Abstract
The property of homogeneous and isotropic contraction accompanying the slow polymerization of a photoelastic epoxy resin is utilized to produce a photoelastic model of the same size and shape, at the elevated cure temperature, as the container in which it was cast. Reducing the temperature of the bonded model-container composite structure through the epoxy material transition-temperature range results in frozen-stress photoelastic patterns which correspond to the forces of mutual elastic restraint of differential thermal contraction.
The requirements for model-prototype similarity and the model-calibration method are discussed. Particular experiments with calibration specimens and with more complex structures in two and three dimensions are described. The validity of the technique is further demonstrated by correlation with a three-dimensional numerical solution.
The properties of a material that was specially developed for use in this new technique are given.
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Abbreviations
- a :
-
Cylinder inner radius, in.
- b :
-
Cylinder outer radius, in.
- c :
-
Half-length of short cylinder, in.
- C :
-
Calibration specimen coefficient
- E :
-
Effective frozen-stress elastic modulus of photoelastic material, psi
- E c :
-
Elastic modulus of container material, psi
- f :
-
Photoelastic frozen-stress fringe value, psi per fringe per in.
- h :
-
Thickness of container, in.
- L :
-
Characteristic length, in.
- n :
-
Observed fringe order, fringes
- N :
-
Observed fringe order per unit slice thickness, fringes per in.
- \(\bar N\) :
-
Observed calibration specimen fringe order per unit thickness, fringes per in. (Subscripts 1, 2, 3 and 4 pertain to the specimen shape, and subscripts C, D and E pertain to specific points in its processing history, see Fig. 1.)
- p-q :
-
Principal stress difference in complex model, psi
- Q :
-
Effective frozen-stress photoelastic figure of merit, fringes per in.
- r :
-
Radial position, in.
- T :
-
Temperature, °C
- x,y,z :
-
Position coordinates of point in complex model
- \(\alpha _c\) :
-
Linear expansion coefficient of container material, in./in.-°C
- α:
-
Linear expansion coefficient* of photoelastic material, in./in.-°C
- β:
-
Factor of proportionality between complex model principal stress difference and reference stress
- ε:
-
Elastic strain, in./in.
- Δ:
-
Differential thermal strain, in./in.
- λ:
-
Factor of proportionality between complex model strain and free differential thermal strain
- \(\bar \sigma\) :
-
Calibration specimen stress, psi
- ν:
-
Effective frozen-stress photoelastic material Poisson's ratio
- \(v_c\) :
-
Poisson's ratio of container material
References
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Sampson, R.C. A three-dimensional photoelastic method for analysis of differential-contraction stresses. Experimental Mechanics 3, 225–235 (1963). https://doi.org/10.1007/BF02325868
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DOI: https://doi.org/10.1007/BF02325868