The Bending Stress Distribution at the Base of a Stationary Crack

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  • M. L. Williams
    Guggenheim Aeronautical Laboratory, California Institute of Technology, Pasadena, Calif.

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<jats:p>Extending an earlier paper dealing with extensional stress distributions, this study considers the stresses around a crack point owing to bending loads. It is found first that the stresses possess the characteristic inverse square-root singularity in terms of distance from the crack point. Along the crack prolongation direction the symmetric principal stresses are of opposite sign and in the ratio (1 − ν)/(3 + ν), in contrast to the extensional situation where they are identically equal. This leads to the observation that more yielding might be expected as the percentage of bending to extension stress at the crack increases. In the antisymmetrical loading, the shear stress is a maximum ±90 deg to the side of the crack, where the distortion energy is also a maximum. Interesting reciprocity relationships are also shown to exist between the symmetrical and antisymmetrical loading conditions for the isochromatic fringe lines and the stress trajectories. Finally, the results are discussed in connection with the combined extensional and bending loading.</jats:p>

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