PSI - Issue 66

132 Mansi Gupta et al. / Procedia Structural Integrity 66 (2024) 122–134 Mansi Gupta et al. / Structural Integrity Procedia 00 (2025) 000 – 000 11 Where, ∆ is the change in free energy of the system, ∆ denotes the change in surface area due to breakage of atomic bonds, is the change in free energy of system, ∆ ∞ is surface area after crack propagation, , , are the initial dimensions of the simulation box, and the integration term ( ∫ ∈ 0 ) represents the area under stress-strain curve. The fractured surface area of the nano-beam is calculated by surface mesh modifier function in OVITO. Thus, the value of fracture energy as calculated by above equation is 1.41 J/m 2 . The fracture energy is then used to calculate the fracture toughness (K IC ) of the CSH specimen. Fracture toughness quantifies the resistance of the material to crack propagation. In the case of C-S-H gel, it is directly linked to its complex hierarchical structure, which includes nanoscale pores, layered arrangements of silicate chains, and interlayer water molecules. The fracture toughness can be calculated by Irwin’s formula [ Irwin (1957)] as: =√ 1− 2 ⋅ (3) Where, E is the Young ’ s modulus obtained from the slope of stress-strain curve and ν is Poisson ’ s ratio. Substituting the values in equation 3 gives the fracture toughness as 0.31 MPa √ m. The obtained value of fracture toughness is in the range (0.29 – 0.40 MPa √ m) specified in the literature [Hillemeier et al. (1977), Brown and Pomeroy (1973), Bauchy et al. (2015), Diaz et al. (2021)].

Fig. 9. Stress-strain curve for CSH gel under bending.

Fig. 10. Progression of crack opening displacement with time.