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A measurement method of scattered light photoelasticity using unpolarized light

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Abstract

This paper describes an automatic measurement method for the stress analysis of a three-dirnensional photoelastic model having the rotation of the principal stress by scattered-light photoelasticity using unpolarized light. The relative phase retardation and the principal stress directions of a linear retarder for a distance in the solid model are expressed in terms of measurable Stokes parameters. The method was used for measurements on a frozen stress sphere under diametral compression.

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Abbreviations

ρ:

relative phase retardation

P Emphasis>/j i :

relative phase retardation at λi between the pointsy j andy j−1 in the model

λi :

light wavelength

ψ:

angle of one of the principal stress directions

ψj :

angle of one of the principal stress directions between the pointsy j andy j−1 in the model

E yj,θλi :

incident unpolarized light at λi along θ deg with thex-axis in thexz plane at the pointy j

S(y j ;θ)λi :

Stokes vector of resultant scattered light ofE yj,θλi observed from they-axis, which is the linearly polarized light of azimuth θ measured from thez-axis in thexz plane

M jλi :

Mueller matrix of linear retarder between pointsy j andy j−1 at λi

U(y j ,y 0)λi :

Mueller matrix of the photoelastic model between pointsy j andy 0

M j−1,1λi :

Mueller matrix of linear retarder with retardation p j-1,1 i , principal axes of azimuths ψ j-1,1 and ψ j-1,1 + σ/2 of optically equivalent model between pointsy j−1 andy 0

R(ωj-1,1):

Mueller matrix of pure rottor with rotatory power ωj-1,1, of optically equivalent model between pointsy j−1 andy 0

S(y j ,y 0;θ)λi :

Stokes vector of the light emerged through the medium between pointsy j andy 0 from the scattered lightS(y j ;θ)λi at pointy j

s(y j ,y 0;θ)λi :

normalized Stokes vector ofS(y j ;y 0;θ)λi

S 0(y j ;θ)λi :

intensity of the scattered lightS(y j ;θ)λi

N :

integer

T(θ,β2,α2):

light intensity emergin from analyzing system

β2,α2 :

azimuth of the fast axis ofQ 2 and azimuth of the transmission axis ofP 2 of analyzing system, as measured fromz-axis, respectively

Δρ i :

phase difference error ofQ 2 to λ i

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Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Science and Technology, Kinki University, Kowakae, 577, Higashi-Osaka, Japan

    T. Kihara (Associate Professor)

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  1. T. Kihara
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Kihara, T. A measurement method of scattered light photoelasticity using unpolarized light. Experimental Mechanics 37, 39–44 (1997). https://doi.org/10.1007/BF02328748

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