PSI - Issue 13

Takayuki Kitamura et al. / Procedia Structural Integrity 13 (2018) 2180–2183 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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Table 1 .Elastic constants of silicon single crystal Material constants [GPa] C 11 C 12 C 44 167.4 65.23 79.57

The size of Λ is dependent on the shape and size of specimen and crack, and is usually smaller than 1/10 of them in the scale. The conventional fracture mechanics concept tells us the cracking is uniquely governed by the magnitude of K I and the critical value, K Ic , gives the fracture toughness. It should be noted that K Ic is independent of size of singular zone Λ (sizes of specimen and crack length) in macro components. In this experiments, the precrack length as well as the specimen size is controlled so as to make the small Λ in the specimen. Specimens are manufactured by means of a Focused Ion Beam (FIB). Controlling the current and the direction, the specimen shape with the size is carefully formed. If necessary, the argon milling is also used for finishing the surface. For atomic level testing, the removal of damage layer on the fabricated surface becomes a critical issue for the accurate evaluation of fracture toughness, as described in Section 4.

Figure 2. Loading device 2.3. Loading devise for nanospecimen under in situ observation

The loading devise is consisted of actuator, loading tip and load sensor mounted in a frame, Fig.3. The specimen bottom is fixed on a gold wire which is connected with the 3D piezo-actuator, which precisely controls the specimen position. Pushing the specimen onto the diamond tip, we can apply the load on the specimen. Devise can be set in a Transmission Electron Microscope (TEM) or Scanning Electron Microscope (SEM) for in situ observation during fracture toughness testing. Beginning of cracking and process of propagation can be clearly observed by the system.

Figure 3. Dependence of fracture toughness on the size of singular stress field up to 60 nm.

3. Fracture toughness in nanometer scale

Figure 4 shows the experimental results of fracture toughness in nanometer scale specimen. It is clear that the critical stress intensity factor is almost constant in the range of 60-300 nm of singular stress field. As the fracture toughness in a bulk single crystal silicon is about 1 MPam 1/2 , the toughness obtained here coincides very well with one in a bulk. This size independence points out that the fracture mechanics is effective until nanometer scale if the methodology is appropriate in terms of mechanical requirements (extensively clean cracking morphology in an extensively clean material from an extensively clean starter.)