Strength-toughness relation of single crystalline and nano-polycrystalline silicon specified by atomic-/nano-crystalline microstructures

An asymptotic non-LEFM model is developed for shallow surface cracks comparable to material microstructures. The characteristic microstructure size (C_ch) of single crystal silicon (SCS) is the atomic diameter (0.235 nm), and C_ch of a nano-grained polycrystalline silicon (N-PCS) is its average grain size. N-PCS with C_ch from 150 nm to 3 μm is considered in this study. The fracture toughness (K_IC) of both SCS and N-PCS can be predicted from their intrinsic strengths and respective C_ch. Predicted K_IC values of 0.90–1.40 MPa √m for SCS and 1.56–5.31 MPa √m for N-PCS are confirmed by collected experimental data of 0.74–1.38 MPa √m for SCS and 1.43–3.46 MPa √m for N-PCS. The intrinsic relation between the K_IC, intrinsic strength and characteristic microstructure is both practically useful and fundamentally significant. The macroscopic K_IC and intrinsic strength, previously considered as two separate material properties, are now linked together by the atomic-/nano-scale microstructures. This fundamental relation on strength, toughness and microstructure for brittle solids, verified by SCS and N-PSC, is comparable to the classic “Hall-Petch relation” for ductile metals.