PSI - Issue 2_B

Ralf Urbanek et al. / Procedia Structural Integrity 2 (2016) 2097–2104 Author name / Structural Integrity Procedia 00 (2016) 000–000

2104

8

Two essential effects of uncompensated measurements have strong influence on the stress values at the crack tip: the shifting effect of the E-Amplitude T E and the demerging effect of the maximum of the average temperature T A . The theoretical elastic stress at the crack tip is given by the thermoelastic effect (compare Equation 2) given by Thomson (1853). The factor 2 is necessary because the DFT gives only amplitudes and not the maximum range. Both effects strongly influence the determination of the elastic stress near the crack tip. Therefore motion compensation is an indispensable part of the lock-in analysis for stress measurements.

2 T ⋅

K = ⋅

∆σ

E

(2)

thermo elastic −

T

A

A global analysis of the amplitude images is not reliable because, for example, examination of the crack path shows a phase step in the region of the crack tip, connecting different regions to tension or compression. A differential analysis considering the crack directly and structure of the spotted region is necessary. Jones (2006) also did this differentiation and divided it in two parts: crack tip effects and crack face rubbing. The analysis shows that Phase images and the Amplitude images would refer to nearly matching but different crack tip position. This position matches within its errors with the crack length of the potential drop. This enhanced detectability of the crack tip is a clear advantage of the MC. A clear identification of the crack tip is possible at all stress intensities and even in experiments with long cracks and high loads. The postulated parts (E-Mode and D-Mode) respond with the result of the DFT. The fundamental frequency (loading frequency) respond with E-Mode and the first harmonic frequency with the D-Mode. Furthermore, higher harmonic responses related with the loading frequency exist. These higher harmonic responses had been ignored in the lock-in algorithm. However, the amplitude of second harmonic (60 Hz) and the third (80 Hz) are in the size of the first harmonic. This could refer to further nonlinear effects or could be a mathematical effect. These higher harmonics and their possible depended energy dissipations should be the task of a further investigation. Bär, J., Volpp T., 2001. Vollautomatische Durchführung von Ermüdungsrissausbreitungsexperimenten, Material Testing, 43, 242-247. Bär, J., Vshivkov, A, Plekhov, O., 2015. Combined lock-in thermography and heat flow measurements for analysing heat dissipation during fatigue crack propagation. Frattura ed Integrità Strutturale, 34, 456-465; DOI: .3221/ IGF_ESIS.34.51. Brémond, P., 2007. New developments in Thermo Elastic Stress Analysis by Infrared Thermography. IV Conferencia Panamericana de END. Diaz, F.A., Yates, J.R., Patterson, E.A. Patterson, 2004, Some improvements in the analysis of fatigue cracks using thermoelasticity, Int. J. Fatigue 26, 365-376. Fedorova A., Bannikov, A., Plekhov O., Plekhova E., 2012.Infrared thermography study of the fatigue crack propagation, Frattura ed Integrità Strutturale 21, 46-53; DOI: .3221/ IGF_ESIS.21.06. Jones, R., Pitt S., 2006. An experimental evaluation of crack face energy dissipation, Int. J. Fatigue 28, 1716-1724 Sakagami, T., Kubo, S., Tamura, E., Nishimura, T., 2005. Identification of plastic-zone based on double frequency lock-in thermographic temperature measurement, In: ICF11, Italy. Sakagami, T., Kubo, S., Yamaguchi, Nishimura, T., 2007. A new full-field compensation technique for infrared stress measurements using digital image correlation, J. Strain Analysis Vol. 43, 539-549. Thomson W. 1853. On the dynamical theory of heat. Transaction of the Royal Society of Edinburgh 20, 261–288. References