The Bree problem with different yield stresses on-load and off-load and application to creep ratcheting

• The Bree problem is solved for differing yield stresses on and off load.
• The modified Bree problem with cycling primary load is also solved.
• These solutions can be applied to creep ratcheting using a pseudo-yield stress.

The ratchet boundaries and ratchet strains are derived for the Bree problem and an elastic-perfectly plastic material with different yield stresses on-load and off-load. The Bree problem consists of a constant uniaxial primary membrane stress and a cycling thermal bending stress. The ratchet problem with differing yield stresses is also solved for a modified loading in which both the primary membrane and thermal bending stresses cycle in-phase. The analytic solutions for the ratchet boundaries are compared with the results of deploying the linear matching method (LMM) and excellent agreement is found. Whilst these results are of potential utility for purely elastic–plastic behaviour, since yield stresses will often differ at the two ends of the cycle, the solution is also proposed as a means of assessing creep ratcheting via a creep ductility exhaustion approach.