Infrared Thermographic Testing of Steel Structures by Using the Phenomenon of Heat Release Caused by Deformation

  • E. A. Moyseychik
  • V. P. Vavilov
  • M. V. Kuimova


Deformation of steel parts is accompanied by either heating or cooling of particular zones depending on deformation mechanism. The use of infrared thermographic equipment allows analyzing spatial/temporal temperature distributions on the surface of steel parts thus allowing the evaluation of heat release caused by deformation in bulk material. Determination of stressed state in critical parts by analyzing infrared thermograms can be most simply conducted for components subjected to uniaxial tension–compression. The paper describes some potentials and problems of nondestructive testing of steel parts and constructions based on the analysis of heat release caused by deformation. By analyzing this methodology, it is possible to better evaluate the life expectancy of critical parts in steel structures (components of offshore oil platforms, seismic-resistant buildings, frames of large mining trucks, etc.).


Infrared thermography Nondestructive testing Steel part Deformation Heat generation 

1 Introduction

Detecting defects in steel parts remains an important technical task in the industrial environment [1, 2, 3]. A number of studies [4, 5, 6, 7, 8, 9, 10, 11] have demonstrated that deformation of steel is accompanied by either cooling or heating depending on a prevailing deformation mechanism (Fig. 1a). The cooling of steel parts subjected to mechanical loading by the temperature signal \(\Delta T_{pl}\) takes place during elastic work, see the \(\sigma \) vs. \(\varepsilon \) stress-strain curves in Fig. 1b. The nature of this effect relates to the anharmonicity of thermal vibrations of atoms [9]. During elastic-plastic deformation, steady heating of samples occurs until their destruction (Fig. 1b: curves \(\Delta T_{1}-\varepsilon _{1}\) for section 1-1 and \(\Delta T_{2}-\varepsilon _{2}\) for section 2-2 with an external or internal defect).
Fig. 1

Steel sample under tensile testing (a) and temperature change in vicinity of sections 1-1, 2-2 during deformation in accordance with \(\upsigma -\upvarepsilon \) curve (b)

The change in the temperature of steel during deformation is a result of the interaction between two processes: cooling of elastically-strained grains and heating of shear sections under physico-chemical reactions. In the elastic region, under stresses up to the proportionality limit \(\sigma _{pl}\) here are no shears in the grains of steel; so the temperature drops by \(\Delta T_{pl}\) With increasing stress, the number of shears increases (see section 1-1 in Fig. 1) and, accordingly, the average surface temperature of deformed sections grows up. When defects such as notches or holes are present, the deformations given by the curves 1 and 2 in Fig. 2a in the transversal direction will be different than those in the longitudinal direction like in Fig. 2b.

Appearance of plastic deformations in local zones and the corresponding heating of deformed zones which change from state 1 to state 2 will occur in vicinity of defects: i.e. in the areas with the maximum relative deformations \(\varepsilon _{m}\). The nominal values of relative deformation in defect-free areas \(\varepsilon _{n}\) are within the elastic values. In defect areas, the highest metal temperature occurs in the zones with a characteristic size \(\rho \) that can be determined by the methods of fracture mechanics.
Fig. 2

Development of relative deformations in cross sections and by force direction in steel samples

There are a couple of methods to evaluate temperature at some points of steel components [10]. Contact methods (thermocouples, etc.) are often used to directly determine temperature within a bulk material; whereas, contact and non-contact methods are used to measure surface point temperatures. The use of modern infrared (IR) thermographic equipment allows analyzing spatial/temporal temperature distributions on the surface of metallic parts [10]. When evaluating temperature patterns in mechanically deformed parts (parts under mechanical stress) to predict the failure of the parts, one should take into account residual stresses and deformations in the near-surface layer of the parts, as well as the changes in the temperature pattern during part operation or cyclic loading.

In this paper, we consider some potentials and problems of nondestructive testing (NDT) of steel parts and constructions based on the analysis of deformation heat generation.

2 Describing a Stressed State of Surface Layers in Steel Parts Under Elastic Deformation

The relationship between the change in the stress state of an infinitesimal element and its temperature (\(\Delta T)\) was first found by W. Thomson in 1857 [8], afterwards, its experimental confirmation has been carried out by many other researchers [4, 5, 6, 7, 8, 9, 10, 11]. We remind this dependence in the form proposed by Bio [12]:
$$\begin{aligned} \Delta T=-\frac{T\alpha }{C_p \rho }\Delta \left( {\sigma _1 +\sigma _2 +\sigma _3 } \right) , \end{aligned}$$
where T is the absolute temperature of the element; \(\alpha \) is the coefficient of thermal expansion of steel; \(C_p \) is the specific thermal capacity at constant pressure; \(\rho \) is the steel density; \(\sigma _1 ,\sigma _2 ,\sigma _3 \) are the primary stresses.
Equation (1) can be rewritten by using the notion of the first invariant of the stress tensor \(I_1 \) with \(K_m =\frac{\alpha }{\rho C_p }\):
$$\begin{aligned} \Delta T=-\frac{\alpha }{\rho C_p }T \Delta I_1 =-K_m T \Delta I_1 \end{aligned}$$
The value of \(\Delta I_1\) can be represented in the following form:
$$\begin{aligned} \Delta I_1= & {} \Delta \left( {\sigma _1 +\sigma _2 +\sigma _3 } \right) =\Delta \sigma _1 \left( {1+\frac{\Delta \sigma _2 }{\Delta \sigma _1 }+\frac{\Delta \sigma _3 }{\Delta \sigma _1 }} \right) \nonumber \\= & {} \Delta \sigma _1 \left( {1+K_{21} +K_{31} } \right) . \end{aligned}$$
Numerically \(K_{21} \le 1\),    \(K_{31} \le 1\).
Table 1

\(K_m \) values for some types of Russia-made steels


\(K_m, 10^{-6}\, \hbox {mm}^{2}/\hbox {N}\)


\(K_m, 10^{-6}\,\hbox {mm}^{2}/\hbox {N}\)

08, 08kp, 08ps,












15, 15kp, 15ps




15K, 20K








20kp, 20ps






Fig. 3

Scheme of shear samples: a no structural/ technological defects in the wall, b a 20 mm-diameter single hole in the wall, c two side notches in the wall, d two notches in the sample border shelves

Under a uniaxial stress state: \(\Delta I_1 =\Delta \sigma _1 \). Elastic tension–compression of a homogeneous, isotropic sphere for an element in the center of the sphere yields: \(1+K_{21} +K_{31} =3\). For other situations: \(1<1+K_{21} +K_{31} <3\).

Such uncertainty does not occur only if \(K_{21} +K_{31} =0\) For other specific situations, the sum \((K_{21} +K_{31} )\) can be determined by a preliminary analytical or finite-element analysis of a part. The coefficient \(K_m \) can be determined by calculation or experimentally for a particular type of steel and the corresponding temperature range. For temperatures from 223 to 373 K, the values of \(K_m \) for a number of Russia-made steels can be borrowed from the Table 1:

For example, if the surface temperature of a statically stretched element made of 22K steel (by Russian nomenclature) changes by \(\Delta T=0.1\, \hbox {K}\), then, at the temperature \(T=293 \,\hbox {K}\), this corresponds to the change in the surface layer stresses of \(\Delta \sigma _1=110.6\, \hbox {Pa}\).

An estimate calculation has shown that the determination of stress state on material surface via the corresponding surface temperature distribution imposes rigid requirements on devices and software to accurately measure surface temperature.

3 Identifying Plastic Deformation in Steel Parts

If the quantitative evaluation of stresses by the measurement of surface temperature patterns in a part is not required, the deformation heat concept can be used to analyze the initiation and development of destruction, i.e. evaluate how a test part approaches its limit state. We verified this by examining static deformation of specially designed samples of steel St3 (Fig. 3) on a P-100 test machine. In these samples, the built-in work elements are the wall 1 and the shelf 2, which ensure a proper distribution of forces and sample local stability. Such samples are used as energy absorbers, or dampers, of seismic vibrations in buildings and other structures. In total, 8 samples (two for each design in Fig. 3) were tested up to destruction according to the Russian national standard GOST 1497-84.

The surface temperature distributions were analyzed by using an IRTIS-2000 IR imager (a Russia-made radiometric IR camera ensuring high accuracy and repeatability of temperature read-outs due to a liquid nitrogen-cooled IR detector and the scanning principle of operation, see Fig. 4). Data processing was fulfilled by using the IRTIS accompanying software package.

The change in the surface temperature of plate 1 when the samples are being loaded during the time period \(\uptau \) is illustrated by Fig. 5. It follows that in the elastic stage of plate deformation, the surface temperature distribution in the vicinity of the defects is uniform. Appearance and development of plastic deformation leads to an increase of the deformation heating in the vicinity of defects. With further deformation, the diagonal dimension of the sample increases along the direction of the tensile force. Around the defects, a pre-destruction zone appears, as well as a zone with local temperature elevation. With further deformation of the sample and the growth of the emerging crack, the zone of local temperature elevation moves, remaining a few millimeters ahead of the tip of the crack. Both the stiffness of the endangered area of the plate and the value of the deforming force decrease in accordance to the descending section of the sample deformation curve. The power of the heat released due to deformation decreases, and the plate surface temperature diminishes respectively. Note that the temperature distributions on the surface of the samples are shown in Fig. 5 at some particular times prior the samples revealed visible signs of damage. The photos of the samples at the same times are presented in Fig. 6.
Fig. 4

Experimental setup (IRTIS-2000 IR imager and P-100 test machine)

Fig. 5

Surface temperature distributions in the wall 1 (diagonal tensile testing of the sample): a no structural/ technological defects in the wall, b a 20 mm-diameter single hole in the wall, c two side notches in the wall, d two notches in the sample border shelves

Fig. 6

Photos of samples (sample design by Fig. 3, IR thermograms in Fig. 4): a local loss of sample wall stability (design by Fig. 3a, IR thermogram in Fig. 4a, \(\uptau = 177\, \hbox {s}\)), b local loss of sample wall stability and crack initiation (design by Fig. 3b, IR thermogram in Fig. 4b, \(\uptau = 174.6 \,\hbox {s}\)), c crack initiation at side notch (design by Fig. 3c, IR thermogram in Fig. 4c, \(\uptau = 144.3\, \hbox {s}\)), d sample damage between two notches in sample border shelves (design by Fig. 3d, IR thermogram in Fig. 4d, \(\uptau = 114.2\, \hbox {s}\))

4 Temperature Distributions in Extended Weld Joints

Figure 7 shows the scheme of the samples with padded overlays and their photos before and after failure.
Fig. 7

Testing welded samples with padded overlays (all dimensions in mm): a sample scheme (0.35 and 70 mm gaps), b sample photo, c photos of fractured zones (maximal gap of 70 mm shown)

Figure 8 shows some IR images recorded when performing a tensile test on the sample with the 70 mm gap between the butt ends of the joined plates by using the experimental setup shown in Fig. 4. The IR video has clearly illustrated that the fracture trajectory in such samples can pass either at a certain angle or normally to the direction of the tensile force. Also, the damage of the samples initiated from the weld joint flank seams. The sliding traces, which are visually seen as calx cracking, show that, with zero gap, a narrow strip of the metal adjacent to the fracture surface is being deformed (Fig. 7c, sample on the right). With the 35 mm gap between the ends of the joined plates (Fig. 7c, middle sample), the entire overlay section which overlaps the gap becomes subjected to deformation, and a part of the steel sample located over the joined plates is stretching. The fracture of the sample with the 70 mm gap (Fig. 7c, the leftmost sample) can be explained in the accordance with the kinetics of destruction. In this case, destruction can take place also according to the scheme in Fig. 7c (middle sample). However, such case has been not realized because of practically simultaneous initiation and propagation of the respective cracks along with their resulting movement towards each other. Thus, by analyzing the characteristics of the joint deformation and the accompanying temperature distributions, we may conclude that the fracture resistance of samples with padded overlays is determined primarily by the gap between the joined plates.

5 Testing Screw Joints by Deformation Temperature Distributions

It has been shown elsewhere [13] that the problem of the damage of mounting studs in turbine covers widely used at hydroelectric power stations (HPS) is still actual for both high-pressure (Sayano-Shushenskaya, Nurek HPS) and low-pressure turbines (Uch-Kurgan HPS, Grand Rapids HPS). Moreover, the analysis of some accidents which occurred at power production installations in Russia has shown that dangerous cracks may appear in studs operating under cyclic loading being accompanied with abnormal temperature elevations over \(100{^{\circ }}\hbox {C}\). Therefore, such accidents can be duly prevented by using IR thermographic diagnostics.

A significant attention has been paid to the fatigue of the studs when analyzing the causes of the notoriously-known accident which occurred at the hydroelectric unit No. 2 of Sayano-Shushenskaya HPS [14], see Fig. 9. The accident investigation revealed that the cracks in the studs originated from the side of axis 2 of the hydroelectric unit. In their turn, the studs significantly warmed up to their limit tolerance state. By considering investigation results obtained by several experts, it has been concluded that identification of the technical factors, which caused crack initiation in the studs, should be conducted with reference to the work peculiarities of the system “cover-stud-frame” in hydraulic units. It has been also confirmed that lids have a finite stiffness, therefore, in both the normal and emergency operating modes of hydraulic units, the lid cross-sections may slightly move according to the scheme in Fig. 10.
Fig. 8

IR images when performing tensile test on the welded sample with 70 mm gap (time period 62.9–114.0 seconds after loading applied)

Fig. 9

Studs for fastening covers in the hydraulic unit at Sayano-Shushenskaya HPS (a) and their recommended optimized shape (b)

Fig. 10

Deformation scheme of stud-joined parts

These displacements have the largest value in the center of lid 2 and decrease toward its edges (Fig. 10). In the vicinity of studs 3, such movements are determined by elastic contact deformations and cause uneven contact pressure on both the washer and the nut 4. If the stud is significantly pre-stressed, the angle \(\theta \) cannot be visually observed. Therefore, a pre-stressed stud (with initial tension) will operate as an element that is loaded by both the eccentric stretching force N and the moment \(M=Ne\) (Fig. 10). The magnitude of the contact pressure q depends on the force P produced by the turbine, but the ordinates of the epure of the contact pressure, which occurs in section \(a-a\), will be larger on the side of the hydrogenerator 2. A crack start point must arise in the most loaded fillets of the stud thread, i.e. in sections \(a-a\) or \(b-b\) and, accordingly, fracture may start in these sections. Hence, when designing the studs for fastening a lid to a stator, it is recommended to produce initial stress in the thread sections with the stress sign being opposite to the work stress in the thread sections. Most reliably this can be achieved by thread knurling instead of performing cutting and heat treatment, because the latter procedure creates compressive stresses in the surface layers of studs. It will be also useful to make fillets in the inter-thread portion of stud surface (Fig. 9b).

Heat generation takes place at all stages of deformation of structural elements including crack initiation and development. Therefore, the monitoring system based on the continuous recording of the deformation release in endangered components cross-sections allows evaluating a work state of structural elements, for example, initiation and development of fracture in a stud. If IR radiation can be directly recorded from endangered areas, IR imaging radiometers can be used to visualize heat release in structural elements. If there is no access to structural elements, the component temperature can be measured by using contact sensors, such as thermocouples. In this case, the sensors must be installed in the stud in sections \(a-a\) and \(b-b\) (Fig. 9b). Then the signals from thermocouples are to be transferred to a data collection unit for further processing and analysis. The suggested idea of IR thermographic monitoring can be applied to evaluate work capacity of many important structures and parts (critical nodes of offshore platforms, earthquake-proof buildings, frames of mine dump trucks, etc.).

6 Conclusion

  • Determination of stressed state in critical parts by analyzing surface temperature distributions can be most simply conducted for components subjected to uniaxial tension–compression. For components under two- or three-axial stressed states, a preliminary theoretical analysis is highly recommended in order to determine contribution of stress components. Analysis of temperature in elastically-loaded parts should be performed in real time by taking into account the dynamics of temperature distributions.

  • If there is no need to quantitatively evaluate stress tensor components, the technique of IR thermography that allows detecting and evaluating heat release caused by deformation in bulk material seems to be an efficient tool for identifying zones with stress concentration and plastic deformation including initiation of cracks.

  • By analyzing deformation heat, it is possible to better evaluate the life expectancy of critical parts in steel structures which are typical for power production installations.



This study was supported by Tomsk Polytechnic University Competitiveness Enhancement Program, and in part by the Russian Scientific Foundation Grant #17-19-01047.


  1. 1.
    Bulnes, F.G., García, D.F., de la Calle, F.J., Usamentiaga, R., Molleda, J.: A non-invasive technique for online detection on steel strip surface. J. Nondestruct. Eval. 35(4), 54 (2016). CrossRefGoogle Scholar
  2. 2.
    Siakavellas, N.J.: The influence of the heating rate and thermal energy on crack detection by eddy current thermography. J. Nondestruct. Eval. 35(29), 29 (2016). CrossRefGoogle Scholar
  3. 3.
    Cadelano, G., Bortolin, A., Ferrarini, G., Molinas, B., Giantin, D., Zonta, P., Bison, P.: Corrosion detection in pipelines using infrared thermography: experiments and data processing methods. J. Nondestruct. Eval. 35(3), 49 (2016). CrossRefGoogle Scholar
  4. 4.
    Sharkeev, Y.P., Vavilov, V.P., Belyavskaya, O.A., Skripnyak, V.A., Nesteruk, D.A., Kozulin, A.A., Kim, V.M.: Analyzing deformation and damage of VT1-0 titanium in different structural states by using infrared thermography. J. Nondestruct. Eval. 35, 42 (2016). CrossRefGoogle Scholar
  5. 5.
    Bell, J.F.: The experimental foundations of solid mechanics. In: Truesdell, C. (ed.) Mechanics of Solids: Volume 1. Springer, New York (1973)CrossRefGoogle Scholar
  6. 6.
    Weber, W.: Über die specifische Wärme fester Körper, insbesondere der Metalle. Annalen der Physik und Chemie. Zweite Serie 20, 177–213 (1830)Google Scholar
  7. 7.
    Hort, H.: Die Wärmevorgänge beim Recken von Metallen. Mitt. Forschungsarbeit. Ing.Wes, H. 41, pp. 1-53 (1907)Google Scholar
  8. 8.
    Thomson, W.: On the thermoelastic and thermomagnetic properties of matter. Quart. J. Math. 1, 57–77 (1857)Google Scholar
  9. 9.
    Cottrell, A.H., Stokes, R.J.: Effects of temperature on the plastic properties of aluminium crystals. Proc. R. Soc. Lond. Ser. A. 233(1192), 17–34 (1955)CrossRefGoogle Scholar
  10. 10.
    Basinski, Z.S.: Thermally activated glide in face-centred cubic metals and its application to the theory of strain hardening. Philos. Mag. 4, 393–432 (1959)CrossRefGoogle Scholar
  11. 11.
    Hilarov, V.L., Slutsker, A.I.: Description of the thermoelastic effect in solids in a wide temperature range. Phys. Solid State 56(12), 2493–2495 (2014). CrossRefGoogle Scholar
  12. 12.
    Biot, M.A.: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27(3), 240–253 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Ivanchenko, I.P., Voevodin, S.I., Prokopenko, A.N.: Full-scale investigation of hydrodynamic loads on the fasteners of the turbine cover. Gidroénergetika 3(28), 5–11 (2012). (in Russian)Google Scholar
  14. 14.
    Moyseychik, E.A.: The elastic limit of mounting studs for securing the cover of the turbine of the hydroelectric unit and the development of a monitoring system for evaluating their working capacity. Gidrotehnicheskoe Stroitel’stvo 3, 43–47 (2015)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • E. A. Moyseychik
    • 1
  • V. P. Vavilov
    • 2
    • 3
  • M. V. Kuimova
    • 2
  1. 1.Mechanical Engineering DepartmentNovosibirsk State Academy of BuildingNovosibirskRussia
  2. 2.Institute of Nondestructive TestingNational Research Tomsk Polytechnic UniversityTomskRussia
  3. 3.Mechanical Engineering DepartmentNational Research Tomsk State UniversityTomskRussia

Personalised recommendations