Issue 47

P. Gallo et alii, Frattura ed Integrità Strutturale, 47 (2019) 408-415; DOI: 10.3221/IGF-ESIS.47.31 411 E VALUATION OF FRACTURE TOUGHNESS USING NANOSCALE NOTCHED SPECIMENS t very small scale, even a small notch radius can drastically change the stress singularity, and the fracture toughness obtained [16,17]. At the same time, the realization of crack is difficult and very challenging. For this reason, it is worth of investigating alternative procedures for the determination of those mechanical properties that would overcome these difficulties. Among the methods available in the literature, the theory of critical distances (TCD) has proved to be very versatile and simple. First developments on “material length parameters” were addressed by Neuber [18] and Peterson [19]. The recent history of the TCD, instead, was formalized by Taylor [20] and Susmel [21]. TCD in the form of the Point Method assumes that “failure occurs when the linear elastic maximum principal stress at a given distance L /2 from the notch root equals the inherent material strength of the material σ 0 ”. L is the so-called material characteristic length, and it takes the following form under static loading [22]: 2 0 1 IC K L          (1) From Eqn. (1), it is clear that when the material characteristic length and the inherent stress are known, the fracture toughness can be quickly evaluated as: 0 IC K L    (2) Susmel at al. [22,23] and Taylor et al. [20,24] proposed an efficient strategy to evaluate the material characteristic length and the inherent material stress. At least two static tests considering notch of different sharpnesses need to be carried out to determine the static strengths. Subsequently, the linear elastic stress fields of the two notches under incipient failure conditions can be plotted and overlapped in a single picture. The intersection of the two stress distributions permits to evaluate both σ 0 and L. Once these two parameters are defined, Eqn. (2) can be employed. The advantages tied-in to the procedure in the realization of simple geometries are relevant and worth of investigating. Therefore, to determine the fracture toughness of single crystal silicon, two notched nano-cantilever beams of different sharpnesses were realized by focused ion beam (FIB) processing system. The fabrication process reported in [11] was followed. The specimens had a notch radius ρ of 6.3, 20.2 nm and opening angle 2 α of 68° and 59°, respectively. These geometries gave stress concentration factor K tn (net section) of 4.9 and 2.9, respectively. The specimens were later loaded into the TEM by using an indenter provided with a load sensor (see visual abstract). Fig. 3(a) presents a sample during the experiment. Deflection at failure δ f and load at failure P f were obtained. The results are summarized in Tab. 2. Following the definition provided earlier, the fracture toughness K IC and the material characteristic length L were determined as is shown in Fig. 3(b). The value of the fracture toughness was 1.05 MPa·m 0.5 , while L was 1.8 nm. The inherent material strength σ 0 was approximately 14 GPa. These results have been further confirmed by additional tests in [11,25]. Figure 3 : Example of (a) nanoscale notched specimen (TEM image) and (b) synthesis by using the TCD. A (a) (b) Indenter tip 1.E+02 1.E+03 1.E+04 1.E+05 0.01 0.1 1 10 100 Distance from notch root [nm] Sharp Blunt 10 5 10 2 σ 1 [MPa] K tn = 4.9 K tn = 2.9 σ 0 ≈ 14 GPa L/2 = [0.9] nm K IC = 1.05 MPa∙m 0.5 K IC = σ 0 (πL) 0.5