The Photoelastic Investigation of Three-Dimensional Stress and Strain Conditions Page: 4 of 19
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N.A.C.A. Technical Memorandum No. 824
passed through the center of the triaxial ellipsoid whose
sections with the ellipsoidal surface are circles. The
directions of these two planes are called .th.e optic axes.
There is only one ray velocity for the axes. The axes
lie in the plane through the maximum and minimum principal
velocity of the light.
In the case of the optically uniaxial crystal, the
light velocity and Vibratory relations of the unidirec-
tional condition of concentrated stress just considered
can be represented by Fresnelts ellipsoid with two equal
principal axes. The optic behavior of a small homogene-
nously deformed particle is determined if Fresnel's ellip-
soid, with the directions of its principal axes are known.
The numerous photoelastic studies available on two-
dimensional stresses in the common materials (glass,
trolon, bakellte) show that the directions of the princi-
pal stress and strain, in the range of purely elastic be-
havior of the material coincide with the directions of the
principal light velocities of Fresnel's ellipsoid.
Figure 1 shows that a light ray in the direction of
the principal light velocity vI penetrates the sub-
stance at velocity vII if the plane of vibration of the
ray is coincident with the plane through vIII and vii.
According to the data for the two-dimensional stress con-
dition the difference of velocity vII in the deformed
and of velocity v0 in the nondeformed particle is pro-
portional to the principal axial stress c.1I, which is
perpendicular to the plane of vibration of the light ray:
vii - vo = C 0I
(C = a constant for the material, determined by a cali-
Brewster stated this law in similar form in 1816 for
the conditions of unidirectional stress (references 3, 4,
and 5). For small deformations the relation between
stress and strain follows Hooke's law.
If the effect on the light of the proximity of a par-
ticle can be shut out - the deformations and the optical
properties of the neighborhood are different, in general -
the shape and the directions of the principal axes of
Fresnel's ellipsoid for a small, homogeneously deformed
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Oppel, G. The Photoelastic Investigation of Three-Dimensional Stress and Strain Conditions, report, April 1937; (https://digital.library.unt.edu/ark:/67531/metadc63373/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.