PSI - Issue 13

Fuzuli Ağrı Akçay / Procedia Structural Integrity 13 (2018) 1695 – 1701 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1698

4

(

)

e C  + =

1

(6)

I

I

I

with

l l −

I

I

,0

e

=

(7a)

I

l

I

,0



C

=

I

,0 (7b) The parameter is the specific surface energy density (surface energy per unit area per unit length) for the material, having same dimensions as stress, and ,0 represents the characteristic length relevant to brittle fracture process. The use of critical state equation is not limited to uniaxial tension, and both the critical effective energy release rate ( Γ I ) and the characteristic length ( ,0 ) are material specific (Karr & Akçay, 2016). 3. Application of the theory For a linear, isotropic material, the maximum principal elastic strain, , is given by ( ) 1 I I II III e E     = − +     (8) where , represents Young’s modulus and Poisson’s ratio of the material, respectively. In the case of uniaxial tension, Eq. (8) simplifies to I I e E  = (9) Substituting Eq. (9) into the critical state equation, Eq. (6), yields 2 0 I I I E EC   + − = (10) The roots of Eq. (10) are obtained as ( ) 2 1,2 2 4 I I E E EC  = − + (11a) ( ) 2 1,2 ,0 2 4 I I I E E E l   = − + (11b) The positive root provides the tensile strength of the material of interest, that is, I I l

2 2 4 E E = − + +

E





(12)

I

Ic

l

I

,0

Rewriting Eq. (12) provides the characteristic length (relevant to brittle fracture)

2 E    + I E

l

=

(13a)

I

,0

Ic

Ic