G. Ravichandran et G. Subhash, A MICROMECHANICAL MODEL FOR HIGH-STRAIN RATE BEHAVIOR OF CERAMICS, International journal of solids and structures, 32(17-18), 1995, pp. 2627-2646
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).