This thesis is concerned with the development of computational procedures in the assessment of the structural integrity and lifetime of cracked bodies subjected to cyclic variable loads and temperatures.\ud The foundation of these techniques is the Linear Matching Method (LMM), related to the methods of elastic compensation and Gloss r-node, used in design calculations for a number of years. It involves matching the behaviours of a non-linear material to that of a linear material, whereby sequences of linear solutions with spatially varying linear moduli are produced. The developed iterative programming algorithms, implemented within the finite element scheme, ABAQUS, would then generate a monotonically reducing sequence of upper bounds, ultimately converging to the least upper bound loads.\ud In their applications, the significance of these programming methods is two-fold. The first is the investigations into the overall behaviour of cracked structures under the combined actions of mechanical and thermal loads. The numerical limit loads and ratchet limits so identified, which describe the onset of plastic collapse and the unlimited accumulation of plastic strains respectively, were found to be stable, with good converged solutions achieved within 40-60 iterations. The analyses also revealed the insensitivity of the ratchet boundaries to cyclic hardening, as the perfectly plastic and complete cyclic hardening limits yielded almost identical results.\ud The other is the examination into the relationship between the near crack tip fields and the cyclic loading histories, in creep and plasticity conditions. It was established that the HRR field criterion is an appropriate representation of the behaviour of the mechanically and thermally induced crack tip fields. This enabled the crack tip fracture criterion to be evaluated in all conditions, with the observed phenomenon described by two distinct behaviours; strongly influenced by the effect of the elastic stress intensity factor and the reference stress respectively.\ud The analyses conducted demonstrated the capability of the adopted numerical procedures in appraising the behaviour of cracked structures under cyclic loading histories, with the conservativeness of current solution procedures in R5 clearly evident in the results enclosed
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