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The performance of behaviour of brittle materials depends upon discrete deformation mechanisms operating during the loading process. The critical mechanisms determining the behaviour of armour ceramics have not been isolated using traditional ballistics. It has recently become possible to measure strength histories in materials under shock. The data gained for the failed strength of the armour are shown to relate directly to the penetration measured into tiles. Further the material can be loaded and recovered for post-mortem examination. Failure is by micro-fracture that is a function of the defects and then cracking activated by plasticity mechanisms within the grains and failure at grain boundaries in the amorphous intergranular phase. Thus it is the shock-induced plastic yielding of grains at the impact face that determines the later time penetration through the tile. [ABSTRACT FROM AUTHOR]

Constitutive models for brittle materials such as glass can be very complex as they are dependent on strains, strain rates, pressures, temperatures, damage and other parameters. There may also be significant (pressure-dependent) strength after failure such that the constitutive response is much different for intact material and failed material. A large number of laboratory tests is required to develop a comprehensive constitutive model. Another approach is to develop simple models by using penetration-velocity data obtained from ballistic experiments. Here various functional forms of simple models (with a limited number of constants) can be used to (computationally) match the penetration velocity over a range of impact velocities. This allows for the determination of the most important parameters and it provides an approximation of the stresses that occur during penetration. This article presents several simple computational models for borosilicate glass, including single-state models and dual-state models (that include an intact strength and a failed strength). [ABSTRACT FROM AUTHOR]