PSI - Issue 57

Lorenzo Bercelli et al. / Procedia Structural Integrity 57 (2024) 437–444 439 L. Bercelli, C. Guellec, B. Levieil, C. Doudard, F. Bridier, S. Calloch Author name / Structural Integrity Procedia 00 (2019) 000 – 000 3 with ℎ the temperature linked to the thermoelastic coupling under adiabatic conditions, the coefficient of thermal expansion, 0 the initial temperature and 1 the first invariant of the stress tensor. From this equation, it comes that for a sample under a sinusoidal loading below the yield stress at frequency , the temperature response linked to the thermoelastic coupling is also sinusoidal at the same frequency. Moreover, the amplitude of the temperature’s first harmonic 1 is proportional to the amplitude of the stress tensor’s first invariant 1 . In that regard, TSA allows for a live mechanical field measurement of samples submitted to a constant amplitude cyclic loading. In practice, the adiabatic condition is not met, and due to conduction effects (which intensity is governed both by the material properties and the mechanical frequency ), the field of 1 measured via an infrared camera is only a locally averaged image of the field of 1 .

Fig. 1. Test set-up of the four-point bending on welded T-joints monitored via TSA, in the =0.1 configuration. 3. Experimental results and post-processing 3.1. Detection and monitoring of cracks through TSA Infrared films are recorded regularly for each test, during a sufficient number of loading cycles (here from 60 to 150 ) and with enough frames per cycle (here from 50 to 20 ) to allow for the estimation of harmonic’s amplitudes with a good signal to noise ratio via the lock-in method from the work of Breitenstein et al. (2010). For each of these films, the amplitude of the first harmonic at each pixel is computed,giving an image of the mechanicalfield (in the sense of 1 ) at different times throughout the fatigue test. At the start of a test, before the occurrence of any fatigue damage, the stress concentrations at both weld toes are clearly visible as red bands (high values of 1 ) at each side of the stiffener in blue (low values of 1 , Fig. 2.a and Fig. 2.c). As soon as a crack initiates along the weld toe, as its presence necessarily causes a discontinuity in the linear stress concentration of the weld toe, it can be detected in the infrared data, as shown for = 0.1 on Fig. 2.b, for which three cracks exist on the left weld toe. In this manner, it is possible to monitor the propagation of multiple cracks before failure of the welded joint, as exposed in the work of Carteron et al. (2020). As for the case of repeated compression when =10 , the presence of cracks is less obvious in the first harmonic’s amplitude 1 field. Indeed, as it is shown on Fig. 2.c and Fig. 2.d (before and after crack initiation, respectively), while cracks are indeed present, it appears difficult to acknowledge their size and position along the weld toes, only via the information of 1 . This is explained by the presence of a crack closure phenomenon: at = 10 , because of the presence of tensile residual stresses at the weld toe, the effective stress ratio close to the crack is < 0 . This results in the crack working in tension-compression in Mode I, leading the crack to alternatively open and close within a loading cycle. This can actually be observed in the temperature signal of pixels close to a fatigue crack, where a second harmonic amplitude appears that corresponds to the alternation from an open crack (with small temperature variations) to a closed crack (with temperature variations comparable to that of the uncracked weld toe,