Bundesanstalt für Materialforschung und -prüfung

International Symposium (NDT-CE 2003)

Non-Destructive Testing in Civil Engineering 2003
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Ivanka Boras, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
Srecko Svaic, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia


The paper presents the method for determination and characterization of subsurface defects in material by means of IR thermography and 3D non-stationary numerical model of heat conduction. The numerical model is based on the control volume numerical method with control volume net adjustable to the problem. The software developed enable the record of temperatures field in different planes and time as well as changing the duration of thermal stimulation time. Inverse method is also included and enables the estimation of defect length on the base of experimentally obtained thermograms.

The method was applied on the specimen made of steel with the defects in form of cylinders containing air. The comparison of temperature fields obtained experimentally and numerically was done for the same time expired as well as the dependence of the current contrast vs. time curves related to the defects depth. The mutual interaction of defects on the surface temperature field was analyzed and their influence on the current contrast determined with the aim to recognize the possible errors in determination of defect geometry and position.


The research presented includes experiments and numerical simulation, with the goal to contribute in solving the problems of visualization of the object subsurface structure.

The temperature field, which appears on the surface of an object stimulated with heat flux is the result of heat conduction through its structure. It represents a 3D distribution of temperature parameters and mutual interaction of the object and its surrounding.

According to that if the geometry of the object is known, as well as its interaction with the surrounding it is possible to investigate its invisible structure.

In the paper, beside the analysis of the non-stationary temperature fields which appears on the surface of the specimen including subsurface defects as a result of heat stimulation, the mutual interaction of defects itself and influence on the temperature contrast was also observed. Applying the inverse method in numerical simulation the length of the defect was estimated and influence of the neighboring defects discussed.


The specimen used in testing consists of two parts (see fig. 1) both made of the same quality steel. The defects are located in the base plate, which was covered by the cover plate.

The dimensions of the plates are as follows:

  • base plate: 155 x 146 x 19 mm
  • cover plate: 155 x 146 x 5 mm

Fig 1: The base plate.

All six defects are in the form of cylinders having diameter of 18 mm, but located on different depth (see fig. 2).

Fig 2: Cross section of the base plate (dimension in mm)

The thermodynamic properties of the specimen material and air are given in table 1.

  Steel Air
Heat conduction coefficient W/(mK) 58 0.0272
Density kg/m3 7800 1.057
Specific heat capacity J/(kgK) 460 717.8
Table 1:


In numerical analysis the control volume method was applied. By means of implicit discretization of 3D non-stationary heat conduction equation a certain number of algebraic equations was obtained for each control volume and they are solved iteratively. In this equations the thermal properties were assumed to be independent on temperature.



The control volume net was made much closer in the area where greater temperature gradients have been expected. The total number of control volumes was 38x30x12 having base dimensions between 1 and 12 mm. The time step was 0,04 sec. The heat transfer through defects was assumed as conduction and the heat conduction coefficient for the boundary control volumes (steel-air) calculated according to equation 3.


Fig 3: Boundary control volume. Fig 4: Boundary conditions.

Interaction between specimen and surrounding was defined through boundary conditions shown on fig.4.

In numerical analysis the heat transfer coefficient (free convection) was calculated for each control volume placed on monitored and stimulated surface from previous calculating step and used for calculation of new values of current temperatures with iteratively made corrections.

The analysis of numerically obtained temperature field on specimen surface was done by means of current contrast as a time dependent value using equation 4.


Where: Tnd - is a surface temperature over homogeneous material and Td - is a surface temperature over defect

For developed model and particular boundary conditions the numerical analysis was first carried out for the case of only one defect in the specimen. The reason was to eliminate the influence of neighboring defects. By varying the defect depth (distance from the observed surface) the relation between time of maximal current contrast and defect depth was determined (see. fig. 5).

Fig 5: The time of maximum current contrast versus defect depth.

It can be shown that the time of maximal current contrast depends only on the defect depth. The defect length can be found by means of inverse method and experimentally obtained results, thermograms recorded for identical start, boundary conditions and expired time. The inverse method is based on iteration, which start with chosen defect length. In each step the chosen value is corrected till the satisfied accuracy. The principle of the inverse method is shown on fig. 6. and iteration on fig. 7.

Fig 6: Principe of inverse method. Fig 7: Iterative procedure.

It must be denoted that when six defects are located in specimen its mutual influence on maximum current contrast must be taken into consideration. If not, the results obtained by inverse method are less accurate. It is very important to choose the right points on the surface for recording the data, which will be used for calculation of current contrast. The influence of one and six defects on the surface temperature distribution obtained by simulation can be seen on fig. 8 and 9.

Fig 8: Temperature field on object surface - one defect in object. Fig 9: Temperature field on object surface - six defects in object.


The experiment was performed on the rig shown on fig. 10. The heat source of 500 W was used for heat stimulation of the specimen. The temperature distribution on the observed surface was recorded by means of IR camera AGA 680 Standard and referent temperature measured by thermocouples. Measurement uncertainty for temperature was 0,5 oC, emission coefficients was determined as e =0,31 for heated surface and e =0,7 for monitored surface.

Fig 10: Experimental rig.

5. Comparison of the results obtained by simulation and experiment

On fig. 11. the thermogram obtained by experiment and temperature distribution obtained by simulation can be seen. They are recorded in the same expired time and for the same start and boundary conditions. The differences between the temperatures obtained by simulation and measurement are within 7%.

Fig 11: Left-experimentally obtained temperature distribution on the specimen surface, Right-numerically obtained temperature distribution. Expired time is 120 s after thermal stimulation.


Combination of thermographic measurement and numerical simulation gives possibility for development of new TNDT methods which will help in solving many problems relating to non-homogeneities in the material structure without its destruction. Using a new IR camera and power computer the accuracy of methods can be essentially improved.


  1. D.P. Almond, P.M. Patel, Photothermal Science and Technique, London, Chapman & Hall, 1996.
  2. V. Vavilov, Transient thermal NDT: conception in formulae, Quantitative Infrared Thermography, QUIRT 92, Chatenay-Malabry, France, pp. 229-234, 1992.
  3. I. Boras, S. Svaic, Determination of the Defect Parameters in Specimen by Means of Thermography and Numerical Methods, Proceeding of The International Society for Optical Engineering, San Antonio, Texas, USA, Vol. 3396, pp. 271-281, 1998.
  4. I. Boras, S.Svaic, A.Galovic, Mathematical model for simulation of defects under material surface applied to thermographic measurements, Quantitative Infrared Thermography, QIRT 98, Lodz, Poland, pp. 53-58, 1998.
  5. I. Boras, S. Svaic, Characterisation of subsurface defects by means of thermography and 3D numerical model, SPIE - International Symposium, Orlando, USA Vol. 4360, 516-523, 2001.
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