β Scribed by N.A. Weil
No coin nor oath required. For personal study only.
This paper deals with the bursting of vessels under slowly increasing pressures. The equations governing instability (bursting) are formulated for tensile bars and for vessels under internal pressures, assuming that the octahedral shear stress and strain uniquely describe the straining history of the material, and that the Hencky-Mises theory governs plastic behavior.
Closed form solutions are obtained by adopting a parabolic expression for the true tensile stress-strain properties of the material. The results show that the bursting stress in vessels may be either lower or higher than the ultimate tensile stress, depending upon the properties of the material. The safety factor for bursting is shown to depend solely upon the strain-hardening exponent, while the U.T.S. is proven to represent no real property of the material.
Results are compared with recent proposals advanced by the Subcommittee on Pressure Vessel Shell Theory for inclusion in the ASME Code. It is shown that a rational explanation of the proposed code equation can be advanced, provided that the thickness-diameter ratio is replaced by a factor containing the strain-hardening exponent of the material.
The solution is extended to cover bursting under a pressure rise due to adiabatic combustion, and to the case of gas volume compression from atmospheric conditions to instability. Some experimental values for material properties are also presented, followed by predictions for the stresses, strains, instability pressures, safety factors, limiting combustion pressure rise and gas volume compression at bursting for an SAE 285, Grade B steel having assumed material properties. * Equations 17 and 18 represent the "octahedral shear" stress and strain, respectively, provided that both equations are multiplied by a constant of 2/3. The adoption of unusual constants is done here only to simplify some of the numerical results derived; this choice has no bearing on the final results obtained in the paper.
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