PSI - Issue 57

Mathilde Renault et al. / Procedia Structural Integrity 57 (2024) 22–31 Mathilde RENAULT / Structural Integrity Procedia 00 (2019) 000 – 000

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Thermal marking of the fatigue crack front is associated with the formation of an oxide layer on the lips of the crack exposed to the open air (Lambourg). The procedure therefore involves interrupting the fatigue test and heating the specimen to the target oxidation temperature. Preliminary studies carried out on material coupons have shown that the marking time must be long enough for the over-thickness of oxide created to be visible. The oxidation temperature was set at 200°C and the holding time was 30 minutes. 4. Post-treatment Thermoelastic stress analysis (TSA) is an experimental method that allows the surface stress field to be monitored from an infrared measurement. In this section, a brief presentation of the theoretical framework of TSA is given along with the post-processing technique of infrared data used to allow the determination of mechanical field. 4.1. TSA Method Thermoelastic stress analysis is based on small temperature changes that occur when a material is subjected to a change in elastic strain, and this physical behavior is typically referred to as the thermoelastic effect. When a material is subjected to a cyclic load, the strain induced produces a cyclic variation in temperature which is opposite in phase to the loading signal. Solving the heat equation with the adiabaticity assumption (Boulanger,2004) leads to a variation in temperature related Eq 4 where is the mechanical frequency, α' is the coefficient of thermal expansion of the material, 0 is the initial temperature and 1 is the amplitude of the first invariant of the stress tensor with 1 = ( ) . The amplitude of this signal is therefore directly proportional to the amplitude of the first stress invariant. Infrared measurements can therefore be used to trace the surface stress field (without considering conduction effects). 4.2. Lock-in method To obtain the ℎ amplitude maps, the lock-in method (Breinstein,2010) was implemented in an in-house software dedicated to infrared image analysis. This method can be used to extract data from a noisy signal, provided that the frequency of the signal of interest is known and that at least 4 images per loading cycle are recorded to avoid poor signal to noise ratio. The term thermo-elastic coupling is used in the case of solving the heat equation in a purely adiabatic framework. As this condition is not perfectly respected in the tests presented above, we will refer to the amplitude of the 1st harmonic of the temperature signal (which can be interpreted as the thermo-elastic coupling averaged over a zone), and this quantity will be noted as 1ℎ . to thermoelastic coupling given by : ℎ ( ) = 1 ′ 0 cos (2 + 2)