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

Petr Skalka,Michal Kotoul

doi:10.3390/ma14226864

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.

Highlights

A number of studies devoted to identification of material properties such as Young’s modulus, yield stress, and work hardening modulus by using experimental indentation data, finite element (FE) simulations, and optimisation procedures for solving inverse problems have occurred in the literature
While previous studies available in the literature, e.g., [7,8,9,10], which use cohesive zero. These data werestudies determined forineach indentation loading force and they w available the literature, e.g., [7,8,9,10], which cohesive zoneWhile finite previous element techniques for simulation of indentation cracks in brittleuse solids, tried compared with experimental observation and measurement of the radial crack zone finite element techniques for simulation of indentation cracks brittle solids, tried to improve methods for the evaluation of material toughness frominthe indentation load,length, tocrack improve the evaluation material toughness from indentation load, Equation size, methods hardness,for elastic constants, of and indenter geometry, thisthe study focuses on the 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 determined using the well-known Griffith-Irwin formula
With the cohesive energy density determined as 2Γ = 5.30 J/m2 the Formula (19)

Summary

Introduction

A number of studies devoted to identification of material properties such as Young’s modulus, yield stress, and work hardening modulus by using experimental indentation data, finite element (FE) simulations, and optimisation procedures for solving inverse problems have occurred in the literature. Various optimisation techniques have been used by researchers, see, e.g., [1,2,3,4] to determine material properties from indentation load–displacement curves tests. Identification of elastic and/or elasto-visco-plastic constitutive laws from indentation tests in terms of general theoretical framework of inverse problems solution has been described in [5,6]. For indentation crack initiation and propagation modelling a cohesive interface consisting of cohesive elements is placed in the plane of potential cracking and only mode I type crack is considered. The behaviour of the cohesive elements in this interface is governed by a traction-separation law which mostly has the bilinear form characterised by three parameters- peak cohesive traction σmax , corresponding damage-initiating displacement ∆c and failure displacement

Objectives

Methods

Results

Conclusion