reversibility and hysteresis of martensitic transformations

E. HORNBOGEN: Reversibility and Hysteresis of Martensitic Transformations 161

phys. stat. sol. (b) 172, 161 (1992)

Subject classification: 62.40 and 64.60; 75.60; SI

Institut f u r Werkstoffe, Ruhr- Uniuersitat Boclium ')

Reversibility and Hysteresis of Martensitic Transformations

BY E. HORNBOGEN

Dedicated to Professor Dr. PETER HAASEN on the occasion of his 65th birthday

The term martensitic is used for a diffusionless structural phase transformation p -+ aM which is associated with a considerable amount of lattice variant shear: ypm z 0.2. This reaction is defined as reversible if the reverse reaction aM + p faultlessly restores the original parent crystal p. Sets of factors are established which favour the reversible (or irreversible) mode. Hysteresis is due to lattice friction acting on the moving p/a,-transformation interfaces during a transformation cycle. It can vary by several orders of magnitude. Analogies are indicated between ferromagnetic and martensitic hysteresis.

AIs martensitisch wird ein diffusionsloser, struktureller Phasenubergang p + aM bezeichnet, der mit einer betrachtlichen gittervarianten Scherung ymp % 0.2 verbunden ist. Diese Reaktion wird als reversibel definiert, wenn die Umkehrreaktion den Ausgangskristall fehlerlos wiederherstellt. Eine Reihe von Faktoren werden zusammengestellt, die die reversible (oder irreversible) Mode begunstigen. Die Hysterese ist auf Gitterreibung an den bewegten p/aM-TranSfOrmatiOnSgren~aChen wahrend eines Umwandlungszyklus zuruckzufuhren. Sie kann sich um mehrere Groknordnungen andern. Es werden Analogien zwischen ferromagnetischer und martensitischer Hysterese aufgezeigt.

1. Introduction

Hysteresis is a well-known phenomenon in ferromagnetic materials [ 11. Its origin is based on interactions between domain structure and microstructure [2]. Hysteresis characterized by the coercive field can vary by more than lo7. It may approach zero for very fine (superparamagnetic) structures [2, 31.

There exist some remarkable phenomenological analogies between ferromagnets and shape memory alloys (Fig. 1). Instead of reorientation spins these materials show anomalous shape changes as a function of stress CT or temperature T: E = f ( o , T ) . Normal materials deform reversibly (elastic) E, or irreversibly (plastic) E,,

E(B, T ) = ~,(cr) + E,((T) + ~~(7'). (1)

ze( T ) is due to thermal expansion and reversible just as elastic deformation. In shape memory (SM) materials these components are supplemented by three additional strains,

where E,,(cT) is the pseudo elastic and cpp(cr, T ) the pseudoplastic deformation and zZw(T) the two-way effect. Diffusion-controlled time-dependent deformations E ~ ( C T , T , t ) can be excluded in this context. The strains epe, E,,, and E~~ are shown in the cr-, T- , &-space in

') PF 102148, W-4630 Bochum, FRG.

1 I physica (b) 172/1

162

I "0° 0

0

aJ U c 0

.G 0.75 L

,? 0.5 0 E Y)

0.2 5

Fig. 1. Extend of martensitic hysteresis for FeNi,, and NiTi

E. HORNBOGEN

-100 0 100 200 300 400 500 T ( O C ) -

Fig. 2. They are all related to a diffusionless (martensitic) structural phase transformation of a high temperature phase p into martensite aM. This transformation is of first order but it corresponds to the electronic transformation para -+ ferromagnetic by the formation of a domain structure in the low-temperature phase (Fig. 3). These domains minimize strain energy which is required by the lattice variant shear from the parent phase p (Fig. 3). The crystallographic p --f CL transformation shear in an alloy system yp, determines the limits for the bulk strain of all three SM effects.

yB,, amounts to 0.2 in b.c.c c, f.c.c transformation (P-CuZnX, P-NiTiX, y-FeNiX). Complete randomness of the domains leads to a bulk strain of zero. In some alloys premartensitic (R) states form by a second-order reaction, which induces very small shears yR < 0.02. It shows analogies to superparamagnetic solids, i.e. minimum hysteresis.

2. Reversible and Irreversible Course

At the martensite start temperature M , (Fig. 4) a first set of crystals forms, the size of which is limited by the diameter of the crystallites of the parent phase. This temperature is determined by an equilibrium temperature To and an additional undercooling AT which is required to provide the energy for nucleation and motion of the a,-crystals into 0 (Fig. 4,5),

M , = To + A T . (4 a)

Reversibility and Hysteresis of Martensitic Transformations 163

U A IS = const.

C

b U

U

6Y

9 0

Fig. 2. Properties of alloys in G-, E-, T-space. a) Normal behaviour, b) pseudoelasticity, c) two-way effect, d) one-way effect or pseudoelasticity (As, Af austenite start, finish temperature; M,, MI martensite start, finish temperature)

Often several subsequent generations of a,-crystals can be distinguished which form during further cooling [4]. Then a fractal microstructure forms which is represented in a schematic way in Fig. 6. The consequence is a spectral size distribution of the newly formed phase. In case of a stress-free transformation (i.e. no external or internal shear stresses z are acting, (9 b), it is subdivided in orientational variants which lead to zero shape change of the bulk material. The critical driving free enthalpy G,, which determines AT (Fig. 4) depends not only on the enthalpy for nucleation G, but also on a frictional force Gf and the eleastic constraint G, which opposes the motion of the o/a,-interface and therefore restricts sidewise growth [5],

G,, = G" + G, + G f . (4b)

11"

164 E. HORNBOGEN w d Z

r--

I

I

a+

a

-I Fig. 3. Domain structures in martensite. a) Lat- tice variant shape change yp, is completely or partially compensated by formation of a+-, cr--domains. b) Domains in martensitic CuZnAl alloy. c) Fractal domains in partially martensitic FeNiAl alloy

Reversible transformation may take place during reheating of the low-temperature phase. Then the reverse reaction takes exactly the same path as the forward reaction. This implies removal of the a,-crystals and their defects by shear in the opposite direction in the sequence in which they had formed (Fig. 6). Then no new nucleation is required GL = 0, the reversible elastic deformation favours the reverse transformation G, = 1 - Gil, only a frictional force Gf has to be overcome and requires overheating AT' (Fig. 7),


a

a M a

P

I -

martensite ( o/o ) - Fig. 4. a) Free enthalpy vs. temperature plot of p- and a-phase with equal composition. aM contains energy stored by lattice invariant deformation (elastic stresses, domain boundaries). b) Course of a transformation cycle for P-CuZn,,

The term G, contains not only eleastic deformation but also the energy of all lattice defects which form a part of lattice-invariant deformation and which are annihilated during the reverse transformation (Fig. 3). Their energy is regained in addition to the elastic energy and becomes part of the term 1 - G',I (4c).

Irreversible transformation represents a different mechanism. New nucleation of p is required. There are no elastic back stresses which aid reversion, but friction exists with a positive sign. A back stress caused in p requires the energy + Gi,

166 E. HORNBOGEN

Fig. 5 Structure of moving p/a-transformation interfaces (schematic). a) Homogeneous alloy, b) coherent ordered particles in P-solid solution

Fig. 6. Reversible and irreversible transformation (schematic). Revers- ibility restores completely the original crystal of the high-temperature phase p

T-

b 0 0.5 1.0

& (%) - Fig. 7. Increasing hysteresis due to the formation of lattice defects (dislocations, antiphase domain boundaries in CuZnAl alloy). a) Effect of plastic deformation of martensite on temperature hysteresis. b) Effect of mechanical cycling of stress hysteresis in the superelastic state (oa = 75 MPa)

168 E. HORNBOGEN

3. Causes for Irreversibility

Irreversible martensitic transformation takes place during hardening of tool steels. Iron- based alloys are therfore especially suited to define the prerequisites for irreversibility. Several factors have to be considered, which may act in combination.

The following phenomena increase the frictional forces on the reverse a -+ p-transformation. They impede the motion of the a + p-transformation interface. In the extreme case of their immobility new nucleation of the high-temperature phase (p) may be required. If diffusional processes interfere with the structural transformation the reaction is no longer martensitic. Then the effective period of heating of the low-temperature phase to the complete formation of the high-temperature phase tup exceeds the hop time for diffusion zua in this temperature range AT = A, - M,,

bZ tup 2 Zap = -

D ’

where b is the atomic spacing and D the diffusion constant. The following reactions are characteristic of Fe-based martensite. They will impede or inhibit reversibility :

a

2 a) - (111)-dislocations, which originated by lattice invariant shear interact to immobile

a (100)-nodes,

a a - [iii] + - [ i i i ] + a [iOO] . 2 2

b) The same is valid for dislocations induced by subsequent plastic deformation of as-formed martensite ad or the formation of highly deformed zones at intersections of martensite crystals.

c) Segregation of interstitial or substitutional atoms X into these defects (d = dislocations, twin boundary, stacking fault, pa-phase boundary),

a d + x m d - x . (6 b)

%dcr adisorder . (6 c)

d) Order or disordering reactions in martensite,

e) Decomposition reactions from supersaturated ass, for example formation of incoherent interstitial or intermetallic compounds AXBY,

The reactions a) ana b) are independent of diffusion, i.e. they occur also for tmP < z~~ ((5)). Lattice defects act as obstacles to the motion of the pa-interfaces, which is required for a reversible reverse 01 + p reaction (Fig. 5). A quantitative treatment of G, ((4)) requires the application of dislocation obstacle interactions driven by chemical or mechanical energies [6,7]. An increased frictional energy for the reverse reaction will raise the temperature range in which this reaction takes place (stabilization of martensite). This, in turn, can lead into a temperature range in which the reactions c), d), e) become effective. These may not only increase the frictional energy (by a dispersion of particles) but may also reduce the driving


free energy Gap due to precipitation of elements which raises the temperature To ((4)). This leads to a situation in which not only growth of the high-temperature phase becomes diffusion assisted, but where new orientational variants are nucleated. Then the .parent crystallite of the p-phase is not restored and martensitic reversibility is lost (Fig. 6).

4. Causes for Reversibility

Reversibility is required for shape memory. Therefore, the established alloys P-CuZnX and P-NiTiX fulfil requirements which, in turn, must contradict those listed in the preceding chapter:

a) temperature and rate of heating and cooling for the fl t, q,, transformations must fulfil the condition

i.e., no diffusion should interfere with the transformation. b) Lattice invariant strain (Fig. 3 ) should exclusively create defects which are able to

move reversibly and annihilate during the reverse transformation: twin boundary, stacking fault, but no interacting dislocations.

c) Coherency strains between the two phases should be elastic. This requires either a small volume change V,, or a high yield stress of the parent phase p. Formation of immobile misfit dislocations must be avoided.

d) Order in the crystal structure of p increases its strength. This implies that shear into a will cause a metastable ordered phase. Reverse shear is the only diffusionless path by which the original order is restored during a a + P-reaction.

e) A similar effect is caused by coherent ordered particles which are dispersed in the disordered P-phase (cf. (6d)),

(7) p + pdisorder + p d e r --f (adisorder + aorder )M '

Full reversibility requires that the phase aEder stays coherent with the matrix c ~ E ~ ~ ~ ~ ~ ~ during the transformation. The particle diameter should stay below d,(d < d,) because coherency is lost during transformation for particles above this size,

(y,,, y, are the specific interfacial energies for non-coherency and coherency, Cis a geometrical factor given by the shape of the particles, AGba (in JmP3)) (Fig. 2 and 5b).

These five aspects plus a large lattice variant deformation ( (3 ) ) characterize a martensitic transformation which provides shape memory. Irreversible or reversible behaviour or transitions between the two modes can be demonstrated by alloys of iron. Adisorder --f order transition is found in y-Fe-Pt alloys. Order stabilizes the high-temperature phase and induces reversibility [8]. In FeNiAl alloys, (Fe, Ni),Al particles can form prior to the transformation. Reversibility is induced depending on volume fraction and size ((8)) of the particles and connected with a narrowing of hysteresis (Fig. 8) [9]. Reversibility is most pronounced if the volume change of about 3% which usually accompanies the transformation of iron is reduced (Table 1). This, in turn, is associated with a paramagnetic + ferromagnetic transformation. An addition of Co will raise the Curie temperature of the high-temperature

170 E. HORNBOGEN

Fig. 8. Effect of plastic deformation E~ (%) and ageing at 600 "C of the austenite on hysteresis during thermal cycling of an FeNi,,Co, 5Ti4 alloy. The hysteresis of the homogeneous (unaged) alloy amounts to about 500 K (see Fig. 1)

phase, the ferromagnetic + ferromagnetic transformation is associated with reduced volume change and full reversibility induced (Fig. 8) [lo]. Present research applies these principles to develop reversible alloys of iron.

In case of reversibility of martensitic transformation, external hydrostatic stress p , a shear stress 2, and a magnetic field H will be able to raise or lower the transformation temperature and modify the course of the transformation. This can be expressed by three Clausius- Clapeyron-type equations [5, 111. The effect of a hydrostatic stress depends on sign and amount of the volume change k V,,, which should be small,

Table 1 Volume change V,, and lattice variant shear yBa due to martensitic transformation

high-tempera- crystal structure v,m yp, defects caused magnetic ture phase A A - M by lattice in- states

variant shear A - M

P-CuZnX b.c.c. - close-packed % 0 ~ 0 . 2 twin, stacking P*P

0-NiTiX bee. - close-packed Y 0 ~ 0 . 2 twin, stacking P-P

y-FeNiX f.c.c. * b.c.c., b.c.t. +0.03 = 0.2 dislocation, P- f

fault

fault

(twin)

elastic strain

austenite) elastic strain, few stacking stacking

y-FeNiCoX f.c.c. * b.c.c., b.c.t. < f0.02 -0.2 (dislocation) twins, f * f

y-FeMnX f.c.c. * h.c.p. -0.01 Y 0.2 (dislocation in p * af


where S,, is the entropy of transformation. As a large lattice variant shear yo, is aspired, external or internal shear stress components in this direction will raise the transformation temperature. The same stress will however retard the reverse transformation. In this way the hysteresis and the course of the transformation with temperature can be modified,

Equation (9b) is valid up to To (Fig. 4a) and until the shear stress t reaches the yield stress of the P-phase zyp. In a temperature range above M, the chemical driving force provided by undercooling ((4a)) can be supplemented by mechanical energy from a stress tensor z parallel to G.

If the high-temperature phase is paramagnetic and transforms into a ferromagnetic martensite an external field H will raise the martensite start temperature depending on the ferromagnetic-paramagnetic difference in magnetic induction Jf - J , in the two phases

5. Summary and Conclusion

Crystallographic reversibility is a characteristic feature of a martensitic phase transformation. Semi-martensitic reactions are diffusionsless for the formation of the low-temperature phase p 4 uM, but take a different path for the reverse reaction ct + 8. The latter are well known especially in interstitial alloys of iron. There exist a set of physical conditions which favour reversibility and consequently shape memory [ 121.

1. Negligible diffusion in the total transformation range AT = A, - M,. 2. Minimum volume change V,, associated with the P tf aM transformation. 3. Crystallographic order in the high-temperature phase P. 4. Ordered particles of subcritical size (d < d,) in a solid solution of the high-temperature

5 . Lattice invariant shear by defects (stacking faults, twin boundaries) which do not

6. High perfection of the crystals of the high-temperature phase prior to transformation. 7. A high yield stress of the high-temperature phase. 8. Absence of magnetic transformations simultaneous with the structural transformation

which cause an additional change in volume. In case of reversibility the hysteresis of a transformation cycle is determined by the lattice

friction experienced by the moving P/a,-interface [7]. The introduction of lattice defects or incoherent particles can cause an increase of hysteresis by several orders of magnitude [5]. Irreversibility implies nucleation of new crystallographic variants during the reverse transformation. This leads to a further extension of hysteresis and a modification of the microstructure of the high-temperature phase.

There exist phenomenological analogies between martensitic and ferromagnetic hysteresis. Both are based on the existence of a domain structure in the low-temperature phase. The extent of hysteresis depends on the friction due to domain walls, obstacle interactions, pinning of domain walls, and the necessity to nucleate new domains.

phase.

rearrange irreversibly and which annihilate during the reverse transformation.

172 E. HORNBOGEN: Reversibility and Hysteresis of Martensitic Transformations

References

[I] E. HORNBOGEN and H. WARLIMONT, Metallkunde, 2nd ed., Springer-Verlag, Berlin 1991 (p. 283). [2] E. KNELLER, in: Magnetism and Metallurgy, Academic Press, New York 1969 (p. 365 to 371). [3] E. KNELLER and R. HAWIG, IEEE Trans. Magn. 27, 3588 (1991). [4] E. HORNBOGEN and N. JOST, Europ. Symp. on Martensitic Transformation and Shape Memory

[5] E. HORNBOGEN, Acta metall. 33, 595 (1985). [6] E. HORNBOGEN, Trans. MS AIME A10 947 (1979). [7] G. B. OLSON and M. COHEN, in: Dislocations in Solids, Ed. F. R. N. NABARRO et al., Elseviers

181 S. OWEN, Mater. Sci. Engng. A129, 197 (1990). [9] E. HORNBOGEN and W. MEYER, Z. Metallk. 58, 297, 372, 445 (1967).

Properties, les editions de physique, Les Ulis, France, C4-199, 1991.

Publ. Co., Amsterdam/New York 1986 (pp. 285 to 407).

[lo] E. F. WASSERMANN, M. ACET, and W. PEPPERHOFF, J. Magnetism magnetic Mater. 90/91, 126

[I I] LI Lu, E. AERNOUDT, et al., Z. Metallk. 81 613 (1990). [ 121 E. HORNBOGEN, Legierungen mit Formgedachtnis, Westdeutscher Verlag, Opladen 1991.

(1990).

(Received January 27, 1992; in revised form March 4, 1992)

reversibility and hysteresis of martensitic transformations

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