Reinforcing effect of birefringent coatings

Birefringent coatings carry a portion of the load that would otherwise be carried by the structure. Thus, strains at the structure-coating interface are somewhat less than those in an uncoated part. In addition, strain gradients through the coating thickness must be taken into account to determine the surface strains that would be developed in an uncoated part. Correction factors are derived for plane stress, flexure of plates, torsion of shafts and cylindrical pressure vessels, and the case of combined plane and flexural loads is treated. For plane and flexural loading, the correction factors are equally applicable to regions surrounding common geometrical discontinuities.     

Effects of the thickness of birefringent coatings

It is known that birefringent coatings are a powerful experimental technique for the determination of surface strains of metals or other opaque bodies. In this paper the complete state of strain in such a coating is determined for an arbitrary one-dimensional variation of the displacement at the metal surface. It is shown that strain gradients or curvature of the surface have a pronounced effect on the observed birefringence, and must be taken into consideration. This can be done by means of two correction factors derived in the paper which take into account the elastic properties of the coating and its thickness. An experimental procedure is outlined for determining an unknown distribution of strain at the metal surface on the basis of the observed photoelastic pattern.     

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.     

Bonding of birefringent coatings to composite flat-belt-drive materials

The bonding of birefringent coatings to composite flat-belt-drive materials is described. The belts were subsequently subjected to tension tests without apparent disassociation of the coating from the belt. Additionally, lengths of photoelastic coating bonded to endless flat belts run at speeds approaching 50 m/s exhibited no evidence of disassociation.     

Thickness effects in birefringent coatings with radial symmetry

One method of determining the strains on the surface of a metal part is by the use of a birefringent coating. Because of the thickness of the coating, however, the observed fringe order depends not only on the surface strains but also on two other factors, namely, the curvature that the surface undergoes and the variation of strain acrose the thickness of the coating. These thickness effects have already been studied in a paper dealing with one dimensional variations in strain. In the present paper, the solution is extended to a two-dimensional deformation with radial symmetry. An experiment is described in which the surface strains produced by the impact of a bullet on a flat plate are determined from the birefringence of a surface coating taking into account the effects of strain gradients and curvature. The values of surface strain are compared with measurements made by means of a square grid inscribed on the metal surface. A procedure is suggested for determining an unknown surface strain having radial symmetry from the total birefringence of the surface coating when the change in curvature of the metal surface under load is known or can be determined separately.     

Strain measurement with asymmetric oblique-incidence polariscope for birefringent coatings

A method for measuring principal-strain components is presented. Retardation in the birefringent coatings is measured with a compensator in normal and oblique-incidence. In order to reduce the errors and increase the angle of oblique incidence, a prism made of optically homogeneous material with an asymmetric polariscope is used. The plane of incidence of light is arbitrarily chosen and does not have to be changed during the measurement. Jones calculus is used to analyze the light transformation in the polariscope and in birefringent coatings.     

On a type of radially retractable plate structures

The radially retractable plate structures (RPS) are a family of new retractable structures consisting of a set of cover plates connected by revolute hinges. The concept evolves from the foldable bar structures (FBS) by replacing the beams in an FBS with cover plates. With a single degree of freedom, the structures close to form a covered enclosure and expand to reveal a large central opening space, which makes them ideal for use as retractable roofs. In designing the plates of an RPS, two primary requirements have to be met. First, the boundary of these plates must be designed such that they form an enclosure without any gaps or overlaps in both closed and open configurations, and the plates do not interfere with each other during deployment. Second, all of the pivots of a beam must remain within the boundary of its corresponding RPS plate. This paper tackles the second problem. To meet the requirement, an analytical method is proposed. A feasible design area, defined by closed and open angles of the corresponding FBS, can be identified under this approach. The designers are no longer limited to use the empirical or numerical means to determine whether all of the pivots of a multi-angulated beam are within its corresponding plate. The analytical approach can be used regardless of the boundary’s profile. The approach can be extended into both symmetrical and non-symmetrical structures. Physical models built to validate our approach have shown that the analysis is correct.     

An experimental investigation of cog-root strains in V-belts using birefringent coatings

A birefringent photoelastic coating was used in conjunction with a linear-elastic finite-element analysis in order to deline critical regions of cogged V-belts subjected to a purely geometric loading. The results indicate that cord-ply delamination in the midcog region adjacent to the cog root is a probable mode of failure.     

On the fiber-reinforced birefringent composite materials

The isochromatic and isoclinic parameters for fiber-reinforced birefringent materials are examined. Experimental results reveal residual birefringence and an initial isoclinic coincident with the axis of material symmetry. These preliminary data also indicate that the isoclinic angle is neither a measure of the principal strain nor the principal-stress directions within the composite.     

New method for the determination of oblique-incidence coefficients for birefringent coatings and models

Results are developed which may enable the direct determination of oblique-incidence coefficients in coatings or models, thereby virtually eliminating errors due to Poisson's ratio, the oblique angle and the relative index of refraction.     

Measurements of thermally induced stress waves in a thin rod using birefringent coatings

When an elastic body is heated rapidly, significant inertial stresses are developed if the imposed heating rates cause a substantial temperature change in times which are short relative to the mechanical response time of the body. This work describes a method for inducing and measuring the thermally induced elastic stress waves in an unrestrained thin rod. Rapid heating was accomplished electrically by discharging a low-inductance capacitor bank (0.1 μH, 2800 J) through the rod. Utilizing the frozen-stress technique, an initial fringe pattern was introduced into thin strips of a birefringent material securely bonded to each side of the rod. The longitudinal strain oscillations were measured by direct observation of the movement of the fringe patterns with a high-speed framing camera. Interpretation of these measurements required a dynamic calibration and application of a dynamic correction factor for the reinforcing effect of the coating. Oscillations with periods from 35 to 250 μsec and stress amplitudes up to 900 psi were measured and compared with the uncoupled thermoelastic theory. Good agreement was obtained, and it was concluded that this technique is suitable for transient measurements in the presence of large magnetic fields which normally restrict the use of electronic methods.     

Kagome plate structures for actuation

A class of planar, pin-jointed truss structures based on the ancient Kagome basket weave pattern with exceptional characteristics for actuation has been identified. Its in-plane stiffness is isotropic and has optimal weight among planar trusses for specified stiffness or strength. The version with welded joints resists plastic yielding and buckling, while storing minimal energy upon truss bending during actuation. Two plate structures are considered which employ the planar Kagome truss as the actuation plane. It is shown that these plates can be actuated with minimal internal resistance to achieve a wide range of shapes, while also sustaining large loads through their isotropic bending/stretching stiffness, and their excellent resistance to yielding/buckling.     

The application of birefringent coatings to metal surfaces which are to undergo large plastic strains

A direct-casting method is proposed for applying a birefringent coating to a flat metallic surface which will enable strains of at least 10 percent to be examined. This technique will assist the investigation of such problems as sheet-metal forming and plastic anisotropy.     

薄板结构的安定优化设计

本文通过对薄板的Ｂ样条函数插值及结构中残余应力场的温度参数模拟，研究了薄板安定分析的样条有限元列式，在分析结构安定分析的数学规划列式的基础上，解决了薄板结构在给定可变载荷作用下的安定最小厚度设计问题。由于温度参数的引用，使得研究的问题的自由度大幅度减少。算例表明本文所提出的方法及所编程序的可行和有效。     

Effect of reinforcing elements on the growth of cracks near a hole in a plate

Novosibirsk. Translated from Prikladnaya Mekhanika, Vol. 24, No. 11, pp. 91–98, November, 1988.