Mathematical modelling of the creep of weldments using the Cosserat theory of plates and shells

The creep deformation, cracking and ultimate failure of a weldment has attracted much attention, particularly within the power generation industries. In the electricity supply industry, a type of cracking which occurs during the mid-term design life expectancy of a weldment has been identified. This type of cracking always occurs within the low temperature heat affected zone, close to the interface with the parent metal and has been classified as type IV cracking. This thesis is concerned with extending the modelling of weldments using the Cosserat theory of plates and shells, an approach first considered by Nicol (1985). We present a more realistic model than Nicol, of a weldment contained in a flat plate, the weldment comprising the parent low and high temperature heat affected zones and weld metal, and we then analyse the effect of the material properties of the different zones which constitute the weldment on the complex stresses and strain rates induced in the region of the plate near to the weld. Alternative models for a plate weldment subjected to uniform axial tension are then presented, and similarities and contrasts with the model of Nicol are discussed. Cracking in weldments in pipes is of particular interest, and thus a simple pipe weldment subjected to end tension and internal and external pressures is modelled. We do not consider the buckling which may occur in pipes under compressive loading and externally pressure. It is found that the pipe bends on a length scale associated with the average initial radius of the pipe, and in addition, thins about this radius on a much smaller length scale, which the thickness of the pipe walls. Both analytical and asymptotic solutions for the elastic stress case are derived, and comparisons with earlier, more simple models are made. Finally the deformation of an initially curved shell subjected to tension and pressure on one face is considered. This model shows significant differences to the model of the pipe, both in the structure of the differential equations and character of the solutions.