FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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processing the time resolved signal is pointed out in this section.
One of the problems encountered in thermographie NDT is related to the spatial
fluctuations of the recorded thermal image caused by changes in the surface
emlssivity or by non-uniformities of the heating-source distribution«. A
differential approach using a short heating period and monitoring the
temperature decay rate of the heated area is an effective way to avoid such
problems . The temperature history within a homogeneous sample after the
surface absorption of a short heat pulse can be represented in a first
approximation by the one-dimensional model for an instantaneous pulse > :
T(z,t) - — exp (1)
(ïïKpct) 1 / 2
where z and t are respectively the depth and time variables, Q is the injected
energy density, K is the thermal conductivity, p is the density, c the
specific heat, and a = K/pc is the thermal diffusivity. We can see from ea.
(1) that the surface temperature of a homogeneous sample decays as (t) '
after the absorption of the pulse.
The effect of the finite pulse duration and non-uniform heat distribution are
best analyzed by a numerical model. A two-dimensional (axially symmetric)
finite-difference model was thus used to study the heat propagation en the
stratified material. under transient surface heating . The surface
temperature history obtained from such a model in a configuration typical of
our experimental tests is shown in fig. 1. In this figure, curve (a)
represents the thermal history after the absorption of a 50 ps pulse by a
homogeneous steel sample (K = 0.7 W/cm °C, p = 7.8 g/cm and c = 0.5 j/g °C).
We can see that, apart from an initial perturbation caused by the finite pulse
duration, the thermal decay slope is equal to - 1/2 on the log-log scale, in
agreement with eq. (1). Curve (b) corresponds to a lower-conductivity layer
(K * 0.14 W/cm °C), 100 pm thick, perfectly bonded to a steel (K. = 0.7 W/cm
°C) substrate. The curve slope presents a discontinuity when the thermal
front reaches the interface after a period which is of the order of the
thermal propagation time t = I /4a through the thickness I of the coating.
The position of this discontinuity can thus be used to obtain the coating
thickness I if its thermal diffusivity is known. Moreover, the vertical
displacement Tjj between the coated-sample curve (curve b) and its asymptote
for large values of t (curve a) can be used to obtain the ratio between the
effusivity e = Kpc of the coating and the substrate:
T,i = log (2)
2
as can be inferred from eq. (1). Curve (c) corresponds to an unbonded layer
where the interface defect has been represented by a I um-thick air layer.
The presence of the defect is apparent in this curve.
\ graphite-epoxy laminate comprising four layers of Hercules AS 3501-6 prepreg
bonded together with equal orientation was inspected by such method. Each
layer has a thickness of 125 \m and is composed of a large number of
equally-oriented, 8 )im-diameter graphite fibers embedded in an epoxy matrix.