PSI - Issue 52

Ben M B Sargeant et al. / Procedia Structural Integrity 52 (2024) 472–479 Ben M B Sargeant , Catrin M Davies and Paul A Hooper / Structural Integrity Procedia 00 (2023) 000 – 000

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1.1. Models of Sample Thickness Effects Sample thickness has been observed to impact fracture toughness. Relatively thin samples experience plane stress conditions, causing high equivalent stress and promoting fracture by ductile tearing. Toughness increases as increased volume absorbs energy. This trend peaks at a critical thickness ( B 0 ), giving a plane stress critical fracture toughness ( K C ). As thickness is increased, the material becomes less influenced by plasticity at the free surface of a cracked geometry and transfers to plane strain loading conditions, where strain constrained in the cracked geometry and an out of plane stress is induced. Plane strain conditions cause a low equivalent stress and promote brittle fracture [1]. B 0 is approximated to the plane strain plastic zone radius [2]. With continued increase of thickness, a larger proportion of a sample experiences plane strain conditions; this lowers the overall toughness as brittle fracture requires less energy, and the plastic zone size is reduced. Toughness plateaus when plane strain condition becomes dominant and the free surface regions that are under plane stress become negligible; a schematic of this trend is shown in Fig. 1. Plane strain conditions promote a high triaxiality and mean (hydrostatic) stress which can promote both brittle and ductile fracture mechanisms. For plasticity dominated materials such as the SA508 steel used in this work, plane strain promotes void growth and hence the ductile fracture mechanism micro-void-coalescence (MVC). This is illustrated by the ‘crack tunnelling’ effect, where the mid thickness of a cracked geometry (experiencing plane strain) initiates from lower loads and grows further than the crack sides (experiencing plane stress) [1,3]. Plane strain fracture toughness ( J IC and K IC ) is the most conservative value of toughness and may be considered independent of sample size. This makes planes strain conditions appropriate for use in most structural integrity assessments [1,2]. ASTM (ASTM E1820) prescribe a minimum sample thickness of approx. 25 times the plane strain plastic zone size, r p , for valid plane strain testing, shown in Fig. 1 [3]. Samples of this size are rarely achievable in laboratory settings as most metallic samples would be near 1 meter in scale. J-integral fracture toughness can be more achievable as small-scale yielding is included in calculations. This, in theory, allows for valid results to be found using smaller samples that experience loading within the transition from plane strain to planes stress [1]. Wallin [4] described the total trend as a combination of several effects but found the reduction of toughness to plane strain to be inversely proportional to the square-root of thickness [4]. Shahani et al. [2] sort to fit a polynomial to the full range; this resulted in a well-fitting fifth power model but was highly driven by the provided data [2].

Fig. 1 Schematic of material toughness against sample thickness, with illustrations of fracture surface appearance for an SEN(B) sample. Points of plane stress and plane strain conditions are labelled and accompanying derivation of the valid ASTM plane strain sample thickness criteria