International audienceCircular-fronted cracks in round bars subject to tension, bending and twisting are considered. Numerical expressions are given allowing the calculation of stress intensity factors $K_I$, $K_{II}$, $K_{III}$ at every point on the crack front for a wide range of crack geometries. Comparisons are made with analytical, experimental and numerical results available in the literature. Crack shapes satisfying the iso-$K_I$ criterion are also determined, making it possible to investigate the problem of crack growth behaviour under tensile or bending fatigue loads
Integral equations derived by means of the potential theory for statical crack problems are singular in the sense of the principal value. In the present paper, these integrals are transformed into weakly singular ones and the so-called regularized integral equation is thus obtained. The conditions which permit the transformation are discussed and the weak singularity is proved. The kernel of the regularized equation is written in terms of the density, equal to the displacement discontinuity on the crack surface, in such a way that no extension of this density is involved. The results obtained hold for either embedded or surface crack problems.
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