When a compression wave crosses from a wedge into the test material at an angle, it splits. Part of it refracts as a compression wave and part mode-converts to a shear wave, each obeying sin θ₁ / c₁ = sin θ₂ / c₂. Because the shear velocity in steel is much lower than the compression velocity, the shear wave always refracts at a smaller angle than the compression wave from the same incident angle.

This is the whole basis of angle-beam weld inspection. The wedge angle of a 45°, 60° or 70° shear probe is chosen so that the incident angle lies between the first and second critical angles (about 27.6° and 57.4° for perspex on steel). Above the first critical angle the compression wave has been refracted out of the material completely and only the shear wave remains, giving a single, unambiguous beam. Below it you have two beams in the part at once and every indication has two possible depths.

A refracted angle only exists while the calculated sine is 1 or less. When c₂/c₁ · sin θ₁ > 1 that mode has gone past its critical angle and is no longer propagating into the bulk material — the calculator returns no value for it, which is the correct physical answer, not an error.

Wedge velocity matters. Perspex/acrylic is about 2730 m/s, but Rexolite is nearer 2330 m/s and cross-linked polystyrene wedges vary between manufacturers. Wedges also warm up in service and the velocity drops, which is why the actual refracted angle should be verified on a calibration block at working temperature rather than trusted from the label. Enter the wedge temperature below and the calculator de-rates the wedge velocity (about 0.09 % per °C for acrylic) so you can see how far the beam has moved before you verify it.

Compression or shear

Worked example

Incident angle in wedge	20 deg
Wedge velocity (compression)	2730 m/s
Material compression velocity	5900 m/s
Material shear velocity	3240 m/s
Wedge temperature	20 °C
Wedge velocity temperature coefficient	0.0009
Refracted shear angle θ_S	23.95 deg
Refracted compression angle θ_L	47.66 deg
First critical angle	27.56 deg
Second critical angle	57.41 deg
Wedge velocity at temperature	2730 m/s

sin 20° = 0.34202. Shear: (3240/2730) × 0.34202 = 0.40591 → θ_S = 23.95°. Compression: (5900/2730) × 0.34202 = 0.73916 → θ_L = 47.66°. At 20° incidence the wedge is below the 27.56° first critical angle, so both beams exist in the steel at once — which is why a usable shear probe uses a wedge angle above 27.6°. At a 50 °C wedge the velocity falls to 2730 × (1 − 0.0009 × 30) = 2656 m/s and the refracted shear angle opens to 24.66°.

Use at your own risk — verify before you act

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