PSI - Issue 57

Lorenzo Bercelli et al. / Procedia Structural Integrity 57 (2024) 437–444 443 L. Bercelli, C. Guellec, B. Levieil, C. Doudard, F. Bridier, S. Calloch Author name / Structural Integrity Procedia 00 (2019) 000 – 000 7 30% , and for / =1.13 (Fig. 6.d and g), ≈50% , regardless of the initial configuration (as-welded or pre loaded). 4. Fatigue life prediction In order to validate the order of magnitude found for the opening rate ( i.e. the effective stress range Δ ) and its link with the crack propagation kinetics, it is proposed to forecast the fatigue life of tested T-joints using Linear Elastic Fracture Mechanics (LEFM). The model adopted in this study is inspired from the one presented by Bercelli et al. (2023), that relies on the Paris-Erdogan law which parameters and are identified on the same experimental database, from infrared results. This model is formulated as follows d d N a = ( ( )Δ √ ) , (6) with ( ) a correction factor to consider multiple effects (such as the crack shape as well as sample geometry) which expression is taken from the work of Hobbacher (1993), Newman and Raju (1984) and Recho (2012). Integrating equation 6, one can determine a fatigue life ( ) to reaching of a 2 long crack, estimating an initial size 2 0 (i.e. ( 0 ) = 0 ) based on TSA crack monitoring data. In this study, the value =5 is chosen as it is the typical half-size of a crack prior to coalescence (which is not taken into account in the proposed model). This predicted lifetime ( =5 ) is compared to the experimental number of cycles to reaching a through-width crack . Confrontation of estimated lifetimes ( =5 ) with experimental lifetimes are illustrated in Fig. 7: - in Fig. 7.a, no effect of stress ratio is considered ( i.e. Δ =Δ is considered regardless of the closing phenomenon) leading to an exaggerated conservative forecast; - in Fig. 7.b, the effect of stress ratio is considered ( i.e. Δ = Δ where is estimated from infrared measurements), leading to a corrected forecast of fatigue lives.

(a) (b) Fig. 7. Confrontation of fatigue life forecasts ( = 5 ) to experimental lifetime regardless of the closing phenomenon by imposing =1 (a) and considering the closing phenomenon using values of from infrared data (b). Comparing the two graphs Fig. 7.a and Fig. 7.b, it appears the consideration of the closing phenomenon, through the estimation of an opening rate assessed via TSA, significantly improves fatigue life forecasts. This tends to prove that the closing phenomenon as detected via infrared monitoring is intimately linked to the local stress state around the fatigue crack, and so the fatigue life of the welded joints. Although, forecasts appear to be a bit on the non-conservative side, especially for the two samples tested at a high stress range Δ / = 1.13 for which it was estimated ≈ 0.5 . Nevertheless, this acts as a proof of concept of the proposed methodology. A more robust signal processing technique should be achieved, especially an automated and user independent approach for the processing of full infrared films, in order to study the likely variability of along the crack as well as its evolution with the crack length 2 .