ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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(Eq 9)

where C is a constant that can be estimated from the details of each mode; values of C for the models

mentioned are given in Table 2. For all models, with the exception of that proposed by Gittus, D = D

; in the

case of Gittus's model, D = D

IPB

, where D

IPB

is the interphase boundary diffusion (Ref 41). As indicated by

8aEq 8b, the models of GBS accommodated by dislocation motion predict the correct stress, temperature, and

grain-size dependencies. In addition, the fact that for each model C does not depend on the impurity level of the

superplastic alloy is in line with the experimental finding that region II behavior is insensitive to this parameter.

Despite this excellent agreement, various objections were raised against the assumptions and details of some of

the models mentioned. These objections are discussed in detail elsewhere (Ref 2, 45). In addition to these

objections, the agreement between the values of the experimental creep rates in region II and those rates

predicted from the models is not satisfactory (Ref 33); for example, in case of Pb-62Sn (Ref 15, 33), the

experimental creep rates of Pb-62Sn at low stresses are two orders of magnitude faster than those estimated

from the model by Ball and Hutchinson (Ref 38), which predicts the fastest rate among the GBS models listed

in Table 2.

Table 2 Grain-boundary-sliding models accommodated by dislocation motion (Eq 9)

Model Values

for C (Eq

Comments

Reference

Sliding of

groups of

grains

300 Sliding of group of grains. Dislocations are created at triple points

and annihilated by the process of climb into grain boundaries.

Individual

grain sliding

12 Grain slide individually. Dislocations are produced by ledges and

protrusions.

D = D

Dislocation

glide and climb

384 Dislocation movement by glide and climb in the mantle along the

adjacent grains

D = D

Dislocation

pile up

320 Pile-up of boundary dislocations at interphase boundaries

D = D

IPB

. τ

is ignored for region II.

Bardeen-

Herring source

480 The creation of dislocations on a solute-free mantle by Bardeen-

Herring multiplication

D = D

Grain rolling 30 Grain rolling. Grain-boundary sliding by the glide of grain-

boundary dislocations on sliding grain facets. Accommodation

by the climb of grain-boundary-sliding dislocations on facets

with normal stresses

D = D

Ω = atomatic size = 0.7b

δ = boundary thickness ~2b

Note: The table does not include a model (Ref 44) that predicts a grain-size exponent of 3 and is based on

boundary sliding controlled by intragranular disclocation motion.

Region I Deformation Mechanisms. In earlier analyses of superplastic flow, region I behavior in superplastic

materials was explained in terms of three possibilities: (a) the presence of threshold stress processes that are not

sensitive to temperature, such as the interaction between boundary dislocations and ledges (Ref 41), and

fluctuations in the grain boundary area (Ref 37); (b) the operation of a new deformation process related to pure

boundary sliding (Ref 40), and for which Q = 0.2 Q

, where Q

is an activation energy for lattice diffusion; and

they cannot account for the higher activation energy measured in region I (Ref 30, 31). Possibility (c) is not

supported by experimental evidence that has shown the presence of a well-defined region I under experimental

conditions involving negligible grain growth (Ref 13, 14, 15, 23, 30, 31).

Recent experimental work shows that the characteristics of creep in region I are influenced by impurity level

(Ref 13, 14, 15, 33). On the basis of this evidence, it is most likely that region I behavior is related to one of the

following processes: (a) viscous glide (Ref 13, 48), (b) grain-boundary migration controlled by impurities (Ref

49), and (c) an impurity-dominated threshold stress (Ref 50). Consideration of the details of processes (a) and

(b) suggests that they do not provide a satisfactory explanation for all the creep characteristics associated with

region I for two reasons.

First, viscous glide creep, whether it is dominant in the interiors of grains or along the mantle in case of

“mantle-and core” models, leads to an activation energy (equal to that for impurity diffusion) that is higher than

, in agreement with available experimental evidence; however, it fails to account for grain size and stress

dependencies in region I. In addition, the observation of extensive primary creep in the creep curves at low

stresses is not compatible with the characteristics of viscous glide creep as reported in solid-solution alloys of

class I (Ref 51).

Second, grain boundary migration controlled by impurity drag, which was proposed by Gifkins (Ref 49) and

represents a modification of his original grain-emergence model (Ref 52), is associated with two characteristics

that are consistent with region I behavior: an activation energy higher than Q

and a high stress exponent.

However, the occurrence of grain emergence, a feature on which the model is based, is debatable (Ref 53), and

the exact value of the stress exponent is not predicted. In addition, the model has not been developed

quantitatively, and, as a result, no comparison regarding the experimental values of creep rates in Zn-22Al can

be made.

It has been suggested on the basis of an analysis of superplastic flow at low stresses (Ref 50), that region I

behavior may be a consequence of the operation of a threshold-stress process whose origin is related to the

segregation of impurity atoms at boundaries and their interaction with boundary dislocations; in this case, the

threshold stress (τ

) is equivalent to the stress that must be exceeded before boundary dislocations can break

away from the impurity atmosphere and produce deformation. Recent creep data reported for several grades of

Zn-22Al containing different levels of impurities, in particular iron, have revealed the presence of a threshold

stress with characteristics consistent with various phenomena associated with boundary segregation, as

summarized in the following paragraphs (Ref 54, 55, 56, 57, and 58).

No threshold stress is observed for super-plastic flow in high-purity Zn-22Al as shown by Fig. 16(a) (Ref 13,

14). A similar trend for high-purity Pb-62Sn is shown in Fig. 16(b). As reported elsewhere (Ref 13, 14, 15, 33,

and 50) and illustrated by Fig. 16(a) and (b), τ

is determined from experimental creep data obtained for a

superplastic alloy by plotting

1/n

(n = 2.5) against τ at a single temperature on a double linear scale and

extrapolating the resultant line to zero strain rate.

Fig. 16 Threshold stress behavior. (a) Determination of the threshold stress (τ

for superplastic flow in

Zn-22Al at 433K. Source: Ref 14. (b) Determination of the threshold stress for superplastic flow in high-

purity Pb-62Sn at 392 K. Source: Ref 15. (c) A plot of the logarithm of τ

/G as a function of 1/T for

grades 0, A, B, and C of Zn-22Al having a grain size of 2.5 μm and containing 1460 ppm, 423 ppm, 125

ppm, and 40 ppm of iron, respectively

According to the experimental data reported for superplastic alloys (Ref 13, 14, 15, 33) the temperature

dependence of the threshold stress is described by the following (Ref 13, 14, 15, 33, and 54):

(Eq 10)

where B

is a constant and Q

is an activation energy term. The plot of Fig. 16(c), in which experimental data

on the threshold-stress behavior of several grades of Zn-22Al doped with iron are plotted as τ

/G versus 1/T on

a logarithmic scale, provides a graphical presentation for this relation. Equation 10 resembles in form the

following equation (Ref 55) that gives, to a first approximation, the concentration of impurity atoms segregated

to boundaries, c, as a function of temperature:

c = c

exp(-W / RT)

(Eq 11)

where c

is the average concentration of impurity, and W is the interaction energy between a boundary and a

solute atom.

As indicated by Fig. 13(a) and (b), the experimental data for two superplastic alloys, Pb-62Sn and Zn-22Al, in

region II (the superplastic region) can be best described by the following:

(Eq 12)

The concept of an impurity-dominated threshold stress signifies that the same deformation process controls

both region II (the superplastic region) and region I (the low-stress region) and that the apparent difference in

stress and temperature dependencies between the two regions are the result of the increasing importance of τ

with decreasing creep stress in grades containing sufficient impurity levels. On this basis, it is expected that the

experimental data obtained for superplastic alloys in regions I and II at various temperatures can be described

by a single deformation process that incorporates τ

and may be given by:

(Eq 13)

The data for both Pb-62Sn and Zn-22Al are plotted as normalized creep rate, ( kT / D

Gb) (d / b)

versus (τ -

)/G on a logarithmic scale in Fig. 17(a) and (b), respectively (for high-purity Pb-62Sn and Zn-22Al, (τ - τ

) is

equivalent to τ for all stresses, and s = 2.3 and 2.4 for Pb-62Sn and Zn-22Al, respectively). Examination of the

figures demonstrates that the data of each alloy can be represented by a straight line that extends over several

orders of magnitude of normalized creep rate.

Fig. 17 Normalized creep rate versus normalized effective stress, (τ - τ

)/G. (a) For both Pb-62Sn doped

with cadmium and high-purity Pb-62Sn under intermediate and low stresses. Source: Ref 15. (b) For

both commercial-purity Zn-22Al and high-purity Zn-22Al under intermediate and low stresses. Source:

Ref 14

References cited in this section

2. A.K. Mukherjee, Deformation Mechanisms in Superplasticity, Annu. Rev. Mater. Sci., Vol 9, 1979, p

191

3. R.C. Gifkins, Mechanisms of Super-plasticity, Proc. of a Symp. on Superplastic Forming of Structural

Alloys, N.E. Paton and C.H. Hamilton, Ed. (San Diego), Metallurgical Society of AIME, 1980, p 2

13. P.K. Chaudhury and F.A. Mohamed, Effect of Impurity Content on Superplastic Flow in the Zn-22% Al

Alloy, Acta. Metall., Vol 36, 1988, p 1099

14. P.K. Chaudhury, V. Sivaramakrishnan, and F.A. Mohamed, Superplastic Deformation Behavior in

Commercial and High Purity Zn-22 pct Al, Metall. Trans. A, Vol 19, 1988, p 2741

15. S. Yan, J.C. Earthman, and F.A. Mohamed, Effect of Cd on Superplastic Flow in the Pb-62 wt% Sn

Eutectic, Philos. Mag. A, Vol 69, 1994, p 1017

22. J.E. Bird, A.K. Mukerjee, and J.E. Dorn, Correlations between High-Temperature Creep Behavior and

Structure, Proc. of a Symp. on Quantitative Relation Between Properties and Microstructure, D.G.

Brandon and A. Rosen, Ed., Israel University Press, 1969, p 22

23. F.A. Mohamed and T.G. Langdon, Creep at Low Stress Levels in the Superplastic Zn-22% Al

Eutectoid, Acta Metall., Vol 23, 1975, p 117

30. F.A. Mohamed, S. Shen-Ann, and T.G. Langdon, The Activation Energies Associated with Superplastic

Flow, Acta Metall., Vol 23, 1975, p 1443

31. F.A. Mohamed and T.G. Langdon, Creep Behavior in the Superplastic Pb-62% Sn Eutectic, Philos.

Mag. A, Vol 32, 1975, p 697

33. P.K. Chaudhury, K.T. Park, and F.A. Mohamed, Effect of Fe on the Superplastic Deformation of Zn-22

pct Al, Metall. Mater. Trans. A, Vol 25, 1994, p 2391

34. F.A. Mohamed and T.J. Ginter, The Stress Dependence of Subgrain Size in Al, J. Mater. Sci., Vol 17,

1982, p 2007

35. F.A. Mohamed and T.G. Langdon, Deformation Mechanism Maps for Superplastic Materials, Scr.

Metall., Vol 10, 1976, p 759

36. S.A. Shei and T.G. Langdon, The Mechanical Properties of a Superplastic Quasi-Single Phase Copper

Alloy, Acta Metall., Vol 26, 1978, p 638

37. M.F. Ashby and R.A. Verrall, Diffusion-Accommodated Flow and Superplasticity, Acta Metall Vol 21,

1973, p 149

38. A. Ball and M.M Hutchinson, Super-plasticity in the Aluminum-Zinc Eutectoid, Met. Sci., Vol 3, 1969,

p 1

39. A.K. Mukherjee, The Rate Controlling Mechanism in Superplasticity, Mater. Sci. Eng., Vol 8, 1971, p

40. R.C. Gifkins, Grain-Boundary Sliding and Its Accommodation during Creep and Superplasticity,

Metall. Trans. A, Vol 7, 1976, p 1225

41. J.H. Gittus, Theory of Superplastic Flow in Two-Phase Materials: Role of Interphase-Boundary

Dislocations, Ledges, and Diffusion, J. Eng. Mater. Technol. (Trans. ASME), Vol 99, 1977, p 244

42. A. Arieli and A.K. Mukherjee, A Model for the Rate-Controlling Mechanism in Superplasticity, Mater.

Sci. Eng., Vol 45, 1980, p 61

43. V. Paidar and S. Takeuchi, Superplastic Deformation Carried by Grain Boundaries, Acta Metall. Mater.,

Vol 40, 1992, p 1773

44. H.W. Hayden, S. Floreen, and P.D. Goodell, The Deformation Mechanisms of Superplasticity, Metall.

Trans., Vol 3, 1972, p 833

45. R.C. Gifkins and T.G Langdon, Comments on Theories of Structural Superplasticity, Mater. Sci. Eng.,

Vol 36, 1978, p 27

46. G. Rai and N.J. Grant, On the Measurements of Superplasticity in an Al-Cu Alloy, Metall. Trans. A, Vol

6, 1975, p 385

47. A. Arieli and A.K. Mukherjee, On Concurrent Grain Growth and Deformation Mechanism in Region I

for Superplastic Zn-22% Eutectoid Alloy, Scr. Metall., Vol 13, 1979, p 331

48. J. Weertman, Steady-State Creep of Crystals, J. Appl. Phys., Vol 28, 1957, p 1185

49. R.C. Gifkins, “Mechanisms for Low-Stress Region I of Superplasticity,” in Proceedings of a

Symposium on Strength of Metals and Alloys, R.C. Gifkins, Ed., Pergamon, Oxford, 1982, p 701

50. F.A. Mohamed, Interpretation of Superplastic Flow in Terms of Threshold Stress, J. Mater. Sci., Vol 18,

1983, p 582

51. F.A. Mohamed and T.G. Langdon, The Transition from Viscous Glide to Dislocation Climb, Acta

Metall., Vol 22, 1974, p 779

52. R.C. Gifkins, Grain Rearrangements during Superplastic Deformation, J. Mater. Sci., Vol 13, 1978, p

1926

53. I.I. Novikov, V.K. Portnoy, and V.S. Levchenko, Investigation of Structural Changes during

Superplastic Deformation of Zn-22% Al Alloy by Replica Locating Technique, Acta. Metall., Vol 29,

1981, p 1077

54. S.T. Yang and F.A. Mohamed, On the Characteristics of the Threshold Stress for Superplastic Flow in

Zn-22 pct Al, Metall. Mater. Trans. A, Vol 26, 1995, p 493

55. H. Gleiter and B. Chalmers, High Angle Grain Boundaries, Prog. Mater. Sci., Vol 16, 1973

56. X.G. Jiang, S.T. Yang, J.C. Earthman, and F.A. Mohamed, Effect of Fe on Ductility and Cavitation in

the Superplastic Zn-22 pct Al Eutectoid, Metall. Mater. Trans. A, Vol 27, 1996, p 863

57. M.P. Seah, Grain Boundary Segregation and the T-t Dependence of Temper Brittleness, Acta Metall.,

Vol 25, 1977, p 34

58. P. Gas, M. Guttmann, and J. Bernardini, The Interactive Co-Segregation of Sb and Ni at the Grain

Boundaries of Ultra-High Purity Fe-Base Alloys, Acta Metall., Vol 30, 1982, p 1309

Superplastic Deformation at Elevated Temperatures

Farghalli A. Mohamed, University of California, Irvine

Effect of Impurities on Superplastic Flow

The preceding discussion indicates that the creep characteristics, including the stress exponent and the

activation energy for deformation, are influenced by the presence of impurities. In the following section, the

effects of impurities on boundary sliding, cavitation, and ductility are presented.

Grain-Boundary Sliding. The occurrence of micrograin superplasticity in metallic systems requires a stable and

equiaxed grain size of less than 10 μm. This requirement, along with the strong sensitivity of steady-state creep

rates measured during superplastic flow to changes in grain size, d, has demonstrated the significant influence

of boundaries on the superplastic behavior. Over the past three decades, considerable efforts have been made to

characterize the nature and significance of their role. For example, as mentioned previously, the concept of

boundary sliding accommodated by some form of dislocation activity was adopted in developing several

deformation models that treated steady-state superplastic deformation in region II (Ref 38, 39, 40, 41, 42, and

43). In addition, many investigations have been performed in tension on several different superplastic alloys to

evaluate the significance of grain-boundary sliding in the three regions of behavior previously mentioned.

In these investigations, measurements were taken of sliding offsets along prescribed marker lines on the surface

of tensile specimens, and the contribution of boundary sliding to the total strain was estimated using appropriate

equations. Despite minor differences in the procedures and equations used in boundary-sliding estimates, the

results reported in the investigations are generally consistent and show that, at low elongations (typically of the

order of 20–30%), the percentage contribution of boundary sliding to total strain generally ranges from 50 to

70% in region II, but it decreases sharply to approximately 20 to 30% in regions I and III (Ref 24, 29).

In a very recent study (Ref 28), the effect of impurity level on the contribution of boundary sliding to the total

strain was examined in the superplastic Zn-22Al alloy. The results of that study follow.

Figure 18 shows a plot of the contribution from boundary sliding to the total strain, ξ, against initial strain rate,

, for three grades of Zn-22Al (Ref 28). Grades 1 and 2 contain 180 and 100 ppm of impurities, respectively,

whereas grade 3 is a high-purity grade containing 6 ppm of impurities. In this plot, the vertical lines A and B

represent the transitions from region I to region II and from region II to region III, respectively. (As mentioned

previously, these three regions characterize the sigmoidal relation between stress and strain rate.) An

examination of such a plot reveals that the values of the contribution of boundary sliding to the total strain in

Zn-22Al at low strain rates (region I) are affected by the presence of impurities, unlike those at intermediate

and high strain rates (region II and region III, respectively). This finding is reflected in the following

observations: (a) for all three grades, ξ exhibits the same value of 20% at high-strain rates, (b) for grade 3 (high-

purity Zn-22Al), ξ at low strain rates is not only significant (61%) but also comparable to that at intermediate

strain rates (~60%), (c) at the same strain rate in region I, the values of ξ in grades 1 and 2 are less than that in

grade 3, and (d) at the same strain rate in region I, ξ in region I (180 ppm of impurities) is less than that in grade

2 (100 ppm of impurities).

Fig. 18 The contribution of boundary sliding to the total strain, ξ, as a function of strain rates for grades

1, 2, and 3 of Zn-22Al containing 180, 100, and 6 ppm of impurities, respectively. Grain size 5.4 μm;

temperature, 493 K. Source: Ref 59

As mentioned earlier, the sensitivity of region I to impurity level is most likely a reflection of the presence of a

threshold stress for creep in Zn-22Al (Ref 13, 14, 33, 50), which is related to strong impurity segregation at

boundaries and which strongly depends on temperature, according to Eq 9. The interpretation of the creep

behavior of superplastic alloys, in terms of a threshold stress arising from impurity atom segregation, signifies

that region I and II are controlled by the same deformation mechanism. However, it is not immediately clear

why, as shown by the results on grades 1 and 2, ξ in region I is lower than that in region II if the rate-controlling

mechanism is the same in the two regions. It is quite possible that the correlation between impurity level and

the sliding contribution at low strain rates is a reflection of the influence of impurities on accommodation

processes for boundary sliding such as boundary migration (Ref 49, 52) and lattice dislocation motion (Ref 59).

This possibility is discussed in detail in Ref 28.

According to the preceding discussion, the effect of impurity level on the boundary-sliding contribution

corresponds well with the effect of impurity level on steady-state creep characteristics reported for the present

alloy (Ref 13, 14, and 33). This correspondence, the main aspects of which are summarized in Table 3,

indicates that under the present experimental conditions, boundary sliding is an important feature of the

deformation process that controls steady-state superplastic flow. Further studies are needed to investigate the

effect of impurities on the contribution of boundary sliding to the total strain in Zn-22Al and other superplastic

alloys at large strains (>30%). The data of such studies can be used to clarify whether the characteristics of

boundary sliding reflect those of steady-state superplastic flow at all strains (small and large) (Ref 24, 60, 61,

62, and 63).

Table 3 Correspondence between effect of impurity level on the sliding contribution and that on steady-

state superplastic flow

Strain rate region Effect of impurity level

on the sliding contribution

Effect of impurity level

on steady-state superplastic flow

High-strain-rate region

(region III)

Impurity level has no effect on the

contribution of boundary sliding to

the total strain, ξ.ξ ~24%.

Impurity level has no effect on the advent

of region III.

Intermediate-strain-

rate region (region II

or the superplastic

region)

Impurity level has no noticeable

effect on the contribution of

boundary sliding. Sliding

contribution to the total strain is

equal to ~60%.

Impurity level has no effect on the values of

the stress exponent and the activation

energy for superplastic flow. n = 2.5 and Q

= Q

Low-strain-rate

region (region I in

grades 1 and 2)

For a high purity alloy, ξ is equal

to that in the intermediate strain

rates. The sliding contribution

decreases with increasing impurity

level.

For a high-purity alloy, the intermediate-

stress region (region II) extends to the

lowest strain rate with no evidence for

region I. Both n and Q

increase with

increasing impurity level.

Cavitation. It is well-established that during superplastic deformation most materials develop internal cavities,

which grow and coalesce, leading to cavitation damage. Such damage in turn gives rise to premature failure of

the material, thereby imposing a serious limitation on the mechanical properties of components prepared by

superplastic forming. A solution of this problem necessitates (a) a detailed understanding of the cavitation

process in superplastic alloys over wide ranges of experimental conditions, and (b) an identification of various

factors that may control the nucleation and growth of cavities. In recent years, the effect of impurities on

cavitation during superplastic flow has received considerable attention.

As mentioned previously, segregation of impurities at boundaries has been suggested as a probable cause for

occurrence of region I, which micrograin superplastic alloys often exhibit at low stresses. In support of the

previously mentioned concept regarding impurity segregation, experimental results have revealed the following

observations: (a) cavities are not observed in high-purity Zn-22Al (Ref 56, 64, 65, and 66), and (b) the extent of

cavitation in Zn-22Al depends on the impurity content of the alloy (Ref 56, 60). Figure 19 illustrates these two

observations. The observed correlation between the level of impurities and the extent of cavitation in Zn-22Al

is most probably related to effects associated with the presence of excessive impurities at boundaries due to

their segregation. As mentioned elsewhere (Ref 56, 59, 60, 61, and 67), impurity segregation may lead to

accelerated cavitation rates through the following processes: (a) reduction of the surface energy, (b) formation

of precipitates that serve as cavity nucleation sites, (c) reduction of grain-boundary diffusivity, (d) reduction of

boundary cohesive strength, and (e) retardation of grain growth that involves boundary migration.

Fig. 19 Cavitation in Zn-22Al grades at 1.33 × 10

-4

. (a) Grade 1 (180 ppm of impurities). (b) Grade 2 (100

ppm of impurities). (c) Grade 3 (6 ppm of impurities). Source: Ref 60

Ductility. The results of several analyses have demonstrated that ductility, defined as the percentage of

elongation to fracture, is a sensitive function of the stress exponent n, which equals 1/m (Ref 68, 69, 70, 71). In

general, ductility increases as the value of the stress exponent decreases (or as the value of the strain rate

sensitivity increases), because, as suggested by several investigators, the lower the stress exponent, the larger

the necking resistance (Ref 68, 69, 70, and 71). Mathematically, the dependence of ductility on the stress

exponent can, for example, be expressed by the following equation, the development of which is based on

consideration of plastic instabilities in a tensile specimen (Ref 68):

e% = [exp (c/n)-1]%

(Eq 14)

where c = ln (400/n) and e represents elongation.

For a superplastic alloy, such as Zn-22Al, the stress exponent (n) exhibits a minimum at intermediate stresses or

intermediate strain rates where the superplastic region dominates (Ref 13, 14, 23, and 30). Accordingly, it is

expected that the ductility of the alloy, when plotted as the elongation to fracture versus stress or strain rate,

would exhibit a maximum at intermediate stresses or intermediate strain rates. This behavior is presented in Fig.

20, where the average elongation for Zn-22Al is plotted as a function of initial strain rate (Ref 72).

Fig. 20 Tensile fracture strain as a function of initial strain rate for a testing temperature of 473 K and a

grain size of 2.5 μm (upper); the corresponding plots of maximum flow stress versus initial strain rate

(lower). Source: Ref 72

The effect of iron on the ductility of the superplastic Zn-22Al alloy was recently investigated (Ref 56). Some of

the results of the investigation are shown in Fig. 21, where the average elongation to failure (e

) estimated from

several specimens that were pulled to failure at 1.33 × 10

-4

-1

in region II (the superplastic region), where n =

2.5, is plotted as a function of iron content. As shown by the figure, there are two regions of behavior: (a) e

decreases slowly for iron concentrations less than 125 ppm, and (b) e

decreases rapidly at higher iron levels. It

has been suggested in Ref 56 that introducing high iron levels in Zn-22Al, while not changing the stress

exponent for creep in region II, leads to a loss in the ductility of the alloy in this region for the following reason.

Well documented experimental evidence has implied that during superplastic flow, segregation of impurities at