Active thermography gives the possibility to characterize thermophysical properties and defects in complex structures presenting heterogeneities. The produced thermal fields can be rapidly 3D. On the other hand, due to the size of modern thermographic images, pixel-wise data processing based on 1D models is the only reasonable approach for a rapid image processing. The only way to conciliate these two constraints when dealing with time-resolved experiments lies in the earlier possible detection/characterization. This approach is illustrated by several different applications and compared to more classical methods, demonstrating that simplicity of models and calculations is compatible with efficient and accurate identifications.
The evolution of thermophysical properties metrology and nondestructive evaluation (NDE) is characterized by the increased use of refined inverse techniques [
How to conciliate the existence 3D thermal situations involving numerous parameters and the necessity to have rapid calculations compatible with the very high number of information to process in a thermographic image sequence?
A solution lies in the use of 1D thermal models for pixel-wise data processing and the choice of a limited early time domain (for time-resolved techniques) or high frequency domain (for modulated techniques) for which the measured temperatures are essentially depending on the sole parameter to be identified and weakly affected by the 3D heat transfer. To achieve that, the proposed approach consists in performing the identification at the earlier possible time (or at the higher possible frequency) after the thermal stimulation. Here, we will mainly consider time-resolved techniques and early time detection (emerging signal).
The present work wants to show the following. A detailed procedure can be defined for early detection and characterization (see Section That this approach is not new. In a first step, it has been applied in the field of thermophysical properties measurements (period 1970–1990). This review is the subject of Section The application to NDE, started at the beginning of the 90’s, continues to give rise to new developments (Section
The goal of the present work is to put into perspective results spread over three decades, showing the unity of the approaches up to now hidden by the diversity of the applications and to emphasize that in thermal methods precociousness is as important as signal-to-noise ratio.
The early detection approach can be considered as the sequence of the following six operations: choice of a model simpler than the actual configuration, generally 1D, choice of an early time window for the analysis of the thermograms, in such a way that very few parameters (one if possible) be influent, inverse problem solving in these conditions, Analysis of the time evolution of the so-identified parameter for the assessment of its accuracy, choice of a fitting function, extrapolation to zero time (thermophysics application) or zero contrast (NDE) for obtaining the most precise parameter estimate.
Most of the examples that will be given consider models with only one parameter to be identified. Nevertheless, more complex situations are possible. The second example of Section
The early detection approach defined in Section
In Section
In flash thermal diffusivity measurements on the face opposite to the pulsed heat deposition the sample heat losses distort the rear face temperature time history. These thermal losses occurring necessarily after the flash, the temperature is all the less disturbed as time is nearer the origin. Consequently, the diffusivity identification by extrapolating towards the initial time the apparent diffusivity-versus-time history resulting from the use of an adiabatic solution was proposed in 1982 [
Figure
Test no. 2 on plaster identified apparent diffusivity law and regression parabola with a uniform weight and with a nonuniform weight linked to the accuracy of the measurement, taken from [
Table The Parker’s formula, The more precise method at the time of the publication of the present method: the partial times method of Degiovanni [ The method of partial moments, proposed by Degiovanni [
Present method result and comparison to Parker’s and Degiovanni’s methods.
Sample | Identified diffusivity (m2 s−1) × 107 | ||||||||
---|---|---|---|---|---|---|---|---|---|
Material | Test number | ||||||||
Thickness (mm) |
|
Parker’s method | Degiovanni [ |
Degiovanni [ |
Balageas [ | ||||
|
|
|
|||||||
Plaster | #1 | 9.96 | 1.206 | 4.759 | 3.675 | 3.703 | 3.689 | 3.69 |
|
Plaster | #2 | 9.96 | 1.206 | 4.734 | 3.618 | 3.644 | 3.645 | 3.64 |
|
Chalk | #3 | 6.16 | 1.950 | 3.548 | 2.861 | 2.881 | 2.886 | 2.89 |
|
Compared results of Degiovanni’s partial times method and present method, taken from [
The types of materials here considered are PDRCs (periodic directional reinforced composites) in which the reinforcement is arranged following preferential directions. For instance, unidirectional carbon/epoxy composites and 3D carbon/carbon composites belong to this family of materials and the identification method here presented can be applied to them. These materials are difficult to homogenize when there is a large difference between the thermal conductivities of the composite components (matrix and reinforcement) and when the main heat transfer is parallel to a reinforcement direction [
Considering the same type of measurements as in the previous section (rear face flash diffusivity), a more complex procedure is presented, which identifies the
The simplest PDRCs that can be imagined are presented in Figure
Simple configurations of unidirectional PDRCs: (a) stack of parallel layers, (b) chessboard pattern (from [
A slightly more general arrangement for 1D PRDC is given in Figure
(a) Model of the elementary volume (1/4 of the repetitive cell) of a 1D PDRC, (b) idem for a 1D C/epoxy composite, (c) idem for a 3D C/C with
Based on numerous numerical simulations [ volume content of the reinforcement, the reinforcement-to-matrix ratio of thermal conductivities, the reinforcement-to-matrix ratio of volume specific heats, the specific contact surface between reinforcement and matrix per unit surface of composite: the specific contact thermal resistance between reinforcement and matrix:
This mean temperature
Let us consider a 1D PDRC with a periodic pattern such as those of Figures
At the beginning, the energy that arrives at the rear face of a sample of thickness
Using several samples of different thicknesses the law
On the contrary, the energy arriving at the end of the experiment can be considered as representative of a partially homogenized material. In effect, for long times, 3D heat transfers have enough time to become important and homogenize the temperature of the two components (reinforcement and matrix). These 3D effects, which are generally considered as a disturbing phenomenon, have in the present case a beneficial role, becoming a source of information about the material. The identified diffusivity law presents a final asymptote that can be considered as an approximate estimate of the fully homogenized material
Thanks to the series of measurements performed with the different samples of various thicknesses, the law of partially homogenized diffusivity versus thickness can be extrapolated to an infinite thickness and the so-extrapolated value can be considered as the best estimate of the diffusivity of the fully homogenized material equivalent to the composite
In a third step, with a few assumptions which depends on the considered composite, from
The method has been applied to two 3D C/C composites in which the reinforcement is constituted of bundles of carbon fibers highly anisotropic and highly axially conductive, oriented in the three Cartesian directions
The first step consists to consider the 1D PDRC model of Figure
Figure
Identified thermal parameters | Materials | ||
---|---|---|---|
3-D C/C no. 1 | 3-D C/C no. 3 // | 3-D C/C no. 3 |
|
Mean volume heat capacitya | |||
|
1.4 | 1.4 | 1.4 |
Homogenized properties | |||
|
1.09 | 0.90 | 1.06 |
|
154 | 127 | 149 |
Reinforcement//heat flux | |||
|
3.0 | 2.6 | 3.1 |
|
423 | 366 | 437 |
Equivalent matrix | |||
|
0.27 | 0.33 | 0.48 |
|
38 | 46 | 68 |
Reinforcement/matrix interface | |||
|
0.01 | 1.6 | 6.6 |
|
2.0·10−7 | 2.8·10−5 | 5.7·10−5 |
aEstimated value.
Normalized experimental pulse diffusivity rear face thermograms (mean temperature) obtained with a series of 3D C/C coupons of different thicknesses. Comparison to the homogeneous medium solution with the identified homogenized diffusivity,
These results were obtained with an IR radiometer viewing an area of the rear face much larger than a mesh of material to obtain a mean temperature measurement. It could be easily performed with an IR camera.
The main merit of the method is the fact that the measured properties are relative to
The front-face and rear face pulse experiments are complementary [
Compared mean temperature time histories of the front- and rear faces in the case of the 3D C/C #3// and comparison to the calculated thermograms corresponding to the thermal properties of the bulk reinforcement (longitudinal properties), bulk equivalent matrix, and fully homogenised composite, taken from [
For NDE, the experimental data from which defect parameters can be identified are not thermograms (temperature increase, a function of time:
Principle of the detection of the emerging contrast.
This attitude is contrary to common practice. In effect, traditionally, pulse thermography users favored the maximum contrast to identify the depth and thermal resistance of defects, starting from the
Let us consider the simple 1D configuration of a thermally imperfect interface (thermal resistance) inside two layers of solid materials. The interface is characterized by an extrinsic parameter, its location depth,
The problem is that the time-evolution of
Figure
The virtues of the emerging contrast: universality, precociousness, and simple modeling. Comparison to the maximum contrast.
A simple explicit expression relating the time of occurrence and the amplitude of the maximum relative contrast, a universally known and used approach, cannot be
Nevertheless, the main lesson which can be drawn from this graph is the existence, at the origin, of a narrow tail-shaped domain in which all curves merge, thus where a unique correlation between the relative contrast
If we suppose that one can evaluate the occurrence time of a contrast of 1%, the maximum error on the identified depth is ±7%. Of course an earlier identification, based on a still lower contrast, leads to a more precise identified depth. The aim to be reached is clear; the problem is in the way to practically achieve the required experimental accuracy.
This simple example illustrates the main virtue of the emerging contrast: the “universality” of its applicability.
Another illustration of this universality is given by the following study of the characterization of a defect embedded at different depths in a slab of a homogeneous sample. Let us consider a slab of thickness
On the left: Influence of the normalized defect depth,
Sample finite thickness effect on the relative contrast
Emerging contrast domain
Figure
Both Figures
At the beginning of the 90’s, the attention of several authors was drawn to the fact that it would be better to consider the contrast at its beginning to achieve an early detection.
The idea of an early identification of the defect depth,
The weakness of this approach was double: (i) the relation between defect depth and divergence time was totally empirical and no precise procedure was proposed since the emergence had to be localized by the simple examination of the contrast curve without any indication given concerning the relative contrast value to consider for this determination of
Finally, Krapez et al. [
In parallel to this research, another way to perform early detection was explored. Almond et al. [
Recently, Sun [
This approach, although constituting a progress compared to the use of the occurrence time of the maximum contrast, is not as interesting as the early detection from the emerging contrast because the contrast slope peak occurs later than the emergence of the contrast
Balageas [
The early detection approach using the described procedure allows to reach the optimum accuracy on both the depth and the thermal resistance of defects: between 0.1% and 10% for the depth, and less than 30% for the thermal resistance (see Figure
Simulation results: (a) identification of the depth profile of a circular defect
The TSR method [
The advantages of the fitting are as follows: (i) a noticeable noise reduction; (ii) the replacement of the sequence of temperature rise images,
The logarithmic derivations are interesting too, because they produce a remarkable increase of detectivity and a “precession” of the detection [
So, it is easy to understand that both methods (early detection by emerging contrast and TSR) pursue identical purposes, and that consequently coupling them is beneficial. The increase of signal-to-noise ratio (SNR) given by the logarithmic fitting is particularly welcome since experimental crude thermal contrasts may have weak SNR, especially when deep defects are considered. In this case, the TSR technique is used as a preprocessing tool before application of the early detection process. An example of such a coupling is shown in [
A deeper coupling could be used, consisting in considering the emerging contrast of the 1st or 2nd logarithmic derivatives instead of the emerging contrast of the thermogram itself for the characterisation of the defect. Such an early detection method, which remains until now to be established regarding the quantitative identification of the defect parameters, is better than the one based on the half-rise time of the first derivative or the time of the maximum of the second derivative. Nevertheless, if the sole qualitative aspect is considered (detection of defects from thermographic images), the use of early images of the first and second logarithmic derivatives produces sharper defect images, a noticeable improvement compared to traditional maximum contrast images. Figure
Comparison between the best images obtained by the TSR method coupled with an early detection approach and an ultrasonic D-scan: (a) Thermograms,
The early detection and characterization approach based on the emerging contrast has been extended to step-heating thermography, leading to comparable improvements. The theory is given in [
A review of the literature of the early time detection approach in the field of thermophysical properties measurements and NDE has been made.
This approach has been built progressively and never presented as a well-defined general procedure. This is due to the fact that the applications of the method were spread in time (3 decades) and pertaining to different fields. Putting these works in perspective, it has been possible to describe and formalize the general procedure here called “the early detection and characterization.”
In the field of thermophysical properties measurements, two examples of flash diffusivity identification using rear face thermograms have been presented. They illustrate the philosophy of the approach and are well suited to thermography.
This paper demonstrates that in NDE by pulse-stimulated thermography, the generally followed attitude that consists in taking into account the sole signal-to-noise ratio when optimizing an identification process is an error. The optimization must consider with the same weight the signal-to-noise ratio and the precociousness for both qualitative and quantitative purposes.
A way to conciliate both signal-to-noise ratio and precociousness is now more easily feasible by combining the early detection/characterization and the thermographic signal reconstruction (TSR) technique. Presently, this combination has given rise to recent developments in the field of NDE, increasing the attractiveness of time-resolved thermography.