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The fracture behaviour of a round pipe with a circular-arccircumferential notch is analysed in the case of tension and bending loading , byassuming that an elliptical-arc external surface crack exists at the notch root. Thestress concentration factor (SCF) is determined through theoretical expressionsand a finite element analysis. Then, the stress-intensity factor (SIF) along thesurface crack front is computed for four values of the dimensionless notch radius.The effect of stress concentration is discussed for both thick- and thin-walledpipes.