December 3, 2001

• Here we perform an elastic-plastic analysis of a pipe with circumferential crack on the inner surface. Although the scale of the analysis is not so large, it takes a long time, and it is an example of a very heavy calculation.
  • Model: quarter symmetry
  • Length of the pipe: 200mm
  • Thickness: 20mm
  • Crack depth ratio a/t: 0.8
  • Aspect ratio of the crack a/c: 0.4
  • Stress-strain curve: bilinear approximation
  • Young's modulus: 178.5×10^6kPa
  • Poison ratio: 0.3
  • Initial yield stress: 183.4×10^3kPa
  • Hardening constant: 193.0×10^3kPa
  • Loading condition: Tensile load 10MPa is applied in each of the 16 incremental steps. Totaly 160MPa.

• The mesh used in this analysis is as follows:
  • Elements: Tetrahedral quadratic elements
  • Number of elements: 442,259
  • Number of nodes: 614,893
  • DOFs: 1,844,679

• The platform used is seven Pentium III-14CPU cluster. It took 17 hours to complete. The following figures show the propagation of the plastic region. We call here the ratio of the plastic deformation, the "plastic ratio". Let the plastic ratio indicate 1 (red) if the four integral points yield, while 0.75 (light brown), 0.5 (light green) and 0.25 (light blue) indicate that three, two and one integral points yield, respectively. The blue area represents the elastic region.

if you have any questions.