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Integrated-plane photoelastic method—Application of photoelastic isodynes

Paper presents basic theory and examples of application of a new photoelastic method developed to determine all components of a plane-stress field, including contact problems, by means of simple optical measurements only. This single-model, nondestructive and simple method uses a new type of scattered-light modulation, called a field of isodynes by the authors, which represents a generalization of the integrated method developed by Pindera and Straka

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Abstract

It has been shown by Pindera and Mazurkiewicz that a new type of scattered-light modulation in the plane of a two-dimensional photoelastic object can be obtained when the stationary integrated photoelastic method developed by Pindera and Straka is applied in a scanning mode and when the transfer function of the photoelastic system satisfies certain conditions. The new type of light modulation, called field of isodynes by the authors, carries information on stress components normal to the direction of propagation of primary beam, and on corresponding total-force component. The points where this stress component is equal to zero can be easily determined.

The classical scattered-light modulation along a chosen line represents a cross section of a corresponding isodynes field.

It is shown that these features of the method of isodynes make it possible to easily determine the distribution and values of normal stress components at any arbitrary rectilinear cross section, and to check immediately the accuracy of measurements. The experimental determination of contact stresses and contact regions using the method of isodynes is especially simple and elegant.

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Abbreviations

σ:

stress

σ1, σ2, σ3 :

principal-stress components

σ '1 , σ '2 , σ '3 :

secondary principal-stress components

σx, σy, σz :

normal-stress components

α:

azimuth of isoclinics; angle between the direction of polarization and the closer principal direction

α s :

azimuth of electric vector of primary beam: angle between the electric vector and the principal-stress component σ s

γ:

azimuth of scattered beam with respect to σ s -direction

I to :

initial intensity of transmitted light

I so :

initial intensity of primary beam

k, K :

coefficients related to light attenuation

I t :

final intensity of transmitted light

I s ′, I s :

intensities of scattered light, in a general case and in optimal conditions, respectively

(I s ′) c ,(I s ) c :

intensities of complementary scattered beams

I s1 ,I s2 :

optimal intensities of the first-order scattered beam and the complementary scattered beam, respectively

R, ψ:

linear and phase retardation, respectively

R t,ψ :

linear and phase retardation, respectively, of the transmitted beam

R s ,ψ s :

linear and phase retardation, respectively, of the primary beam

Δψ:

additional retardation produced outside of specimen

m t ,m s :

normalized linear retardation of the transmitted and primary beam, respectively; order of isochromatics or of isodyne, respectively

m :

normalized linear retardation with respect to the corresponding wavelength of detecting radiation

λ:

wavelength of radiation; dominant wavelength

C σ ,C σ ′ :

photoelastic coefficients and normalized photoelastic coefficient with respect to wavelength of light, respectively

S σ (λ, t), S σ ′(λ, t) :

model stress-optic coefficient, and material stress-optic coefficient for unit path length (1 cm), respectively, both dependent on the wavelength of detecting radiation and on the loading time

b :

thickness of specimen

s :

optical path

x, y, z :

Cartesian coordinates

S 1 :

first-order scattered beam

S 2 :

complementary scattered beam

S R :

reference scattered beam

P :

external force

dm/dS :

slope of the linear retardation curve along thes-path

t :

time

t o :

time of recording

T :

temperature

θ:

angle of observation: angle between the primary beam and the scattered beam carrying information

n :

principal index of refraction

n′ :

secondary index of refraction

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Authors and Affiliations

  1. Technical University of Cracow, Cracow, Poland

    S. B. Mazurkiewicz (Docent)

  2. University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    S. B. Mazurkiewicz (Docent)

  3. Department of Civil Engineering, University of Waterloo, Canada

    J. T. Pindera (Professor)

Authors
  1. S. B. Mazurkiewicz
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  2. J. T. Pindera
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Mazurkiewicz, S.B., Pindera, J.T. Integrated-plane photoelastic method—Application of photoelastic isodynes. Experimental Mechanics 19, 225–234 (1979). https://doi.org/10.1007/BF02328651

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