• Corpus ID: 5624103

On the Stress Distribution at the Base of a Stationary Crack

@inproceedings{Williams1956OnTS,
  title={On the Stress Distribution at the Base of a Stationary Crack},
  author={M. L. Williams},
  year={1956}
}

• M. Williams
• Published 1 March 1956
• Engineering, Physics

In an earlier paper it was suggested that a knowledge of
the elastic-stress variation in the neighborhood of an
angular corner of an infinite plate would perhaps be of
value in analyzing the stress distribution at the base of a
V-notch. As a part of a more general study, the specific
case of a zero-angle notch, or crack, was carried out to
supplement results obtained by other investigators. This
paper includes remarks upon the antisymmetric, as well
as symmetric, stress distribution, and the circumferential
distribution of distortion strain-energy density. For the
case of a symmetrical loading about the crack, it is shown
that the energy density is not a maximum along the direction
of the crack hut is one third higher at an angle ± cos^(-1)
(1/3); i.e., approximately ±70 deg. It is shown that at the
base of the crack in the direction of its prolongation, the
principal stresses are equal, thus tending toward a state of
(two-dimensional) hydrostatic tension. As the distance
from the point of the crack increases, the distortion strain
energy increases, suggesting the possibility of yielding
ahead of the crack as well as ±70 deg to the sides. The
maximum principal tension stress occurs on ±60 deg rays.
For the antisymmetrical stress distribution the distortion
strain energy is a relative maximum along the crack and
60 per cent lower ± 85 deg to the sides.