Scripts METALLURGICA
`
`Vol. 15, pp. 287-292, 1981
`Printed in the U.S.A.
`
`Pergamon Press Ltd.
`All rights reserved
`
`TRANSFORMATION PSBUDOELASTICITY AND DEFORMATION
`BEHAVIOR IN A Ti—50.6&t%Ni ALLOY
`
`S .Miyazaki’.‘ K .Otsuka*and Y . Suzuki“
`* Institute of Materials Science, University of Tsukuba,
`Sskura—mura. Ibaraki—ken 305, Japan
`** Central Research Laboratory, Furukawa Electric Company.
`2-9—15 Futaba-cho. Shinagawa—ku. Tokyo 141. Japan
`(Received November 22, 1980)
`(Revised December 22, 1980)
`
`Introduction
`
`In fact it is the only
`The 'I‘i—Ni alloy is so famous with the associated shape memory effect.
`alloy which is used for the practical applications of the shape memory effect on a commercial basis
`at present, such as coupling, connectors and medical applications [1) .
`In order to develop such
`applications. it is necessary to investigate mechanical behavior associated with the martensitic
`transformation and/or in the martenaitic state. Various investigations have been made along this
`line so far, but the number and scope of these investigations are not very many not so deep from
`a fundamental point of view. Rozner and Wasilewski (2). and Cross at al.
`(3) made rather sys—
`tematic works on the stress—strain curves (S-S curves) in wide temperature and strain ranges.
`They found that the s-s curves in the 'l‘i—Ni alloys consisted of three stages which are apparently
`similar to three stages in FCC and HG? single crystals. However, they did not study the un-
`loading process. and did not clarify the nature of these stages. The presence of the transforma-
`tion pseudoelasticlty (4) in Ti—SlattNi and Ti—52at5iNi alloys has been reported by Waailewsld (5)
`and Home (6) respectively. but no detailed data such as the temperature dependence etc. have
`been reported. The purpose of the present short note is to report the transformation pseutb-
`9183th in this alloy in some detail. and to clarify the nature of the three stages by carefully
`observing the stress-strain curves upon loading and unloading and by measuring the strains
`recovered upon unloading and subsequent heating.
`After the pioneering works by Homer and Wasilewaki, and Cross at al.. several investigations
`- have been made to clarify the nature of each stage. Although it is not well established as yet. we
`summarize those in the following. Mohamed and Washburn (7) have provided evidence that the
`martensite-martensite interface moves in the early stage [stage I) of an initially partially trans-
`formed material.
`SDme authors (7.3) have suggested that the deformation in stage 11 is an elastic
`deformation of the martenaltes formed in stage I. But Melton and Mercier (9) reported evidence
`inconsistentwith the above suggestion. They observed microstructure in a specimen deformed into
`stage lI'by transmission electron microscopy and found an intersecting array of martensite lathe in
`some part and dislocations in another part. However.their observation is limited toa small region
`of stage II. and the deformation modes throughout the stage II are not well clarified. On stage
`In. Mohamed and Washburn (7) made an electron microscopy observation of specimens elongated by
`8% and found heavy irregularity ofmertsnsite boundaries. Thus they suggested that slip occurred
`at the stage at. Michael (10) and Tadakl and Wayman (11) also made the electron microscopy
`observation of heavily cold-rolled (=30‘l) specimens. which roughly corresponded to stage III in
`tensile tests. They both found high density of dislocations and the segmentation of martensites.
`These results are clear evidence to show that slip occurs in stage III. but are lacking for the
`qualitative data by tensile'tests as to the recovery of strains. Meanwhile, apparently quite similar
`three stage stress—strain curves are reported in Cu-Al-Ni single crystals in specific orientations;
`the deformation modes in stages n and m in this case are proved unambiguously to be due to the
`elastic defamation of a martensite and martensite-to—martensite transformation, respectively. by
`careful measurement of strains by extensometer and neutron diffraction under stress (4) .
`It is
`interesting to compare the nature of the three stages in the Ti—Ni alloy with those in the above
`case.
`
`'
`
`287
`0036-9748-81/030287-06$DZ.00/0
`Copyright
`(c) 1981 Pergamon Press Ltd.
`
`Lombard Exhibit 1032, p. 1
`
`Lombard Exhibit 1032, p. 1
`
`

`

`288
`
`TRANSFORMATION PSEUDOELASTICITY
`
`Vol. 15, N0. 3
`
`Experimental Procedures ‘
`
`The alloy was prepared from 99.7w“ Ti and 99.97wt’t electrolytic Ni by melting in a high—
`fraquency vacuum induction furnace. followed by casting into an iron mold. The composition ofthe
`alloy was determined by chemical analysis to be Ti-50.6at%Ni (i0.1at%Ni)
`(nominal composition was
`'n-smum. The ingot of the alloy was awaged at R.T. and than drawn at 1LT.
`to wire speci-
`mens with thqadiameter of 0.4 mm. Thespecimens were solution treated at 1273 K for 1 hr in a
`vacuum of 10 Pa.
`and then rapidly quenched into ice water. The transformation tempera-
`tures after this heat treannent were measured by electrical resistance method. and the iyiJi-JMfiAfl
`and Af temperatures were 128, 190, 188 and 221 K , respectively. After these heat treatments.
`wire specimens with the diameter of 0.35 mm and with gauge length of 16 mm long were made by
`electropoliabing in a solution of acetic anhydrlda and 7.5% perchloric acid. Tensile tests were
`carried out with an instran type tensile machine Shinko TOM-1000M. For testing at various
`temperatures. the specimens were kept in a solution of methanol or iaopentane which was cooled by
`pouring liquid nitrogen. The strain rate used was 5.2x10'4lsec.
`Results and Discussion
`
`(1) Effect of defamation temperature on stress-strain curves
`The defamation modes of materials which exhibit themoelastic martensitic transformations are
`affected strongly by defamation temperature (T). Such stress-strain curves as a function of
`temperature are shown in Fig.1. These curves are divided into four temperature regimes as
`follows according to the characteristics of the curves.
`In range (I)
`tT<M81 the curves (a)~(e)
`are characterized by smooth and parabolic curves. The flow stress increases with decreasing
`temperature in this range. because the deformation in this range proceeds with the movement of
`mobile defects such as boundaries between martensite plates or internal twins which move by a
`thermal activation process.
`
`(M9<T<Af) the curves are characterized by a sharp bending at the yield point.
`In range (11)
`where the apparent plastic defamation starts by the formation of stress-induced martensite (SIM) .
`The serration of curve (h) corresponds to the fomatlon of SIM. Although curves (f) and (g)
`also belong to range (ll). both curves do not show the serration. This may be due to the easi—
`ness of the formation of SIM at low stress. The common feature of the curves in both ranges (I)
`and (11) are characterized by thepresance of residual strain after unloading and perfect recovery
`of the strain after beefing, i.e. the specimen shows the shape memory effect in these temperature
`ranges.
`.
`.
`,
`.
`
`<T<Tc) are characterized by the formation of.
`The curves in the third temperature range (
`SIM upon loading and by the reversible reverse t nsformation upon unloading. which leads to
`the transformation pseudaelastictty.
`liars 1;, represents the critical temperature where the plastic
`deformation by dislocation motion starts. The stress hystereses of the curves are almost the same
`in this range and the stress level increases with increasing temperature. according to the
`Clausius- Clapeyron relation.
`In range (1V)
`(Tc<'l‘]
`the curves are characterized by plastic defamation preceding the for-
`mation of SIM as is evident from the deviation from linearity before serratian occurs. As expected
`from the Clausiua-CIepeyron equation. the critical stress. required to induce martensitic trans-
`formation in this temperature range becomes so large that the plastic defamation by the movement
`of dislocations occurs prior to the fomation of SIM. Curve (:1) is a typical example of such a
`case. The slip defamation induced in this range is the cause of the presence of residual strain
`after unloading which increases with increasing temperature as shown in Fig. 1(m)—-(p).
`It is
`noted in the 5-5 curves In) ~(p) that the serrations are present upon loading but they are
`difficult to detect upon unloading. The serration in general is caused by the defamation in
`which the defamation unit is large enough and the defamation process is so rapid (12).
`Therefore the smoothness of the curve during reverse transformation upon unloading implies that
`the tranefomstion unit has become small and the transformation process has been decelerated
`owing to the dislocation obstacles which are formed upon loading. Although the behavior in this
`range is very interesting. it is difficult to make a quantitative analysis from the present data.
`which has been taken for a single specimen.
`(2) Temperature dependence of critical stresses for stress-induced transformation ('lea ) and
`for yielding (T<Ms).
`As mentioned in the previous section, the temperature d endence of the yield stress is very
`complex because the defamation modes differ with each other
`the four temperature reglign .
`The critical stresses are plotted in Fig. 2 as a function of temperature. Open circles in
`ate the
`stresses at which martenaites are induced when M34 or boundaries between martensites or
`
`Lombard Exhibit 1032, p. 2
`
`Lombard Exhibit 1032, p. 2
`
`

`

`Vol. 15, No.
`
`3
`
`TRANSFORMATION PSEUDOELASTICITY
`
`289
`
`(cHS4. IK
`
`(dHTI.2K
`
`((1)77.
`
`.
`
`o.(e)l827K
`
`[00
`
`(b)|53.OK
`
`(fH93.3K
`
`(9)fig
`
`o.(h)2l35K
`
`203.OK
`
`oill25I.OK-
`
`0
`
`
`
`0
`
`(k)24l.0K
`
`(1)2237K
`
`iy 1232.5K
`
`‘
`
`E:
`2
`E200
`2 I
`:73
`
`%
`
`E
`
`(r0273.2K
`
`oto)276.5K
`
`
`
`(“"2634K:ogz4cfiE2
`
`4
`
`Strain 00
`
`FIG. 1
`
`Stress—strain curves as a function of temperature.
`
`internal twin boundaries begin to move when use. Closed circles show the stresses at which
`reverse transformation starts. The critical stress takes the minimum value near the M8 point and
`increases with decreasing temperature in the range below the M,3 point At temperatures above
`the My point.
`the critical stress increases with increasing temperature. and it satisfies the
`Clausius-Clapeyron relation between 210 and 260 K. At temperatures above 260 K. where resi-
`dual atrain remains after unloading. both the critical stresses for inducing martensltes and
`reverse transformation deviate from the relation. but the former deviates to the upper side while
`the latter to the lower side of the relation.
`
`[3) Deformation mode in each stage of the stress-strain curves
`The defamation modes are strongly affected not only by the deformation temperature as
`shown in Fig. 1 but also by the amount of strain.
`In this section the deformation modes of both
`specimens which are in a parent phase and in partially martensitic state prior to defamation are
`examined.
`
`Figure 3 shows the stress-strain curves of a specimen deformed at 243 K (>Af). where the
`specimen was in parent phase prior to deformation. The specimen was subjected to cyclic stress-
`ing as shown by curves 1~9. If there is residual strain after unloading, the specimen was
`
`Lombard Exhibit 1032, p. 3
`
`Lombard Exhibit 1032, p. 3
`
`

`

`290
`
`TRANSFORMATION PSEUDOELASTICITY
`
`V01. 15, No. 3
`
`60°
`
`400
`
`
`
`J
`J/
`
`,
`
`(MPO) TensileStress
`
`200 HLO
`
`‘0‘
`./
`°\°
`/
`\ /
`°
`/
`
`77 "5°
`“-2“ “i
`2‘"
`3°°
`Temperature (K)
`
`V
`
`.
`
`FIG 2
`'
`Critical sin-eases as a function of
`temperature for inducing matensites
`(T>M8) and for yielding (T<M8)
`(open circles) and for reverse
`transformation (solid circles].
`
`heated to 373 K in order to recover the
`residual strain as shown by dotted lines.
`The stress-strain curve can be divided into
`three stages conventionally.
`In stage I.
`this material shows Ll'xdera like defamation
`until about 7% strain as shown by curves
`1~3. The serrations during the defamation
`were caused by the formation of SIM. The
`amount of strain by SIM upon loading is
`the same as that recovered by reverse
`transformation upon unloading. This fact
`shows that all the deformation in this stage
`is proceeded by the formation of SIM alone.
`
`After the Lilders like deformation the
`flow stress increases rapidly with increasing
`' strain in the stage l! as shown by curves
`4‘7. When the specimen was deformed to
`this stage. the strain is not recovered com-
`pletely upon unloading and even after
`heating. The existence of residual strain
`means that plastic deformation by the move-
`ment of lattice defects such as dislocations
`
`-
`
`occurs as one of the deformation modes in
`this stage. By comparing the strain of the
`serrated region in stage I (as) with the sum
`of the strain recovered by unloading and
`that by the subsequent heating (er),it is
`found that the latter (=6‘k) is larger than
`the former (= 5%) when the specimen is de-
`formed into stage II as shown by curves
`
`
`
`
`
`TensileStress(MPG)
`
`<-Stoge I->l<—Stage lI—H<———- Stage III—lt~———>
`
`
`
`Deformed at 243K
`
`
`M5 = l90K
`Af = 22IK
`
`
`20
`
`31min
`FIG. 3
`
`(7e)
`
`Stress—strain curves of a specimen deformed at 248 K (>A ).
`Dotted lines represent the recovered strain upon heating 0
`373 K. The symbol (x) represents the fracture point.
`
`Lombard Exhibit 1032, p. 4
`
`Lombard Exhibit 1032, p. 4
`
`

`

`V01. 15, No.
`
`3
`
`TRANSFORMATION PSEUDOELASTICITY
`
`291
`
`«Sm: l—+—Sluee li-—-i-—-—Sm l——+—o
`
`
`
`T“ we“
`
`FIG. 4
`'
`30:03:12223111: $3333: 21:23:13?!“
`deformed at 243 K (>A )
`f '
`
`4'8. These facts mean that there are two
`defamation modes in the second stage. Le.
`the normal plastic deformation by the move-
`ment of dislocations and the formation of SIM
`in the residual parent phase and/or the de—
`formation by the movement of martensite-
`martensite boundaries and twin boundaries.Aa
`these two deformation modes coexist in stage
`11, the SIM and dislocations relax the strain
`fields formed by them to each other and the
`stress field formed by the dislocations makes
`the marteneite atabler. As a consequence.
`'
`both critical stresses for inducing martensites
`and for the reverse transformation decrease
`with increasing strain as shown in Fig. 3.
`In stage III the strain 8
`recovered by
`reverse transformation rapid]; decreases and
`the residual strain (E ) after heating to 373 K
`inoreasee rapidly as &own by curve a. so
`that most of the deformation mode in stage 111'
`is plastic deformaflon by the movement of
`dislocations. Thus it is quite unlikely that
`the stage Ill is associated with a martensite—
`to—msrtensite transformation.
`in spite of the
`great similarity to that of Cu—Al—Ni single
`crystal in the 8-8 curves upon loading.
`
`These three kinds of strains ( 53:51»; ends?) in the specimen used in Fig.3 are plotted as a
`function of total tensile strain in Fig. 4. These strains are defined schematically in Fig. 4.
`It
`is found that the residual strain [a
`appears at about 8% strain in stage ll. This means that
`the deformation mode up to the ini
`region of stage n is the formation of SIM or the movement
`of boundaries of msrtensites or twin boundaries in martensites and does ,not contain the movement
`of dislocations.
`
`‘Stogelrh-Stoge 1H<—'—~———— Stage l————R———
`
`(MPO)
`
`Stress
`
`Tensile
`
`FIG. 5
`
`Stress—strain curves of a specimen deformed at 173 K (<Ms).
`Dotted lines represent the recovered strain upon heating to
`373 K. The symbol (X) represents the fracture point.
`
`Lombard Exhibit 1032, p. 5
`
`Lombard Exhibit 1032, p. 5
`
`

`

`292
`
`TRANSFORMATION PSBUDOELASTICITY
`
`V01. 15, No. 3
`
`A similar behavior has been examined at
`the defamation temperature of 173 K (die) as
`shown in Fig. 5 and 8.
`It is seen that the
`behavior is essentially the same as the above
`case exept for stage I and the initial part of
`stage II. where the deformation occurs by the
`formation of SIM in residual parent phase and
`the movement of martensite—martsnsite
`boundaries or twin boundaries in martensits.
`
`«Stage l-‘l-—Stooo l—‘is—“Shge I—H
`
`
`
`Tmscmeo
`
`FIG. 6
`
`Plot of two types of strains as a
`function of total tensile strain in a
`specimen defomed at 173 K (dis).
`
`Acknowledgments
`The authors are grateful to Mr. S. Tansks at Suwa Seikoaha for his cooperation in the early
`stage of this work. They also would like to thank Drs. H. Shiraishi and N.Kainums at Tsukuba
`Laboratories. National Research Institute for Metals for allowing us to use the tensile machine.
`This work was partially supported by the Grant~in—Aid for Fundamental Scientific Research
`(Energy Tokubetsu, 1980) from the Ministry of Education of Japan. and the sponsorship is greatly
`appreciated.
`
`References
`
`(1) C.M. Way-man. Bulletin of the Japan Inst. Met. 19. 323 (1990).
`(2) A. G.Roznsr and R. J. Waeilewsld, J. Inst. Metals 94.189 (1966).
`(3) W. B. Cross. A. H. Ksriotis and F J. Stimler. NASA 011—1439. September (1969)
`(4) K. Otsuka. H. Saksmoto and K. Shimizu, Acts Met. 27. 595 (1979).
`(5) R. J. Wasilewsld. Scripts Met. 5. 127 (1971).
`(6) T .Honma. Bull. Res. Inst. Mineral Dressing and Metallurgy 27. 245 (1971).
`(7) H. A.Mohamed and J. Washburn. J. Mater. Sci.12.489 (1977).
`[8)
`J.Perkins. Scripts Met. 9. 1489 (1974).
`(9) K. N .Melton and O.Mercier. Met. Trans. 9A.1487 (197B).
`(19) G.M ..Michael Ph. D. thesis. Stanford Univ. November (1979).
`(11) T.T11(1st and 0.101 .Wayman. Scripta Mat.14, 911 (1980).
`(12) N.Narita and J .Takamura. Phil. Mag. 2_9.1001 [1974).
`
`Lombard Exhibit 1032, p. 6
`
`Lombard Exhibit 1032, p. 6
`
`