On strain-rate sensitivity and size effect of brittle solids: transition from cooperative phenomena to microcrack nucleation

An idealized brittle microscale system is subjected to dynamic uniaxial tension in the medium-to-high strain-rate range $(\dot \varepsilon \in 100s^{-1},1 \times 10^{7} s^{-1}])$ to investigate its mechanical response under constrained spatial and temporal scales. The setup of dynamic simulations is designed to ensure practically identical in-plane stress conditions on a system of continuum particles forming a two-dimensional, geometrically and structurally disordered, lattice. The rate sensitivity of size effects is observed as well as the ordering effect of kinetic energy. A simple phenomenological expression is developed to account for the tensile strength sensitivity of the small-sized brittle systems to the strain-rate and extrinsic size effects, which may serve as a guideline for formulation of constitutive relations in the MEMS design. The representative sample is defined as a square lattice size for which the tensile strength becomes rate-insensitive and an expression is proposed to model its evolution between two asymptotes corresponding to the limiting loading rates. The dynamics of damage accumulation is analyzed as a function of sample size and loading rate.