Numerical modeling of cone cracking in ceramics via indentation

Abstract

Ceramic is a hard and brittle material with little ductility. It has wide applications in diverse industries viz. metallurgy, atomic energy, electronics, communication, space, military, insulation, biomechanical appliances etc. It is preferred material for armour protection due to its high strength-weight ratio. Its plastic deformation and failure behavior have, therefore, become a subject of extensive research in the recent past. Consequently, several material models were formulated in the second half of the nineteenth century by researchers such as
Johnson- Holumquist, Rajendran-Grove, Deshpande-Evans etc. to study ceramic response under high-velocity impact. But these models are complex and require extensive calibration, while the Drucker-Prager (DP) Model is easy to implement. It was developed for study in soil and rock and is chosen to analyze ceramic quasi-plastic and tensile behaviour as part of research through the current thesis.
Tensile ring and cone cracks, first observed by Hertz, are one of the modes of failure in brittle materials like ceramic. The prime objective of the thesis is the study of ceramic failure as well as cone crack initiation and its propagation through the ceramic body under the influence of varying material parameters such as cohesion, friction angle, dilatancy and softening of ceramics besides confinement by indentation. The Drucker Prager model is employed to study
indentation by simulation through numerical methods in JEM JIVE FEM library. Verification of the model was done through simulation of unit cubes subjected to unidirectional stresses at prescribed displacements. Suitable modification for pressure dependent softening behaviour of the ceramic is also made into the model and simulations undertaken in order to get insight into the nonlinear strength degradation of the ceramic post-elastic limit. Since the DP criterion
tends to overestimate material strength, a suitable mechanism to limit the material strength is integrated with DP yield function and also to facilitate the comparison of results arrived through DP and modified yield functions.
The results obtained by a simulated indentation in accordance with the DP formulation suggest that ceramic having high dilatancy, low friction angle and small softening modulus under confined conditions is more suited for use as armor protection. The pressure dependent softening behavior of ceramic is favorable for it being a good armor protection material. The DP Yield function modified to limit the material strength to a finite value, did not have any significant impact on crack initiation though the zone of compressive plastic strain grew in size during indentation. The DP based numerical model suffered from mesh sensitivity. The introduction of viscoplasticity to the numerical model was observed to have a positive influence in mitigating mesh sensitivity.