Interaction between an interface and cracks

The problem of interaction between macrocrack and microcrack has become a topic studied by many researchers since Hutchinson [1] pointed out that the toughness of the material might be improved or reduced in the presence of the microcracks within the process zone [2][3][4][5][6][7][8][9][10]. Few works, however, discussed the problem of the macrocrack interacting with the microcrack on the interface, which often played a key role in laminated structures, especially in composite materials. This report will deal with this problem with the use of simulating the macrocrack and the microcrack with dislocation arrays.Muskhelishvili's theory described the stress and displacement components as [11] ~= + % = 214,(z) + ¢(z)] C1)where ~ is the shear modulus, ~: = 3-4v and (3-v)/(l+v) for plane strain and plane stress, respectively. ~(z) and ~(z) are the complex potentials. If a dislocation is on the interface (shown in Fig. 1), they are as follows [12] • (z) "-B(1 + ~*)/(z -s) n(z) = ~(1 -~*)/(z -s) 1+ o~ 1 (bx + iby) B -cz(i-~2) rciwhere c=(l+~:)/I.t, 9"=13 for y>0 and ~*=-1~ for y<0, s is the location of the edge dislocation, b x by are the two components of the edge dislocation, (x ~ are the Dunder's parameters. C2)Int Journ of Fracture 73 (1995) R72If we simulate the macrocrack and microcrack (shown in Fig. 2) with arrays of continuously distributed dislocations, a group of singular integral formula are obtained. The stress components of the interfacial macrocrack and microcrack are as followsTo make (3) a suitable form for the numerical solution, take the transform-1 o'= (r/)+to-xy (7/)= 2~rfliBc'~)(r/)+ °"°(~)d~ + -1 -1 (4) -I h2 (rl, t)BCW) ( t)dt (5) where in (5) 2 h~(u, ~) -z~_ ) _ s u-1 z~.O + Z(raa) --u+l' s= 4 h a (r/,t) = (z

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confidence: 99%