Issue 47

P. Gallo et alii, Frattura ed Integrità Strutturale, 47 (2019) 408-415; DOI: 10.3221/IGF-ESIS.47.31 410 E VALUATION OF FRACTURE TOUGHNESS USING NANOSCALE PRE - CRACKED SPECIMENS hree micro-specimens were fabricated by a focused ion beam (FIB) processing system (see previous section). V- shape grooves were used as a guide for straight pre-crack introduction, and a notch was then introduced at the top of the specimen. The notches were, on average, 100 nm wide (mouth width) and 700 nm deep. Example of the specimen is depicted in Fig. 2(a) together with material properties, while geometrical parameters are reported in Tab. 1. The pre-crack was realized by applying an opening displacement with a wedge-shaped indenter according to Fig. 2(c). The upper part of the specimen was later cut by FIB to obtain shorter pre-cracks. The experiments were conducted using a sample holder with a loading device inserted in a TEM (transmission electron microscope) provided with in situ observation camera. The opening displacement was applied to the sample by pushing the wedge-shape indenter in the pre- crack mouth while a sensor beneath the indenter detected the applied load (see visual abstract). The stress in the specimens was later re-analyzed by finite element method (FEM) by properly considering the material anisotropy and 3D model was used. The material constants and the model employed are reported in Fig. 2(b). The fracture toughness was evaluated by the intensity of the singular field at the critical load (at crack propagation). The results are summarized in Tab. 1 which reports the fracture toughness K IC , the length of the singular stress field Λ K and the critical crack opening displacement δ C . From the results, it is possible to conclude that the average fracture toughness K IC is 1 MPa·m 0.5 . This value agrees with the bulk silicon value, i.e., 0.75-1.08 MPa·m 0.5 [12–14]. This finding proves that the fracture toughness is independent of the size. The K IC is also independent of the length of the singular stress field. Results in Tab. 1 are, indeed, all very close to the same average value of 1 MPa·m 0.5 . These results have been recently further confirmed by additional experiments and sophisticated first-principles density functional theory (DFT) simulations [10,15] which considered the discrete nature of atoms. In those works, Griffith criterion was applied to 4 nm stress singularity, and the fracture toughness resulted in being 0.95 ± 0.07 MPa·m 0.5 , in agreement with values presented here. Figure 2 : Example of (a) nanoscale notched specimen, (b) 3D FE model and (c) introduction of pre-crack. a (nm) w (nm) t (nm) Λ k (nm) δ C (nm) K IC (MPa·m 0.5 ) Specimen 1 3982 830 580 23 205 0.83 Specimen 2 1412 600 480 25.4 62 1.09 Specimen 3 4359 474 302 57.5 237 1.08 Table 1 : Pre-crack length a and width w ; Thickness of the thinned region t ; Synthesis of the results: length of singular stress field Λ k and critical crack opening displacement δ C . T Precrack Material constants C11=167.4 GPa C12=65.23 GPa C44=79.57 GPa (a) (b) 1 μm 1 μm (c) Indenter Notch Crack