ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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configured. The tube furnace was positioned right in front of the rolling mill to ensure an accurate starting

temperature. During rolling, temperature data was acquired continuously by a computer. The thermal responses

of the thermocouples are presented in Fig. 22. When the workpiece entered the roll gap, the temperature

dropped immediately. As it came out of the roll gap, the temperature recovered to a level lower than the initial

temperature. Figure 23 shows the detailed temperature reading for thermocouple 2 inside the roll gap.

Fig. 20 The workpiece used to measure temperature during hot rolling, showing the positions of the

thermocouples. Source: Ref 36

Fig. 21 Experimental setup for temperature measurement during hot rolling. Source: Ref 36

Fig. 22 Thermal responses of two thermocouples (TC1 and TC2) in the workpiece during hot rolling.

Source: Ref 36

Fig. 23 Detailed temperature reading for thermocouple 2 in the roll gap. Source: Ref 36

The rolling process was then modeled. The contact time of the workpiece in the roll gap is divided into a

number of time steps. For each time step, the calculated temperature with the trial heat-transfer coefficient is

compared to the measured temperature. When the two temperature values are close enough—for instance,

within 1 to 2 °C (1.75–3.5 °F)—the assumed heat-transfer coefficient is accepted as the real heat-transfer

coefficient. The calculation process is then repeated for the next time step. Results of the heat-transfer

coefficient at two different rolling temperatures are shown in Fig. 24.

Fig. 24 Inversely calculated results of the heat-transfer coefficient during contact. Source: Ref 36

References cited in this section

1. H.E. Boyer, Atlas of Stress-Strain Curves, ASM International, 1987

2. Y.V.R.K. Prasad and S. Sasidhara, Hot Working Guide: A Compendium of Processing Maps, ASM

International, 1997

3. Atlas of Formability Bulletins, National Center for Excellence in Metalworking Technology (NCEMT),

Johnstown, PA

4. T. Altan, S. Oh, and H. Gegel, Metal Forming: Fundamentals and Applications, ASM International,

1983, p 86

5. C.M. Sellars and W.J.McG. Tegart, Mem. Sci. Rev. Metall., Vol 63, 1966, p 731

6. A. Laasroui and J.J. Jonas, Prediction of Steel Flow Stresses at High Temperatures and Strain Rates,

Metall. Trans. A, Vol 22, 1991, p 1545–1558

7. S.B. Brown, K.H. Kim, and L. Anand, An Internal Variable Constitutive Model for Hot Working of

Metals, Int. J. Plast., Vol 5, 1989, p 95–130

8. M. Thirukkonda, D. Zhao, and A.T. Male, “Materials Modeling Effort for HY-100 Steel,” Technical

Report TR 96-027, NCEMT, Johnstown, PA, March, 1996, p 27

9. M.G. Cockrcraft and D.J. Lahtam, Ductility and the Workability of Metals, J. Inst. Met., Vol 96, 1968, p

33–39

10. D. Zhao, J.P. Bandstra, H.A. Kuhn, A New Fracture Criterion for Fracture Prediction in Metalworking

Processes, Concurrent Engineering Approach to Materials Processing, S.N. Dwivedi, A.J. Paul, and F.

R. Dax, Ed., TMS, 1992, p 107–119

11. H.A. Kuhn, Workability Theory and Application in Bulk Forming Processes, Forming and Forging, Vol

14, Metals Handbook, ASM International, 1988, p 388–404

12. J.P. Bandstra, “3D Extension of Kuhn Surface Fracture Criterion,” CTC memorandum CTC/JPB-

M0469-95, Johnstown, PA, 1995

13. “Standard Test Methods of Compression Testing of Metallic Materials at Room Temperature,” ASTM E

9, Annual Book of ASTM Standards, 1994

14. “Standard Practice for Compression Tests of Metallic Materials at Elevated Temperatures with

Conventional or Rapid Heating Rates and Strain Rates,” ASTM E 209, Annual Book of ASTM

Standards, 1994

15. “Standard Test Methods for Tension Testing of Metallic Materials,” ASTM E 8, Annual Book of ASTM

Standards, 1994

16. “Standard Test Methods for Elevated Temperature Tension Tests of Metallic Materials,” ASTM E 21,

Annual Book of ASTM Standards, 1994

17. D. Zhao and H. Dong, unpublished technical report, Concurrent Technologies Corporation, Johnstown,

PA, 1996

18. S.L. Semiatin and J.J. Jonas, Formability and Workability of Metals: Plastic Instability and Flow

Localization, American Society for Metals, 1984

19. M.C. Mataya, Simulating Microstructural Evolution during the Hot Working of Alloy 718, JOM, Jan

1999, p 18–26

20. R. Chait and C.H. Curll, “Evaluating Engineering Alloys in Compression,” ASTM STP 608, Recent

Developments in Mechanical Testing, 1976, p 3–19

21. M.L. Lovato and M.G. Stout, Compression Testing Techniques to Determine the Stress/Strain Behavior

of Metals Subject to Finite Deformation, Metall. Trans. A, Vol 23, 1992, p 935–951

22. O. Alnik, D.D. Murphy, T. Terada, A.K. Koul, and J.-P. Immarigeon, “Modeling of Deformation and

Microstructural Changes in P/M Rene 95 Under Isothermal Forging Conditions,” Conf. Proc. No. 426

presented at Aerospace Materials Process Modeling, Oct 2–4, 1987 (Cesme, Turkey), AGARD

23. Merlin IV Test Application Package, Instron Corporation, Canton, MA, 1998

24. J.F. Thomas, Jr. and R. Srinivasan, Constitutive Equations for High Temperature Deformation,

Computer Simulation in Materials Science, R.J. Arsenault, J. R. Beeler, Jr., and D.M. Esterling, Ed.,

ASM International, 1988, p 269–290

25. W.F. Hosford and R.M. Caddell, Metal Forming: Mechanics and Metallurgy, Prentice-Hall, Inc., 1983

26. D. Zhao, Temperature Correction in Compression Tests, J. Mater. Process. Technol., Vol 36, 1993, p

467–471

27. H.L. Gegel, J.C. Malas, S.M. Doraivelu, and V.A. Shende, Acquisition of Data for Forging Process

Design, Forming and Forging, Vol 14, ASM Handbook, ASM International, 1988, p 439–442

28. D.N. Tishler and C.H. Wells, An Improved High-Temperature Extensometer, Mater. Res. Stand., Vol 6

(No. 1), ASTM, MTRSA, 1966, p 20–22

29. “Standard Test Method for Tensile Strain-Hardening Exponents (n-Values) of Metallic Sheet

Materials,” ASTM E 646, Annual Book of ASTM Standards, 1994

30. “Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus,” ASTM E 111,

Annual Book of ASTM Standards, 1994

31. H.A. Kuhn, P.W. Lee, and T. Erturk, A Fracture Criterion for Cold Forming, J. Eng. Mater. Technol

(Trans. ASME), Oct 1973, p 213–217

32. A.T. Male and G.E. Dieter, Hot Compression Testing, Workability Testing Techniques, G.E. Dieter, Ed.,

American Society for Metals, 1984, p 51–72

33. V. DePierre, F.J. Gurney, and A.T. Male, Mathematical Calibration of the Ring Test with Bulge

Formation, Technical Report AFML-TR-37, U.S. Air Force Materials Lab, March 1972

34. A.T. Male and V. DePierre, Proc. 10th Int. Machine Tool Design and Research Conf., Pergammon

Press, 1969, p 537

35. A.T. Male and V. DePierre, J. Lubr. Technol. (Trans. ASME), Vol 92, 1970, p 389

36. W.C. Chen, I.V. Samarasekera, and E.B. Hawbolt, Fundamental Phenomena Governing Heat Transfer

During Rolling, Metall. Trans. A, Vol 24, June 1993, p 1307–1320

Testing for Deformation Modeling

Dan Zhao, Johnson Controls, Inc.

Testing for Sheet-Metal Forming

Sheet-metal forming comprises deep drawing, stamping, stretching, drape forming, spin forming, coining,

ironing, bending, blanking, and superplastic forming. Sheet metals are usually produced by rolling, and so

mechanical properties vary along different directions in relation to the rolling direction (RD). Figure 25 shows a

schematic of a sheet-metal specimen and its directions relative to the rolling direction. In addition, spring-back

is significant for sheet metals, and elastic properties are much more important than in bulk forming.

Fig. 25 Schematic of a sheet-metal specimen and its directions relative to the rolling direction

A very important parameter for sheet metal is the ratio (R) of plastic strains in width (transverse) and thickness

directions:

(Eq 24)

Because the strains in thickness direction are difficult to measure, they are usually calculated by using volume

constancy:

= -(ε

+ ε

)

(Eq 25)

R-values vary in different directions on the plane of the sheet metal, and are usually denoted by the angle (in

degrees) to rolling direction. In the rolling direction, R is denoted as R

, and in the transverse direction, as R

Most sheet-metal forming operations, such as deep drawing and stamping, are performed at room temperature.

However, sheet forming in the aerospace industry with titanium alloys and superalloys almost always are done

at elevated temperatures. Forming at elevated temperatures is also done to achieve the desirable benefits of

superplastic behavior, which is described in more detail in the article “Superplastic Deformation at Elevated

Temperatures” in this Volume.

Constitutive Equations

For elastic deformation, generalized Hooke's law holds (Ref 37):

= C

i,j = 1, …, 6

(Eq 26)

where σ

is the stress component, C

is the stiffness matrix, and ε

is the strain component. Due to symmetry, C

has a maximum number of 21 independent constants. Table 2 lists the independent constants for different types

of materials. For orthotropic material, there are nine independent constants; for transversely isotropic materials,

there are five independent constants; and for isotropic materials, there are only two independent constants. The

elastic constants can be measured using nondestructive testing techniques (Ref 38). Once these constants are

determined, they can be directly input into modeling software.

Table 2 Independent constants in stiffness matrix for different types of materials

Material

Independent constants

Orthotropic

, C

Transversely isotropic

, C

Isotropic C

, C

For plastic deformation, Hill's anisotropic yield criterion (Ref 39) has wide recognition:

2f(σ

) = F(σ

- σ

)

+ G(σ

- σ

)

+ H(σ

- σ

)

+ +

+ = 1

(Eq 27)

where F, G, H, L, M, and N are constants that characterize the anisotropy. Tensile tests can be used to determine

constants F, G, and H, and shear tests can be used to evaluate constants L, M, and N.

A tensile test in the x-direction provides the yield strength X. Similarly, tensile tests in the y- and z-directions

provide yield strengths Y and Z. Inputting these yield strengths into Eq 27 solves F, G, and H (Ref 26):

(Eq 28)

However, a tensile test in the thickness direction (z-direction) is very difficult. R-values in rolling and width

directions can be used to obtain Z (Ref 26):

(Eq 29)

The plastic constitutive behavior for anisotropic material can also be described by Eq 2 for different directions.

Tensile tests can be conducted in the rolling direction, width direction, and the direction 45° from the rolling

direction. Yield strength, tensile strength, uniform elongation, total elongation,the strain-hardening exponent

(n), K-values, R-values, and the strain-rate sensitivity (m) are recorded or calculated. The data can subsequently

be input into commercial software for deformation modeling (Ref 40).

Failure of Sheet Metal

Failure of sheet metals can be caused by either fracture or plastic instability. A general way of describing the

failure is a forming-limit diagram (FLD) (Ref 41). A typical FLD for a low carbon steel is shown in Fig. 26

(Ref 25, 42). If the combination of major and minor strains is above the solid line, failure is likely to occur. If

this combination is under the line, the forming process is safe. Theoretical equations for calculating critical

major strain ( ) have also been developed, including an equation for local necking (Ref 25):

(Eq 30)

where n is strain-hardening exponent, provided that σ

= is followed; and ρ is the ratio of minor strain to

major strain, ε

/ε

. For diffuse necking, the critical major strain ( ) is (Ref 43):

(Eq 31)

Fig. 26 Typical forming-limit diagram for steel

Tensile Test

Tensile tests for sheet metal are specified in ASTM standards (Ref 15, 16, 29, and 44). Several special issues

for sheet metals are discussed in the following sections.

Specimen Preparation. Specimens can be rectangular with or without reduced section. The specimens can be

either machined or sheared. Sawing is also permitted by the applicable ASTM standard (Ref 44), but may not

provide good dimensional control. Shearing with a precise punch and die is the most efficient way of making

specimens. Computer numerical control machining, though slower than punching, is very precise and

introduces little deformation along the machined surfaces. Specimens should be made along different directions

to reflect anisotropy. Figure 27 shows the orientation of specimens on a piece of sheet metal.

Fig. 27 Sheet-metal specimen orientations for tensile testing. RD, rolling direction; TD, transverse

direction

Commercial extensometers are available for strain measurement. To measure local strains, grid patterns can be

put on the specimen surface over the gage length, as shown in Fig. 28. The patterns can be inscribed on a layer

of paint (Ref 45, 46), photoetched, or thermally transferred from printed transparencies. Thermally transferred

patterns printed with a laser printer can stand testing temperatures up to 1200 °C (2190 °F). The size of the grid

can be 1 to 2 mm (0.04–0.08 in.) to permit accurate local measurement.

Fig. 28 Grid pattern on the specimen gage length

Alignment of the Specimen. Special care should be taken to ensure the alignment of the specimen with a

gripping apparatus. Improper gripping results in bending of the specimen, especially in the width direction. It is

helpful to mark the specimen with gripping lines for reference.

Measurement of Strain. Displacement of the grid on the specimen can be recorded with a high-speed camera for

calculation of instantaneous strains (Fig. 29). If a camera is not available, displacement can be measured

manually. However, manual measurement is difficult at elevated temperatures. The fracture strains can always

be measured manually with a microscope. Some specialized three-dimensional displacement-measurement

systems, as shown in Fig. 30, are also available (Ref 45, 46).

Fig. 29 Strain recording with a camera during a tensile test of a sheet-metal specimen. Source: Ref 46

Fig. 30 Automatic noncontact 3-D surface-deformation measuring system. Source: Ref 46

Punch Testing

The punch test is used to obtain data for constructing FLDs of sheet metals. A schematic is shown in Fig. 31 for

a punch-test apparatus. Punch testing can also be used to measure the workability for deep drawing. An