Kinetic grain growth in β-copper shape memory alloys

Materials Science and Engineering A241 (1998) 114 – 121

Kinetic grain growth in b-copper shape memory alloys F.J. Gil a,*, J.M. Guilemany b, J. Ferna´ndez b a

Departamento de Ciencia de Materiales e Ingenierı´a Metalu´rgica, ETS, Ingenieros Industriales de Barcelona, Uni6ersidad Polite´cnica de Catalun˜a, Diagonal 647, 08028, Barcelona, Spain b Ciencia de Materiales-Ingenierı´a Metalu´rgica, Dept. Ingenierı´a Quı´mica y Metalurgia, Facultad de Quı´mica, Uni6ersidad de Barcelona, Barcelona, Spain Received 3 March 1997; received in revised form 10 June 1997

Abstract The kinetic grain growth has been studied for b-CuZnAl, b-CuAlMn, b-CuZnAlMn, b-CuAlMnSi and b-CuZnAlCo shape memory alloys by the calculation of different grain parameters and the ratio of the grain boundary area per unit volume from measurements obtained at different temperatures and heat treatment times. The growth exponent and activation energy have been evaluated. The martensitic transformation temperatures and stress induced martensite were studied in relation to grain growth for different heat treatment temperatures and times. Linear decreases in the Ms and As temperatures and a linear increase in the critical stresses with respect to the grain growth have been obtained. © 1998 Elsevier Science S.A. Keywords: b-copper; Kinetic grain growth; Shape memory

1. Introduction The technological importance of grain growth stems from the dependence of properties, and in particular the mechanical behaviour, on grain size. In materials for structural application at lower temperatures, a small grain size is normally required to optimise the strength and toughness. However, in order to improve the high temperature creep resistance of a material of large grain size is required [1]. The b-Copper-based shape memory alloys are known to show excessive grain growth when heat treated at temperatures corresponding to single b phase region. Because of requirements concerning mechanical properties, grain refinement is necessary. This can be achieved by addition of adequate refining elements and by applying the proper thermo-mechanical treatments. In this work, the effects of Si and Co on the grain growth kinetic have been studied; but the first step towards the understanding and the control of grain growth in these alloys consists in a study of the grain growth behaviour in b-Copper based alloys which do not contain grain refining elements [2 – 4]. * Corresponding author. Tel.: +34 3 4016706; fax: + 34 3 4016706; e-mail: [email protected] 0921-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 9 2 1 - 5 0 9 3 ( 9 7 ) 0 0 4 8 0 - 2

The grain growth produces changes in the transformation temperatures and in the stress induced martensite. Coarse grain sizes should be avoided: they decreases the uniformity and reproducibility of properties, they can cause pseudoelastic brittleness due to the high compatibility stresses between neighbouring grains leading to intergranular fracture and they decrease the stress-corrosion resistance [5–7]. The kinetic grain growth has been determined for different b-copper based shape memory alloys by the determination of different grain size parameters. The growth exponent and activation energy have been evaluated. The martensitic transformation temperatures and stress-induced martensite have been also studied in relation to grain growth for different heat treatment temperatures and times.

2. Experimental procedure This study was carried out on ten different b-copper shape memory alloys with the chemical compositions given in Table 1. These alloys were obtained by vacuum-sealing the various materials in quartz tubes. These tubes were then placed in a resistance furnace for 6 h at 1250°C after which they were air cooled.

F.J. Gil et al. / Materials Science and Engineering A241 (1998) 114–121

For each of these alloys, 23 slices were cut from the same bar, measuring 5 mm in diameter and 4 mm in height. The sample weight was approximately 400 mg. Two of them were used as reference samples, while the rest were subjected to different heat treatments at 700, 800 and 900°C for 1, 3, 5, 10, 15 30 and 60 min at each temperature. A set of specimens was placed in the furnace at the fixed temperature for each experiment and then taken from the furnace after the appropriate time of heat treatment and quenched into water at 20°C; this gave the same cooling rate for all the samples. Afterwards, they were metallographically polished and etched with FeCl3 alcoholic solution. The grain size parameters (perimeter, area and diameter) were obtained by an image analysis technique with a Matrox MWP – AT installed in a PC – AT computer using a software in a TITN SAMBA system. The image acquired with a normal camera was then processed by enhancing the contrast in order to improve the image quality and a pseudo-colour representation was carried out to improve the ease of interpreting the results. After optimising the image, the parameters which had to be evaluated were recorded for each grain of the polycrystal and the average values then obtained. All the samples had a b phase structure. The martensitic transformation temperatures for the samples of alloys 1,3,5 and 6 were measured after the different heat treatments. The calorimetric system used was described in previous papers [8 – 10]. The flow calorimeter measures differential signals by means of Melcor thermobatteries. The temperature was measured by means of a standard Pt-100 probe. The Ms and As, starting transformation temperatures can be determined when there is a sudden increase in the calorimetric signal, while the finish temperatures, Mf and Af, are determined when the calorimetric signal returns to the baseline. The transformation temperatures of the heat treated specimens were measured during the first heating and cooling cycle. No significant differences from these values were found when the sample was thermally cycled several times. Compression tests were carried out on the same samples, after the calorimeter test, using an Instron machine at room temperature. The cross-head speed was 1 mm min − 1. The transformation stress (b“ Stress Induced Martensite) and reverse transformation stress (Stress Induced Martensite “b) have been determined.

3. Results and discussion

3.1. General remarks on the kinetic of grain growth The kinetic of the grain growth in a single-phase material is generally expressed by the Burke and Turnbull model [11,12]. Burke and Turnbull deduced the

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kinetics of grain growth on the assumption that the driving pressure (P) on a boundary arises only from the curvature of the boundary. If the principal radii of curvature of a boundary of energy gb are r1 and r2 then P= gb



1 1 + r1 r2



(1)

if the boundary is part of a sphere of radius r, then r= r1 = r2 and P=

2gb r

(2)

Burke and Turnbull then made the following assumptions: 1. gb is the same for all boundaries. 2. The radius of curvature r is proportional to the mean radius (R) of an individual grain, and thus P=

agb R

(3)

where a is a small geometric constant. 3. The boundary velocity is proportional to the driving pressure P and to dR/dt =cP, where c is a constant. Hence, dR aC1gb = dt R

(4)

and therefore R 2 − R 20 = 2aC1gbt

(5)

which may be written as R 2 − R 20 = C2t

(6)

where R is the mean grain size at a time t, R0 is the initial mean size and C2 is a constant. The previous equation may be written in more general form R− R0 = C3t n

(7)

The constant n, often termed the grain growth exponent, is in this analysis equal to 0.5. This is the ideal Table 1 Alloy compositions in weight percentage Alloy

No.

%Zn

%Al

%Mn

%Si

%Co

CuZnAl CuZnAl CuAlMn CuAlMnSi CuZnAlMn CuZnAlCo CuZnAlCo CuZnAlCo CuZnAlCo CuZnAlCo

1 2 3 4 5 6 7 8 9 10

21.04 20.85 — — 6.09 20.2 20.2 21.8 20.2 20.2

6.66 6.15 10.82 9.80 19.28 6.5 6.5 6.5 6.4 7.3

— — 6.48 7.5 3.44 — — — — —

— — — 0.5 — — — — — —

— — — — — 0.4 0.8 0.8 1.0 1.0

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F.J. Gil et al. / Materials Science and Engineering A241 (1998) 114–121

Fig. 1. Diameters at different temperatures and heat treatment times for alloy CuZnAl.

case, but generally is observed to be lower than 0.5 because of different grain growth influencing parameters such as impurity-drag, free-surface effect, textured material, dislocation substructure, heterogeneities....[13–15] Moreover, if the assumption would be correct that atomic diffusion across the grain boundary is a simple activated process, and when n is independent of the temperature, it follows that K can be written as [11,12]:

Fig. 3. Diameters at different temperatures and heat treatment times for alloy CuAlMnSi.

where Ea is the activation energy, T is the absolute temperature, K0 is the pre-exponential rate constant and R is the gas constant. For many alloys Ea is also temperature dependent because n varies with temperature and thus only an approximated ‘apparent’ activation energy can be given. The measured grain size parameters of the microstructures in relation to the time and temperatures

of heat treatment are presented in Figs. 1–5 for a CuZnAl, CuAlMn, CuAlMnSi, CuZnAlMn and CuZnAlCo shape memory alloys. The shape of these curves is similar in all samples for the different alloys. The grain growth kinetics of the b-copper based shape memory alloys follow the Hillert distribution [16] since the maximum radius is smaller than 1.8 times the value of the average radius. This means that growth takes place in an uniform way in the whole specimen and that the distribution of sizes obeys an asymptotic law, typical of equilibrium states. Such kinetic behaviour agrees with Eq. (7), since after taking logarithms, linear equations are obtained with correlation coefficients greater than 0.95. These graphs show that rapid grain growth occurs during the first 10 min of heat treatment, but subsequently the growth rate decreases. This is the usual type of behaviour during grain growth. The results show

Fig. 2. Diameters at different temperatures and heat treatment times for alloy CuAlMn.

Fig. 4. Diameters at different temperatures and heat treatment times for alloy CuZnAlMn.

K =K0 exp(− Ea/RT)

(8)

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Fig. 6. As cast microstructure of CuAlMnSi shape memory alloy. Fig. 5. Diameters at different temperatures and heat treatment times for alloy CuZnAlCo with a 0.8% of Cobalt.

that the growth exponent is about 0.55 for CuZnAl alloy. In general, the maximum value of the growth exponent in the kinetic normal growth is 0.5. Departures from n = 0.5 to higher values have been currently interpreted in term of solute drag or the effect of texture [7,17,18]. It can be noticed from the results that the growth exponent for the CuZnAl alloy is slightly higher than 0.5. The physical explanation of such behaviour lies in the diffusion of solute atoms which induces the grain boundary migration. The diffusion process which leads to solute depletion at the grain boundaries induces an increase in the rate of growth [19–21]. It does not seem that a preferred orientation texture may play an important role since an abnormal grain growth has not been observed in this alloy. Experimental values for the growth exponent for CuZnAlMn and CuAlMn shape memory alloys are 0.33. Since the parabolic law for grain growth kinetics was deduced, experimentalists have devoted much effort to extracting grain growth exponents and then making declarations about how far their samples approach the ideal epitomised by n = 0.5. This tendency has been further encouraged by schemes to identify a variety of different values of n with different factors controlling grain growth (e.g. impurities inhibiting the migration of boundaries). The most commonly observed value of 0.33 can, for example, be indicative of any of five separate processes as can be seen below [1]: Pore control: Surface diffusion Vapour transport (P = constant) Boundary control: Impure system: Coalescence of second phase by lattice diffusion. Diffusion through continuous second phase. Impurity drag (low solubility).

As, CuZnAlMn and CuAlMn shape memory alloys present a single phase with boundary control, only the mechanism of impurity drag with low solubility is possible. For the CuAlMn with Si in the ‘as cast’ condition the microstructure of the alloy showed the presence of particles of Mn5Si2, as can be see in Fig. 6. After heat treatment at 700°C followed by water quenching the morphology of the particles changed and many particles were present at the grain boundaries, see Fig. 7. The chemical composition of the particles was determined by using an EDS microanalysis system attached to a scanning electron microscope. After treatment at 800°C the Mn5Si2 particles dissolved, but on cooling it appeared that the cooling rate was insufficient to prevent precipitation since many very fine particles were now present at the boundaries. The grain growth exponent at 800 and 900°C using each of the three parameters is about 0.17. However at 700°C the growth exponent is much lower at 0.07. It would seem that the low growth order at 700°C could be a result of particle inhibition of the growth. The presence of particles of Mn5Si2 at both the grain

Fig. 7. Microstructure obtained after heat treatment at 700°C.

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Fig. 8. The interaction between a grain boundary and a spherical particle.

boundaries and within the grains would support this view. The dissolution of the particles at 800°C and above then allows growth to occur under the less stringent limitations of solute drag effects. The Burke and Turnbull analysis of grain growth kinetic can be applied at this system which contains precipitates. In our case, the microstructures obey the assumption that the driving pressure P at the grain boundary arises only from the curvature of the boundary [11,12], as it is confirmed by the potential growth law according to Eq. (7). However, the precipitates are an important factor which affect grain growth, since they hinder the grain boundary mobility. This fact is observed in the lower values of the growth exponent at 700°C. A dispersion of particles will exert a retarding force on a low angle or high angle grain boundary and this has a deep effect on the grain growth kinetic as can be seen by the growth exponent for CuAlMn with manganese silicide precipitates. This effect is known as Zener drag [22] which considers the interaction of a boundary of specific energy g with a spherical particle of radius r which has an incoherent interface, as is the case of Mn5Si2. If the boundary meets the particle at an angle u as shown in Fig. 8 then the restraining force on the boundary is [1]: F=2prg cos u sin u

growth exponent arrives at values below 0.1 for cobalt contents of 0.9 and 1.0%. The results show that the boundaries mobility decreases rapidly with increasing cobalt content. Note that only very low concentrations of cobalt are required to change growth exponent by orders of magnitude. The reason for this type of behaviour arises from differences in the interactions of cobalt with different boundaries. When the boundary moves the solute atoms migrate along with the boundary and exert a drag that reduces the boundary velocity. The magnitude of drag will depend on the binding energy and the concentration in the boundary. The Cahn–Lu¨cke–Stu¨we (CLS) model is still widely accepted as giving a good semi-quantitative account of the effects of solute and boundary migration [23–25]. The CLS theory is based on the concept that atoms in the region of a boundary have a different energy (U) to those in the grain interior because of the different local atomic environment. There is therefore a force (dU/dx) between the boundary and the solute atom which may be positive or negative, depending on the specific solute and solvent. The total force from the boundary on all solute atoms is dU dx

P= %

(11)

and an equal opposite force is exerted by the solute atoms on the boundary. The result of this interaction is an excess or deficit of solute in the vicinity of the boundary, and the solute concentration (C) is given by

 

C= C0 exp

−U KT

where C0 is the equilibrium solute concentration. The extent to which an element segregates to a stationary boundary is usually related to its solubility, and as a general rule the tendency for segregation increases as the solubility decreases.

(9)

The maximum restraining effect is obtained when u= 45°, giving Fs =pg

(10)

It should be noted that when a boundary intersects a particle, the particle effectively removes a region of boundary equal to the intersection area and thus the energy of the system is lowered. Boundaries are therefore attracted to particles. From Fig. 7 it can be seen that a big amount of Mn5Si2 precipitates on grain boundaries obstruct the grain growth kinetics. The cobalt produces a linear decrease of the growth exponent, as can be seen in Fig. 9. This decrease of the

(12)

Fig. 9. Variation of growth exponent with cobalt content.

F.J. Gil et al. / Materials Science and Engineering A241 (1998) 114–121 Table 2 Activation energies for the different alloys studied Alloy

No.

Activation energy Ea (KJ mol−1)

CuZnAl CuZnAl CuAlMn CuAlMnSi CuZnAlMn CuZnAlCo CuZnAlCo CuZnAlCo CuZnAlCo CuZnAlCo

1 2 3 4 5 6 7 8 9 10

110.0910.0 105.597.1 35.19 2.1 35.791.3 34.29 1.5 39.290.3 33.89 0.2 35.59 0.4 35.89 0.6 35.29 0.9

The relationship between the driving pressure (P) and boundary velocity (6) at low velocities is found to be P=

n + aC0n M

(13)

where M is the mobility of the boundary in the absence of solute, and a is a constant. It may be seen from equation that the velocity is predicted to be inversely proportional to the solute concentration in this case cobalt content (C0). The slope of a plot of ln K against 1/T therefore yields a value of Ea. The apparent activation energy may be related to the atom-scale thermally activated process which controls boundary migration. The activation energies for grain growth are virtually independent of the grain size parameters used in their determination. The values are shown in Table 2. For pure copper the activation energy for grain growth in the temperature range 425–700°C is about 120 kJ mol − 1 [26] and for a CuZnAl memory alloy, a value of about 160 KJ mol − 1 has been obtained within the temperature range 700– 900°C. It is usual to expect that the addition of alloying elements would raise the activation energy for grain growth. It is somewhat surprising, therefore, with CuAlMn, CuAlMnSi, CuZnAlMn and CuZnAlCo that such a low activation energy is obtained. It is generally accepted that the activation energy for grain growth decreases as the temperature is increased, and with pure metals, a sharp transition occurs at about 0.8Tm, expressed in K, which for copper is about 800°C [27–30]. For the copper with small contents of lead, the ratio of the low to high activation energies in the two temperature regimes is about 0.2 [31]. The ratio of the activation energy for the CuAlMn, CuZnAlMn,... alloys to that for the CuZnAl alloy given above is about 0.22. This would suggest that Mn and Co have the effect of lowering the transition temperature from the low to the high activation energy regime. This variation of activation energies could also be explained by the change of the mechanism of boundary

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migration at high temperatures, showing a discontinuous transition to a high temperature regime of higher boundary mobility and low activation energy for migration. Gleiter [32] has detected a discontinuous change in properties for B100\ tilt boundaries in high purity metals at temperatures in the range 0.7–0.8Tm, the actual temperature depending on the crystallography of the boundary. Kopetski et al. [33], Gleiter [32,34,35] and Gondi [36] interpreted that the small amounts of specific solutes played a role in terms of a change in the mechanism of boundary migration from one controlled by diffusion to one involving cooperative atomic shuffles: the dislocations can glide in the boundary plane and therefore boundary migration is possible [37,38]. Consequently, the results indicate apparently that CuZnAl alloy presents a mechanism of boundary migration controlled by boundary diffusion and that the role of Mn and Co produce a change in this mechanism to cooperative atomic shuffles; but the reasons for this are not readily apparent. The ratio of the grain boundary area per unit volume (Gv) has been determined for each temperature and heat treatment time. Assuming that the grains have the ideal shape of a tetrakaidecahedron, the value of Gv can be determined from the mean grain boundary area of a random section (A) for the relationship [39]: Gv = 3.059A − 1/2

(14)

Fig. 10 shows a very rapid decrease of Gv with times of up to 10 min for CuZnAl, CuAlMn, CuZnAlMn, CuAlMnSi and the alloys with a 0.8% of Co respectively corresponding to 900°C heat treatment temperature. The Ms and As temperatures, which correspond to the start of the forward martensitic transformation and reverse transformation. respectively, are shown in relation to the grain size in Figs. 11 and 12 respectively, for the different alloys studied. Both temperatures show a

Fig. 10. Ratio of the grain boundary area per unit volume (Gv) versus heat treatment time at each test temperature.

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F.J. Gil et al. / Materials Science and Engineering A241 (1998) 114–121

Fig. 13. Transformation stresses versus grain size parameter. Fig. 11. Ms transformation temperatures versus grain size parameter.

growth D as: linear decrease with grain growth. This shows the influence of grain boundaries, which favour the martensitic transformation and at the same time obstruct the retransformation. The influence of the grain boundaries does not have a place in the nucleation of the first martensite plates, instead it takes place in the propagation that occurs in the polycrystals when the plates interact with the grain boundaries. This interaction produces an increase in the local elastic energy which facilitates the nucleation of new plates. Also, from this elastic energy the samples with small crystals possess greater internal stresses, due to the anisotropy which is produced by the different orientations of these grains which helps the martensitic transformation, and therefore results in Ms for samples with small grain size being greater than Ms for samples with large grain size. These results are in evident opposition to those obtained by Adnyana [40] and Wu Jianxin [41] who proposed a Hall– Petch equation between Ms and grain

Ms(polycrystal)=Ms(single crystal)+ K D

(15)

being Ms the start temperature of martensitic transformation for a poly and single crystal, D is the grain size and K is a constant which is always negative [40]. These authors only measured the Ms temperature for a very small grain sizes between 30 and 50 mm for a Cu-20.6 wt% Zn-5.7 wt% Al alloy containing a small quantity of zirconium [40] and boron [41] for grain refinement. In these works the transformation temperatures were determined by electrical resistance measurements less sensitive than the calorimetric studies [42,43]. The As temperature of the sample with small grain size is greater than that of the sample with large grain size; this is caused by the martensitic plates disappearing in the same way in which they appear. A great deal of energy must be applied in order to separate the plates from the grain boundaries [44]. The effect of the grain size on the critical stress for martensitic formation can be seen in the Fig. 13. An increase in grain size produces a linear increase in the stress required for nucleation martensite. It has been established that the stress required to induce a martensitic transformation decreased with increasing Ms transformation temperature [45]. Furthermore, the elastic energy stored in grain boundary favours the stress induced martensitic transformation.

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Fig. 12. As transformation temperatures versus grain size parameter.

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