13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Intensity Factor and Crack Relative Displacement Factor, such that: real K C K ε σ α α α = ⋅ (7) Equation (6) yields a physical interpretation for Mq in the Stress Intensity Factor definition, i.e.: ( ) ( ) ( ) ( ) ( ) ( ) ? = ? = = = 骣 骣 鼢 珑珑桫 桫 1 2 1 2 1 2 1 2 8 1, 0 8 0, 1 v v v v u u M K K M K K K K C C and s s s s s s q q (8) For orthotropic media, these arbitrary reduced elastic compliance functions are defined by the following equations: ° ° 鬃 + 鬃 + = ? 鬃 % % % % % % % % % % % % % % 11 22 22 12 33 11 11 22 12 33 1 2 11 11 11 11 2 2 2 2 2 2 a a a a a a a a a a C andC a a a a (9) Where: ° ° ° ° ° = = - = - = = % % % % % % 11 12 22 33 1 1 1 ; ; ; RL LR L R L R LR a a a a E E E E G n n in plane stress (10) ° ° ° ° - ? ? = = - = = % % % % % % % % % 11 33 12 22 1 1 1 ; ; ; LT TL RL RL TL RT TR L R R LR a a a a E E E G n n n n n n n in plane strain (11) In which °E and n% are the arbitrary elastic orthotropic properties of material. In the case of isotropic material the arbitrary reduced elastic compliance functions are defined by: ° ° + = % 1 Ca k m (12) Where m is the Lamé coefficient given by : ° ° ( ) = 2? 1 % E m n (13) And: = - - = + 3 4 3 1 in plane strain in plane stress k n n k n (14) Now, in assuming a plane stress state, by substituting Equation (7) into the classical energy release rate expression, we obtain a new formalism: ( ) ( ) × = = 1;2 8 real K K G s e a a a a (15) In Eq. (15) Gα represents the portion of opening and shear modes in terms of energy release rate. Next, using the numerical values of CRDFs and SIFs calculated above, the energy release rate can be estimated from Equation (15) independently of the material's elastic proprieties.
RkJQdWJsaXNoZXIy MjM0NDE=