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Journal of Pressure Vessel Technology | Volume 134 | Issue 6 | research-article
Research Papers: Design and Analysis

Mechanical Behavior of Internally Pressurized Copper Tube for New HVACR Applications

[+] Author and Article Information
Frank F. Kraft

Mechanical Engineering Department
Ohio UniversityAthens,
OH 45701
e-mail: kraftf@ohio.edu

Tommy L. Jamison

Jamison Engineering,
5075 Treadway Road Hernando,
MS 38632
e-mail: tjamison5075@att.net

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 12, 2011; final manuscript received April 18, 2012; published online November 21, 2012. Assoc. Editor: Xian-Kui Zhu.

J. Pressure Vessel Technol 134(6), 061213 (Nov 21, 2012) (9 pages) doi:10.1115/1.4007035 History: Received August 12, 2011; Revised April 18, 2012
Article
References
Figures
Tables

This paper reviews and simplifies basic theory to predict plastic strain and burst pressure of internally pressurized, thin-walled copper tube for (heating, ventilation, air conditioning, and refrigeration applications. Predictions are based upon material stress–strain data obtained from basic tensile tests. A series of pressure tests was performed at 635 to 1500 psi (4.38–10.34 MPa), and until burst, on tubes ranging from 0.625 in. (15.87 mm) to 2.125 in. (53.97 mm) in diameter. A Voce type equation is shown to provide superior correlation to tensile and instability data, such that accurate projections can be made. An assessment of the classical power-law (Ludwik–Hollomon) equation is also presented, and it did not simultaneously correlate well with stress–strain data and satisfy the Considère instability criterion in uni-axial tension. Nevertheless, its use still led to reasonably accurate burst pressure predictions due to the strain range over which it was applied. Property variation (with respect to tube size) and anisotropy were observed in the transverse and axial tube directions for 1.125 in. (28.6 mm) and 2.125 in. (54.0 mm) diameter tube. Thus, the importance of representative and accurate material data in the transverse (hoop) direction is emphasized.
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References

1
Jamison, T., and Stout, C., 2011, “Development and Evaluation of Copper Tube an Fittings in R-410A Applications,” ASHRAE, Publication ML-11-022.
2
Urieli, I., 2011, “Chapter 9: Carbon Dioxide (R744)—The New Refrigerant,” Engineering Thermodynamics—A Graphical Approach (Open source text). [Online] March 17, 2011. [Accessed August 3, 2011.] http://www.ohio.edu/mechanical/thermo/Applied/Chapt.7_11/Chapter9.html.
3
ASME, B31.5-2007, Refrigeration Piping and Heat Transfer Components, American Society of Mechanical Engineers, New York.
4
ASTM, B280-08, 2008, Standard Specification for Seamless Copper Tube for Air Conditioning and Refrigeration Field Service, ASTM International, West Conshohocken, PA.
5
Antaki, G. A., 2005, Piping and Pipline Engineering, Marcel Dekker, New York, pp. 84–90.
6
Fishburn, J. D., 2007, “A Single Technically Consistent Design Formula for the Thickness of Cylindrical Sections Under Internal Pressure,” ASME J Pressure Vessel Technol., 129, pp. 211–215. [CrossRef]
7
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8
Sachs, G., and Lubahn, J. D., 1946, “Failure of Ductile Metals in Tension,” Trans. ASME, 68, pp. 271–276.
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Svensson, N. L., 1958, “Bursting Pressures of Cylindrical and Spherical Vessels,” ASME J. Appl. Mech., 25, pp. 89–96.
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Brabin, T. A., Christopher, T., and Rao, B. N., 2011, “Bursting Pressure of Mild Steel Cylindrical Vessels,” Int. J. Pressure Vessels Piping, 88, pp. 119–122. [CrossRef]
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Rajan, K. M., Deshpande, P. U., and Narasimhan, K., 2002, “Experimental Studies on Bursting Pressure of Thin-Walled Flow Formed Pressure Vessels,” J. Mater. Process. Technol., 125–126, pp. 228–234. [CrossRef]
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Christopher, T., Sarma, B. S. V. R., Potti, P. K. G., Rao, B. N., and Sankarnarayanasamy, K., 2002, “A Comparitive Study on Failure Pressure Estimations of Unflawed Cylindrical Vessels,” Int. J. Pressure Vessels Piping, 79, pp. 53–66. [CrossRef]
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Tiryakioglu, M., Staley, J. T., and Campbell, J., 2000, “A Comparative Study of the Constitutive Equations to Predict the Work Hardening Characteristics of Cast Al-7wt.%Si-0.20wt.%Mg Alloys,” J. Mater. Sci. Lett., 19, pp. 2179–2181. [CrossRef]
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Kleemola, H. J., and Nieminen, M. A., 1974, “On the Strain-Hardening Parameters of Metals,” Metall. Trans., 5, pp. 1863–1866. [CrossRef]
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Kleemola, H. J., and Ranta-Eskola, A. J., 1976, “Comparison of the Strain Hardening Parameters of Sheet Metals in Uniaxial and Biaxial Tension,” Metall. Mater. Trans. A, 7, pp. 595–599. [CrossRef]
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Sing, W. M., and Rao, K. P., 1997, “Role of Strain-Hardening Laws in the Prediction of Forming Limit Curves,” J. Mater. Process. Technol., 63, pp. 105–110. [CrossRef]
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Voce, E., 1955, “A Practical Strain-Hardening Function,” Metallurgia, 51, pp. 219–226.
22
Hosford, W. F., 2010, Mechanical Behavior of Materials, Cambridge University, New York, pp. 70–74.
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Marin, J., and Sharma, M., 1958, “Design of a Thin Walled Cylindrical Vessel Based Upon Plastic Range and Considering Anisotropy,” Weld Research Council Bulletin, Vol. 40.
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Azrin, M., and Backofen, W. A., 1970, “The Deformation and Failure of a Biaxially Stretched Sheet,” Metall. Trans., 1, pp. 2857–2865.
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Hosford, W. F., and Caddell, R. M., 2011, Metal Forming, Mechanics and Metallurgy, 4th ed., Cambridge University, New York, p. 254.
29
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Figures

Grahic Jump Location
Fig. 1

Stress–strain data for fully annealed (CDA 122) copper. Strain measurements were taken with an extensometer attached to the sample. Note the virtually nonexistent elastic region.

+Stress–strain data for fully annealed (CDA 122) copper. Strain measurements were taken with an extensometer attached to the sample. Note the virtually nonexistent elastic region.
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Stress–strain data for fully annealed (CDA 122) copper. Strain measurements were taken with an extensometer attached to the sample. Note the virtually nonexistent elastic region.
Grahic Jump Location
Fig. 2

Illustration of the stress state in the wall of a thin-walled cylindrical vessel. The hoop stress (σh) is equal to the σ1 principal stress, the longitudinal stress (σℓ) is equal to the σ2 principal stress, and the radial stress σr = σ3 ≈ 0. D is the tube diameter, p is the internal pressure, and t is the wall thickness.

+Illustration of the stress state in the wall of a thin-walled cylindrical vessel. The hoop stress (σh) is equal to the σ1 principal stress, the longitudinal stress (σℓ) is equal to the σ2 principal stress, and the radial stress σr = σ3 ≈ 0. D is the tube diameter, p is the internal pressure, and t is the wall thickness.
View Large  |  Save Figure  |  Download Slide (.ppt)
Illustration of the stress state in the wall of a thin-walled cylindrical vessel. The hoop stress (σh) is equal to the σ1 principal stress, the longitudinal stress (σℓ) is equal to the σ2 principal stress, and the radial stress σr = σ3 ≈ 0. D is the tube diameter, p is the internal pressure, and t is the wall thickness.
Grahic Jump Location
Fig. 3

This illustration shows basic tensile specimen geometry and orientation with respect to the tube. The specimens are not to scale with respect to the tube. Specimens were flattened, machined, and then annealed prior to testing.

+This illustration shows basic tensile specimen geometry and orientation with respect to the tube. The specimens are not to scale with respect to the tube. Specimens were flattened, machined, and then annealed prior to testing.
View Large  |  Save Figure  |  Download Slide (.ppt)
This illustration shows basic tensile specimen geometry and orientation with respect to the tube. The specimens are not to scale with respect to the tube. Specimens were flattened, machined, and then annealed prior to testing.
Grahic Jump Location
Fig. 4

True stress–strain results from longitudinal and transverse samples of 1.125 in. OD tube. Longitudinal samples exhibited a higher tensile stress and a higher strain at instability.

+True stress–strain results from longitudinal and transverse samples of 1.125 in. OD tube. Longitudinal samples exhibited a higher tensile stress and a higher strain at instability.
View Large  |  Save Figure  |  Download Slide (.ppt)
True stress–strain results from longitudinal and transverse samples of 1.125 in. OD tube. Longitudinal samples exhibited a higher tensile stress and a higher strain at instability.
Grahic Jump Location
Fig. 5

True stress–strain results from transverse samples of 1.125 in. OD tube. The instability strains were 0.34 and 0.32. Ludwik–Hollomon (power-law) and a Voce (first order exponential) equations were fit to the data.

+True stress–strain results from transverse samples of 1.125 in. OD tube. The instability strains were 0.34 and 0.32. Ludwik–Hollomon (power-law) and a Voce (first order exponential) equations were fit to the data.
View Large  |  Save Figure  |  Download Slide (.ppt)
True stress–strain results from transverse samples of 1.125 in. OD tube. The instability strains were 0.34 and 0.32. Ludwik–Hollomon (power-law) and a Voce (first order exponential) equations were fit to the data.
Grahic Jump Location
Fig. 6

True stress–strain results from transverse samples of 2.125 in. OD tube. Ludwik–Hollomon (power-law) and a Voce (first order exponential) equations were fit to the data. (Instability was not achieved within the gauge area of the extensometer.)

+True stress–strain results from transverse samples of 2.125 in. OD tube. Ludwik–Hollomon (power-law) and a Voce (first order exponential) equations were fit to the data. (Instability was not achieved within the gauge area of the extensometer.)
View Large  |  Save Figure  |  Download Slide (.ppt)
True stress–strain results from transverse samples of 2.125 in. OD tube. Ludwik–Hollomon (power-law) and a Voce (first order exponential) equations were fit to the data. (Instability was not achieved within the gauge area of the extensometer.)
Grahic Jump Location
Fig. 7

Tube sample assemblies for pressure testing

+Tube sample assemblies for pressure testing
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Tube sample assemblies for pressure testing
Grahic Jump Location
Fig. 8

Photographs of the pressure test apparatus used for these tests

+Photographs of the pressure test apparatus used for these tests
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Photographs of the pressure test apparatus used for these tests
Grahic Jump Location
Fig. 9

Tensile and pressure test results, and constitutive equations for Ø1.125 in. tube in the transverse direction

+Tensile and pressure test results, and constitutive equations for Ø1.125 in. tube in the transverse direction
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Tensile and pressure test results, and constitutive equations for Ø1.125 in. tube in the transverse direction
Grahic Jump Location
Fig. 10

Tensile and pressure test results, and constitutive equations for Ø2.125in. tube in the transverse direction

+Tensile and pressure test results, and constitutive equations for Ø2.125in. tube in the transverse direction
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Tensile and pressure test results, and constitutive equations for Ø2.125in. tube in the transverse direction
Grahic Jump Location
Fig. 11

Effective stress–strain data that were determined from the pressure tests for each tube. Test pressures were 635, 800, 1000, and 1500 psi (4.38, 5.52, 6.90, and 10.3 MPa, respectively). Two tube samples were tested at each pressure.

+Effective stress–strain data that were determined from the pressure tests for each tube. Test pressures were 635, 800, 1000, and 1500 psi (4.38, 5.52, 6.90, and 10.3 MPa, respectively). Two tube samples were tested at each pressure.
View Large  |  Save Figure  |  Download Slide (.ppt)
Effective stress–strain data that were determined from the pressure tests for each tube. Test pressures were 635, 800, 1000, and 1500 psi (4.38, 5.52, 6.90, and 10.3 MPa, respectively). Two tube samples were tested at each pressure.
Grahic Jump Location
Fig. 12

Strain as a function of internal tube pressure and the predictive models

+Strain as a function of internal tube pressure and the predictive models
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Strain as a function of internal tube pressure and the predictive models
Grahic Jump Location
Fig. 13

Graphical representation depicting the instability points for tensile test data, the exponential (Voce) model, and that predicted for the tube wall

+Graphical representation depicting the instability points for tensile test data, the exponential (Voce) model, and that predicted for the tube wall
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Graphical representation depicting the instability points for tensile test data, the exponential (Voce) model, and that predicted for the tube wall
Grahic Jump Location
Fig. 14

Comparison of the best fit power-law equation and the one meeting the Considère (instability) criterion. The best fit equation overpredicts the instability strain at 0.436 whereas the actual instability strain is ∼ 0.3.

+Comparison of the best fit power-law equation and the one meeting the Considère (instability) criterion. The best fit equation overpredicts the instability strain at 0.436 whereas the actual instability strain is ∼ 0.3.
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Comparison of the best fit power-law equation and the one meeting the Considère (instability) criterion. The best fit equation overpredicts the instability strain at 0.436 whereas the actual instability strain is ∼ 0.3.

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