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Elongation minimum and strain rate sensitivity minimum of zircaloy-4
Journal of Nuclear Materials 116 (1983) 314-316 North-Holland Publishing Company
314
LETTER TO THE EDITORS ELONGATION MINIMUM AND STRAIN RAm SENSITIVITY MINIMUM OF ZIRCALOY-4
In zirconium and zirconium alloys, an anomalous mechanical behavior over the temperature range of approximately 473-875 K has been reported. The observed phenomena include (1) the discontinuous plastic flow [ 1,3,4,5,6,73, (2) the appearance of plateaus or peaks [3,4,7,8,9] in the flow stress-temperature diagram, (3) activation energy peak [7], (4) low strain rate sensitivity [2,3,4]. Many of these phenomena have been related to some form of dynamic strain aging, and a variety of mechanisms has been proposed. However, these phenomena have not yet been adequately characterized because of the multiplicity of alloying elements and impurities. In 1970, Ramachandran et al. [3] observed hardening peak and elongation minimum in the temperature range of 675-875 K and concluded that the elongation minimum is due to an interaction between dislocations and oxygen, nitrogen and/or carbon without suggesting clear evidence. The purpose of this study is to identify the elongation minimum and strain rate sensitivity minimum of Zircaloy-4. Annealed Zircaloy-4 sheets of 0.965 mm thickness were supplied by Teledyne Wah Chang, Albany. The supplier’s composition of this material is listed in table 1. Tensile specimens with 20 mm gauge length and 5 mm width were machined with the axis parallel to the
Table 1 Chemical composition otherwise stated)
rolling direction and tested in an Instron machine in the temperature range of 298-798 K. Fig. 1 shows the fracture elongation of the Zircaloy-4 specimens as a function of temperature. The elongation minimum occurs at each strain rate and the minimum is shifted to higher temperature with increasing strain rate. However, reduction of area at fracture increases continuously with temperature irrespective of strain rate and there is no minimum in the reduction of area (fig. 2). The intense concentration of deformation in the neck was observed in the specimens fractured at the temperature and strain rate corresponding to the elongation ~nimum. This result implies that the elongation minimum is apparently not associated with brittle fracture. The strain rate sensitivity calculated by the usual formula m = ln( ol/o,)/ln( a,/;,) is plotted as a function of temperature in fig. 3. Here, m is the strain rate sensitivity at the mean strain rates of 6, and i,, and u, an uz are the yield stresses at strain rates 1, and k2. The value of the strain rate sensitivity m does not increase monotonically with temperature as in the case for a simple thermally activated process. In each curve there is a minimum in the temperature range of 639-756 K which is coincident with the elongation minimum tem-
v:
60-
1.33
x IO-‘/UC
.:c3.37 x IO-‘/UC A.: 3.33x IO-VW l : 1.33x lo-2/s*c to
of Zircaloy-4 (ppm by weight unless
6Q-
Element
Composition
Element
Composition
Sn Fe Cr Al B Cd co cu Hf H
1.54% 0.20% O.llX 41 4 0.25 1.50 < IO 15 64 cz5
Mg Mn Ni N Si W Ti U 0 Zr
< 10 < 10 < 35 39 75 < 50 i 25 < 1.0 1360 Batance
0022-3115/83/0000-0000/$03.00
-
3 L
0 1983 North-Holland
0” F 4
so-
w 40 -
30 -
*O11 300
.
I
400
I
I
.
I
500
603
TEMPERATURE
CK)
#
I
.
700
Fig. 1. The percentage elongation of Zircaloy-4 versus temperature for the four strain rates.
XI. Hong et al. / Elongation minimum of Zircaloy
-4
315
yield stress versus temperature diagram and this was reconfirmed previously by the authors [lo]. Generally, in ultra high purity metals, the flow stress consists of an athermal component ua and a thermal component u*. However, in the metals containing alloying elements or impurities, the solute strengthening term should be considered and the total flow stress is given by
a
a, = oa + u* + OSO,= u + a,,,,
401’ 300
’
’
’
400
’
’
TEMPERATURE
’
’
700
1
’
( K)
Fig. 2. The percentage temperature.
reduction
of area for Zircaloy-4
versus
perature
over
whole
range
range,
and
the
temperature
the temperature dependence of strain rate sensitivity follows the same trend as that of elongation as shown in fig. 1 and fig. 3. Therefore, the elongation minimum can be explained in terms of the strain rate sensitivity minimum. When a neck forms, the strain rate in the necked region increases. If the strain rate sensitivity is high, the increase of strain rate in the necked region may increase the resistance to flow sufficiently so that deformation tends to occur above and below the neck. On the other hand, the low value of the strain rate sensitivity concentrates the deformation in the neck, once a neck is formed, resulting in low ductility. In zirconium alloys, the plateau which is a manifestation of dynamic strain aging appears [3,4,7,8,9] in tlhe
(1)
where u is the flow stress in the absence of dynamic compostrain aging and a,,, is the solute strengthening nent due to dynamic strain aging. In fig. 4, the schematic flow stress versus temperature plot of annealed Zircaloy-4 is shown which indicates that a low strain rate sensitivity can be related to the yield stress plateau. In the shaded region in fig. 4, the flow stress curves at different strain rates are close to each other, implying low strain rate sensitivity. In general, solute strenghtening has its maximum potential at some intermediate temperature. At low temperatures, the mobility of solute atoms is so low that they effectively cannot keep up with moving dislocations and, at high temperatures, the mobility of solutes is so high that they can easily move with the dislocations and again cannot exert strong drag force. From these considerations, we can also deduce that the solute strengthening term a,,, is strain rate and temperature dependent. Namely, when the strain rate rises, a,,, moves towards high temperature, the plateau leading to region of low strain rate sensitivity as shown in fig. 4, moves
0.12 v:1.33
XW4/HC
.
l :s.s7XlO-‘/*~o
O.lO-
&3.33
XIO-~/.*C
TEMPERATURE O.OO&’
’ 400
.
’ x)0
.
TEMPERATURE
’ PK)
Fig. 3. The temperature dependence of the strain rate sensitivity of flow stress for the three strain rates.
Fig. 4. Schematic flow stress versus temperature plots. The total flow stress e, consists of two separable parts: o (would exist in the absence of dynamic strain aging), and es,,, (the solute strenghtening term due to dynamic strain aging). The region of low strain rate sensitivity is shaded.
XI. Hong et al. / Elongation minimum of Zircaloy 4
316
(207 kJ/mol) [II], (213 kJ/mol) [12], and Zircaloy-2 (220 kJ/mol) [13]. From the above, it is clear that the stress plateau, leading to a low strain rate sensitivity and ductility minimum is closely associated with the drag force due to oxygen atoms. It is reasonable to conclude that oxygen atoms are responsible for strain aging, for the strain rate sensitivity minimum and for the ductility minimum in the temperature range of 298-798 K.
References
I 1.2
1.3
1.4
t 1.5
I.6
fx103 K Fig. 5. Determination of activation energy for elongation minimum in Zircaloy-4.
towards high temperature and accordingly the ductility minimum temperature also increases. Therefore, we can conclude that the activation energy obtained from a shift of the elongation minimum temperature with the change in strain rate is equal to that of dynamic strain aging and in turn to that of solute diffusion. The Arrhenius plot of the strain rate versus the reciprocal of the elongation minimum temperature as shown in fig. 5 led to an activation energy of 205 kJ/mol for Zircaloy-4. This value corresponds to the activation energy for oxygen diffusion in a-zirconium
Received
29 March
1983; accepted
30 May 1983
B. Ramaswami and G.B. Graig, Trans. AIME 239 (1967) 1226. PI D, Lee, Met. Trans. 1 (1970) 1607. I31 V. Ramachandran and R.E. Reed-Hill, Met. Trans. I (1970) 2105. I41 A.M. Garde, E. Aigeltinger, B.N. Woodruff and R.E. Reed-Hill, Met. Trans. 6A (1975) 1183. [51 W.R. Thorpe and 1.0. Smith, J. Nucl. Mater. 78 (1978) 49. [61 W.R. Thorpe and 1.0. Smith, J. Nucl. Mater. 80 (1979) 35. [71J.L. Derep, S. Ibrabim, R. Rouby and G. Fantozzi, Acta. Met. 28 (1980) 607. PI O.D. Sherby and A.K. Miller, Development of the Materials Code, MATMOD. EPRI NP-567 (1977). [91 E. Alp, ELESIM 2, MOD 9, User’s Manual and Code Description, CWAPD-336 (1978). Core Safety Research, WI C.S. Rim, Power Reactor KAERI/RR-336/8 1 (198 1). illIJ.J. Kearns and J.N. Chirigos, WAPD-TM-306 (1962). [I21 LG. Ritchie and A. Atrens, J. Nucl. Mater. 67 (1977) 254. [I31 R. Choubey and J.J. Jonas, Metal. Sci. 15 (1981) 30.
Sun Ig Hong, Woo Seog Ryu and Chang Saeng Rim Division of Nuclear Fuel Design, Korea Advanced Energy Research Institute, P.O. Box 7, Daeduk, ChoongNam, Korea
314
LETTER TO THE EDITORS ELONGATION MINIMUM AND STRAIN RAm SENSITIVITY MINIMUM OF ZIRCALOY-4
In zirconium and zirconium alloys, an anomalous mechanical behavior over the temperature range of approximately 473-875 K has been reported. The observed phenomena include (1) the discontinuous plastic flow [ 1,3,4,5,6,73, (2) the appearance of plateaus or peaks [3,4,7,8,9] in the flow stress-temperature diagram, (3) activation energy peak [7], (4) low strain rate sensitivity [2,3,4]. Many of these phenomena have been related to some form of dynamic strain aging, and a variety of mechanisms has been proposed. However, these phenomena have not yet been adequately characterized because of the multiplicity of alloying elements and impurities. In 1970, Ramachandran et al. [3] observed hardening peak and elongation minimum in the temperature range of 675-875 K and concluded that the elongation minimum is due to an interaction between dislocations and oxygen, nitrogen and/or carbon without suggesting clear evidence. The purpose of this study is to identify the elongation minimum and strain rate sensitivity minimum of Zircaloy-4. Annealed Zircaloy-4 sheets of 0.965 mm thickness were supplied by Teledyne Wah Chang, Albany. The supplier’s composition of this material is listed in table 1. Tensile specimens with 20 mm gauge length and 5 mm width were machined with the axis parallel to the
Table 1 Chemical composition otherwise stated)
rolling direction and tested in an Instron machine in the temperature range of 298-798 K. Fig. 1 shows the fracture elongation of the Zircaloy-4 specimens as a function of temperature. The elongation minimum occurs at each strain rate and the minimum is shifted to higher temperature with increasing strain rate. However, reduction of area at fracture increases continuously with temperature irrespective of strain rate and there is no minimum in the reduction of area (fig. 2). The intense concentration of deformation in the neck was observed in the specimens fractured at the temperature and strain rate corresponding to the elongation ~nimum. This result implies that the elongation minimum is apparently not associated with brittle fracture. The strain rate sensitivity calculated by the usual formula m = ln( ol/o,)/ln( a,/;,) is plotted as a function of temperature in fig. 3. Here, m is the strain rate sensitivity at the mean strain rates of 6, and i,, and u, an uz are the yield stresses at strain rates 1, and k2. The value of the strain rate sensitivity m does not increase monotonically with temperature as in the case for a simple thermally activated process. In each curve there is a minimum in the temperature range of 639-756 K which is coincident with the elongation minimum tem-
v:
60-
1.33
x IO-‘/UC
.:c3.37 x IO-‘/UC A.: 3.33x IO-VW l : 1.33x lo-2/s*c to
of Zircaloy-4 (ppm by weight unless
6Q-
Element
Composition
Element
Composition
Sn Fe Cr Al B Cd co cu Hf H
1.54% 0.20% O.llX 41 4 0.25 1.50 < IO 15 64 cz5
Mg Mn Ni N Si W Ti U 0 Zr
< 10 < 10 < 35 39 75 < 50 i 25 < 1.0 1360 Batance
0022-3115/83/0000-0000/$03.00
-
3 L
0 1983 North-Holland
0” F 4
so-
w 40 -
30 -
*O11 300
.
I
400
I
I
.
I
500
603
TEMPERATURE
CK)
#
I
.
700
Fig. 1. The percentage elongation of Zircaloy-4 versus temperature for the four strain rates.
XI. Hong et al. / Elongation minimum of Zircaloy
-4
315
yield stress versus temperature diagram and this was reconfirmed previously by the authors [lo]. Generally, in ultra high purity metals, the flow stress consists of an athermal component ua and a thermal component u*. However, in the metals containing alloying elements or impurities, the solute strengthening term should be considered and the total flow stress is given by
a
a, = oa + u* + OSO,= u + a,,,,
401’ 300
’
’
’
400
’
’
TEMPERATURE
’
’
700
1
’
( K)
Fig. 2. The percentage temperature.
reduction
of area for Zircaloy-4
versus
perature
over
whole
range
range,
and
the
temperature
the temperature dependence of strain rate sensitivity follows the same trend as that of elongation as shown in fig. 1 and fig. 3. Therefore, the elongation minimum can be explained in terms of the strain rate sensitivity minimum. When a neck forms, the strain rate in the necked region increases. If the strain rate sensitivity is high, the increase of strain rate in the necked region may increase the resistance to flow sufficiently so that deformation tends to occur above and below the neck. On the other hand, the low value of the strain rate sensitivity concentrates the deformation in the neck, once a neck is formed, resulting in low ductility. In zirconium alloys, the plateau which is a manifestation of dynamic strain aging appears [3,4,7,8,9] in tlhe
(1)
where u is the flow stress in the absence of dynamic compostrain aging and a,,, is the solute strengthening nent due to dynamic strain aging. In fig. 4, the schematic flow stress versus temperature plot of annealed Zircaloy-4 is shown which indicates that a low strain rate sensitivity can be related to the yield stress plateau. In the shaded region in fig. 4, the flow stress curves at different strain rates are close to each other, implying low strain rate sensitivity. In general, solute strenghtening has its maximum potential at some intermediate temperature. At low temperatures, the mobility of solute atoms is so low that they effectively cannot keep up with moving dislocations and, at high temperatures, the mobility of solutes is so high that they can easily move with the dislocations and again cannot exert strong drag force. From these considerations, we can also deduce that the solute strengthening term a,,, is strain rate and temperature dependent. Namely, when the strain rate rises, a,,, moves towards high temperature, the plateau leading to region of low strain rate sensitivity as shown in fig. 4, moves
0.12 v:1.33
XW4/HC
.
l :s.s7XlO-‘/*~o
O.lO-
&3.33
XIO-~/.*C
TEMPERATURE O.OO&’
’ 400
.
’ x)0
.
TEMPERATURE
’ PK)
Fig. 3. The temperature dependence of the strain rate sensitivity of flow stress for the three strain rates.
Fig. 4. Schematic flow stress versus temperature plots. The total flow stress e, consists of two separable parts: o (would exist in the absence of dynamic strain aging), and es,,, (the solute strenghtening term due to dynamic strain aging). The region of low strain rate sensitivity is shaded.
XI. Hong et al. / Elongation minimum of Zircaloy 4
316
(207 kJ/mol) [II], (213 kJ/mol) [12], and Zircaloy-2 (220 kJ/mol) [13]. From the above, it is clear that the stress plateau, leading to a low strain rate sensitivity and ductility minimum is closely associated with the drag force due to oxygen atoms. It is reasonable to conclude that oxygen atoms are responsible for strain aging, for the strain rate sensitivity minimum and for the ductility minimum in the temperature range of 298-798 K.
References
I 1.2
1.3
1.4
t 1.5
I.6
fx103 K Fig. 5. Determination of activation energy for elongation minimum in Zircaloy-4.
towards high temperature and accordingly the ductility minimum temperature also increases. Therefore, we can conclude that the activation energy obtained from a shift of the elongation minimum temperature with the change in strain rate is equal to that of dynamic strain aging and in turn to that of solute diffusion. The Arrhenius plot of the strain rate versus the reciprocal of the elongation minimum temperature as shown in fig. 5 led to an activation energy of 205 kJ/mol for Zircaloy-4. This value corresponds to the activation energy for oxygen diffusion in a-zirconium
Received
29 March
1983; accepted
30 May 1983
B. Ramaswami and G.B. Graig, Trans. AIME 239 (1967) 1226. PI D, Lee, Met. Trans. 1 (1970) 1607. I31 V. Ramachandran and R.E. Reed-Hill, Met. Trans. I (1970) 2105. I41 A.M. Garde, E. Aigeltinger, B.N. Woodruff and R.E. Reed-Hill, Met. Trans. 6A (1975) 1183. [51 W.R. Thorpe and 1.0. Smith, J. Nucl. Mater. 78 (1978) 49. [61 W.R. Thorpe and 1.0. Smith, J. Nucl. Mater. 80 (1979) 35. [71J.L. Derep, S. Ibrabim, R. Rouby and G. Fantozzi, Acta. Met. 28 (1980) 607. PI O.D. Sherby and A.K. Miller, Development of the Materials Code, MATMOD. EPRI NP-567 (1977). [91 E. Alp, ELESIM 2, MOD 9, User’s Manual and Code Description, CWAPD-336 (1978). Core Safety Research, WI C.S. Rim, Power Reactor KAERI/RR-336/8 1 (198 1). illIJ.J. Kearns and J.N. Chirigos, WAPD-TM-306 (1962). [I21 LG. Ritchie and A. Atrens, J. Nucl. Mater. 67 (1977) 254. [I31 R. Choubey and J.J. Jonas, Metal. Sci. 15 (1981) 30.
Sun Ig Hong, Woo Seog Ryu and Chang Saeng Rim Division of Nuclear Fuel Design, Korea Advanced Energy Research Institute, P.O. Box 7, Daeduk, ChoongNam, Korea