Method Of Birefringent Coatings Research Articles

The method of caustics in conjunction with the method of birefringent coatings for the solution of fracture mechanics problems

Optical methods of stress analysis including photoelasticity, moirr, holographic and moire interferometry and caustics have extensively been used in fracture mechanics problems. Among them, the optical method of caustics is gaining ground in the determination of stress intensity factors in crack problems under static and dynamic loading. In this method [ 1,2], the area in the vicinity of the crack tip is illuminated by a collimated light and the reflected or transmitted rays from an envelope in space. When this envelope is cut by a reference plane, a highly illuminated curve, the caustic, is formed. By measuring a diameter of the caustic the stress intensity factor is determined. The caustic is the image of the circumference of a circle on the specimen centered at the crack tip, which is called the initial curve. In the application of the method care should be taken to ensure that the initial curve lies in the plane-stress region, so that the plane-stress assumption made in developing the evaluation equations of caustic is valid. The implication of this assumption regarding the selection of material, load level, specimen size and optical arrangement has been discussed by Konsta-Gdoutos and Gdoutos [3-5]. In the beginning, the method of caustics was applied to transparent specimens and later on its use was extended to metals by Theorcaris and Gdoutos [6,7]. The optical quality of the specimens used in the method of caustics should meet high standards. Specimens used in transmission arrangements must have constant thickness and density. On the other hand, specimens used in reflection arrangements must have an optically planar surface of high reflectivity at least in the neighborhood of the crack tip where the caustic is generated. In metal specimens mirrored surfaces are prepared by grinding, lapping and polishing their front surface. Preparation of mirror-like surfaces of specimens used in the method of caustics constitutes not only an elaborate task but difficulties arise in a number of cases. A characteristic example is bone, which due to its spongy nature cannot be adequately polished to the point that Snell's reflection law applies. Analogous problems are encountered in fiber or particulate composite materials. Another class of problems in which the method of caustics cannot be

A photoelastic determination of the elastic-plastic boundary

It is proved that the elastic-plastic boundary in a transparent body made of an elastic-perfectly plastic material that obeys the Tresca yield criterion and is subjected to any system of applied loads can be determined photoelastically. This simple method of the determination of the elastic-plastic boundary is extended to the case of metals by using the method of birefringent coatings. Substantial experimental evidence is given from the existing literature.

On the birefringent-coating method of stress analysis for fiber-reinforced laminated composites

A general relation based upon laminated-plate theory is developed which relates the state of stress throughout the thickness of the fiber-reinforced composite laminate to experimentally determined surface strains. The usefulness of the developed relation is discussed through an example given for a typical graphite-epoxy structural laminate. Birefringent coatings employed as a method to determine laminate surface strains are investigated. Isochromatic disturbances in the vicinity of a laminate free-edge, due to a Poisson's ratio mismatch between coating and laminate and interlaminar stress transfer between discrete lamina of the laminate, are investigated through exact elasticity solutions.

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 Poisson's 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.

Stress Analysis on Flat Plates with Rivet Holes by the Birefringent Coating Method

In this paper, an experimental stress analysis is reported on flat plates with rivet holes of zigzag arrangement. The birefringent coating method was used in combination with the electrical analogy method to measure the principal strain ε3 normal to the plate surface. The material used was heat-treated 13% Cr steel with thickness of 3mm, and epoxy resin plate of 2mm thickness was pasted on one surface of the specimen. Nine specimens were tested, the pitch of the rivet hole p and the distance from the hole center to the plate edge e being changed in three ways, respectively.The tensile loads of seven steps were applied to all these specimens, and the isochromatic fringe orders were measured at the boundaries and in the vicinities of circular holes as well as along the main cross sections. For the stress analysis in the plastic range, the Mises' yield criterion and the Prandtl-Reu β incremental strain law were adopted. The principal strain increment dε3 measured from the electrical analogy method combined with the fringe order increment dN obtained photoelastically allows the separation of each principal strain increment (dε1 and dε2), and in consequence, the principal stress increments dσ1 and dσ2 may be calculated. The principal stress σ2 acting in the minimum cross section through the hole was much smaller than the principal stress σ1. The variation of stress concentration factors at the circumference of each hole due to the increase in applied load was examined, and the evolution of plastic ranges in each load step was also investigated. Through this experiment, the spread of plastic regions was fastest in the diagonal direction between the zigzagwise located holes.

Some Problems on the Photoelastic Experiment by a Birefringent Coating Method

Some Problems on the Photoelastic Experiment by a Birefringent Coating Method

Some Problems on the Photoelastic Experiment by a Birefringent Coating Method

Some Problems on the Photoelastic Experiment by a Birefringent Coating Method

Viscoelastic Effects in Birefringent Coatings

The method of birefringent coatings for the determination of elastic and plastic surface strains of opaque bodies like metals assumes perfect elasticity of the coating material. In reality the coating, assumed much softer than the metal, presents the problem of a general viscoelastic layer under prescribed boundary displacements (at the metal-plastic interface). As already shown, this problem is greatly simplified for isotropic linear viscoelastic coatings, for small strains, for a linear law of strain birefringence, and for interface displacements expressed as a product of a function of space co-ordinates by a time function. The obviously advantageous stress-strain-optical linearity was experimentally verified in pure and in plasticized epoxy resins which make the best coatings. Tests were carried out in uniaxial loading and in shear, in creep, as well as in relaxation. The main conclusion is that the pure epoxy resins show negligible inelasticity, and the plasticized have a linear photo-viscoelastic behavior. Explicit laws were fitted to the creep and relaxation curves. Tests were also carried out with deeply notched coated steel bars deformed in the plastic range. The variation of fringe pattern with time was found to be negligible for the pure epoxy resins and to diminish slightly and proportionally with time throughout the model for the plasticized resins.

Accuracy of birefringent-coating method for coatings of arbitrary thickness

Rational concepts of the behavior of birefringent coatings are developed for both plane-stress problems and general surface-strain problems. For plane stress in elastic bodies, accuracy of stress or strain determinations along free boundaries is almost entirely independent of coating thickness; however, where Poisson's ratios of coating and structure are unequal, the state of stress in the structure might be influenced by the presence of the coating. In experimental investigations of four geometrical discontinuities with coating thicknesses up to 0.9 in. and materials of unequal Poisson's ratios, no influence of coating thickness on boundary strains was observed. For some three-dimensional problems, local shear tractions developed at the interface introduce a dependence upon coating thickness, but the resultant error in strain determinations was approximately 5% for a case studied experimentally. Strain distributions on singly and multiply connected surfaces in two- or three-dimensional bodies can be studied effectively by the method of birefringent-coating measurements.