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phase shift between the beams. The variations in strain in the specimen produce a pattern of fringes,
which can be related to the strain field through the strain optic relation.
When a photoelastic model is observed in a plane polariscope, a series of fringes is observed.
The complete extinction of light occurs at locations where the principal strain directions coincide
with the axes of the analyzer or where either the strain is zero or e x À e y ¼ 0. These fringes are
termed isoclinics, and are used to determine the principal strain directions at all points in the
photoelastic model. Figure 11.21 shows the isoclinics in a ring subject to a compression load (as
shown in the figure). A reference direction is selected along the horizontal compression load and
labeled 0 degrees. For each measurement angle, one of the principal strains at a point on an isoclinic
is parallel to the specified angle and the other is perpendicular. For the 0-degree isoclinics, the
principal strains are oriented at 0 and 90 degrees.
Using the fact that the direction of the principal axes is known at a free surface and the fact that
the shear stress is zero on a free surface, the magnitude of the stress on the boundary can be
determined. The primary applications for photoelasticity, especially in a historical sense, have been
in the study of stress concentrations around holes or reentrant corners. In these cases, the maximum
stress is at the boundary and corresponds to one of the principal stresses. This maximum stress can
be obtained directly by the optical method, since the shear stress is zero on the boundary.
Optical methods provide information about the strain and stress at every point in the object
being examined, in contrast to a strain gauge that supplies information about the strain at a single
location on the object. The optical methods provide the possibility of identifying stress concentration locations and may allow for an improvement in design or guide detailed measurements with
strain gauges.
Moir e Methods
A moir e pattern results from two overlaid, relatively dense patterns that are displaced relative to
each other. This observable optical effect occurs, for example, in color printing, where patterns of
dots form an image. If the printing is slightly out of register, a moir e pattern results. Another
common example is the striking shimmering effect that occurs with some patterned clothing on
television. This effect results when the size of the pattern in the fabric is essentially the same as the
resolution of the television image.
In experimental mechanics, moir e patterns are used to measure surface displacements, typically
in a model constructed specifically for this purpose. The technique uses two gratings, or patterns of
parallel lines spaced equally apart. Figure 11.22 shows two line gratings. There are two important
properties of line gratings for moir e techniques. The pitch is defined as the distance between the
centers of adjacent lines in the grating, and for typical gratings has a value of from 1 to 40 lines/mm.
The second characteristic of gratings is the ratio of the open, transparent area of the grating to the
total area, or, for a line grating the ratio of the distance between adjacent lines to the center-to-center
distance, as illustrated in Figure 11.22. Clearly, a greater density of lines per unit width allows a
greater sensitivity of strain measurement; however, as line densities increase, coherent light is
required for practical measurement.
To determine strain using the moir e technique, a grating is fixed directly to the surface to be
studied. This can be accomplished through photoengraving, cementing film copies of a grating to the
surface, or interferometric techniques. The master or reference grating is next placed in contact with
the surface, forming a reference for determining the relative displacements under loaded conditions.
A series of fringes result when the gratings are displaced relative to each other; the bright fringes are
11.7 Optical Strain Measuring Techniques 495
13:14:4 Page 495
phase shift between the beams. The variations in strain in the specimen produce a pattern of fringes,
which can be related to the strain field through the strain optic relation.
When a photoelastic model is observed in a plane polariscope, a series of fringes is observed.
The complete extinction of light occurs at locations where the principal strain directions coincide
with the axes of the analyzer or where either the strain is zero or e x À e y ¼ 0. These fringes are
termed isoclinics, and are used to determine the principal strain directions at all points in the
photoelastic model. Figure 11.21 shows the isoclinics in a ring subject to a compression load (as
shown in the figure). A reference direction is selected along the horizontal compression load and
labeled 0 degrees. For each measurement angle, one of the principal strains at a point on an isoclinic
is parallel to the specified angle and the other is perpendicular. For the 0-degree isoclinics, the
principal strains are oriented at 0 and 90 degrees.
Using the fact that the direction of the principal axes is known at a free surface and the fact that
the shear stress is zero on a free surface, the magnitude of the stress on the boundary can be
determined. The primary applications for photoelasticity, especially in a historical sense, have been
in the study of stress concentrations around holes or reentrant corners. In these cases, the maximum
stress is at the boundary and corresponds to one of the principal stresses. This maximum stress can
be obtained directly by the optical method, since the shear stress is zero on the boundary.
Optical methods provide information about the strain and stress at every point in the object
being examined, in contrast to a strain gauge that supplies information about the strain at a single
location on the object. The optical methods provide the possibility of identifying stress concentration locations and may allow for an improvement in design or guide detailed measurements with
strain gauges.
Moir e Methods
A moir e pattern results from two overlaid, relatively dense patterns that are displaced relative to
each other. This observable optical effect occurs, for example, in color printing, where patterns of
dots form an image. If the printing is slightly out of register, a moir e pattern results. Another
common example is the striking shimmering effect that occurs with some patterned clothing on
television. This effect results when the size of the pattern in the fabric is essentially the same as the
resolution of the television image.
In experimental mechanics, moir e patterns are used to measure surface displacements, typically
in a model constructed specifically for this purpose. The technique uses two gratings, or patterns of
parallel lines spaced equally apart. Figure 11.22 shows two line gratings. There are two important
properties of line gratings for moir e techniques. The pitch is defined as the distance between the
centers of adjacent lines in the grating, and for typical gratings has a value of from 1 to 40 lines/mm.
The second characteristic of gratings is the ratio of the open, transparent area of the grating to the
total area, or, for a line grating the ratio of the distance between adjacent lines to the center-to-center
distance, as illustrated in Figure 11.22. Clearly, a greater density of lines per unit width allows a
greater sensitivity of strain measurement; however, as line densities increase, coherent light is
required for practical measurement.
To determine strain using the moir e technique, a grating is fixed directly to the surface to be
studied. This can be accomplished through photoengraving, cementing film copies of a grating to the
surface, or interferometric techniques. The master or reference grating is next placed in contact with
the surface, forming a reference for determining the relative displacements under loaded conditions.
A series of fringes result when the gratings are displaced relative to each other; the bright fringes are
11.7 Optical Strain Measuring Techniques 495