Applications of scattered light photoelasticity to study the influence of elastic constants in fracture mechanics and contactstress problems

Abstract

Among the different experimental methods available to explore the state of stress in a general three-dimensional body, photoelasticity occupies a primary position. However, the analysis of stresses in a general three-dimensional model by transmission light photoelastic techniques, in a non-destructive manner, is complicated because not only do the magnitudes of the secondary principal stresses vary along the light path, but their directions also vary. Consequently, it is not possible to determine the distribution of stresses along the light path in a general model by analyzing the outcoming light ellipse or the integrated retardation. In order to analyze a general three-dimensional model without resorting to the freezing and slicing process, one has to take recourse to the scattered-light method. The techniques of scattered-light photoelasticity have been well established and applied to a variety of problems. These techniques, as practiced today, are slightly involved.

The main objectives of the present investigations are: (i) to develop a new scattered-light technique which dispenses with some of the complications involved in the existing methods and renders the technique simpler and faster; (ii) to prove theoretically that the conventional methods of finding the photoelastic and characteristic parameters are particular cases of a general minimum-light method, giving positions of the optical elements in a polariscope; (iii) to study the influence of elastic constants on the nature of stress distributions in three-dimensional isotropic elastic bodies under non-accelerating stress states; and (iv) to establish the potentialities of the scattered-light technique as an effective non-destructive tool in the investigation of interior stresses in general space problems, with special reference to fracture mechanics and contact stress problems.

Several methods have been suggested for the determination of the photoelastic information in the analysis of three-dimensional problems using scattered-light photoelasticity and are adopted in the present investigations. In these methods, either the model under test or the sensing unit which monitors the scattered-light intensity, or both, have to be rotated. This essentially requires that the model under test be submerged in a liquid of the same refractive index as the model material to overcome the effects of refraction of light as it enters and emerges from the model. The rotation of the scattered-light sensing unit, like a photomultiplier tube centered about the beam of light, also demands high precision. In the present research work, a new scattered-light method is proposed which dispenses with the above necessities, and the information needed to determine the state of stress is obtained with the model as well as the direction of observation fixed. The details of the new method and its advantages over the existing methods are described in detail.

In conventional photoelasticity, it is customary to start the tests from preset positions of the optical elements to find the photoelastic parameters. For example, the plane polariscope set-up to determine the isoclinic parameters, and the circular polariscope with Tardy’s and Friedel's arrangements to determine fractional fringe orders, are standard techniques in photoelasticity. In these methods, one starts from preset positions of the optical elements (i.e., oriented initially at some fixed positions). In the present investigation, a detailed analysis is carried out to show that the photoelastic parameters can be determined by a simple process of iteration starting from arbitrarily oriented optical elements in a polariscope. The final positions of the elements give absolute extinction of light at the point of interest. The analysis shows that the existing conventional methods of finding photoelastic parameters are particular cases of a general minimum-light method giving positions of the optical elements.

Within the framework of linear theory of elasticity, it is shown that the stress distributions in a general three-dimensional isotropic homogeneous body depend on a dimensionless combination of elastic constants, particularly on Poisson’s ratio. However, the extent to which Poisson’s ratio influences the stress distributions has been a point of much discussion. In the present work, investigations were conducted to study the influence of elastic constants in two- and three-dimensional elastostatic problems involving singular stress distributions near geometrical discontinuities and in contact stress problems. For purposes of investigation, tests were conducted on four sets of araldite models: the first three sets of models contained sharp grooves and slots, and the last set consisted of a cylinder pressing against a plane surface (under normal load) producing contact stresses. One model from each set was subjected to live loads at room temperature conditions and investigated. Under room temperature conditions, the material has Young’s modulus, E=28,000 kgf/cm² E=28,000kgf/cm², and Poisson's ratio v=0.51 v=0.51. A second set of geometrically similar models were taken from each group. These models were subjected to conventional stress-freezing processes and later investigated, without cutting them to slices or sub-slices, using scattered-light techniques. Under stress-frozen conditions, the material has E=870 kgf/cm² E=870kgf/cm² and v=0.49 v=0.49.

The results of the two sets of models were compared to study the influence of elastic constants.

The importance of stress-intensity factor is well known in the field of fracture mechanics. Stress-intensity factor is a parameter which represents the intensity of stress in the near vicinity of a crack and is a function of the applied load, geometry of the structure, and the crack. A knowledge of the stress-intensity factor permits one to assess the residual strength and life of the structure when it contains cracks.

In the present work, the results of a series of experimental investigations conducted on two- and three-dimensional photoelastic models containing geometrical discontinuities in the form of cracks and crack-like defects on the surface as well as in the interior of the bodies are reported. The techniques of scattered-light photoelasticity were used advantageously to determine the stress distributions near the discontinuous zones. The objectives of the investigations were to determine:

(i) the stress distributions near crack tips; (ii) the thickness-wise distribution of stresses in three-dimensional models to bring out the distinction between plane stress and plane strain situations; (iii) the influence of elastic constants ( E E and v v) on the stress distributions in the presence of cracks; (iv) the stress distributions near an interior crack tip in a three-dimensional body; and (v) methods to evaluate stress-intensity factors using scattered-light photoelastic techniques.

Investigations were conducted on models (with cracks) with stresses locked-in, as well as on models under live-load conditions. The results obtained were compared to study the influence of elastic constants on the singular stress distributions near crack tips and on the corresponding stress-intensity factors. The results obtained have also been compared with available analytical solutions.