PSI - Issue 13

Fuzuli Ağrı Akçay / Procedia Structural Integrity 13 (2018) 1695 – 1701 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1700

6

I   =

C



,0 (17b) Eq. (17b) provides an interesting physical interpretation for the specific surface energy density ( ): Specific surface energy density, which is defined as the ratio of critical effective energy release rate to characteristic length (relevant to brittle fracture), is approximately equal to the tensile strength of the (brittle) material. Furthermore, in the case of tensile strength being approximately equal to yield stress (i.e., ≈ ), Eq. (17a) turns into 2 ,0 Ic I y l K E   (18) This equation is in accordance with the (elastic component of) critical crack tip opening displacement ( CTOD c ). CTOD c (at plane stress condition) is given as (Anderson, 2005; Telichev, 2016) 2 Ic c y K CTOD E  = (19) Therefore, when tensile strength is approximately equal to yield stress (i.e., ≈ ) – with Young’s modulus being much larger than the tensile strength of the material (i.e., ≫ ) – characteristic length relevant to brittle fracture ( ,0 ) is as large as the (elastic component of) critical crack tip opening displacement. This is consistent with the fact that use of CTOD c as a characteristic length has been suggested by some researchers (see e.g., Gao et al., 1998). 3.1. Material The material to be used for the validation of the theoretical model is gray cast iron (GCI). The reason for the use of gray cast iron is that gray cast iron not only exhibits brittle behavior but also is the most common form of cast iron and widely used in the industry (Brauer et al., 2017). Potential applications of gray cast iron are engine cylinder blocks, flywheels, gearbox cases as well as machine-tool bases (URL-1, 2017). 3.2. Results and Discussion Required data for gray cast iron to implement the theory is obtained from the open literature. Recently, Han et al. (2013) conducted experimental investigation on pearlitic graphite cast iron to study the effects of micro-structural factors on fracture toughness. The article investigated the fracture toughness of pearlitic graphite cast iron with six different nodularities. The data of G60N6, corresponding to nodularity of 60% and nodule count of 6 ea/mm 2 , is to be used in this article, as the sample still remains within the elastic limit at fracture, with 0.2% strain at fracture. Additionally, as the cracks initiated at graphites, the characteristic length relevant to fracture process is to be taken as the average spacing between graphites. Average spacing between graphites for G60N6 sample is provided as 157  m with plane strain fracture toughness of 58 MPa √m (Han et al., 2013). Hence, the critical energy release rate for Mode I fracture can be calculated as Γ = 31 kJ/m 2 . We use plane strain fracture toughness to determine the critical energy release rate, as it is a true material property (Dieter, 1986) unlike plane stress fracture toughness. On the other hand, Young’s modulus of G60N6 is not provided by the authors. However, experimentally calculated tensile strength of G60N6 remains between the tensile strength of ASTM 30 class and ASTM 35 class gray cast irons (White, 2010). Therefore, accordingly, a mid-value between ASTM 30 class and ASTM 35 class is taken as a representative for Young’s modulus of G60N6, i.e., ≈ 105 GPa. Substituting aforementioned values of the critical energy release rate, Young’s modulus, and the characteristic length into Eq. (12) yields theoretical tensile strength of G60N6 gray cast iron as = 197 MPa. This theoretical tensile strength is 15% lower than the experimental one, which is 232 ∓ 12 MPa, provided by Han et al. (2013). The main reason for this difference is attributed the fact that the theory estimates the lower bound of tensile strength, as it provides the necessary condition for fracture. Remarkably, considering the fact that 99.7% of the observations would Ic I I l