J. W. Dally

Photo-orthotropic-elasticity

A method of producing transparent model materials for photo-orthotropic-elastic studies is presented. This material fabricated from glass fibers and a modified polyester matrix exhibits continuous relatively smooth fringe patterns which are linearly related to the state of stress. As such, the heterogenous material can be treated as a homogenous medium with orthotropic properties.Three photoelastic constantsfL,fT andfLT are necessary to describe the photoelastic response of the orthotropic materials to a general state of stress. Methods are established for predicting these photoelastic constants from the properties of the constituents. These methods are based on stress proportioning between the fibers and the matrix and upon the linear summation of the retardation from each constituent. The relations derived forfL,fT andfLT were verified experimentally and found to be in close agreement with measured values.A stress-optic law is derived on the basis of stress partitioning between the two constituents in a unidirectionally fiber-reinforced laminate. The adequacy of this stress-optic relation is confirmed by experimental verification. Comparison of this stress-optic relation with the expression advanced by Pih and Knight shows the validity of their initial concepts but the inadequacy of their partitioning functions. Detailed comparison of the stress-optic law with the analog relation proposed by Sampson shows excellent agreement. Indeed, the use of Sampsons stress-optic law is recommended and the law based on stress partitioning is to be considered as a fundamental theoretical proof of the Sampson relation. Finally, the applicability of Sampsons stress-optic law to bidirectionally reinforced materials was confirmed with a thorough experimental verification.

Recording dynamic fringe patterns with a Cranz-Schardin camera

The requirements of a high-speed recording system in dynamic photoelastic studies are closely met with a Cranz-Schardin camera. This camera, which operates at framing rates between 32,000 and 815,000 frames/sec, is capable of resolving a dynamic fringe pattern with a fringe gradient of 20 fringes/in. traveling with a velocity of 75,000 ips. Design details of the Cranz-Schardin system are given, and typical results obtained are illustrated.

Application of birefringent coatings to glass-fiber-reinforced plastics

The application of birefringent coatings to plane-stress problems associated with orthotropic-glassreinforced plastic materials is treated. The improvement in the sensitivity of the birefringent-coating method due to the high strength and low modulus of the glassfiber-reinforced plastic materials is noted. Next, the effect of a mismatch in Poissons ratio between the specimen material and coating is examined and a correction factor is developed which permits determination of boundary stresses even when the mismatch is large. Finally, the stress-strain relations for an orthotropic material are reviewed and an example of a nonsymmetric stress distribution associated with a symmetric fringe pattern is covered.

An analytic separation method for photoelasticity

A method for separating principal stresses in photoelasticity is presented. This method is based upon the series solution of Laplaces equation and the determination of the unknown coefficients arising in this series by a least-squares numerical technique. By selecting an adequate number of terms in the series, the representation of the boundary values of the first stress invariant can be established as accurately as the initial photoelastic data. This form of representation of the first stress invariant at interior points in the region is moe accurate than the boundary values employed.

A dynamic photoelastic investigation of stress-wave propagation in cones

The embedded-polariscope method was employed to isolate the central plane in cylindrical and conical models subjected to axial loads. Light-field isochromatic-fringe patterns associated with each of the five models studied were recorded by using a multiple-gap camera. Results obtained indicate that the maximum stress decays with distance propagated approximately as indicated by the elementary one-dimensional wave theory.

Data analysis in dynamic photoelasticity

A method to separate the principal stresses and to obtain displacements from dynamic photoelastic fringe patterns is presented. The method utilizes geometric characteristics of either the model or the stress wave to provide the additional equation necessary for separation. The method is illustrated in ten specific cases.

ON THE FIDELITY OF HIGH-SPEED PHOTOGRAPHIC SYSTEMS FOR DYNAMIC PHOTOELASTICITY

A general theory has been developed which predicts the influence of the characteristics of a high-speed recording system on the fidelity of a dynamic photoelastic-fringe pattern. The general theory was applied to recording systems currently employed in dynamic photoelasticity which include the high-speed framing camera, the spark-gap camera and the Q-spoiled laser system. Equations for a nondimensional form of the exposure as a function of normalized position have been developed for each of these three recording systems. From these equations, criteria to measure the fidelity of the recording systems were established. The methods developed are applied to the spark-gap system and examples of resolution limits, time shift and distortion are illustrated.

Experimental study of large-diameter thin-wall pressure vessels

An experimental stress analysis of three cylindrical pressure vessels with radius/thickness ratios ranging from 100 to 238 and different head closures is described. Brittle coatings and electrical strain gages were employed to determine stress distributions over the entire outer surface of the vessels. Electrical strain gages alone were used to determine stresses on the inside surface of the vessels. Particular emphasis was placed on determining stress concentrations and on nonlinear effects produced by geometric imperfections. An attempt was also made to correlate the failure, which started in the cylindrical portion of the three vessels, with the elastic-stress distribution. It was found that the imperfections in the cylinder were not significant if the vessel was fabricated from a ductile steel. However, if the vessel was constructed from a high-strength but brittle steel, the imperfections significantly lower the bursting strength of the vessel.

A class of zero-birefrngent polymers

A class of photoelastically insensitive materials consisting of a blend of rigid and flexible polyesters is described. The mechanical and optical response of these polymers is viscoelastic in character. For a wide range of the compositions, the birefringence changes from positive to negative under constant load or constant displacement. The influence of composition, time under load, and principal stress difference on the birefringence is studied.Isochromatic-fringe development in a diametrally loaded disk shows that a major region of the stressed body becomes optically insensitive after a reasonable period of time under load and remains insensitive for a time sufficiently large for associated photoelastic operations. A typical operating-time band is presented during which the optical response of a model characterized by the fringe order per unit thickness is reasonably small.It appears that this class of photoelastically insensitive materials can be employed to produce composite models with glass-fiber reinforcements. Compared to other zero-birefringent polymers, the present material has the advantage of easier processing (casting and curing), improved adhesion to glass fibers and closer matching of the refractive index with that of glass.