An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved. The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poisson's ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions. The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.     

New compensation method in photoelasticity

Proposed compensation method eliminates the necessity to align the principal directions in the model with compensator for determination isoclinic parameter and fringe order. The advantage and limitation of the proposed method are discussed from the point of view of its potential use in the automatic data collection.     

A scattered-light method in photoelasticity

The birefringence and, thereby, the stresses in a photoelastic model are investigated utilizing the light scattered from a beam of light propagating through the model. The retardance from the entry point of the beam into the model to a certain point along the beam is expressed in terms of the intensity of the scattered light. The retardance for a short distance along the light path within the model is determined as a function of the total retardances from the entry point of the model to the two end points of the distance investigated. The effects of retarders and polarizers on the state of polarization of the light beam are treated by Mueller calculus. It is not necessary to make other assumptions than those made in the usual stress-freezing and slicing method.     

Computer aided photoelasticity by an optimum phase stepping method

In this paper an automated photoelastic method based on the phase stepping technique is described. It provides full-field maps of the isoclinic parameter and the relative retardation. The technique is based on processing six images of a photoelastic specimen acquired using plane and circularly polarized light. The number of acquisitions and the type of polariscope used in this approach have been chosen with the aim at reducing the influence of quarter wave plate errors and obtaining raw photoelastic data in a periodic form suitable for easy applications of automatic unwrapping routines.     

Two-wavelength method for full-field automated photoelasticity

A new method for the whole-field determination of the isoclinic angle α and the isochromatic parameter ϕ is presented. The problems appearing during the calculation of these two parameters are solved with the use of two different wavelengths. Indeed, when a monochromatic light is used as an incident light, α is not measurable at the points where ϕ is equal to 2kπ. In this method, each monochromatic light can compensate for the influence of ϕ to obtain the isoclinic angle for the entire model. Also, most of the methods calculate the fractional fringe order that is unwrapped afterward to obtain the isochromatic parameter. This unwrapping process needs an initialization, which cannot be automatic with only one isochromatic fringe pattern. The use of two wavelengths permits a complete automatic unwrapping of the isochromatic parameter, even for the initialization of the process.     

Direct oblique-incidence method for reflection photoelasticity

Experimental Techniques - The method presented in this paper has a good practical application, which may be used in all cases of oblique-incidence measurements in reflection photoelasticity. The...     

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 Laplace's 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.     

The generic nature of the absolute-retardation method of photoelasticity

The method of absolute-retardation measurements does not depend upon the use of any specific interferometer. Any one of the many extended field interferometers can be employed, including the Series, Michelson, Mach-Zehnder and Fizeau types. Where adequate monochromatic purity of light source is available, reflections from the two surfaces of the model can form the interferogram, thus dispensing with the necessity of any separate optical interferometer. The two-dimensional stress-optical relationships are derived in their most general form. The relationships are identical for all instruments or interference systems—only the calibration constants change with different systems. Interferograms from four distinctly different systems are shown. Interference-fringe sharpening is introduced and demonstrated. A laser-light source was used with two systems to provide high monochromatic purity. The interferometric method of Nisida and Saito is correlated with the absolute-retardation method. The opportunity to obtain information for a complete stress solution from one photograph makes the method attractive for both static and dynamic problems.     

The practical use of the hole method in photoelasticity

A small circular hole has already been used in plane elasto-static photoelasticity to determine the stress tensor for any general loading situation. Originally the idea required the determination of the stress at four points at the free boundary of the hole, then it was found that more precision would be obtained if the measurements were taken at points located at a distance from the center of the hole equal to twice its radius. Later it was suggested that probably still better results would be obtained from points located at 1.4 times the radius. This paper has three objectives: (1) to improve the precision of the measurements by taking them at any point in the vicinity of the hole, which requires that the expressions giving the principal stresses be presented in a different form, as a function of the normalized variable distance from the center of the hole; (2) to show the consistent application of the method, using the values of the birefringence at various arbitrary radial locations, to plane elasto-static loading problems; and, (3) to present the application of this approach in a concise form so that its application is practical.     

A new method to increase the sensitivity of photoelasticity

A method is proposed to read the isochromatic-fringe order continuously as a function of position. It utilizes the fact that the fringe order is a continuous function of the light intensity, which is converted into the density of a photographic negative and then traced out either by a microdensitometer or isodensitracer. Explicit relationship between the fringe order and the film density is obtained. Hundreds of points can be read between a half and an adjacent integral order. The method is whole field in nature and offers the possiblity of direct computer processing of photoelastic information.     

Corneal studies by photoelasticity

Freshly enucleated andin vivo eyes of cats were analyzed to determine the detailed distribution of birefringence across the cornea and through its thickness, and to determine the change of birefringence with intraocular pressure. Scattered light and oblique-incidence photoelasticity were used. The experiments are summarized and special considerations are discussed. These include the necessity for a laser-light source; diffraction limitation in producing a narrow ribbon of light; rotation of the plane of polarization; inequalities in reflected components of polarized light.