The ARL (Army Research Lab) and a UF (University of Florida) team collaborated to employ an improved granular response model in conjunction with a dynamic cavity expansion modeling framework to capture the response of ceramics to the complex impact-induced stress state that includes compression, tension and shear. The dynamic cavity expansion modeling framework uses the pressure required to expand a cavity in an intact material to characterize its ability to resist deep penetration. This pressure, of course, is dependent on how the material responds to compression, tension and shear forces. Due to the applicability of this new model to a broad class of ceramics, the need for expensive experiments to characterize penetration response is significantly reduced. The new penetration model improves the understanding of how brittle ceramic responds to high impact stress by fracturing and comminuting to granular like material, and increases modeling ability of penetration events.
The improved model has been shown to better predict the resistance of a wide range of ceramic targets when shot at by a long-rod projectiles at velocities up to 3km/s. The important material parameters for penetration performance of a ceramic target have been identified through this collaborative effort, which will guide how the failure processes in ceramic can be controlled through improved material design or through a multi-materials systems approach.
International Journal of Solids and Structures – An improved dynamic expanding cavity model for high-pressure and high-strain rate response of ceramics
• A dynamic expanding cavity model to describe penetration in ceramics is proposed.
• A constitutive model for comminuted ceramics is developed.
• Both models may be used in the absence of relevant experimental data.
• The expanding cavity model identifies vital properties governing impact behavior.
An extended Mohr–Coulomb (M–C) model, capable of capturing the high pressure-dependent shear deformation of ceramics, is incorporated into a spherical dynamic expanding cavity model (d-ECM) to capture the dynamic response of semi-infinite brittle ceramics under steady-state penetration. It is shown that this improved d-ECM can better predict the target resistance of structural ceramics reported in penetration experiments. The brittle ceramic is assumed to undergo cracking when the hoop stress reaches its tensile strength and is subsequently comminuted when the radial stress reaches its compressive strength. The constitutive behavior of the comminuted ceramic is predicted using a modified form of the extended M–C model. The extended M–C model captures the strain rate-independent exponential pressure-shear response of intact ceramics in a normalized universal strength model. A single set of three parameters can be used to describe the response of all intact ceramics. This constitutive model has been suitably modified into a two-parameter exponential model, applicable to comminuted ceramics. These two parameters have been calibrated using experimental penetration data along with analytical estimations, and it has been shown that a single set of universal parameters can be used to describe the response of most comminuted ceramics. By incorporating these models, the improved d-ECM can be used to estimate the target resistance of a ceramic when relevant experimental data is not readily available. The results of the analysis further reveal that, in the case of steady-state penetration into semi-infinite monolithic targets, the properties of the comminuted material have a greater influence on the target resistance of ceramics than those of its intact state. The model proposed is applicable for thick monolithic ceramic targets under steady-state penetration conditions, and not for layered targets.
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