
Basic Experimental Mechanics 


Caustics 





Basic principles: The shadow
optical method of caustics is an experimental technique which may be used in stress
concentration problems and is particularly useful in the determination of
stress intensity factors. The figure shows a transparent plate in tension
containing a mode I crack. The singular stresses at the crack tip cause: (1)
a reduction in thickness due to Poisson's Ratio effects (2) a change in the
refractive index. If light is incident on the plate, both the thickness and
the refractive index influence the light rays as the light passes through the
plate. If a screen is placed at some distance from the specimen, the light
pattern may be viewed. The light concentration is a caustic curve and
the shadow area is known as the shadow spot. This diagram is in two
dimensions. In reality the rays form a three dimensional envelope of light which
is cut by a two dimensional screen or reference plane in order to view the
caustic. This light deflection due to a stress field is the main principle
behind the method of caustics. Since the shape and size of the caustic are
caused by light deflections, which are due to the change in thickness and
refractive index of the material; and these are due to the stress
singularity; then the caustic shape is related directly to the singularity
and therefore can be related to parameters such as the stress intensity
factor. The method of caustics may be used in any engineering problem where a
steep stress gradient exists. Examples of these include crack tip analysis,
contact mechanics and stress concentrations around holes. Bibliography 1. Theocaris, P S, Elastic Stress Intensity
Factors Evaluated by Caustics, in G C Sih (ed.)
Mechanics of Fracture, Vol. 7, Sijthoff and Noordhoff, (1981) 2. Theocaris, P S, Local Yielding Around a
Crack Tip in Plexiglas, Jnl. of Applied Mechanics,
37, (1970), 409415 3. Theocaris, P S and Razem,
C I, Error Analysis in Evaluating Stress Intensity Factors by Reflected
Caustics, Int. J. Mech. Sci., 23, (1981), 275284 4. Kalthoff, J F, The Shadow Optical Method
of Caustics, in A S Kobayashi (ed.), Handbook on Experimental Mechanics,
Prentice Hall, Englewood Cliffs, New Jersey, (1987), 430500 5. Beinert, J, and Kalthoff,
J F, Experimental Determination of Dynamic Stress Intensity Factors by Shadow
Patterns, in G C Sih (ed.) Mechanics of Fracture,
Vol. 7, Sijthoff and Noordhoff,
(1981) 6. Kitchin, R A and Patterson, E A, The
practical use of virtual reflection caustics, Fat Fract.
Eng Mat. Struct., 16, (6), (1993), 597602 7. CarazoAlvarez, J. and Patterson E.A. Study of contact loads by
using image processing and nonlinear regression with caustics. Proc of Int.
Congress on Exp. Mech., (1995), 812819. 