1.  Attended and presented a paper in Tenth Canadian Congress of Applied Mechanics



Venue: University of Western Ontario, London, Ontario, Canada, N6A 5B8













A campus view of University of Western Ontario


Date: June 2-7, 1985

Paper Title: Analysis of a Line Contact Problem Using Scattered-Light Photoelasticity


Abstract of Paper


A large number of practical problems are not amenable to the theoretical analysis. Consequently, the experimental methods in stress analysis, such as photoelasticity are assuming greater prominence in engineering design. In conventional photoelastic processes, general three-dimensional models are tested under stress frozen conditions, i.e., the stresses are locked in the model at the critical temperature of model material. For stress-frozen model at critical temperature, the elastic constants (E and u, the Young’s modulus and Poisson’s ratio) which affect the stress distribution [1] are entirely different from those of the prototype. Similarity in stress distribution can be obtained by suitable adjustment of load with respect to Young’s Moduli, but no such adjustment is possible to compensate for the differences in Poisson’s ratio. The objectives of the present investigations are:


1.  to determine theoretically (i.e., based on Thomas and Hoersch solution [1]) the influence of Poisson’s ratio on stress components in a line contact problem and experimentally verify it; and


2.      to compare theoretical solutions with experimental results and to find to what extent the theory is applicable to finite bodies.


For purposes of investigation, tests were conducted on two sets of models (cylinders pressed against rectangular blocks under normal loading conditions). Figure 1 shows the geometry of the models that were investigated. One set of the models was subjected to live loads at room temperature conditions and investigated. A second set of geometrically similar models was subjected to the conventional stress freezing process and later investigated. Table 1 gives the details regarding applied loads and properties of the material.





















                                             Table 1: Material properties and applied loads


LL model

SF model

Normal load transmitted through

the line of contact (kgf)  



Young’s Modulus (kgf/cm2)



Poisson’s Ratio  



Material fringe value (kgf/fringe/cm)

(for the He-Ne laser, λ = 6328 A0)



                                                             LL: Live Load; SF: Stress Frozen


The models are made of hot-set araldite material composed of CY-230 resin and HT-901 hardener taken in proportions 100:45 by weight.


The ratio of the load applied to the live-load and stress-frozen model was kept equal to the ratio of their Young’s moduli so that the variation in stresses due to a change in Poisson’s ratio alone could be studied.


As already mentioned, Thomas and Hoersch solution was used in the theoretical investigation. Their general solution was simplified for the line contact problem and for the geometries of the models investigated.  The principal stress distributions along the line of symmetry i.e., along z-axis (Fig. 1) were evaluated for the two values of Poisson’s ratio, u = 0.31 and 0.49 (i.e. for live load and stress frozen models respectively). The results in the two cases were compared to study the effect of Poisson’s ratio on stress distributions.


In the experimental investigations, the techniques of scattered-light photoelastic were used advantageously since investigations can be carried out (in a completely non-destructive manner) on models under live loads as well as on models with stresses locked-in.  The currently available scattered-light techniques completely take care of the problem of rotation of secondary principal axes along the light path using the concept of optically equivalent model and enable one to determine the associated photoelastic parameters along the light path using which one can calculate the corresponding secondary principal stress differences and their axis [2]. A photographic view of the scattered-light polariscope is shown in Fig. 2.























Fig. 2 Photographic view of scattered-light polariscope


The theoretical and experimental results were compared to study the influence of Poisson’s ratio on stress distributions near the area of contact. The results also revel the extent to which the theoretical solution developed for the infinite medium is applicable to finite bodies.


The accuracy of the results obtained shows the potentials of scattered-light technique as a powerful non-destructive experimental tool in the investigation of interior stresses in three-dimensional bodies.




1.     Thomas, H.R. and Hoersch, V.A., ‘Stress due to Pressure of one Elastic Solid upon Another’, Univ. of Illi. Engg. Expt. Station, Bulletin No. 212, July 1930.

2.     Srinath, L.S. Godbole, P.B. and Keshavan S.Y., ‘A New Scattered Light Method to Determine Stresses near an Interior Crack-tip’, Proc., IUTAM Symp. On Optical Methods Mech., Vol.2, pp 775-781, (1962).



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