The computation of shakedown limits for structural components subjected to variable thermal loading - Brussels diagrams

Structures submitted to a constant primary load and a cyclic (thermal) secondary load may for certain combinations of load ratio, geometry and material properties undergo ratchetting, i.e. a situation where the strains increase at each cycle of the applied thermal load until failure or prohibitively large accumulated deformations occur. This report resulting from CEC Study Contract RAP-054-UK having mainly fast breeder reactor applications in mind, discusses the so-called Brussels diagrams which are a practical tool for the designer for assessing a particular design situation with respect to ratchetting. Brussels diagrams show four regions: elastic, shakedown, reverse plasticity and ratchetting. The theory of Brussels diagrams is presented. It is the upper bound shakedown theory, specialized for axisymmetric shell elements and in which the upper bound is minimized by linear programming techniques. This theory is extended to the reverse plasticity region and has been implemented in two finite element axisymmetric shell programs which calculate a sequence of points on the ratchetting boundary. Three classes of problems are discussed: (i) The uniaxial transient Bree problem. (ii) The cylindrical tube subjected to axial load and stationary or moving temperature discontinuity. (iii) A range of Brussels diagrams for axisymmetric geometries and thermal loadings typical of LMFBRs. The discussion includes comparisons with some experiments and considerations on the sensitivity of the diagrams to the material assumptions