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Direct determination of the dilatation parameter for martensite in a CuAlNi shape memory alloy
Scripta METALLURGICA
Vol. 19, pp. 661-664, 1985 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved
DIRECT DETERMINATIONOF THE DILATATION PARAMETERFOR MARTENSITEIN A Cu-AI-Ni SHAPE MEMORYALLOY
N.F. Kennon, D.P. Dunne and L.A. Middleton The University of Wollongong, Wollongong, N.S.W., Australia (Received
February
28, 1985)
Introduction In a recent publication ( I ) , shape strains associated with the formation of thermallyinduced and stress-induced martensite were reported for a Cu-AI-Ni shape memory alloy. There was no significant difference between the two shape strains, which had habit planes near (331)B, displacement vectors near [110]B, magnitudes of about 0.087 and dilatation parameters close to unity. Solutions for the habit plane and direction and magnitude of the displacement vector were obtained d i r e c t l y from experimental measurements using several accurate analytical methods. On the other hand, the dilatation parameters were not determined d i r e c t l y , but from the requirement that the determinant of the shape strain be identical with the volume ratio calculated from l a t t i c e parameters measured by x-ray d i f f r a c t i o n . Thus, the dilatation was used as a parameter that was adjusted to ensure that the experimental data were self-consistent. Nevertheless, the value was consistently found to be indistinguishable from unity. Originally, the dilatation was introduced into the crystallographic theory of martensitic transformations (2,3) to provide for possible small changes in the length of vectors lying in the habit plane. Direct measurements of such changes are usually exceedingly d i f f i c u l t with the consequence that only one determination has been reported. Krauklis and Bowles (4) compared the lengths of lines in the (225) A habit planes of martensite in an Fe-Cr-C alloy with the corresponding lengths in the austenite before transformation. The lengths were measured from etch pits on p a r t i a l l y transformed specimens and on dimensionally stable replicas prepared from the original untransformed austenite. Their results indicated that the change in length was less than about 0.2% and probably zero for the transformation they examined. In the work described in this paper, a method similar to that used by Krauklis and Bowles was developed to make direct measurements of the dilatation parameter for both thermally-induced and stress-induced martensite in the same Cu-AI-Ni shape memory alloy used for the previous shape strain measurements (1). Experimental Methods and Results Material A nominal Cu-14% AI-3.4% Ni alloy was prepared by induction melting and single crystals were grown from pieces of the alloy using the soft mold Bridgeman method (see 5). For this particular alloy M:
661 0036-9748/85 $3.00 + .00 Copyright (c) 1985 Pergamon Press Ltd.
662
MARTENSITE
IN SHAPE MEMORY ALLOY
Vol.
19, No. 5
FIG.1 Photomicrographs showing (a) a plate of thermally-induced y~' martensite, and (b) the same f i e l d after reversion of the martensite to the Bz phase; electropolished in chromic-phosphoric acids; unetched.
Yz' martensite back to the original B~ structure and, after cooling to room temperature, the same f i e l d was re-photographed (negative B) under identical conditions (Figs.l,2). Negative A was searched to find two etch pits located in the martensite plate on a line x as closely parallel to the trace of the habit plane as possible and with separation LM as large as possible. Pairs of etch pits on either side of the plate were selected to define lines y,z adjacent to and closely parallel to the trace of the habit plane and with respective separations L~, L2 about the same as LM. Negative B was then searched to find the same six etch pits to define the separation LB, L3, L4 of the pits on the respective lines x,y,z. The linear separations of the three sets of etch pits were measured from each negative using a high precision Swift-Mitutoyo travelling microscope. The lengths of lines measured in the Bz phase in the presence of the martensite (L~, L2) and after reversion of the martensite (L3, L,) were used to compensate for any linear strain in the 8~ induced by
FIG.2 Photomicrographs showing (a) a plate of stress-induced y~' martensite, and (b) the same f i e l d after reversion of the martensite to the B~ phase; electropolished in chromic-phosphoric acids; unetched.
Vol.
19, No.
5
MARTENSITE
IN SHAPE M E M O R Y ALLOY
formation of the plate and to correct for any variations in dimensional changes of the photographic f i l m during processing. Estimates, 61, 62 of the dilatation parameter were made using corrections obtained from each of the lines y and z: LM L3 61 = LB LI
62
LM L, LB L2
Values of 61 and 62 for thirteen thermally induced and ten stress-induced plates are given in Table 1. TABLE 1 Direct Estimates of the Dilatation Parameter Thermally-induced plates 61 62 1.0004 .9996 1.0009 .9961 1.0013 .9982 1.0011 1.0004 .9986 .9986 .9973 .9985 .9985
Stress-induced plates 61 62
.9994 .9966 1.0036 .9986 .9997 .9982 1.0008 .9984 .9991 .9961 .9982 .9991 .9977
Average .9990
.9997 1.0011 .9979 .9929* .9985 .9983 .9995 .9998 .9973 1.0014
.9972 1.0013 .9971 .9910" .9997 .9987 .9998 .9977 .9978 1.0016
Average .9991
*measurements which d i f f e r e d from unity by more than .4% Discussion Before considering the significance of the results l i s t e d in Table 1, i t is necessary to estimate the accuracy with which the dilatation parameters were determined. There were two principal sources of error in the experimental procedure. Systematic errors of about +.2% were associated with measurements of the lengths LM, LB, LI, L2, Ls, L~ and were due mainly to the etch pits being larger than the ideal size for high precision measurement (see 4). I t did not seem possible to reduce the size of the pits by adjustment of the e l e c t r o l y t i c etching parameters. The second source of error was associated with the selection of the pits to define the line x in the martensite plate and as closely parallel to the habit plane trace as possible. I f this line happened to l i e 10 out of the habit plane, the mean invariant plane strain determined for the alloy by Kennon and Dunne ( I ) shows that i t would be changed in length by .17%. I t is considered that in unfavourable cases the size of the etch pits could result in an error of about this magnitude. Thus the combined errors from both sources suggest that i t is doubtful whether significance can be attached to dilatation measurements that d i f f e r from unity by less than about .4%. Only two of the measured dilatation parameters d i f f e r from unity by mere than .4% and, as shown in Table 1, both were estimates made on the same stress-induced plate. No explanation can be offered for this odd result except the p o s s i b i l i t y that one of the etch pits defining the line x may have been incorrectly i d e n t i f i e d in Negative B. As a l l measurements of the d i l a t a t i o n , other than the two odd results just mentioned, d i f f e r from unity by less than the l i k e l y experimental error, i t is concluded that the parameter is not s i g n i f i c a n t l y d i f f e r e n t from unity for both the thermally-induced and stress-induced martensite in the Cu-AI-Ni alloy used in this work. This conclusion is strengthened by detailed comparison of the present results with those obtained by Krauklis and Bowles (4). They concluded that the dilatation parameter was unity for Fe-Cr-C but estimated t h e i r experimental error to be only +-.2%. Nothwithstanding
663
664
MARTENSITE
IN SHAPE MEMORY ALLOY
Vol.
19, No.
S
the apparent higher precision of t h e i r work, t h e i r detailed results and the present results given in Table 1 are very similar, as shown by the distributions of measurements given in Table 2. TABLE 2 Distributions of Dilatation Parameter Measurements Fraction of Reported Measurements KB(a)
KB(b)
.04 .11 .71 .11 .04
.02 .04 .07 .21 .30 .18 .13 .04 .02 .02
1.004 1.003 1.002 1.001.999 .998 .997 .996 .995 .994 -
1.005 1.004 1.003 1.002 1.001 .999 .998 .997 .996 .995
KB(a)
Krauklis & Bowles (4):
KB(b)
Krauklis & Bowles (4):
KDM(a) present work KDM(b) present work
: :
KDM(c) present work
:
KDM(a)
KDM(b)
.04 .08 .27 .35 .12 .12 .04
KDM(c) .02
.22 .28 .17 .33
.14 .27 .27 .20 .07 .02
Average values calculated from t h e i r Table 2 Values calculated for least favourable combination of errors given in their Table 2 Thermally-induced martensite Stress-induced martensite (two odd values ignored) Combinedthermally-induced and stressinduced martensi te
The conclusion that the present direct measurements are consistent with a dilatation parameter of unity confirms the result reported previously by Kennon and Dunne (1). As that result was obtained by adjusting the dilatation parameter to secure self-consistency of the experimental measurements i t can now be concluded that those measurements were s e l f consistent and, indeed, highly accurate. Thus for both thermally-induced and stress-induced martensite in Cu-AI-Ni the shape strains are exactly invariant plane strains with the same crystallographic elements, as indicated by the previous work ( I ) . Conclusion The direct measurements that have been made for a Cu-AI-Ni shape memory alloy show that the changes in length upon thermally-induced or stress-induced transformation, of lines lying in the habit plane of the 2H orthorhombic YI' martensite, are less than .4% and probably zero. These results confirm previously reported, but indirect measurements of the dilatation parameter and support the conclusion that the two kinds of martensite are indi stingui shable. AcknowledgementS This work was supported by a grant from the Australian Research Grants Scheme. References 1. 2. 3. 4. 5.
N.F. Kennon and D.P. Dunne, Acta Metall. 30, 429 (1982). J.S. Bowles and J.K. Mackenzie, Acta Metall. 2, 129 (1954). J.K. Mackenzie and J.S. Bowles, Acta Metall. 2, 138 (1954). P. Krauklis and J.S. Bowles, Acta Metall. 17, 997 (1969). K. Otsuka, C.M. Wayman, K. Nakai, H. Sukamoto and K. Shimizu, Acta Metall. 24, 207 (1976).
Vol. 19, pp. 661-664, 1985 Printed in the U.S.A.
Pergamon Press Ltd. All rights reserved
DIRECT DETERMINATIONOF THE DILATATION PARAMETERFOR MARTENSITEIN A Cu-AI-Ni SHAPE MEMORYALLOY
N.F. Kennon, D.P. Dunne and L.A. Middleton The University of Wollongong, Wollongong, N.S.W., Australia (Received
February
28, 1985)
Introduction In a recent publication ( I ) , shape strains associated with the formation of thermallyinduced and stress-induced martensite were reported for a Cu-AI-Ni shape memory alloy. There was no significant difference between the two shape strains, which had habit planes near (331)B, displacement vectors near [110]B, magnitudes of about 0.087 and dilatation parameters close to unity. Solutions for the habit plane and direction and magnitude of the displacement vector were obtained d i r e c t l y from experimental measurements using several accurate analytical methods. On the other hand, the dilatation parameters were not determined d i r e c t l y , but from the requirement that the determinant of the shape strain be identical with the volume ratio calculated from l a t t i c e parameters measured by x-ray d i f f r a c t i o n . Thus, the dilatation was used as a parameter that was adjusted to ensure that the experimental data were self-consistent. Nevertheless, the value was consistently found to be indistinguishable from unity. Originally, the dilatation was introduced into the crystallographic theory of martensitic transformations (2,3) to provide for possible small changes in the length of vectors lying in the habit plane. Direct measurements of such changes are usually exceedingly d i f f i c u l t with the consequence that only one determination has been reported. Krauklis and Bowles (4) compared the lengths of lines in the (225) A habit planes of martensite in an Fe-Cr-C alloy with the corresponding lengths in the austenite before transformation. The lengths were measured from etch pits on p a r t i a l l y transformed specimens and on dimensionally stable replicas prepared from the original untransformed austenite. Their results indicated that the change in length was less than about 0.2% and probably zero for the transformation they examined. In the work described in this paper, a method similar to that used by Krauklis and Bowles was developed to make direct measurements of the dilatation parameter for both thermally-induced and stress-induced martensite in the same Cu-AI-Ni shape memory alloy used for the previous shape strain measurements (1). Experimental Methods and Results Material A nominal Cu-14% AI-3.4% Ni alloy was prepared by induction melting and single crystals were grown from pieces of the alloy using the soft mold Bridgeman method (see 5). For this particular alloy M:
661 0036-9748/85 $3.00 + .00 Copyright (c) 1985 Pergamon Press Ltd.
662
MARTENSITE
IN SHAPE MEMORY ALLOY
Vol.
19, No. 5
FIG.1 Photomicrographs showing (a) a plate of thermally-induced y~' martensite, and (b) the same f i e l d after reversion of the martensite to the Bz phase; electropolished in chromic-phosphoric acids; unetched.
Yz' martensite back to the original B~ structure and, after cooling to room temperature, the same f i e l d was re-photographed (negative B) under identical conditions (Figs.l,2). Negative A was searched to find two etch pits located in the martensite plate on a line x as closely parallel to the trace of the habit plane as possible and with separation LM as large as possible. Pairs of etch pits on either side of the plate were selected to define lines y,z adjacent to and closely parallel to the trace of the habit plane and with respective separations L~, L2 about the same as LM. Negative B was then searched to find the same six etch pits to define the separation LB, L3, L4 of the pits on the respective lines x,y,z. The linear separations of the three sets of etch pits were measured from each negative using a high precision Swift-Mitutoyo travelling microscope. The lengths of lines measured in the Bz phase in the presence of the martensite (L~, L2) and after reversion of the martensite (L3, L,) were used to compensate for any linear strain in the 8~ induced by
FIG.2 Photomicrographs showing (a) a plate of stress-induced y~' martensite, and (b) the same f i e l d after reversion of the martensite to the B~ phase; electropolished in chromic-phosphoric acids; unetched.
Vol.
19, No.
5
MARTENSITE
IN SHAPE M E M O R Y ALLOY
formation of the plate and to correct for any variations in dimensional changes of the photographic f i l m during processing. Estimates, 61, 62 of the dilatation parameter were made using corrections obtained from each of the lines y and z: LM L3 61 = LB LI
62
LM L, LB L2
Values of 61 and 62 for thirteen thermally induced and ten stress-induced plates are given in Table 1. TABLE 1 Direct Estimates of the Dilatation Parameter Thermally-induced plates 61 62 1.0004 .9996 1.0009 .9961 1.0013 .9982 1.0011 1.0004 .9986 .9986 .9973 .9985 .9985
Stress-induced plates 61 62
.9994 .9966 1.0036 .9986 .9997 .9982 1.0008 .9984 .9991 .9961 .9982 .9991 .9977
Average .9990
.9997 1.0011 .9979 .9929* .9985 .9983 .9995 .9998 .9973 1.0014
.9972 1.0013 .9971 .9910" .9997 .9987 .9998 .9977 .9978 1.0016
Average .9991
*measurements which d i f f e r e d from unity by more than .4% Discussion Before considering the significance of the results l i s t e d in Table 1, i t is necessary to estimate the accuracy with which the dilatation parameters were determined. There were two principal sources of error in the experimental procedure. Systematic errors of about +.2% were associated with measurements of the lengths LM, LB, LI, L2, Ls, L~ and were due mainly to the etch pits being larger than the ideal size for high precision measurement (see 4). I t did not seem possible to reduce the size of the pits by adjustment of the e l e c t r o l y t i c etching parameters. The second source of error was associated with the selection of the pits to define the line x in the martensite plate and as closely parallel to the habit plane trace as possible. I f this line happened to l i e 10 out of the habit plane, the mean invariant plane strain determined for the alloy by Kennon and Dunne ( I ) shows that i t would be changed in length by .17%. I t is considered that in unfavourable cases the size of the etch pits could result in an error of about this magnitude. Thus the combined errors from both sources suggest that i t is doubtful whether significance can be attached to dilatation measurements that d i f f e r from unity by less than about .4%. Only two of the measured dilatation parameters d i f f e r from unity by mere than .4% and, as shown in Table 1, both were estimates made on the same stress-induced plate. No explanation can be offered for this odd result except the p o s s i b i l i t y that one of the etch pits defining the line x may have been incorrectly i d e n t i f i e d in Negative B. As a l l measurements of the d i l a t a t i o n , other than the two odd results just mentioned, d i f f e r from unity by less than the l i k e l y experimental error, i t is concluded that the parameter is not s i g n i f i c a n t l y d i f f e r e n t from unity for both the thermally-induced and stress-induced martensite in the Cu-AI-Ni alloy used in this work. This conclusion is strengthened by detailed comparison of the present results with those obtained by Krauklis and Bowles (4). They concluded that the dilatation parameter was unity for Fe-Cr-C but estimated t h e i r experimental error to be only +-.2%. Nothwithstanding
663
664
MARTENSITE
IN SHAPE MEMORY ALLOY
Vol.
19, No.
S
the apparent higher precision of t h e i r work, t h e i r detailed results and the present results given in Table 1 are very similar, as shown by the distributions of measurements given in Table 2. TABLE 2 Distributions of Dilatation Parameter Measurements Fraction of Reported Measurements KB(a)
KB(b)
.04 .11 .71 .11 .04
.02 .04 .07 .21 .30 .18 .13 .04 .02 .02
1.004 1.003 1.002 1.001.999 .998 .997 .996 .995 .994 -
1.005 1.004 1.003 1.002 1.001 .999 .998 .997 .996 .995
KB(a)
Krauklis & Bowles (4):
KB(b)
Krauklis & Bowles (4):
KDM(a) present work KDM(b) present work
: :
KDM(c) present work
:
KDM(a)
KDM(b)
.04 .08 .27 .35 .12 .12 .04
KDM(c) .02
.22 .28 .17 .33
.14 .27 .27 .20 .07 .02
Average values calculated from t h e i r Table 2 Values calculated for least favourable combination of errors given in their Table 2 Thermally-induced martensite Stress-induced martensite (two odd values ignored) Combinedthermally-induced and stressinduced martensi te
The conclusion that the present direct measurements are consistent with a dilatation parameter of unity confirms the result reported previously by Kennon and Dunne (1). As that result was obtained by adjusting the dilatation parameter to secure self-consistency of the experimental measurements i t can now be concluded that those measurements were s e l f consistent and, indeed, highly accurate. Thus for both thermally-induced and stress-induced martensite in Cu-AI-Ni the shape strains are exactly invariant plane strains with the same crystallographic elements, as indicated by the previous work ( I ) . Conclusion The direct measurements that have been made for a Cu-AI-Ni shape memory alloy show that the changes in length upon thermally-induced or stress-induced transformation, of lines lying in the habit plane of the 2H orthorhombic YI' martensite, are less than .4% and probably zero. These results confirm previously reported, but indirect measurements of the dilatation parameter and support the conclusion that the two kinds of martensite are indi stingui shable. AcknowledgementS This work was supported by a grant from the Australian Research Grants Scheme. References 1. 2. 3. 4. 5.
N.F. Kennon and D.P. Dunne, Acta Metall. 30, 429 (1982). J.S. Bowles and J.K. Mackenzie, Acta Metall. 2, 129 (1954). J.K. Mackenzie and J.S. Bowles, Acta Metall. 2, 138 (1954). P. Krauklis and J.S. Bowles, Acta Metall. 17, 997 (1969). K. Otsuka, C.M. Wayman, K. Nakai, H. Sukamoto and K. Shimizu, Acta Metall. 24, 207 (1976).