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Creep deformation of Pb–Sn–Zn ternary alloys
Materials Chemistry and Physics 74 (2002) 43–51
Creep deformation of Pb–Sn–Zn ternary alloys A.A. El-Daly∗ , A.M. Abdel-Daiem, M. Yousf Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt Received 1 November 2000; received in revised form 4 May 2001; accepted 10 May 2001
Abstract The steady state creep of Pb–65Sn–1Zn and Pb–65.5Sn–3.4Zn ternary alloys was investigated in the temperature range from 353 to 413 K under different constant stresses. The results of creep characteristics show two deformation regions (below and above 383 K). The strain rate sensitivity parameter (m) has been found to increase by increasing the working temperature up to about 0.53 and 0.64 for the first and second alloys, respectively. The activation energies of steady state creep of the first and second alloys have been found to be 41–59.7 and 40–58 kJ mol−1 , respectively, characterising grain boundary diffusion. Metallographic observations and X-ray analysis have been confirmed that grain boundary sliding (GBS) accommodated by dislocation motion is the important mode of deformation. It was also established that Pb–Sn–Zn ternary alloys show superior superplastic behaviour compared with Pb–Sn binary alloys as a result of its lower melting temperature (Tm ), finer grain size, and the multiplicity of types of interphase boundaries. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Creep; Pb–Sn–Zn ternary alloys; Grain boundary sliding (GBS)
1. Introduction Micrograin superplasticity refers to the ability of some polycrystalline materials to exhibit very large elongations of several hundreds of percent when pulled in tension [1]. The two basic requirements for the observation of micrograin superplasticity in these materials are (a) a temperature greater than about one-half of the melting temperature, (Tm ), and (b) a thermally-stable very fine equiaxied grain size during high temperature deformation [2]. Superplastic flow is considered to arise from a combination of three mechanisms of deformation: diffusional creep, dislocation motion, and grain boundary sliding (GBS). The only commonly accepted viewpoint based on direct experimental observations is that GBS play an important role. In so far as GBS without bulk flow cannot lead to large elongations, therefore, a satisfactory accommodation of diffusion and/or dislocation is necessary to explain the lack of void formation at triple lines [3]. It is well known that [4–6] the mechanical response of metals and alloys can be controlled by varying their structural state, in particular, the grain boundaries area, and the addition of various alloying elements. Even through a great deal of efforts has been carried out on Pb–Sn eutectic alloys [7–11], which is currently used in computer industry for various microelectronic connections. ∗ Corresponding author. E-mail address: [email protected] (A.A. El-Daly).
Accordingly, while these efforts have been aimed at studying the various parameters that may play an active role in its plasticity, there have been rare studies regarding the effect of the presence of a third phase on its behaviour. In the earlier papers [12,13], it was reported that the addition of a third phase did not affect the material response during superplastic flow. Recently [14], it was found that the addition of Cd or Bi to Pb–Sn alloys increases the alloy response during superplastic flow. However, the present paper is, therefore, describe our study on the superplastic behaviour of Pb–Sn eutectic in which 1 and 3.4% Zn was added to form the respective ternary Pb–65Sn–1Zn and the eutectic Pb–65.5Sn–3.4Zn ternary alloys. The tensile creep behaviour of the two alloys have been studied, the reason why Zn enhances (or not) the plasticity in the ternary alloys has been analysed.
2. Experimental The ternary eutectic Pb–65.5Sn–3.4Zn and ternary Pb–65Sn–Zn alloys were prepared from high purity (99.99%) Pb, Sn, and Zn by vacuum melting. The ingots were rolled into wires of diameter 0.8 and 50 mm gauge length. In this study, the samples were annealed at 413 K for 2 h and then slowly cooled to room temperature at cooling rate T = 2 × 10−2 K s−1 , then the samples were annealed at room temperature for several days before testing. This procedure permitted a small amount of grain stabilisation
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to occur. Tensile creep tests were then performed under constant stress conditions at temperature ranging from 353 to 413 K in step of 10 K for both alloys. These tests were carried out in an improved model of creep machine similar to that described earlier [15]. The accuracy of temperature measurements is of the order of ±1 K. The strain measurements were done with accuracy of ±1 × 10−2 mm. The microstructure of both alloys was investigated using X-ray diffraction (XRD), optical microscopy and scanning
electron microscopy (SEM). Grain sizes were measured using a linear intercept technique [16], the initial grain sizes were 3.05 ± 0.15 m for the Pb–Sn–Zn eutectic alloys and 3.35 ± 0.25 m for Pb–65Sn–1Zn alloy. Static grain-growth studies showed that Pb–Sn–Zn eutectic alloys was essentially stable for long time periods (up to 500 h) at 343 K [8]. In Pb–Sn (eutectic composition) heat treatments of 24 h at 433 K result in mean phase-boundary intercept length of 5.9 m [17].
Fig. 1. Creep curves at different applied stresses and different temperatures for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn ternary alloys.
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Fig. 2. Strain rate–stress relationship for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
Fig. 3. Steady state strain rate ε˙ st and strain rate sensitivity parameter m as a function of creep temperature for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
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3. Results Steady state creep measurements were carried out principally on Pb–65.5Sn–3.4Zn eutectic and Pb–65Sn–1Zn ternary alloys. The samples were investigated in the temperature range 353–413 K in steps of 10 K under constant applied stresses. The results are shown in Fig. 1a and b and a comparison between these leads to the following remarks. First, creep deformation rate is significantly pronounced at high temperatures (above 383 K) on both alloys. Second, the flow stresses in the ternary eutectic is lower than the respective stresses in the ternary alloy. Third, the total elongation in the eutectic composition is higher than that of the ternary composition at the same temperatures. In fact, it becomes clear from this that increasing the Zn-content in Pb–Sn base alloys from 1 to 3.4% seems to affect the overall behaviour. Accordingly, it has verified that the eutectic alloy is more superplastic than the ternary alloy. Strain rate sensitivity parameter m = ∂ ln σ/∂ ln ε˙ st was derived from the slope of the straight lines relating ln σ and
ln ε˙ st . The value of m calculated from the data in Fig. 2 as well as the steady state strain rate ε˙ st are plotted versus temperature in Fig. 3. It is obvious that m exhibits low value (0.31 ± 0.04) up to about 383 K for both compositions. After that m increases with temperature until 413 K reaching the value of 0.64 and 0.53 for the eutectic and ternary composition, respectively, illustrating that the sensitivity parameter m for both compositions becomes temperature dependent. The activation energy of steady state creep at constant stresses was calculated using ∂ ln ε˙ st Q=R (1) ∂(1/T ) where R and T are the gas constant and absolute temperature, respectively. The activation energies for the eutectic and ternary alloys have been found to be 40, 58 and 41, 59.7 kJ mol−1 in the low and high temperature regions (below and above 383 K), respectively (see Fig. 4). The average particle size and X-ray half line width ( 2θ )
Fig. 4. Relation between ln ε˙ st and 1000/T at different applied stresses for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
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Fig. 5. The effect of temperature on X-ray half line width ( 2θ ) and the average particle size d for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
were found to change with increasing working temperature. The particle size reached a minimum value at 383 K, while ( 2θ ) reached a maximum for both alloys (see Fig. 5). Also, the temperature dependence of the precise value of lattice constant a0 of Pb-rich phase and c0 /a0 , of Zn- and Sn-rich phases of two alloys are shown in Fig. 6. It is clear that the lattice parameter a0 exhibited maximum for Pb-rich phase, while c0 /a0 , exhibited minimum for Zn- and Sn-rich phases. Fig. 7a and b shows the metallographic observations of Pb–Sn–Zn specimens pre-annealed at 413 K for 2 h, the samples were crept at
temperatures 353 and 403 K at a fixed stress of 4.88 MPa. The main features of all the samples is that (a) the grains have an eqiaxed shape, (b) some grains are displaced as a whole at the triple line, (c) the grain and the phase boundaries become wavy or curved with cusps, (d) finger-like protuberances. All the above observations are consistent with GBS having occurred. Similar results were published in several superplastic alloy-deformed materials [18,19]. Their conclusions support the above arguments. Fig. 7b shows a group of grains slide along the plane of GBS.
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Fig. 6. Temperature dependence of a0 for Pb-rich phase and c0 /a0 for Zn- and Sn-rich phases for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
4. Discussion The present investigation shows that creep tests are more sensitive to the variation of the alloy compositions, this may reflect the effect of Zn-content on the behaviour of the two samples (see Fig. 1). The fact that eutectic composition showed a lower flow stresses and a higher elongations than the ternary compositions, clearly indicates that this behaviour is mainly attributed to the finer microstructure encountered in case of the former. Jiang and Lian [20] showed that the smaller grain size also reduces the resistance to the transmission of slip across grain boundaries, which can decrease flow stress. The rapidly decrease of stress with decreasing grain size reflect the evidence that GBS is the principal deformation mechanism at low strain rates [18]. The temperature dependence of the sensitivity parameter m shows that a basic change in the concentration of the co-existing phases with raising temperature above (383 K) occurred. As noted by Bochvar [1], this change in composition implies diffusion current and movement direction of atoms leading to viscous deformation or superplasticity. It is well known that the large contribution by GBS is associated
with fine grained materials [21]. On the other hand, the value of the parameter m is in direct proportion to the contribution of GBS to the total deformation [22,23]. Accordingly, the enhanced values of m obtained at temperatures >0.5Tm may reflect the evidence that GBS is the principle mode of deformation. Moreover, the obtained results verify the equation of steady state creep σ 1/m Q ε˙ st = c (2) exp d kT where m = 0.5 for dislocation climb along grain boundaries [23,24], therefore, it is considered here that the higher elongation is attributed to the dislocation motion results in GBS and accommodated it during the deformation. Metallographic observation is more direct and provides very interesting data concerning the mechanism for the development of superplasticity in the present alloys. Some specific effects of GBS accommodated by dislocation motion were observed so that all data do not correlate with GBS alone. As was seen from Fig. 7b, when the creep deformation proceeds, the movement of group of grains along the plane of GBS can produce dislocations, which are piled-up
A.A. El-Daly et al. / Materials Chemistry and Physics 74 (2002) 43–51
at the grain and interphase boundaries, pile-up groups of dislocation can produce the stresses concentration at the grain boundaries necessary for grain cleavage of the blocking grain [25,26]. It appears that these process are considered also responsible for the observed decrease in the average grain size [26,27]. Accordingly, the homogeneity of microstructure increases due to the refining of coarse grains and simultaneous growth of very fine grains. Besides the temperature dependence of precise values of the lattice constants, and half line width is due to the relief of internal strains at the transition temperature. Therefore, the microstructure confirms the above mentioned mechanisms. Similar results reported by Ball and Hutchison have been used as evidence for
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dislocation motion along the plane of GBS [24]. According to these authors, sliding accommodated by dislocation motion leads to superplastic flow. When group of grains slide, the dislocations traversed the blocking grains and pile-up against the opposite boundaries until the back stress prevents further sliding, therefore, dislocation climb into and along grain boundaries make further sliding possible as shown in Fig. 8. To compare the results for Pb–Sn eutectic [7] with Pb–Sn–Zn ternary systems taking into account that both materials are investigated at the same conditions of heat treatment and working temperature range, the direct comparison of the creep characteristics depending on the
Fig. 7. (a) Metallographic micrographs of Pb–Sn–Zn samples pre-annealed at 413 K for 2 h and crept under a stress of 4.88 MPa at temperatures 353 and 403 K. (b) A schematic representation of Pb–Sn–Zn samples show the plane of grain boundary sliding between a group of grains.
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Fig. 7. (Continued ).
Fig. 8. A schematic representation of the model of Ball and Hutchison [24] showing sliding between a group of grains.
Zn-content is possible. Thus, it follows from Table 1 that the superplasticity in the binary eutectic Pb–Sn is extremely altered by addition of the third phase (Zn-content). The fact that the ternary composition showed high elongation and low stresses more than the binary is quite remarkable in that a small Zn-addition enhances superplasticity of Pb–Sn eutectic. This implies that the microstructure in the ternary alloys must be uniform and finer grain size. The reason why Zn enhances the superplasticity of Pb–Sn eutectic can be analysed as follows. In the model of Bochvar [1], two conditions are necessary to observe superplasticity: (a) the rapid variation in composition with temperature; (b) high rate of diffusion. The second condition implies increasing grain boundary area and decreasing diffusion length, which enhances superplasticity. Accordingly, the Zn-addition seems to lead to a finer grain size which, in turn, increased the rate of diffusion and
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Table 1 Comparison of the steady state creep characteristics of Pb–Sn–Zn ternary alloys with Pb–Sn binary alloys Materials
Pb–10Sn (binary) [7] Pb–Sn (eutectic) [7] Pb–65Sn–Zn (ternary) Pb–Sn–Zn (eutectic)
Melting temperature, Tm
Flow stresses (MPa)
Maximum elongation (%)
588 456 455 447.9
12.73–22.91 7.63–12.73 5.86–6.25 4.88–6.25
9 70 140 150
enhanced the creep parameters of Pb–Sn–Zn alloys. Moreover, the addition of Zn leads to reduction of Tm of the ternary alloys and increasing the homogeneity of micro structure (see Table 1).
5. Conclusion 1. Significant improvement in superplasticity of Pb–Sn binary eutectic alloys was observed due to the Zn-addition within the range of 1–3.4% Zn. 2. The Pb–Sn–Zn ternary alloys show superior superplastic behaviour in comparison with Pb–Sn binary eutectic as a result of the lower melting temperature (Tm ), the finer microstructure, and the multiplicity of types of interphase boundaries. 3. Under condition of optimal superplastic flow, the present results are consistent with the model of Ball and Hutchison [24] in both of mechanical and microstructural evidence. References [1] [2] [3] [4]
P. Chauhari, Acta Met. 15 (1967) 1771. P. Griffiths, G. Hammond, Acta Met. 20 (1972) 935. P. Chauhari, S. Marder, App. Polym. Symp. 12 (1969) 1. O.A. Kaibyshev, Superplasticity of Commercial Alloys, Metallvrgia, Moscow, 1984.
Specimen dimensions (mm) Length
Diameter
50 50 50 50
1.0 1.0 0.8 0.8
Activation energy, Q (kJ mol−1 )
Sensitivity parameter (m)
46.2–88.2 42–63 41–59.7 40–58
0.17–0.43 0.54–0.88 0.3–0.53 0.34–0.64
[5] K. Hashimoto, H. Doi, K. Kassahara, T. Tsujimoto, T. Sazuki, J. Jpn. Inst. Met. 52 (1988) 816. [6] R. Honecomb, Plastic Deformation of Metals, Mir, Moscow, 1972. [7] M.S. Sakr, A.Z. Mohamed, M.M. Shehab, A.H. Bassyouni, Czech. J. Phys. 41 (1991) 785. [8] H.E. Cline, T.H. Alden, Trans. Met. Soc. Am. 239 (1967) 710. [9] D.E. Newbury, D.C. Joy, Script. Met. 4 (1970) 825. [10] M.P. Robert, A. Zubelewicz, L.M. Keer, J. Eng. Mech. 117. [11] M.M. Ahmed, T.G. Langdon, Metallurgy 8A (1977) 1932. [12] A.E. Geckinli, C.R. Barrett, J. Mater. Sci. 11 (1976) 510. [13] M.D.C. Moles, G.J. Davies, Met. Sci. 10 (1976) 314. [14] A.Z. Mohamed, M.H. El-Ghazaly, E.A. El-Saadani, Egypt. J. Sol. 223 (1997). [15] R. Kamel, J.A. Bessa, J. Appl. Phys. 34 (1963) 1882. [16] B.D. Cullity, X-ray Diffraction, London, 1959, p. 262. [17] J.H. Schneibel, P.M. Hazzledine, J. Mater. Sci. 18 (1983) 562. [18] G.A. Chadick, D.A. Smith, Grain Boundary Structure and Properties, Academic Press, London, 1976, pp. 236–254. [19] T.H. Alden, Acta Met. 15 (1967) 464. [20] Z. Jiang, J. Lian, Acta Met. 40 (1942) 1587. [21] G.V. Smith, Properties of Metals at Elevated Temperatures, McGraw-Hill, New York, 1950. [22] M. Knji, U. Yasuhide, Y. Mosao, J. Jpn. Inst. Met. 3 (1974) 219. [23] S. Zhov, D. Zhang, D. Lin, Mater. Roc. Soc. Symp. Proc. 196 (1990) 227. [24] A. Ball, M. Hutchison, Met. Sci. J. 3 (1964) 1. [25] M.S. Sakr, A.A. El-Daly, A.Z. Mohamed, E.A. El-Saadani, A.H. Bassyouni, Egypt. J. Sol. 13 (1990) 26. [26] J. Friedel, Dislocation, Pergamon Press, London, 1964, p. 328. [27] K.A. Padmanabhan, G.J. Davies, Superplasticity: mechanical and structural aspects, in: Environmental Effects, Fundamentals and Applications, Springer, Berlin, New York, 1980, p. 170.
Creep deformation of Pb–Sn–Zn ternary alloys A.A. El-Daly∗ , A.M. Abdel-Daiem, M. Yousf Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt Received 1 November 2000; received in revised form 4 May 2001; accepted 10 May 2001
Abstract The steady state creep of Pb–65Sn–1Zn and Pb–65.5Sn–3.4Zn ternary alloys was investigated in the temperature range from 353 to 413 K under different constant stresses. The results of creep characteristics show two deformation regions (below and above 383 K). The strain rate sensitivity parameter (m) has been found to increase by increasing the working temperature up to about 0.53 and 0.64 for the first and second alloys, respectively. The activation energies of steady state creep of the first and second alloys have been found to be 41–59.7 and 40–58 kJ mol−1 , respectively, characterising grain boundary diffusion. Metallographic observations and X-ray analysis have been confirmed that grain boundary sliding (GBS) accommodated by dislocation motion is the important mode of deformation. It was also established that Pb–Sn–Zn ternary alloys show superior superplastic behaviour compared with Pb–Sn binary alloys as a result of its lower melting temperature (Tm ), finer grain size, and the multiplicity of types of interphase boundaries. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Creep; Pb–Sn–Zn ternary alloys; Grain boundary sliding (GBS)
1. Introduction Micrograin superplasticity refers to the ability of some polycrystalline materials to exhibit very large elongations of several hundreds of percent when pulled in tension [1]. The two basic requirements for the observation of micrograin superplasticity in these materials are (a) a temperature greater than about one-half of the melting temperature, (Tm ), and (b) a thermally-stable very fine equiaxied grain size during high temperature deformation [2]. Superplastic flow is considered to arise from a combination of three mechanisms of deformation: diffusional creep, dislocation motion, and grain boundary sliding (GBS). The only commonly accepted viewpoint based on direct experimental observations is that GBS play an important role. In so far as GBS without bulk flow cannot lead to large elongations, therefore, a satisfactory accommodation of diffusion and/or dislocation is necessary to explain the lack of void formation at triple lines [3]. It is well known that [4–6] the mechanical response of metals and alloys can be controlled by varying their structural state, in particular, the grain boundaries area, and the addition of various alloying elements. Even through a great deal of efforts has been carried out on Pb–Sn eutectic alloys [7–11], which is currently used in computer industry for various microelectronic connections. ∗ Corresponding author. E-mail address: [email protected] (A.A. El-Daly).
Accordingly, while these efforts have been aimed at studying the various parameters that may play an active role in its plasticity, there have been rare studies regarding the effect of the presence of a third phase on its behaviour. In the earlier papers [12,13], it was reported that the addition of a third phase did not affect the material response during superplastic flow. Recently [14], it was found that the addition of Cd or Bi to Pb–Sn alloys increases the alloy response during superplastic flow. However, the present paper is, therefore, describe our study on the superplastic behaviour of Pb–Sn eutectic in which 1 and 3.4% Zn was added to form the respective ternary Pb–65Sn–1Zn and the eutectic Pb–65.5Sn–3.4Zn ternary alloys. The tensile creep behaviour of the two alloys have been studied, the reason why Zn enhances (or not) the plasticity in the ternary alloys has been analysed.
2. Experimental The ternary eutectic Pb–65.5Sn–3.4Zn and ternary Pb–65Sn–Zn alloys were prepared from high purity (99.99%) Pb, Sn, and Zn by vacuum melting. The ingots were rolled into wires of diameter 0.8 and 50 mm gauge length. In this study, the samples were annealed at 413 K for 2 h and then slowly cooled to room temperature at cooling rate T = 2 × 10−2 K s−1 , then the samples were annealed at room temperature for several days before testing. This procedure permitted a small amount of grain stabilisation
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to occur. Tensile creep tests were then performed under constant stress conditions at temperature ranging from 353 to 413 K in step of 10 K for both alloys. These tests were carried out in an improved model of creep machine similar to that described earlier [15]. The accuracy of temperature measurements is of the order of ±1 K. The strain measurements were done with accuracy of ±1 × 10−2 mm. The microstructure of both alloys was investigated using X-ray diffraction (XRD), optical microscopy and scanning
electron microscopy (SEM). Grain sizes were measured using a linear intercept technique [16], the initial grain sizes were 3.05 ± 0.15 m for the Pb–Sn–Zn eutectic alloys and 3.35 ± 0.25 m for Pb–65Sn–1Zn alloy. Static grain-growth studies showed that Pb–Sn–Zn eutectic alloys was essentially stable for long time periods (up to 500 h) at 343 K [8]. In Pb–Sn (eutectic composition) heat treatments of 24 h at 433 K result in mean phase-boundary intercept length of 5.9 m [17].
Fig. 1. Creep curves at different applied stresses and different temperatures for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn ternary alloys.
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Fig. 2. Strain rate–stress relationship for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
Fig. 3. Steady state strain rate ε˙ st and strain rate sensitivity parameter m as a function of creep temperature for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
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3. Results Steady state creep measurements were carried out principally on Pb–65.5Sn–3.4Zn eutectic and Pb–65Sn–1Zn ternary alloys. The samples were investigated in the temperature range 353–413 K in steps of 10 K under constant applied stresses. The results are shown in Fig. 1a and b and a comparison between these leads to the following remarks. First, creep deformation rate is significantly pronounced at high temperatures (above 383 K) on both alloys. Second, the flow stresses in the ternary eutectic is lower than the respective stresses in the ternary alloy. Third, the total elongation in the eutectic composition is higher than that of the ternary composition at the same temperatures. In fact, it becomes clear from this that increasing the Zn-content in Pb–Sn base alloys from 1 to 3.4% seems to affect the overall behaviour. Accordingly, it has verified that the eutectic alloy is more superplastic than the ternary alloy. Strain rate sensitivity parameter m = ∂ ln σ/∂ ln ε˙ st was derived from the slope of the straight lines relating ln σ and
ln ε˙ st . The value of m calculated from the data in Fig. 2 as well as the steady state strain rate ε˙ st are plotted versus temperature in Fig. 3. It is obvious that m exhibits low value (0.31 ± 0.04) up to about 383 K for both compositions. After that m increases with temperature until 413 K reaching the value of 0.64 and 0.53 for the eutectic and ternary composition, respectively, illustrating that the sensitivity parameter m for both compositions becomes temperature dependent. The activation energy of steady state creep at constant stresses was calculated using ∂ ln ε˙ st Q=R (1) ∂(1/T ) where R and T are the gas constant and absolute temperature, respectively. The activation energies for the eutectic and ternary alloys have been found to be 40, 58 and 41, 59.7 kJ mol−1 in the low and high temperature regions (below and above 383 K), respectively (see Fig. 4). The average particle size and X-ray half line width ( 2θ )
Fig. 4. Relation between ln ε˙ st and 1000/T at different applied stresses for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
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Fig. 5. The effect of temperature on X-ray half line width ( 2θ ) and the average particle size d for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
were found to change with increasing working temperature. The particle size reached a minimum value at 383 K, while ( 2θ ) reached a maximum for both alloys (see Fig. 5). Also, the temperature dependence of the precise value of lattice constant a0 of Pb-rich phase and c0 /a0 , of Zn- and Sn-rich phases of two alloys are shown in Fig. 6. It is clear that the lattice parameter a0 exhibited maximum for Pb-rich phase, while c0 /a0 , exhibited minimum for Zn- and Sn-rich phases. Fig. 7a and b shows the metallographic observations of Pb–Sn–Zn specimens pre-annealed at 413 K for 2 h, the samples were crept at
temperatures 353 and 403 K at a fixed stress of 4.88 MPa. The main features of all the samples is that (a) the grains have an eqiaxed shape, (b) some grains are displaced as a whole at the triple line, (c) the grain and the phase boundaries become wavy or curved with cusps, (d) finger-like protuberances. All the above observations are consistent with GBS having occurred. Similar results were published in several superplastic alloy-deformed materials [18,19]. Their conclusions support the above arguments. Fig. 7b shows a group of grains slide along the plane of GBS.
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Fig. 6. Temperature dependence of a0 for Pb-rich phase and c0 /a0 for Zn- and Sn-rich phases for (a) Pb–65.5Sn–3.4Zn and (b) Pb–65Sn–1Zn.
4. Discussion The present investigation shows that creep tests are more sensitive to the variation of the alloy compositions, this may reflect the effect of Zn-content on the behaviour of the two samples (see Fig. 1). The fact that eutectic composition showed a lower flow stresses and a higher elongations than the ternary compositions, clearly indicates that this behaviour is mainly attributed to the finer microstructure encountered in case of the former. Jiang and Lian [20] showed that the smaller grain size also reduces the resistance to the transmission of slip across grain boundaries, which can decrease flow stress. The rapidly decrease of stress with decreasing grain size reflect the evidence that GBS is the principal deformation mechanism at low strain rates [18]. The temperature dependence of the sensitivity parameter m shows that a basic change in the concentration of the co-existing phases with raising temperature above (383 K) occurred. As noted by Bochvar [1], this change in composition implies diffusion current and movement direction of atoms leading to viscous deformation or superplasticity. It is well known that the large contribution by GBS is associated
with fine grained materials [21]. On the other hand, the value of the parameter m is in direct proportion to the contribution of GBS to the total deformation [22,23]. Accordingly, the enhanced values of m obtained at temperatures >0.5Tm may reflect the evidence that GBS is the principle mode of deformation. Moreover, the obtained results verify the equation of steady state creep σ 1/m Q ε˙ st = c (2) exp d kT where m = 0.5 for dislocation climb along grain boundaries [23,24], therefore, it is considered here that the higher elongation is attributed to the dislocation motion results in GBS and accommodated it during the deformation. Metallographic observation is more direct and provides very interesting data concerning the mechanism for the development of superplasticity in the present alloys. Some specific effects of GBS accommodated by dislocation motion were observed so that all data do not correlate with GBS alone. As was seen from Fig. 7b, when the creep deformation proceeds, the movement of group of grains along the plane of GBS can produce dislocations, which are piled-up
A.A. El-Daly et al. / Materials Chemistry and Physics 74 (2002) 43–51
at the grain and interphase boundaries, pile-up groups of dislocation can produce the stresses concentration at the grain boundaries necessary for grain cleavage of the blocking grain [25,26]. It appears that these process are considered also responsible for the observed decrease in the average grain size [26,27]. Accordingly, the homogeneity of microstructure increases due to the refining of coarse grains and simultaneous growth of very fine grains. Besides the temperature dependence of precise values of the lattice constants, and half line width is due to the relief of internal strains at the transition temperature. Therefore, the microstructure confirms the above mentioned mechanisms. Similar results reported by Ball and Hutchison have been used as evidence for
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dislocation motion along the plane of GBS [24]. According to these authors, sliding accommodated by dislocation motion leads to superplastic flow. When group of grains slide, the dislocations traversed the blocking grains and pile-up against the opposite boundaries until the back stress prevents further sliding, therefore, dislocation climb into and along grain boundaries make further sliding possible as shown in Fig. 8. To compare the results for Pb–Sn eutectic [7] with Pb–Sn–Zn ternary systems taking into account that both materials are investigated at the same conditions of heat treatment and working temperature range, the direct comparison of the creep characteristics depending on the
Fig. 7. (a) Metallographic micrographs of Pb–Sn–Zn samples pre-annealed at 413 K for 2 h and crept under a stress of 4.88 MPa at temperatures 353 and 403 K. (b) A schematic representation of Pb–Sn–Zn samples show the plane of grain boundary sliding between a group of grains.
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Fig. 7. (Continued ).
Fig. 8. A schematic representation of the model of Ball and Hutchison [24] showing sliding between a group of grains.
Zn-content is possible. Thus, it follows from Table 1 that the superplasticity in the binary eutectic Pb–Sn is extremely altered by addition of the third phase (Zn-content). The fact that the ternary composition showed high elongation and low stresses more than the binary is quite remarkable in that a small Zn-addition enhances superplasticity of Pb–Sn eutectic. This implies that the microstructure in the ternary alloys must be uniform and finer grain size. The reason why Zn enhances the superplasticity of Pb–Sn eutectic can be analysed as follows. In the model of Bochvar [1], two conditions are necessary to observe superplasticity: (a) the rapid variation in composition with temperature; (b) high rate of diffusion. The second condition implies increasing grain boundary area and decreasing diffusion length, which enhances superplasticity. Accordingly, the Zn-addition seems to lead to a finer grain size which, in turn, increased the rate of diffusion and
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Table 1 Comparison of the steady state creep characteristics of Pb–Sn–Zn ternary alloys with Pb–Sn binary alloys Materials
Pb–10Sn (binary) [7] Pb–Sn (eutectic) [7] Pb–65Sn–Zn (ternary) Pb–Sn–Zn (eutectic)
Melting temperature, Tm
Flow stresses (MPa)
Maximum elongation (%)
588 456 455 447.9
12.73–22.91 7.63–12.73 5.86–6.25 4.88–6.25
9 70 140 150
enhanced the creep parameters of Pb–Sn–Zn alloys. Moreover, the addition of Zn leads to reduction of Tm of the ternary alloys and increasing the homogeneity of micro structure (see Table 1).
5. Conclusion 1. Significant improvement in superplasticity of Pb–Sn binary eutectic alloys was observed due to the Zn-addition within the range of 1–3.4% Zn. 2. The Pb–Sn–Zn ternary alloys show superior superplastic behaviour in comparison with Pb–Sn binary eutectic as a result of the lower melting temperature (Tm ), the finer microstructure, and the multiplicity of types of interphase boundaries. 3. Under condition of optimal superplastic flow, the present results are consistent with the model of Ball and Hutchison [24] in both of mechanical and microstructural evidence. References [1] [2] [3] [4]
P. Chauhari, Acta Met. 15 (1967) 1771. P. Griffiths, G. Hammond, Acta Met. 20 (1972) 935. P. Chauhari, S. Marder, App. Polym. Symp. 12 (1969) 1. O.A. Kaibyshev, Superplasticity of Commercial Alloys, Metallvrgia, Moscow, 1984.
Specimen dimensions (mm) Length
Diameter
50 50 50 50
1.0 1.0 0.8 0.8
Activation energy, Q (kJ mol−1 )
Sensitivity parameter (m)
46.2–88.2 42–63 41–59.7 40–58
0.17–0.43 0.54–0.88 0.3–0.53 0.34–0.64
[5] K. Hashimoto, H. Doi, K. Kassahara, T. Tsujimoto, T. Sazuki, J. Jpn. Inst. Met. 52 (1988) 816. [6] R. Honecomb, Plastic Deformation of Metals, Mir, Moscow, 1972. [7] M.S. Sakr, A.Z. Mohamed, M.M. Shehab, A.H. Bassyouni, Czech. J. Phys. 41 (1991) 785. [8] H.E. Cline, T.H. Alden, Trans. Met. Soc. Am. 239 (1967) 710. [9] D.E. Newbury, D.C. Joy, Script. Met. 4 (1970) 825. [10] M.P. Robert, A. Zubelewicz, L.M. Keer, J. Eng. Mech. 117. [11] M.M. Ahmed, T.G. Langdon, Metallurgy 8A (1977) 1932. [12] A.E. Geckinli, C.R. Barrett, J. Mater. Sci. 11 (1976) 510. [13] M.D.C. Moles, G.J. Davies, Met. Sci. 10 (1976) 314. [14] A.Z. Mohamed, M.H. El-Ghazaly, E.A. El-Saadani, Egypt. J. Sol. 223 (1997). [15] R. Kamel, J.A. Bessa, J. Appl. Phys. 34 (1963) 1882. [16] B.D. Cullity, X-ray Diffraction, London, 1959, p. 262. [17] J.H. Schneibel, P.M. Hazzledine, J. Mater. Sci. 18 (1983) 562. [18] G.A. Chadick, D.A. Smith, Grain Boundary Structure and Properties, Academic Press, London, 1976, pp. 236–254. [19] T.H. Alden, Acta Met. 15 (1967) 464. [20] Z. Jiang, J. Lian, Acta Met. 40 (1942) 1587. [21] G.V. Smith, Properties of Metals at Elevated Temperatures, McGraw-Hill, New York, 1950. [22] M. Knji, U. Yasuhide, Y. Mosao, J. Jpn. Inst. Met. 3 (1974) 219. [23] S. Zhov, D. Zhang, D. Lin, Mater. Roc. Soc. Symp. Proc. 196 (1990) 227. [24] A. Ball, M. Hutchison, Met. Sci. J. 3 (1964) 1. [25] M.S. Sakr, A.A. El-Daly, A.Z. Mohamed, E.A. El-Saadani, A.H. Bassyouni, Egypt. J. Sol. 13 (1990) 26. [26] J. Friedel, Dislocation, Pergamon Press, London, 1964, p. 328. [27] K.A. Padmanabhan, G.J. Davies, Superplasticity: mechanical and structural aspects, in: Environmental Effects, Fundamentals and Applications, Springer, Berlin, New York, 1980, p. 170.