The role of thermal and residual stresses in linear elastic and post yield fracture mechanics

Abstract

The general role played by thermal and residual (TR) stresses in fracture mechanics is still unclear. It is sometimes argued (a) that in the linear elastic fracture mechanics (LEFM) regime TR stresses are secondary (rather than primary) i.e. that the overall loading is relaxed (rather than maintained) as well as redistributed as the crack grows, and (b) that because TR stresses do not influence the plastic limit load of a structure they have little influence on the post yield fracture mechanics (PYFM) regime. This paper demonstrates the dangers of these views. Examples are given of TR stresses behaving in either primary or secondary manner in both the LEFM and PYFM regimes. The danger of drawing general conclusions in fracture mechanics from the nearness of a structure to its plastic limit load is demonstrated, and it is shown that “local” rather than global (limit-analysis) collapse parameters must be used in empirical formulae that interpolate between LEFM and plastic-collapse regimes. In LEFM it is shown that the standard Green's function (weight or influence function) method can be applied to TR stress calculations. The method also applies in the PYFM regime if the Dugdale-type strip yield model is assumed. A general method of analysing fixed-grip loadings in the plastic regime, based on Rice's J contour integral is also given.