Issue 36

V. Petrova et alii, Frattura ed Integrità Strutturale, 36 (2016) 8-26; DOI: 10.3221/IGF-ESIS.36.02 25 2 2 2 2 3 1 ( , ) (1 ) ( , ) 2 2 ( ) 1 ( ) ( ) ( ) k n n n i i nk nk nk n k n k i i n k k k n k n k e e R t x K t x X T X T e X T e T T X T X T                                    (A.1) 2 2 2 1 ( , ) (1 ) ( , ) 2 ( ) ( ) k n i i k k n k nk nk nk n k n k n k T T X T e S t x L t x e X T X T X T                      (A.2) and the kernels K nk ( t,x ) and L nk ( t,x ) are 2 1 ( , ) 2 k n i i nk k n k n e e K t x T X T X              (A.3) 2 2 1 ( , ) 2 ( ) k n i i k n nk k n k n T X e L t x e T X T X                (A.4) where 0 0 , n i n k i k z xe X z te T n k       , N kn ,..., 2,1 ,  (A.5) and  . 1 ; 0 k n for k n for nk     The kernels K nk ( t,x ) and L nk ( t,x ) are the same as for the system of cracks in an infinite plane, and the additional terms in Eqs. (A.1) and (A.2) are responsible for the influence of the edge of the half plane. α n is the inclination angle of n-th crack to the x-axis and n n    , Fig. 1; 0 n z is the coordinate of the center of crack in global coordinate system ( x, y ). R EFERENCES [1] Anderson, T. L., Fracture Mechanics: Fundamentals and Applications, third ed., Taylor & Francis, (2005). [2] Daud, R., Ariffin, A. K., Abdullah, Sh., Ismail, Al E., Interacting cracks analysis using finite element method, in: A. Belov (Ed.), Applied Fracture Mechanics, InTech, (2012) 359 – 380. DOI: 10.5772/54358. [3] https://en.wikipedia.org/wiki/Crocodile_cracking. [4] Rangaraj, S., Kokini, K., Multiple surface cracking and its effect on interface cracks in functionally graded thermal barrier coatings under thermal shock, Trans. ASME J. Appl. Mech., 70 (2003), 234-245. DOI: 10.1115/1.1533809. [5] Kawasaki, A., Watanabe, R., Thermal fracture behavior of metal/ceramic functionally graded materials, Eng. Fract. Mech., 69 (2002) 1713–1728. [6] Gilbert, A., Kokini, K., Sankarasubramanian, S., Thermal fracture of zirconia-mullite composite thermal barrier coatings under thermal shock: An experimental study, Surf. Coat. Technol., 202(10) (2008), 2152-2161. DOI: 10.1016/j.surfcoat.2007.09.001. [7] Petrova, V., Schmauder, S., Thermal fracture of a functionally graded/homogeneous bimaterial with a system of cracks, Theor. Appl. Fract. Mech., 55 (2011) 148–157. [8] Petrova, V., Schmauder, S., Mathematical modelling and thermal stress intensity factors evaluation for an interface crack in the presence of a system of cracks in functionally graded/ homogeneous bimaterials, Comp. Mater. Sci., 52 (2012) 171-177. DOI:10.1016/j.commatsci.2011.02.028.