The finite element method and the Infrared Thermography principle applied to the control of homogeneity between a weld and the structure to weld
A. EDDAZI, S. BELATTAR
Cadi Ayyad University Faculty of Sciences Semlalia department of physicsBP 2390, 4000
Marrakech, Morocco [email protected]
Abstract— The main purpose of this work is to investigate by a numerical method the effect of the thermophysical nature of solder, used to connect two pipe elements, on the distribution of the surface temperature of aconsidered structure. The analysis of the obtained thermograms can reveal the thermophysical quality of the used solder. The finite element method is used to calculate the temperature distribution on the welded region. The thermal response of the structure, which is subjected to a thermal flux step, is presented and analyzed. The simulations results are presented in the form of surface thermographic images, to show the contrast in temperature due to the presence of the weld zone.
To better quantify the contrast induced by the presence of welding on temperature distribution we present the spatial variation of the temperature along a surface axis of the pipe.
Keywords-thermographical images; finite element; infrared thermography; surface temperature; pipe; welding
I. INTRODUCTION
Non-destructive Testing (NDT) are techniques and inspection methods used to evaluate the presence of defects within the material without destructing its physical integrity.
The use of NDT and Evaluation techniques for the inspection of aerospace materials has progressively increase in the last few decades as commercial and military aircrafts exceed their initial design life. Infrared Thermography (ITR) is one of the main NDT methods and one of the most attractive and promising techniques, especially in the evaluation of defects in composites materials [1][2].
Infrared thermography has proved to be an effective tool for fast and qualitative inspection of damaged structures, it is a non-contact and optical technique, based on the temperature analysis and strain patterns respectively, after the application of an external stimulation over the material surface, this technique proved to be useful for application in semi quantitative estimation of concrete homogeneity. In fact, when compared with other methods, the right order of magnitude of material homogeneity of concrete walls was acquired with infrared thermography [1][3].
Infrared thermography as a non-destructive testing (NDT) measures and interprets the temperature field of the surface of the specimen to be studied. The theoretical principle is based on the fact that the internal structure of the inspected specimen and its flaws will have a different thermal behavior. The defects affect the flow of a previously applied heat source, which will be heated or cooled at different rates. The result is
thermograms showing temperature field on the surface of the object (thermal contrast), resulting from differences in radiation emission. Data processing techniques are applied to the acquired data when the acquired signal is weak to improve the results, making defect detection possible[4].
In thermography NDT, the infrared (IR) spectrum is used for mapping the chosen specimen temperature of the structure to be inspected. In general, some source of energy is used to create a temperature difference between the chosen specimen and the surrounding environment, and the heat flux is monitored as the chosen specimen returns to thermal equilibrium. Variations in structure or material properties result in variations in heat flux and the surface temperature.
The most useful wavelengths are between 0.7 and 20 µm. The energy emitted by the chosen specimen depends on its temperature and on photon’s wavelength [5].
Multitude of different factors influences in the reliability of non-destructive evaluation techniques. These range from physical aspects of the used technology to application issues and human factors. Wide variety of different Non-Destructive Evaluation methods is available and new ones are constantly developed [6].
The main objective of this study is to analyze the temperature disturbance of a welded along a chosen specimen using infrared thermography as a nondestructive technique by a commercial finite element software « COMSOL Multiphysics », the simulation concerned an aluminum pipe welded in the middle by a filler material that we will take its thermal conductivity and its heat capacity as parameters varying around aluminium thermal conductivity and heat capacity vlues.
II. STUDIED MODEL
The modeled structure in this work, showed in figure1, is a weld joining two parts of a pipe in aluminum. The welding material has a cylindrical form. The pipe geometry is defined by the external diameter of d = 110 mm, the pipe thickness of ep= 30 mm, and the length of l = 3020 mm. the welding is defined by a an external diameter of 110 mm, width of es=10mm and a depth of 30 mm.
The following figure (figure 1) shows the specimen welded in the middle with more details describing the structure in the space.
With (x,y,z) is an orthonormal reference frame in the space.
Figure 1 The Studied structure III. MATHEMATICAL MODELING
The temperature evolution in the system to be studied (pipe + welding) is given by the heat equation, in the orthonormal reference frame (x, y, z), for a homogeneous and isotropic material:
With:
ρ : is the material density [kg/m3]
Cp: is the heat capacity at constant pressure [J/kg.K]
k : is the material thermal conductivity [W/m.K]
T : is the temperature to be calculated [°K]
q : is the voluminal heat source [W/m3].
With the boundary conditions:
: is the imposed temperature on a surface : is the imposed flux on a surface S : is the solid surface
: is the unit normal to S directed outwardly The initial condition at the instant t=t0:
In this paper the heat equation solution is given by the finite element method using the commercial software
"COMSOL Multiphysics" which allowed us to analyze the field of temperature along the studied specimen.
The material is considered isotropic without voluminal source with the boundary conditions:
A heat pulse is applied to the outer surface of the aluminum pipe, with a flux density Q=600W/m² (flat faces excluded).
The inner surface of the pipe subjected to convective cooling of the heat transfer coefficient h=10W/(m2.K) and external temperature Text=25°C.
The flat faces are assumed thermally insulated.
The initial temperature of the subdomains is 25°C.
IV. C.RESULTS OF SIMULATION
In this part, the aluminum pipe is welded by another material having:
In a first time, the same thermophysical parameters of aluminum pipe to assemble, except the thermal conductivity which is variable around the aluminum thermal conductivity value 160[W/m.K].
In a second time, the same thermophysical parameters of aluminum tube to assemble, except the heat capacity which is variable around the aluminum thermal capacity 900[J/Kg.K].
To clarify the simulation results we present relative thermal parameters: relative thermal conductivity kr, relative heat capacity Cpr and relative density ρr, defined by the ratio of thermal parameters of Welding by thermal parameters corresponding of the pipe to be welded, taken as references
kr=Kmaterial/kreference, Cpr =Cpmaterial/Cpreference and ρr=ρmaterial/ρreference
The thermophysical parameters of the aluminum pipe used in the study are :
k=160[W/m.K] is the aluminium thermal conductivity Cp=2700[Kg/m3] is the aluminium heat capacity ρ=900[J/Kg.K].is the aluminium density A. The thermal conductivity influene
By varying the thermal conductivity of the welding material around the thermal conductivity of the aluminium chosen as a reference, we obtained thermograms representing the temperature field on surface of the pipe.
The chosen interval of the simulated relative thermal conductivity is [0.25; 0.5; 0.75; 1; 1.25; 1.5; 1.75]. The other thermophysical paramaters such as heat capacity and density are the same such as the aluminium pipe and the welding material then Cpr=1 and ρr=1.
Figure 2 shows the thermograms and a curve of temperature field calculated by varying the thermal conductivity of the solder, different cases were simulated.
The interested results are for the lateral surface of the pipe for a time of 20.
Figure 2 Thermograms and a curve of temperature field along the line AB with changing kr
In the TABLE I and Figure 3 below we have summarized the temperature differences, depending on the value of the report kr=kmaterial/kréférence due to variation of thermal conductivity between the solder and the pipe to be welded.
The temperature difference decreases by increasing thermal conductivity relative.
TABLE I. TEMPERATURE DIFFERENCE VARYING THERMAL CONDUCTIVITY
Order
Parameters Thermal
conductivity
k[W/m.K] kr=kmaterial/kreference
Temperature difference
∆T[°C]
1 40 0,25 0,035
2 80 0,5 0,014
3 120 0,75 0,006
4 160 1 0
5 200 1,25 -0,004
6 240 1,5 -0,007
7 280 1 ,75 -0,009
The TABBLE I allows as to draw the following curve in Figure 3 representing temperature difference as a function of thermal conductivity relative.
Figure 3 Temperature difference in °C depending on relative thermal conductivity kr
B. The heat capacity influence
In this case we are varying in heat capacity of the welding material, and we keep the other thermophysical parameters the same such as the aluminium pipe.
The chosen interval of the simulated relative heat capacity is [0.25; 0.5; 0.75; 1; 1.25; 1.5; 1.75]. The other thermophysical paramaters such as thermal conductivity and density are the same for the pipe and the welding material then kr=1 and ρr=1.
Figure 4 shows the thermograms and a curve of temperature field calculated by varying the heat capacity of the solder, different cases were simulated.
The interested results are for the lateral surface of the pipe for a time of 20.
Figure 4 Thermograms and a curve of temperature field along the line AB with changing Cpr
Analogously, in the TABLE II and Figure 5 below we have summarized the temperature differences, depending on the value of the report Cpr=Cpmaterial/Cpreference due to the variation of the heat capacity between the solder and the aluminium pipe to be welded.
The temperature difference decreases by increasing heat capacity relative.
TABLE II. TEMPERATURE DIFFERENCEVARYING HEAT CAPACITY
Order
Parameters heat capacity
Cp[J/kg.K] Cpr=Cpmaterial/Cpreference
Temperature difference
∆T[°C]
1 225 0,25 0,046
2 450 0,5 0,03
3 675 0,75 0,015
4 900 1 0
5 1125 1,25 -0,014
6 1350 1,5 -0,028
7 1575 1 ,75 -0,042
The TABLE II allows as drawing the following curve in figure 5.
Figure 5 Temperature difference in °C depending on relative heat capacity Cpr
C. Comparison
The figure 6 and 7 summarise the comparison between the effect of thermal conductivity and the influence of the heat capacity on the temperature difference and the width of contrast on the studied specimen.
Figure 6 temperature difference as function of kr and Cpr It is seen from Figure 6 that the temperature difference is a decreasing function of the relative thermal conductivity and linearly decreasing by report to the relative heat capacity.
Figure 7 cotrast width
It is seen from figure 7 that the width of the contrast of the welded zone created by varying the heat capacity is larger than that created by varying the thermal conductivity and we can find in this study that :
WCpr/Wkr> 3 times
With WCpris the width of the contrast created by varying the heat capacity relative Cpr and Wkr is the width of the contrast created by varying the thermal conductivity relative kr .
So by observing a thermographic image of a weld area, it is possible, from the width of the transition zone, to predict whether the material of the weld is thermally more conductive or capacitive.
CONCLUSION
In this paper, we studied the evolution of the temperature field on a welded aluminum tube depending on two parameters: the thermal conductivity effect and the heat capacity effect, this allows us to draw the following conclusions:
The temperature difference in absolute value decreases by increasing thermal conductivity relative kr if kr≤1, and increases by increasing thermal conductivity relative kr if kr≥1.
The temperature difference in absolute value decreases linearly by increasing heat capacity relative Cpr if Cpr≤1, and increases linearly by increasing heat capacity relative Cpr if Cpr≥1.
Infrared thermography has proved its capability to detect anomalies and non-homogeneity of materials without destruct or contact them, and that take in consideration the temperature difference sufficient comparing it with the used material in inspection.
References
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