- Email: [email protected]
Evaluation of gluing of CFRP onto concrete structures by infrared thermography coupled with thermal impedance
Accepted Manuscript Evaluation of gluing of cfrp onto concrete structures by infrared thermography coupled with thermal impedance Chauchois Alexis, Brachelet Franck, Defer Didier, Antczak Emmanuel, Choi Hangseok PII: DOI: Reference:
S1359-8368(14)00446-6 http://dx.doi.org/10.1016/j.compositesb.2014.10.002 JCOMB 3216
To appear in:
Composites: Part B
Received Date: Revised Date: Accepted Date:
29 July 2013 24 September 2014 1 October 2014
Please cite this article as: Alexis, C., Franck, B., Didier, D., Emmanuel, A., Hangseok, C., Evaluation of gluing of cfrp onto concrete structures by infrared thermography coupled with thermal impedance, Composites: Part B (2014), doi: http://dx.doi.org/10.1016/j.compositesb.2014.10.002
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
EVALUATION OF GLUING OF CFRP ONTO CONCRETE STRUCTURES BY INFRARED THERMOGRAPHY COUPLED WITH THERMAL IMPEDANCE CHAUCHOIS Alexisa,b, BRACHELET Francka, DEFER Didiera, ANTCZAK Emmanuela, CHOI Hangseokb a
LGCgE – Université Lille Nord de France F59000,FSA - Université d'Artois, Technoparc Futura, 62400 Bethune, France Tel : (33) 3 21 63 71 31 Fax : (33) 3 21 61 17 80 E-mail: [email protected] b
School of Civil, Environmental, and Architectural Engineering, Korea University, Seoul, Republic of Korea
Abstract Carbon Fiber Reinforced Polymers (CFRPs) have been increasingly employed for structural strengthening, and are attached to structures using bonding adhesives. The aim of this work is to characterize defects in the bond between CFRP and concrete (after they are located by pulse infrared thermography), and assign the defects a “numerical value” (ranging from 0 for a complete air-gap to 1 for a fully glued bond). Quantitative characterization is performed by measuring the thermal impedance, and then identifying the thermophysical parameters of the system through fitting the measured impedance to a theoretical model. An inversion procedure is carried out to estimate the unknown parameters, without prior knowledge of sample properties. In particular, it is possible to estimate more accurately both the amount of glue within a defect and the thermal contact resistance.
Keywords CFRP, heat flux sensor, pulse infrared thermography, defect detection and characterization, thermal impedance
1. Introduction
Aging civil engineering infrastructure is at the center of current concerns of many countries. Indeed, after World War II, construction of concrete structures (such as road infrastructure, buildings, and parking garages) heightened. So, for over 60 years, these structures have suffered the ravages of time and various attacks. Many of these concrete structures show changes in material composition or structural damage (caused, for example, by poor design, poor construction or changes in boundary conditions as a result of scour, landslides or other external agents). Some structures can no longer meet the requirements for safe use; in some cases the way the structures are used has evolved over the years as well (for example the increased size and number of vehicles). The demolition and reconstruction solution is usually too costly. In fact, alternatives are possible, [1-3] including: repair of the surface, concrete protection, materials regeneration, strengthening and adding extra material. The best solution depends on the importance of the structure and the amount of damage or disorder that has occurred.
One way of strengthening structures is by reinforcing with a composite material plate, which has the advantages of not corroding, being lightweight and high-strength. These composites are referred to as "FRP", fiber reinforced plastics or "CFRP", carbon fiber reinforced plastics/polymers. This process allows the strength and stiffness of the structure to be increased by the combined action of the plate and the concrete. FRP are composite materials made of high-strength fibers (glass, carbon or aramid) impregnated with a matrix (such as polyester, vinyl ester, or epoxy).
As they are becoming less expensive, composites are an attractive solution for strengthening buildings and other infrastructure. [4] The strengthening or retrofitting of reinforced concrete structures by externally bonded FRP systems is now a widespread and accepted technique, [5, 6] which has been widely studied, for example in [7–15].
The quality of bonding at externally bonded CFRP-concrete interfaces is very important. For external reinforcing with FRP composites to be most effective, the work must be very carefully carried out [16-18], and, crucially, the adhesive layer must not suffer too much damage when exposed to aggressive environments [19]. Otherwise, voids or flaws at the interface can occur; these defects are quite common. In the first case; “flaws” are formed because of poor workmanship during the initial application of the CFRP strips onto the concrete surface. Adhesion problems sometimes occur because not enough glue is used, or because some areas have not been glued at all. The second type of defect is “delamination”, and occurs because of stress concentrations associated with physical/chemical degradation of the binding layer [20] (when the composite is exposed to aggressive environments such as elevated temperatures, ultraviolet radiation, infiltration of moisture or extreme temperatures caused by fire). These invisible defects embedded in the interface between the CFRP and concrete can significantly reduce the effective contact area, and therefore the overall bond strength. Ultimately, the durability and service life of the CFRP-strengthened concrete structure is adversely affected. This means that quality control though “in situ” verification of bonded FRP systems is of paramount importance. Conventional methods for evaluating the bond quality of the CFRPconcrete composites are hammer-tapping and pull-off tests. Hammer-tapping requires the
inspectors to manually tap each point to be checked, while the pull-off test is destructive. Both types of tests are regarded as local tests, and do not allow effective, large-scale inspection. The Infrared Thermographic (IRT) technique has been widely accepted as an effective means of identifying and quantifying unseen surface flaws in a wide range of composite materials [21- 23]. This is because the presence of a defect (i.e. an "air layer") at the interface in a composite material reduces the rate of heat diffusion when thermal stimulus is applied. In fact, of all the Non-Destructive Testing Techniques (NDT) under investigation for bondquality assessment, (active) infrared thermography is of particular interest, because it is easy to deploy and can be used to rapidly inspect large surfaces, where only one side is accessible. However, even if these techniques are able to locate the defects, most of the time they are unable to provide sufficient specific information such as the depth and width of the disbonded area, or to assess the degree of adhesion between the composite and the adhesive. Indeed, during the early applications of IRT, the majority of published work simply focused on locating defects in a qualitative manner. It is more useful to quantify the size of the defects so that the extent of damage can be assessed. Quantitative defect characterization using infrared data can be achieved on the basis of direct analytical methods [24, 25] and inverse methods [26]. Approaches by direct analysis can be used to model the characteristics of the defects, but these approaches can be very complex, even when the defect geometries are simple, and can become impossible once anisotropic properties and defects in the surface are considered [24]. Consequently, in this work we will couple two methods: a pulse thermographic detection method to visually locate the defect, and a thermal method based on a heat flux sensor (also known as “fluxmeter”), to characterize it in more detail. Our aim is to quantify the quality of the bonding between CFRP and concrete.
2. Theory
For several years, our research team has been developing thermophysical characterization methods based on the study of thermal impedance, as measured using heat flux sensors [27]. Thermal impedance represents the relationship between the frequency components of temperature and the frequency-dependent flux density in the same surface. From an experimental point of view, it is determined simply by measuring the flux density and temperature simultaneously in a measurement plane surface. In practice, a heat flux sensor [28] in which a thermocouple has been embedded is placed in contact with the sample. The changes in flux density and temperature measured in this way are different from those in the material access plane. The reasons for this perturbation are the presence of the sensor and the sensor/material contact resistance. This original approach is based on a frequency-dependent study of the changes at the surfaces of materials.
2.1. Notion of thermal impedance a) Definition
By definition, the thermal impedance Z [29] is a complex parameter, defined in the frequency domain as the ratio of the temperature and heat flux. Thus, Z(f) can be written as: =
ω = ω
where Z is a function of the frequency f or of the pulse-duration ω.
(1)
Both quantities can be measured simultaneously using a heat flux sensor fitted with a thermocouple. If the thermal impedance is estimated for characterization purposes, both the imposed stress and temperature response are observed simultaneously, and their interaction can be analyzed. Such an analysis is carried out in the frequency domain, enabling the system to be studied on the basis of random signals. The frequency approach facilitates an understanding of the phenomena, and, along with the sensitivity study, transformation into the spectral domain enables us to target precisely which frequency range should be selected to identify the required parameters. The thermophysical parameters can be identified by fitting a theoretical model to the experimentally determined impedance. The thermal impedance can be expressed theoretically, as will be shown in this paper. The experimental procedure for calculating the apparent thermal impedance of the input side of a material requires both temperature and flux sensors to be positioned on the sample. Then one may observe either the natural exchanges between the material and the environment, or as in our case, heat the sensor/material assembly directly. To ensure exchanges are one-directional heat flow, the sensor consists of a sensitive measuring area surrounded by a ring with a similar but inert material acting as a guard ring. The sensor is a tangential-gradient fluxmeter (heat flux sensor) [30], 0.5 mm in thickness, whose temperature is measured with an embedded T-type thermocouple. Theoretically, the system that we study may be represented by a series connection of five elements (Fig. 1): •
the part of the sensor between the measurement plane and the output plane, which can be modeled by a thermal capacitance Cf (J·m-²·K-1) [28]
• •
a thermal contact resistance Rc (K·m²·W-1) between the sensor and the composite plate the composite plate with known thermal characteristics (λ and ρc) and width ℓ
•
a thickness made up of glue and air-gap in proportions depending on the quality of the bond, and modeled using a thermal resistance R (K·m²·W-1) and a heat capacity C (J·m-²·K-1)
•
a thick concrete layer acting as a semi-infinite medium, of thermal effusivity characterized by b (J·m-2·s-1/2·K-1).
Each part is associated with a matrix [31]
Fig. 1. Schematic of the experimental setup with the five parameters to be identified
Each layer can be described as follows:
2.2. The sensor The measurements are performed by a heat flux sensor (in which a thermocouple is embedded), placed into contact with the composite plate. We can assume that the plane in which the measurements are performed corresponds to the median plane of the sensor (Fig.
1), and the portion between the measurement plane and the material is the part of the sensor system which needs to be included in the model. Previous work [32] has shown that when working frequencies are below 0.1 Hz, this part of the sensor behaves like a constant thermal resistance in parallel with a constant thermal capacity. The respective thicknesses and thermal characteristics of the materials of this part of the sensor mean that Rf is very small compared to the contact resistance, and can be neglected in the model. Thus, the sensor portion downstream of the measurement plane is represented by the following matrix: 1 ω
0 1
(2)
Where Cf [J/(K.m²)] is the relevant capacity of the fluxmeter (i.e., the capacity of the part between the measurement plane and the plane of the sensor output). It is a constant value, regardless of the material being tested. It depends on the materials (Kapton, copper, constantan) which constitute the sensor, and can be calculated from the properties of these materials and the geometry of the sensor: Cf = 650 J·m-2·K-1.
2.3. The contact resistance Although the heat flux sensor and the composite plate have very smooth surfaces, there are imperfections and defects which create a thermal contact resistance Rc (which relates the temperature drop between the contacting surfaces to the flux density). However, the nature of the surfaces suggests that this resistance will be small. The following transfer matrix is associated with this resistance [33]:
1 0 1
(3)
Usually, in different methods, the contact resistance is neglected, or its value is fixed at a nominal value in the model. In our case, this contact resistance can be identified as part of the parameter fitting; this has the huge advantage that the value of the contact resistance can be compared with an expected value to help validate the other parameters obtained from the fitting process.
2.4. Composite Reinforcement Plate (CFRP)
This plate is considered in this work to be a homogeneous medium. The general form of the transfer matrix associated with a homogeneous medium can be written as: ω ℎ ω ω. !ℎ
ω $ . !ℎ # # # ω # ℎ # " 1
(4)
Where is the thermal diffusivity [m²/ s] of the plate, the thermal effusivity [J/ K.m².s1/2] and l the thickness of the plate [m]. 2.5. The bonding layer Characterization of this layer is the aim of the measurement. The layer consists of a portion of glue (30 SikaDur Epoxy resin), with vacuum (air) when the bonding is imperfect. To evaluate the bonding quality, we have introduced a coefficient α (“occupancy ratio”), related to the volume ratio of glue in the space between the reinforcing plate and the concrete block. This
coefficient α can vary between 0 and 1. α approaches 0 when there is no glue (i.e., when the medium is an air gap), and α tends to 1 when the space between CFRP and the concrete is filled with glue. Analysis of the thermal impedance measurement will yield an estimate of the equivalent thermal resistance Rα [m2.K.W-1] of the bonding layer. The value of this resistance will be between the resistances of a layer of air and of a thickness "e" filled with glue, and can be interpreted as a “ratio of bonding” or an “occupancy ratio”, making the assumption that the glue region and the air region are both parallel to the composite surface. This configuration is obviously unrealistic, but the parameter α (as defined in equation 5) is still a useful way to translate the quality of the bond into a number between 0 and 1. (FIG. 2):
Fig 2. Expanded view of a bonding failure
.&'() 1 1 1 .+,= * = * % &'() +,/ ∙ 1 1 2 / ∙ 1
(5)
This can be written as: % =
.&'()
/ ∙ 1 2 / . .&'() * .+,- ∙ .+,- ∙ 1 2 / ∙ .&'() * / ∙ .+,-
We can introduce the corresponding thermal capacity Cα
(6)
% = /. 3&'() * 1 2 /. 3+,-
(7)
The sensitivity analysis presented below shows that the value of the capacitance Cα has very little influence on exchanges in the system. The value of α may be identified from the thermal resistance Rα of the layer of glue. The value of the associated capacity Cα may not be particularly accurate, but its value does not take part in the exchanges. From the general relationship (as shown in the matrix for the homogeneous medium) and the above equations, we can write the matrix for the glue and air layer as follows : ω $ % . !ℎ 1 ∙ # ℎ4 % . % . ω5 % . ω # # ω % . ω # . !ℎ 1 ∙ ℎ4 % . % . ω5 # % "
(8)
2.6. Concrete The short test time allows us to treat the concrete as a semi-infinite medium. The thermal behavior of the concrete is characterized by its impedance, Zc. ω =
1
ω
(9)
The parameter b [J·m-2·s-1/2·K-1] represents the thermal effusivity of the material, in other words the material's ability to absorb heat from a medium in contact with it, especially via transient exchanges.
2.7. Overall impedance of the system (sensor + contact + composite plate + glue/vacuum + concrete)
To determine the overall impedance, it is necessary to determine the transfer matrix of the assembly sensor/contact/composite plate/bonding layer and consider a semi-infinite boundary condition imposed by the layer of concrete. The transfer matrix [M1] of the assembly is the result of the product of all the individual matrices characterizing each part:
678 9 =
1 ω
ω ℎ 0 1 1 × 0 1 × ω ω. !ℎ
ω $ . !ℎ # ω # #×… ω # ℎ # " 1
ω $ % . !ℎ 1 ∙ # ℎ4 % . % . ω5 % . ω # …× # ω % . ω # . !ℎ 1 ∙ ℎ4 % . % . ω 5 # % "
The state vector
(10)
) ω determined in the plane of temperature measurement can be written ) ω
as:
1 . = ω ) ω > = 678 9 × < ω ) ω = ω
(11)
Where φe is the heat flux entering the system and θe is the temperature response; we can take (φe, θe) as the input parameters of such a system. φs, is the heat flux entering the concrete slab. This allows us to write a general expression for the input impedance:
) ω =
) ω ) ω
(12)
The impedance as described thus depends on three parameters that must be identified (given that the thermal capacity of the sensor Cf is known):
• The occupancy rate α which sets the values of the heat capacity Cα and the thermal resistance Rα of the bonding layer • The concrete effusivity b • The contact resistance Rc between the sensor and the composite plate
3. Analysis of Sensitivity of Impedance to Thermophysical Parameters
The objective of such a sensitivity study is to define the influence of each system parameter on the impedance, and to optimize the choice of frequency range to be used for identification purposes [34, 35]. In an inverse technique procedure, thermophysical parameters are estimated by seeking the grouping in which the experimental impedance is best approximated by the theoretical impedance. The possibility of simultaneously identifying these parameters can be discussed on the basis of a sensitivity study. This is performed by observing variations in the given function when subjected to a change in one of the parameters. Thus, the analysis takes into account the range of variation and finds the conditions where the quantities can be identified individually. In this way, the frequency range under study can be optimized as a function of the required objectives. It may even enable the model to be simplified, if certain parameters are shown to have negligible influence on the observation range. The impedance is a complex function of frequency. The sensitivity of the magnitude of the impedance to various parameters is studied. The sensitivity functions Spi of the modulus of Z to the parameters pi are defined by:
sZ , pi ( f ) =
∆Z / Z ∆ pi / pi
(13)
In this expression, Z represents the modulus of the impedance. To simplify interpretation over a wide frequency range, the ratio of the relative variations in the parameters to the response function is calculated and expressed as a percentage of the tested function. Since S Z,p is defined as a ratio of two non-dimensional functions, it follows that it is also non-dimensional. The calculation, numerically obtained, involves introducing nominal values of the various parameters. Introduction of these values does not detract from the aim of determining these parameters, because the sensitivity functions are only used qualitatively. They highlight which parameters most affect the behavior of the response function. Any correlations, or situations where an effect could be attributed to a change in more than one parameter, are also identified. The sensitivity analysis can allow us to choose optimum frequency ranges for identifying the main parameters. Only a rough estimate of the parameter values is needed to determine the sensitivity functions. In this case, the following values were chosen: Cf = 650 J·m-2·K -1 for the sensor capacity, Rc = 3×10-3 K·m2·W-1, b = 2000 J·m -2 s -1/2·K-1 for the thermal effusivity of the material and α =1 for a fully glued layer (which corresponds to R = 0.01 m2.K.W-1 for the resistance of the glue, and C = 2930 J.K-1 for the thermal capacity of the glue (because C = e . ρ . c). This situation represents the maximum value of the thermal conductivity of the glue layer.
Fig. 3. Modulus sensitivity to parameters as a function of frequency, case of “good bonding”
Figure 3 shows the sensitivity of the modulus to each parameter. The fully glued case with no air gap is presented; because the poorly-bonded case (with a low value of α) leads to the same conclusions. This example shows that the best choice of frequency range is between ~10 -4Hz and some 10 -2 Hz, because, in this range, the impedance is highly sensitive to the occupancy ratio of the glue, α, and to the thermal effusivity of the material. It should also be noted that there is high sensitivity to contact resistance Rc (which increases with frequency), and that none of the sensitivity curves for b, Rc or α are proportional, indicating that the sensitivities are not correlated in the frequency range studied, and thus all three parameters can be determined simultaneously. It should be noted that the sensitivity to the sensor capacity is much lower, as expected. If we took a lower frequency range, we could neglect the Rc parameter; however, in such a case, the experimental time would be much longer, and this may mean that the exchanges are no longer unidirectional.
Finally, to check if parameters b, Rc or α are correlated, the sensitivities to Rc and to α are plotted as a function of sensitivity to b. If those parameters are correlated, the graph will be a line going through the origin.
Fig. 4.1. Evolution of the sensitivity to the occupancy
Fig. 4.2. Evolution of the sensitivity to the
ratio of the glue α depending on the sensitivity to the
resistance Rc depending on the sensitivity to the
thermal effusivity b.
thermal effusivity b.
Both sensitivities are non-dimensional and expressed as percentages in Fig.4.1 and Fig.4.2. Correlations were not found, so in this study, parameters b, Rc and α can be simultaneously determined in the studied area, from the same test.
4. Determination of thermophysical parameters of system 4.1. Calculation of experimental impedance
The principle involves considering the material as a linear system that does not vary in time [36]. It may be assumed that, when the system is excited by a flux stress, its response is a
change in surface temperature. The analogue signal of temperature T(t), observed at a constant rate, may be represented by the series {T(1); T(2); T(3);...; T(p)}. It is assumed that this signal is the response to an excitation of flux F(t). F(t) is also observed at discrete times {F(1); F(2); F(3);...; F(p)}. The samples of the two signals may be linked by the following linear relationship: ?@A * 8 @A 2 1 * ⋯ * C @A 2
= ? D A * 8 D A 2 1 * ⋯ * E D A 2 F
(14)
This equation constitutes a discrete linear model of order (p,q). It expresses the fact that the value of function T at a given instant depends on the past and present excitation values F and on the previous values of T. Normalizing with respect to a0 gives the commonly used expression: C
E
,I8
,I?
@A = 2 G , @A 2 H * G , D A 2 H
(15)
Hence θ(z) is the z transform of the sequence T(k) and φ(z) that of F(k): MN
J = G @A J KL
(16)
φJ = G D A J KL
(17)
LIKN MN
LIKN
From the time-dependent equation linking the input and the output signals of the linear system, an equivalent equation may be written connecting the various z transforms: J * 8 J K8 J * ⋯ * C J KC J = ? φJ * 8 J K8 φJ * ⋯ * E J KE φJ
Or:
(18)
J ? * 8 J K8 * ⋯ * E J KE = = J φJ 1 * 8 J K8 * ⋯ * C J KC
(19)
Z(z) is referred to as the z transfer function of the discrete-time linear system. Assuming z = ejωTe(where Te represents the sampling rate) brings the calculation back into the Fourier domain, where the experimental impedance of the system Z(f) is obtained. Parameters ai and bj are determined by a least-squares error estimation procedure that involves adopting the group that minimizes the magnitude of the difference between each value of the output signal and the predicted value of the impedance. The thermophysical parameters of the system are estimated by fitting the theoretical model to the experimental impedance. The theoretical impedance is a non-linear function of the thermophysical parameters and frequency. It is adjusted using an iterative procedure based on minimizing a least-squares error criterion (by finding a minimum of the sum of squares of the differences between the functions described).
5. Experiments
5.1. Sample characteristics The constituents of the concrete used for the preparation of the specimens consisted of ordinary Portland cement, sand with a maximum diameter of 5 mm, coarse aggregate with a maximum diameter of 15 mm and tap water. The 28 days axial compressive strength of concrete was found to be 24.0 MPa on an average.
A sample (Fig. 5) was reinforced with CFRP plate (SIKA Carbodur 1012), externally bonded onto a concrete block (50×50×4 cm). The CFRP plate was bonded by the manufacturerspecified glue (Epoxy resin Sikadur 30). An artificial defect was created on the concrete block when gluing the laminates. This defect was an air gap, 5×5 cm in size. The implementation of the glue has been made with a "new" glue and according to the procedure indicated by the SIKA specifications.
Fig.5. Schematic of the tested experimental sample
The main characteristics of the CFRP plates (Carbodur 1012), epoxy resin and cement concrete used are reported in Table 1, which also reports their thermal properties (and those of an air gap).
Table 1 Main characteristics and thermal properties of elements making up the sample
Material
Thickness
λ
e [m]
[W.m .K ]
1.2.10-3
0.7
2.10-3
Air (defect)
2.10-3
Cement concrete block
Semi-∞
SIKA Carbodur 1012 (CFRP) Epoxy resin (glue) Sikadur 30
-1
-1
c
ρ
a
b
R
[kg.m-3] -1
-1
-2
-1
-1
-2
-
2
-1
[J.kg .K ]
[m .s ]
[J.K .m .s 1/2 ]
[m .K.W ]
1530
840
5.44.10-7
948
1.71.10-3
0.2
1200
1220
1.36.10-7
541
1.10-2
0.026
1.184
1000
2.2.10-5
5.55
7.69.10-2
1.8
2300
920
8.5.10-7
1952
5.2. Active infrared thermography detection
NDT techniques using infrared thermography typically fall into three categories: pulsed thermography [37], modulated thermography [38] and pulsed phase thermography [39], the latter being often presented as a further development of the first two techniques. These NDT techniques are distinguished by different thermal stresses and different data processing. In this experiment, infrared thermography is not used as a technique for quantitative NDT, but as a tool for defect viewing. So, unlike conventional NDT using infrared thermography, it is not necessary here to control the amplitude or duration of the thermal excitation signals. The thermal energy emitted by halogen lamps serves only to slightly heat the reinforcing plate. Under these conditions, the thermal resistance created by an air gap or bonding failure causes a higher temperature rise.
The test specimen is placed in front of the infrared camera and a frame fitted with two halogen lamps. This is set at a distance of 2 meters from the sample, to provide a field of view which allows observation of the whole specimen. The thermal stress is applied by means of two halogen lamps with a maximum power of 1 kW each. The infrared camera used in this experiment is a CEDIP Silver 220 cooled camera equipped with a matrix of 320×256 InSb detector elements which are sensitive to medium waves, 3–5 µm. It has a typical NETD of 20 mK and allows acquisition as a function of time. The first part of the experimental test bench is shown in Fig. 6.
Fig.6. Defect detection experimental device and experimental results
The excitation signal is a rectangular function of 15 s duration. Figure 6 shows the changes in average temperatures of two zones. One (green curve) is at a healthy area and the other area (red) has a bonding failure. After 30 seconds the temperature difference between healthy and defective areas can reach nearly 3 °C. This defect detection made using the infrared camera is a first step, and helps locate potential poorly-bonded areas. 5.3.Experimental set-up
Fig. 7 shows the experimental set-up for thermal characterization of the defective areas. The objective is to apply a thermal stress onto the surface by means of electrical resistance. To ensure that the majority of the energy is dissipated through the fluxmeter and reaches the material, thermal insulation is placed above the resistance. The thermal flux and temperature values are recorded by the fluxmeter, located between the resistance and the sample surface. The unidirectionality of transfer is ensured by an insulating belt surrounding the material studied; the sensor is equipped with a guard ring and its surface is less sensitive than that of the sample. Edge effects are avoided. The weight placed on the device keeps everything in a stable position and reduces contact resistance. The thermal stress imposed by the heater is based on a pseudo-random binary signal generated by the computer.
We tested our experimental device on two separate cases: • On an area where we had previously identified a lack of bonding using the infrared camera (position 1 in Fig.7). • On a fully bonded, sound area (position 2 in Fig.7).
Fig. 7. Experimental set-up for thermal characterization of the defective bond
The heat flux values and temperature readings will allow us to calculate the transfer function for each of the positions (the defective and sound areas).
5.4.Excitation signal
This method has the advantage of not requiring any control of the boundary conditions and being able to exploit random signals. It is perfectly suited to in situ use under any disturbance conditions. The experiments for the present study were performed in the laboratory and stress was imposed on the system by dissipating heat through a flat resistance. Pseudo-random binary signals (PRBS) were used. This type of signal has the advantage of selecting and exciting a wide spectral band, while limiting the amount of energy introduced into the system.
5.5. Experimental results
As described previously, the z transfer function is determined. The impedance obtained is represented in Fig. 10 in the form of a graph showing the moduli of the impedance plotted as a function of the frequency. Thermophysical parameters (b, Rc, α) are thus determined by adopting the group that minimizes the difference between each value of the output signal and the predicted value, following the flowchart shown in Fig. 8.
Fig. 8. Data flowchart showing the parameter estimation procedure
Fig. 9. Comparison of the experimental impedance moduli and the values found by the theoretical study
The fitting of the optimized theoretical impedance with the measured impedance (obtained from the temperature and flux using the z transfer function), gave the parameter values shown in Table 2.
Table 2 Thermophysical parameters derived from the theoretical study Sample well adhered
Values
Values
Values
Values
resulting
from
resulting
from
resulting
from
resulting
from
from the
laborato
from the
laborato
from the
laborato
from the
laborato
optimizati
ry
optimizati
ry
optimizati
ry
optimizati
ry
on
testing
on
testing
on
testing
on
testing
(glue)
Units
Contact resistanc e (Rc)
[K.m².W− 1 ]
Sample with defect
intermediate state: Sample with defect (air) close to 5% Values Values
0.005
(*)
0.012
(*)
intermediate state: Sample with defect (air) close to 15% Values Values
(air) close to 100%
0.008
(*)
Occupan 0.99 (*) (*) (*) 0.94 0.85 cy ratio ( α) Thermal [J m Effusivit 2 −1/2 2.04.103 1.95.103 2.08.103 1.95.103 2.1.103 1.95.103 .s y of the −1 K ] concrete (b) [%] Deviatio 4.61 6.67 7.69 n in (b) (*) Nota : it is impossible to determine these parameters from a laboratory test
0.017
(*)
0.023
(*)
2.09.103
1.95.103
7.18
The standard deviation of the estimated values of the thermal effusivity b compared to the value of the thermal effusivity b from the laboratory study ([NF-EN 12664]) is quite low (<8%). We also note that the occupancy ratio is close to 1 when the reinforcing plate is well bonded, and close to zero in the case of the air gap. The method seems to be able to define quantitatively the bond quality of a concrete block reinforced with CFRP.
6. Conclusion
As we described previously, CFRP plates are used to reinforce civil engineering structures. Infrared thermography is one of the techniques currently used to examine bonding of phases in composites in situ, and more often as a qualitative analysis technique to locate defects. Here we have coupled infrared thermography with thermal impedance characterization which
allows us to estimate the occupancy ratio of the interface (α, which varies from 1 for a fully glued interface to 0 for a complete void). This then provides a numerical indication of the quality of the bond between the carbon fiber plate and concrete block. The method is easily applied on site, and quickly provides an estimate of the degree of bonding of reinforcing plates to a structure. Indeed, the method developed does not require control of boundary conditions; it can calculate the contact resistance and CFRP have the advantage of having a good surface (smooth). The only restriction for in situ application is in the first approach by infrared thermography (not too much wind, rain, etc.). In the future, various defects with different α values could be created and thermally characterized. The thermal characterization could potentially be correlated with the mechanical properties of these assemblies. If a strong correlation was demonstrated, thermal characterization could then provide an indirect estimate of the mechanical effectiveness of the CFRP reinforcement.
References
[1] Calgaro, J.-A. et Lacroix, R., Maintenance et réparation des ponts, Presses de l’Ecole Nationale des Ponts et Chaussée, 1997
[2] Pakvor, A., Repair and strengthening of concrete structures: general aspects, Structural Engineering International, 2, 1995
[3] Y.Y. Kim, B.Y. Lee, J.W. Banga, B.C. Han, L. Feo, C.G. Cho, Flexural performance of reinforced concrete beams strengthened with strain-hardening cementitious composite and high strength reinforcing steel bar, Composites Part B: Engineering, Volume 56, January 2014, Pages 512–519
[4] J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis –- CRC Press Inc - ISBN-10: 0849315921 – 2003
[5] M. Ei-Mikawi, A. S. Mosallam, A methodology for evaluation of the use of advanced composites in structural civil engineering applications, Composites Part B: Engineering, Volume 27, Issues 3–4, 1996, Pages 203–215
[6] ACI 440.2R-02. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. American Concrete Institute, Farmington Hills, Michigan; 2002
[7] N.M. Hassan, R.C. Batra, Modeling damage in polymeric composites, Composites Part B: Engineering, Volume 39, Issue 1,January 2008, Pages 66–82
[8] P. Neto, J. Alfaiate, J. Vinagre, A three-dimensional analysis of CFRP–concrete bond behavior, Composites Part B: Engineering, Volume 59, March 2014, Pages 153-165
[9] S. C. Florut, G. Sas, C. Popescu, V. Stoian, Tests on reinforced concrete slabs with cut-out openings strengthened with fibre-reinforced polymers, Composites Part B: Engineering, Volume 66, November 2014, Pages 484-493
[10] T. D’Antino, C. Pellegrino, Bond between FRP composites and concrete: Assessment of design procedures and analytical models, Composites Part B: Engineering, Volume 60, April 2014, Pages 440-456
[11] C. Lesmana, H.S. Hu, F.M. Lin, N.M. Huang, Numerical analysis of square reinforced concrete plates strengthened by fiber-reinforced plastics with various patterns, Composites: Part B 55, 2013, Pages 247–262
[12] Antonio R. Marí, Eva Oller, Jesús M. Bairán, Noemí Duarte, Simplified method for the calculation of long-term deflections in FRP-strengthened reinforced concrete beams, Composites Part B: Engineering, Volume 45, Issue 1, February 2013, Pages 1368-1376
[13] J. Yao, J.G. Teng, J.F. Chen, Experimental study on FRP-to-concrete bonded joints, Composites: Part B 36, 2005, Pages 99–113
[14] K.T. Lau, P.K. Dutta, L.M. Zhoua, D. Hui, Mechanics of bonds in an FRP bonded concrete beam, Composites Part B: Engineering, Volume 32, Issue 6, September 2001, Pages 491–502
[15] N. Pešić, K. Pilakoutas, Concrete beams with externally bonded flexural FRP-reinforcement: analytical investigation of debonding failure, Composites Part B: Engineering, Volume 34, Issue 4, 1 June 2003, Pages 327-338
[16] ACI Committee 440.2R02-08.”Guide for the Design and Construction of Externally Bonded Systems for Strengthening Concrete Structures”, American Concrete Institute, Michigan, U.S.A., 2008
[17] AFGC. 2007. “Réparation et renforcement des structures en béton au moyen des matériaux composites – Recommandations provisoires”, Bulletin scientifique et technique de l’AFGC. (in French)
[18] Fib Task Group 9.3. ,2001, Externally bonded FRP reinforcement for RC structures, fib bulletin 14, Lausanne, Switzerland
[19] Rawaa Al-Safy, Riadh Al-Mahaidi, George P. Simon, A study of the use of high functionalitybased resin for bonding between CFRP and concrete under harsh environmental conditions, Composite Structures 95, 2013, 295–306
[20] W.L. Lai, S.C. Kou, C.S. Poon, W.F. Tsang, C.C. Lai, Characterization of the deterioration of externally bonded CFRP-concrete composites using quantitative infrared thermography, Cement & Concrete Composites 32, 2010, Pages 740–746
[21] J. Tashan, R. Al-Mahaidi, Detection of cracks in concrete strengthened with CFRP systems using infra-red thermography Composites Part B: Engineering, Volume 64, August 2014, Pages 116-125
[22] V. Feuillet, L. Ibos, M. Fois, J. Dumoulin, Y. Candau, Defect detection and characterization in composite materials using square pulse thermography coupled with singular value decomposition analysis and thermal quadrupole modeling, NDT&E International 51, 2012, Pages 58–67
[23] C. Maierhofer, P. Myrach, M. Reischel, H. Steinfurth, M. Röllig, M. Kunert, Characterizing damage in CFRP structures using flash thermography in reflection and transmission configurations, Composites Part B: Engineering, Volume 57, February 2014, Pages 35–46
[24] X.Maldague, Theory and practice of infrared technology for non-destructive testing. WileyInterscience, John Wiley&Sons, Inc.; 2001
[25] P.H. James, C.S. Welch, W.P. Winfree. A numerical grid generation scheme forthermal simulation in laminated structures. In: Thompson DO, Chimenti DE,editors. Review of progress in quantitative nondestructive evaluation, vol.8A. New York: Plenum Press; 1989. Pages 801–9
[26] J.C. Krapez, P. Cielo, Thermographicnondestructive evaluation: data inversion
procedures part I: 1D analysis. Res NondestructEval 1991;3(2), Pages 81–100
[27] A. Chauchois, D. Defer, E. Antczak, and B. Duthoit, Use of noninteger identification models for monitoring soil water content, Meas. Sci. Technol. 14, 868, 2003
[28] A. Chauchois, E. Antczak, D. Defer, and F.Brachelet In situ characterization of thermophysical soil properties—Measurements and monitoring of soil water content with a thermal probe, J. Renewable Sustainable Energy 4, 043106, 2012
[29] D. Defer, E. Antczak, B. Duthoit, The characterization of thermophysical properties by thermal impedance measurements taken under random stimuli taking sensor-induced disturbance into account - Meas. Sci. Technol. 9, 496, 1998,
[30] P. Hérin, P. Théry, Measurements on the thermoelectric properties of thin layers of two metals in electrical contact. Application for designing new heat flow sensors, J. Meas. Sci. Technol., 3 ,1993, Pages 158–163
[31] A. Degiovanni, Thermal conduction in a multilayer slab with internal sources; using a quadripole method, Int. J. Heat Mass Transfer 31, 553, 1988
[32] A. Chauchois, E. Antczak, D. Defer, O. Carpentier, Formalism of thermal waves applied to the characterization of materials thermal effusivity, Review of Scientific Instruments 82, 074902, 2011
[33] D. Defer, A. Chauchois, E. Antczak, and O. Carpentier, Determination of Thermal Properties in the Frequency Domain Based on a Non-integer Model: Application to a Sample of Concrete, Int. J. Thermophys., 30(3), 1025, 2009
[34] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M.Saisana, and S. Tarantola, Global Sensitivity Analysis. The primer, (Wiley, New York, 2008)
[35] Y. Jannot, A. Degiovanni, and G. Payet, Thermal conductivity measurment of insulating materials with a three layers device, Int. J. Heat Mass Transfer 52, 1105-1111, 2009
[36] R. Pintelon and J. Schoukens, System identification: A frequency domain approach (IEEE Press, Piscat-away, New Jersey, 2001)
[37] X. Maldague, Theory and practice of infrared technology for nondestructive testing, WileyInterscience, New York (2001)
[38] O. Breitenstein, W. Warta, M. Langenkamp, Lock-in Thermography - Basics and Use for Evaluating Electronic Devices and Materials ,(book) Springer, 2003
[39] X. Maldague, F. Galmiche, A. Ziadi, Advances in pulsed phase thermography, Infrared Physics & Technology, vol. 43, June 2002, Pages 175-181
Table 1 Main characteristics and thermal properties of elements making up the sample
Material
Thickness
λ
e [m]
[W.m .K ]
1.2.10-3
0.7
2.10-3
Air (defect)
2.10-3
Cement concrete block
Semi-∞
SIKA Carbodur 1012 (CFRP) Epoxy resin (glue) Sikadur 30
-1
-1
ρ
c
a
b
R
[kg.m-3] -1
-1
-2
-1
-1
-2
-
2
-1
[J.kg .K ]
[m .s ]
[J.K .m .s 1/2 ]
[m .K.W ]
1530
840
5.44.10-7
948
1.71.10-3
0.2
1200
1220
1.36.10-7
541
1.10-2
0.026
1.184
1000
2.2.10-5
5.55
7.69.10-2
1.8
2300
920
8.5.10-7
1952
Table 2 Thermophysical parameters derived from the theoretical study Sample well adhered
Values
Values
Values
Values
resulting
from
resulting
from
resulting
from
resulting
from
from the
laborato
from the
laborato
from the
laborato
from the
laborato
optimizati
ry
optimizati
ry
optimizati
ry
optimizati
ry
on
testing
on
testing
on
testing
on
testing
(glue)
Units
Contact resistanc e (Rc)
[K.m².W− 1 ]
Sample with defect
intermediate state: Sample with defect (air) close to 5% Values Values
0.005
(*)
0.012
(*)
intermediate state: Sample with defect (air) close to 15% Values Values
(air) close to 100%
0.008
(*)
Occupan 0.99 (*) (*) (*) 0.94 0.85 cy ratio ( α) Thermal [J m Effusivit 2 −1/2 2.04.103 1.95.103 2.08.103 1.95.103 2.1.103 1.95.103 .s y of the −1 K ] concrete (b) [%] Deviatio 4.61 6.67 7.69 n in (b) (*) Nota : it is impossible to determine these parameters from a laboratory test
0.017
(*)
0.023
(*)
2.09.103
1.95.103
7.18
S1359-8368(14)00446-6 http://dx.doi.org/10.1016/j.compositesb.2014.10.002 JCOMB 3216
To appear in:
Composites: Part B
Received Date: Revised Date: Accepted Date:
29 July 2013 24 September 2014 1 October 2014
Please cite this article as: Alexis, C., Franck, B., Didier, D., Emmanuel, A., Hangseok, C., Evaluation of gluing of cfrp onto concrete structures by infrared thermography coupled with thermal impedance, Composites: Part B (2014), doi: http://dx.doi.org/10.1016/j.compositesb.2014.10.002
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
EVALUATION OF GLUING OF CFRP ONTO CONCRETE STRUCTURES BY INFRARED THERMOGRAPHY COUPLED WITH THERMAL IMPEDANCE CHAUCHOIS Alexisa,b, BRACHELET Francka, DEFER Didiera, ANTCZAK Emmanuela, CHOI Hangseokb a
LGCgE – Université Lille Nord de France F59000,FSA - Université d'Artois, Technoparc Futura, 62400 Bethune, France Tel : (33) 3 21 63 71 31 Fax : (33) 3 21 61 17 80 E-mail: [email protected] b
School of Civil, Environmental, and Architectural Engineering, Korea University, Seoul, Republic of Korea
Abstract Carbon Fiber Reinforced Polymers (CFRPs) have been increasingly employed for structural strengthening, and are attached to structures using bonding adhesives. The aim of this work is to characterize defects in the bond between CFRP and concrete (after they are located by pulse infrared thermography), and assign the defects a “numerical value” (ranging from 0 for a complete air-gap to 1 for a fully glued bond). Quantitative characterization is performed by measuring the thermal impedance, and then identifying the thermophysical parameters of the system through fitting the measured impedance to a theoretical model. An inversion procedure is carried out to estimate the unknown parameters, without prior knowledge of sample properties. In particular, it is possible to estimate more accurately both the amount of glue within a defect and the thermal contact resistance.
Keywords CFRP, heat flux sensor, pulse infrared thermography, defect detection and characterization, thermal impedance
1. Introduction
Aging civil engineering infrastructure is at the center of current concerns of many countries. Indeed, after World War II, construction of concrete structures (such as road infrastructure, buildings, and parking garages) heightened. So, for over 60 years, these structures have suffered the ravages of time and various attacks. Many of these concrete structures show changes in material composition or structural damage (caused, for example, by poor design, poor construction or changes in boundary conditions as a result of scour, landslides or other external agents). Some structures can no longer meet the requirements for safe use; in some cases the way the structures are used has evolved over the years as well (for example the increased size and number of vehicles). The demolition and reconstruction solution is usually too costly. In fact, alternatives are possible, [1-3] including: repair of the surface, concrete protection, materials regeneration, strengthening and adding extra material. The best solution depends on the importance of the structure and the amount of damage or disorder that has occurred.
One way of strengthening structures is by reinforcing with a composite material plate, which has the advantages of not corroding, being lightweight and high-strength. These composites are referred to as "FRP", fiber reinforced plastics or "CFRP", carbon fiber reinforced plastics/polymers. This process allows the strength and stiffness of the structure to be increased by the combined action of the plate and the concrete. FRP are composite materials made of high-strength fibers (glass, carbon or aramid) impregnated with a matrix (such as polyester, vinyl ester, or epoxy).
As they are becoming less expensive, composites are an attractive solution for strengthening buildings and other infrastructure. [4] The strengthening or retrofitting of reinforced concrete structures by externally bonded FRP systems is now a widespread and accepted technique, [5, 6] which has been widely studied, for example in [7–15].
The quality of bonding at externally bonded CFRP-concrete interfaces is very important. For external reinforcing with FRP composites to be most effective, the work must be very carefully carried out [16-18], and, crucially, the adhesive layer must not suffer too much damage when exposed to aggressive environments [19]. Otherwise, voids or flaws at the interface can occur; these defects are quite common. In the first case; “flaws” are formed because of poor workmanship during the initial application of the CFRP strips onto the concrete surface. Adhesion problems sometimes occur because not enough glue is used, or because some areas have not been glued at all. The second type of defect is “delamination”, and occurs because of stress concentrations associated with physical/chemical degradation of the binding layer [20] (when the composite is exposed to aggressive environments such as elevated temperatures, ultraviolet radiation, infiltration of moisture or extreme temperatures caused by fire). These invisible defects embedded in the interface between the CFRP and concrete can significantly reduce the effective contact area, and therefore the overall bond strength. Ultimately, the durability and service life of the CFRP-strengthened concrete structure is adversely affected. This means that quality control though “in situ” verification of bonded FRP systems is of paramount importance. Conventional methods for evaluating the bond quality of the CFRPconcrete composites are hammer-tapping and pull-off tests. Hammer-tapping requires the
inspectors to manually tap each point to be checked, while the pull-off test is destructive. Both types of tests are regarded as local tests, and do not allow effective, large-scale inspection. The Infrared Thermographic (IRT) technique has been widely accepted as an effective means of identifying and quantifying unseen surface flaws in a wide range of composite materials [21- 23]. This is because the presence of a defect (i.e. an "air layer") at the interface in a composite material reduces the rate of heat diffusion when thermal stimulus is applied. In fact, of all the Non-Destructive Testing Techniques (NDT) under investigation for bondquality assessment, (active) infrared thermography is of particular interest, because it is easy to deploy and can be used to rapidly inspect large surfaces, where only one side is accessible. However, even if these techniques are able to locate the defects, most of the time they are unable to provide sufficient specific information such as the depth and width of the disbonded area, or to assess the degree of adhesion between the composite and the adhesive. Indeed, during the early applications of IRT, the majority of published work simply focused on locating defects in a qualitative manner. It is more useful to quantify the size of the defects so that the extent of damage can be assessed. Quantitative defect characterization using infrared data can be achieved on the basis of direct analytical methods [24, 25] and inverse methods [26]. Approaches by direct analysis can be used to model the characteristics of the defects, but these approaches can be very complex, even when the defect geometries are simple, and can become impossible once anisotropic properties and defects in the surface are considered [24]. Consequently, in this work we will couple two methods: a pulse thermographic detection method to visually locate the defect, and a thermal method based on a heat flux sensor (also known as “fluxmeter”), to characterize it in more detail. Our aim is to quantify the quality of the bonding between CFRP and concrete.
2. Theory
For several years, our research team has been developing thermophysical characterization methods based on the study of thermal impedance, as measured using heat flux sensors [27]. Thermal impedance represents the relationship between the frequency components of temperature and the frequency-dependent flux density in the same surface. From an experimental point of view, it is determined simply by measuring the flux density and temperature simultaneously in a measurement plane surface. In practice, a heat flux sensor [28] in which a thermocouple has been embedded is placed in contact with the sample. The changes in flux density and temperature measured in this way are different from those in the material access plane. The reasons for this perturbation are the presence of the sensor and the sensor/material contact resistance. This original approach is based on a frequency-dependent study of the changes at the surfaces of materials.
2.1. Notion of thermal impedance a) Definition
By definition, the thermal impedance Z [29] is a complex parameter, defined in the frequency domain as the ratio of the temperature and heat flux. Thus, Z(f) can be written as: =
ω = ω
where Z is a function of the frequency f or of the pulse-duration ω.
(1)
Both quantities can be measured simultaneously using a heat flux sensor fitted with a thermocouple. If the thermal impedance is estimated for characterization purposes, both the imposed stress and temperature response are observed simultaneously, and their interaction can be analyzed. Such an analysis is carried out in the frequency domain, enabling the system to be studied on the basis of random signals. The frequency approach facilitates an understanding of the phenomena, and, along with the sensitivity study, transformation into the spectral domain enables us to target precisely which frequency range should be selected to identify the required parameters. The thermophysical parameters can be identified by fitting a theoretical model to the experimentally determined impedance. The thermal impedance can be expressed theoretically, as will be shown in this paper. The experimental procedure for calculating the apparent thermal impedance of the input side of a material requires both temperature and flux sensors to be positioned on the sample. Then one may observe either the natural exchanges between the material and the environment, or as in our case, heat the sensor/material assembly directly. To ensure exchanges are one-directional heat flow, the sensor consists of a sensitive measuring area surrounded by a ring with a similar but inert material acting as a guard ring. The sensor is a tangential-gradient fluxmeter (heat flux sensor) [30], 0.5 mm in thickness, whose temperature is measured with an embedded T-type thermocouple. Theoretically, the system that we study may be represented by a series connection of five elements (Fig. 1): •
the part of the sensor between the measurement plane and the output plane, which can be modeled by a thermal capacitance Cf (J·m-²·K-1) [28]
• •
a thermal contact resistance Rc (K·m²·W-1) between the sensor and the composite plate the composite plate with known thermal characteristics (λ and ρc) and width ℓ
•
a thickness made up of glue and air-gap in proportions depending on the quality of the bond, and modeled using a thermal resistance R (K·m²·W-1) and a heat capacity C (J·m-²·K-1)
•
a thick concrete layer acting as a semi-infinite medium, of thermal effusivity characterized by b (J·m-2·s-1/2·K-1).
Each part is associated with a matrix [31]
Fig. 1. Schematic of the experimental setup with the five parameters to be identified
Each layer can be described as follows:
2.2. The sensor The measurements are performed by a heat flux sensor (in which a thermocouple is embedded), placed into contact with the composite plate. We can assume that the plane in which the measurements are performed corresponds to the median plane of the sensor (Fig.
1), and the portion between the measurement plane and the material is the part of the sensor system which needs to be included in the model. Previous work [32] has shown that when working frequencies are below 0.1 Hz, this part of the sensor behaves like a constant thermal resistance in parallel with a constant thermal capacity. The respective thicknesses and thermal characteristics of the materials of this part of the sensor mean that Rf is very small compared to the contact resistance, and can be neglected in the model. Thus, the sensor portion downstream of the measurement plane is represented by the following matrix: 1 ω
0 1
(2)
Where Cf [J/(K.m²)] is the relevant capacity of the fluxmeter (i.e., the capacity of the part between the measurement plane and the plane of the sensor output). It is a constant value, regardless of the material being tested. It depends on the materials (Kapton, copper, constantan) which constitute the sensor, and can be calculated from the properties of these materials and the geometry of the sensor: Cf = 650 J·m-2·K-1.
2.3. The contact resistance Although the heat flux sensor and the composite plate have very smooth surfaces, there are imperfections and defects which create a thermal contact resistance Rc (which relates the temperature drop between the contacting surfaces to the flux density). However, the nature of the surfaces suggests that this resistance will be small. The following transfer matrix is associated with this resistance [33]:
1 0 1
(3)
Usually, in different methods, the contact resistance is neglected, or its value is fixed at a nominal value in the model. In our case, this contact resistance can be identified as part of the parameter fitting; this has the huge advantage that the value of the contact resistance can be compared with an expected value to help validate the other parameters obtained from the fitting process.
2.4. Composite Reinforcement Plate (CFRP)
This plate is considered in this work to be a homogeneous medium. The general form of the transfer matrix associated with a homogeneous medium can be written as: ω ℎ ω ω. !ℎ
ω $ . !ℎ # # # ω # ℎ # " 1
(4)
Where is the thermal diffusivity [m²/ s] of the plate, the thermal effusivity [J/ K.m².s1/2] and l the thickness of the plate [m]. 2.5. The bonding layer Characterization of this layer is the aim of the measurement. The layer consists of a portion of glue (30 SikaDur Epoxy resin), with vacuum (air) when the bonding is imperfect. To evaluate the bonding quality, we have introduced a coefficient α (“occupancy ratio”), related to the volume ratio of glue in the space between the reinforcing plate and the concrete block. This
coefficient α can vary between 0 and 1. α approaches 0 when there is no glue (i.e., when the medium is an air gap), and α tends to 1 when the space between CFRP and the concrete is filled with glue. Analysis of the thermal impedance measurement will yield an estimate of the equivalent thermal resistance Rα [m2.K.W-1] of the bonding layer. The value of this resistance will be between the resistances of a layer of air and of a thickness "e" filled with glue, and can be interpreted as a “ratio of bonding” or an “occupancy ratio”, making the assumption that the glue region and the air region are both parallel to the composite surface. This configuration is obviously unrealistic, but the parameter α (as defined in equation 5) is still a useful way to translate the quality of the bond into a number between 0 and 1. (FIG. 2):
Fig 2. Expanded view of a bonding failure
.&'() 1 1 1 .+,= * = * % &'() +,/ ∙ 1 1 2 / ∙ 1
(5)
This can be written as: % =
.&'()
/ ∙ 1 2 / . .&'() * .+,- ∙ .+,- ∙ 1 2 / ∙ .&'() * / ∙ .+,-
We can introduce the corresponding thermal capacity Cα
(6)
% = /. 3&'() * 1 2 /. 3+,-
(7)
The sensitivity analysis presented below shows that the value of the capacitance Cα has very little influence on exchanges in the system. The value of α may be identified from the thermal resistance Rα of the layer of glue. The value of the associated capacity Cα may not be particularly accurate, but its value does not take part in the exchanges. From the general relationship (as shown in the matrix for the homogeneous medium) and the above equations, we can write the matrix for the glue and air layer as follows : ω $ % . !ℎ 1 ∙ # ℎ4 % . % . ω5 % . ω # # ω % . ω # . !ℎ 1 ∙ ℎ4 % . % . ω5 # % "
(8)
2.6. Concrete The short test time allows us to treat the concrete as a semi-infinite medium. The thermal behavior of the concrete is characterized by its impedance, Zc. ω =
1
ω
(9)
The parameter b [J·m-2·s-1/2·K-1] represents the thermal effusivity of the material, in other words the material's ability to absorb heat from a medium in contact with it, especially via transient exchanges.
2.7. Overall impedance of the system (sensor + contact + composite plate + glue/vacuum + concrete)
To determine the overall impedance, it is necessary to determine the transfer matrix of the assembly sensor/contact/composite plate/bonding layer and consider a semi-infinite boundary condition imposed by the layer of concrete. The transfer matrix [M1] of the assembly is the result of the product of all the individual matrices characterizing each part:
678 9 =
1 ω
ω ℎ 0 1 1 × 0 1 × ω ω. !ℎ
ω $ . !ℎ # ω # #×… ω # ℎ # " 1
ω $ % . !ℎ 1 ∙ # ℎ4 % . % . ω5 % . ω # …× # ω % . ω # . !ℎ 1 ∙ ℎ4 % . % . ω 5 # % "
The state vector
(10)
) ω determined in the plane of temperature measurement can be written ) ω
as:
1 . = ω ) ω > = 678 9 × < ω ) ω = ω
(11)
Where φe is the heat flux entering the system and θe is the temperature response; we can take (φe, θe) as the input parameters of such a system. φs, is the heat flux entering the concrete slab. This allows us to write a general expression for the input impedance:
) ω =
) ω ) ω
(12)
The impedance as described thus depends on three parameters that must be identified (given that the thermal capacity of the sensor Cf is known):
• The occupancy rate α which sets the values of the heat capacity Cα and the thermal resistance Rα of the bonding layer • The concrete effusivity b • The contact resistance Rc between the sensor and the composite plate
3. Analysis of Sensitivity of Impedance to Thermophysical Parameters
The objective of such a sensitivity study is to define the influence of each system parameter on the impedance, and to optimize the choice of frequency range to be used for identification purposes [34, 35]. In an inverse technique procedure, thermophysical parameters are estimated by seeking the grouping in which the experimental impedance is best approximated by the theoretical impedance. The possibility of simultaneously identifying these parameters can be discussed on the basis of a sensitivity study. This is performed by observing variations in the given function when subjected to a change in one of the parameters. Thus, the analysis takes into account the range of variation and finds the conditions where the quantities can be identified individually. In this way, the frequency range under study can be optimized as a function of the required objectives. It may even enable the model to be simplified, if certain parameters are shown to have negligible influence on the observation range. The impedance is a complex function of frequency. The sensitivity of the magnitude of the impedance to various parameters is studied. The sensitivity functions Spi of the modulus of Z to the parameters pi are defined by:
sZ , pi ( f ) =
∆Z / Z ∆ pi / pi
(13)
In this expression, Z represents the modulus of the impedance. To simplify interpretation over a wide frequency range, the ratio of the relative variations in the parameters to the response function is calculated and expressed as a percentage of the tested function. Since S Z,p is defined as a ratio of two non-dimensional functions, it follows that it is also non-dimensional. The calculation, numerically obtained, involves introducing nominal values of the various parameters. Introduction of these values does not detract from the aim of determining these parameters, because the sensitivity functions are only used qualitatively. They highlight which parameters most affect the behavior of the response function. Any correlations, or situations where an effect could be attributed to a change in more than one parameter, are also identified. The sensitivity analysis can allow us to choose optimum frequency ranges for identifying the main parameters. Only a rough estimate of the parameter values is needed to determine the sensitivity functions. In this case, the following values were chosen: Cf = 650 J·m-2·K -1 for the sensor capacity, Rc = 3×10-3 K·m2·W-1, b = 2000 J·m -2 s -1/2·K-1 for the thermal effusivity of the material and α =1 for a fully glued layer (which corresponds to R = 0.01 m2.K.W-1 for the resistance of the glue, and C = 2930 J.K-1 for the thermal capacity of the glue (because C = e . ρ . c). This situation represents the maximum value of the thermal conductivity of the glue layer.
Fig. 3. Modulus sensitivity to parameters as a function of frequency, case of “good bonding”
Figure 3 shows the sensitivity of the modulus to each parameter. The fully glued case with no air gap is presented; because the poorly-bonded case (with a low value of α) leads to the same conclusions. This example shows that the best choice of frequency range is between ~10 -4Hz and some 10 -2 Hz, because, in this range, the impedance is highly sensitive to the occupancy ratio of the glue, α, and to the thermal effusivity of the material. It should also be noted that there is high sensitivity to contact resistance Rc (which increases with frequency), and that none of the sensitivity curves for b, Rc or α are proportional, indicating that the sensitivities are not correlated in the frequency range studied, and thus all three parameters can be determined simultaneously. It should be noted that the sensitivity to the sensor capacity is much lower, as expected. If we took a lower frequency range, we could neglect the Rc parameter; however, in such a case, the experimental time would be much longer, and this may mean that the exchanges are no longer unidirectional.
Finally, to check if parameters b, Rc or α are correlated, the sensitivities to Rc and to α are plotted as a function of sensitivity to b. If those parameters are correlated, the graph will be a line going through the origin.
Fig. 4.1. Evolution of the sensitivity to the occupancy
Fig. 4.2. Evolution of the sensitivity to the
ratio of the glue α depending on the sensitivity to the
resistance Rc depending on the sensitivity to the
thermal effusivity b.
thermal effusivity b.
Both sensitivities are non-dimensional and expressed as percentages in Fig.4.1 and Fig.4.2. Correlations were not found, so in this study, parameters b, Rc and α can be simultaneously determined in the studied area, from the same test.
4. Determination of thermophysical parameters of system 4.1. Calculation of experimental impedance
The principle involves considering the material as a linear system that does not vary in time [36]. It may be assumed that, when the system is excited by a flux stress, its response is a
change in surface temperature. The analogue signal of temperature T(t), observed at a constant rate, may be represented by the series {T(1); T(2); T(3);...; T(p)}. It is assumed that this signal is the response to an excitation of flux F(t). F(t) is also observed at discrete times {F(1); F(2); F(3);...; F(p)}. The samples of the two signals may be linked by the following linear relationship: ?@A * 8 @A 2 1 * ⋯ * C @A 2
= ? D A * 8 D A 2 1 * ⋯ * E D A 2 F
(14)
This equation constitutes a discrete linear model of order (p,q). It expresses the fact that the value of function T at a given instant depends on the past and present excitation values F and on the previous values of T. Normalizing with respect to a0 gives the commonly used expression: C
E
,I8
,I?
@A = 2 G , @A 2 H * G , D A 2 H
(15)
Hence θ(z) is the z transform of the sequence T(k) and φ(z) that of F(k): MN
J = G @A J KL
(16)
φJ = G D A J KL
(17)
LIKN MN
LIKN
From the time-dependent equation linking the input and the output signals of the linear system, an equivalent equation may be written connecting the various z transforms: J * 8 J K8 J * ⋯ * C J KC J = ? φJ * 8 J K8 φJ * ⋯ * E J KE φJ
Or:
(18)
J ? * 8 J K8 * ⋯ * E J KE = = J φJ 1 * 8 J K8 * ⋯ * C J KC
(19)
Z(z) is referred to as the z transfer function of the discrete-time linear system. Assuming z = ejωTe(where Te represents the sampling rate) brings the calculation back into the Fourier domain, where the experimental impedance of the system Z(f) is obtained. Parameters ai and bj are determined by a least-squares error estimation procedure that involves adopting the group that minimizes the magnitude of the difference between each value of the output signal and the predicted value of the impedance. The thermophysical parameters of the system are estimated by fitting the theoretical model to the experimental impedance. The theoretical impedance is a non-linear function of the thermophysical parameters and frequency. It is adjusted using an iterative procedure based on minimizing a least-squares error criterion (by finding a minimum of the sum of squares of the differences between the functions described).
5. Experiments
5.1. Sample characteristics The constituents of the concrete used for the preparation of the specimens consisted of ordinary Portland cement, sand with a maximum diameter of 5 mm, coarse aggregate with a maximum diameter of 15 mm and tap water. The 28 days axial compressive strength of concrete was found to be 24.0 MPa on an average.
A sample (Fig. 5) was reinforced with CFRP plate (SIKA Carbodur 1012), externally bonded onto a concrete block (50×50×4 cm). The CFRP plate was bonded by the manufacturerspecified glue (Epoxy resin Sikadur 30). An artificial defect was created on the concrete block when gluing the laminates. This defect was an air gap, 5×5 cm in size. The implementation of the glue has been made with a "new" glue and according to the procedure indicated by the SIKA specifications.
Fig.5. Schematic of the tested experimental sample
The main characteristics of the CFRP plates (Carbodur 1012), epoxy resin and cement concrete used are reported in Table 1, which also reports their thermal properties (and those of an air gap).
Table 1 Main characteristics and thermal properties of elements making up the sample
Material
Thickness
λ
e [m]
[W.m .K ]
1.2.10-3
0.7
2.10-3
Air (defect)
2.10-3
Cement concrete block
Semi-∞
SIKA Carbodur 1012 (CFRP) Epoxy resin (glue) Sikadur 30
-1
-1
c
ρ
a
b
R
[kg.m-3] -1
-1
-2
-1
-1
-2
-
2
-1
[J.kg .K ]
[m .s ]
[J.K .m .s 1/2 ]
[m .K.W ]
1530
840
5.44.10-7
948
1.71.10-3
0.2
1200
1220
1.36.10-7
541
1.10-2
0.026
1.184
1000
2.2.10-5
5.55
7.69.10-2
1.8
2300
920
8.5.10-7
1952
5.2. Active infrared thermography detection
NDT techniques using infrared thermography typically fall into three categories: pulsed thermography [37], modulated thermography [38] and pulsed phase thermography [39], the latter being often presented as a further development of the first two techniques. These NDT techniques are distinguished by different thermal stresses and different data processing. In this experiment, infrared thermography is not used as a technique for quantitative NDT, but as a tool for defect viewing. So, unlike conventional NDT using infrared thermography, it is not necessary here to control the amplitude or duration of the thermal excitation signals. The thermal energy emitted by halogen lamps serves only to slightly heat the reinforcing plate. Under these conditions, the thermal resistance created by an air gap or bonding failure causes a higher temperature rise.
The test specimen is placed in front of the infrared camera and a frame fitted with two halogen lamps. This is set at a distance of 2 meters from the sample, to provide a field of view which allows observation of the whole specimen. The thermal stress is applied by means of two halogen lamps with a maximum power of 1 kW each. The infrared camera used in this experiment is a CEDIP Silver 220 cooled camera equipped with a matrix of 320×256 InSb detector elements which are sensitive to medium waves, 3–5 µm. It has a typical NETD of 20 mK and allows acquisition as a function of time. The first part of the experimental test bench is shown in Fig. 6.
Fig.6. Defect detection experimental device and experimental results
The excitation signal is a rectangular function of 15 s duration. Figure 6 shows the changes in average temperatures of two zones. One (green curve) is at a healthy area and the other area (red) has a bonding failure. After 30 seconds the temperature difference between healthy and defective areas can reach nearly 3 °C. This defect detection made using the infrared camera is a first step, and helps locate potential poorly-bonded areas. 5.3.Experimental set-up
Fig. 7 shows the experimental set-up for thermal characterization of the defective areas. The objective is to apply a thermal stress onto the surface by means of electrical resistance. To ensure that the majority of the energy is dissipated through the fluxmeter and reaches the material, thermal insulation is placed above the resistance. The thermal flux and temperature values are recorded by the fluxmeter, located between the resistance and the sample surface. The unidirectionality of transfer is ensured by an insulating belt surrounding the material studied; the sensor is equipped with a guard ring and its surface is less sensitive than that of the sample. Edge effects are avoided. The weight placed on the device keeps everything in a stable position and reduces contact resistance. The thermal stress imposed by the heater is based on a pseudo-random binary signal generated by the computer.
We tested our experimental device on two separate cases: • On an area where we had previously identified a lack of bonding using the infrared camera (position 1 in Fig.7). • On a fully bonded, sound area (position 2 in Fig.7).
Fig. 7. Experimental set-up for thermal characterization of the defective bond
The heat flux values and temperature readings will allow us to calculate the transfer function for each of the positions (the defective and sound areas).
5.4.Excitation signal
This method has the advantage of not requiring any control of the boundary conditions and being able to exploit random signals. It is perfectly suited to in situ use under any disturbance conditions. The experiments for the present study were performed in the laboratory and stress was imposed on the system by dissipating heat through a flat resistance. Pseudo-random binary signals (PRBS) were used. This type of signal has the advantage of selecting and exciting a wide spectral band, while limiting the amount of energy introduced into the system.
5.5. Experimental results
As described previously, the z transfer function is determined. The impedance obtained is represented in Fig. 10 in the form of a graph showing the moduli of the impedance plotted as a function of the frequency. Thermophysical parameters (b, Rc, α) are thus determined by adopting the group that minimizes the difference between each value of the output signal and the predicted value, following the flowchart shown in Fig. 8.
Fig. 8. Data flowchart showing the parameter estimation procedure
Fig. 9. Comparison of the experimental impedance moduli and the values found by the theoretical study
The fitting of the optimized theoretical impedance with the measured impedance (obtained from the temperature and flux using the z transfer function), gave the parameter values shown in Table 2.
Table 2 Thermophysical parameters derived from the theoretical study Sample well adhered
Values
Values
Values
Values
resulting
from
resulting
from
resulting
from
resulting
from
from the
laborato
from the
laborato
from the
laborato
from the
laborato
optimizati
ry
optimizati
ry
optimizati
ry
optimizati
ry
on
testing
on
testing
on
testing
on
testing
(glue)
Units
Contact resistanc e (Rc)
[K.m².W− 1 ]
Sample with defect
intermediate state: Sample with defect (air) close to 5% Values Values
0.005
(*)
0.012
(*)
intermediate state: Sample with defect (air) close to 15% Values Values
(air) close to 100%
0.008
(*)
Occupan 0.99 (*) (*) (*) 0.94 0.85 cy ratio ( α) Thermal [J m Effusivit 2 −1/2 2.04.103 1.95.103 2.08.103 1.95.103 2.1.103 1.95.103 .s y of the −1 K ] concrete (b) [%] Deviatio 4.61 6.67 7.69 n in (b) (*) Nota : it is impossible to determine these parameters from a laboratory test
0.017
(*)
0.023
(*)
2.09.103
1.95.103
7.18
The standard deviation of the estimated values of the thermal effusivity b compared to the value of the thermal effusivity b from the laboratory study ([NF-EN 12664]) is quite low (<8%). We also note that the occupancy ratio is close to 1 when the reinforcing plate is well bonded, and close to zero in the case of the air gap. The method seems to be able to define quantitatively the bond quality of a concrete block reinforced with CFRP.
6. Conclusion
As we described previously, CFRP plates are used to reinforce civil engineering structures. Infrared thermography is one of the techniques currently used to examine bonding of phases in composites in situ, and more often as a qualitative analysis technique to locate defects. Here we have coupled infrared thermography with thermal impedance characterization which
allows us to estimate the occupancy ratio of the interface (α, which varies from 1 for a fully glued interface to 0 for a complete void). This then provides a numerical indication of the quality of the bond between the carbon fiber plate and concrete block. The method is easily applied on site, and quickly provides an estimate of the degree of bonding of reinforcing plates to a structure. Indeed, the method developed does not require control of boundary conditions; it can calculate the contact resistance and CFRP have the advantage of having a good surface (smooth). The only restriction for in situ application is in the first approach by infrared thermography (not too much wind, rain, etc.). In the future, various defects with different α values could be created and thermally characterized. The thermal characterization could potentially be correlated with the mechanical properties of these assemblies. If a strong correlation was demonstrated, thermal characterization could then provide an indirect estimate of the mechanical effectiveness of the CFRP reinforcement.
References
[1] Calgaro, J.-A. et Lacroix, R., Maintenance et réparation des ponts, Presses de l’Ecole Nationale des Ponts et Chaussée, 1997
[2] Pakvor, A., Repair and strengthening of concrete structures: general aspects, Structural Engineering International, 2, 1995
[3] Y.Y. Kim, B.Y. Lee, J.W. Banga, B.C. Han, L. Feo, C.G. Cho, Flexural performance of reinforced concrete beams strengthened with strain-hardening cementitious composite and high strength reinforcing steel bar, Composites Part B: Engineering, Volume 56, January 2014, Pages 512–519
[4] J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis –- CRC Press Inc - ISBN-10: 0849315921 – 2003
[5] M. Ei-Mikawi, A. S. Mosallam, A methodology for evaluation of the use of advanced composites in structural civil engineering applications, Composites Part B: Engineering, Volume 27, Issues 3–4, 1996, Pages 203–215
[6] ACI 440.2R-02. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. American Concrete Institute, Farmington Hills, Michigan; 2002
[7] N.M. Hassan, R.C. Batra, Modeling damage in polymeric composites, Composites Part B: Engineering, Volume 39, Issue 1,January 2008, Pages 66–82
[8] P. Neto, J. Alfaiate, J. Vinagre, A three-dimensional analysis of CFRP–concrete bond behavior, Composites Part B: Engineering, Volume 59, March 2014, Pages 153-165
[9] S. C. Florut, G. Sas, C. Popescu, V. Stoian, Tests on reinforced concrete slabs with cut-out openings strengthened with fibre-reinforced polymers, Composites Part B: Engineering, Volume 66, November 2014, Pages 484-493
[10] T. D’Antino, C. Pellegrino, Bond between FRP composites and concrete: Assessment of design procedures and analytical models, Composites Part B: Engineering, Volume 60, April 2014, Pages 440-456
[11] C. Lesmana, H.S. Hu, F.M. Lin, N.M. Huang, Numerical analysis of square reinforced concrete plates strengthened by fiber-reinforced plastics with various patterns, Composites: Part B 55, 2013, Pages 247–262
[12] Antonio R. Marí, Eva Oller, Jesús M. Bairán, Noemí Duarte, Simplified method for the calculation of long-term deflections in FRP-strengthened reinforced concrete beams, Composites Part B: Engineering, Volume 45, Issue 1, February 2013, Pages 1368-1376
[13] J. Yao, J.G. Teng, J.F. Chen, Experimental study on FRP-to-concrete bonded joints, Composites: Part B 36, 2005, Pages 99–113
[14] K.T. Lau, P.K. Dutta, L.M. Zhoua, D. Hui, Mechanics of bonds in an FRP bonded concrete beam, Composites Part B: Engineering, Volume 32, Issue 6, September 2001, Pages 491–502
[15] N. Pešić, K. Pilakoutas, Concrete beams with externally bonded flexural FRP-reinforcement: analytical investigation of debonding failure, Composites Part B: Engineering, Volume 34, Issue 4, 1 June 2003, Pages 327-338
[16] ACI Committee 440.2R02-08.”Guide for the Design and Construction of Externally Bonded Systems for Strengthening Concrete Structures”, American Concrete Institute, Michigan, U.S.A., 2008
[17] AFGC. 2007. “Réparation et renforcement des structures en béton au moyen des matériaux composites – Recommandations provisoires”, Bulletin scientifique et technique de l’AFGC. (in French)
[18] Fib Task Group 9.3. ,2001, Externally bonded FRP reinforcement for RC structures, fib bulletin 14, Lausanne, Switzerland
[19] Rawaa Al-Safy, Riadh Al-Mahaidi, George P. Simon, A study of the use of high functionalitybased resin for bonding between CFRP and concrete under harsh environmental conditions, Composite Structures 95, 2013, 295–306
[20] W.L. Lai, S.C. Kou, C.S. Poon, W.F. Tsang, C.C. Lai, Characterization of the deterioration of externally bonded CFRP-concrete composites using quantitative infrared thermography, Cement & Concrete Composites 32, 2010, Pages 740–746
[21] J. Tashan, R. Al-Mahaidi, Detection of cracks in concrete strengthened with CFRP systems using infra-red thermography Composites Part B: Engineering, Volume 64, August 2014, Pages 116-125
[22] V. Feuillet, L. Ibos, M. Fois, J. Dumoulin, Y. Candau, Defect detection and characterization in composite materials using square pulse thermography coupled with singular value decomposition analysis and thermal quadrupole modeling, NDT&E International 51, 2012, Pages 58–67
[23] C. Maierhofer, P. Myrach, M. Reischel, H. Steinfurth, M. Röllig, M. Kunert, Characterizing damage in CFRP structures using flash thermography in reflection and transmission configurations, Composites Part B: Engineering, Volume 57, February 2014, Pages 35–46
[24] X.Maldague, Theory and practice of infrared technology for non-destructive testing. WileyInterscience, John Wiley&Sons, Inc.; 2001
[25] P.H. James, C.S. Welch, W.P. Winfree. A numerical grid generation scheme forthermal simulation in laminated structures. In: Thompson DO, Chimenti DE,editors. Review of progress in quantitative nondestructive evaluation, vol.8A. New York: Plenum Press; 1989. Pages 801–9
[26] J.C. Krapez, P. Cielo, Thermographicnondestructive evaluation: data inversion
procedures part I: 1D analysis. Res NondestructEval 1991;3(2), Pages 81–100
[27] A. Chauchois, D. Defer, E. Antczak, and B. Duthoit, Use of noninteger identification models for monitoring soil water content, Meas. Sci. Technol. 14, 868, 2003
[28] A. Chauchois, E. Antczak, D. Defer, and F.Brachelet In situ characterization of thermophysical soil properties—Measurements and monitoring of soil water content with a thermal probe, J. Renewable Sustainable Energy 4, 043106, 2012
[29] D. Defer, E. Antczak, B. Duthoit, The characterization of thermophysical properties by thermal impedance measurements taken under random stimuli taking sensor-induced disturbance into account - Meas. Sci. Technol. 9, 496, 1998,
[30] P. Hérin, P. Théry, Measurements on the thermoelectric properties of thin layers of two metals in electrical contact. Application for designing new heat flow sensors, J. Meas. Sci. Technol., 3 ,1993, Pages 158–163
[31] A. Degiovanni, Thermal conduction in a multilayer slab with internal sources; using a quadripole method, Int. J. Heat Mass Transfer 31, 553, 1988
[32] A. Chauchois, E. Antczak, D. Defer, O. Carpentier, Formalism of thermal waves applied to the characterization of materials thermal effusivity, Review of Scientific Instruments 82, 074902, 2011
[33] D. Defer, A. Chauchois, E. Antczak, and O. Carpentier, Determination of Thermal Properties in the Frequency Domain Based on a Non-integer Model: Application to a Sample of Concrete, Int. J. Thermophys., 30(3), 1025, 2009
[34] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M.Saisana, and S. Tarantola, Global Sensitivity Analysis. The primer, (Wiley, New York, 2008)
[35] Y. Jannot, A. Degiovanni, and G. Payet, Thermal conductivity measurment of insulating materials with a three layers device, Int. J. Heat Mass Transfer 52, 1105-1111, 2009
[36] R. Pintelon and J. Schoukens, System identification: A frequency domain approach (IEEE Press, Piscat-away, New Jersey, 2001)
[37] X. Maldague, Theory and practice of infrared technology for nondestructive testing, WileyInterscience, New York (2001)
[38] O. Breitenstein, W. Warta, M. Langenkamp, Lock-in Thermography - Basics and Use for Evaluating Electronic Devices and Materials ,(book) Springer, 2003
[39] X. Maldague, F. Galmiche, A. Ziadi, Advances in pulsed phase thermography, Infrared Physics & Technology, vol. 43, June 2002, Pages 175-181
Table 1 Main characteristics and thermal properties of elements making up the sample
Material
Thickness
λ
e [m]
[W.m .K ]
1.2.10-3
0.7
2.10-3
Air (defect)
2.10-3
Cement concrete block
Semi-∞
SIKA Carbodur 1012 (CFRP) Epoxy resin (glue) Sikadur 30
-1
-1
ρ
c
a
b
R
[kg.m-3] -1
-1
-2
-1
-1
-2
-
2
-1
[J.kg .K ]
[m .s ]
[J.K .m .s 1/2 ]
[m .K.W ]
1530
840
5.44.10-7
948
1.71.10-3
0.2
1200
1220
1.36.10-7
541
1.10-2
0.026
1.184
1000
2.2.10-5
5.55
7.69.10-2
1.8
2300
920
8.5.10-7
1952
Table 2 Thermophysical parameters derived from the theoretical study Sample well adhered
Values
Values
Values
Values
resulting
from
resulting
from
resulting
from
resulting
from
from the
laborato
from the
laborato
from the
laborato
from the
laborato
optimizati
ry
optimizati
ry
optimizati
ry
optimizati
ry
on
testing
on
testing
on
testing
on
testing
(glue)
Units
Contact resistanc e (Rc)
[K.m².W− 1 ]
Sample with defect
intermediate state: Sample with defect (air) close to 5% Values Values
0.005
(*)
0.012
(*)
intermediate state: Sample with defect (air) close to 15% Values Values
(air) close to 100%
0.008
(*)
Occupan 0.99 (*) (*) (*) 0.94 0.85 cy ratio ( α) Thermal [J m Effusivit 2 −1/2 2.04.103 1.95.103 2.08.103 1.95.103 2.1.103 1.95.103 .s y of the −1 K ] concrete (b) [%] Deviatio 4.61 6.67 7.69 n in (b) (*) Nota : it is impossible to determine these parameters from a laboratory test
0.017
(*)
0.023
(*)
2.09.103
1.95.103
7.18