Elastic–plastic behaviours of pressurised tubes under cyclic thermal stresses with temperature gradients

Elastic–plastic behaviours of pressurised tubes under cyclic thermal stresses are investigated, incorporating temperature (and resulting the yield strength) gradient through the tube thickness. Based on analytical investigations, explicit equations for various stress regimes representing elastic–plastic behaviours are obtained. In the limiting case of no temperature (and yield strength) gradient through the thickness, proposed equations recover those for the well-known Bree diagram. The proposed results are then validated against the results from full-cyclic elastic–plastic finite element analysis.