogeneous microstructure with 80 urn
(2) (3)
where e,, is the energy associated with thermoelastic coupling that appears during loading and elastic unloading of the specimen. During homogeneous tensile deformation, on the assumption of linear and isotropic law for the elastic behaviour: e,=
--
ffT,Z PO
(4)
Fig. 3. Optical 0.0106.
micrograph
of the
sample
surface
after
strain
of
1124
Fig. 4. Optical micrograph 0.0450. At this strain de,/de,
W. Oliferuk
et al. /Materials
of the sample surface reaches maximum.
after
Science
strain
and Engineering
of
grain size and were identical to those used for determination of the dependence de,/de, versus E (Fig. 1).
4. Discussion In a polycrystalline metal the slip in individual grains leads to a change in the shape of the grains. This aspect of slip is seen in the relief on the free surface of the sample (Fig. 2). However, in order to preserve material continuity during straining, the change of shape of the individual grains within the sample must be the same as the change of the sample’s shape. In other words, some components of the deformation tensor are forbidden and therefore additional stress (internal stress) is generated at the grain boundaries. This effect is called elastic accommodation [9]. It can be seen that the relief on the sample surface at E = 0.0106 (Fig. 3) is deeper than at E = 0.0042 (Fig. 2), indicating that the process of stress generation at the grain boundaries intensifies with strain in the initial stage of plastic deformation. The patterns shown in Figs. 2 and 3 correspond to the rising segment of the de,/de, versus E curve. This suggests that the increase of the rate energy storage is caused not only by the rise of dislocation density, but also by the
A234-236
(1997)
1122-1125
does not need elastic accommodation because the deformation of the affected individual grains is then compatible. Effect of grain size on the rate of energy storage confirms such mezostructural interpretation. Fig. 1 shows the dependence de,/de, versus E during tension of fine-grained and coarse-grained samples. The maximum de,/de, for the fine-grained samplesis higher than for coarse-grained ones. This may be related to the stressesgenerated at the grain boundaries. The stresses are stronger in the fine-grained samplesthan in coarsegrained ones. The fine-grained samples have a greater volume fraction of grain boundary and consequently more dislocations in the vicinity of the boundaries. The location of the maximum de,/de, depends on the grain size (Fig. 1). However, after reaching a certain deformation the plots of de,/de, versus E for the samplesof both groups are practically the same; the grain boundaries have no effect on the energy storage rate. Micro shear banding then becomes the dominating mode of deformation. The correlation of the e, versus E dependence with the flow stress versus E in tested steel shows that the elastic accommodation influences the rate of energy storage in initial stage of plastic deformation. In numerous studies it has been shown, that the energy storage is proportional to square of flow stress c? [l]. In austenitic steel tested in present work this proportionality occurs after reaching maximum of the de,,deW (Fig. 5). This relationship is in accordance with another empirical dependence: a2 M p [l 11, where p is dislocation density, provided that the stored energy is proportional to p. This is not the case in the initial stage of plastic deformation of austenitic steel, where the energy storage shows the up-rise deviation from the linearity of the e, versus g2 plot. The presence of the internal stressesseemsto provide the explanation to this difference. 1.5
increase of stressat grain boundaries. The further increase of the internal stress must initiate slip in secondary systems [lo]. From this instant the rate of energy storage ceasesto increase and reaches the maximum value because the rate of energy dissipation increases. The images of the sample surface corresponding to the maximum rate of energy storage are shown in Fig. 4. A coarse slip operating in several systems and the micro shear bands are seen. The appearance and development of micro shear bands can be considered as dissipative processes,which diminish the rate of energy storage (Fig. 1). The micro shear band expands over a set of neighbouring grains. The strain in shear band
Fig. 5. Stored energy as a function of the flow stress square during uniaxial tension of the austenitic steel. The measurements were performed on eight samples (average grain diameter 80 pm).
W. Oliferuk
et al. /Materials
Science and Engineering
(1997)
1122-l
125
1125
Scientific Research (Poland) for financial support under Grant No. 7 TO8A 025 11.
5. Conclusions
It has been shown that an increase in the rate of energy storage in the initial stage of plastic deformation of polycrystalline metal is associated not only with the rise of dislocation density but also with stresses generated at the grain boundaries. The experimental evidence proves that the strain stage characterised by the increase in the rate of energy storage corresponds to homogeneous multisystem slip. The change from a homogeneous multisystem slip into micro shear banding is manifested by a maximum on the de,/de, versus E. The decrease in the rate of energy storage follows the evolution of the micro shear bands. Such interpretation is in accordance with the result of correlation of the dependence of the energy storage rate on strain with the stress-strain curve.
is expressed to the State Committee
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [IO] [ll]
Acknowledgements
Gratitude
A234-236
for
M.B. Bever, D.L. Holt, A.L. Titchener, Prog. Mater. Sci. 17 (1973) 56 and 124. W. Oliferuk, W.A. Swiatnicki, M.W. Grabski, Mater. Sci. Eng. A161 (1993) 55. W. Oliferuk, S.P. Gadaj, M.W. Grabski, Mater. Sci. Eng. 70 (1985) 131. W. Oliferuk, W.A. Swiatnicki, M.W. Grabski, Mater. Sci. Eng. Al97 (1995) 49. I. Bacer, L. Liu, Ser. Metall. Mater. 30 (9) (1994) 1167. M.B. Srichai, D.C. Dunand, A. Mortensen, Ser. Metall. Mater. 30 (12) (1994) 1509. I. Bacer, L. Liu, D. Mandal, Ser. Metall. Mater. 32 (2) (1995) 267. D. Mandal, I. Backer, Ser. Metall. Mater. 33 (5) (1995) 831. A. Korbel, W. Bochniak, J. Mater. Proc. Technol. 53 (1995) 229. G.I. Taylor, Proc. R. Sot. Al45 (1934) 362. D. Kuhlmann-Wilsdorf, N.R. Comins, Mater. Sci. Eng. 60 (1983) 7.
Slip behaviour
and energy storage process during uniaxial deformation of austenitic steel
tensile
Wiera Oliferuk a,*, Andrzej Korbel b, Maciej W. Grabski c a Institute ‘Department
of Fundamental Technological Research, Polish Academy of Science, iwietokrzyska b University of Mining and Metallurgy, Mickiewicza 20, 30-059 Krakdw, of Maierials Science and Engineering, Warsaw University of Technology, Narbutta
21, 00-049 Warsaw, Poland Poland 85, 02-524 Warsaw, Poland
Received 28 March 1997; received in revised form 14 April 1997
Abstract The mechanism of slip and its consequence in the process of energy storage during uniaxial tension of austenitic steel were studied. Interpretation of the energy storage process in terms of slip development and microscopic shear band formation is presented. 0 1997 Elsevier Science S.A. Keywords:
Austenitic steel; Energy storage; Polycrystalline metals
1. Introduction
When metals are cold worked, some mechanical energy e, expended in plastic deformation is converted into heat. The residual part of the energy, known as the stored energy e,, is retained in the metal. The energy conversion at a given instant is characterised by the instantaneous rate de,/de, of energy storage [1,2]. Since the beginning of this century, the process of energy storage has been investigated in numerous studies, reviewed by Bever et al. [l]. Recent studies [2-81 have shown that a polycrystalline metal stores much more energy than a single crystal. The process of energy storage during tensile test of austenitic steel has been investigated previously [2-41. The stored energy, e,, as a function energy expanded, e,, in plastic deformation and as a function strain Ewas measured using E = ln(l/l,)), where I is the instantaneous gauge length of the sample and 1, is the initial length. It has been shown experimentally that, in the initial stage of plastic deformation during uniaxial tensile tests of austenitic steel dependence, de,lde, versus E has a maximum (Fig. 1). These results have been interpreted in terms of the evolution of low-energy dislocation structure. The consequences of slip evolution in * Corresponding author. Tel.: +48 22 261281 ext. 177; fax: +48 22 269815.
0921-5093/97/$17.00 Q 1997 Elsevier Science S.A. All rights reserved. PIISO921-5093(97)00354-7
energy conversion have not been taken into consideration. The present work fills this gap. Slip within an individual grain in polycrystalline metal meets several constraints from the neighbouring grains. Incompatible deformations of neighbouring grains must be accommodated by the elastic or elastoplastic deformation in order to ensure the continuity of the deformed material [lo]. In both cases, additional energy must be provided.
0.50 A
: z
0.40
-
0.30
-
0.20
-
f
0.10 0.00 ,,,,,,,,,,,,,,,,,,,,,,,,,,,,‘T”‘,,,,,I,, 0.05 0.10 True
0.15 Strain,
0.20
0.
5
E
Fig. 1. Dependence of de,/de, on strain obtained during uniaxial tension of austenitic steel for fine-grained (curve A, average grain diameter 8 pm) and coarse-grained (curve B, average grain diameter 80 pm) samples. Strain rate 0.12 min- ‘. The bars represent the mean square deviation [4].
W. Oliferuk
et al. /Materials
Science
and Engineering
A decrease of the rate of accumulation of dislocations is commonly attributed to the strain intensified recovery processes. However, it is known that homogeneous multisystem slip evolves into transsubstructural coarse slip and finally into shear banding [9]. The first stage of this evolution results in an increase of the free path of dislocations, i, which according to the Orowan relationship, y = bpl, affects the density of necessary dislocations, p, where y is the homogeneous shear strain. A much stronger effect may be caused by the replacement of multisystem slip by shear banding. It may be expected, therefore, that the change from a homogeneous multisystem slip into micro shear banding is manifested by a maximum on the de,/de, versus E curve. The aim of the present work is a verification of the possible correlation between the mode of slip and the energy storage rate during the tensile deformation of a polycrystalline metal.
2. Method of determination
A234-236
Fig. 2. Optical 0.0042.
ew -
qd
r r(h) dh s0
qd = 4 -
ete
sample
1123
surface
after
strain
of
r(tJ dt, -:
Jo
T,z PO
A unique feature of the method is the possibility of determining the stored energy at any given instant without interrupting the tensile tests and without using a calorimeter [3].
(1)
The energy e, is found from the load versus elongation curve. The heat qd is determined by simulating the process of sample heating during deformation by means of controlled supply of electrical power u(tJ in such a way that the temperature increase with time t, during the simulation is identical to that measured during tensile testing. When the straining and the simulation are conducted under identical conditions, then the heat q that would have been transferred to the surroundings if the temperature of the unloaded sample had returned to the initial temperature is the same in both cases and is equal to: q=
125
of the
f
e, = e, -
es =
micrograph
1122--l
where c( is the coefficient of linear thermal expansion, To is the initial absolute temperature, z is the Cauchy stress tensor and p. the density of tested metal. From Eqs. (l)-(4) the stored energy is obtained as:
of the stored energy
As in our previous reports [2-41, the method employed is based on the first law of thermodynamics. The stored energy, e,, is determined as the difference between the energy e, expended during plastic deformation and energy qd dispersed in the form of heat, i.e.:
(1997)
3. Experimental The optical microscope observation of the surface of samples after various degrees of deformation were performed under Nomarsky contrast conditions. The samples had a flat and well-polished surface before the tension. Photomicrographs are shown in Figs. 2-4. The samples were prepared from stainless austenitic steel. They had the homogeneous microstructure with 80 urn
(2) (3)
where e,, is the energy associated with thermoelastic coupling that appears during loading and elastic unloading of the specimen. During homogeneous tensile deformation, on the assumption of linear and isotropic law for the elastic behaviour: e,=
--
ffT,Z PO
(4)
Fig. 3. Optical 0.0106.
micrograph
of the
sample
surface
after
strain
of
1124
Fig. 4. Optical micrograph 0.0450. At this strain de,/de,
W. Oliferuk
et al. /Materials
of the sample surface reaches maximum.
after
Science
strain
and Engineering
of
grain size and were identical to those used for determination of the dependence de,/de, versus E (Fig. 1).
4. Discussion In a polycrystalline metal the slip in individual grains leads to a change in the shape of the grains. This aspect of slip is seen in the relief on the free surface of the sample (Fig. 2). However, in order to preserve material continuity during straining, the change of shape of the individual grains within the sample must be the same as the change of the sample’s shape. In other words, some components of the deformation tensor are forbidden and therefore additional stress (internal stress) is generated at the grain boundaries. This effect is called elastic accommodation [9]. It can be seen that the relief on the sample surface at E = 0.0106 (Fig. 3) is deeper than at E = 0.0042 (Fig. 2), indicating that the process of stress generation at the grain boundaries intensifies with strain in the initial stage of plastic deformation. The patterns shown in Figs. 2 and 3 correspond to the rising segment of the de,/de, versus E curve. This suggests that the increase of the rate energy storage is caused not only by the rise of dislocation density, but also by the
A234-236
(1997)
1122-1125
does not need elastic accommodation because the deformation of the affected individual grains is then compatible. Effect of grain size on the rate of energy storage confirms such mezostructural interpretation. Fig. 1 shows the dependence de,/de, versus E during tension of fine-grained and coarse-grained samples. The maximum de,/de, for the fine-grained samplesis higher than for coarse-grained ones. This may be related to the stressesgenerated at the grain boundaries. The stresses are stronger in the fine-grained samplesthan in coarsegrained ones. The fine-grained samples have a greater volume fraction of grain boundary and consequently more dislocations in the vicinity of the boundaries. The location of the maximum de,/de, depends on the grain size (Fig. 1). However, after reaching a certain deformation the plots of de,/de, versus E for the samplesof both groups are practically the same; the grain boundaries have no effect on the energy storage rate. Micro shear banding then becomes the dominating mode of deformation. The correlation of the e, versus E dependence with the flow stress versus E in tested steel shows that the elastic accommodation influences the rate of energy storage in initial stage of plastic deformation. In numerous studies it has been shown, that the energy storage is proportional to square of flow stress c? [l]. In austenitic steel tested in present work this proportionality occurs after reaching maximum of the de,,deW (Fig. 5). This relationship is in accordance with another empirical dependence: a2 M p [l 11, where p is dislocation density, provided that the stored energy is proportional to p. This is not the case in the initial stage of plastic deformation of austenitic steel, where the energy storage shows the up-rise deviation from the linearity of the e, versus g2 plot. The presence of the internal stressesseemsto provide the explanation to this difference. 1.5
increase of stressat grain boundaries. The further increase of the internal stress must initiate slip in secondary systems [lo]. From this instant the rate of energy storage ceasesto increase and reaches the maximum value because the rate of energy dissipation increases. The images of the sample surface corresponding to the maximum rate of energy storage are shown in Fig. 4. A coarse slip operating in several systems and the micro shear bands are seen. The appearance and development of micro shear bands can be considered as dissipative processes,which diminish the rate of energy storage (Fig. 1). The micro shear band expands over a set of neighbouring grains. The strain in shear band
Fig. 5. Stored energy as a function of the flow stress square during uniaxial tension of the austenitic steel. The measurements were performed on eight samples (average grain diameter 80 pm).
W. Oliferuk
et al. /Materials
Science and Engineering
(1997)
1122-l
125
1125
Scientific Research (Poland) for financial support under Grant No. 7 TO8A 025 11.
5. Conclusions
It has been shown that an increase in the rate of energy storage in the initial stage of plastic deformation of polycrystalline metal is associated not only with the rise of dislocation density but also with stresses generated at the grain boundaries. The experimental evidence proves that the strain stage characterised by the increase in the rate of energy storage corresponds to homogeneous multisystem slip. The change from a homogeneous multisystem slip into micro shear banding is manifested by a maximum on the de,/de, versus E. The decrease in the rate of energy storage follows the evolution of the micro shear bands. Such interpretation is in accordance with the result of correlation of the dependence of the energy storage rate on strain with the stress-strain curve.
is expressed to the State Committee
References [l] [2] [3] [4] [5] [6] [7] [8] [9] [IO] [ll]
Acknowledgements
Gratitude
A234-236
for
M.B. Bever, D.L. Holt, A.L. Titchener, Prog. Mater. Sci. 17 (1973) 56 and 124. W. Oliferuk, W.A. Swiatnicki, M.W. Grabski, Mater. Sci. Eng. A161 (1993) 55. W. Oliferuk, S.P. Gadaj, M.W. Grabski, Mater. Sci. Eng. 70 (1985) 131. W. Oliferuk, W.A. Swiatnicki, M.W. Grabski, Mater. Sci. Eng. Al97 (1995) 49. I. Bacer, L. Liu, Ser. Metall. Mater. 30 (9) (1994) 1167. M.B. Srichai, D.C. Dunand, A. Mortensen, Ser. Metall. Mater. 30 (12) (1994) 1509. I. Bacer, L. Liu, D. Mandal, Ser. Metall. Mater. 32 (2) (1995) 267. D. Mandal, I. Backer, Ser. Metall. Mater. 33 (5) (1995) 831. A. Korbel, W. Bochniak, J. Mater. Proc. Technol. 53 (1995) 229. G.I. Taylor, Proc. R. Sot. Al45 (1934) 362. D. Kuhlmann-Wilsdorf, N.R. Comins, Mater. Sci. Eng. 60 (1983) 7.