Stress and Strain Induced Martensitic Transformations
`
`K. Otsuka* and K. Shimizu*
`
`Abstract
`
`After some discussions on stress-induced vs. strain-induced trans-
`some recent developments on the stress-induced transfor-
`formations :
`mation in 8 phase alloys are described.
`The included topics are
`succeSSiVe stressfinduced transformations, phase diagrams in tempera-
`ture.5tress coordinates, marten51te-to-marten51te transformations,
`the
`mation pseudoelast1c1ty and the effect of sense of stress on
`transfer
`tic transformations.
`martensl
`
`I.
`
`Introduction
`
`The stress-induced martensitic transformation is a current topic
`among other subjects on martensitic transformations from the following
`three reasons. Firstly the stress—induced transformation is more
`easily controlled than the ordinary transformation by cooling, and the
`associated variables describing a transformation [e.g. CRSS to induce
`the martensite etc.) is easily obtained when one uses single crystals.
`Thus, it is more convenient for the study of transformation mechanisms
`than the latter.
`Secondly, new phases or new phenomena (e.g. marten—
`site—to-martensite transformations) may appear under stress which are
`not realized under cooling alone, since stress is a thermodynamic
`variable independent of temperature. Thirdly interesting mechanical
`properties are associated with the stress—induced transformation, which
`have a variety of potential applications, such as the shape memory ef—
`fect, transformation pseudoelasticity and transformation induced plas-
`ticity.
`
`The effect of stress on martensitic transformation has first been
`explored theoretically by Scheil[l] in early 1930's.
`A more quantita-
`tive theory has been developed by Patel and Cohen[2]
`to predict the
`change of transformation temperature as a function of stress, and it
`has been shown that the transformation temperature increases with
`uniaxial stress.
`The same result has been obtained by Burkart and
`Read[3] by applying the Clausius-Clapeyron equation to shear stress.
`Until now both theories have been tested successfully by a number of
`experiments. After 1970 the studies on the stress—induced transfor—
`mation has become very popular, and the transformation pseudoelasticity
`has been found and studied in detail in a number of 8 phase alloys [4,
`51-
`In the present paper some of the later developments, which have
`been obtained within a few or several years, will be highlighted.
`
`_.__.___——-——-————
`
`1:
`
`The Institute of Scientific and Industrial Research, Osaka Universi—
`ty, Yamadakami, Suita, Osaka 565, Japan.
`
`-607-
`
`Lombard Exhibit 1031, p. 1
`
`Lombard Exhibit 1031, p. 1
`
`

`

`_7\\‘-.
`
`II.
`
`Stress—induced vs. strain-induced transfomati Ons
`As described above, an applied uniaxial stress as
`SiSts the
`sitic transformation thermodynamically. This is a str
`mart 8.
`BSS~indu
`Ced
`n
`transformation.
`In fact,
`the transformations occurri
`ng Under
`8 phase alloys above MS are stress-induced transformations
`Stres
`’ as evi-
`denced by the conformity to the Clausius-Clapeyron eqUatio
`n and the
`pseudoelastic behavior at temperatures above Af. However
`1 It is
`in some ferrous alloys under special conditions that a Plast'
`kmmn
`mation always preceeds the martensitic transformatiOn (e.g 1c defor_
`atures above HQ in Fig. l), and that martensites are Often. at temper.
`the intersection of two slip bands.
`ormmiat
`This case is controversial as to
`whether the transformation is stress-
`
`Sin
`
`In fact,
`induced or strain—induced.
`this is a matter of definition to some
`
`Some authors[6] call it a
`extent.
`strain-induced transformation, simply
`because the introduction of strains
`
`lowers the critical stress to induce
`
`martensites from the Clausius-Clapeyron
`relationship, while others[7] call it a
`stress-induced transformation because
`
`they consider that an applied stress
`and local stresses around the source of
`
`
`
`strains add up to the stress required
`by the Clausius-Clapeyron equation.
`Based on their nucleation mechanism,
`Olson and Cohen[8, 9]
`seem to preserve
`the term more rigorously such that
`geometrically favorable nucleation
`sites are created in the strain-induced
`transformations.
`They further claim
`that the transformation above Mg in
`Fig.
`1
`is a strain-induced transfor—
`mation
`in their rigorous terminology.
`However, Tamura and Onodera[10] re-
`ported to have obtained experimental
`results opposing the Olson-Cohen's
`supposition.
`Since this is a delicate'problem, we will not pursueit
`any further.
`See Refs.[9, 10] for further discussion.
`
`Fig. 1. Stress vs. martap
`sitic transformation tmmmr-
`ature in Fe-31.24wt.%Ni4L21
`wt.%C alloy (After Tokizmm
`[35]).
`
`In ferrous alloys such as stainless steels and Fe—Mn-C alloysifi
`proper compositions,
`the formation of e martensites and / or a P135tiC
`deformation always preceeds the y-+-a'
`transformation. More compli-
`cations will arise in these alloys such as the negative temperature
`dependence of the critical stress to induce the a' marteHSite and UN
`"window effect”[1l]. These will not be discussed in the present Pepe?
`Thus, we will solely concern with the stress-induced transformations1n
`the 8 phase alloys in the next section.
`
`III. Stress-induced transformations and transformation
`pseudoelasticity.
`
`-608-
`
`Lombard Exhibit 1031, p. 2
`
`.4_-lIll!H
`
`Lombard Exhibit 1031, p. 2
`
`

`

`sucC8551V8 stress—induced transformations and phase diagrams
`
`3.1.
`
`One of the interesting findings in a recent few years is the suc—
`’
`e stress-induced transformations in 8 phase a110ys[12 — 15]
`as
`f
`..
`.
`Cessiv
`The re-
`11y shown or a Cu—Al—Nl Single crystal in Fig. 2[13]
`.
`typica
`occurrlng on each stage has been determined as indicated by
`.
`action
`neutron dlf—
`action, X-ray
`tion and
`
`(0)223K
`
`5:" “XI
`
`(0')
`
`(b)273K(T<Mfl fi}—;a;
`recriemal Ion
`
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`
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`
`
`(U303 K( Mf< T<M5)
`reorientation
`
`
`
` $500
`
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`
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`
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`3 mo
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`o
`
`o
`
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`
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`
`ElongationPl.)
`
`Fig. 2. Stress-strain curves as a function of
`temperature in a Cu—l4.0wt.%Al—4.2wt.%Ni single
`crystal. Dotted lines in (b),
`(c) and (d) re-
`present the S-S curves in the second cycle.
`(a)
`5-8 curves obtained
`(b‘)(b”) and (d') are the
`' single variant marten—
`from the stress-induced Y1
`site.
`
`—609-
`
`Lombard Exhibit 1031, p. 3
`
`naIYSis'
`has been found
`[12, 16 ‘ 20]
`that the
`structures Of
`the martensites
`are all long.
`eriod stacklng
`order structures
`with the common
`
`The unit
`cells of these
`martensites
`have been found
`to be all mono-
`clinic.
`The
`monoclinicity
`
`originates
`partly from the
`deviation of the
`
`stacking po-
`sitions from the
`ideal ones and
`partly from the
`elastic defor—
`mation of marten—
`sites under
`stress.
`See
`
`to
`Ref.[17, 20]
`be presented at
`this symposium
`for the details
`of the structure
`
`analysis of
`stress—induced
`
`martensites.
`
`By plotting
`the critical
`stresses as a
`
`Lombard Exhibit 1031, p. 3
`
`

`

`function of temperature,
`we obtain the curves shown
`in Fig. 3[13].
`Since the
`hysteresis associated with
`each transformation is very
`large,
`the curves are quite
`complicated.
`But if one
`takes a mid—point between
`the two critical stresses
`upon loading and unloading
`as an equilibrium point, a
`phase diagram schematically
`shown in Fig. 4[13, 21] may
`be deduced. Here the two
`diagrams are drawn by
`broken lines and full lines.
`The former is the one which
`the present authors[12]
`proposed some years ago,
`while the latter is the
`one they recently deduced
`from the experimental
`results of Fig. 3. Although
`the former is more reasona—
`ble according to the phase
`rule, we will use the
`latter in the following,
`since it follows experi—
`mental results.
`The follow-
`ing comments, which have
`been confirmed by further
`investigations, may be
`necessary for understanding
`the phase diagram.
`In phase
`field 01CD02, 81'
`is a
`stable phase, while 81” a
`metastable one[13, 21].
`Anyway 81” is always
`stress-induced from Y1'
`[18, 16], while 81'
`is
`stress-induced from 81[l7,
`22]. Both transform into
`01' by further loading[12, 17,
`transforms back to 51
`19], but the al'
`. 17
`19,
`irrespective of whether it has been transformed from 81” 0T 81 I
`’
`21],
`indicating that 81'
`is stabler than 81”.
`The reason why Bf'iS
`.
`.
`.
`-
`-
`-
`the
`stress—induced from Y1'
`in spite of its metastability.15 ihaghmithat
`mechanism of the Y1'-*'31” transformation is more favorab :d conditflm
`of the Y1'-*'Bl'
`transformation under an uniax1ally stress
`-
`[13].
`The 81' phase in the phase field OZEFG 15 also a m:::: mec
`phase, which appears due to the lack of direct transforma
`a1 1
`the stress-
`between 81 and a1'[13].
`Based on the phase diagram,
`strain curves in Fig.
`2 can be consistently explained-
`
`Fig. 3. Critical stress vs.
`temperature
`plots for each transformation indicated
`in Fig. 2.
`
`Stress-)
`
`Tensile
`
`Temperature —’
`
`Schematic phase diagram of a
`Fig. 4.
`Cu—Al—Ni alloy.
`See text for details.
`
`I
`
`.
`
`table
`haniSm
`
`We believe Fig. 4 is a prototype of the phase d
`
`.
`iagram 1n tempe
`
`I"
`
`Lombard Exhibit 1031, p. 4
`
`—610—
`
`
`
`Temperature (K)
`
`500
`
`30.
`
`z mm 3 G 3
`
`.
`'5C
`0p.
`
`Lombard Exhibit 1031, p. 4
`
`

`

`unfi‘
`
`In fact similar but
`ess coordinates in 5 phase alloys.
`.
`ent phase diagrams have been proposed in other 8 phase
`Zn[l4], Cu-Zn-Al[23] and Au—Ag—Cd[15] alloys.
`
`7 Characteristics of martensite—to—martensite transformations.
`In martensite—tO—martensite transformations[24 - 26, 12 - 20]
`e are some characteristics which are quite distinct from those in
`therl matrix_to.martensite transformations. Firstly the structural
`-5 very simple, since it is described by a change in stacking
`”5‘”
`alone. Recent studies by neutron diffraction showed that
`rameters changed linearly even among different martensitic
`struCtUres[17]‘ This means that the lattice distorsions are negligible
`ansformation under a constant stress. Lattice invariant
`usually absent except for the 8f'—>Y1'
`(or Elk—syl') trans—
`since the common basal plane itself is a habit plane[13].
`formation)
`he number of possible variants in martensite—to-martensite
`tions are only two, since the common basal plane is unique and
`Secondly '5
`trans forma
`directions are allowed only in the two directions (depending
`the shear
`and compression respectively.). This is quite distinct
`he familiar 24 variants in matrix—to-martensite transformations.
`his,
`there is a strong orien-
`tation dependence on the realization of
`martensite-to-martensite transformations.
`That is, martensite-to—martensite trans—
`formations or successive stress-induced
`transformations in Cu-Al—Ni alloys can
`be realized only in single crystals with
`such orientations as in the close vicini-
`ty of <001>Bl. This strong orientation
`dependence has been rationalized[13] .
`Thirdly the reverse transformations are
`sometimes not reversible.
`For example,
`the transformations on the first stage
`and the second stage in Fig. 2(b') are
`irreversible, but the strains completely
`recover during unloading.
`The reason for
`in."
`'
`such a recovery will be explained in
`
`Section 3.5.
`The Yl' 281" transformation {q
`_
`
`(Fig. 2(b")) is interesting.
`It is re—
`=‘
`‘
`'
`versible structure-wise, but the transfor- (
`)
`mation process is not reversible as shown
`in Fig. 5.
`The Y1"+ 81" transformation
`Upon loading proceeds with the habit plane
`.(001)Y1' without introducing any lattice
`invariant shear, while the 81"-—~Y1‘
`transformation upon unloading always
`proceeds by introducing (lOl)Y1'
`twins
`1n the Yi' martensite and the habit plane
`thus deviates from the (001)Y1'
`. This
`irreversibility is unique, and the trans—
`formation is discussed more in detail in
`the next section.
`
`Fig. 5. Optical micro—
`graphs indicating the
`irreversible nature 0f
`the transformation
`process in the Yl' 2'81”
`transformation in Cu-Al—
`Ni alloys.
`(a) the Yl'
`—" Bi" transformation
`upon loading, and (b)
`the
`81"F’Y1'
`transformation
`upon umloading.
`
`
`
`'
`
`_611_
`
`Lombard EthbIt 1031, p. 5
`
`Lombard Exhibit 1031, p. 5
`
`

`

`Phenomenological
`
`theore
`
`tical analysis of the 81
`
`mation.
`
`‘
`
`n unloading in CU-Al-Ni 3110y5‘ls
`transformation upo
`.
`.
`following two respects. Flrstly 1t PTOVides a
`nomenological theoretical considerations,
`SECOndl
`e lattice invariant shear is introduced byY
`lane condition.
`
`ti
`
`cal analysis of this transformation
`
`as
`
`‘
`
`le shear,
`
`_
`
`We
`
`
`0 observed habit plane normal;
`
`
`.catCuIaled habit plane
`normals
`
`'
`henomenological theore
`ngfi Earried out based on the W—b-R theory. As seen fr0m Fig.2
`rsion is described by a shear 0n (001)B”1
`e
`the lattice disto
`.
`_
`.
`'
`'
`The lattice invariant shear is the twhn
`plane in 1100131"
`-
`t‘ n
`S'
`d'
`b
`.
`lane In [101]
`v
`irec io .
`ince
`oth Operatlo
`,
`ning on (101)Y1' p
`Yine, which is the intersection of 3:6
`?331§;TR plane and (lOIJYI. planef
`is always present.
`In Other Words
`the solutions of the phenomenological
`theory are present for any vaer
`of the parameter x, a relative tw1n Width, and the invariant plane con-
`tisfied. This is quite distinct from the ordinary
`dition is always sa
`_
`_
`_
`case of matrix-to—martenSite transformations, where the solutions are
`e of x.
`The result of the numerical
`present only for a particular valu
`‘
`calculations is shown in Fig. 6.
`The observed habit planes were found
`to be pretty close to one of the two solutions for x = 1,
`The magni—
`ncrease with increasing x.
`tude of the shape strain was
`found to i satisfied and the shape strain
`Since the invariant plane condition is
`_
`- O,
`the introduction of (101)Y1'
`twins during the
`is minimum for x —
`e ascribed to the invariant plane condition.
`transformation cannot b
`believe this is due to the Le Chatelier principle as follows.
`We know from both theory and experiments that the introduction of
`(l01)Y1u twins shorten
`the specimens in the
`present experimental
`conditions.
`Thus the
`stress will go up if
`the (101) 1'
`twins
`are introduced in the
`Yl' martensite.
`Now
`let us consider the
`situation where we
`start unloading from
`higher stress level
`in the 81” phase.
`the (101) 1'
`twins
`are intro uced in the
`Bfl'—'Y1'
`transfor-
`mation,
`the trans-
`formation will start
`
`9’
`
`If
`
`from a higher stress
`level
`than the case
`without
`the twins.
`wit: :ielzeacLord
`Thi
`'
`~
`'
`Chat 1'
`.
`_
`
`e ier pr1nc1ple.
`
`X . twm lhnckness ratio
`
`
`
`(may;
`(mom:
`
`(00
`1
`
`
`)nl
`00mm
`The results of the PhenomenOIOglfal
`Fig. 6.
`.
`'
`theoretical calculations for the 5V"’Y1
`
`transformation.
`
`-612—-
`
`Lombard Exhibit 1031, p. 6
`1
`fl
`
`Lombard Exhibit 1031, p. 6
`
`

`

`same
`
`argument» the Y1'—- 81" transformation upon loading will
`a higher stress level if the twins are introduced, but this
`from
`‘olate the Le Chatelier prlnciple. This is the reason why the
`V1
`twins are not
`introduced in the Y1'-—v-B1" transformation upon
`'
`(101)Y1'
`Thus» the twinning behavior in the Yl': 81" transformation
`load‘ijggr'1 rationalized by the Le Chatelier principle.
`
`has
`
`3 4
`
`Transformation pseudoelasticity.
`Various pseudoelastic loopsare shown in a series of stress—strain
`es in Fig. 2.
`As described in the figure: all the pseudoelastic
`curV
`vioI‘ is due to the stress—induced marten51t1c transformations and
`reversions. This type of pseudoelasticity has been termed the
`bah?
`:::;:formation pseudoelasticity [13].
`The driving force for the pseudo-
`elastic behavior is clear from Fig. 4.
`It is the free energy diffrence
`of two phases con—
`
`function 0f
`stress.
`The “.3—
`cover)’ of strain
`during unloading
`
`35
`
`300
`
`is due to the re—
`
`250
`
`3
`g
`£200
`20
`18
`
`1.0
`
`4.5
`
`5
`
`s
`
`7
`
`a
`
`9
`
`IO
`
`11
`
`3.5
`30
`(”0-3 K4)
`1/T
`Fig. 7. Temperature dependence of the hysteresis
`(H vs' I” plot) for various transformations in
`Fig. 2.
`
`versible nature
`of the transfor-
`nation of con—
`cern, which es—
`sentially origi—
`nates from the
`ordered structures.
`In case where the
`transformation is
`not_rever51ble'
`as 1“ Flg- 2(1) L
`a trans format ion
`mechanism to
`account for it
`will be presented in the next
`section.
`
`2.0
`
`2.5
`
`The pseudoelastic strains as
`a function of crystal orientations
`have been calculated for various
`transformations using the values
`of the shape strains calculated
`from the phenomenological theory.
`Generally speaking, good agreements
`have been found between calculated
`and observed values except for
`detailsIS,
`l3].
`
`.5 o
`
`9’w
`
`$4on
`
`
`
`:8“
`
`335
`
`{3
`
`5.:h
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`
`
`
` 10“ 10 1o
`
`61!")
`
`The e
`ffeCt 0f temperature .
`and st
`.
`ra1n rate on the hystereSis
`of pseudoelastic loops have been
`measured for various t
`-
`ransfor
`
`Fig. 8. Strain rate dependence of
`.
`.
`the hystere51s (l/H vs.
`in e plot)
`for the Yl' $3581" transformation
`in a Cu—l4 lwt “Ml—4 2wt
`116Ni
`single crystal.
`
`—613—
`
`Lombard Exhibit 1031, p. 7
`
`Lombard Exhibit 1031, p. 7
`
`

`

`mations[13, 27, 28] as typically shown in Figs
`linear relationships with positive slopes have b7 and 8[13].
`hysteresis (h) and l/T, except for the case of t::“ fOund betw:?hh
`mation. Similarly a linear relationship has been fBI::'31'tran:f
`OuH
`or.
`rate (é) and l/H.
`In order to understand these behav d bet”
`1
`n
`-
`ee
`to introduce the notion of the effective stress
`or, it }18trfi“
`.
`(I
`-
`15 ”Se
`sum of external stress and chemical stress, which eff) deflned a
`fu1
`3
`-
`shown for the 81::‘Y1'
`transformation in Fig. g[27i5 SChematiqulyUm
`dislocation theory, which has originall
`b
`‘
`If the sur
`_
`_
`y
`een deVeloped b
`fax
`to account for the growth kinetics of the deformation
`.y gmfinopg]
`plied to the stress-induced transformation, one obta'
`twlnnlng,is a
`equationSBO],
`“‘5 the following
`
`U = aAnt
`
`Gt
`~—————————
`(4n(1 — v)
`
`
`1
`2
`) teff
`
`.
`. _
`fin e - 2n 81 —
`
`2
`
`Ant
`a
`,
`kr
`
`Gt
`—————————— 2
`(4n(l
`- v)) Teff
`
`
`1
`
`(3.1;
`
`[3 2)
`
`where U is the activation energy for the process
`_
`
`J
`
`O'- a C0
`
`‘
`
`to 5/6, A a function of the critical radius of a sgzpatiéeT1§1‘c
`equal
`and a half of the step width (Q), G a bulk shear modulus
`v th
`Poisson's ratio, t the magnitude of the Burgers vector ofthe :if
`dislocation, E; a constant term and k the ioltzmun constant
`Itrizice
`easily seen that the above temperature and strain rate dependencezf
`the hysteresis of pseudoelastic loops are rationalized by eq.(3 2)
`Furthermore, by measuring the slope of an experimentallv obtahmd ..
`hysteresiswstrain rate relationship,
`the activation energyllcanbe
`obtained.
`
`The heat of transformation (AH) or the entropy of transfinnaUen
`(AS) may be obtained from the Clausius—Clapeyron equation bynwammnm
`the slopes of 0 vs. T curves in Fig. 3, and the result is shownin
`Table l[13].
`The comparison of these values with those of the ante
`sponding hysteres in Fig.
`2 is of quite interest.
`it
`is to be mfled
`that in martensite—to—martensite transformations in is very smallbUt
`the hysteresis is large, while that
`in the 21:: 51'
`transfommuionLH
`is relatively large but
`the hysteresis is very small. This r6flflt
`clearly shows that
`the amout of hysteresis has nothing to do Hifiléia
`as excepted.
`Since all the long period stacking OTJCT Strwnfire:are
`on
`interactions 3
`the same internal energy when nearest neighbor
`in martensite-to-
`taken into account, AH is expected to be small
`site transformations. However, such ex—
`pectation cannot be held on their hyster—
`eses, since the latter represent
`nuclea—
`tion barriers in respective transfor—
`mations.
`
`A—n'_
`V
`
`
`
`3.5. Mechanism of martensite—to~
`martensite transformations.
`
`Since the structural changes in
`martensite-to-murtensite transformations
`
`—6l&—
`
`Lombard Exhibit 1031, p. 8
`
`

`

`-2.04
`
`-0.139-
`
`Fig.
`10 shows the structural changes when the Yl' martensite is
`loaded and unloaded[13].
`It is easily seen that these structural
`changes can be accomplished by the regular slips by partial dislo-
`cations with Burgers vectors b = :
`a/3[100]Y11 = i a/3[100]31n etc. as
`indicated by arrows.
`the transformations can be described by
`Thus,
`successive nucleation of these partial dislocations and their subse—
`quent expansions.
`
`Firstly the pseudoelastic behavior is easily explained by con-
`traction or renucleation of these dislocations .
`Since stacking faults
`are inevitably associated with the partial dislocations,
`the cross slip
`leading to dislocation interactions,
`which will hinder the strain re—
`covery, will be avoided.
`The reason why the strain recovers even in
`irreversible transformations such as the Bl”—+-a1'
`transformation upon
`loading and the a1‘—+-81'
`transformation upon unloading (Fig. 3(b')) is
`easily seen from Fig. 10(b) and (c). That is,
`the two slips every six
`layers in (b)
`is just cancelled by the two slips in opposite direction
`in (c) as an averaged shear.
`
`
`
`-———— Loodlng
`
`“—91 ————— Unloadmg ——————— at
`
`=e
`
`=s
`
`=3
`
`
`
`Secondly the
`strain attained
`on each stage in
`Fig.
`2 has been
`found to be con-
`sistent with
`that calculated
`from the above
`mechanism.
`
`Thirdly the
`observed habit
`Planes (001)Y1"
`(001)61" etc.
`are consistent
`With the above
`
`ABC'
`'[100]y_“
`(a)r.’[2H(I'1)]
`
`ABC'
`1100],: "
`(b)pԤ[18R2(fi3l),]
`
`ABC.
`11001.5"
`(mammal
`
`ABC.
`1‘00”,"
`(d)p'1[aaR‘(ZT)6]
`
`ABC.
`‘UOOlif"
`(e)7§'[2H(fi)]
`
`A mechanism of successive transformations.
`Fig. 10.
`yl'_..Bl”—-»ou' upon loading and ou'a-Blh—u-Yl'
`upon unloading. Arrows indicate necessary slips to
`produce the subsequent structure.
`
`Lombard Exhibit 1031, p. 9
`
`—6lS—
`
`Lombard Exhibit 1031, p. 9
`
`

`

`the observed habit plane is d
`As noted above,
`mechanism.
`the basal P13“8 in the 81"-“Y1'
`transformation. This is b
`(101)Y1l
`twins are introduced in this particular transfermation
`In the fourth place one may argue the
`partial dislocation loops.
`The activation
`can be estimated from eqs.
`(3.1.) and (3.2.
`value for the slope in eq.
`(3.2.).
`The est'
`eV, which was not an unrealistic value f
`by thermal activation.
`
`3.6. Effect of sense of stress on stress—induced transformations
`In order to see the effect of sense 0
`transformations,
`tension-compression tests
`extensively in Cu-Al-Ni alloys.
`Two typica
`shown in Fig. 11, which have been taken at
`below Mf respectively.
`Asymmetric nature
`the curves.
`Prev1ously a stress—strain cur
`
`Miura et al.[31] and it has
`martensite stress—induced
`on tension and compre531on Sides. However, it was confirmed in the
`present study that it was due to the different martensitic transfor-
`mations on both sides. That is,
`the {3128f transformation on tension
`side and the 8133'Y1'
`transformation on compression side. We believe
`this behavior originates from the non-uniaxiality in compression test.
`
`A(
`
`)286K
`
`5(3C)
`
`(8)217K 400
`
`(MPa)
`
`
`
`
`
`3(3()
`
`2C)O
`
` Compression
`
`_
`-
`.
`.
`es
`sion
`Fig. 11. Typical stress-strain curves in ten51on compr
`M5 = 242K’
`tests in a Cu-l4.5wt.%Al-4.2wt.%Ni single crystal-
`Mf = 226K, AS = 250K and Af = 276K.
`
`"616_ Lombard Exhibit 1031, p. 10
`i...-Illlll!
`
`Lombard Exhibit 1031, p. 10
`
`

`

`.
`
`§
`
`due to a twinning in the Yi' martensite. This asymmetry in de-
`mode is what is expected from the low symmetry of the marten—
`:Er further details see Ref.
`[32]
`to be presented at this
`
`established that the Schmid law usually holds in the
`eems
`I? i of a variant of the stress—induCCd martensite[5].
`Furthermore
`501?Ct10 erally accepted in S phase alloys that the shear system inter-
`it?§ genth an applied stress is the shape strain[l3, 27, 33]. However,
`attlng glMori[34] reported that in stainless steels the interacting
`Kata an stem was not the shape strain but that the {111}<§ll>f shear
`5h?a? Szing frOm the Bogers-Burgers mechanism. This could mean that the
`orlglnating shear system in the nucleation stage may be different from
`interfic 6 strain, as they suggested. Meanwhile it is knowu in 18-8
`the.sla25 steels that the formation of the c martensite preceeds that of
`:;:1na? [11].
`If that is the case,
`the formation of the
`o‘ phase is
`t determined solely by the applied stress and the result is not quite
`Eiliable. This point is not quite unambiguous.
`
`Acknowledgments
`
`to Mr. H. Sakamoto and Professor M.
`The authors are grateful
`lbkonami for useful discussions and collaborations for some of the work
`included in this paper.
`
`References
`
`l—‘Il——1f—'\I'-—|4:.(1.]NF".._u_n_n_a
`
`[5]
`
`[6]
`[7]
`[8]
`[9]
`[10]
`[11]
`
`[14]
`[15]
`U6]
`
`Ichihara:
`
`Z. Anorg. Chem., 207(1932)21.
`E. Scheil:
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`1 (19531531.
`M. w. Burkart and T. A. Read: Trans. XIME, 197(1953)1516.
`L. Delaey, R. V. Krishnan, H. Tag and H. Warlimont:
`J. Mat. Sci.,
`9(1974)1521, 1536, 1545.
`K1 Otsuka and C. M. Wayman:
`in Reviews on the Deformation Be-
`havior of Materials (P.
`Feltham, Ed.), Freund Publishing House
`Ltd., Israel,
`(1977)vol. II, No.2, p.81.
`I. Tamura, T. Maki and H. Hato: Trans.
`ISIJ,
`l9j1970)163.
`?. C. Maxwell, A. Goldberg and J. C. Shyne: Met. Trans., §fi1974)
`1305.
`G. B. Olson and M. Cohen:
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`M. Cohen:
`Proc.
`ICOMAT 1977, Kiev, p.69.
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`this conference.
`TX Suzuki, H. Kojima, K. Suzuki, T. Hashimoto and M.
`_Acta Met., 25(1977)1151.
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`Scripta Met.,
`lg(1976)983.
`K. Otsuka, H. Sakamoto and K. Shimizu:
`Acta Met.,
`in press.
`TH A. Schroeder and C. M. Wayman: Acta Met., §§11978)1745.
`S. Miura, M. Ito, F. Hori and N. Nakanishi:
`Proc. lst JIM Int.
`Symp., Suppl. Trans.
`JIM (1976)p.257.
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`in press.
`M. Tokonami, K. Otsuka, K. Shimizu, Y.
`conference.
`
`Iwata and l. Shibuya:
`
`this
`
`“617‘
`
`Lombard Exhibit 1031, p. 11
`
`Lombard Exhibit 1031, p. 11
`
`

`

`V. V. Martynov and L. G. Khandros: Dok11 - Aca
`d” Nauk SSSR,233
`(1977)345.
`V. V. Martynov and L. G. Khandros: Dokll. Acak, Nauk
`‘xx
`(1977)1349.
`SSSR,237
`L. G. Khandros and V. V. Martynov:
`this conference
`.‘\
`12
`K. Shimizu, H. Sakamoto and K. Otsuka: Scripta Met
`K. Otsuka, T. Nakamura and K. Shimizu: Trans. JIM 15Tfi997m7n‘
`L. Delaey et a1.: private communication (1978)
`“'
`WUZOQ
`H. Tas, L. Delaey and A. Deruyttere: Scripta Met 5(1971
`)1U7.
`K. Otsuka, H. Sakamoto and K. ShimiZu:
`S
`ha e Memor Effects.
`Alloxs(J. Perkins, Ed.) Plenum Press,
`(1975), p. 327
`in
`C. Rodriguez and L. C. Brown: Met. Trans. , 7A(1976)265
`K. Otsuka, C. M. Wayman, K. Nakai, H. Sakamoto and K Shnm
`Acta Met. ,24(1976)207.
`J. Van Humbeeck, L. Delaey and A. Deruyttere:
`Z. Metall.
`(1978)575.
`K. Sumino: Acta Met.
`l4(1966)1607.
`K. Sumino and M. Suezawa:
`unpublished work (1976).
`Ref. [13].
`N. Nakanishi, T. Mori, S. Miura, Y. Murakami and S. Kachi:
`Mag., g§j1973)227.
`H. Sakamoto, M. Tanigawa, K. Otsuka and K. Shimizu:
`conference.
`T. Saburi, S Nenno, J. Hasunuma and H. Takii:
`Symp. Suppl. Trans. JIM. ,
`(1976)p. 251.
`M. Kato and T. Mori:
`Proc. lst JIM Int. Symp. Suppl. Traw..HM
`(1976)p.333.
`M. Tokizane:
`p.345.
`
`Proc. lst JIM Int. Symp. Suppl. Trans. JIM., 097®
`
`Z“-
`69
`
`’
`
`Cited in
`
`Phil.
`
`this
`
`Proc.
`
`lstJIMInL
`
`Lombard Exhibit 1031 p. 12
`-618— A
`
`Lombard Exhibit 1031, p. 12
`
`

`

`
`
`PROCEEDINGS
`
`OF THE
`
`INTERNATIONAL
`
`CONFERENCE
`
`ON
`MARTENSITIC
`TRANSFORMATIONS
`ICOMAT 1979
`
`CAMBRIDGE, MASSACHUSETTS
`
`USA
`
`24-29 JUNE 1979
`
`Lombard Exhibit 1031, p. 13
`
`Lombard Exhibit 1031, p. 13
`
`