The paper discusses the results of fatigue crack growth rate tests conducted in the presence of residual stresses. Three different residual stress distributions, obtained by laser welds, were employed in order to characterize the crack propagation behaviour under different conditions, producing either an increase or a reduction of the stress intensity factor due to external loads. Test results are analysed by means of a non-linear numerical model (based on the weight function method) and a knowledge of the fatigue crack growth properties of the base material, free from residual stresses. The results of the analysis are discussed with reference to experimental trends, in order to clarify the predictive capabilities of the method and aspects needing further investigation. NOMENCLATURE a = crack length in CT specimen, measured from the load line K = stress intensity factor N = elapsed fatigue cycles R = ratio between minimum and maximum stress intensity factor in the fatigue cycle AK = stress intensity factor range max, min = maximum and minimum values in the fatigue cycle, respectively

An overview is presented of studies conducted at the University of Pisa on the Weight Function technique as applied to Fatigue Crack Grown analysis. The fundamental theoretical aspects of the technique are summarised, discussing some recent methods for the determination of the Weight Function. The application of the technique to non-linear (contact) problems and to the evaluation of the crack tip stress field is also discussed. It is shown that the Weight Function method allows one to efficiently consider many crack propagation problems, some examples of which are provided. NOMENCLATURE a, a,,, a, = generic, initial and critical crack length KEXT, K, , I(,,, = stress intensity factor produced by external forces, residual stress and total value K , AK, K, = stress intensity factor in mode I (value and range) and in mode I1 N, NF = elapsed fatigue cycles, cycles to failure R = K-/K, = R-ratio u = crack opening displacement function h = weight function u, OP = stress and nominal stress

SUMMARYThe paper deals with the development of a numerical method for determining Weight Functions in twodimensional problems. After a short review of some recent numerical techniques an original approach is presented. The method is based on Finite Element calculations with coarse meshes and on the knowledge of some values of the Stress Intensity Factor for one reference loading condition. The validity of the method is demonstrated for a theoretical case and its accuracy and suitability are discussed with reference to practical applications.

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