PSI - Issue 60

Brahmadathan V B et al. / Procedia Structural Integrity 60 (2024) 214–221 Brahmadathan V B, C Lakshmana Rao/ Structural Integrity Procedia 00 (2019) 000 – 000

217

4

a

b

Figure 2 a. Schematic representation of ceramic material with pre-existing flaws, b. Representative volume element.

Effective modulus = (1 − ) In rate form ̇ = (1 − ) ̇ − ̇

(6)

(7)

Effective stress acting on the crack, = − ( 11 2 + 22 2 + 12 2 ) + ( 1 2 ( 11 − 22 ) 2 − 12 2 ) (8) The local values of stress are evaluated by using Eshelby's inclusion principle.

Stress intensity factor at the tip, = −2 ( ) √2 ( +0.27 ) + 22 √ Crack growth criteria: Stress Intensity factor, = Crack growth rate, ̇ = ( − −0.5 )

(9)

(10)

TSI evolution, ̇ =

̇ (− ∆ )

(11)

The energy release rate for fracture propagation can be used to calculate entropy. = 2 , , and are Crack orientation, initial crack length and wing crack length and are coefficients of dry friction and cohesion. 11 , 22 and 12 are the stresses in the elliptical inclusion which contains the crack, this is used to include the effect of interaction between the crack. =Critical stress intensity factor. =Rayleigh wave velocity; , and are constants. is the crack density. ( ) is probability distribution function. E and are the modulus of elasticity and Poisson's ratio. The properties of Alumina used in this study are given in Table 1. (12)