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

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.

Copyright © 2012 by ASME
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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.

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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 (σ) 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.

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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.

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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.

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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.

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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.)

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Fig. 7

Tube sample assemblies for pressure testing

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Fig. 8

Photographs of the pressure test apparatus used for these tests

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Fig. 9

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

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Fig. 10

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

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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.

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Fig. 12

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

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Fig. 13

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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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.



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