A MICROMECHANICAL MODEL FOR HIGH-STRAIN RATE BEHAVIOR OF CERAMICS

A constitutive model applicable to brittle materials such as ceramics subjected to biaxial compressive loading is developed. The model is ba sed on non-interacting sliding microcracks that are uniformly distribu ted in the material. Tension Cracks nucleate and propagate from the ti p of the sliding cracks in the direction of maximum applied compressio n when the stress-intensity factor reaches its critical value. For hig h strain rate deformation, the rate of crack growth is governed by a u niversal relation in dynamic fracture. The constitutive model provides strain components for plane deformation which consists of an elastic part and a part due to sliding and growth of the tension cracks. The f ailure of the material is linked to a critical density of damage and h ence a critical length for the tension cracks. The constitutive model is used to study material behavior under uniaxial compressive constant strain rate loading. A critical strain rate beyond which the material would exhibit rate sensitivity is proposed. The model predicts the fa ilure or peak strength to increase with increasing strain rate. For en gineering ceramics, the rate sensitivity exponent is found to be a fun ction of the relation between the rate of crack growth and the toughne ss of the material. The model predictions are compared with the rate-d ependent behavior of a hot pressed aluminum nitride tested in uniaxial compression in the strain rate range of 5 x 10(-6)-2 x 10(3) s(-1).