Limitation of fourier transform photoelasticity: Influence of isoclinics

Abstract

ABSTRACT--The application of the Fourier transform to photoelasticity was used in the evaluation of the retardation using a carrier system of fringes. In photoelasticity, the light intensity from the analyzer in a circular polariscope depends on both the retardation (isochromatics) and the isoclinic parameter. The theoretical analysis shows that the angle between the principal stresses in the model and in the carrier system of fringes influences the evaluation of the retardation (isochromatics), as occurs when misaligned compensators (namely, Babinet) are used. As a consequence, this method may not be applied as a full-field technique, although the error is small if the angle between the principal stresses in the model and in the carrier is less than 25 deg. Numerical simulations and experimental tests were conducted to corroborate this prediction. KEY WORDS--Experimental mechanics, image processing, photoelasticityNomenclature C = stress optic coefficient d = thickness of the model f = fringe frequency of the model fc = fringe frequency of the carrier I --light intensity emerging from the polariscope I0 = background intensity I1 = modulation term 12 = noise If = intensity of the in-phase signal Iq = intensity of the in-quadrature signal ---angle between the maximum principal stress in the model and the horizontal reference axis ~c --angle between the maximum principal stress in the carrier and the horizontal reference axis fir = angle between the maximum principal stresses in the model and in the carrier (absolute value) --retardation of the model ~c = retardation of the carrier ~c* = wrapped retardation of the carrier ~t = total retardation 8;" --wrapped total retardation k = light wavelength 01, or2 = principal stresses in the model (gl > or2) Crlc, ~2c = principal stresses in the carrier (eric > Cr2c)

Review of RGB photoelasticity

“…(20). The isoclinic value is unwrapped in the range À π/2 to þπ/2 using the adaptive quality-guided phase unwrapping algorithm described in [88].…”

“…The retardation is determined using a single image. The benefit of using a single image is partly limited by the restriction due to the orientation of the principal stresses that need to be aligned (less than about 251) in the model and in the carrier [20,21]. The combined effect of the error of quarter-wave plates and the misalignment of principal stresses between model and carrier is considered in [22].…”

Photoelastic Analysis of Edge Residual Stresses in Glass by Automated “Test Fringes” Methods

“…2 is given by the relationship valid for the Fourier transform method of fringe analysis [10]. Without considering the disturbances due to background intensity and noise, this relationship can be written as follows:…”

“…The glass specimen and the bent beam must be placed in such a way that the principal stresses in both elements are properly aligned, like in the cases of the manual method based on the Babinet compensator and of the Fourier transform method of fringe analysis [10].…”

Analyzing square plate in diagonal compression using Beltrami-Michell methodology

“…It is noted that the determination of θ isoclinic parameter in its physical range remains, generally, a difficult problem (Fernàndez, 2011). Several works have been published concerning this topic; see for example (Mangal and Ramesh, 1999;Siegmann et al, 2011;Ajovalasit and Zuccarello, 2000). Besides, in the Beltrami-Michell Boundary Value Problem (B-M BVP), each stress component being subject to its values on the boundary form a BVP individually.…”