Issue 48

J. Bär et alii, Frattura ed Integrità Strutturale, 48 (2019) 563-570; DOI: 10.3221/IGF-ESIS.48.54 564 For a specimen loaded at the temperature T m with a stress amplitude  a and a frequency f L the temperature at the time t is given by Eq. (1):       0 sin 2 sin 2 m a L m a L p T t T K f t T f t c                    (1) The parameter K 0 represents the thermoelastic constant, which can be calculated from the coefficient of thermal expansion  , the density  and the specific heat capacity c p of the material. To enhance the thermal emissivity of the metallic surface, the specimens have to be painted. The emissivity of the coating has to be taken into account for a correct determination of elastic stresses out of the measured temperature amplitude. When the thermal emissivity of the coating is unknown, a thermoelastic constant K c including the emissivity of the paint can be determined by calibrating the system with defined stress amplitudes [6]. In this case, K c replaces the constant K 0 in Eq. (1). With the Thermoelastic Stress Analysis (TSA) it is possible to measure local stress fields of cyclic loaded components using Eq. (1). Unfortunately, only the stress amplitude and not the maximum stress can be determined. Several authors [7-10] have shown that in case of plastic deformation a second mode coupled with the double loading frequency appears. They assigned it to dissipative energies and integrated that part as the so-called D-Mode into the evaluation. The corresponding evaluation is based on an incomplete Discrete Fourier Transformation (DFT) and can be written as:           sin 2 sin 2 2 m E L E D L D average Temperature Noise E Mode D Mode T t T T f t T f t t                             (2) In this evaluation, the temperature signal is dissected into a mean temperature T m , a thermoelastic part coupled with the loading frequency (E-Mode) and a dissipative part, the so-called D-Mode, coupled to the double loading frequency. The noise  (t) of the temperature signal can be eliminated with this dissection of the temperature signal. This evaluation generates an image for the E- and D-Amplitude (T E and T D ), the E- and D-Phase (  E and  D ) and the average temperature T m , respectively. Due to the limited recording frequency, f R , of thermographic cameras, normally several cycles were used for the evaluation. Therefore, it is necessary to use a recording frequency f R that is not an even multiple of the testing frequency f L . During the measurement, the average temperature T m is assumed to be constant. A changing mean temperature is considered in the approach published by de Finis et al [11]. Urbanek and Bär [12, 13] extended the approach to higher harmonic frequencies up to the Nyquist frequency, resulting in additional D1 and D2 modes: ሺ ሻ ൌ ௠ ด ௔௩௘௥௔௚௘ ௧௘௠௣௘௥௔௧௨௥௘ ൅ ா ∙ ଶగ௜ሺ௙ ಽ ∙௧ାఝ ಶ ሻ ᇣᇧᇧᇧᇧᇤᇧᇧᇧᇧᇥ ௧௛௘௥௠௢ି௘௟௔௦௧௜௖ ሺாିெ௢ௗ௘ሻ ൅ ஽ ∙ ଶగ௜ሺଶ௙ ಽ ∙௧ାఝ ವ ሻ ᇣᇧᇧᇧᇧᇤᇧᇧᇧᇧᇥ ௗ௜௦௦௜௣௔௧௜௩௘ ଶ௙ ಽ ି௣௔௥௧ ሺ஽ିெ௢ௗ௘ሻ ൅ ∑ ஽ ೖ ∙ ଶగ௜൫ሺ௞ାଶሻ௙ ಽ ∙௧ାఝ ೖ ൯ ே ಿ೤೜ೠ೔ೞ೟ ௞ୀଵ ᇣᇧᇧᇧᇧᇧᇧᇧᇧᇧᇤᇧᇧᇧᇧᇧᇧᇧᇧᇧᇥ ௛௜௚௛௘௥ ௛௔௥௠௢௡௜௖௦ ሺ஽ భ ,஽ మ ,,….ିெ௢ௗ௘ሻ ൅ Φሺ ሻถ ே௢௜௦௘ (3) In all approaches, the noise of the temperature measurement is suppressed, leading to a good temperature resolution of about 1.6 mK in the resulting amplitude images [12, 13]. The Lock-In Thermography is suitable for the investigation of dynamic processes, for example in crack propagation experiments. E XPERIMENTAL D ETAILS Crack Propagation Experiments he experiments were carried out on single edge notched specimens with a size of 80 mm x 12 mm x 2.85 mm machined from EN AW 7475-T761 clad sheet material. A U-type notch with a notch radius of 0.5 mm and a width and a depth of 1 mm was milled into one side of each specimen. The fatigue crack propagation experiments were performed under fully reversed loading conditions at a frequency of 20 Hz in a special equipped servohydraulic testing machine with fixed grips to minimize bending forces. The direct measurement of the potential drop and the subsequent online calculation of the crack length enables experiments under stress intensity controlled conditions. Bär and Volpp [14] give a detailed description of the testing equipment. T