The effect of creep ratchetting on thin shells

The behavior of thin shells, in particular, cylindrical and spherical shells, which are subjected to a long-time cyclic thermal gradient is discussed. Like many reactor components (shells) which are subjected to start-up and shut-down conditions, provided the temperature is high enough, the shell will exhibit a progressive growth with each cycle of temperature. This phenomena is often referred to as ratchetting and is caused by inelastic strains developed by creep. Although the thermal stress distribution is biaxial it is possible to represent the material behavior using a simple uniaxial-stress model. Assuming thermal stress interaction occurs, the equations which determine the solution of the strain growth and stress per cycle are presented. The flexibility of the analysis provides a means for including the effects of an arbitrary temperature-cycle time and temperature dependence of material properties. A step temperature variation is considered. During each part of the temperature cycle it is necessary to satisfy the equilibrium and compatibility conditions for the model. At any instant, the total strain will depend upon elastic, thermal, and creep strain components in addition to prior inelastic creep strains accumulated during previous temperature cycles. Accounting for all these conditions, the relations describing the behavior of the material can be determined during an arbitrary jth cycle of temperature. In particular, the cases of material properties are considered which are used for reactor components. Where possible, a closed form solution is given for appropriate values of the creep law exponents n and m. For the general case, an algorithm for the computer-solution to the problem is given. Using the general solution, the analysis appears to offer a suitable compromise between accurate behavior description and analytical complexity