Pulsed thermography depth and observation time

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.

α = k / (ρ · c_p)
t_characteristic ≈ d² / α
d_max ≈ √(α · t_observation)
t½ = 0.1388 · L² / α    (ASTM E1461 flash method)