Mechanical Behavior of Internally Pressurized Copper Tube for New HVACR Applications

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.

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

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.

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 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 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.)

Tube sample assemblies for pressure testing

Photographs of the pressure test apparatus used for these tests

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 Ø2.125in. tube in the transverse direction

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.

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

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

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.