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. 2021 Nov 14;14(22):6864.
doi: 10.3390/ma14226864.

Determination of Mechanical and Fracture Properties of Silicon Single Crystal from Indentation Experiments and Finite Element Modelling

Petr Skalka  1 , Michal Kotoul  1   2
Affiliations

Determination of Mechanical and Fracture Properties of Silicon Single Crystal from Indentation Experiments and Finite Element Modelling

Petr Skalka et al. Materials (Basel). .

Abstract

It is well-known that cracks are observed around the impression during indentation of brittle materials. The cracks inception depends on load conditions, material and indenter geometry. The paper aims to use experimental micro-indentation data, FE simulations with cohesive zone modelling, and an optimisation procedure to determine the cohesive energy density of silicon single crystals. While previous studies available in the literature, which use cohesive zone finite element techniques for simulation of indentation cracks in brittle solids, tried to improve methods for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, this study focuses on the evaluation of the cohesive energy density 2Γ from which the material toughness can be easily determined using the well-known Griffith-Irwin formula. There is no need to control the premise of the linear fracture mechanics that the cohesive zone is much shorter than the crack length. Hence, the developed approach is suitable also for short cracks for which the linear fracture mechanics premise is violated.

Keywords: finite element analysis; mechanical and fracture properties identification; micro-indentation; optimisation analysis.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Photographs of indentation with radial cracks.
Figure 2
Figure 2
(a) FE model of Vickers indentation test on silicon crystal. (b) Calibration of the tip shape based on the hardness.
Figure 3
Figure 3
Representative force–depth curves from indentation tests: (a) experiment, (b) numerical simulation after calibration.
Figure 4
Figure 4
Cohesive zone model (a) definition and boundary conditions, (b) the traction-crack opening length relationship.
Figure 5
Figure 5
Experimental values of radial crack length.
Figure 6
Figure 6
Crack length as function of the indentation depth and the cohesive energy density.
Figure 7
Figure 7
Crack extension during the indentation test for maximal loading force of 300 mN: loading force (a) F = 105 mN, (b) F = 230 mN, (c) F = 300 mN and (d) F = 0 N.
Figure 8
Figure 8
Dependence of differential hardness on (a) force, (b) depth.
Figure 9
Figure 9
Indentation with the maximal loading force Pmax = 300 mN: (a) state at maximal load (numerical simulation), (b) state after complete unloading (numerical simulation), (c) state after complete unloading (experimental observation).
Figure 10
Figure 10
Distribution of the crack opening ∆ along the crack flanks for Pmax = 300 mN (a) maximal loading, (b) complete unloading.
Figure 11
Figure 11
Size effect of mesh density on crack length.
See this image and copyright information in PMC

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