Micromechanical testing is now widespread in academic laboratories [1], for example for the local characterization of fracture properties of brittle materials [2]. However, this type of test is subjected to a size effect and presents apparent strength values that are much higher than those measured at the macroscopic scale. As the size of the failure-inducing defects is much smaller in microscopic than in macroscopic specimens, it may partly explain the higher apparent stress at failure for micromechanics tests, but it would not fully explain the observed increase [3].
 
Following the coupled criterion approach proposed by Leguillon [4], two criteria must be satisfied for failure to occur: a stress condition and a cracking energy condition. Under a characteristic dimension dependent on the Young's modulus, the tensile strength and the fracture energy of the material, the energy criterion drives the failure, above failure is rather driven by the stress criterion. Thus, for micromechanical tests, fracture is rather driven by the energy criterion, leading to an increase in the apparent stress at fracture with the decrease in the volume tested.
 
The aim of this study is therefore to verify the applicability of the coupled criterion over a wide range of specimen volumes prepared in a known brittle and crystalline material with as few defects as possible: for this purpose, we have chosen monocrystalline alumina (sapphire).
 
The material is tested under bending over a wide range of specimen sizes: from a few µm (prepared with Ga FIB and tested with nano-indentation system) to conventional macroscopic testing (cm), passing through intermediate sizes, a few hundred µm (Xe FIB) or millimetre (laser cut). A modelling approach is then used to exploit the data from the bending tests. Fracture criteria are extracted and discussed in relation to the same quantities measured conventionally at different scales.
 
References
[1] G. Dehm; Acta Mater., 2017, 142, 248-282.
[2] D. Di Maio; J. Mater. Res., 2005, 20, 299-302.
[3] A. Doitrand; J. Am. Ceram. Soc., 2020, 103, 6991-7000.
[4] D. Leguillon; European Journal of Mechanics, 2022, 21, 61-72