Brittle Failure of Nanoscale Notched Silicon Cantilevers: A Finite Fracture Mechanics Approach

Abstract

The present paper focuses on the Finite Fracture Mechanics (FFM) approach and verifies its applicability at the nanoscale. After the presentation of the analytical frame, the approach is verified against experimental data already published in the literature related to in situ fracture tests of blunt V-notched nano-cantilevers made of single crystal silicon, and loaded under mode I. The results show that the apparent generalized stress intensity factors at failure (i.e., the apparent generalized fracture toughness) predicted by the FFM are in good agreement with those obtained experimentally, with a discrepancy varying between 0 and 5%. All the crack advancements are larger than the fracture process zone and therefore the breakdown of continuum-based linear elastic fracture mechanics is not yet reached. The method reveals to be an efficient and effective tool in assessing the brittle failure of notched components at the nanoscale.

Finite fracture Mechanics at the micro-scale. Application to bending tests of micro cantilever beams

“…where (1) p Π and (1) k Π are the potential and kinetic energy related to the final state, respectively, c G is the fracture energy per unit surface, and 𝛿𝛿𝛿𝛿 is the newly created crack surface. Both the final potential and kinetic energy can be defined as (1) (0) p p p δ Π =Π + Π and (1)…”

“…Advances in micro-technology over the past century have highlighted the need for studies to understand the mechanical behaviour of materials at the micro-scale. Among the latest developments are the evolution of the microelectronics industry, with the manufacture of small size components [1], such as inter-layer dielectric and chip passivation films [2]. Furthermore, the nuclear industry is also in demand for a better knowledge of the behaviour of fuels such as UO2 in pressurized water reactors [5,6].…”

“…In this paper we focus on Finite Fracture Mechanics (FFM) [16][17][18][19] and more precisely on the Coupled Criterion (CC) [18,19] which have been successfully used to predict the crack onset at the macro-scale. Attempts to use the CC at the micro-scale have been made [1,5] and have brought into evidence how important a good knowledge of the fracture parameters (strength and fracture energy or toughness) is at this scale.…”

Variability in porous ceramic fracture: Influence of apparent density and critical pores

“…The CC is able to account for size effects such as, for instance, in composite materials [13,16,17,18], in specimens with notches [19,20,21,22] or holes [20,22,23,24,25,26]. It was also recently extended to explain the large apparent failure stress obtained when studying nanoor micro-scale specimens [27,28,29,30]. The CC was used in previous works first to study the bending strength variation as a function of the specimen width in elastic brittle materials such as gypsum [31].…”

Coupling Finite Element Analysis and the Theory of Critical Distances to Estimate Critical Loads in Al6060-T66 Tubular Beams Containing Notches

“…Among the latter, the theory of critical distances (TCD) stands out, and its applicability in fracture assessments has been widely reported in the literature for a variety of materials (such as polymers [12,13], metals [14,15], composites [16], or ceramics [17,18]). Moreover, the TCD has also been validated to analyze phenomena such as fatigue [19] or environmentally assisted cracking [20] and has been applied to different length scales [19,21,22].…”