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.

References

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
.10.1115/1.2389035
7.
Cooper
,
W.E.
,
1957
, “
The Significance of the Tensile Test to Pressure Vessel Design
,”
Weld. J.
,
36
(Suppl), pp.
49s
59s
.
8.
Sachs
,
G.
, and
Lubahn
,
J. D.
,
1946
, “
Failure of Ductile Metals in Tension
,”
Trans. ASME
,
68
, pp.
271
276
.
9.
Svensson
,
N. L.
,
1958
, “
Bursting Pressures of Cylindrical and Spherical Vessels
,”
ASME J. Appl. Mech.
,
25
, pp.
89
96
.
10.
Weil
,
N. A.
,
1958
, “
Bursting Pressures and Safety Factors for Thin-Walled Vessels
,”
J. Franklin Inst.
,
265
(
2
), pp.
97
116
.10.1016/0016-0032(58)90432-0
11.
Xue
,
L.
,
Widera
,
G. E. O.
, and
Sang
,
Z.
,
2008
, “
Burst Analysis of Cylindrical Shells
,”
ASME J. Pressure Vessel Technol.
,
130
, pp.
1
5
.10.1115/1.2826454
12.
Zhu
,
X.-K.
, and
Leis
,
B. N.
,
2007
, “
Theoretical and Numerical Predictions of Burst Pressure of Pipelines
,”
ASME J. Pressure Vessel Technol.
,
129
, pp.
644
652
.10.1115/1.2767352
13.
Law
,
M.
, and
Bowie
,
G.
,
2007
, “
Prediction of Failure Strain and Burst Pressure in High Yield-to-Tensile Strength Ratio Linepipe
,”
Int. J. Pressure Vessels Piping
,
84
, pp.
487
492
.10.1016/j.ijpvp.2007.04.002
14.
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
.10.1016/j.ijpvp.2011.01.001
15.
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
.10.1016/S0924-0136(02)00298-4
16.
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
.10.1016/S0308-0161(01)00126-0
17.
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
.10.1023/A:1006706912301
18.
Kleemola
,
H. J.
, and
Nieminen
,
M. A.
,
1974
, “
On the Strain-Hardening Parameters of Metals
,”
Metall. Trans.
,
5
, pp.
1863
1866
.10.1007/BF02644152
19.
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
.10.1007/BF02643973
20.
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
.10.1016/S0924-0136(96)02608-8
21.
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
.
23.
Güven
,
U.
,
2007
, “
A Comparison on Failure Pressures of Cylindrical Pressure Vessels
,”
Mech. Res. Commun.
,
34
, pp.
466
471
.10.1016/j.mechrescom.2007.05.001
24.
Zhu
,
X.-K.
, and
Leis
,
B. N.
,
2006
, “
Average Shear Stress Yield Criterion and Its Application to Plastic Collapse Analysis of Pipelines
,”
Int. J. Pressure Vessels Piping
,
83
, pp.
663
671
.10.1016/j.ijpvp.2006.06.001
25.
Soboyejo
,
W.
,
2003
,
Mechanical Properties of Engineered Materials
,
Marcel Dekker
,
New York
, pp.
128
131
.
26.
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.
27.
Azrin
,
M.
, and
Backofen
,
W. A.
,
1970
, “
The Deformation and Failure of a Biaxially Stretched Sheet
,”
Metall. Trans.
,
1
, pp.
2857
2865
.
28.
Hosford
,
W. F.
, and
Caddell
,
R. M.
,
2011
,
Metal Forming, Mechanics and Metallurgy
,
4th ed.
,
Cambridge University
,
New York
, p.
254
.
29.
SciDAvis Home Page. [Online] April 14, 2010. [Accessed July 18, 2011.] http://scidavis.sourceforge.net/index.html.
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