- Email: [email protected]
Cavitation characteristics of a superplastic 8090 Al alloy during equi-biaxial tensile deformation
Materials Science and Engineering A291 (2000) 1 – 8 www.elsevier.com/locate/msea
Cavitation characteristics of a superplastic 8090 Al alloy during equi-biaxial tensile deformation Horng-yu Wu * Department of Mechanical Engineering, Chung-Hua Uni6ersity, Hsinchu, Taiwan, ROC Received 24 February 2000; received in revised form 4 May 2000
Abstract Cavitation behavior of a superplastic 8090 Al alloy during equi-biaxial tensile deformation has been investigated by deforming the sheet into a right cylindrical die. Cavitation characteristics could be separated into two stages. In stage I, the sheet deformed freely as part of a spherical dome, and the cavity volume increased exponentially with deformation. The evolution of cavity volume was due to both nucleation and growth of cavities. In the second stage, the surface friction would restrict thinning of the sheet, and the cavity volume first increased and then decreased with forming time for all test strain rates. Decrease in cavity volume in the later stage could be related to the cavity shrinkage that resulted from the sintering effect. A higher imposed pressure during forming leaded to a greater average cavity shrinkage rate. The cavitation level could be effectively reduced by a post-sintering procedure. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Superplastic deformation; Cavitation; Cavity growth; Cavity shrinkage
1. Introduction A significant problem with superplastic aluminum alloys is the internal cavity formation during superplastic deformation. The cavities nucleate at second-phase particles or grain boundaries; their subsequent growth and coalescence could cause premature failure during superplastic forming, and the presence of these cavities in the superplastically formed parts would have a deleterious effect on any post-form applications. Several investigations have been performed to study the characteristics of cavitation during superplastic deformation [1 –10]. It is widely accepted that cavity nucleation arises from stress concentrations generated at secondphase particles or triple points as a result of grain boundary sliding [1,11 – 13]. Cavity nucleation is a very complex problem since cavities can either nucleate or possibly develop from pre-existing cavities. Cavity growth has been studied either experimentally or theoretically. Vacancy diffusion and strain-controlled
* Tel.: +886-3-5374281; fax: + 886-3-5373771. E-mail address: [email protected] (H.-y. Wu).
growth have been proposed as the two main mechanisms for cavity growth [1,3–5,14,15]. The growth rates of these two mechanisms depend on the superplastic conditions; diffusion growth is only predominant at low strain rates and for very small cavities, and cavity growth is essentially strain-controlled during superplastic deformation. Some fundamental information on the characteristics of cavity development has been obtained. However, most of these studies explored cavitation using a tensile test. In order to reduce cavitation levels, it is important to understand the microstructural and deformation parameters that affect the cavitation behavior under multiaxial deformation. The work presented in this article evaluates the effects of equi-biaxial tension on cavitation of a superplastic (SP) 8090 Al alloy during superplastic deformation. Gas pressure forming was carried out to deform the sheets into a right cylindrical die. Focus was placed on the evolution of cavitation during superplastic deformation. The experimental results were quantitatively analyzed and compared with the empirical model. A simplified post-sintering procedure was also proposed to investigate the effect of the extended forming time on the reduction of cavitation level.
0921-5093/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0921-5093(00)00986-2
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
2
Table 1 Chemical composition of the SP8090 Al alloy Alloy element
Li
Cu
Mg
Zr
Fe
Ti
Zn
Al
Mass%
2.42
1.24
0.67
0.11
B0.05
B0.03
B0.03
Balance
2. Material and experimental procedures
2.3. Metallographic inspection
2.1. Material and preparation
Optical microscopy was used to inspect cavitation of the test piece. The specimens for metallographic examination were mechanically polished and then slightly etched to remove smeared metal covering the cavities. Cavity volume fractions were measured by computer imaging equipment and calculated by using OPTIMAS 5 software [17]. The optical image was first converted into a binary video image. The number of pixels in the cavity (black area) were counted and divided by the total number of pixels in the image to obtained cavity volume fraction.
The SP8090 Al alloy utilized in this study was provided by Superfom Metals Limited (Worcester, UK). Table 1 shows the analyzed chemical composition. The alloy has the form of a 2 mm thick sheet. The sheet was recrystallized at 530°C for 10 min, resulting in an average grain size of 6.98 mm before superplastic forming. Grid circles of diameter do etched on the sheets were used to measure strain levels in each test. During forming, the etched circles were distorted into ellipses. Measurements of the major, d1, and minor, d2, diameters after deformation were carried out to determine the principal strains, which are presented in Fig. 1. The effective strain can be expressed as o¯ =2/ 3(o 21 +o1o2 + o 22)1/2.
2.2. Superplastic plastic forming tests The superplastic sheet was formed into a right cylindrical die by compressed argon gas. The die cavity had an inner diameter of 40 mm with a depth of 20 mm. Incremental step strain rate tensile tests were first conducted at 520°C covering the range of strain rates from 5×10 − 5 to 2×10 − 3 s − 1 to determine the superplastic flow characteristics. The variation of strain rate sensitivity, m, over a wide range of strain rates, with strain was determined using separate specimens strained to various amounts prior to the step strain rate test. The material constant and m values obtained from the tensile tests were then used as the input data for the computer program SUPFORM2 [16] to calculate the pressure profiles for the desired strain rates. Test runs were also made to modify the pressure profile predicted by the computer program in order to achieving the desired strain rate at the pole. Gas blow forming was performed at 520°C and over a range of average strain rate from 8 × 10 − 4 to 1.8 × 10 − 4 s − 1. Several interrupted tests were performed to bulge the sheets to various depths for each strain rate, the depth of the pole region, hence the strain, could then be utilized to evaluate the effect of strain on cavitation. In order to obtain the fundamental information on the characteristics of cavity development in SP8090 Al alloy, lubricant and back pressure were not used in this study.
3. Results and discussion
3.3.1. Forming into a right cylindrical die Since the sheets were bulged to various depths, the configuration of the formed component could be obtained for each test. Fig. 2 demonstrates the deformation sequence of the sheet formed at an average strain rate of 8 × 10 − 4 s − 1. The numbers in Fig. 2 represent the forming time for each configuration. The forming
Fig. 1. Principal strain directions for the hemispherical dome.
Fig. 2. Experimentally determined deformation sequence of the sheet formed into a right cylindrical die at a strain rate of 8 × 10 − 4 s − 1.
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
Fig. 3. Circumferential to meridional strain ratio distribution along the centerline of the hemispherical dome with H/R=1 formed at various strain rates.
3
without applying lubricant on the die surface; such as the cases carried out in this work. Fig. 3 depicts the variation of circumferential to meridional strain ratio along the centerline of the formed hemispherical dome with forming depth to dieradius ratio (H/R) of 1 in stage I. The circumferential and meridional strains are equal at the poles, and deviate from each other from the pole to the edge. There is a stress state gradient from the pole of the dome to the edge in this geometry. While a circular sheet clamped at the edge is subjected to a gas pressure to develop into part of hemispherical geometry, the orthogonal stresses are equal at the pole, and the stress state is that of equi-biaxial tensile. At the edge of the dome, the constraint of the clamped sheet around the periphery results in a plane strain state. Fig. 4 shows the variation of circumferential to meridional strain ratio along the centerline of the completely formed cylindrical cup in stage II. The measured circumferential and meridional strains are equal at the bottom center of the cup, and the stress state is equi-biaxial tensile at this point. Therefore, the central region was used to analyze the effect of equi-biaxial tension on the cavitation characteristics.
3.4. Ca6itation in stage I Fig. 4. Circumferential to meridional strain ratio distribution along the centerline of the cylindrical cup formed at various strain rates.
Fig. 5. Cavity volume fraction versus strain showing the effect of strain rate.
operation for forming into a right circular cylindrical die can be considered to separate into two stages. In stage I, the sheet will freely deform as part of a spherical dome until its central point touches the bottom surface of the die. In the second stage of formation, the sheet is overlaid on the bottom surface and on the sidewall surface as the deformation proceeds. After the central region of sheet is deformed into contact with the bottom surface of the die, the surface condition of the die will affect the subsequent deformation of the overlaid region. The thinning of the sheet will be restricted by the surface friction for forming, performed
Fig. 5 illustrates the cavity volume fraction at the pole of the hemispherical dome as a function of effective strain forming at various strain rates. The decrease in cavitation with strain rate is found in this alloy over the test strain rate range of 8× 10 − 4 to 1.8× 10 − 4 s − 1. This consequence should result from a lower flow stress at a lower strain rate [11]. Since flow stresses influence the stresses built up at grain boundary and thus the tendency for cavity nucleation, a lower flow stress at a lower strain rate means smaller stresses accumulated at grain boundary. Moreover, at a lower strain rate, the stresses generated by the grain boundary sliding would have greater time to become relaxed. Thus, superplastic deformation performed at a lower strain rate could reduce the local stresses at grain boundary irregularities and decrease the cavitation level in SP8090 Al alloy. The semilog plots show a linear relationship between cavity volume fraction (plotted logarithmically) and strain; as presented in Fig. 5. This result indicates that strain-controlled growth should be the dominant mechanism for the increase of cavity volume fraction. If a strain-controlled growth rate of cavities is assumed [14,15], the evolution of cavity volume with strain may be expressed as V= V0 exp(ho)
(1)
where o is strain, h is the cavity growth rate parameter, and V0 is a fitting constant. Stowell et al. [3] has proposed that the V0 is the volume fraction of the
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
4
pre-existing cavities. However, it has been pointed out that V0 is always a positive value, whether or not cavities pre-exist [18]. Thus, V0 may be related to the tendency of cavity nucleation associated with strain rate. Following the analysis of Cocks and Ashby [4] and Stowell et al. [3], the cavity growth rate parameter can be shown as: h=
n
3 m +1 2 −m ks sinh 2 2 m 2 +m 3
(2)
where m is the strain-rate sensitivity, and ks a geometric factor whose value depends on the test geometry (uniaxial, equi-biaxial or plane strain) and the extent of grain boundary sliding [19]. For most superplastic alloys, about 50% of the accumulated strain is believed to be due to grain boundary sliding; thus, the value ks = Table 2 Comparison of the calculated and experimentally determined cavitation parameters Strain rate (s−1)
m value
h h V0 (Calculated) (Experiment) (Experiment)
8×10−4 1.8×10−4
0.495 0.472
4.68 4.99
4.82 5.48
0.0325 0.0131
Fig. 6. Variation of strain rate sensitivity with strain rate after deformation to various strains.
Fig. 7. Variation of strain rate sensitivity with strain during deformation at various strain rates.
2.25 could be adopted for equi-biaxial deformation [14]. In Table 2, the values of h with strain rate (m value) predicated by Eq. (2) are given and compared with those determined from the experimental data. It is found that V0 is indeed related to strain rate. V0 decreases with decreasing strain rate and is sensitive to strain rate. The calculated values of h are smaller than those determined experimentally. The difference is most likely to be caused by a combination of two factors. First, the m value to the material changes with strain. Second, continuous cavity nucleation and cavity coalescence during deformation will cause an increase in the cavity growth rate. The variations of m with strain rate at several strains and with strain determined by incremental step strain rate tensile tests are illustrated in Figs. 6 and 7, respectively. The variation of m with strain during deformation at a given strain rate is dependent on the strain rate relative to that at which the maximum m value occurs. If the deformation strain rate is greater and near the strain rate with maximum m value, such as the strain rate of 8×10 − 4 s − 1 used in this work, the m value decreases with increasing strain. Since the cavity growth rate parameter, h, increases as the m value decreases, this effect raises the cavity volume fraction and gives a greater value of h than predicted by Eq. (2). If the deformation strain rate is less than the strain rate of the maximum m value, the m value would first increase and then decrease with increasing strain. This is the case for forming at a strain rate of 1.8 ×10 − 4 s − 1 in the present work. As the m value increases with increasing strain during deformation, the cavity growth rate parameter, h, should decrease. However, this result was not observed in this work; on the contrary, a greater value of h is observed for the deformation at a strain rate of 1.8× 10 − 4 s − 1, the difference may have arisen from the effects of the continuous nucleation of cavities and grain growth during deformation. Eq. (2) is basically deduced from the model proposed by Cocks and Ashby [4]. Cavity nucleation and cavity coalescence during deformation were not taken into account in this model. A plot of total number density of cavities (number mm − 2) as a function of effective strain is shown in Fig. 8. It shows that the total number of cavities increases with increasing strain. The increase of total number density of cavities due to cavity nucleation can be observed from the actual distribution of cavity sizes and their variation with strain. Fig. 9 shows the number density of cavities as a function of cavity size forming at various strain rates. The density for all cavity sizes appears to increase with strain, especially for the smallest cavity size ( 2 mm). These results reveal that new cavities continue to nucleate during deformation as cavity growth occurs. The development of a high-radius tail with increasing strain indicates some cavity coalescence do take place; as shown in Fig.
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
Fig. 8. Total number of cavities per unit area versus strain showing the effect of strain rate.
5
9. The effect of cavity nucleation and coalescence is to increasingly raise the cavity volume towards the higher strains and, hence, give a higher value of h than predicted by Eq. (2). Fig. 8 also indicates that the higher strain rate produces quite a large number of cavities in the early stage of deformation. In a fine-grained superplastic material, grain boundary sliding is the dominant mechanism of deformation during superplastic forming. Grain boundary sliding is believed to cause the development of stress concentration at sites where sliding is impeded. If the stress concentrations are not attenuated rapidly by processes like local diffusion flow or plastic deformation, to meet the requirements imposed by the deformation rate, cavity nucleation occurs at these sites. The number of nucleation sites would be high due to the high flow stress at the higher strain rate resulting in large number of cavities.
3.5. Ca6itation in stage II
Fig. 9. Number of cavities per unit area versus cavity diameter at various levels of strain formed at various strain rates. (a) o; = 8 × 10 − 4 s − 1, (b) o; =1.8 ×10 − 4 s − 1
Fig. 10. Evolution of cavity volume fraction and thickness at the central point of the formed part versus forming time at a strain rate of 8×10 − 4 s − 1.
Fig. 10 depicts the evolution of cavity volume fraction and the thickness at the central region of the deformed sheet with forming time for the deformation at a strain rate of 8× 10 − 4 s − 1. For forming at a strain rate of 8×10 − 4 s − 1, the center of the sheet touched the bottom surface at around 19 min, and it took about 34 min to completely form a cylindrical cup. Hence, the time span from 19 to 34 min accounts for the deformation of stage II. In this stage, the cavity volume fraction of the central region keeps on increasing in the early stage; it reaches a maximum value at a forming time around 25 min, then it decreases until the end of forming, as shown in Fig. 10. The variation of cavity volume fraction with time in stage II could be associated with the thinning behavior of the sheet. The thickness of the central point decreases with increasing forming time, reaching a thickness about 0.68 mm at a forming time around 25 min and then remaining almost as a constant. Changes of cavity volume fraction in stage II are associated with the variations of the thickness at the central point of the deformed sheet. The cavity volume fraction increases with a decrease in thickness in the early stage of stage II; it begins to decrease as significant thinning of the deformed sheet comes to an end. It is believed that cavity closure occurs, giving rise to the decrease in cavity volume fraction in the later stage during superplastic forming while the sheet has been overlaid on the die surface. Similar results are also observed for forming at a lower strain rate, as shown in Fig. 11. The deformed sheet comes into contact with the bottom surface of the die at a forming time around 71 min for forming at a strain rate of 1.8× 10 − 4 s − 1. The maximum cavity volume fraction occurs at about 100 min, which is also the time that significant thinning of the sheet stops.
6
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
The decrease in cavity volume fraction in the later stage for forming a superplastic sheet into a right cylindrical die could be related to the cavity shrinkage as a result of sintering effect. After the significant thinning of the deformed sheet is prevented by the restriction of the surface friction, the decrease in cavity volume in the region at which significant thinning does not occur could be described as the sintering of cavities at elevated temperature under pressure. Figs. 12 and 13 illustrate the variation of mean cavity diameter and
Fig. 11. Evolution of cavity volume fraction and thickness at the central point of the formed part versus forming time at a strain rate of 1.8×10 − 4 s − 1.
cavity density at the central points of the formed parts with forming time in the later stage of deformation with imposed pressures of 0.889 and 0.228 MPa, respectively. Both mean cavity diameter and cavity density decrease with forming time; these results show that cavity shrinkage does occur in this time span. For the plasticity controlled cavity shrinkage mechanism, the imposed external pressure has a significant effect on the cavity shrinkage rate [20]. In the present work, the imposed forming pressures in the later stage were 0.889 and 0.228 MPa for the strain rates of 8× 10 − 4 and 1.8 × 10 − 4 s − 1, respectively. In the later stage of stage II, no significant thinning occurs in the overlaid regions; hence, strain rate is not responsible for the variation of the cavitation levels in these regions. The imposed pressure is then the major factor to cause the changes of cavity volume fraction. A greater imposed pressure accelerates cavity closure resulting in a higher average cavity shrinkage rate. The flow stresses for 8090 Al alloy at strain rates of 2× 10 − 4 to 1× 10 − 3 s − 1 are of the order of 5–9 MPa. The imposed pressures in the later stage during forming are much smaller than the flow stresses. According to the plasticity controlled cavity growth mechanism, growth of cavities during deformation can be suppressed theoretically by hydrostatic pressure equal to one-third of the flow stress in uniaxial tension [21]. The imposed pressures in the present work are also smaller than those required by suppressing the cavity growth.
3.6. Effect of post-sintering on ca6itation
Fig. 12. Mean cavity diameter and number of cavities per unit area at the central point of the formed part versus forming time in stage II with a forming pressure of 0.889 MPa.
Fig. 13. Mean cavity diameter and number of cavities per unit area at the central point of the formed part versus forming time in stage II with a forming pressure of 0.228 MPa.
An important requirement for cavitation during superplastic deformation is the presence of a local tensile stress. Cavities produced during superplastic tensile deformation can be reduced by subsequent compressive flow [22]. Cavitation can be suppressed, or at least reduced, by various procedures before, during, or after superplastic deformation. These procedures are based on annealing with or without superimposed pressure [20,23] or deformation under pressurized atmosphere [2,14]. These methods are likely to be limited in application because of complex procedures, restriction in component size, or cost. On the basis of the analysis described in Section 3.3, cavity closure occurs as a result of sintering effect while the deformed sheet has been overlaid on the die surface. A simplified procedure was proposed to reduce cavitation level in the present work. In this procedure, the formed part was left in the die and remained under pressure for an extra period of time after the cylindrical cup was completely deformed. Since it took about 158 min to form a cylindrical cup at a strain rate of 1.8×10 − 4 s − 1, it is not so meaningful to extend the forming time to reduce cavitation at a low strain rate; the proposed procedure was only performed for forming at a strain rate of 8×10 − 4 s − 1.
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
Fig. 14. Cavity volume fraction distribution along the centerline of the cylindrical cup showing the effect of post-sintering time with an imposed pressure of 0.889 MPa.
Fig. 14 shows the effect of post-sintering time (the extended forming time after the part is completely formed) with an imposed pressure of 0.889 MPa on the cavity volume fraction distribution along the centerline of the cylindrical cup formed at a strain rate of 8× 10 − 4 s − 1. Since the bottom corner that is about 20 mm away from the bottom center is the latest region to be formed for forming into a right cylindrical die, it is the thinnest portion of the formed cup, and it is also the region where the greatest cavitation level presents. Fig. 14 appears that post-sintering does have significant effect on the reduction of cavitation levels. Fig. 14 also reveals that the procedure of post-sintering does not show much influence on the cavity volume fractions less than 1.5%. Since plasticity, which is more effective for shrinkage of large cavities, is the dominant mechanism for cavity shrinkage during post-sintering treatment, the shrinkage rate will decrease as the large-sized cavities have been reduced. Therefore, the benefit of postsintering treatment could not be observed for small cavity volume fractions, it may be necessary to use a longer sintering time for the diffusion-controlled mechanism to take place for further reduction in cavitation level.
4. Conclusions An analysis of cavitation characteristics of a SP8090 Al alloy through use of blow forming was undertaken in the present study. Cavitation characteristics due to equi-biaxial tension were analyzed and compared with the empirical model. The following conclusions were determined on the basis of this work. First, the formation of a right cylindrical cup during superplastic forming could be divided into two stages. In the first stage, the sheet deformed freely into a hemispherical segment until its pole contacted the bottom surface of the die. The second stage started when the sheet just touched the bottom surface of the die.
7
The central region of the deformed sheet was overlaid on the bottom surface of the die as the deformation proceeded; the surface friction of the die would influence the deformation of the overlaid region of the deformed sheet in stage II. Therefore, cavitation behavior due to equi-biaxial tensile deformation should be examined separately in theses two stages. In stage I, the relationship between the cavity volume fraction and strain is consistent with cavity growth dominated by the plasticity-controlled mechanism. The values of cavity growth rate parameter, h, determined experimentally were greater than those calculated by empirical model; changes of m value with strains, continuous cavity nucleation and cavity coalescence during deformation should be the possible factors to cause this difference. Third, in the second stage of deformation, variation of cavity volume fraction was related to the thinning behavior of the deformed sheet. The cavity volume fraction increased with decreasing thickness, and then turned to a decrease while the thickness of the sheet remained as a constant. Decrease in cavity volume was believed to be the result of a cavity sintering effect. A higher imposed pressure during forming resulted in a greater average cavity closure rate. Finally, a post-sintering treatment was proposed to reduce the cavitation level for forming at a higher strain rate. The cavity volume fractions for the cup formed at a strain rate of 8× 10 − 4 s − 1 were significantly reduced by a post-sintering treatment with an imposed pressure of 0.889 MPa for 30 min.
Acknowledgements This work was conducted through grant from National Science Council under contract NSC 89-2612-E216-002. The author is grateful to Jiin-her Hwang for his help with part of the work.
References [1] R. Raj, M.F. Ashby, Acta Metall. 23 (1975) 653. [2] C.C. Bampton, M.W. Mahoney, C.H. Hamilton, A.K. Ghosh, R. Raj, Metall. Trans. A 14A (1983) 1583. [3] M.J. Stowell, D.W. Liversy, N. Ridley, Acta. Metall. 32 (1984) 35. [4] A.C.F. Cocks, M.F. Ashby, Metal Sci. 16 (1982) 465. [5] I.W. Chen, A.S. Argon, Acta. Metall. 29 (1981) 1759. [6] M.G. Zelin, H.S. Yang, R.Z. Valiev, A.K. Mukherjee, Metall. Trans. A 24A (1993) 417. [7] M.W. Mahoney, C.H. Hamilton, A.K. Ghosh, Metall. Trans. A 14A (1983) 1593. [8] R. Verma, P.A. Friedman, A.K. Ghosh, S. Kim, C. Kim, Metall. Trans. A 27A (1996) 1889. [9] A.K. Ghosh, D.H. Bae, in: A.H. Chokshi (Ed.), Proceedings of Superplasticity in Advanced Materials, ICSAM-97, Materials
8
[10]
[11]
[12]
[13] [14] [15]
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8 Science Forum, vols. 243–245, Trans Tech Publications, Switzerland, 1997, p. 89. J. Pilling, R. Ridley, in: H. Heikkenen, T. McNelley (Eds.), Proceedings of Superplastcity in Aerospace, The Metallurgical Scoiety, Warrendale, PA, 1988, p. 183. B. Ren, C.H. Hamilton, in: C.H. Hamilton (Ed.), Proceedings of Superpasticity and Superplastic Forming, TMS, Warrendale, PA, 1988, p. 121. M.J. Stowell, in: N.E. Paton, C.H. Hamilton (Eds.), Proceedings of Superplstic Forming of Structural Alloys, The Metallurgical Society of AIME, Warrendale, PA, 1982, p. 321. R. Raj, Acta Metall. 26 (1978) 995. J. Pilling, R. Ridley, Acta Metall. 34 (1986) 669. J. Pilling, Mater. Sci. Tech. 1 (1985) 461.
.
[16] CEMEF, SUPFORM2 User’s guide, Version 1.0, Fcole des Mines de Paris, 1989. [17] Optimas Corporation, OPTIMAS 5 Software, 6th edition, Optimas Corporation, Seattle, WA, 1995. [18] A.H. Chokshi, A.K. Mukherjee, Acta Metall. 37 (1989) 3007. [19] J. Pilling, N. Ridley, Superplasticity in Crystallines Solids, The Institute of Metals, London, 1989, p. 102. [20] A. Varloteaux, J.J. Blandin, M. Suery, Mater. Sci. Tech. 5 (1989) 1109. [21] C.C. Bampton, R. Raj, Acta Metall. 30 (1982) 2043. [22] D.W. Livesey, N. Ridley, Metal Sci. 16 (1982) 563. [23] H. Ahmed, R. Pearce, in: R. Pearce, L. Kelly (Eds.), Proceedings of Superplasticity in Aerospace — Aluminum, SIS, Cranfield, Bedford, UK, 1985, p. 146.
Cavitation characteristics of a superplastic 8090 Al alloy during equi-biaxial tensile deformation Horng-yu Wu * Department of Mechanical Engineering, Chung-Hua Uni6ersity, Hsinchu, Taiwan, ROC Received 24 February 2000; received in revised form 4 May 2000
Abstract Cavitation behavior of a superplastic 8090 Al alloy during equi-biaxial tensile deformation has been investigated by deforming the sheet into a right cylindrical die. Cavitation characteristics could be separated into two stages. In stage I, the sheet deformed freely as part of a spherical dome, and the cavity volume increased exponentially with deformation. The evolution of cavity volume was due to both nucleation and growth of cavities. In the second stage, the surface friction would restrict thinning of the sheet, and the cavity volume first increased and then decreased with forming time for all test strain rates. Decrease in cavity volume in the later stage could be related to the cavity shrinkage that resulted from the sintering effect. A higher imposed pressure during forming leaded to a greater average cavity shrinkage rate. The cavitation level could be effectively reduced by a post-sintering procedure. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Superplastic deformation; Cavitation; Cavity growth; Cavity shrinkage
1. Introduction A significant problem with superplastic aluminum alloys is the internal cavity formation during superplastic deformation. The cavities nucleate at second-phase particles or grain boundaries; their subsequent growth and coalescence could cause premature failure during superplastic forming, and the presence of these cavities in the superplastically formed parts would have a deleterious effect on any post-form applications. Several investigations have been performed to study the characteristics of cavitation during superplastic deformation [1 –10]. It is widely accepted that cavity nucleation arises from stress concentrations generated at secondphase particles or triple points as a result of grain boundary sliding [1,11 – 13]. Cavity nucleation is a very complex problem since cavities can either nucleate or possibly develop from pre-existing cavities. Cavity growth has been studied either experimentally or theoretically. Vacancy diffusion and strain-controlled
* Tel.: +886-3-5374281; fax: + 886-3-5373771. E-mail address: [email protected] (H.-y. Wu).
growth have been proposed as the two main mechanisms for cavity growth [1,3–5,14,15]. The growth rates of these two mechanisms depend on the superplastic conditions; diffusion growth is only predominant at low strain rates and for very small cavities, and cavity growth is essentially strain-controlled during superplastic deformation. Some fundamental information on the characteristics of cavity development has been obtained. However, most of these studies explored cavitation using a tensile test. In order to reduce cavitation levels, it is important to understand the microstructural and deformation parameters that affect the cavitation behavior under multiaxial deformation. The work presented in this article evaluates the effects of equi-biaxial tension on cavitation of a superplastic (SP) 8090 Al alloy during superplastic deformation. Gas pressure forming was carried out to deform the sheets into a right cylindrical die. Focus was placed on the evolution of cavitation during superplastic deformation. The experimental results were quantitatively analyzed and compared with the empirical model. A simplified post-sintering procedure was also proposed to investigate the effect of the extended forming time on the reduction of cavitation level.
0921-5093/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S0921-5093(00)00986-2
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
2
Table 1 Chemical composition of the SP8090 Al alloy Alloy element
Li
Cu
Mg
Zr
Fe
Ti
Zn
Al
Mass%
2.42
1.24
0.67
0.11
B0.05
B0.03
B0.03
Balance
2. Material and experimental procedures
2.3. Metallographic inspection
2.1. Material and preparation
Optical microscopy was used to inspect cavitation of the test piece. The specimens for metallographic examination were mechanically polished and then slightly etched to remove smeared metal covering the cavities. Cavity volume fractions were measured by computer imaging equipment and calculated by using OPTIMAS 5 software [17]. The optical image was first converted into a binary video image. The number of pixels in the cavity (black area) were counted and divided by the total number of pixels in the image to obtained cavity volume fraction.
The SP8090 Al alloy utilized in this study was provided by Superfom Metals Limited (Worcester, UK). Table 1 shows the analyzed chemical composition. The alloy has the form of a 2 mm thick sheet. The sheet was recrystallized at 530°C for 10 min, resulting in an average grain size of 6.98 mm before superplastic forming. Grid circles of diameter do etched on the sheets were used to measure strain levels in each test. During forming, the etched circles were distorted into ellipses. Measurements of the major, d1, and minor, d2, diameters after deformation were carried out to determine the principal strains, which are presented in Fig. 1. The effective strain can be expressed as o¯ =2/ 3(o 21 +o1o2 + o 22)1/2.
2.2. Superplastic plastic forming tests The superplastic sheet was formed into a right cylindrical die by compressed argon gas. The die cavity had an inner diameter of 40 mm with a depth of 20 mm. Incremental step strain rate tensile tests were first conducted at 520°C covering the range of strain rates from 5×10 − 5 to 2×10 − 3 s − 1 to determine the superplastic flow characteristics. The variation of strain rate sensitivity, m, over a wide range of strain rates, with strain was determined using separate specimens strained to various amounts prior to the step strain rate test. The material constant and m values obtained from the tensile tests were then used as the input data for the computer program SUPFORM2 [16] to calculate the pressure profiles for the desired strain rates. Test runs were also made to modify the pressure profile predicted by the computer program in order to achieving the desired strain rate at the pole. Gas blow forming was performed at 520°C and over a range of average strain rate from 8 × 10 − 4 to 1.8 × 10 − 4 s − 1. Several interrupted tests were performed to bulge the sheets to various depths for each strain rate, the depth of the pole region, hence the strain, could then be utilized to evaluate the effect of strain on cavitation. In order to obtain the fundamental information on the characteristics of cavity development in SP8090 Al alloy, lubricant and back pressure were not used in this study.
3. Results and discussion
3.3.1. Forming into a right cylindrical die Since the sheets were bulged to various depths, the configuration of the formed component could be obtained for each test. Fig. 2 demonstrates the deformation sequence of the sheet formed at an average strain rate of 8 × 10 − 4 s − 1. The numbers in Fig. 2 represent the forming time for each configuration. The forming
Fig. 1. Principal strain directions for the hemispherical dome.
Fig. 2. Experimentally determined deformation sequence of the sheet formed into a right cylindrical die at a strain rate of 8 × 10 − 4 s − 1.
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
Fig. 3. Circumferential to meridional strain ratio distribution along the centerline of the hemispherical dome with H/R=1 formed at various strain rates.
3
without applying lubricant on the die surface; such as the cases carried out in this work. Fig. 3 depicts the variation of circumferential to meridional strain ratio along the centerline of the formed hemispherical dome with forming depth to dieradius ratio (H/R) of 1 in stage I. The circumferential and meridional strains are equal at the poles, and deviate from each other from the pole to the edge. There is a stress state gradient from the pole of the dome to the edge in this geometry. While a circular sheet clamped at the edge is subjected to a gas pressure to develop into part of hemispherical geometry, the orthogonal stresses are equal at the pole, and the stress state is that of equi-biaxial tensile. At the edge of the dome, the constraint of the clamped sheet around the periphery results in a plane strain state. Fig. 4 shows the variation of circumferential to meridional strain ratio along the centerline of the completely formed cylindrical cup in stage II. The measured circumferential and meridional strains are equal at the bottom center of the cup, and the stress state is equi-biaxial tensile at this point. Therefore, the central region was used to analyze the effect of equi-biaxial tension on the cavitation characteristics.
3.4. Ca6itation in stage I Fig. 4. Circumferential to meridional strain ratio distribution along the centerline of the cylindrical cup formed at various strain rates.
Fig. 5. Cavity volume fraction versus strain showing the effect of strain rate.
operation for forming into a right circular cylindrical die can be considered to separate into two stages. In stage I, the sheet will freely deform as part of a spherical dome until its central point touches the bottom surface of the die. In the second stage of formation, the sheet is overlaid on the bottom surface and on the sidewall surface as the deformation proceeds. After the central region of sheet is deformed into contact with the bottom surface of the die, the surface condition of the die will affect the subsequent deformation of the overlaid region. The thinning of the sheet will be restricted by the surface friction for forming, performed
Fig. 5 illustrates the cavity volume fraction at the pole of the hemispherical dome as a function of effective strain forming at various strain rates. The decrease in cavitation with strain rate is found in this alloy over the test strain rate range of 8× 10 − 4 to 1.8× 10 − 4 s − 1. This consequence should result from a lower flow stress at a lower strain rate [11]. Since flow stresses influence the stresses built up at grain boundary and thus the tendency for cavity nucleation, a lower flow stress at a lower strain rate means smaller stresses accumulated at grain boundary. Moreover, at a lower strain rate, the stresses generated by the grain boundary sliding would have greater time to become relaxed. Thus, superplastic deformation performed at a lower strain rate could reduce the local stresses at grain boundary irregularities and decrease the cavitation level in SP8090 Al alloy. The semilog plots show a linear relationship between cavity volume fraction (plotted logarithmically) and strain; as presented in Fig. 5. This result indicates that strain-controlled growth should be the dominant mechanism for the increase of cavity volume fraction. If a strain-controlled growth rate of cavities is assumed [14,15], the evolution of cavity volume with strain may be expressed as V= V0 exp(ho)
(1)
where o is strain, h is the cavity growth rate parameter, and V0 is a fitting constant. Stowell et al. [3] has proposed that the V0 is the volume fraction of the
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
4
pre-existing cavities. However, it has been pointed out that V0 is always a positive value, whether or not cavities pre-exist [18]. Thus, V0 may be related to the tendency of cavity nucleation associated with strain rate. Following the analysis of Cocks and Ashby [4] and Stowell et al. [3], the cavity growth rate parameter can be shown as: h=
n
3 m +1 2 −m ks sinh 2 2 m 2 +m 3
(2)
where m is the strain-rate sensitivity, and ks a geometric factor whose value depends on the test geometry (uniaxial, equi-biaxial or plane strain) and the extent of grain boundary sliding [19]. For most superplastic alloys, about 50% of the accumulated strain is believed to be due to grain boundary sliding; thus, the value ks = Table 2 Comparison of the calculated and experimentally determined cavitation parameters Strain rate (s−1)
m value
h h V0 (Calculated) (Experiment) (Experiment)
8×10−4 1.8×10−4
0.495 0.472
4.68 4.99
4.82 5.48
0.0325 0.0131
Fig. 6. Variation of strain rate sensitivity with strain rate after deformation to various strains.
Fig. 7. Variation of strain rate sensitivity with strain during deformation at various strain rates.
2.25 could be adopted for equi-biaxial deformation [14]. In Table 2, the values of h with strain rate (m value) predicated by Eq. (2) are given and compared with those determined from the experimental data. It is found that V0 is indeed related to strain rate. V0 decreases with decreasing strain rate and is sensitive to strain rate. The calculated values of h are smaller than those determined experimentally. The difference is most likely to be caused by a combination of two factors. First, the m value to the material changes with strain. Second, continuous cavity nucleation and cavity coalescence during deformation will cause an increase in the cavity growth rate. The variations of m with strain rate at several strains and with strain determined by incremental step strain rate tensile tests are illustrated in Figs. 6 and 7, respectively. The variation of m with strain during deformation at a given strain rate is dependent on the strain rate relative to that at which the maximum m value occurs. If the deformation strain rate is greater and near the strain rate with maximum m value, such as the strain rate of 8×10 − 4 s − 1 used in this work, the m value decreases with increasing strain. Since the cavity growth rate parameter, h, increases as the m value decreases, this effect raises the cavity volume fraction and gives a greater value of h than predicted by Eq. (2). If the deformation strain rate is less than the strain rate of the maximum m value, the m value would first increase and then decrease with increasing strain. This is the case for forming at a strain rate of 1.8 ×10 − 4 s − 1 in the present work. As the m value increases with increasing strain during deformation, the cavity growth rate parameter, h, should decrease. However, this result was not observed in this work; on the contrary, a greater value of h is observed for the deformation at a strain rate of 1.8× 10 − 4 s − 1, the difference may have arisen from the effects of the continuous nucleation of cavities and grain growth during deformation. Eq. (2) is basically deduced from the model proposed by Cocks and Ashby [4]. Cavity nucleation and cavity coalescence during deformation were not taken into account in this model. A plot of total number density of cavities (number mm − 2) as a function of effective strain is shown in Fig. 8. It shows that the total number of cavities increases with increasing strain. The increase of total number density of cavities due to cavity nucleation can be observed from the actual distribution of cavity sizes and their variation with strain. Fig. 9 shows the number density of cavities as a function of cavity size forming at various strain rates. The density for all cavity sizes appears to increase with strain, especially for the smallest cavity size ( 2 mm). These results reveal that new cavities continue to nucleate during deformation as cavity growth occurs. The development of a high-radius tail with increasing strain indicates some cavity coalescence do take place; as shown in Fig.
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
Fig. 8. Total number of cavities per unit area versus strain showing the effect of strain rate.
5
9. The effect of cavity nucleation and coalescence is to increasingly raise the cavity volume towards the higher strains and, hence, give a higher value of h than predicted by Eq. (2). Fig. 8 also indicates that the higher strain rate produces quite a large number of cavities in the early stage of deformation. In a fine-grained superplastic material, grain boundary sliding is the dominant mechanism of deformation during superplastic forming. Grain boundary sliding is believed to cause the development of stress concentration at sites where sliding is impeded. If the stress concentrations are not attenuated rapidly by processes like local diffusion flow or plastic deformation, to meet the requirements imposed by the deformation rate, cavity nucleation occurs at these sites. The number of nucleation sites would be high due to the high flow stress at the higher strain rate resulting in large number of cavities.
3.5. Ca6itation in stage II
Fig. 9. Number of cavities per unit area versus cavity diameter at various levels of strain formed at various strain rates. (a) o; = 8 × 10 − 4 s − 1, (b) o; =1.8 ×10 − 4 s − 1
Fig. 10. Evolution of cavity volume fraction and thickness at the central point of the formed part versus forming time at a strain rate of 8×10 − 4 s − 1.
Fig. 10 depicts the evolution of cavity volume fraction and the thickness at the central region of the deformed sheet with forming time for the deformation at a strain rate of 8× 10 − 4 s − 1. For forming at a strain rate of 8×10 − 4 s − 1, the center of the sheet touched the bottom surface at around 19 min, and it took about 34 min to completely form a cylindrical cup. Hence, the time span from 19 to 34 min accounts for the deformation of stage II. In this stage, the cavity volume fraction of the central region keeps on increasing in the early stage; it reaches a maximum value at a forming time around 25 min, then it decreases until the end of forming, as shown in Fig. 10. The variation of cavity volume fraction with time in stage II could be associated with the thinning behavior of the sheet. The thickness of the central point decreases with increasing forming time, reaching a thickness about 0.68 mm at a forming time around 25 min and then remaining almost as a constant. Changes of cavity volume fraction in stage II are associated with the variations of the thickness at the central point of the deformed sheet. The cavity volume fraction increases with a decrease in thickness in the early stage of stage II; it begins to decrease as significant thinning of the deformed sheet comes to an end. It is believed that cavity closure occurs, giving rise to the decrease in cavity volume fraction in the later stage during superplastic forming while the sheet has been overlaid on the die surface. Similar results are also observed for forming at a lower strain rate, as shown in Fig. 11. The deformed sheet comes into contact with the bottom surface of the die at a forming time around 71 min for forming at a strain rate of 1.8× 10 − 4 s − 1. The maximum cavity volume fraction occurs at about 100 min, which is also the time that significant thinning of the sheet stops.
6
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
The decrease in cavity volume fraction in the later stage for forming a superplastic sheet into a right cylindrical die could be related to the cavity shrinkage as a result of sintering effect. After the significant thinning of the deformed sheet is prevented by the restriction of the surface friction, the decrease in cavity volume in the region at which significant thinning does not occur could be described as the sintering of cavities at elevated temperature under pressure. Figs. 12 and 13 illustrate the variation of mean cavity diameter and
Fig. 11. Evolution of cavity volume fraction and thickness at the central point of the formed part versus forming time at a strain rate of 1.8×10 − 4 s − 1.
cavity density at the central points of the formed parts with forming time in the later stage of deformation with imposed pressures of 0.889 and 0.228 MPa, respectively. Both mean cavity diameter and cavity density decrease with forming time; these results show that cavity shrinkage does occur in this time span. For the plasticity controlled cavity shrinkage mechanism, the imposed external pressure has a significant effect on the cavity shrinkage rate [20]. In the present work, the imposed forming pressures in the later stage were 0.889 and 0.228 MPa for the strain rates of 8× 10 − 4 and 1.8 × 10 − 4 s − 1, respectively. In the later stage of stage II, no significant thinning occurs in the overlaid regions; hence, strain rate is not responsible for the variation of the cavitation levels in these regions. The imposed pressure is then the major factor to cause the changes of cavity volume fraction. A greater imposed pressure accelerates cavity closure resulting in a higher average cavity shrinkage rate. The flow stresses for 8090 Al alloy at strain rates of 2× 10 − 4 to 1× 10 − 3 s − 1 are of the order of 5–9 MPa. The imposed pressures in the later stage during forming are much smaller than the flow stresses. According to the plasticity controlled cavity growth mechanism, growth of cavities during deformation can be suppressed theoretically by hydrostatic pressure equal to one-third of the flow stress in uniaxial tension [21]. The imposed pressures in the present work are also smaller than those required by suppressing the cavity growth.
3.6. Effect of post-sintering on ca6itation
Fig. 12. Mean cavity diameter and number of cavities per unit area at the central point of the formed part versus forming time in stage II with a forming pressure of 0.889 MPa.
Fig. 13. Mean cavity diameter and number of cavities per unit area at the central point of the formed part versus forming time in stage II with a forming pressure of 0.228 MPa.
An important requirement for cavitation during superplastic deformation is the presence of a local tensile stress. Cavities produced during superplastic tensile deformation can be reduced by subsequent compressive flow [22]. Cavitation can be suppressed, or at least reduced, by various procedures before, during, or after superplastic deformation. These procedures are based on annealing with or without superimposed pressure [20,23] or deformation under pressurized atmosphere [2,14]. These methods are likely to be limited in application because of complex procedures, restriction in component size, or cost. On the basis of the analysis described in Section 3.3, cavity closure occurs as a result of sintering effect while the deformed sheet has been overlaid on the die surface. A simplified procedure was proposed to reduce cavitation level in the present work. In this procedure, the formed part was left in the die and remained under pressure for an extra period of time after the cylindrical cup was completely deformed. Since it took about 158 min to form a cylindrical cup at a strain rate of 1.8×10 − 4 s − 1, it is not so meaningful to extend the forming time to reduce cavitation at a low strain rate; the proposed procedure was only performed for forming at a strain rate of 8×10 − 4 s − 1.
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8
Fig. 14. Cavity volume fraction distribution along the centerline of the cylindrical cup showing the effect of post-sintering time with an imposed pressure of 0.889 MPa.
Fig. 14 shows the effect of post-sintering time (the extended forming time after the part is completely formed) with an imposed pressure of 0.889 MPa on the cavity volume fraction distribution along the centerline of the cylindrical cup formed at a strain rate of 8× 10 − 4 s − 1. Since the bottom corner that is about 20 mm away from the bottom center is the latest region to be formed for forming into a right cylindrical die, it is the thinnest portion of the formed cup, and it is also the region where the greatest cavitation level presents. Fig. 14 appears that post-sintering does have significant effect on the reduction of cavitation levels. Fig. 14 also reveals that the procedure of post-sintering does not show much influence on the cavity volume fractions less than 1.5%. Since plasticity, which is more effective for shrinkage of large cavities, is the dominant mechanism for cavity shrinkage during post-sintering treatment, the shrinkage rate will decrease as the large-sized cavities have been reduced. Therefore, the benefit of postsintering treatment could not be observed for small cavity volume fractions, it may be necessary to use a longer sintering time for the diffusion-controlled mechanism to take place for further reduction in cavitation level.
4. Conclusions An analysis of cavitation characteristics of a SP8090 Al alloy through use of blow forming was undertaken in the present study. Cavitation characteristics due to equi-biaxial tension were analyzed and compared with the empirical model. The following conclusions were determined on the basis of this work. First, the formation of a right cylindrical cup during superplastic forming could be divided into two stages. In the first stage, the sheet deformed freely into a hemispherical segment until its pole contacted the bottom surface of the die. The second stage started when the sheet just touched the bottom surface of the die.
7
The central region of the deformed sheet was overlaid on the bottom surface of the die as the deformation proceeded; the surface friction of the die would influence the deformation of the overlaid region of the deformed sheet in stage II. Therefore, cavitation behavior due to equi-biaxial tensile deformation should be examined separately in theses two stages. In stage I, the relationship between the cavity volume fraction and strain is consistent with cavity growth dominated by the plasticity-controlled mechanism. The values of cavity growth rate parameter, h, determined experimentally were greater than those calculated by empirical model; changes of m value with strains, continuous cavity nucleation and cavity coalescence during deformation should be the possible factors to cause this difference. Third, in the second stage of deformation, variation of cavity volume fraction was related to the thinning behavior of the deformed sheet. The cavity volume fraction increased with decreasing thickness, and then turned to a decrease while the thickness of the sheet remained as a constant. Decrease in cavity volume was believed to be the result of a cavity sintering effect. A higher imposed pressure during forming resulted in a greater average cavity closure rate. Finally, a post-sintering treatment was proposed to reduce the cavitation level for forming at a higher strain rate. The cavity volume fractions for the cup formed at a strain rate of 8× 10 − 4 s − 1 were significantly reduced by a post-sintering treatment with an imposed pressure of 0.889 MPa for 30 min.
Acknowledgements This work was conducted through grant from National Science Council under contract NSC 89-2612-E216-002. The author is grateful to Jiin-her Hwang for his help with part of the work.
References [1] R. Raj, M.F. Ashby, Acta Metall. 23 (1975) 653. [2] C.C. Bampton, M.W. Mahoney, C.H. Hamilton, A.K. Ghosh, R. Raj, Metall. Trans. A 14A (1983) 1583. [3] M.J. Stowell, D.W. Liversy, N. Ridley, Acta. Metall. 32 (1984) 35. [4] A.C.F. Cocks, M.F. Ashby, Metal Sci. 16 (1982) 465. [5] I.W. Chen, A.S. Argon, Acta. Metall. 29 (1981) 1759. [6] M.G. Zelin, H.S. Yang, R.Z. Valiev, A.K. Mukherjee, Metall. Trans. A 24A (1993) 417. [7] M.W. Mahoney, C.H. Hamilton, A.K. Ghosh, Metall. Trans. A 14A (1983) 1593. [8] R. Verma, P.A. Friedman, A.K. Ghosh, S. Kim, C. Kim, Metall. Trans. A 27A (1996) 1889. [9] A.K. Ghosh, D.H. Bae, in: A.H. Chokshi (Ed.), Proceedings of Superplasticity in Advanced Materials, ICSAM-97, Materials
8
[10]
[11]
[12]
[13] [14] [15]
H.-y. Wu / Materials Science and Engineering A291 (2000) 1–8 Science Forum, vols. 243–245, Trans Tech Publications, Switzerland, 1997, p. 89. J. Pilling, R. Ridley, in: H. Heikkenen, T. McNelley (Eds.), Proceedings of Superplastcity in Aerospace, The Metallurgical Scoiety, Warrendale, PA, 1988, p. 183. B. Ren, C.H. Hamilton, in: C.H. Hamilton (Ed.), Proceedings of Superpasticity and Superplastic Forming, TMS, Warrendale, PA, 1988, p. 121. M.J. Stowell, in: N.E. Paton, C.H. Hamilton (Eds.), Proceedings of Superplstic Forming of Structural Alloys, The Metallurgical Society of AIME, Warrendale, PA, 1982, p. 321. R. Raj, Acta Metall. 26 (1978) 995. J. Pilling, R. Ridley, Acta Metall. 34 (1986) 669. J. Pilling, Mater. Sci. Tech. 1 (1985) 461.
.
[16] CEMEF, SUPFORM2 User’s guide, Version 1.0, Fcole des Mines de Paris, 1989. [17] Optimas Corporation, OPTIMAS 5 Software, 6th edition, Optimas Corporation, Seattle, WA, 1995. [18] A.H. Chokshi, A.K. Mukherjee, Acta Metall. 37 (1989) 3007. [19] J. Pilling, N. Ridley, Superplasticity in Crystallines Solids, The Institute of Metals, London, 1989, p. 102. [20] A. Varloteaux, J.J. Blandin, M. Suery, Mater. Sci. Tech. 5 (1989) 1109. [21] C.C. Bampton, R. Raj, Acta Metall. 30 (1982) 2043. [22] D.W. Livesey, N. Ridley, Metal Sci. 16 (1982) 563. [23] H. Ahmed, R. Pearce, in: R. Pearce, L. Kelly (Eds.), Proceedings of Superplasticity in Aerospace — Aluminum, SIS, Cranfield, Bedford, UK, 1985, p. 146.