Abstract
The failure probability of tensile bars containing circular notches is calculated using the multiaxial Weibull theory. The influence exerted by the stress concentration factor, the stress gradient in the notch root, and the Weibull exponent are analysed. A local risk of rupture is defined, and it is shown how characteristic sub-volumes of the notched tensile bar contribute to the failure probability. An analytical expression is derived which is based on a linear approximation of the stress field in the vicinity of the notch root, and which yields the dependence of the leading term of the failure probability on characteristic quantities such as the stress concentration factor and the Weibull modulus.
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