Change specimen geometry, load and fringe constant to visualize isochromatic fringe patterns corresponding to the principal stress difference in real time. Experience the foundation of FEM validation.
Specimen and Load
Specimen shape
Load P
N
Specimen diameter / width D
mm
Thickness t
mm
Material fringe value f
N/mm
Results
Results
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σ₁ (MPa)
—
σ₂ (MPa)
—
τmax (MPa)
—
Fringe order N
Isochromatic Fringe Pattern (Canvas)
Wavelength560 nm
N=0 (isotropic point)Higher orders = denser fringesLoad P
Disk centre (Frocht solution): $\sigma_x = \dfrac{2P}{\pi D t},\quad \sigma_y = -\dfrac{6P}{\pi D t}$ ($x$: perpendicular to the load, $y$: along the load)
The larger the principal stress difference, the denser the fringes.
What Is Photoelastic Stress Analysis?
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How can coloured fringes show the stress in photoelasticity?
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Roughly speaking, when a transparent material is loaded it deforms and the way light travels through it changes — a phenomenon called "birefringence". The amount of birefringence is proportional to the difference of the principal stresses ($\sigma_1 - \sigma_2$), and that appears as coloured fringes (isochromatics). Move the "Load P" slider in the simulator and you will see the fringes multiply and crowd together as the force increases.
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Really! So are the places with many fringes the dangerous ones?
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Exactly! A region where the fringes crowd together has a large principal stress difference — a sign of stress concentration. You often see it at corners of car parts or at the edges of holes. Change the "Specimen shape" from "Disk" to "Plate with central hole" and you should see the fringes suddenly bunch up at the edge of the hole (where the stress is three times the far-field value).
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I see. But how does this relate to real CAE (FEM)?
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In practice, the "trend" of a stress distribution computed by FEM is checked against the photoelastic fringe pattern. If the mesh or the boundary conditions of the FEM model are wrong, the fringe pattern comes out quite different. Changing the "Material fringe value f" in the simulator changes how the fringes look for the same stress, so you can also get a feel for the effect of the material.
Frequently Asked Questions
In photoelasticity the same colour sequence repeats each time the order N, which is proportional to the principal stress difference, passes an integer. In white light N = 0 is black, and as N approaches 1 a sharp change from red to blue (the tint of passage) appears, which marks the integer orders. The colour sequence repeats for N = 1, 2, 3…, and the fringes are denser where the stress is higher. This tool labels the integer orders ("N=1" and so on).
The material fringe value f is a constant expressing how sensitively a material shows birefringence under stress. The smaller f, the larger the birefringence for a given stress difference, so a higher order N appears for the same stress difference. In other words, the more sensitive the material, the denser the fringes.
Increasing the load P increases the principal stress difference inside the disk in proportion, and the fringe order rises in proportion too. Even at the centre of the disk σ₁ − σ₂ = 8P/(πDt), not zero, and the stress difference rises steeply towards the load points, where the fringes become dense. With the defaults D = 50 mm, t = 10 mm and f = 12 N/mm, the order at the centre is N ≈ 4.2 at P = 1000 N and about 17 at P = 4000 N.
The simulator is based on theoretical solutions (Frocht's solution for the diametrally compressed disk, the Kirsch solution for the plate with a hole, and elementary bending theory for the beam), so under ideal conditions it agrees well with real photoelastic experiments. Real specimens, however, have material non-uniformity, residual stresses and edge effects, so the tool is suited to grasping qualitative trends and to basic learning for FEM validation.
Real-World Applications
Early design verification:For parts with complex shapes such as car linkages and aircraft window frames, full-size transparent models are made and tested photoelastically. This identifies visually and intuitively, at the design stage, the danger spots where stress concentration is likely.
Validation of numerical analysis (CAE/FEM):Used as a benchmark for checking the reliability of stress results from the finite element method and similar. The isochromatic pattern from photoelasticity is compared with the FEM contour plot of the principal stress difference to confirm that the distributions agree.
Material evaluation and quality control:Used to measure the material fringe value (f) of different materials (epoxy, polycarbonate, etc.) and to assess internal residual stresses in castings and welds. Where stress is locked in, fringes are seen even before any load is applied.
Education and research:A powerful teaching aid in mechanics and materials courses, making the invisible concept of "stress" visible as beautiful coloured fringes. In fracture mechanics, research determines the stress intensity factor at a crack tip from the photoelastic fringe pattern.
Common Misconceptions and Points to Note
First,it is tempting to think "darker fringes = larger stress", but strictly that is not so. Isochromatics show the principal stress "difference", so uniform tension (large σ1, σ2 = 0) and pure shear (σ1 and σ2 equal in magnitude, opposite in sign) are completely different stress states with the same stress difference. Choose "Disk" in the simulator, apply a load and look at the centre: fringes appear, caused by the large stress difference from the combination of tension and compression. In uniform simple tension, on the other hand, σ2 = 0 so the fringe order is proportional to σ1, but the whole specimen takes the same order (the same colour) and no fringe "pattern" appears. Fringes look dense where the gradient of the stress difference is large. Always remember that you are looking at the "difference" and its distribution, not the "magnitude" of the stress.
Next,the handling of the material fringe value "f". This value is specific to the material and varies widely: about 7 for polycarbonate, about 10 for epoxy and over 100 for acrylic (PMMA) (all in kN/m·fringe = N/mm·fringe). When you change this value in the simulator the number of fringes changes greatly for the same load, doesn't it? Knowledge gained from experiments on a known material (epoxy) cannot be applied directly to the design of another material (aluminium, say), because the difference in f changes the "apparent danger".
Finally,the fundamental limitation that only "two-dimensional in-plane stress" can be evaluated. The method assumes that the stress is constant through the thickness the light passes through (plane stress). In real thick parts a "three-dimensional stress" state arises in which the stress differs between the surface and the interior. It is therefore not suited to precise evaluation of complex 3-D shapes, and it is important to understand its role as a tool for grasping trends and validating FEM.
Choose the "Specimen shape": disk (diametral compression), plate with central hole (hole diameter 15% of the width) or beam (3-point bending, depth 15% of the length). The presets set the shape and load together.
Set the "Load P" (100–5000 N), "Specimen diameter / width D" (20–150 mm), "Thickness t" (3–30 mm) and "Material fringe value f" (2–50 N/mm). During playback the load cycles from 0 to P and the fringes come and go.
Read σ₁, σ₂, τmax and the fringe order N at the reference point (disk centre, hole edge or mid-span bottom of the beam) and the stress-distribution graph along the load axis. Try the "White light / Monochromatic" and "Isoclinics" switches to see the different views.
Worked Example
A disk specimen (diameter 50 mm, thickness 10 mm) under a diametral compressive load of 5 kN: at the centre, a tensile stress σ₁ = 2P/(πDt) = 2×5000/(π×50×10) ≈ 6.4 MPa acts perpendicular to the load and a compressive stress σ₂ = −6P/(πDt) ≈ −19.1 MPa along it, giving a principal stress difference of about 25.5 MPa and τmax ≈ 12.7 MPa. With a material fringe value f = 12 N/mm the fringe order at the centre is N = (σ₁ − σ₂)·t/f = 25.5×10/12 ≈ 21.2, and the fringes become denser still towards the load points. For the plate with a hole (P = 3000 N, D = 50 mm, t = 10 mm) the stress at the edge of the hole is three times the far-field stress P/(Dt) = 6 MPa, i.e. 18 MPa, which can be used to check the stress concentration factor Kt = 3.
Practical Notes
Check the initial birefringence of the specimen. Residual stress from moulding or machining produces fringes even without load and cannot be separated from the load-induced fringes; specimens are usually annealed before use.
The material fringe value f varies with material batch and temperature, so use a value measured on a calibration specimen with known stress, such as a disk in diametral compression.
Polymers are viscoelastic, so the fringes drift slowly (creep) while the load is held. Take readings at a fixed time after loading, and avoid fast loading and temperature changes.