**A localized stress field approach for calculating the critical stress
intensity factor for an isotropic solid at atomistic scale**

A Singh and G Singh, MECHANICS OF MATERIALS, 181, 104632 (2023).

DOI: 10.1016/j.mechmat.2023.104632

Crack growth initiation in brittle materials is generally studied using the stress intensity factor (SIF) since linear elasticity is assumed to be valid in the crack-tip region. The critical SIF is the SIF just before the onset of crack growth. In atomistic simulations, the "local"critical SIF is usually found indirectly by relating it to the "global"energetically calculated critical energy release rate. Since the crack growth happens at the crack tip, a method for calculating critical SIF (at a state just before crack growth initiation) directly by near- tip stress field has been implemented. The implementation of this methodology for amorphous isotropic solids is not trivial due to the random arrangement of atoms. Further, the presence of two types of elements in amorphous solids (silica is considered here) complicates the process since the volume occupied by each atom will be different (making the use of virial stress extremely complicated). In the present work, it has first been shown that the amorphous solid is indeed linear elastic isotropic by conducting various tests for finding elastic constants and showing that only two of them are independent. Then, a near-tip stress field is calculated by averaging the analytically calculated stress. The near-tip stresses in amorphous silica, validates the presence of linear elasticity beyond a small region from the crack tip. Even with the truly amorphous nature of silica, the minimum reported R2 for the inverse square-root fit (K-dominance) is around 80% at the critical state just before the onset of crack growth. The value of critical SIF calculated directly from the near-tip stresses in the present work comes out to be very close to those predicted by other indirect methods (experiments and atomistic simulations). The proposed method in the present work has a general applicability to measure the critical SIF directly using the near-tip stress field for any amorphous isotropic solid at the atomistic scale irrespective of the number of type of constituent elements.

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