Experimental Stress Analysis

Prof. K. Ramesh
Department of Applied Mechanics
Indian Institute of Technology Madras

Lecture No. # 07
Introduction to Shearography, TSA, DIC and Caustics

In the last class we had looked at rudiments of hologram interferometry. There, we
pointed out there is a requirement of a reference beam, and also you need double
exposure which impose as stringent restriction on vibration isolation. And you should
also keep in mind holography is the very sensitive technique, where you talk of
displacement measurements of the order of wave lengths. So, even a small disturbance
can affect the measurement. Then, we moved on to speckles and we had seen how
speckles are formed. We had also looked at, what is objective speckles and what are
subjective speckles. And I said in subjective speckle you use a lens, in the case of
objective speckles you do not use a lens. And you normally perceive only subjective
speckles. Because human eyes have a lens, so when an object is illuminated by laser
what you perceive is through a lens. So, it is always subjective. You need to take special
efforts to record objective speckle.
Now, what we will do is will go and see what are the speckle methods that we can think
of and what are its key features different from hologram interferometry.
(Refer Slide Time: 01:48)

So, for the first thing is, unlike hologram interferometry which requires a very high
resolution recording medium, the speckle fringes can be easily recorded by a CCD
camera. It is lot more simpler here also you need a good camera for you to do it. And
what is done is by selecting the appropriate aperture size, the speckles size is easily
adjusted to the size of the pixel of the recording camera for high contrast fringe
recording. So, you have a provision by which you can adjust the optical system until you
get good fringes in your recording medium you have a provision to do that.
(Refer Slide Time: 02:46)

And if you look at speckle interferometry it is again same as hologram interferometry. It
is very similar to what is there in hologram interferometry, and we had seen that
hologram recording is a lens less photography. Once you come to speckles, we record
only subjective speckles, and subjective speckles are recorded by a lens. So, the
difference here is the image is recorded using a lens. And you know the example what I
have taken here is from a memes application, because we had seen whether it is
holography or speckle interferometry, where ideally suited for small scale object
measurements.
(Refer Slide Time: 03:38)

And what you have here is a pressure sensor, and I can change the load here and you can
see the fringes, and first impression you get is they have very low contrast, and they are
not as more as what you get in photo elasticity. They have specular, you will see dots
everywhere and you have collection of dots. So, you have the quiet difficult for you to
extract information. So, in all these speckle interferometric methods people spend lot of
effort on filtering. Filtering is the very important step in speckle interferometry.
(Refer Slide Time: 04:32)

And what you have here is in all these modern techniques they employ computers.
Because of computer processing, the double exposure technique is done digitally. So,
initially you store be initial configuration in a file and use it for viewing the deformed
configuration. And it is easy to see fringes in real time as the model is loaded. So, what
you find here is you are able to see fringes in real time that is because of your computer
processing of data and you have fast computers to process image information quickly,
and it gives a semblance of real time appearance of fringes.
And you know when you want to paste a strain gauge you have to have a elaborate
preparation, same is the case when I go for photo elastic coating application. Compare to
these methods surface preparation is simple, the surfaces is painted white with a matt
finish for speckle formation. You want a specularly reflecting surface. So, you want to
have only a simple surface preparation, but even the simple preparation is not simple in
the real sense, you need to have some practice on applying your white paint uniformly. It
should not have smudges on the surface, when you come to experiments you need to
develop skill. The methodology is discuss in comparison to other techniques this method
is simple, but even a simple technique requires some kind of a skill development and
skill development comes only through practice. You cannot do it on one day, one day
you wake up and then you want to go and do speckle interferometric is not possible; you
need to have some training and perfect the steps involved in this, then you go and make
measurement, your measurements will become reliable. So, simple or difficult is a
relative term right.
(Refer Slide Time: 07:11)

You have to get a uniform thin coating on the surface and we can also have a look at the
close up view of this, and this is actually a microscope which is used, and you have a
pressure sensor which is very, very small, and you see the fringe pattern of this, and this
was done in Professor Kothiyals lab, applied optics lab, IIT madras. And which you
want to have further details you can go to this reference, and you know there is always a
discussion in academic circles whether to label a method as speckle interferometry or
holography. This debate is one they have called it as TV holography here, 3-D surface
profile characterization and so on. So, this debate is always on.
(Refer Slide Time: 07:51)

And in speckle interferometry also you can get the displacement vector. And I had
mentioned earlier when you get a displacement vector interpretation becomes little more
complex. And you need to have methods and if you go to this literature they will talk of
something like sensitivity vector and how to extract data these are all mathematical
details. We are not getting in to those mathematical details at this stage. Our focus is
mainly to appreciate the principles involved in various techniques and also look at
broadly for which class of problem these techniques are applicable, and also limitations
broadly speaking what way these techniques look and how these can be compared; some
kind of information which will aid you to arrive at appropriate technique for the given
application.
So, what you find here is mostly you will get out of plane displacement measurements,
but you can get the displacement vector by choosing appropriately the illumination
viewing angles and also constraining the object motion. This is common to both
hologram interferometry and speckle interferometry. We want to get u and v
displacement, and you have to choose the illumination, viewing angles and also
constraining the object motion all these have to be used for finding out specific
components of displacements. On the other hand moir by choosing the grating your
interpretation becomes simple. Here it is involved, because you collect more information
and so you have to be systematic in filtering out what is in that you need.
(Refer Slide Time: 09:48)

And another popular version of speckle interferometry is shearography, and this is a very
useful technique for non destructive testing. In fact, for honeycomb panels, this is the
very popular technique with composites becoming very important structural materials;
where again you have problem of delamination and techniques like this go a long way in
identifying. And this shows a shearing element will have a closer look of it.
(Refer Slide Time: 10:30)


So, what I have is I have a beam splitter. One ray goes straight and hit this mirror and
comes back, the other ray goes there, and get sheared and on the image plane you have
for one incident ray two rays are seen. Same thing we can watch it for the second ray. So,
I get one ray from the mirror two and I get another ray from mirror one. You make a
sketch of it I will do the animin repeat the animation again for you to understand how
you perceive this. And because of the shearing action you essentially measure this slope.
You measure the slope essentially. So, you have the ray goes and hits its mirror, this is
kept perpendicular and the mirror one is slightly tilted. So, beam splitter sends one ray to
this mirror and sends other component to this, and whatever comes from this because of
the tilde it gets shifted, and this is called it is also said it is shear to this point. So, for
each incident ray, you will have two rays impinging on the image plane. And we will just
have a look at the animation again.
And this is what you see here, I have the ray goes straight and hits this mirror. Another
component goes to mirror one and this gets shear. And in shearography, the vibration
isolation requirements are less stringent that is why it is become a very popular technique
in an industry. And many manufactures of giving out shearographic equipment. It is used
routinely for non destructive testing of several composite panels, honeycomb panels and
so on.
(Refer Slide Time: 13:08)

And when you do this what you get, you get essentially slope fringes and we also noted
that these are butterfly fringes, because of the shake, because on the shop floor they
would like to classify this as butterfly fringes for easy identification. In fact, it is dou w
by dou x contours. So, what we find here is by introducing a lateral shearing element in
the optical path, one can get fringes corresponding to the slope of out-of-plane
displacements that is what you get here. And this, there is nothing like one is a reference
for the other, other the is reference for this and nothing like a single reference beam for
fringe formation and hence robust for an industrial scenario.
So, what you find here is shearography is a robust technique compare to speckle
interferometry or hologram interferometry. If you put a shading element it makes your
life lot more simpler. And you get (( )) information, you get only a slope information you
do not get out of plane displacement. So that is the difference. It makes your experiment
simpler at the same time gives your different type of information. So, we have so for
seen quite a few techniques; what is a physical principle and what is the essential
difference between them.
(Refer Slide Time: 15:04)

Now, we move on to another experimental technique which is again a whole field
technique which is known as thermoelastic stress analysis. It is a whole field technique
and it gives the variation of sum of principle stresses under sinusoidal or more recently
random loading, because if we look at the history initially it was developed for sinusoidal
loading. Once the technique has mature people are found methodology to extract data
even for random loading situations. And it does not give sigma 1 plus sigma 2, it gives
variation of sigma 1 plus sigma 2 that is a difference. So, you have to have a cyclical
loading on the object and you find out what happens, and here again you are a employing
a physics, we will see what is the physics behind this technique.
And the name of the technique comes from the physical principle; one common danger is
thermoelastic, if I want to find out stresses due to thermal loading you can directly use
the technique; there is a misnomer, you cannot do it like that depends on the principle on
which it is based upon. So, that is what is mentioned here the name should not be
confused to mean that it is a technique to measure thermal stresses; it is not so. What the
physical principle is, under cyclic loading, the local temperature of the specimen changes
and this change is very small, you cannot go and touch and feel it, which of the order of
0.001 degree centigrade or so, so very small measurement from temperature point of
view. And this is recorded by expensive infrared cameras for data interpretation.
So, people have identify and see as technology as advanced, we are able to measure even
small changes in temperature. People identify the small changes in temperature takes
place and this is exploited to reveal information of the stress field and it gives a
particular kind of stress field, and it was originally develop for high temperature
application, because you cannot go near and then make any measurement and people
wanted to have non-contact measurement and they want to have a technique which could
work at high temperatures particular for gas turbines when they work at high temperature
they want to make measurement. And what you find here is the temperature change is
very small, we have also looked at while we looked at strain gauges. We were talking of
micro strain and that is 10 power minus 6, you are looking at 10 power minus 6 of
change in resistance or change in the strain. When you come to temperature were able to
go only to the order of 10 power minus 3, but even this is very, very small.
And if you look at moir or if you look at photo elasticity or you hologram
interferometry, you see the fringe contours, after processing you see the fringe contours.
In a technique like this you do not see fringe contours as such; it is all plotted from the
infrared camera result post processed that is why you get the result. Here the technique is
also slightly different you have to do post processing for you to look at the kind of
information that you have recorded.
(Refer Slide Time: 19:09)

And another important aspect here is you use thermodynamical principle for data
interpretation. So, as you go advanced you also have more complicated mathematical
development for you to interpret experimental data. And you have be very careful in
conducting the experimental method, you should be worried about other thermal sources,
you should suppress those information, because you are essentially recording emissivity
of the surface whatever the emissive characteristics. And if you have other sources of
thermal disturbance they have to be suppressed. So, the experiment has to be conducted
very carefully. And you need to maintain adiabatic conditions for successful data
interpretation. And this adiabatic condition comes in the form of what is this frequency
of loading. There is a recommendation, what is a minimum frequency of loading you
have to maintain. So, you have to look at this, so the requirement of adiabatic conditions
imposes certain restrictions on how you do the experiment.
And the main advantage here is the technique is non-contact. And again you know when
there is a small advantage you should take note of it. It has a relative ease of surface
preparation, it is again a relative term. And here what is the kind of surface preparation
you do? You have to improve the emissivity of the surface, a thin coat of black paint is
coated on the specimen. It is not white paint like in speckles, but it is the thin coat of
black paint. And again it is a comparison that is what is summarized here. This is the
only surface preparation needed which is much simpler than to provide birefringent
coating for reflection photoelasticity or bonding specimen grating as in moir
interferometry so on and so forth. We can sight many such comparisons that is not
something difficult. So, what you find here is you have to apply a thin coat of black paint
and as I have said earlier even to get a thin uniform coat you need to develop skill.
Though it is simply said it is a comparatively less difficult.
But even this you will have do a with care; unless you do it with care you will not be
able to do it; you will not be able to get reliable experimental results. And people have
combine thermoelastic stress analysis with photoelasticity and try to find out stress
separation and all those exercises have done. And it is (( )) that you have a look at what
is the measurement scheme employed here.
(Refer Slide Time: 22:17)

I will give an idea how you go about and what do you do is as I said you do not see the
information directly; the output of a thermoelastic system is the result of correlation
between observed infrared response of a loaded body and the loading event. So, you
have to make a correlation and you have do post processing of it, then displays the result.
So, I need a signal to a record how the body is loaded. So, you need a reference signal.
So, while performing an experiment, one needs to record a reference signal which is
representative of the applied load. This is done this can be done in various ways that is
what is listed below.
And what I find here is the reference signal could come from a surface strain gauge
mounted on the specimen, or from load transducers or from the signal generator used to
drive the loading event. So, what I need is I need a reference signal; I need to have a
correlation between the loading event and the recording phenomena. So, for recording
the loading event we need a reference signal that could come from a surface strain gauge
or that could come from a load transducers or from the signal generator. This idea would
become clear if you have a look at how the whole arrangement is may ready for a
thermoelastic measurement that we will see immediately.
I will be in able to write write down this, you know since all these statements are
available on a readymade platform as I am not going and writing. You may have to take
abbreviated information of this rather than long sentences; you may write it do that when
you want to take down the notes. I will also try to go as slowly as possible. So that you
have ample time to record this information. And what we will see is these ideas will
become clear if you look at how a thermoelastic test is done. This is depicted in the line
sketch here.
(Refer Slide Time: 24:55)

And levels look at part by part. I will also give you sufficient time for you to take down
this sketch. You make your sketches little brief, you will not have to put these pillars
with lot of effort minimize that. The essence here is I have a specimen the region of
interest is painted black and this arrow shows that I am applying a cyclical loading, I do
up and down, I do a cyclical loading. So, the model is subjected to a cyclical loading.
And this event is recorded by a thermoelastic camera and mind you thermoelastic
cameras are very expensive, it is not like visual range cameras in a thermoelastic even
the lens is very, very expensive, and the other restriction is you need to have better
cooling systems for you to cool down the thermoelastic camera, because the temperature
generated because of that can give Fourier signal. In fact, they have a specific engines for
cooling this camera, you have certain cycles are used for cool this camera. So, what I
have is I have a specimen mounted on a loading frame which is cyclically loaded and the
region of interest is painted black, and you have a thermoelastic camera which focuses
on this. And you get a response from the thermoelastic camera. It could be a response
something like this.
And from the load cell of the testing equipment, you also get a reference signal. So, what
you need to do is in thermoelastic stress analysis, you need a reference signal how the
system is loaded. You want to correlate whatever the results that you get with respect to
a reference signal. The camera by itself does not give you any information for you to
visually look at. So, it has to be post processed and then display appropriate. So, what I
have is I have a data processing unit which takes the reference signal, and which gives
you the output once you take it to the computer, you could display this result in a fashion
which is convenient for you to interpret. So, what elements you have, you have a loading
system, you have a thermoelastic camera and this is taken to the data processing unit,
you also have a reference signal and you post process this data and display the result. So,
you have a plate with the hole with sigma 1 plus sigma 2 contours. They appear like this.
(Refer Slide Time: 28:13)

We can also have a larger picture of this. This is how you have the a display and it is the
post processed display. And this is the case when you go to the next technique, here
again you do not see the fringe patterns visually. You only you have to post process the
data and displayed in a fashion convenient for you to understand. So, what you find here
is more and more computers are used in experiments that becomes evident in some of
these sophisticated techniques, and if you go and look at the price it is (( )) cost, because
of the thermoelastic camera and also the whatever the lens system that is used, and if you
look at the resolution not as comparable to as what you get from a visual range optical
system. It is in operating and infra red regime, so very expensive. So, unless you have
very high level of funding, you would not be able to do a test of thermoelastic stress
analysis.
(Refer Slide Time: 29:30)

And the next technique what we will go and look at is one of the very new and emerging
technique called Digital Image Correlation. You know the name itself is very interesting
it is the image correlation; we have seen in the previous methodology, there is also some
other type of correlation was taking place between the reference signal and your
thermoelastic response. And this uses speckles and these are called white light speckle.
In the speckle method, what we did was we had a laser beam impinging of the model,
and you had speckles develop naturally, it was not artificially created. If you have a
specularly reflecting surface, you had speckles, because of laser illumination and that
was used for all the measurement. And this is the offshoot of that kind of an approach.
Here you have this speckles arbitrarily done; you have the speckle arbitrarily done. It is
done externally on the specimen under consideration, artificially it is done, and you use
white light for data interpretation. So, you can really cover large areas comfortably. And
you have to look at this is the fine example of a technique where advancements in
statistical data processing is fully used for interpretation of experimental data. So, it is
more of I always tell that is more of computer processing and less of seen the joy of
looking at fringe patterns in real time; you will not see fringe patterns real time in this.
You will only see dots speckles on the surface, they have to be post processed and they
have to be plotted in a fashion convenient for you to interpret. But this is becoming a
very, very important technique, because of development of newer materials. There are
certain materials you will not be able to do experiments otherwise.
And as again, this is an optical technique. All optical techniques are buy and launch non-
contact in nature. And here again you know you do not need a complicated surface
preparation, but I should caution the speckle formation is not simple. You have to have
randomness, you have to have particular characteristics and formation of speckles again
you have to develop skill and size of the speckle matters, because you can do for multi
scale analysis depending on the scale on which you operate, you need to have that
correct size of the speckle. So, though it said surface preparation simple in relation to
strain gauge where you will have several steps for surface preparation. Compare to that
here you have only put the speckle by a spray gun, but that requires again skill.
And what is the information it gives; it provides displacement, you have 2D DIC which
helps to find in-plane displacements and you also have three-dimensional DIC which is
useful for metrology applications as well as for determination of the three components of
displacements; u, v and w. So, this is the your directly getting displacement information.
And it uses quite a bit of data processing which is not seen in other experimental
techniques. Here more of number fringing is done, and when you go to 3D DIC you have
(( )) images recorded with two cameras, calibration is very, very intensive and people
have developed proprietary software how to the calibration. So, the technique is
emerging that is the way you have to look at it.
(Refer Slide Time: 33:57)

And what I have here is for large deformation problems the technique has been used
successfully that is how people start we have seen when we looked at moir, people had
grid methods and then from the grid method they graduated to having the grid, put a
circle inside, look at the stress direction, then they refined it by putting two grids one
over the other that is why moir was developed. And then if I am geometric moir, they
graduated to moir interferometry, where they could go for finer and finer displacements.
And digital image correlation as successfully applied for large deformation problems.
And these days we do encounter in our design large deformation being allowed, and so
you need to have techniques which do this.
And you also have several new materials cellular materials like polymeric or metallic
foams in automobile manufacture they want to put metallic foam in your structure, so
that it absorbs energy when you have a collision. See in earlier days and stream engines
were developed, 15 kilometers per hour was considered terrific. Now, you travel at 350
kilometers per hour. And when you increase the speed any collision becomes dangerous.
So, you need to have productive mechanism for you to have a and people all thinking of
using metallic foams, syntactic foams and all this materials are very peculiar even to find
out the material property they cannot be a conventional test and they depend on digital
image correlation to find out even the material property.
So, the development of new material, a force also the development of newer techniques
for data gathering and interpretation; and the technique is very simple, if you go from
one scale to another scale the methodology is essentially same only thing is your optics
has to be sensitive enough and your speckle size should be adjusted suitably. In view of
that the technique has been extended to study deformation at multiple length scales.
You know could today is the I mean these days we talk of nano mechanics. So, nano
scale studies have been made in conjunction with atomic force microscopy, where you
have a whatever the beam that we used inside, if you want to make measurement, people
have used digital image correlation and we are able to do even nano scale studies.
Holography is also applied for nano scale studies. So, the advantage here is once you
have the software developed for image correlation by varying the size of the speckle and
also your optical arrangement, it is possible for you to go to smaller and smaller scales or
even large scales. People also use image correlation for finding out the buckling behavior
of wind mills, you have huge wind mills; now renewable sources of energy people are
paying attention, you have very large wind mills have come and for that those blades are
sensitive for buckling, and you have a very large area, and you need to find out the
buckling whether buckling takes place or not and people use image correlation.
(Refer Slide Time: 37:50)

And being an optical technique they also find out how to find out information at interior
planes in transparent models. And you should also accept at this stage of development,
the accuracy of the method is not very high. So, that is the scope for research. So, if the
accuracy is not high; this is the ideal area where people can refine; it is a very useful
technique to get some information where conventional techniques fail such as at very
high temperature measurements. People have done, people have done at very high
temperature whatever is the particularly when you are looking at re-entry vehicle
systems, in space technology they look at re-entry vehicle system, they all subject to very
high temperatures. And unit has some measurement and people have attempted using
image correlation, because of non-contact nature and they have been able to get useful
information for the design. And if time permits we make spend little more time on image
correlation - the main body of the course.
(Refer Slide Time: 39:06)

Now, we move on to another interesting optical technique which is the method of
caustics. And what I want to mention here is caustic is the envelope of light rays
reflected that is what you have seen earlier in the beginning of the course. It can also be
refracted by a curved surface or object, or the projection of that envelope of rays on
another surface.
(Refer Slide Time: 39:41)

So, what you see here is, I have a caustic by reflection, I have a tea cup, and because of
this curved nature and with appropriate lighting, light hits on this curved surface and gets
reinforce and you see a silver line as a (( )). This is by whatever the line that you get, the
principle is called caustics. The same name is also given to the optical technique; we use
it for measuring high stress variant problems. But this is the physical principle.
(Refer Slide Time: 40:19)

And when you go to a pond you may also see a nice structures like this and all these
silver lines what you see then, they are all because of the phenomenon of caustics. Now,
you can go and see you might have noticed it, but you may not have named it; now, you
can go and see these are all nothing but caustics. So, caustics is seen in a tea cup or on
the surface of a pond. What is its use for me in stress analysis? See if I have to use even
there is join looking at all these patterns and name them as caustics, but I must also have
its utility from the stress analysis point of view; how it is seen; we will have a look at it,
we will also elaborate up on it.
(Refer Slide Time: 41:06)

First we look at the what is the principle, and this is what is shown here, I have a
aluminum specimen which has a crack and you see a dimple formation here. First we
will see this then look at the reason behind it.
(Refer Slide Time: 41:06)

Can you see the dimple very clearly at the tip of the crack, you use see a very large
deformation here, and this occurs when I apply load. When I this is in three point
bending, when I apply the load I have a dimple formation. So, what you find here is
when a plane specimen under in plane loading deforms, the thickness of the specimen
changes due to Poisons effect. If I do not have a crack, I would not see the change in the
thickness very prominently. Because of the crack which is the high introduces high stress
concentration, the change and thickness is also very significant and that is seen as a
dimple.
So, in this is particularly seen in zones of high stress concentration, the effect is
pronounced and when you look at here when I send the collimated beam of light I can
have a transmission arrangement as well as the reflection arrangement. If I have a
transparent model then it behaves like a divergent lens and the light rays whatever I send
it is gets deflected. And it forms a particular pattern on the speed. Now, you relate what
causes the deviation of that rays, by relating these two you will be in a position to find
out what cause this change and hence the level of stress concentration. So that is the
basic principle behind it.
(Refer Slide Time: 43:06)

As I mentioned earlier it is applicable to transmission as well as reflection modes - the
reflection arrangement is suitable for studying metallic specimens. This also I have said
that you need to have techniques to find out for models as well as prototypes,
photoelasticity has transmission photoelasticity and deflection photoelasticity. So, in
method of caustics you can do it on transparent models as well as on opaque - metallic
specimens. And particular in fracture mechanics when people wanted to understand the
plastic deformation at the crack tip caustic really helped and it really helped for people
who know little bit of fracture mechanics establishing the concept of HRR field-
Hutchinson-Rice-Rosengrenfield near the crack tip was very well established with the
method of caustics. And what I will do is I will elaborate this, this aspect of the specimen
becoming a divergent lens, we will have a look at it and this I am going to the chapter on
caustics.
(Refer Slide Time: 44:28)

I will just show you how this deformation is recorded. So, this is the specimen I have, I
have a stress concentration here, I pull this model and from this from this you know it is
exaggerated that you see a thickness change very prominently noted near the stress
concentration. Stresses alter the optical properties of a transparent body; you will also
have change in the refractive index. If it is a metallic specimen, there is no question of
refractive index getting changed. In the thickness change because of Poisson effect is
very prominent near the stress concentration zone. And if I use the transparent model
most of the transparent models which we use also birefringent. So, the refractive index
also has an influence. So, the combined influence of these causes the formation of
caustics. So, what is see here is I have an incident ray and it get transmitted, it does not
go straight it gets deflected it gets deflected.
And because of these changes when I send a beam of light I will get a shadow essentially
behind the specimen in transmission arrangement and on the reflected this one you will
see on this plane. And you have certain parameters, you do not at worry about than now,
when you go into mathematical development which may be may not do in this first level
course. So, you have to take those parameters appropriately. And here again you have
shown, for a transmission arrangement this is very clear, for the reflection arrangement
you have this dimple very prominently seen. So, when a send the ray will you get
reflected light (( )), and because of this you will have a family of rays emerging and that
forms a shadow. And if possible I will also illustrated by a simple experiment, but before
we going to the experiment, we will also see take a specimen with crack, and make a
very simple sketch of it, and look at what happens. I will just show that animation for a
minute then we move on to the experiment.
(Refer Slide Time: 47:10)

And this ex this is very formation of caustics is very clear; just observed the specimen.
So, what I have here is I have a specimen with a crack, I have parallel beam of light
impinging on the specimen, and because of the Poisson ratio effect the light does not go
straight. If I do not load the model, the light will go straight and light gets deflected like
this. And because this gets deflected, you get a shadow region on this screen, and you
have reinforcement of these rays form a silver line enclosed in the shadow line. Because
that is found becomes of the principle of caustics, you call the entire methodology as
method of caustics; we derives the name from that. So, you have a family of rays which
reinforce and give you a silver line. Is the idea clear? And what we will do is you can
actually illustrate caustic by a very simple experiment even in the lecture class.
And what I have here is I have a I have a polyurethane specimen, because this I can
stretch easily and I have a crack, I do not think it is very clear the may be I will put a
white background, I will put a white background you are able to see the you are able to
see the crack here you are able to see the crack here and I do not whether the camera is
good enough to show the If I stretch it I will see a dimple that is getting formed. I will
get a dimple being formed at the crack tip. Even visually you can see even visually you
can see, you can have a dimple formed at the crack tip and I pull it you will see the
dimple, and if you are not able to see the dimple we will see, we will send a laser beam
of light and then find out what happens. So, what we will do is, can I have one person
come and help me.
(No audio from 49:27 to 49:38)
So, what I have here is I have the model here, and I will send the laser beam of light it is
not loaded, I see that has a point, it is load this specimen. And you will find that the rays
are getting deflected the rays are getting deflected. The rays are not going, because I am
just doing it with hand I am not able to show you the shadow completely. But this is
what happens. We are able to see that the rays are not going straight, but that they get
deflected. And if you come here, if you look at the sketch again, what you have here is
you have this stress concentration and rays get deflected. And if you actually perform the
experiment you will get the shadow like this; we will have a look at a (( )) moment I will
show you this.
(Refer Slide Time: 50:39)

And this is a caustic is shown for different problems of stress concentration. It is a semi
infinite plate with a concentrated load. This is a plate with a hole, you have a figure of 8
and this is a plate with a crack. I have the crack here and I have a caustic envelope like
this. So, you have a shadow bound by a silver region. And you can see very clearly I
have a shadow; this is bound by a silver region that what you have. And this is the
caustic shadow for a mode one crack.
So, you send a beam of light you get a shadow; you do not get light pass through and
there is mainly because you have the specimen behaved in a fashion where you have
thickness change. So, the light whatever the light rays impinged on it, it diverged; it
behave like a divergent lens. And you do not have a light here and that becomes shadow
and that is what you see in the screen. And this is what I try to show and in fact, you can
do it (( )) very carefully will be able to see it, your hands are shaking you are not able to
see that in the glass and So, it is a very interesting phenomena. So, what will have to
keep in mind is if people find out the physics they are waiting to exploit and developing
(( )). And this has found very good application the early development of fracture
mechanics to establish HRR field, this was a very ideal technique. And
So, in this class what we have looked at is we have looked at we continue our discussion
on speckle interferometry, we saw what is shearography, then we moved on to
thermoelastic stress analysis. I caution that you should not interpret that this is meant for
finding out stresses due to thermal loading. You it exploits the temperature change and
finds out the information of variation of sums of principle stress. When we looked at
image correlation I said it is one of the very nice emerging techniques. It is also
becoming a general purpose tool like strain gauges and photoelasticity.
As of now the equipments are little expensive and also this software is proprietary in
nature, people have developed their own software, they are becoming cost effective.
Then we also saw very interesting aspect of how caustics is employed to reveal high
stress gradient information, it is not a general purpose tool. If you use image correlation
it is a general purpose tool, if you use photoelasticity it is a general purpose tool, if you
use strain gauges that is also a general purpose tool. The moment you come to caustics it
is particularly sensitive to high stress gradient information. And I have shown the caustic
shadow for three problems; one is for the semi infinite plate with a concentrated load,
plate with a hole and the third one is plate with a crack stretched. Thank you.