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Starting from the classical definition of stress-life Wohler curve in theform of Basquin's law, an analytical procedure for the calibration of the fourparameters Wohler curve (Weibull's law) for a plain specimen is proposed. Theobtained parameters are then adjusted by means of an additional slope factorpreserving the inflection point of the curve while changing its slope in orderto model the experimental observations in which an increase of the scatter inlife prediction is observed when reducing the stress amplitude. The sameapproach has then been adopted to calibrate the Weibull's law parameters for anotched specimen, and the fitting slope factor has been found to be a valuethat changes with the material but remains constant with the stressconcentration factor. The findings have been validated with existingexperimental data on 2024-T3 aluminum alloy and normalized SAE 4130 steel.

An analytical relation between Weibull's and Basquin's laws for smooth and notched specimens and application to constant amplitude fatigue