PSI - Issue 5

Ralf Urbanek et al. / Procedia Structural Integrity 5 (2017) 785–792 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

792

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The measured differences in the E-Mode between the notched and the cracked specimen can be attributed to the presence of higher harmonics. This higher harmonics are normally caused by plastic deformation as already shown by the investigations of Sakagami (Sakagami 2005). The investigated steel shows a stress induced martensitic transformation. The influence of this transformation on the thermographic measurements is still an open question. According to Wong ’s equation of the thermo-elastic effect (equation 2), the mean stress reduces the thermal response with loading frequency (E-Mode). According to Patterson’s approach in this kind of experiment the mean stress is influenced by residual stress hence plasticity. The size of the area of reduced E-Mode response is much bigger than a typical plastic zone. In this region the D-Mode shows increased values. That supports Sakagami’s 2f -method (D-Mode) for determining plastic deformation. To evaluate the influence factors frequency, load level, local gradients, experiments with unnotched specimen were carried out to calibrate the measurement method. The results show that a calibration with simple specimen at fully reversed conditions and defining a thermoelastic constant according the Thompson approach leads to more reliable results than the calculation of the elastic constant with values from the literature. Elastic stress fields and dissipated energies were determined on specimens with different notch depths as well as specimens with propagating cracks. The experiments showed that the maximum stress at the notch root measured by TSA increases with the loading frequency and tends to a boundary value. Obviously the local adiabatic conditions are injured due to the more complex specimen shape. Additionally, the experiments indicate that the TSA is influenced by the heat flow in the material. That limits the applicability of the TSA for measuring stresses at cracks and notches in fatigue experiments. For accurate measurements, a correction depending on the loading frequency has to be applied. Lock-In TSA-measurements on notched and cracked specimen showed, that the maximum stress in front of crack is lower than the maximum stress in front of a notch with an equivalent length. In case of the notched specimen, dissipative effects are only observable close to the notch. In the cracked specimen, the dissipative effects exhibit higher values and reach further out into the specimen. For a mathematical description the equation of Wong should be extended to involve the plasticity effects also the 2f-method should widen to higher harmonics. Nevertheless, the 2f method is still reliable for a general or first estimation. Bär, J.; Volpp T. 2001. Vollautomatische Durchführung von Ermüdungsrissausbreitungsexperimenten, Materials Testing, 43, 242-247. Brémond, P. 2007. New developments in thermal stress analysis by infrared thermography. IV Pan American Conf. for Non Destructive Testing. Dulieu-Barton, J.M.; Stanley, P. 1998. Development and applications of thermoelastic stress analysis. J. Strain Analysis 33, 93-104. Gyekenyesi, A. L.; Baaklini, G. Y. 1999. Thermoelastic Stress Analysis: The Mean Stress Effect in Metallic Alloys. NASA / TM--1999-209376. DOI: 10.1117/12.339842. Kupferinstiut 2017 https://www.kupferinstitut.de/de/persoenlicheberatung/shop-verlag-downloads/downloads/werkstoffe/werkstoff datenblaetter.html. Lovell, D. J. 1968. Herschel's Dilemma in the Interpretation of Thermal Radiation. Isis-A Journal of the History of Science Society 59, 46-60. matweb 2017 http://matweb.com/search/DataSheet.aspx?MatGUID=6653b72914864cc0a0ff7adf5b720167&ckck=1. Patterson, E.; Du, Y.; Backman, D. (2008) A new approach to measuring surface residual stress using thermoelasticity, Proc. SEM XI Int. Congress and Exposition, Orlando, FL. Robinson, A. F.; Dulieu-Barton, J. M.; Quinn, S.; Burguete, R. L. 2010, Paint coating characterization for thermoelastic stress analysis of metallic materials. Measurement Science and Technology 21, DOI: 10.1088/0957-0233/21/8/085502 Sakagami, T.; Kubo, S.; Tamura, E.; Nishimura, T.; Identification of plastic-zone based on double frequency lock-in thermographic temperature measurement, In: ICF11, (2005) Italy. Thomson W. 1853. On the dynamical theory of heat. Transaction of the Royal Society of Edinburgh 20, 261–288. Urbanek, R.; Bär, J. 2017. Influence of motion compensation on lock-In thermographic investigations of fatigue crack propagation. Engineering Fracture Mechanics, In Press, http://doi.org/10.1016/j.engfracmech.2017.03.043 Wong, A. K.; Jones, R.; Sparrow, J. G. 1987. Thermoelastic constant or thermoelastic parameter? Journal of Physics and Chemistry of Solids 48, 749–753. DOI: 10.1016/0022-3697(87)90071-0 Wong, A. K.; Sparrow, J. G.; Dunn, S. A. 1988. On the revised theory of the thermoelastic effect. Journal of Physics and Chemistry of Solids 49, 395-400. DOI: 10.1016/0022-3697(88)90099-6 References 4. Conclusions