Experimental stress analysis module 4 Part-A (ME832) notes by Dr. Mohammed Imran

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GHOUSIA COLLEGE OF ENGINEERING
RAMANAGARAM-562159
EXPERIMENTAL STRESS ANALYSIS
[15ME832]
Dr. MOHAMMED IMRAN
ASST PROFESSOR
DEPARTMENT OF MECHANICAL ENGINEERING

2. THREE DIMENSIONAL PHOTOELASTICITY
THE STRESS-FREEZING METHOD
A three dimensional model of a photoelastic material is made and stresses due to
external load are locked in the model during a stress
completion of stress process, the model is cut into thin slices and interior region of the
model is photoelastically analyzed.
Figure 1
Some polymeric materials exhibit di
 Molecular chains are well boned in a three
bonds (having longer molecules chains),
 A large number of molecules are less solidly bonded by secondary bonds
(having shorter molecular chains) as shown in
At room temperature, both sets of molecular bonds, i.e. primary and secondary bonds
resist external load. Photoelastic model (made of polymeric material) is now loaded
and its temperature is raised. At a critical temperature, the shorter secondary bonds
are broken but longer primary bonds remain intact and carry the entire external load.
Deformations caused by the external load are locked in the secondary bonds. Now the
model is cooled to room temperature, the secondary bonds are reformed again
between the deformed primary bonds and these secondary bonds serve to lock the
deformations (stresses) in these deformed primary bonds.
After the load is removed, the primary bonds a
large part of deformation is not recovered. So, the elastic deformation in the body is
permanently locked into the model by reformed secondary bonds.
shown in Fig.2.
(a) Unloaded model at room temperature; pr
(b) Loaded model at room temperatures; primary and secondary bonds.
(c) Loaded model at room temperatures; primary bonds.
(d) Loaded model at room temperatures; primary bonds.
(e) Loaded model at room temperatures; primary bonds.
(f) Unloaded model at room temperature; primary and secondary bonds
2
Module-4 Part-A
THREE DIMENSIONAL PHOTOELASTICITY
FREEZING METHOD
A three dimensional model of a photoelastic material is made and stresses due to
external load are locked in the model during a stress–freezing process. After the
stress process, the model is cut into thin slices and interior region of the
model is photoelastically analyzed.
Figure 1 Primary and secondary bonds
Some polymeric materials exhibit di-phase behavior, i.e.
Molecular chains are well boned in a three dimensional network of primary
bonds (having longer molecules chains),
A large number of molecules are less solidly bonded by secondary bonds
(having shorter molecular chains) as shown in Figure 1.
At room temperature, both sets of molecular bonds, i.e. primary and secondary bonds
resist external load. Photoelastic model (made of polymeric material) is now loaded
d its temperature is raised. At a critical temperature, the shorter secondary bonds
are broken but longer primary bonds remain intact and carry the entire external load.
Deformations caused by the external load are locked in the secondary bonds. Now the
del is cooled to room temperature, the secondary bonds are reformed again
between the deformed primary bonds and these secondary bonds serve to lock the
deformations (stresses) in these deformed primary bonds.
After the load is removed, the primary bonds are relaxed by a small amount at the
large part of deformation is not recovered. So, the elastic deformation in the body is
permanently locked into the model by reformed secondary bonds. These steps are
Unloaded model at room temperature; primary and secondary bonds.
Loaded model at room temperatures; primary and secondary bonds.
Loaded model at room temperatures; primary bonds.
Loaded model at room temperatures; primary bonds.
Loaded model at room temperatures; primary bonds.
at room temperature; primary and secondary bonds
THREE DIMENSIONAL PHOTOELASTICITY
A three dimensional model of a photoelastic material is made and stresses due to
freezing process. After the
stress process, the model is cut into thin slices and interior region of the
dimensional network of primary
A large number of molecules are less solidly bonded by secondary bonds
At room temperature, both sets of molecular bonds, i.e. primary and secondary bonds
resist external load. Photoelastic model (made of polymeric material) is now loaded
d its temperature is raised. At a critical temperature, the shorter secondary bonds
are broken but longer primary bonds remain intact and carry the entire external load.
Deformations caused by the external load are locked in the secondary bonds. Now the
del is cooled to room temperature, the secondary bonds are reformed again
between the deformed primary bonds and these secondary bonds serve to lock the
re relaxed by a small amount at the
large part of deformation is not recovered. So, the elastic deformation in the body is
These steps are
imary and secondary bonds.
Loaded model at room temperatures; primary and secondary bonds.
at room temperature; primary and secondary bonds

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Fig2: Process of locking stresses
Example: One can describe graphically the behavior of the diphase material by the
spring-ice analogy given by Frocht. In this, at ordinary conditions, the model is made
of a set of springs embedded in ice, as shown in Fig. 3(a). When the model is
subjected to load P, both ice and springs resist deformation. If the temperature is now
raised with the load P still acting, the ice becomes water and the load is carried
entirely by the springs. At this configuration, the model is cooled so that the water
becomes ice completely enclosing the deformed springs [Fig 3(d)]. If the load P is
now removed, the springs try to regain their original undeformed configuration, but
are prevented from doing so by the surrounding ice. They attain some intermediate
equilibrium position [Fig 3 (e)] which does not differ much from the completely
deformed configuration due to the volume of ice and its resistance.
Fig.3 Analog for stress-locking
The importance of this locking in the deformation process lies in a very useful aspect
which can be seen from the spring-ice analog. If the assembly as shown in Fig 3 (e) is

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now cut into thin slices, each slice will retain the corresponding parts of the deformed
springs.
Fig 4 Stress pattern in a slice taken from a stress-frozen model
Experiments with diphase materials reveal that even very thin slices can be carefully
cut and polished without destroying their locked-in birefringent characteristics. It is
this important aspect that is extensively used in three-dimensional photoelastic
analysis. Fig 4 shows the stress pattern in a slice taken from a stress-frozen model.
Scattering of light
When a wave of light which is traversing space meets an obstacle, such as a small
water particle or a dust particle or even a gaseous molecule like that of oxygen, the
obstacle acts as a secondary source and scatters some of the light. If the wave passes
through a cloud of such obstacles its intensity is weakened owing to the loss of light
by scattering. The percentage of light scattered is proportional to -4
, where  is the
wavelength. Considering red light ( = 7200 A0
or 720 nm) and violet light ( = 4000
A0
or 400 nm), the law predicts that violet light is scattered (720/400)4
or ten times
more than red light from particles which are smaller than the wavelength of either
colour. When a clear sky is observed at an angle to the direction of the sun’s rays, the
molecules of air scatter light, and the sky appears blue. This is because the violet end
of the spectrum is scattered more than the red end. At the time of sunrise or sunset the
surrounding region appears reddish or orange because while travelling the great
thickness of the atmosphere the scattering removes the blue rays more effectively than
the red. Hence the transmitted light observed appears red.
Polarization associated with scattering

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Fig.5. Polarization associated with the scattering
Let us suppose that a ray passing through a scattering medium is viewed transversely
so that the line of vision is at right angles to it. The electro-magnetic vibrations
corresponding to the scattered light are transverse to the incident ray. If the incident
ray is unpolarized, the scattered light vibration in the transverse plane will be as
shown in Fig.5. The scattered light that the eye perceives arises entirely from the
component vibrating at right angles to the line of vision, whereas the component of
vibration along the line of vision will have no effect. Consequently, for observation
along OE the apparent vibration is along M1N1, and for observation along OF, the
apparent vibration is along M2N2. Therefore, for direction of observations at right
angles to the incident ray, the scattered light is completely polarised. This
phenomenon of polarization associated with scattering can be made use of as either a
polarizer or an analyzer.
Scattered as Polarizer
Consider a beam of unpolarized light travelling through a material, Fig.6. The
incident light has all possible directions of` vibrations in the wave- front, but the light
scattered in a particular direction at right angles to the direction of incidence always
vibrates at right angles to the plane containing the direction of incidence and direction
of observation.
Fig.6. Scattering as polarizer
Consider the light scattered from point C. If the model Considered is stressed, the
polarized light scattered from this point gets divided into two components along the
directions of the secondary principal stresses in the plane transverse to CE. In
traversing the stressed medium CD, these two vibratory components acquire a certain
relative phase difference. If an analyzer is now interposed between the eye E and D,
the resulting picture is either bright or dark depending upon the phase difference
acquired over the distance CD. if the section that is illuminated is moved from BC to
B'C', the resulting picture as observed from the same E will be different since the

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polarized light now has traversed the stressed medium C'
D. Let us assume that the
directions of the secondary principal stresses '1, '2 do not change over the length CD
or C’D. If N is the birefringence caused over the distance CD, and N + N the
birefringence caused over the distance C'D, then the difference N is due to the slice
C'C = y. Hence, N/y is the space rate of formation of fringes (or birefringence) in
successive planes normal to the direction of observation. It should be noted that the
photoelastic effect one observes is entirely due to the retardations acquired over CD
or C'D and the distance BC or B'C' has no effect (other than diminishing the
intensity).
In this respect, the stress-optic law does not differ from the one used in the
conventional transmission type. However, the major advantage of scattered light is in
being able to obtain the values of ('1-'2) at every point along the path C'D. This can
be seen from Fig.7. By moving the incident light successively along Bl, B2, B3, . . . ,
the birefringence caused over the path lengths ClD, C2D, C3D, . . . , are measured at E.
If N1 is the birefringence due to CID, N2 the birefringence due to C2D, N3 due to C3D,
etc., then
( − ) =
l
(s′
-s′ ) D ( )
where ('1'2) is the average secondary principal stress difference over the length
C2C1 = yl. Similarly,
( − ) =
l
(s′
-s′ ) D
where y2 =C3C2, etc. It should be noted that we have assumed no rotation of '1, '2-
axes along C3D.
Fig.7. Secondary stress along CD
Scattered Light as an Interior Analyzer or polarizer
Let the incident light be now linearly polarized. This light gets divided into two
components along the secondary principal axes at the point of entrance (Fig.8). In
travelling from B to C, these components pass through a stressed medium BC and at

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point C, the vibratory components along the secondary axes '1, '2 will have a certain
relative phase difference.
The particle at C acts as an analyzer (because the light scattered from point C
effectively vibrates at right angles to the plane containing the
direction of incidence and the line of vision), and for an observer along DE, the
resulting point image will have a definite light intensity depending on the relative
retardation acquired by the light components over the distance BC. If the line of
observation is moved to D'E', the resulting picture varies depending upon the
additional retardation acquired over the distance CC'. Now, if CC’ = z and the
additional birefringence added over that distance is N, then N/z is the space rate
of formation of bire- fringence in successive planes normal to the incident light
beam. The resulting light intensity as seen from E or E' is not affected by the
birefringence picked up in the distance CD or C'D', since there is no analyzer between
D and E. It is again assumed as before that the secondary axes do not rotate along the
path BC or BC'.
Fig.8. Scattering as analyzer
C. Scattered-Light Polariscope
A scattered-light polariscope differs in many respects from the conventional
transmitted-light polariscope, and it is therefore usually advisable to construct a new
polariscope for scattered-light applications rather than modify a transmitted light
polariscope. A schematic illustration of a simple scattered-light polariscope is
presented in Fig.9.
In a scattered-light polariscope the light beam is usually projected in the vertical
direction either upward or downward to permit the observation of the scattered-light
pattern in the horizontal plane. The light source must be quite intense because of the

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inefficiency of the scattering process. For this reason a l000 to 1500-Wmercury-arc
lamp or a laser light source is usually employed together with a condenser lens and an
adjustable light slit to provide a high-intensity sheet of light which can be used to
illuminate any plane in the model.
The model is placed in an immersion tank with an appropriate fluid of the same index
of refraction to permit observation from any direction in the horizontal viewing plane.
The camera located on this horizontal plane should be capable of rotation about the
vertical axis of the polariscope so that the scattered-light pattern can be photographed
at any arbitrary angle (x. Moreover, the polarizer located forward of the adjustable slit
should be mounted so that it can be rotated to vary the angle p. Finally, it is
sometimes desirable to locate a compensator or a quarter-wave plate or both in the
light path forward of the model. Mountings for these two elements should be provided
so that they can also be freely rotated.
Fig .9. Scattered light Polariscope.