Case Study 12 - Pressurised Cylinder Creep Benchmark
Pressurised Cylinder Creep Benchmark
NAFEMS publication Understanding Non-Linear Finite Element Analysis gives a concise overview of non-linear analysis and contains a series of illustrative benchmarks.
Creep is the permanent deformation resulting from prolonged application of stress below the elastic limit. It is influenced by the magnitude of the load, the time the load is applied, and the temperature. Metals at high temperatures creep, while plastics creep even at room temperature.
The Pressurised cylinder creep benchmark demonstrates creep stress redistribution in a multi-axial stress situation until a steady state of stress is reached. This problem concerns an internally pressurised 100mm thick-wall cylinder, where the top and bottom surfaces of the cylinder are restrained to move only in the radial direction.
Thus, the problem can either be modelled as an axisymmetric problem in the R-Z plane (R is the radius, Z is the axis of the cylinder) or as a 2D plane strain problem in the R-Theta plane. The former is given in the publication, while both are given herein, calculated by HERA.
In addition, the numerical solutions are compared from the axisymmetric and 2D plane strain model, which shows some discrepancy between the numerical solutions. Total creep time of 100 hours is given in the NAFEMS publication, while the Abaqus Benchmark Manual uses 1,000 hours.
Figu re 2 Hoop stress (left) and radial stress (right) along the cylinder wall thickness from an axisymmetric and from a 2D plane strain finite element model (FEM). Elastic and creep stresses (creep time: 1000 hours) are shown.
Figure 3 Creep stresses from a 2D plain strain model versus analytical solution.
The errors reported herein, has been found to be slightly larger than reported ones in the Abaqus Benchmark Manual version 6.10-EF.