Issue 47

P. Gallo et alii, Frattura ed Integrità Strutturale, 47 (2019) 408-415; DOI: 10.3221/IGF-ESIS.47.31 414 The results can be summarized as follows:  The fracture toughness of silicon is 1 MPa·m 0.5 and is independent of the size and crystal orientation;  While accurate control of the geometry in the specimen fabrication is challenging, small crack tip radius has a relevant influence on the fracture toughness value when pre-cracked samples are employed;  The TCD simplifies the experimental procedure for the evaluation of the fracture toughness by employing notched specimens instead of pre-cracked samples;  The crack propagation at this small scale, where ideally there is no defect, is due to the breaking of atomic bonds along the cleavage plane;  The TCD also yields a good approximation of the magnitude of the fracture process zone, defined as the zone near the crack tip or notch root where the discrete motion of atoms is highly concentrated;  The results obtained here agree with those reported in the literature that define the breakdown of continuum fracture mechanics when the K -dominant region critical size is in the range of 3 to 6 times the fracture process zone. A CKNOWLEDGMENTS i deos of experiments are available in the visual abstract. The authors are grateful to the Japan Society for the Promotion of Science (JSPS) for supporting the present research (Grant-in-Aid for JSPS Fellows No. 16F16366, P16366). R EFERENCES [1] Liebowitz, H. (1968). Fracture, New York, Academic Press. [2] Kitamura, T., Sumigawa, T., Hirakata, H., Shimada, T. (2016). Fracture Nanomechanics, Singapore, Pan Stanford Publishing. [3] Wilson, D., Zheng, Z., Dunne, F.P.E. (2018). A microstructure-sensitive driving force for crack growth, J. Mech. Phys. Solids. DOI: 10.1016/j.jmps.2018.07.005. [4] Mosby, M., Matouš, K. (2016). Computational homogenization at extreme scales, Extrem. Mech. Lett., 6, pp. 68–74. DOI: 10.1016/j.eml.2015.12.009. [5] Shimada, T., Kitamura, T. (2015). Fracture Mechanics at Atomic Scales. In: Altenbach, H., Matsuda, T., Okumura, D., (Eds.), Advanced Structured Materials, 64, pp. 379–396. [6] Sato, K., Yoshioka, T., Ando, T., Shikida, M., Kawabata, T. (1998). Tensile testing of silicon film having different crystallographic orientations carried out on a silicon chip, Sensors Actuators A Phys., 70(1–2), pp. 148–152. DOI: 10.1016/S0924-4247(98)00125-3. [7] Yi, T., Li, L., Kim, C.-J. (2000). Microscale material testing of single crystalline silicon: process effects on surface morphology and tensile strength, Sensors Actuators A Phys., 83(1–3), pp. 172–178. DOI: 10.1016/S0924-4247(00)00350-2. [8] Gallo, P., Sumigawa, T., Kitamura, T., Berto, F. (2016). Evaluation of the strain energy density control volume for a nanoscale singular stress field, Fatigue Fract. Eng. Mater. Struct., 39(12), pp. 1557–1564. DOI: 10.1111/ffe.12468. [9] Shimada, T., Ouchi, K., Chihara, Y., Kitamura, T. (2015). Breakdown of Continuum Fracture Mechanics at the Nanoscale, Sci. Rep., 5(1), pp. 8596. DOI: 10.1038/srep08596. [10] Sumigawa, T., Ashida, S., Tanaka, S., Sanada, K., Kitamura, T. (2015). Fracture toughness of silicon in nanometer- scale singular stress field, Eng. Fract. Mech., 150, pp. 161–167. DOI: 10.1016/j.engfracmech.2015.05.054. [11] Gallo, P., Yan, Y., Sumigawa, T., Kitamura, T. (2018). Fracture Behavior of Nanoscale Notched Silicon Beams Investigated by the Theory of Critical Distances, Adv. Theory Simulations, 1(1), pp. 1700006. DOI: 10.1002/adts.201700006. [12] Yasutake, K., Iwata, M., Yoshii, K., Umeno, M., Kawabe, H. (1986). Crack healing and fracture strength of silicon crystals, J. Mater. Sci., 21(6), pp. 2185–2192. DOI: 10.1007/BF00547968. [13] Wong, B. (1987). Microindentation for Fracture and Stress-Corrosion Cracking Studies in Single-Crystal Silicon, J. Electrochem. Soc., 134(9), pp. 2254. DOI: 10.1149/1.2100861. [14] Dukino, R.D., Swain, M. V. (1992). Comparative Measurement of Indentation Fracture Toughness with Berkovich V