Issue 47

P. Gallo et alii, Frattura ed Integrità Strutturale, 47 (2019) 408-415; DOI: 10.3221/IGF-ESIS.47.31 413 process zone value. With the quantification of low limit of continuum theory, it is possible to assume that method such as the TCD can be applied successfully at very small scale; however, once the limitation is reached, discrete nature of atoms cannot be neglected and other methods should be developed. It should be noted that other approaches have similitude with the TCD [31] and therefore have an excellent potential to be applied at small scales considered here. Finite Fracture Mechanics (FFM) [32], for example, shares several aspects with the TCD and its consideration is left as future work. Figure 4 : TEM image of (a) crack propagation of specimen 2 and (b) fracture mode displacements at the onset of nanocrack. B EYOND THE BREAKDOWN OF THE CONTINUUM THEORY his contribution has shown that some continuum theories could be directly extended to micro and nanoscales until their low limit is reached but it does beg the question of how to approach lower scales, where the discrete nature of atoms must be considered. As is shown before, experimental testing is very challenging at the microscale, becomes tough at nanometer-scale and extremely tough at lower scales. However, atomic simulations have developed considerably in the last decade supported by the advancement of computing power and numerical techniques. These simulations, based on interatomic potentials, have drawn considerable attention in the scientific community because of their versatility in the reproduction of qualitative phenomena and are nowadays a reliable tool. When approaching atomic scale and in general beyond the breakdown of continuum theory, the validity and definitions of usual macromechanics parameters (e.g., stress, strain, elastic constant) should be reconsidered. Approaches based on energy, instead, seem to be very versatile and their concepts showed to be easily extensible and valid at the atomic level. If one considers the brittle fracture of silicon, the Griffith criterion, Energy Release Rate (ERR) and others have been reformulated successfully to take into account the atomic structure and validated by using atomic simulations [9,15,33]. As a straightforward extension of the continuum concepts, for example, ERR has been reformulated based on atomic potential energy [34], showing to be more general than continuum counterpart and valid regardless of considered scales. A similar idea is under development by the present authors by considering the strain energy density and preliminary results should be soon available. The silicon, however, is relatively easy to be treated because of its intrinsic “ ideal ” brittle behavior: the fracture process does not involve dislocations but develops clearly by atomic bond breaking along the cleavage plane. In the fracture nanomechanics, fracture of silicon represents the most fundamental and straightforward research target. Challenges toward nanometer scale fracture mechanics rapidly increase when plastic phenomena (e.g., emission of dislocation [35]) and more complex load conditions (e.g., Mode II, Mode III, mixed mode) have to be considered. Ultimately, the definition of these primary mechanisms will depend on the realization of atomic-level fracture mechanics experiments with in situ observation. This final task will require a total reconsideration and improvement of current experimental equipment and techniques. The investigation of atomic fracture mechanics might bring great advancements not only in several academic fields (e.g., multi-physics) but also in industrial miniaturization of future electronic devices. C ONCLUSIONS his contribution has presented a synthesis of some recent micromechanical tests aimed at the evaluation of the fracture toughness of silicon by using pre-cracked nano specimens and alternatively notched nano specimens combined with the theory of critical distances (TCD). T T Propagation δ c /2 δ c /2 Crack tip (a) (b) [011] [011] [100] .