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The hysteresis cycle modification in thermoelastic martensitic transformation of shape memory alloys
ScriptaMaterialia,Vol. 36, No. 11,pp. 1273-1278,1997 Elsevia ScienceLtd Cotwrizht0 1997AetaMetallumicaInc. printedin the USA.All rights”escrved 1359~6462/97 $17.00+ .00
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PI1 S1359-6462(97)00057-2
THE HYSTERESIS CYCLE MODIFICATION IN THXRMOELASTIC MARTENSITIC TRANSFORMATION OF SHAPE MEMORY ALLOYS G. Airoldi1p2,A. Corsi’ and G. Riva2># ’ Dipartimento di Fisica, Universiti di Milano, Via Celoria 16,20 133 Milano, Italia
2 Istituto Nazionale per la Fisica della Materia, Uniti di Milano, Via Celoria 16,20 133 Milano, Italia (Received October 8, 1996) (Accepted December 6, 1996) Introduction The thermoelastic martensitic transformation (TMT) in shape memory alloys (SMAs) is driven by an external field:, temperature or stress, which respectively at constant pressure or constant temperature induces the formation of martensite (1,2). In thermal induced transformations, the transformed l?action vs. temperature currently describes the progress of the transformation, whilst in stress induced transformations the transformation path is given by the stress vs. strain curve. The direct transformation, parent(P)-martensite( follows a path in the phase thermodynamic space which is never retraced in the reverse transformation M-P. It is well known that the direct and reverse transformations trace a loop in the thermodynamic phase space, known as the hysteresis cycle (3,4), which embodies one of the key features of SMAs: its existence is related to the different role played by the energy contributions active during the transformations. Whilst outside the hysteresis cycle the transformed fraction is a single valued function, inside it can be a multivalued function depending upon the specimen history, i.e. is path dependent. Wide experimental evidence, proving it, has already been obtained both related to stress induced transformations (5,6) and to thermal induced ones (6-10). In the second case the different weight played by the energy contributions in the reverse transformation respect to the direct one has been clearly shown in several systems where either one or a sequence of incomplete cycles on heating (ICH), performed in a ranking order, can evidence a fragmentation in the kinetics giving rise to the phenomenology named SMART (Step-wise Martensite to Austenite Reversible Transformation) (11,12). Though wide evidence has been collected on SMART and its generality in different systems has been proved (13,14), all the data (15-19) have been obtained on bulk material. The interest to use shape memory alloys in microdevices, due to their more favorable rate of response when increasing the
#now at Pirelli Coordinamento Pneumatici, Ricerca e Sviluppo Materiali, Viale Sarca 222,20126 Milano, Italia
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surface/volume ratio respect to the bulk state, stimulates to investigate the effect of ICH in shape memory alloy thin wires or films. In the following the modifications induced by incomplete cycling across TMT are presented both on SMA films and thin wires after performing either a single incomplete cycle, or a sequence of incomplete cycles with different arrest temperatures or even a sequence of incomplete cycles with the same arrest temperature named “HAMMER procedure” (18), with the aim to contrast the reversibility behavior with respect to the bulk material. Experimental All the examined specimens were submitted to a heat treatment, followed by an initial number N of complete cycles P-M in order to stabilize the transformation, as described in the following, and exclude side effects: l
l
l
NidsTi&us wires, heat treated at 723 K (3.6 ks) followed by water quenching, were selected to contrast the effects respect to a bulk material where one single transformation is present (B2<=>B 19’). In this case N= 20. nearly equiatomic NiTi thin wires2 (250 pm in diameter), as received, were heat treated at 823 K (1.8 ks) and submitted to N= 70 complete cycles. Ti-48.7at%Ni fihnd, 7p.m in thickness, solution treated at 973 K (3.6 ks) followed by water quenching, were submitted to N=lOO complete cycles.
The martensitic transformations were analyzed by means of Differential Scanning Calorimetry measurements (scan rate S”C/min) using a Perkin Elmer DSC 7 with a calorimetric sensitivity of &O.OlmW. The investigated temperatures ranged from -70°C to 100°C using the Perkin Elmer cooling system Intracooler II. Results
In Figs. 1, 2 the results related to a bulk specimen NissTi&ts are given. In the left hand side of Fig. 1 the heat flow detected on heating (reverse transformation B19’3B2) is given for: a) a stabilized specimen; b) after performing three incomplete cycles on heating, i.e. three (return points) single stops corresponding, in the previous reverse transformations, to respectively the 75, 50, 25% of the transformed fraction; the fragmentation of the heat flow is clearly evident on the SMART curve; c) the heat flow as it appears during the complete transformation subsequent to SMART. In the right hand side the transformed fraction, as deduced from the integration of the related heat flow curves, is given: the modification of the hysteresis cycle during SMART and its reversibility respect to the previous one are clearly evident. In Fig. 2b, at left, the effect of one single stop at 50% of the transformed fraction in the B19’ dB2 transformation appears as a dip in the heat flow of the subsequent complete transformation (SMART), dip which becomes more evident (HAMMER, Fig. 2c) when 6 stops at the same transformed fraction ’ Supplied by Furukawa EI.Co.,J. ‘Commercialized by Dynalloy Inc., Irvine, CA ,USA. 3Obtained by Prof. Miyamki, Tsukuba University,J.
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Figure 1. Heat flow during DSC heating on a Ni4sTiMCuSspecimen: a) stabilized specimen; b) during SMART after 3 ICHs at 75, 50 and 25% transformed fraction (the related temperatures are indicated by dots); c) during the complete transformation after SMART. In a’, b’ and c’ the complete hysteresis cycles related to a, b and c are plotted.
are performed: the formerly present kinetics is restored after either procedure proving the reversibility of the process. In Fig. 2, at right, the correspondent hysteresis cycles, as given by the transformed fraction, well show that the transformation kinetics undergoes an arrest more pronounced in the case of the HAMMER procedure in comparison to one single arrest SMART, nevertheless fully recovering the start kinetics. NiTi Thin Wires
A sequence of three single stops at respectively 75, 50, 25% of the transformed martensite fraction during the reverse B19’ dB2 transformation deeply modifies the transformation kinetics as shown in Fig. 3a, where the heat flow during SMART is given in comparison the heat flow of the previous reverse transformation. The kinetics of the transformation is well reset as it appears in Fig. 3b, on an enlarged scale, where the heat flow detected during the PostSMART is compared to the PreSMART transformation.
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Figure 2. Heat flow during DSC heating on a Ni4~Ti&u~ specimen: a) stabilized specimen; b) during SMART after 1 ICH at 50% transformed fisction (the related temperature is indicated by the dot); c) during HAMMER after 6 ICHs at 50% transformed fraction (the related temperature is indicated by the dot); d) during the complete transformation after SMART which coincides with the complete transformation at& HAMMER. In a’, b’, c’ and d’ the complete hysteresis cycles related to a, b, c and d are plotted.
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The branches of the hysteresis cycles during the reverse transformation, related to the same curves given in Fig. 3a,b, are plotted in Fig. 4a: the staircase transformed fraction during SMART well depicts the stops in the kinetics of transformation. The other curves in the same figure demonstrate the overall reversibility of the process. From the experimental data of the heat flow curves, the overheating detected during the SMART transformation is deduced calculating at each value of the transformed fraction, the temperature increase respect to the previous complete transformation: as depicted in Fig. 4b the overheating vs. the transformed fraction curve well shows a structure with three dips localized approximately at the transformed fraction values correspondent to the previous selected stops. NiTi Films Attention was focused on the comparison between the effect of an incomplete cycle arrested at 50% of the transformed fraction and that of a sequence of 7 arrests at the same transformed fraction. As it can be seen in Fig. 5a the kinetics of the SMART is deeply modified respect to the normal transformation, as found in bulk specimens: the kinetics, however, is not completely recovered during the first cycle after SMART (PostSMART transformation). Some complete cycles, 3+4 at least, are required to restore the original kinetics, as well shown in Fig. 5c. After performing a sequence of 7 arrests at the same transformed fraction (50%), the kinetics of the transformation is more deeply modified as shown both in Fig. 6a,b and in Fig. 7 where the branch at higher temperature of the hysteresis cycle is plotted, altogether with the overheating during the HAMMER transformation, compared to the normal one.
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2030405060m00 Te~pnhrr CC)
Figure 3. Heat flow during DSC heating on a NiTi thin wire: a) during SMART after 3 ICHs at 75, 50 and 25% transformed fraction (the related temperatures are indicated by dots) and during the previous complete cycle (plotted as a thin line); b) during the PreSMART and the PostSMART transformation,
Figure 4. a) Martensite fraction related to the curves given in Fig. 3. during the PreSMART, PostSMART and SMART transformation; b) Overheating of the SMART transformation compared to the PreSMART, plotted in a).
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Figure 5. Heat flow during DSC heating on a NiTi thin film: a) during SMART after 1 ICH at 50% transformed fraction (the related temperature is indicated by the dot) compared to the heat flow during the PreSMART transformation (plotted as a thin line); b) during the PreSMART and the PostSMART trans-formation. c) during the PreSMART transformation and the 3” cycle after SMART transformation.
Discussion
Figure 6. Heat flow during DSC heating on a NiTi thin film: a) during the transformation after a HAMMER procedure (7 ICHs at 50% transformed fraction: the related temperature is indicated by the dot); the heat flow during the PreSMART transformation is plotted (in thin line) for comparison; b) during the PreHAMMER and the PostHAMMER transformation. c) during the PreHAMMER transformation and the transformation related to the 20* cycle after HAMMER transformation.
and Conclusions
The results obtained on the SMART transformation performed either on NiTi thin wires or films, where the surface/volume ratio is respectively 5 or 100 times higher than in bulk material, show: l
l
l
l
The kinetics of the SMART transformation can be fragmented at will and the stops found in the heat flow correspond to the return points of the incomplete cycles; The stops found in the heat flow are more pronounced in the HAMMER procedure: nevertheless the heat flow, completely recovered after HAMMER in the bulk material and in thin wires, is not completely recovered in the case of films; Similarly to previous results on bulk material (14) high overheating corresponds to wide hysteresis transform ations; Overheating however exhibits a structure with maximum values correspondent to the percentage of transformation selected for the return points: this is clearly shown in the case of NiTi thin wires and films where a big change in the kinetics of transformation is found (see Fig. 7a).
The present results related to overheating neatly rule out the results obtained by other investigators (19) who claimed the presence of an undercooling. The lack of complete recovery of the transformation kinetics even after 20 complete cycles after HAMMER in NiTi films suggests some irreversible damage in the microstructure, may be dislocations
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Figure 7. a) Martensite fraction related to the curves given in Fig. 6a). during the PreHAMMER and HAMMER transformation; b) Overheating related to the HAMMER transformation in fig 7a); c) Martensite fraction related to the curves given in Fig. 6b). during the PreHAMMER and PostHAMMER transformation.
at the stop interfaces, has presumably been introduced by the ICH procedure: its nature is however unknown at present and requires further investigation. References 1. “Shape Memory Alloys” (edited by H. Funakubo), Gordon and Breach Science Publishers (1987). 2. “The Martensitic Transformation in Science and Technology” (edited by E. Hornbogen and N. Jost), DGM, Oberursel(1989). 3. L. Delay, J. Ortin, J. Van Humbeeck, in “Phase Transformations ‘87”, (edited by G.W. Lorimer), 60 (1987). 4. R.J. Salzbrenner, M. Cohen, Acta metall., 27,739 (1979). 5. 1. Muller, H. Xu, Actametall., 39,263 (1991). 6. K. Otsuka, C.M. Wayman, K. Nakai, H. Sakamoto, K. Shimizu, Acta metall., 24,207 (1976). 7. S. Miura, T. Mori, N. Nakanashi, Y. Murakami, S. Kachi, Philos. Mag., 34 (3), 337 (1976). 8. R.J. Wasilewski, Metall. Trans., 2,2973 (1971). 9. L. Kaufmann, M. Cohen, Prog. Met. Phys., 7,165 (1958). 10. A. Planes, J.L. Macqueron, J. Ortin, Phil. Mag. Len., 57,6,291 (1988). 11. G. Airoldi, G. Riva, in “The Martensitic Transformation in Science and Technology” (edited by E. Hombogen and N. Jost), p. 305, DGM, Oberursel(l989). 12. G. Airoldi, G. Riva, Key Engineering Materials, 48,5 (1990). 13. G. Airoldi, S. Besseghini, G. Riva, Proc. Int. Conf. on Martensitic Transf. ICOMAT-92 (edited by CM. Wayman and C. Perkins), 959, Monterrey Inst. of Adv. Studies, Cannel, CA, USA (1993). 14. G. Airoldi, S. Besseghini, G. Riva, Nuovo Cimento D, 15,2-3,365 (1993). 15. G. Airoldi, G. Carcano, G. Riva, J. Phys. IV, Coil. C4, 1,277 (1991). 16. G. Airoldi, S. Besseghini, G. Riva, J. Phys. IV, Coil. C2,5,483 (1995). 17. A. Amengual, Scripta Metall. Mater., 26,1795 (1992). 18. G. Airoldi, S. Besseghini, G. Riva, J. Physique IV, Coil. C8,5,877 (1995). 19. K. Madangopal, S. Banerjee, S. Lele, Acta metall. mater., 42,6, 1875 (1994).
Psrgamon
PI1 S1359-6462(97)00057-2
THE HYSTERESIS CYCLE MODIFICATION IN THXRMOELASTIC MARTENSITIC TRANSFORMATION OF SHAPE MEMORY ALLOYS G. Airoldi1p2,A. Corsi’ and G. Riva2># ’ Dipartimento di Fisica, Universiti di Milano, Via Celoria 16,20 133 Milano, Italia
2 Istituto Nazionale per la Fisica della Materia, Uniti di Milano, Via Celoria 16,20 133 Milano, Italia (Received October 8, 1996) (Accepted December 6, 1996) Introduction The thermoelastic martensitic transformation (TMT) in shape memory alloys (SMAs) is driven by an external field:, temperature or stress, which respectively at constant pressure or constant temperature induces the formation of martensite (1,2). In thermal induced transformations, the transformed l?action vs. temperature currently describes the progress of the transformation, whilst in stress induced transformations the transformation path is given by the stress vs. strain curve. The direct transformation, parent(P)-martensite( follows a path in the phase thermodynamic space which is never retraced in the reverse transformation M-P. It is well known that the direct and reverse transformations trace a loop in the thermodynamic phase space, known as the hysteresis cycle (3,4), which embodies one of the key features of SMAs: its existence is related to the different role played by the energy contributions active during the transformations. Whilst outside the hysteresis cycle the transformed fraction is a single valued function, inside it can be a multivalued function depending upon the specimen history, i.e. is path dependent. Wide experimental evidence, proving it, has already been obtained both related to stress induced transformations (5,6) and to thermal induced ones (6-10). In the second case the different weight played by the energy contributions in the reverse transformation respect to the direct one has been clearly shown in several systems where either one or a sequence of incomplete cycles on heating (ICH), performed in a ranking order, can evidence a fragmentation in the kinetics giving rise to the phenomenology named SMART (Step-wise Martensite to Austenite Reversible Transformation) (11,12). Though wide evidence has been collected on SMART and its generality in different systems has been proved (13,14), all the data (15-19) have been obtained on bulk material. The interest to use shape memory alloys in microdevices, due to their more favorable rate of response when increasing the
#now at Pirelli Coordinamento Pneumatici, Ricerca e Sviluppo Materiali, Viale Sarca 222,20126 Milano, Italia
1273
1274
THE HYSTERESISCYCLEMODIFICATION
Vol. 36, No. 11
surface/volume ratio respect to the bulk state, stimulates to investigate the effect of ICH in shape memory alloy thin wires or films. In the following the modifications induced by incomplete cycling across TMT are presented both on SMA films and thin wires after performing either a single incomplete cycle, or a sequence of incomplete cycles with different arrest temperatures or even a sequence of incomplete cycles with the same arrest temperature named “HAMMER procedure” (18), with the aim to contrast the reversibility behavior with respect to the bulk material. Experimental All the examined specimens were submitted to a heat treatment, followed by an initial number N of complete cycles P-M in order to stabilize the transformation, as described in the following, and exclude side effects: l
l
l
NidsTi&us wires, heat treated at 723 K (3.6 ks) followed by water quenching, were selected to contrast the effects respect to a bulk material where one single transformation is present (B2<=>B 19’). In this case N= 20. nearly equiatomic NiTi thin wires2 (250 pm in diameter), as received, were heat treated at 823 K (1.8 ks) and submitted to N= 70 complete cycles. Ti-48.7at%Ni fihnd, 7p.m in thickness, solution treated at 973 K (3.6 ks) followed by water quenching, were submitted to N=lOO complete cycles.
The martensitic transformations were analyzed by means of Differential Scanning Calorimetry measurements (scan rate S”C/min) using a Perkin Elmer DSC 7 with a calorimetric sensitivity of &O.OlmW. The investigated temperatures ranged from -70°C to 100°C using the Perkin Elmer cooling system Intracooler II. Results
In Figs. 1, 2 the results related to a bulk specimen NissTi&ts are given. In the left hand side of Fig. 1 the heat flow detected on heating (reverse transformation B19’3B2) is given for: a) a stabilized specimen; b) after performing three incomplete cycles on heating, i.e. three (return points) single stops corresponding, in the previous reverse transformations, to respectively the 75, 50, 25% of the transformed fraction; the fragmentation of the heat flow is clearly evident on the SMART curve; c) the heat flow as it appears during the complete transformation subsequent to SMART. In the right hand side the transformed fraction, as deduced from the integration of the related heat flow curves, is given: the modification of the hysteresis cycle during SMART and its reversibility respect to the previous one are clearly evident. In Fig. 2b, at left, the effect of one single stop at 50% of the transformed fraction in the B19’ dB2 transformation appears as a dip in the heat flow of the subsequent complete transformation (SMART), dip which becomes more evident (HAMMER, Fig. 2c) when 6 stops at the same transformed fraction ’ Supplied by Furukawa EI.Co.,J. ‘Commercialized by Dynalloy Inc., Irvine, CA ,USA. 3Obtained by Prof. Miyamki, Tsukuba University,J.
Vol. 36, No. 1 I
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Figure 1. Heat flow during DSC heating on a Ni4sTiMCuSspecimen: a) stabilized specimen; b) during SMART after 3 ICHs at 75, 50 and 25% transformed fraction (the related temperatures are indicated by dots); c) during the complete transformation after SMART. In a’, b’ and c’ the complete hysteresis cycles related to a, b and c are plotted.
are performed: the formerly present kinetics is restored after either procedure proving the reversibility of the process. In Fig. 2, at right, the correspondent hysteresis cycles, as given by the transformed fraction, well show that the transformation kinetics undergoes an arrest more pronounced in the case of the HAMMER procedure in comparison to one single arrest SMART, nevertheless fully recovering the start kinetics. NiTi Thin Wires
A sequence of three single stops at respectively 75, 50, 25% of the transformed martensite fraction during the reverse B19’ dB2 transformation deeply modifies the transformation kinetics as shown in Fig. 3a, where the heat flow during SMART is given in comparison the heat flow of the previous reverse transformation. The kinetics of the transformation is well reset as it appears in Fig. 3b, on an enlarged scale, where the heat flow detected during the PostSMART is compared to the PreSMART transformation.
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Figure 2. Heat flow during DSC heating on a Ni4~Ti&u~ specimen: a) stabilized specimen; b) during SMART after 1 ICH at 50% transformed fisction (the related temperature is indicated by the dot); c) during HAMMER after 6 ICHs at 50% transformed fraction (the related temperature is indicated by the dot); d) during the complete transformation after SMART which coincides with the complete transformation at& HAMMER. In a’, b’, c’ and d’ the complete hysteresis cycles related to a, b, c and d are plotted.
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The branches of the hysteresis cycles during the reverse transformation, related to the same curves given in Fig. 3a,b, are plotted in Fig. 4a: the staircase transformed fraction during SMART well depicts the stops in the kinetics of transformation. The other curves in the same figure demonstrate the overall reversibility of the process. From the experimental data of the heat flow curves, the overheating detected during the SMART transformation is deduced calculating at each value of the transformed fraction, the temperature increase respect to the previous complete transformation: as depicted in Fig. 4b the overheating vs. the transformed fraction curve well shows a structure with three dips localized approximately at the transformed fraction values correspondent to the previous selected stops. NiTi Films Attention was focused on the comparison between the effect of an incomplete cycle arrested at 50% of the transformed fraction and that of a sequence of 7 arrests at the same transformed fraction. As it can be seen in Fig. 5a the kinetics of the SMART is deeply modified respect to the normal transformation, as found in bulk specimens: the kinetics, however, is not completely recovered during the first cycle after SMART (PostSMART transformation). Some complete cycles, 3+4 at least, are required to restore the original kinetics, as well shown in Fig. 5c. After performing a sequence of 7 arrests at the same transformed fraction (50%), the kinetics of the transformation is more deeply modified as shown both in Fig. 6a,b and in Fig. 7 where the branch at higher temperature of the hysteresis cycle is plotted, altogether with the overheating during the HAMMER transformation, compared to the normal one.
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I
2030405060m00 Te~pnhrr CC)
Figure 3. Heat flow during DSC heating on a NiTi thin wire: a) during SMART after 3 ICHs at 75, 50 and 25% transformed fraction (the related temperatures are indicated by dots) and during the previous complete cycle (plotted as a thin line); b) during the PreSMART and the PostSMART transformation,
Figure 4. a) Martensite fraction related to the curves given in Fig. 3. during the PreSMART, PostSMART and SMART transformation; b) Overheating of the SMART transformation compared to the PreSMART, plotted in a).
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Figure 5. Heat flow during DSC heating on a NiTi thin film: a) during SMART after 1 ICH at 50% transformed fraction (the related temperature is indicated by the dot) compared to the heat flow during the PreSMART transformation (plotted as a thin line); b) during the PreSMART and the PostSMART trans-formation. c) during the PreSMART transformation and the 3” cycle after SMART transformation.
Discussion
Figure 6. Heat flow during DSC heating on a NiTi thin film: a) during the transformation after a HAMMER procedure (7 ICHs at 50% transformed fraction: the related temperature is indicated by the dot); the heat flow during the PreSMART transformation is plotted (in thin line) for comparison; b) during the PreHAMMER and the PostHAMMER transformation. c) during the PreHAMMER transformation and the transformation related to the 20* cycle after HAMMER transformation.
and Conclusions
The results obtained on the SMART transformation performed either on NiTi thin wires or films, where the surface/volume ratio is respectively 5 or 100 times higher than in bulk material, show: l
l
l
l
The kinetics of the SMART transformation can be fragmented at will and the stops found in the heat flow correspond to the return points of the incomplete cycles; The stops found in the heat flow are more pronounced in the HAMMER procedure: nevertheless the heat flow, completely recovered after HAMMER in the bulk material and in thin wires, is not completely recovered in the case of films; Similarly to previous results on bulk material (14) high overheating corresponds to wide hysteresis transform ations; Overheating however exhibits a structure with maximum values correspondent to the percentage of transformation selected for the return points: this is clearly shown in the case of NiTi thin wires and films where a big change in the kinetics of transformation is found (see Fig. 7a).
The present results related to overheating neatly rule out the results obtained by other investigators (19) who claimed the presence of an undercooling. The lack of complete recovery of the transformation kinetics even after 20 complete cycles after HAMMER in NiTi films suggests some irreversible damage in the microstructure, may be dislocations
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Figure 7. a) Martensite fraction related to the curves given in Fig. 6a). during the PreHAMMER and HAMMER transformation; b) Overheating related to the HAMMER transformation in fig 7a); c) Martensite fraction related to the curves given in Fig. 6b). during the PreHAMMER and PostHAMMER transformation.
at the stop interfaces, has presumably been introduced by the ICH procedure: its nature is however unknown at present and requires further investigation. References 1. “Shape Memory Alloys” (edited by H. Funakubo), Gordon and Breach Science Publishers (1987). 2. “The Martensitic Transformation in Science and Technology” (edited by E. Hornbogen and N. Jost), DGM, Oberursel(1989). 3. L. Delay, J. Ortin, J. Van Humbeeck, in “Phase Transformations ‘87”, (edited by G.W. Lorimer), 60 (1987). 4. R.J. Salzbrenner, M. Cohen, Acta metall., 27,739 (1979). 5. 1. Muller, H. Xu, Actametall., 39,263 (1991). 6. K. Otsuka, C.M. Wayman, K. Nakai, H. Sakamoto, K. Shimizu, Acta metall., 24,207 (1976). 7. S. Miura, T. Mori, N. Nakanashi, Y. Murakami, S. Kachi, Philos. Mag., 34 (3), 337 (1976). 8. R.J. Wasilewski, Metall. Trans., 2,2973 (1971). 9. L. Kaufmann, M. Cohen, Prog. Met. Phys., 7,165 (1958). 10. A. Planes, J.L. Macqueron, J. Ortin, Phil. Mag. Len., 57,6,291 (1988). 11. G. Airoldi, G. Riva, in “The Martensitic Transformation in Science and Technology” (edited by E. Hombogen and N. Jost), p. 305, DGM, Oberursel(l989). 12. G. Airoldi, G. Riva, Key Engineering Materials, 48,5 (1990). 13. G. Airoldi, S. Besseghini, G. Riva, Proc. Int. Conf. on Martensitic Transf. ICOMAT-92 (edited by CM. Wayman and C. Perkins), 959, Monterrey Inst. of Adv. Studies, Cannel, CA, USA (1993). 14. G. Airoldi, S. Besseghini, G. Riva, Nuovo Cimento D, 15,2-3,365 (1993). 15. G. Airoldi, G. Carcano, G. Riva, J. Phys. IV, Coil. C4, 1,277 (1991). 16. G. Airoldi, S. Besseghini, G. Riva, J. Phys. IV, Coil. C2,5,483 (1995). 17. A. Amengual, Scripta Metall. Mater., 26,1795 (1992). 18. G. Airoldi, S. Besseghini, G. Riva, J. Physique IV, Coil. C8,5,877 (1995). 19. K. Madangopal, S. Banerjee, S. Lele, Acta metall. mater., 42,6, 1875 (1994).