PSI - Issue 57

Pierrick Lepitre et al. / Procedia Structural Integrity 57 (2024) 395–403 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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equation can be written as (Chrysochoos and Louche (2000), Boulanger et al. (2004) and Doudard et al. (2005)) + = Δ+ ℎ , (1) with θ the mean temperature variation, τ eq a characteristic time representing the thermal loss, ρ the density, C p the specific heat, Δ the intrinsic dissipation and C the is the thermo-elastic coupling term. As the machine loading frequencies (> 100 Hz) are much higher than the thermocouple integration frequency (~ 10 Hz) and as the mean thermo-elastic coupling term is null for one complete cycle, C the can be neglected. Also, a common occurrence for steel is that the dissipation is constant per cycle, so Δ can be written as Δ= ∗ , (2) with E d the dissipated energy density per cycle, expressed in µJ.mm -3 .cycle -1 . This assumption has been verified and is discussed later in this paper. So, the temperature during a block of self-heating test should vary as a saturating exponential (and an exponential decay for the cool down phase) ( ) = ∗ (1 − exp (− )) . (3) As the loading lasts at least 5 τ eq , θ reaches 99 % of its stabilization value, noted θ stab . Then E d can be computed as = 0 ∗ . (4) Experimentally, θ is computed as ( ) = ( ) − ( ) + ( 2 ) − , (5) with θ x the mean temperature rise during the first 30 seconds of recording (the third phase in Figure 1). To compute θ stab , the average temperature rise between 4 τ eq and 5 τ eq of the solicitation (the fourth phase in Figure 1) is considered. 3. Results Previously detailed self-heating test and post-processing protocol were applied on a bare 300M F50 coupon, with R = -1, f r = 135 Hz and τ eq about 50 seconds. The temperature rise evolution for every block are stacked in Figure 2 (from σ a = 100 MPa to σ a = 975 MPa). It can be noticed that θ follows well a saturating exponential (equation 3) during the solicitation and an exponential decrease during the cool down. Moreover, the thermal signals are very clear as the measurement uncertainty on the stabilized temperature rise values is estimated at ± 10 mK. The test was interrupted after the σ a = 975 MPa loading block, even if the rupture was not reached, because of the limited load capacity of the machine. For every loading block, θ stab is retrieved and E d computed. Then, the 300M self-heating curve can be built by plotting the dissipated energy density per cycle against the loading amplitude. The same protocol was applied on two additionalcoupons to validate the repeatability of the self-heating curve. The second coupon failed during a loading block at σ a = 900 MPa and the third at σ a = 850 MPa. Optical and electronic microscopy observations of the fracture 3.1. Bare 300M self-heating test