Isoclines

It is possible, with the use of plane polarized light, to show the condition of light extinction expressed by the relationship:

2a = nn

This happens for the points of the model that have the principal stress directions coinciding with polarization directions of polarizer and analyzer with crossed axes.

The locus of these points of equal inclination of the principal directions are con­tinuous curves called isoclines.

With the use of circular polarized light, isoclines are deleted and only the isochro­matics appear. It is not possible to operate the inverse, i. e., to eliminate the isochro­matics and keep only the isoclines; nevertheless, it is possible to distinguish these from the first ones following these methods:

• Rotate polarizer and analyzer maintaining their relative directions at 90°. The isocline changes position on the model surface and, during a complete rotation of 90°, cover all the points of the model, while isochromatics remain unchanged.

• The model is observed in white light. The isochromatics are colored, while the isoclines appear as dark lines or bands.

• Reduce the applied loads gradually. The isoclines, that depend only on the principal directions and not on the stress values, remain unaltered, while the isochromatics tend to disappear.

It should be noted that, generally, the isoclines have a band shape with a certain width. The midline is the isocline value for the assigned inclination of the polarizer axes.

If the isocline is recorded for a number of discrete values of the inclination of the polarizing filters, a family of isoclines is generated, each of which can be marked by the value of the inclination from which it derives.

The isoclines have special attributes resulting from their definition, Fig. 3.15:

1. The isocline parameter depends on the initial position of the model with respect to the reference x, y identified by the initial directions of the analyzer and polarizer axes.

2. The isocline parameter depends on the rotation direction of the crossed filters. The same isocline has values complementary to 90° if it is derived by clockwise or counterclockwise rotation. Consequently, symmetrical isoclines have comple­mentary to 90° values.

3. The isocline at a point on a free boundary has, by definition, the value of the angle formed by the tangent (or by the normal) to the border with the x axis, depending on the direction of the crossed filters rotation.

4. The points of a straight free edge belong to the same isocline.

5. In the case of geometrical and physical (forces distribution) symmetry, the sym­metry axis coincides with an isocline.

6. All isoclines pass through the points that have equal principal stresses.