The influence of mechanical and microstructural properties on the rate-dependent fracture strength of ceramics in uniaxial compression

Abstract The objective of the article is to improve our understanding of how material properties and stress state affect the performance of ceramics at both low and high rates of deformation. Accordingly, studies are performed using finite element simulations and a validated constitutive model, due to Deshpande and Evans (V.S. Deshpande and A.G. Evans, Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model, Journal of the Mechanics and Physics of Solids 56 pp. 3077-3100 (2008)), to investigate the relationship between the mechanical and microstructural properties of ceramics and their rate-dependent fracture strengths in uniaxial compression. The compression simulations consider two different cases, delineated by the boundary condition imposed on the circumferential surface of the cylindrical test specimen: (Case I) A traction-free boundary, allowing for radial confining stresses to develop due to radial inertia; and (Case II) a radial velocity boundary condition with a magnitude that prevents radial stresses from developing. Thus, in the Case II, as in the split Hopkinson pressure bar test, the stress state is uniaxial stress for all applied strain rates. Consistent with experimental results, the model predicts two regimes of rate-dependent fracture strength: (i) A quasistatic regime, for strain rates below a characteristic strain rate, in which the fracture strength is constant and thus insensitive to strain rate; and (ii) a dynamic regime, at strain rates above a characteristic strain rate, in which the fracture strength exceeds quasistatic values and is strain rate sensitive. Dynamic strengthening at high rates is shown to be due to two mechanisms that delay ceramic fracture: (i) Inertia-induced radial confinement and (ii) the limited growth velocities of microcracks. Quasistatic strength σ<inf>o</inf> and characteristic strain rate εË™<inf>o</inf> are found to depend on three mechanical properties and two microstructural properties; through control of these parameters the rate-dependent fracture strength, and thus ballistic performance, of manufactured ceramics can be manipulated. Scaling the results by these characteristic parameters reveals self-similarity among all uniaxial stress results (Case II): If the applied strain rate εË™ is normalized by εË™<inf>o</inf> and the fracture strength σ<inf>f</inf> is normalized by σ<inf>o</inf>, all the results collapse down onto a single universal curve described by a power law. Next, we show that experimental results for the compressive behavior of a large number of brittle materials is well described by the derived scaling law. Finally, the model is calibrated to SiC-N, by fitting the scaling law to empirical data, and its response validated.