ASM Metals HandBook Vol. 14 - Forming and Forging

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(Eq 12)

where P

is the pressure of the die entry radius,

is the in-sheet stress in the width direction, h is the sheet thickness,

and R

is the die entry radius. This and the applied gas pressure, g, develop an average through-thickness stress

of:

(Eq 13)

The magnitude of

will be dependent on the local friction coefficient,

, and the position on the radius, so that the

effective stress will vary around the die entry radius. A detailed analytical model of this somewhat complex condition is

available in Ref 27, but it has been shown that a local stress increase is developed in this area, causing a tendency toward

local thinning. If the friction is sufficiently low, the initially thinned section can continue to thin after die contact is made.

Therefore, significant localized thinning can occur, and even rupture may take place if the conditions are sufficiently

severe.

Thinning over the die entry radius is the result of stress gradients; therefore, the strain rate sensitivity m is an important

parameter in determining the extent of thinning that will develop. The influence of these variables is illustrated in Fig. 32

for a titanium alloy part formed under the indicated conditions of lubrication and strain rate. The strain rate variations

resulted in corresponding variations in the m value during the respective forming process. The thinning for the

unlubricated part is in agreement with that expected from the discussion in the previous section in this article. For this

case where lubricant is used, the strain rate, which determines the corresponding m value, is a factor in determining the

extent of thinning over the die entry radius. The average m value corresponding to the die entry radius was higher for the

forming process that developed the lower average strain rate, resulting in a significantly reduced tendency toward local

thinning in that area.

Fig. 32 Observed thickness distribution for Ti-6Al-

4V parts with 1.14 mm (0.045 in.) initial thickness at 927 °C

(1700 °F) formed at 10

-3

-1

with boron nitride lubrication

Thinning Control. Because SPF parts are typically stretched to very large elongations, the thickness variations are

potentially large for a part. Therefore, it is often important to control the thickness variations in order to meet part

tolerance requirements. Although it is seldom possible to prevent thickness variations, there are techniques that can be

utilized to control this problem. In addition to such methods, the designer can often accommodate variations in thickness

if he knows in advance what they might be. This latter approach is an important and viable one, but will not be addressed

in this article because it is a very specialized field of metallurgy.

The methods used to control thinning are:

• Processing of the superplastic material to achieve a high m value

• Use of surface lubrication, as discussed above

• Use of thermo-forming methods to control the localized deformation

• Modification of the die or part design to minimize local stress concentrations

• Forming a thickness-profiled sheet

• Application

of pressure in a controlled and profiled manner to control strain rate to a value

corresponding to a high m value

Because the raw sheet material is generally obtained from a commercial supplier, the material superplastic properties are

under the control of the mill. However, it may be judicious for the forming plant to obtain material under the control of an

appropriate specification. The effect of lubrication is discussed in the section "Die Entry Radius" in this article, along

with the effect of the die entry radius, which may, in some parts, be increased to minimize the thickness gradients.

The thermo-forming method has been shown to offer effective techniques that can control the thinning gradients in single-

pocketed deep-drawn parts (Ref 24, 30). With these methods, a movable tool is usually used to contact the forming sheet

before the finished shape is produced, causing the local friction to minimize deformation in some locations while free-

forming sections continue to deform.

The use of thermo-forming techniques was demonstrated using apparatuses such as those shown in Fig. 33 and 34 (Ref

30). The test rig used consisted of two cylindrical chambers, each 190 mm (7.5 in.) in inside diameter by 178 mm (7 in.)

deep, and a hydraulic ram, positioned in the bottom chamber, that was capable of moving up and down. The material used

was Zn-22Al-1.5Cu sheet 1.27 mm (0.050 in.) thick. For the convex upward die, the deformation was restricted in the

center of the sheet and concentrated at the outer area, resulting in a strain and thickness profile, as shown in Fig. 35, in

which the top center is thicker than the adjacent areas. This thickness profile was substantially modified by the use of a

concave upward die, as shown in the Fig. 36. In this case, the superplastic diaphragm was formed down into the concave

die by gas pressure, and the die was slowly withdrawn until it reached the bottom. The preformed diaphragm was then

formed into the upper cylindrical chamber in the same manner as that of the previous figure. The resulting profile is seen

to be considerably more uniform across the top of the part.

Fig. 33 Apparatus for thermo-

forming superplastic sheet materials using a convex die member to control

thinning in forming of a hat configuration

Fig. 34 Apparatus for thermo-

forming superplastic sheet materials using a concave die member to control

thinning in forming of a hat configuration

Fig. 35 Thickness profile for hat configuration formed with a convex die member, as shown in Fig. 33

. Material

formed is Zn-22Al-0.15Cu at a forming temperature of 250 °C (480 °F).

Fig. 36 Thickness profile for hat configuration formed with a concave die member, as shown in Fig. 34

. Material

formed is Zn-22Al-0.1Cu at a forming temperature of 250 °C (480 °F).

The use of thickness-profiled sheet has been suggested to control the thickness in the final part (Ref 44). The concept

considers that the initial thickness variations can be used to offset the subsequent variations resulting from the stress state

and part geometry effects on the thinning, as shown in Fig. 37. If areas that will thin excessively are thicker than

surrounding areas, it is possible to develop finished part thickness profiles that are more uniform than those formed of

constant thickness sheet.

Fig. 37 Schematic of the concept of forming a sheet material that has a thickness profile before forming

Pressure Profiling. It is now well recognized that the m value for superplastic alloys will vary with strain rate and that

it will also often vary with strain. The strain rate imposed during the forming process will therefore determine the m

value, and if the strain rate varies during the forming process, the corresponding m value and related thinning uniformity

will also vary. For example, the simplest pressurization concept for SPF processing is that of constant pressure. The

resulting strain rate variation for a spherical dome part configuration has been shown to be as much as three orders of

magnitude (Ref 25). A graph of the predicted strain rate for a spherical dome that will be generated under constant

pressure for such a part is shown in Fig. 38. The strain rate drops to 0.001 of the initial value when the part becomes a

hemisphere. The m value for a typical superplastic alloy can vary from a maximum m to a value of less than 0.2 over

strain rate ranges of this magnitude. The consequence of forming a part under these conditions is that excessive thinning

or part rupture during forming is likely. The initial strain rate corresponds to a large m value, and good thinning resistance

is observed. However, this would be transient; other strain rates would be encountered corresponding to low m values,

and poor resistance to localized thinning would be present.

Fig. 38

Ratio of the current to initial strain rate as a function of nondimensional height for a constant pressure

application in the forming of a hemispherical configuration

This condition can be rectified if the strain rate can be maintained at a constant level corresponding to a suitably high m

value. Because the constant pressure is seen to develop a variable strain rate, it is apparent that a variable forming

pressure would be required to develop a constant strain rate. Such pressure profiles have been established analytically for

the spherical dome (Ref 25, 26) and the rectangular (Ref 27) part configurations. Because most of the analytical models of

the SPF process use applied gas pressure to establish the current stress and strain rate conditions, it is possible to utilize

these same models to adjust the current gas pressure to develop the desired stress and strain rate.

The resulting pressure profiles for the constant strain rate forming of the spherical dome and the rectangular parts are

illustrated in Fig. 39 and 40, respectively. It is typical that the pressure initially rises rapidly, followed by decrease. The

rapid initial rise is due to a rapid decrease in the radius of curvature with little change in thickness, and the subsequent

decrease is the result of thinning that is more rapid at this stage than the change in radius of curvature. The depth to which

a part is formed will also affect the pressure profile for constant strain rate control, as shown in Fig. 41 for a rectangular

part formed with no lubrication. For a deep part (w = 305 mm, or 12 in.), the applied pressure never reaches a maximum,

but continues to rise during the forming process. For a shallow part (w = 50 mm, or 2 in.), the pressure is decreased for a

significant time period before being increased to high levels.

Fig. 39

Ratio of current to initial pressure as a function of a time parameter for forming a spherical

configuration under constant strain rate conditions

Fig. 40

Analytically predicted pressure versus time for a constant strain rate in the forming of a long,

rectangular, 1.27 mm (0.050 in.) thick Ti-6Al-4V part fabricated at 870 °C (1600 °F)

Fig. 41 Analytically predicted pressure profiles for the constant strain rate forming of long rectangular par

ts of

different cross section width, b, and height, w, dimensions

References cited in this section

9. A.K. Ghosh and C.H. Hamilton, Metall. Trans. A, Vol 10A, 1979, p 699

21.

A.K. Ghosh and C.H. Hamilton, in Proceedings of the Fifth International Confer

ence on the Strength of

Metals and Alloys, P. Haasen, Ed., 1979, p 905

22.

C.H. Hamilton, Formability: Analysis, Modeling, and Experimentation,

S.S. Hecker, A.K. Ghosh, and H.L.

Gegel, Ed., The Metallurgical Society, 1977

24.

R. Pearce, Mod. Met., April 1986, p 188

25.

F. Jovane, Int. J. Mech. Sci., Vol 10, 1968, p 403

26.

G.C. Cornfield and R.H. Johnson, Int. J. Mech. Sci., Vol 12, 1970, p 479

27.

A.K. Ghosh and C.H. Hamilton, Process Modeling: Fundamentals and Applications to Metals,

American

Society for Metals, 1979, p 303

30.

W. Johnson, T.Y.M. Al-Naib, and J.L. Duncan, J. Inst. Met., Vol 100, 1972, p 45

37.

A.K. Ghosh, Acta Metall., Vol 25, 1977, p 1413

38.

F.A. Nichols, Acta Metall., Vol 28, 1980, p 663

39.

F.A. Mohamed and T.G. Langdon, Acta Metall., Vol 29, 1981, p 911

40.

D.L. Holt, Int. J. Mech. Sci., Vol 12, 1970, p 491

41.

G.G.W. Clemas, S.T.S. Al-Hassani, and W. Johnson, Int. J. Mech. Sci., Vol 17, 1975, p 711

42.

J. Belk, Int. J. Mech. Sci., Vol 17, 1975, p 505

43.

G.J. Cocks, C. Rowbottom, and D.M.R. Taplin, Met. Technol., July 1976, p 332

44.

J. Argyris and J. St. Doltsinis, Plasticity Today, A. Sawczuk and G. Bianchi, Ed., Elsevier, 1985, p 715

45.

K.S.K. Chockalingam, M. Neelakantan, S. Devaraj, and K.A. Padmanabhan, J. Mater. Sci.,

Vol 20, 1985, p

1310

46.

S. Yu-Quan, Mater. Sci. Eng., Vol 84, 1986, p 111

47.

A.K. Ghosh and C.H. Hamilton, Metall. Trans. A, Vol 11A, 1980, p 1915

Superplastic Sheet Forming

C.H. Hamilton, Washington State University; A.K. Ghosh, Rockwell International

Cavitation and Cavitation Control

Most superplastic alloys tend to form voids, or cavities, at intergranular locations during the superplastic deformation.

This process is termed cavitation. Cavitation can lead to the degradation of strength and other design properties, and it is

dealt with in one of two ways:

• Establishing reduced design properties

• Utilizing a back pressure technique to control cavitation

Typical cavitation as a function of strain is shown for an aluminum alloy in Fig. 42. It can be seen that the absolute

amount of cavitation in terms of the volume fraction is not large but depends on the strain imposed. The use of the back

pressure concept imposes a hydrostatic pressure on the sheet during forming, and if this pressure is of the order of the

flow stress, cavitation can be reduced or completely suppressed. An example of the effect of back pressure on the rate of

development of cavitation is shown in Fig. 43.

Fig. 42 Development of cavitation with uniaxial tensile strain in a 7475 aluminum alloy specimen of 0.8 cm

(

in.

) cross-sectional area deformed at 516 °C (961 °F) under a constant strain rate of 2 × 10

-4

-1

Fig. 43

Effect of hydrostatic pressure on the suppression of cavitation in a 7475 aluminum alloy specimen

superplastically deformed at 516 °C (961 °F)

In practice, the back pressure is achieved by imposing a pressure on the back side of the sheet to oppose the forming

pressure and by sustaining this pressure during the forming cycle. The forming pressure must be higher than the back

pressure, and the same forming rates can be achieved with or without back pressure if the pressure differential is the

same. For example, if a pressure profile is desired, such as that shown in Fig. 39 or 40, the pressure profile is simply

raised in magnitude by an amount equal to the back pressure. Because the back pressure is normally of the order of the

material flow properties, pressures of about 690 to 3400 kPa (100 to 500 psi) are generally suitable for suppressing

cavitation.

Superplastic Sheet Forming

C.H. Hamilton, Washington State University; A.K. Ghosh, Rockwell International

Manufacturing Outlook

The SPF process is unique in terms of the complexity of parts that can be produced and the methods that can be used to

shape such a material. A number of processing methods are currently being used, most of which involve significant

stretching of sheet material. The high ductility that can be achieved with these types of materials also has a consequence

that must be understood and dealt with, namely, thinning gradients. The thinning gradients are a natural consequence of

the stress gradients that develop in the various die configurations, and the superplastic property of the strain rate

sensitivity of the flow stress then determines the subsequent thinning gradient that will result in the part. Control of the

forming process, die configuration, and material characteristics are all factors that can affect the thinning.

The SPF processes are being increasingly used for a wide range of structural and nonstructural applications. The

availability of superplastic alloys is considered to be a major impediment to the broader use of these processes, but as the

use of the technology increases, more and perhaps better superplastic alloys can be expected to become available.

Superplastic Sheet Forming

C.H. Hamilton, Washington State University; A.K. Ghosh, Rockwell International

Appendix: Superplasticity in Iron-Base Alloys

Oleg D. Sherby, Stanford University; Jeffrey Wadsworth, Lockheed Missiles and Space Company; Robert D. Caligiuri, Failure Analysis

Associates

Superplasticity is the ability of certain polycrystalline metallic materials to extend plastically to large strains when

deformed in tension. Strains to failure in superplastic materials range from several hundred to several thousand percent. In

general, superplastic materials also exhibit low resistance to plastic flow in specific temperature and strain rate regions.

These characteristics of high plasticity and low strength are ideal for the manufacturer who needs to fabricate a material

into a complex but sound body with a minimum expenditure of energy.

The phenomenon of superplasticity was first observed over 70 years ago (Ref 48), but active research in this field did not

begin until 1962 (Ref 49). Since that time, superplastic effects have been reported in over 100 alloy systems (Ref 49). The

micro-mechanisms that permit extraordinary elongations in these materials are still under investigation (Ref 50), but it is

generally accepted that a major microstructural requirement for superplasticity is the development of a stable, very fine

grain size (typically <10 m, or 400 in.) (Ref 51). This requirement also usually (but not always) leads to the necessity

for a uniform distribution of a fine, second phase to inhibit matrix grain growth. Furthermore, the grain boundaries should

be high angled (that is, disordered), equiaxed, mobile, and must resist separation under tensile stresses (Ref 52). To

prevent cavitation around the second-phase particles, the strengths of the two phases should be similar at the temperature

of deformation (Ref 52). These micro-structural characteristics can lead to a flow stress that is highly sensitive to changes

in strain rate, which in turn resists the formation of instabilities during tensile deformation.

Even though superplasticity has been observed in many metallic alloy systems, only a relatively small number of them are

iron-base. This is because of the difficulty in generating microstructures in these systems with the above characteristics.

As a result, there have been relatively few industrial applications involving the superplastic bulk forming of ferrous

alloys. Those iron-base systems in which the microstructural requirements have been met include:

• Hypoeutectoid and eutectoid plain carbon steels (ferrite-carbide two-phase system)

• Hypereutectoid plain carbon steel (ferrite-carbide and austenite-carbide two-

phase systems) and white

cast iron (ferrite-carbide two-phase system)

• Low-to-medium alloy steels (ferrite-austenite two-phase system)