Distinction between Thermal and Stress-Induced Martensitic Transformations and Inhomogeneity in Internal Stress

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1 Material Tranaction, Vol. 43, No. 9 (2002) pp to 2255 c 2002 The Japan Intitute of Metal Ditinction between Thermal and Stre-Induced Martenitic Tranformation and Inhomogeneity in Internal Stre Hidekazu Sakamoto Department of Aeropace Engineering, School of Science and Engineering, Teikyo Univerity, Utunomiya , Japan A concept of inhomogeneou internal tre called hape change tre (SCS) wa introduced in martenitic tranformation (MT). The SCS wa conidered to be required becaue martenite plate formed on cooling mut deform the urrounding untranformed parent. The concept enabled ucceful elucidation of the reaon for the progre of thermally induced MT (TIMT) with changing temperature and for that of tre-induced MT (SIMT) under contant tre on the bai of the Gibb phae rule. Decreaing SCS with decreaing pecimen ize (ma) explained the downward hift of experimental equilibrium temperature To = (M + A f )/2 with decreaing pecimen ma m o far oberved in the TIMT of ome hape memory alloy. Furthermore, the concept that no SCS i generated either in SIMT or at the ultimate end of m = 0 in TIMT rationalized the following obervation on a monocrytalline Cu 13.4Al 4.2Ni (ma%) alloy. That i, the variation of M and M f with m converged at the extrapolation to m = 0, and thoe of A and A f alo did; M # = M # f and A # = A# f (the upercript # indicate the tranformation temperature at the ultimate end of m = 0). The former coincided with T L (0) where the dependence of tranformation tre σ L on temperature wa extrapolated to tre zero, and the latter coincided with T U (0) where a imilar extrapolation in the cae of revere tranformation tre σ U wa performed. (Received February 28, 2002; Accepted July 10, 2002) Keyword: hape memory alloy, tranformation temperature, tranformation tre, experimental equilibrium temperature, Gibb phae rule, hape change tre, elatic back tre, pecimen ize effect 1. Introduction Martenitic tranformation (MT) are induced not only by cooling ome kind of alloy below the MT tart temperature M but alo by the application of external tre above M. Upon comparing the characteritic of thermally induced MT (TIMT) with thoe of tre-induced MT (SIMT), it i evident that a paradox arie between them, which i decribed a follow. The progre of TIMT occur with changing temperature; tranformation on cooling proceed in the temperature range from M to M f, and their revere tranformation on heating proceed from A to A f. That i, the amount of thermally induced martenite i a function of temperature. Uually, thee temperature range where tranformation and their reverion take place are not mall but are omewhat extended, for example, from everal degree to ome ten of degree in thermoelatic MT. In contrat, SIMT in monocrytalline pecimen 1, 2) and even in polycrytalline one in a Ti Ni alloy ytem 3) progre in a different manner from TIMT. That i, tranformation on loading proceed under an almot contant tre σ L and their revere tranformation on unloading alo proceed under a different almot contant tre σ U. Stre-train (-) curve how almot plateau region during tranformation and their reverion; that i, tre range where tranformation and their reverion take place are rather mall. In other word, the MT tart tre on loading, σ L, i equal or nearly equal to the MT finih tre, σ f L, and the cae for revere tranformation tart and finih tree i almot the ame. That i, the amount of tre-induced martenite i a function of train. The contrat between TIMT and SIMT decribed above i clearly een in Fig. 1. It how a differential canning calorimetry (DSC) curve aociated with the TIMT of a pec- Fig. 1 Diagram howing the contrat between TIMT and SIMT in a Cu 13.4Al 4.2Ni (ma%) alloy ingle crytal; (a) a DSC curve of a pecimen with ma of mg, and (b) a tenile - curve at 453 K. imen with ma of mg, (a), and a tenile - curve aociated with the SIMT at 453 K, (b), of a Cu 13.4Al 4.2Ni 4, 5) (ma%) alloy ingle crytal. Obviouly, mall tre range of tranformation in SIMT make a harp contrat with omewhat extended temperature range of tranformation in TIMT. Thee phenomena are known to mot of reearcher in thi field, but it appear that no one ha dicovered any problem. Therefore, the origin of the differing behavior between TIMT and SIMT ha not been elucidated yet. Another ditinction i alo oberved between them. That i, in TIMT, pecimen remain almot unchanged in term of their hape a a whole. Meanwhile, in SIMT, macrocopic

2 2250 H. Sakamoto hape change of pecimen, uch a elongation under tenile tre, take place. Incidentally, in SIMT, critical tre for inducing a martenite phae on loading, σ L, linearly increae with increaing tet temperature. The Clauiu-Clapeyron equation well explain the linear dependence of σ L on temperature, dσ L /dt. Here, let T L (0) repreent the temperature where dσ L /dt i extrapolated to tre zero. The temperature T L (0) ha been reported to agree with M oberved when tenile 2, 6 8) pecimen were cooled in ome hape memory alloy. Thi agreement intuitively appear to be plauible to almot all reearcher in thi field; therefore, the agreement ha been accepted a correct. Upon conidering the matter carefully, however, it will be found that the agreement i doubtful. The following argument elucidate the problem. Firt, let u preuppoe that M agree with the temperature T L (0) where the dependence of σ L on temperature, dσ L /dt, i extrapolated to tre zero. If thi preuppoition i valid, it i alo valid to aume that M f agree with the temperature T f L(0) where the dependence of σ f L on temperature, dσ f L/dT, i extrapolated to tre zero. Thi aumption, however, create the following paradox. (0) mut alo be equal or nearly equal to T f L L (0), becaue σ i equal or nearly equal to σ f L. Hence, it follow naturally that M mut be equal or nearly equal to M f. Clearly, thi deduction i incompatible with the obervation that in TIMT M i higher than M f by everal degree to ome ten of degree. Thi incompatibility indicate that the aumption i incorrect, that i, M f diagree with T f L(0). On the other hand, a for the revere tranformation, the The temperature T L circumtance are omewhat different. Let T U (0) and T f U (0) repreent the temperature where the dependence of revere (0). The paradox i diagrammatically illutrated in Fig. 2. The paradox i a fundamental problem for MT; it hould not be ignored. If the problem remain unolved, the correpondence between the behavior of TIMT and that of SIMT will not be able to be trictly dicued. Therefore, one purpoe of the preent paper i to reolve thi iue. The other i to explain the reaon for the progre of SIMT at an almot contant tre and for that of TIMT with changing temperature. Both purpoe have been uccefully achieved by introducing a concept of internal tree called hape change tre and elatic back tre generated during the formation of martenite plate in TIMT. tranformation tart tre σ U on temperature, dσ U /dt, and that of finih tre σ U f on temperature, dσ U f /dt, repectively, are extrapolated to tre zero. It ha not been recognized yet that A agree with T U (0) and A f agree with T f U (0). Under thee circumtance, it follow that almot all reearcher in thi field have ome doubt on the agreement realized only between M and T L 2. Concept of Shape Change Stre The concept of hape change tre and elatic back tre introduced to reolve the above iue are explained below. Thee tree are generated when a martenite plate i formed on cooling. Firt, the key to the reolution i outlined. For the martenite plate to form in TIMT, the generation of an internal tre called hape change tre i re- Fig. 2 Diagram illutrating the doubt on the agreement of M, M f, A and A f with T L(0), T f L(0), T U (0) and T f U (0), repectively. Fig. 3 Schematic illutration howing that the generation of hape change tre aociated with the formation of a martenite plate i neceary in TIMT but unneceary in SIMT. quired, becaue the plate mut elatically deform the urrounding untranformed parent to caue the hape change. On the other hand, in SIMT, no generation of uch internal tre i required at all, becaue the hape change of a tre-induced martenite (SIM) plate i caued by the applied external tre. Figure 3 chematically illutrate thee two ituation. The detail are decribed in the following. In TIMT, hape change ha to take place in a certain region about to tranform into a martenite plate without the aid of external tre. For the plate to form, the region itelf ha to generate tre to deform the urrounding untranformed parent elatically. Uually, a elf-accommodation mechanim operate to minimize net hape change by arranging ome

3 Ditinction between Thermal and Stre-Induced Martenitic Tranformation and Inhomogeneity in Internal Stre 2251 Parent Elatic back tre Shape change tre Martenite Elatic back tre Specimen Fig. 4 Three-dimenional chematic illutration howing the generation of hape change tre and elatic back tre aociated with the formation of a martenite plate in TIMT. variant of martenite plate. Perfect elf-accommodation by which no net hape change occur at all i, however, impoible. Moreover, each variant itelf mut caue it own hape change, even though the elf-accommodation mechanim operate. Thu, whether the mechanim operate or not, each variant mut generate tre, or ele no tranformation can occur. The generated tre will henceforth be called hape change tre. The urrounding parent i ubjected to the hape change tre from the martenite plate or the elfaccommodation group of the martenite plate. Little attention ha been paid to uch hape change tre generated during forward tranformation on cooling. On the other hand, it i already known that hape recovery tre i generated when deformed martenite revere tranform into parent on heating. The hape change tre generated on cooling developed here correpond to the hape recovery tre generated on heating. Thu, the concept of hape change tre i relevant. Granted that uch hape change tre i generated, an elatic back tre or contraint effect againt the martenite plate or a group of plate mut be generated a the reaction from the urrounding parent region. In other word, the plate or group of plate i ubjected to the elatic back tre. Thu, the formation of martenite plate involve the generation of internal tree uch a the hape change tre and the elatic back tre. The ituation i chematically illutrated two-dimenionally on the left-hand ide in Fig. 3 and threedimenionally in Fig. 4. Hereafter, the hape change tre and the elatic back tre are abbreviated to SCS and EBS, repectively. Thee internal tree, SCS and EBS, generated are inferred to increae with increaing pecimen ize, becaue a large tre will be neceary to deform the urrounding untranformed parent of a large ma. Furthermore, they are alo expected to increae with increaing ize of a martenite plate formed becaue of it large hape change. That i, they are not intrinic to a ubtance but dependent eentially on both pecimen ize and martenite plate ize. Here, the pecimen ize concerned will be around millimeter cale. The martenite plate ize alo play an important role on the magnitude of the internal tre field. Decreaing plate ize reduce the region where tre field i generated. It i expected that large tre field i generated over the region at leat from everal time to everal ten of time of a martenite plate ize. For example, a for β 1 martenite in Cu-baed hape memory alloy, the plate ize i 0.1 mm. Therefore, the region where a tre field i generated will be on the millimeter cale. Incidentally, the magnitude of SCS in parent and that of EBS in martenite are preumed to be inhomogeneou. That i, their magnitude are expected to vary according to the poition in the pecimen. The SCS and EBS developed here are imilar to thermal tre generated when a ubtance i heated with both end being fixed. Auming that the ubtance i heated with both end or one end free, no contraint and therefore no thermal tre will be generated at all. Likewie, auming that no untranformed parent urround a martenite plate, the hape change of the plate take place freely. Therefore, neither SCS nor EBS will be generated at all. Thi imilarity of SCS and EBS to the thermal tre i becaue the hape train aociated with MT i eigen train, that i, tre-free train, a well a dilatation train. On the other hand, SIMT in ingle crytal pecimen preent a triking contrat to TIMT. External tre applied to a pecimen caue hear-type movement of atom aociated with the formation of a martenite plate of a ingle variant. The ingle variant ha the maximum Schmid factor or give rie to the maximum elongation under tenile loading. 9) The SIM plate travere the pecimen, a chematically hown on the right-hand ide in Fig. 3. That i, the SIM plate i not ubjected to any EBS from the neighboring untranformed parent. In other word, the neighboring parent i not ubjected to any SCS but to the ame external tre a the SIM plate. On further loading, therefore, the parent i alo ubequently going to tranform into the ame variant a that of the SIM plate firt formed by the external tre. That i, no generation of SCS i required at all to form the SIM plate. Thu, a clear ditinction i preent in SCS between TIMT and SIMT. 3. Application of Gibb Phae Rule to MT Introducing the concept of the SCS and EBS enable u to explain the reaon for the progre of SIMT at an almot fixed tre and for that of TIMT with changing temperature. The reaon will be explained on the bai of the Gibb phae rule. It tate that if a ytem containing C component and P phae i in equilibrium, the number of degree of freedom F i given by P + F = C + 2. In MT, C i conidered to be one, becaue no compoitional change occur. Then, it follow that P + F = 3. In a tate where a parent and a martenite coexit, P = 2. Therefore, F = 1; the ytem ha one degree of freedom. Accordingly, only one intenive variable, either temperature or tre, can be varied. For MT, both TIMT and SIMT, hyterei i involved between tranformation and the revere tranformation. The hyterei i unavoidable, becaue MT are diplacive tranformation in olid. That i, frictional reitance i inevitable againt hear-type diplacement of atom aociated with the formation and reverion of a martenite plate and mut be

4 2252 H. Sakamoto overcome by upercooling and uperheating, repectively. 10) Therefore, MT are, in general, irreverible procee. However, at leat in hape memory alloy, a marteite phae perfectly recover it original parent phae by the revere tranformation. Although reverible procee do not actually occur, it i ueful to imagine a hypothetical reverible proce, becaue thermodynamical analyi will be implified. Then, let u aume an idealized frictionle and quaitatic thermoelatic MT and apply the phae rule to the idealized thermoelatic MT. Here, the condition of one degree of freedom in the cae of coexitence of two phae will be applied to SIMT and TIMT. In SIMT, one degree of freedom indicate that when the tet temperature i pecified, tre where the two phae coexit in equilibrium i alo pecified. Accordingly, if the tre where the two phae coexit change, thi contradict the phae rule. Incidentally, if an SIMT take place at a fixed temperature, the tranformation on loading proceed at an almot contant tre σ L and the revere tranformation on unloading proceed at another almot contant tre σ U. Figure 1(b) how an example of uch - curve. The progre of the SIMT at a fixed tre i exactly in agreement with the phae rule. In addition, the behavior indicate that the tre field generated inide the ingle crytal pecimen by the external tre i homogeneou throughout. The plateau region in the preent - curve are, however, omewhat uneven. Thi i probably becaue the uniformity of the cro-ectional area through the gauge length portion of the tenile pecimen wa not altogether atifactory. The plateau will become more even with improving the uniformity of the cro-ectional area. Indeed, in a previou invetigation on a Cu 14.0Al 4.2Ni (ma%) alloy ingle crytal, 1) - curve howing more even plateau than the preent one have been obtained. Thi i becaue the degree of parallelim of the oppoite urface on the gage length portion of the tenile pecimen ued wa carefully adjuted. On the other hand, in TIMT, the externally applied tre i pecified to be zero. Therefore, in a tate maintaining the coexitence of the two phae, the number of degree of freedom i alo calculated to be one. Therefore, in a thermal cycle under no external tre, the temperature where the two phae coexit in equilibrium i alo pecified. Accordingly, the coexitence of the two phae hould proceed under a contant temperature. In reality, changing temperature i, however, neceary for the progre of TIMT, a een in Fig. 1(a). The amount of martenite increae with decreaing temperature. The reaon i that the untranformed parent phae i ubjected to the inhomogeneou internal tre field of SCS from martenite plate already formed. That i, the magnitude of the SCS in the untranformed parent region varie depending on each poition in the parent. Therefore, the tranformation temperature at each poition alter correpondingly. Hence, the progre of TIMT by changing temperature i a phenomenon that obey the Gibb phae rule. Neverthele, TIMT can progre even at a fixed temperature in the following ituation. Salzbrenner and Cohen have reported a rectangular hyterei loop in a % martenite veru temperature diagram in a ingle interface tranformation in a ingle crytal of a Cu 14Al 2.5Ni (ma%) alloy. 11) That i, the forward tranformation ha tarted at a temperature T g and ha finihed at the ame temperature, and the revere tranformation ha tarted at another temperature T r and ha finihed at the ame temperature. The reaon i again explained on the bai of the Gibb phae rule a follow. In ingle interface tranformation, a martenite plate formed travere the pecimen. Hence, the hape change of the plate take place without any contraint. The ituation i imilar to that in SIMT in ingle crytal. Therefore, the untranformed parent i never ubjected to SCS from the neighboring martenite plate. Accordingly, it follow that ingle interface tranformation proceed at a fixed temperature. Incidentally, the pecimen will how a large macrocopic hape change in the ingle interface tranformation, a well a in SIMT. Therefore, it i reaonable to tate the following. When tranformation proceed at a fixed temperature or tre, no SCS i generated during the formation of a martenite plate, and the pecimen undergoe a large hape change. Here, tranformation behavior in a thermal cycle under contant load i referred to. If a ingle crytal pecimen i ubjected to a thermal cycle under contant load, each of tranformation and reverion i expected to take place at a fixed temperature, becaue tre field i homogeneou throughout the pecimen. However, no experiment ha been o far performed on ingle crytal, becaue thi kind of tet i important from the practical point of view. Therefore, tranformation behavior under a contant load ha been invetigated only on polycrytalline pecimen. For example, the following point have been clarified for Ti-Ni alloy ytem. In a polycrytalline Ti 50.2 at%ni alloy, the range of tranformation temperature for bulk pecimen have been found to be larger than that for wire pecimen becaue of a large geometrical contraint effect in the tranvere direction in the bulk. 12, 13) In SIMT of polycrytalline pecimen, hape change of a martenite plate in a grain i ubjected to contraint from the urrounding grain. Therefore, SCS and EBS are generated, different from ingle crytal. In a polycrytalline 50Ti 40Ni 10Cu (at%) alloy, tranformation behavior of bulk material fabricated through conventional melting and of rapidly olidified thin foil have been invetigated under contant load. 14) A a reult, the following point have been revealed. The range of tranformation temperature in the thin foil are narrower than thoe in the bulk, and tranformation train in the former i larger than that in the latter. Thee reult alo ubtantiate the validity of the concept of SCS and EBS developed here. 4. Effect of SCS on Characteritic of TIMT Through Specimen Size The validity of the concept of SCS ha been thu well proved by the ucceful elucidation of the contrat in tranformation behavior between TIMT and SIMT. Let u now return to the doubt on the agreement between M and T L(0). The problem i alo reolved by taking the effect of SCS on the behavior of TIMT into conideration. That i, the magnitude of SCS generated inide a pecimen i expected to increae with increaing pecimen ize. Therefore, one can predict that thi increae in the magnitude of SCS with

5 Ditinction between Thermal and Stre-Induced Martenitic Tranformation and Inhomogeneity in Internal Stre 2253 increaing pecimen ize will alter tranformation temperature in TIMT with pecimen ize. In fact, the preent author and coworker have recently found through DSC meaurement that the characteritic of thermoelatic MT in ome hape memory alloy have altered with pecimen ize (ma). 4, 5, 15 17) Here, the pecimen ize concerned i of millimeter cale. No other reearcher ha ytematically invetigated the effect of pecimen ize on tranformation behavior. The effect of pecimen ma on tranformation temperature ha thu far been invetigated for tranformation between B2 parent and B19 monoclinic martenite in a polycrytalline Ti 50 mol%ni alloy, 15, 16) between B2 parent and B19 orthorhombic martenite in a polycrytalline 49.5Ti 40Ni 10Cu 0.5Al (mol%) alloy, 17) between β 1 parent (D0 3 - type ordered tructure) and β 1 martenite (18R 1-type longperiod tacking-order [LPSO] tructure in Ramdell notation) 4, 5) in a ingle crytal of a Cu 13.4Al 4.2Ni (ma%) alloy, and o forth. A a reult, in any of thee alloy, TIMT characteritic have been found to alter with pecimen ma a follow. With decreaing pecimen ma, M and A f have hifted to lower temperature logarithmically, while M f and A have hifted to higher temperature. Conequently, thee hift have effected the following two alteration. Firt, experimental equilibrium temperature To = (M + A f )/2 have hifted to lower temperature. Second, the temperature range where the tranformation and the revere tranformation take place, from M to M f and from A to A f, repectively, have decreaed. Furthermore, the oberved variation of tranformation temperature with pecimen ma have been extrapolated to pecimen ma zero. A a reult, it ha been revealed that tranformation tart and finih temperature on cooling have converged to coincide at pecimen ma zero; that i, M # = M # f, and for revere tranformation one on heating it i likewie; that i, A # = A# f (the upercript # indicate the tranformation temperature at the ultimate end of pecimen ma zero). Here, the ituation at or near the ultimate end of pecimen ma zero i uch that a martenite plate travere a thin planar (two dimenional) or thin rod (one dimenional) ingle crytal. Incidentally, tranformation temperature will hift alo with canning rate dt /dt, epecially in a large pecimen, probably becaue of inhomogeneity in temperature. A for Ti 50 mol%ni 16) and 49.5Ti 40Ni 10Cu 0.5Al (mol%) 17) alloy, tranformation temperature of pecimen of variou ma have been already invetigated a a function of canning rate. By extrapolating the obtained dt /dt dependence of the MT characteritic to dt/dt = 0, the one under infiniteimally low dt /dt, that i, under quaitatic condition (QSC), ha been deduced. A a reult, the following ha been found. The MT characteritic under QSC have hown pecimen ma dependence, a well a thoe meaured at a finite dt /dt, although the dependence i maller than that meaured at a finite dt /dt. With decreaing pecimen ma, To QSC under QSC, To, ha hifted to lower temperature and tranformation temperature range under QSC, from M QSC to M QSC f, and from A QSC to A QSC f, have decreaed to zero. Beide, M # = M # f and A # = A# f have remained unchanged irrepective of canning rate. Thee reult indicate that, under QSC, the amount of thermally induced martenite in a pecimen of a finite ma i a function of temperature, and that the pure effect of SCS and EBS on tranformation temperature can be derived. Very recently, imilar reult have been obtained on the β 1 β 1 tranformation in a Cu 13.8Al 4.2Ni (ma%) alloy ingle crytal. Moreover, in the ingle crytal of the Cu 13.4Al 4.2Ni alloy, the behavior of β 1 β 1 tranformation puedoelaticity ha alo been invetigated a a function of temperature above M. A a reult, the former M # = M # f ha been found to coincide alo with T L (0) and the latter A # = A # f with T U (0). 4, 5) The oberved coincidence i hown in Fig. 5. It i compoed of two diagram; one illutrate the variation of σ L and σ U with temperature and the other how the variation of tranformation temperature meaured at dt/dt =± K/ with pecimen ma. To clarify the coincidence, the part around σ L = σ U = 0 and pecimen ma zero in Fig. 5 i magnified and chematically illutrated in Fig. 6. The origin of the coincidence i explained a follow. It i reaonable to infer that no SCS i required at all at the ultimate end of the pecimen ize zero in TIMT. The ame ituation that no SCS i required tand alo in the cae of SIMT, a decribed in Chapter 2. Thi rationalize the oberved coincidence: M # = M # f = T L (0) and A # = A# f = T U (0). From thee reult, it can be tated that M of a pecimen of a finite (0). Thu, the finding of the phenomenon that the characteritic of TIMT are altered with pecimen ma ha brought the paradox et up in Chapter 1 to a ettlement. In addition, thee reult alo ubtantiate the validity of the concept of SCS. Incidentally, many reearcher may have ome doubt about the accuracy of tranformation temperature determined through DSC meaurement where the temperature pecimen ize cannot agree with T L Fig. 5 Combined diagram howing the coincidence between M # = M # f and T L (0) and that between A # = A# f and T U (0) in a ingle crytal of the Cu 13.4Al 4.2Ni alloy.

6 2254 H. Sakamoto Fig. 6 Enlarged chematic diagram around σ L = σ U = 0 and pecimen ma zero in Fig. 5. meaured with a thermocouple i the one outide a pecimen cell. Therefore, there may be ome gap between the meaured temperature T m and the temperature of a pecimen T, epecially in the cae of a large ize pecimen and a high canning rate. Strictly peaking, detailed analyi on the gap i neceary. Beide, detailed invetigation i alo required on the tranformation temperature of pecimen of maller ma than 100 mg, although the pecimen preparation i difficult. Neverthele, it i not unreaonable to uppoe the following. The gap i thought to reduce with decreaing pecimen ma and with decreaing canning rate. In other word, the accuracy of tranformation temperature i expected to increae with decreaing pecimen ma. A a reult, the extrapolated temperature to pecimen ma zero are expected to remain unchanged. Therefore, it i afe to tate that the coincidence between M # = M# f and T L (0) and between A # = A# f and T U (0) in Fig. 5 i not entirely erroneou. Paradoxically, if no coincidence exit between them, we have to dicover ome proper reaon for the diagreement. Conequently, the idea that T L(0) agree with M of the tenile pecimen i een to be incorrect. Thi i alo confirmed by the following dicuion. The effect of pecimen ize on tranformation temperature decribed above i clearly oberved in TIMT of tenile pecimen. Hence, M of tenile pecimen will hift with pecimen ize. Meanwhile, no pecimen ize effect i expected to be oberved in SIMT, becaue the parent region neighboring SIM plate i ubjected to no SCS a previouly tated; T L (0) i conidered to remain unaltered, irrepective of tenile pecimen ize. Therefore, a an inevitable conequence, one deduce that T L (0) remaining unaltered cannot agree with M hifting with pecimen ize. Now, the oberved variation of experimental equilibrium temperature T o with pecimen ma are dicued in further detail. In the Cu 13.4Al 4.2Ni alloy hown in Fig. 5, To hift around 30 K to higher temperature with the increae of pecimen ma to 300 mg. On the bai of the above dicuion, one can correctly preume that the variation of To with pecimen ma are alo attributed to the effect of SCS varying have been, however, thu far elucidated to be caued by nonchemical energy 10, 15) G nonc generated when martenite plate form at M. with pecimen ma. The variation of T o Here, the ubcript i appended to denote energy generated when a fraction f o of martenite plate form at M. The preent author and coworker have already derived an equation To = ( H P M + Gnonc P M)/ S P M which give the variation of To P M with Gnonc.10) Here, H P M i the enthalpy change aociated with a tranformation and S P M entropy change, and Gnonc P M i the difference in G nonc between a martenite and a parent; that i, Gnonc M G nonc P. The nonchemical energy G nonc concerned i the um of elatic energy E ela and interfacial energy E face. A for E ela, it i recognized on the bai of the dicuion in Chapter 2 that the generation of the elatic energy in parent Eela P i acribed to SCS developed and that in martenite Eela M,to EBS. If E ela i much larger than E face, G nonc i governed by the former. It ha been previouly hown 11) that, with increaing pecimen ma, Eela P become much larger than Eela M. In thi ituation, it mut have, therefore, become apparent by now that the oberved upward hift of experimental equilibrium temperature To with increaing pecimen ma are caued by increaing the abolute value of Gnonc P M by increaing SCS. Incidentally, the preent author and a coworker have recently hown that the logarithmic upward hift of To with increaing pecimen ma oberved in ome hape memory alloy are acribed to the logarithmic increae of SCS with increaing pecimen ma. 18) On the other hand, in SIMT, externally applied tre i known to caue upward hift of equilibrium temperature under tre T o (σ ). It ha been recently hown that the applied tre caue a larger increae of the elatic energy of a parent than that of a martenite, reulting in the upward hift of T o (σ ). 19) Thi recent reult indicate that the upward hift of To with increaing pecimen ize are imilar to thoe of T o(σ ) with increaing applied tre. Thu, we have found a clue to dicuing the correpondence between TIMT and SIMT. Thu, it ha been proved that SCS and EBS play an important role in determining the characteritic of TIMT. Detail of the alteration of TIMT characteritic caued by varying SCS with pecimen ma will be decribed elewhere. 5. Concluion The preent tudy i ummarized a follow. (1) The progre of TIMT with changing temperature ha been oberved to have a harp contrat to that of SIMT under a contant tre. A paradox ha been et up on the agreement between M in TIMT and temperature T L(0) where the dependence of critical tre for inducing martenite σ L in SIMT on temperature, dσ L /dt, i extrapolated to tre zero. (2) To reolve the paradox, a concept of inhomogeneou internal tre called hape change tre (SCS) ha been introduced a an intenive variable. For martenite plate to form on cooling, the generation of SCS i required, becaue the plate mut deform the urrounding untranformed parent. Increaing pecimen ize (ma) ha been inferred to caue increaing SCS. (3) By applying the Gibb phae rule to MT, the contrat in tranformation behavior between TIMT and SIMT ha been uccefully explained. The progre of TIMT by changing temperature ha been attributed to inhomogeneou

7 Ditinction between Thermal and Stre-Induced Martenitic Tranformation and Inhomogeneity in Internal Stre 2255 SCS, while that of SIMT under a contant tre ha been attributed to homogeneouly applied external tre. (4) The downward hift of experimental equilibrium = (M + A f )/2 with decreaing pecimen ma o far oberved in TIMT of ome hape memory alloy have been attributed to decreaing SCS with decreaing pecimen ma. (5) Conceivably, no SCS i generated at all either in SIMT or at the ultimate end of pecimen ize zero in TIMT. Thi concept ha rationalized the following obervation on a temperature T o monocrytalline Cu 13.4Al 4.2Ni (ma%) alloy. That i, the variation of M, M f, A and A f with pecimen ma have been extrapolated to pecimen ma zero, reulting in M # = M # f and A # = A# f. In addition, the former ha coincided with T L (0) and the latter with T U (0). Thu, the paradox ha been uccefully reolved. (6) It ha been noted that SCS i important in dicuing the correpondence between TIMT and SIMT. REFERENCES 1) K. Otuka, H. Sakamoto and K. Shimizu: Acta Metall. 27 (1979) ) K. Otuka, C. M. Wayman, K. Nakai, H. Sakamoto and K. Shimizu: Acta Metall. 24 (1976) ) S. Miyazaki, Y. Ohmi, K. Otuka and Y. Suzuki: J. Phy. 43 (1982) Suppl. 12. C4-255 C ) H. Sakamoto: Proc. Intern l. Conf. on Solid-Solid Phae Tranformation 99 (JIMIC-3), (The Japan Intitute of Metal, 1999) pp ) H. Sakamoto: Journal of the Jpn. Copper and Bra Reearch Aociation, 39 (2000) ) H. Pop: Metall. Tran. 1 (1970) ) K. Otuka and C. M. Wayman: Review on the Deformation Behavior of Material, Freund Publ. Houe Ltd., Tel Aviv, Irael, 2(2) (1977) ) K. Otuka and C. M. Wayman: Shape Memory Material, (ed. by K. Otuka and C. M. Wayman, Cambridge Univerity Pre, 1998, Cambridge, United Kingdom) pp ) H. Sakamoto and K. Shimizu: Tran., JIM 25 (1984) ) H. Sakamoto, S. Sugimoto and T. Hara: Mater. Tran., JIM 39 (1998) ) R. J. Salzbrenner and M. Cohen: Acta Metall. 27 (1979) ) G. B. Stachowialk and P. G. MaCormick: Acta Metall. 36 (1981) ) Y. M. Jin and G. J. Weng: Metall. Mater. Tran. A. 32A (2001) ) Y. Furuya, M. Matumoto, H. Kimura, K. Aoki and T. Maumoto: Mater. Tran., JIM 31 (1990) ) H. Sakamoto, K. Meguro, A. Tanaka and A. Imai: J. Phy. IV 5 (1995) C8-581 C ) Hi. Sakamoto, Ha. Sakamoto and S. Onai: Proc. Intern l. Conf. on Solid- Solid Phae Tranformation 99 (JIMIC-3), (The Japan Intitute of Metal, 1999) pp ) S. Onai and H. Sakamoto: Mater. Sci. Forum, (2000) ) H. Sakamoto and S. Onai: Collected Abtract of the 2001 Autumn Meeting of Japan Int. Metal (2001) p ) H. Sakamoto and S. Onai: Collected Abtract of the 2001 Autumn Meeting of Japan Int. Metal (2001) p. 76.