Experimental Mechanics

, Volume 44, Issue 5, pp 455–460

Photoelastic model measurement with rotated principal axes by scattered-light photoelasticity

  • Toshiki Kihara
Article

Abstract

The method of measurement of a three-dimensional photoelastic model with rotated principal axes has not yet been fully experimentally established. It is known that a three-dimensional photoelastic model can be reduced to an optically equivalent model. In this paper, the optically equivalent model is realized from a stratified model consisting of two layers of the frozen stress model. The secondary principal stress direction and the relative phase retardation of the frozen disk model in the stratified frozen stress model are determined for the entire field from Stokes parameters obtained by scattered-light photoelasticity using unpolarized light. The accuracy of these values is confirmed by a comparison with results only from the frozen stress disk model.

Key Words

Scattered-light photoelasticity three-dimensional photoelasticity digital photoelasticity rotated principal axes unpolarized light 

Nomenclature

Mj

Mueller matrix of linear retarder between pointsyj andyj−1

ρj

relative phase retardation between pointsyj andyj−1

ψj

angle of one of the principal stress directions between pointsyj andyj−1

Mj−1,0

Mueller matrix of linear retarder of the equivalent model between pointsyj−1 andy0

ρj−1,0

characteristic phase retardation between pointsyj−1 andy0

ψj−1,0

primary characteristic direction between pointsyj−1 andy0

R(2ωj−1,0)

Mueller matrix of pure rotator of the equivalent model between pointsyj−1 andy0

Eyj;θ)

incident unpolarized light along θ deg with thex-axis in thex−z plane at pointyj

S(yj; θ)

Stokes vector of resultant scattered light ofEyj observed from they-axis, which is the linearly polarized light of azimuth θ measured from thez-axis in thex−z plane

S(yj, y0;θ)

Stokes vector of the light emerged through the medium between the pointsyj andy0 from the scattered lightS(yj;θ) at pointyj

s(yj, y0;θ)

normalized Stokes vector ofS(yj, y0;θ)

Ij22)

light intensity through analyzing system from the scattered light at pointyj

θ

azimuth of the linearly polarized light of the scattered light, as measured from thez-axis

β2 and α2

azimuth of the fast axis ofQ2 and aximuth of the transmission axis ofP2 of analyzing system, as measured from thez-axis, respectively

Δρ

phase difference error ofQ2 to light wavelength used

V

Jones matrix of the photoelastic model which allows the rotation of the principal axes

S(A)

rotation matrix with rotary powerA

G(γ)

matrix of the retardation plate with retardation 2γ and fast axis at 0°

J1

Jones matrix of a linear retarder with the principal stress direction ψ2 and the relative retardation ρ1

J(y2, y0)

Jones matrix of the stratified photoelastic model constructed from two linear retardersJ1 andJ2

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Copyright information

© Society for Experimental Mechanics 2004

Authors and Affiliations

  • Toshiki Kihara
    • 1
  1. 1.Department of Mechanical Engineering, School of Science and EngineeringKinki UniversityHigashi-Osaka, OsakaJapan

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