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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenSat, 13 Apr 2024 00:28:03 +0000Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
https://resolver.caltech.edu/CaltechAUTHORS:20140730-111744170
Authors: {'items': [{'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 1952
As an analog to the bending case published in an earlier paper, the stress singularities in plates subjected to extension in their plane are discussed. Three sets of boundary conditions on the radial edges are investigated: free-free, clamped-clamped, and clamped-free. Providing the vertex angle is less than 180 degrees, it is found that unbounded stresses occur at the vertex only in the case of the mixed boundary condition with the strength of the singularity being somewhat stronger than for the similar bending case. For vertex angles between 180 and 360 degrees, all the cases considered may have stress singularities.
In amplification of some work of Southwell, it is shown that there are certain analogies between the characteristic equations governing the stresses in extension and bending, respectively, if ν, Poisson's ratio, is replaced by -ν. Finally, the free-free extensional plate behaves locally at the origin exactly the same as a clamped-clamped plate in bending, independent of Poisson's ratio.
In conclusion, it is noted that the free-free case analysis
may be applied to stress concentrations in V-shaped
notches.https://authors.library.caltech.edu/records/2zph7-ee089On the Stress Distribution at the Base of a Stationary Crack
https://resolver.caltech.edu/CaltechAUTHORS:20140729-122058948
Authors: {'items': [{'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 1956
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.https://authors.library.caltech.edu/records/ty906-me279The stresses around a fault or crack in dissimilar media
https://resolver.caltech.edu/CaltechAUTHORS:20140729-121619274
Authors: {'items': [{'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}]}
Year: 1959
In order to investigate some problems of geophysical interest, the usual consideration of symmetrical or antisymmetrical loading of an isotropic homogeneous plate containing a crack was extended to the case where the alignment of the crack separates two separate isotropic homogeneous regions. It develops that the modulus of the singular behavior of the stress remains proportional to the inverse square root of the distance from the point of the crack, but the stresses possess a sharp oscillatory character of the type r^(-1/2) sin (b log r), which seems to be confined quite close to the point, as well as a shear stress along the material joint line as long as the materials are different.
The off-fault areas of high strain energy release reported by St. Amand for the White Wolf fault are qualitatively shown to be expected.https://authors.library.caltech.edu/records/3c14t-f6v73Crack point stress singularities at a bi-material interface
https://resolver.caltech.edu/CaltechAUTHORS:20140407-143748726
Authors: {'items': [{'id': 'Williams-M-L', 'name': {'family': 'Williams', 'given': 'M. L.'}}, {'id': 'Zak-A-R', 'name': {'family': 'Zak', 'given': 'A. R.'}}]}
Year: 1963
DOI: 10.1115/1.3630064
The mathematical procedure for analyzing stress singularities in infinite wedges has been developed in References (1) and (2) and has been successfully applied to the analysis of stress distribution in the vicinity of a tip of a crack (3) (4). As a continuation of this study, the results presented in this note relate to the symmetrical stress field about a crack point perpendicular to a bi-material interface, and hence complement earlier results (4) wherein the crack lay along the interface.https://authors.library.caltech.edu/records/jq79m-88d85