VM-WB-MECH-068

VM-WB-MECH-068
Plastic Loading of a Thick Walled Cylinder

Overview

Reference:

Timoshenko, S. (1956). Strength of Material, Part II: Elementary Theory and Problems (3rd ed., p. 388, article 70). New York, NY: D. Van Nostrand Co., Inc.

Solver(s):

Ansys Mechanical

Analysis Type(s):Static, Plastic Analysis (Plane Strain)
Element Type(s):2-D Structural Solid

Test Case

A long thick-walled cylinder is subjected to an internal pressure p (with no end cap load). Determine the radial stress, σr, and the tangential (hoop) stress, σt, at locations near the inner and outer surfaces of the cylinder for a pressure, pel, just below the yield strength of the material, a fully elastic material condition. Determine the effective (von Mises) stress, σeff, at the same locations for a pressure, pult, which brings the entire cylinder wall into a state of plastic flow. Use a global mesh size of 0.4 in along with a mapped face meshing.

Figure 91: Schematic

Schematic
Schematic

Material PropertiesGeometric PropertiesLoading
E = 30 x 106 psi
σyp = 30,000 psi
ν = 0.3
a = 4 in
b = 8 in
pel = 12,990 psi
pult = 24,011 psi

Analysis

This problem is modeled as a plane strain problem with only a quarter of the cross-section as shown in the above figures. Symmetry conditions are used on the edges perpendicular to X and Y axes. Load is applied in two steps as shown in the above table. The stresses are calculated at a distance of r = 4.4 in and 7.6 in, w.r.t a cylindrical coordinate system whose origin is same as that of the global coordinate system.

Results Comparison

ResultsTargetMechanicalError (%)
Fully ElasticStressr, psi (X = 4.4 in)-9984-9948.8-0.353
Stresst, psi (X = 4.4 in)1864518609-0.193
Stressr, psi (X = 7.6 in)-468-469.10.235
Stresst, psi (X = 7.6 in)91289129.10.012
Fully PlasticStresseff, psi (X = 4.4 in)30000300000
Stresseff, psi (X = 7.6 in)30000300000