What is the formula for pulsed thermography depth and observation time?

α = k / (ρ · c_p); t_characteristic ≈ d² / α; d_max ≈ √(α · t_observation); t½ = 0.1388 · L² / α (ASTM E1461 flash method). Relates defect depth to the thermal diffusion time for a material, giving the observation window needed and the depth reachable in a given recording time.

What should I check before relying on the result?

Diffusivity values are typical at 20 °C and vary with grade, temper, moisture and lay-up — measure or verify for critical work. Composites are strongly anisotropic: through-thickness diffusivity is several times lower than in-plane, and only the through-thickness value applies here. Contrast falls roughly with the square of depth, so camera noise usually sets the practical limit before diffusion time does. Keep the heat pulse short compared with the characteristic time, or the excitation is no longer an impulse and the timing shifts. These are order-of-magnitude planning figures. Confirm on a representative reference standard with known defects. Verify against the governing edition: General engineering — one-dimensional heat diffusion. Half-rise relation and diffusivity measurement per ASTM E1461-13; infrared thermography practice per ISO 18434-1:2008 and ASTM E2582 (composites)..

Pulsed thermography depth and observation time Calculator

Pulsed thermography floods a surface with a short burst of heat and watches it cool. Heat runs into the part by diffusion, not by travelling at a fixed speed, so depth and time are related quadratically: the characteristic time for a thermal disturbance to reach depth d is t ≈ d²/α, where α = k/(ρ·c_p) is the thermal diffusivity. Turn it round and the depth reachable within an observation window t is d ≈ √(α·t). That square-root behaviour is the single most important fact about the method: doubling the depth costs four times the observation time, and depth capability is bought in ever more expensive increments.

Diffusivity varies over three orders of magnitude across the materials an inspector meets. Carbon steel is about 12 mm²/s, austenitic stainless only 4, aluminium 69, while CFRP through-thickness is around 0.4 and GFRP 0.16. A 3 mm defect in steel therefore announces itself within about 0.7 s and needs a fast camera, while the same depth in CFRP takes tens of seconds and needs a stable, long acquisition instead. The related flash-method half-rise time from ASTM E1461, t½ = 0.1388·L²/α, is the rigorous version of the same relationship for a plate heated on one face and observed on the other, and is what a diffusivity measurement actually uses.

Depth is not the only limit. Lateral heat flow blurs the thermal contrast of a defect as it deepens, so a defect must be wide compared with its depth to be seen at all — the working rule is that the defect diameter should be at least one to two times its depth. Contrast also falls roughly with the square of depth, so the practical detection limit is usually set by camera noise and surface emissivity variation long before the diffusion time becomes inconvenient.

Use these figures to set up the acquisition: frame rate fast enough to catch the early transient (at least ten frames within the characteristic time), recording long enough to cover the deepest feature of interest, and a heat pulse short compared with that characteristic time so the excitation approximates an impulse.

Worked example

Material	carbon_steel
Thermal diffusivity (custom)	12.2 mm2/s
Defect depth below the surface	3 mm
Observation time available	5 s
Diffusivity used	12.2 mm2/s
Characteristic diffusion time	0.738 s
Flash-method half-rise time	0.1024 s
Depth reachable in the observation time	7.81 mm
Guideline minimum defect diameter	6 mm
Suggested minimum frame rate	13.6 Hz

Carbon steel at α = 12.2 mm²/s. t = d²/α = 9/12.2 = 0.738 s to reach 3 mm, so the camera needs about 10/0.738 = 13.6 fps to catch the transient. The ASTM E1461 half-rise time for a 3 mm plate is 0.1388 x 9/12.2 = 0.1024 s. In a 5 s record the diffusion reach is √(12.2 x 5) = 7.81 mm.

Use at your own risk — verify before you act

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