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Determination of elastic coefficients for zircaloy-2
Journal of Nuclear Materials 68 (1977) 345-347 0 North-Holland Publishing Company
DETERMINATION OF ELASTIC COEFFICIENTS FOR ZIRCALOY-2
W.R. CATLIN, D.C. LORD, F. ZAVERL and D. LEE Metullurgy Laboratory, General Electric Corporate Research and Development, Schenectady, New York 12301, USA Received 7 April 1977 Revise received 6 June 1977
In order to develop a predictive capability for structural members undergoing plastic deformation, it is essential that all the elastic constants are available for the computation so that the extent of elastic deformation can be established. Contribution of elastic deformation becomes important when the relative magnitude plastic strain is small, such as in the case of irradiated Zircaloy deforming under an aggressive environment. For this reason, elastic constants of several Zircaloy sheets were determined by using two inde~ndent methods [I 1. One was based on the use of pole figure data to compute elasticity coefficients and the other obtained by direct mechanical methods. Results of elastic coefficients obtained by these two methods over a range of temperature are compared for a Zircaloy-2 plate. A Zircaloy-2 plate designated as J-material had the following composition: 1.51 Sn, 0.14 Fe, 0.101 Cr, 0.05 Ni, and 0.13 1 0, all in percentage weight with the balance consisting of zirconium. The plate was straight cold rolled by 42% in reduction to 0.32 cm in thickness followed by a stress relief heat treatment of 498’C for 3 h.
Sll
Sl2
s*3
0
0
0
s12
s22
s23
0
0
0
02
s13
s23
s33
0
0
0
03
e4
0
0
0
s44
0
0
04
E5
0
0
0
0
%5
0
Qs
.?6 -1
0
0
0
0
0
566,
El
f
f2 E3
=
-I’
fJ1
Lo6_,
Conventions used for reference directions are as folIows: (1) Normal direction (ND); (2) transverse direction (TD); and (3) longitudinal or rolling direction (RD). Mechanical method.
Two types of test specimens were used to obtain elastic coefficients. Uniform gage section specimens with 0.3 1 cm square cross section and 7.62 cm in gage length were pulled in tension’to obtain l/&i values. The initial strain rate was 2.78 X 1O-4/s* A sPecial extensometer assembly was built to measure components of strain in three principal directions of anisotropy to the accuracy of ?OS%. Elevated temperature tests were made in an Instron Box Furnace and only the axial strain was measured. In addition, an hourglass specimen with 2.54 cm radius and 0.3 1 cm diameter were tested to obtain l/Sij values. Diametral displacements along two principal axes of anisotropy were measured by two sets of extensometers while recording the load. Tests were made in a hydraulically-operated, close-loop MTS machine where the average diametral ~splacement rate was held constant so that the axial
Definitions
Using the convention that Hooke’s law can be stated as e=Su, where S is called the elastic compliance constant, or, by matrix notation and from symmet~ ar~ment, 345
W.R. Catlin et al. / Determination
346
Table 1 Experimentally MPa X lo3
measured elastic constants for Zircaloy-2, J-material; mean (x), standard deviation (Sx), standard error (Si)
Temperature (“C) 25
x
llS22
l/S33
l/S12
l/S13
ljs23
101.2
96.1
293.7(9) *
304.2(7) 16.3 6.1
280.7( 12) 13.9 4.0
17.6 5.9
Sx S,_ x
200
of elastic coefficients for Zivcaloy-2
88.8
_
273.0
_
222.6
79.1
70.7
252.5(10) 18.2
221.6(8) 15.7
187.8(14) 12.1
5.8
5.6
3.2
242.1(7) 22.6
198.3(6) 15.2
8.6
6.2
S, S,_ 350
x S, S,_
450
x
73.4
66.3
Sx S,_
171.4(11) 10.6 3.2
* Numbers in parentheses indicate sample size.
strain rate was comparable to that used in simple tension tests. Elevated temperature tests in the MTS machine was made by the induction heating method. Test results are summarized in table 1. Pole figure method. Elastic constants were determined by using the pole figure method as reported by Rosenbaum and Lewis [2]. The computing method consists of estimating the space average of the monocrystal compliance coefficients from the weighted crystallo-
OAIENTATIONPARAWE99, 'n fl
(00021PLANE 0.994 RO9l
graphic pole density and applying the experimentally determined elastic coefficients of zirconium. It is assumed that monocrystal data is applicable to Zircaloy-2. A detailed outline of the pole figure method is reported by Rosenbaum and Lewis [2]. Pole figures and orientation parameters obtained at one quarter thickness are summarized in fig. 1. Results of elastic constants obtained by both mechanical and pole figure methods are summarized in figs. 2 and 3 where the calculated values were obtained
t-NUYY99
(IOigLANE 6448 1.000
.*
l’/
_,,, 10
TEMPERATURE,
Fig. 1. (a) Normal direction pole figure of the (0002) plane and (b) one-quarter removed of schedule J, (lOTO) plane Zircaloy-2 sheet, heat 397598Q.
400
300
500
*C
Fig. 2. Comparison of calculated elastic modulus (l/Sa) with experimental data over a range of?emperatures, J-material, Zircaloy-2.
W.R. Catlin et al. /Determination of elastic coefficients for Zivcaloy-2
347
The predicted elastic coefficients are in excellent agreement with the experimental values making the method proposed by Rosenbaum and Lewis a practical alternative whenever experimental data is lacking for structural analysis method.
25--‘/sa
L”
0
0
-
loo 200 300 TEMPERATURE,
400
500
The authors wish to express their appreciation to Dr. H.S. Rosenbaum and Mr. J.E. Lewis for determining the elastic constants by pole figure method and to Electric Power Research Institute for providing the financial support for this work.
lC
Fig. 3. Comparison of calculated stiffness coefficients (-l/S$ with experimental data over a range of temperatures, J-material, Zircaloy-2.
References [II D. Lee, F. Zaverl, Jr., C.F. Shih and M.D. German, Fifth
from the pole figure method. Measured Young’s moduli values (fig. 2) agree with the predicted values within about 5% and E/v, or l/&i, values agree within about 3.5%.
Quarterly Report to Electric Power Research Institute, General Electric Corp. Research and Development Report, SRD-76-118, Sept., 1976, Schenectady, New York. 121 H.S. Rosenbaum and J.E. Lewis, Use of pole figure data to compute elasticity coefficients of zirconium sheet, J. Nucl. Mater., to be published.
DETERMINATION OF ELASTIC COEFFICIENTS FOR ZIRCALOY-2
W.R. CATLIN, D.C. LORD, F. ZAVERL and D. LEE Metullurgy Laboratory, General Electric Corporate Research and Development, Schenectady, New York 12301, USA Received 7 April 1977 Revise received 6 June 1977
In order to develop a predictive capability for structural members undergoing plastic deformation, it is essential that all the elastic constants are available for the computation so that the extent of elastic deformation can be established. Contribution of elastic deformation becomes important when the relative magnitude plastic strain is small, such as in the case of irradiated Zircaloy deforming under an aggressive environment. For this reason, elastic constants of several Zircaloy sheets were determined by using two inde~ndent methods [I 1. One was based on the use of pole figure data to compute elasticity coefficients and the other obtained by direct mechanical methods. Results of elastic coefficients obtained by these two methods over a range of temperature are compared for a Zircaloy-2 plate. A Zircaloy-2 plate designated as J-material had the following composition: 1.51 Sn, 0.14 Fe, 0.101 Cr, 0.05 Ni, and 0.13 1 0, all in percentage weight with the balance consisting of zirconium. The plate was straight cold rolled by 42% in reduction to 0.32 cm in thickness followed by a stress relief heat treatment of 498’C for 3 h.
Sll
Sl2
s*3
0
0
0
s12
s22
s23
0
0
0
02
s13
s23
s33
0
0
0
03
e4
0
0
0
s44
0
0
04
E5
0
0
0
0
%5
0
Qs
.?6 -1
0
0
0
0
0
566,
El
f
f2 E3
=
-I’
fJ1
Lo6_,
Conventions used for reference directions are as folIows: (1) Normal direction (ND); (2) transverse direction (TD); and (3) longitudinal or rolling direction (RD). Mechanical method.
Two types of test specimens were used to obtain elastic coefficients. Uniform gage section specimens with 0.3 1 cm square cross section and 7.62 cm in gage length were pulled in tension’to obtain l/&i values. The initial strain rate was 2.78 X 1O-4/s* A sPecial extensometer assembly was built to measure components of strain in three principal directions of anisotropy to the accuracy of ?OS%. Elevated temperature tests were made in an Instron Box Furnace and only the axial strain was measured. In addition, an hourglass specimen with 2.54 cm radius and 0.3 1 cm diameter were tested to obtain l/Sij values. Diametral displacements along two principal axes of anisotropy were measured by two sets of extensometers while recording the load. Tests were made in a hydraulically-operated, close-loop MTS machine where the average diametral ~splacement rate was held constant so that the axial
Definitions
Using the convention that Hooke’s law can be stated as e=Su, where S is called the elastic compliance constant, or, by matrix notation and from symmet~ ar~ment, 345
W.R. Catlin et al. / Determination
346
Table 1 Experimentally MPa X lo3
measured elastic constants for Zircaloy-2, J-material; mean (x), standard deviation (Sx), standard error (Si)
Temperature (“C) 25
x
llS22
l/S33
l/S12
l/S13
ljs23
101.2
96.1
293.7(9) *
304.2(7) 16.3 6.1
280.7( 12) 13.9 4.0
17.6 5.9
Sx S,_ x
200
of elastic coefficients for Zivcaloy-2
88.8
_
273.0
_
222.6
79.1
70.7
252.5(10) 18.2
221.6(8) 15.7
187.8(14) 12.1
5.8
5.6
3.2
242.1(7) 22.6
198.3(6) 15.2
8.6
6.2
S, S,_ 350
x S, S,_
450
x
73.4
66.3
Sx S,_
171.4(11) 10.6 3.2
* Numbers in parentheses indicate sample size.
strain rate was comparable to that used in simple tension tests. Elevated temperature tests in the MTS machine was made by the induction heating method. Test results are summarized in table 1. Pole figure method. Elastic constants were determined by using the pole figure method as reported by Rosenbaum and Lewis [2]. The computing method consists of estimating the space average of the monocrystal compliance coefficients from the weighted crystallo-
OAIENTATIONPARAWE99, 'n fl
(00021PLANE 0.994 RO9l
graphic pole density and applying the experimentally determined elastic coefficients of zirconium. It is assumed that monocrystal data is applicable to Zircaloy-2. A detailed outline of the pole figure method is reported by Rosenbaum and Lewis [2]. Pole figures and orientation parameters obtained at one quarter thickness are summarized in fig. 1. Results of elastic constants obtained by both mechanical and pole figure methods are summarized in figs. 2 and 3 where the calculated values were obtained
t-NUYY99
(IOigLANE 6448 1.000
.*
l’/
_,,, 10
TEMPERATURE,
Fig. 1. (a) Normal direction pole figure of the (0002) plane and (b) one-quarter removed of schedule J, (lOTO) plane Zircaloy-2 sheet, heat 397598Q.
400
300
500
*C
Fig. 2. Comparison of calculated elastic modulus (l/Sa) with experimental data over a range of?emperatures, J-material, Zircaloy-2.
W.R. Catlin et al. /Determination of elastic coefficients for Zivcaloy-2
347
The predicted elastic coefficients are in excellent agreement with the experimental values making the method proposed by Rosenbaum and Lewis a practical alternative whenever experimental data is lacking for structural analysis method.
25--‘/sa
L”
0
0
-
loo 200 300 TEMPERATURE,
400
500
The authors wish to express their appreciation to Dr. H.S. Rosenbaum and Mr. J.E. Lewis for determining the elastic constants by pole figure method and to Electric Power Research Institute for providing the financial support for this work.
lC
Fig. 3. Comparison of calculated stiffness coefficients (-l/S$ with experimental data over a range of temperatures, J-material, Zircaloy-2.
References [II D. Lee, F. Zaverl, Jr., C.F. Shih and M.D. German, Fifth
from the pole figure method. Measured Young’s moduli values (fig. 2) agree with the predicted values within about 5% and E/v, or l/&i, values agree within about 3.5%.
Quarterly Report to Electric Power Research Institute, General Electric Corp. Research and Development Report, SRD-76-118, Sept., 1976, Schenectady, New York. 121 H.S. Rosenbaum and J.E. Lewis, Use of pole figure data to compute elasticity coefficients of zirconium sheet, J. Nucl. Mater., to be published.