What is the formula for critical angles?

First critical: θ₁ = asin(c_wedge / c_L); Second critical: θ₂ = asin(c_wedge / c_S); Smallest shear angle obtainable: θ_S,min = asin(c_S / c_L). First and second critical angles for a wedge on a test material, plus the smallest refracted shear angle that can be produced.

What should I check before relying on the result?

A Rexolite wedge (2337 m/s) on the same steel gives 23.33° and 46.16° instead — always use the velocity of the wedge you actually have. Wedge velocity falls as the wedge warms up, so the critical angles shift down in service. In austenitic and dissimilar-metal welds the material velocities are anisotropic and the critical angles vary with beam direction. Verify against the governing edition: General engineering — Snell's law; wedge and steel velocities per EN ISO 7963 / EN ISO 2400 practice..

Critical angles — UT Calculator

The critical angles are the incident angles at which a refracted mode reaches 90° and stops propagating into the material. The first critical angle is where the refracted compression wave grazes the surface, θ₁ = asin(c_wedge / c_L). The second critical angle is where the refracted shear wave grazes the surface, θ₂ = asin(c_wedge / c_S). For a perspex wedge (2730 m/s) on ferritic steel they are about 27.6° and 57.4°.

Between the two, only a shear wave travels in the material. That is the working window for every conventional angle-beam probe, and it is the reason a 45/60/70° shear probe gives one unambiguous beam. Below the first critical angle two beams exist at the same time, so every indication has two possible depths and the DAC curve is meaningless. Just beyond the second critical angle the energy stays at the surface as a Rayleigh wave, which is used deliberately for surface-crack detection but is a nuisance the rest of the time.

The window also sets a floor on the refracted shear angle you can produce. At the first critical angle the shear wave has already refracted to asin(c_S / c_L) — about 33.3° in steel, independent of the wedge material. That is why commercial shear probes start at 35° or 40° and why a true 30° shear beam cannot be made with a simple perspex wedge on steel.

A critical angle only exists if the wedge is acoustically slower than the material for that mode. On a plastic or on some austenitic/nickel weld overlays the second critical angle may not exist at all, and the calculator returns no value rather than a false number.

Compression or shear

Worked example

Wedge velocity (compression)	2730 m/s
Material compression velocity	5900 m/s
Material shear velocity	3240 m/s
First critical angle	27.56 deg
Second critical angle	57.41 deg
Smallest refracted shear angle obtainable	33.31 deg
Shear-only incident window	29.85 deg

Perspex on ferritic steel. θ₁ = asin(2730/5900) = asin(0.46271) = 27.56°. θ₂ = asin(2730/3240) = asin(0.84259) = 57.41°. At the first critical angle the shear wave is already at asin(3240/5900) = asin(0.54915) = 33.31°, so 33.3° is the smallest shear angle a perspex wedge can produce on steel. The shear-only window is 57.41 − 27.56 = 29.85°.

Use at your own risk — verify before you act

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