PSI - Issue 42

Jochen Tenkamp et al. / Procedia Structural Integrity 42 (2022) 328–335 Jochen Tenkamp / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Aluminum alloy are promising candidates for lightweight construction and allow a weight reduction of around 35% compared to steel structures, Menge et al. (2005). Hereby, Aluminum-Silicon (Al-Si) alloys are commonly used for casting and additively manufacturing (AM) due to its great processing properties, e.g. the age-hardenable Al-Si alloys AlSi10Mg and AlSi7Mg, Hernandez et al. (2017) and Davis (2001). The microstructure of Al-Si alloys is characterized by the dendrite arm spacing (DAS) in castings or dendritic width in AM materials of  -Al solid solution (matrix) as well as the morphology of Si precipitates, Warmuzek (2004). The loading capability of Al-Si alloys is dominated by process-induced defects, like porosity (casting) or lack of fusion (AM), Wang et al. (2001) and Siddique et al. (2017). Based on short crack fracture mechanics, Murakami (2012) developed and validated the  area concept for steels to estimate the defect size (  area: cross section perpendicular to loading) and Vickers hardness (HV) related threshold for crack propagation as well as fatigue limit aL or strength at 1E7 cycles a,1E7 . Noguchi et al. (2007) modified the  area concept for light metals by including the Young’s modulus of the alloy and the Young’s modulus of steel St according to equation (1). ∗ ,1 7 = ∙ ( + 120 ∙ St ⁄ ) (√ ) 1⁄6 Surface: = 1.43 Volume: = 1.56 (1) For estimation the effect of defects on fatigue life, Shiozawa and Lu (2008) used the Paris-Erdogan law for crack propagation and integrated the equation between initial crack size i (equal to  area at initial defect) and failure crack size f . Assuming a crack propagation dominated fatigue life ( f  p ) and a significant fatigue crack propagation phase ( i ≪ f ), the Paris-Erdogan law can be transformed to equation (2), Shiozawa and Lu (2008). ∆ i = ′ ∙ ( f i ) ′ (2) The maximum stress intensity factor at initial defect max,i can be estimated based on initial crack size i or defect size  area according to equation (3), Murakami (2012). max,i = ∙ √ ∙ i ∙ = ∙ √ ∙ √ ∙ Surface: = 0.65 Volume: = 0.50 (3) The Shiozawa concept was further modified by Tenkamp et al. (2022a) and (2022b) using elastic-plastic fracture mechanics (J integral) to include material specific crack closure and plasticity effects. For this purpose, the effective J integral of Fischer and Schweizer (2020) is calculated at initial defect according to equations (4a) and (4b). ∆ eff,i = [1.45 ∙ (∆ eff ) 2 + 2.40 ∙ ∆ ∙ ∆ √1 + 3 ′ ] ∙ i Surface (4a) ∆ eff,i = [1.16 ∙ (∆ eff ) 2 + 1.91 ∙ ∆ ∙ ∆ √1 + 3 ′ ] ∙ i Volume (  = 0.3) (4b) The effective stress range ∆ eff can be estimated based on the stress range ∆ and stress ratio = min max ⁄ by using the validated crack opening model for aluminum alloys of Schijve (1981) according to equation (5). ∆ eff = ∆ ∙ (3 − 3.7 2 ) 1.74 (5) For direct comparison of stress intensity factor based (3) and J integral based (4) fatigue assessment, the effective J integral can be transformed to an ∆ -equivalent dimension according to equation (6), Radaj and Vormwald (2007). ∆ J,i = √ ∙ ∆ eff,i (6)