A Hybrid Method to Determine Individual Stresses in Orthotropic Composites Using Only Measured Isochromatic Data

Abstract

Ability to determine the individual stresses photoelastically in orthotropic composites from isochromatic data, but without employing isoclinics or isopachics, is developed and demonstrated. This new capability is achieved by combining isochromatic information, complex stress functions and numerical nonlinear least-squares concepts into a new and effective hybrid method for stress analyzing composite materials. Unlike previous methods of photo-orthotropic-elasticity, the present technique simultaneously smoothes the recorded isochromatic data, provides reliable boundary information, and separates the isochromatics into individual stress components throughout the area of interest. The method is illustrated by evaluating the three individual stresses throughout a region adjacent to a hole in a uniaxially loaded orthotropic composite plate from the measured isochromatics.

Development of a Hybrid Method of Reflection Photoelasticity for Crack Problems in Anisotropic Plates

“…Applying the non-linear least squares method [22,23,25] to equation (16), complex coefficients C n ¼ a n þ ib n ð Þ are determined. Substituting these complex coefficients into equations (6) and (15), the stress components and stress intensity factors of the coating material are determined.…”

“…To obtain isoclinic data very tedious and complicated work is required. Recently, a new photoelastic approach based on hybrid method of photoelasticity and which combines the merits of experimental, numerical and analytical methods, has been introduced [21][22][23][24][25]. It uses only isochromatic data thus eliminating the need for isoclinic data.…”

“…Huang et al [21] developed a hybrid method for separating the stress components around the circular hole of a plane of an isotropic material by using a mapping function and isochromatics. Hawong and Rowlands et al [22] developed a hybrid method of transmission photoelasticity for a plane of a transparent orthotropic material with a circular hole by using a mapping function and isochromatics. Hawong and Shin et al [23][24][25] developed a hybrid method of transmission photoelasticity for plane crack problems of transparent isotropic and orthotropic materials, and its validity was verified.…”

Photoelastic experimental hybrid method for fracture mechanics of anisotropic materials

“…Unequal roots ~j in eq (8) For the case of orthotropic material, the additional symmet_des imply that a16 = a26 = 0 in eq (8). Equation (8) can be transformed into eq (9), and the roots in eq (9) are purely imaginary:l t,12 4 Jr-a66)l.t 2 q-a22 0 Because the stress functions of eq (11) are analytical and continuous, they can be represented by power series.…”

“…Equation (8) can be transformed into eq (9), and the roots in eq (9) are purely imaginary:l t,12 4 Jr-a66)l.t 2 q-a22 0 Because the stress functions of eq (11) are analytical and continuous, they can be represented by power series. Therefore, stress function ~b(zt) can be represented as eq (13), and stress function ~(z2) can be represented as shown in eq (14) using the concept of Gerhardt: 14…”