An exact elastic solution is derived in a decoupled manner for the interaction problem between an edge dislocation and a three-phase circular inclusion with circumferentially homogeneous sliding interface. In the three-phase composite cylinder model, the inner inclusion and the intermediate matrix phase form a circumferentially homogeneous sliding interface, while the matrix and the outer composite phase form a perfect interface. An edge dislocation acts at an arbitrary point in the intermediate matrix. This three-phase cylinder model can simultaneously take into account the damage taking place in the circumferential direction at the inclusion-matrix interface and the interaction effect between the inclusions. As an application, we then investigate a crack interacting with the slipping interface.

Recently, much attention has been given to explaining that the macrocrack is shielded or antishielded by transformation strain point and impurity, especially by microcracking within the macrocrack tip region [1]. The model of discrete distributed microcracks around the main crack tip is often used to analyse the interaction between the main crack and microcracks due to the fact that the model can be accurately concerned with the orientation, position and size of the microcracks [2][3][4]. There is no question that the method to analyse the problem of interaction of the main -microcrack is of considerable significance for obtaining more accurate results as determined by [4]. Now a method to simulate interaction of main -microcracks with dislocation arrays is presented and it shows a higher accuracy.Muskhelishvili [5] gave the analytical function formula for plane elasticity; the stress and displacement components are ~= + % = 2[~(z) + ¢(z)] ~ + i ~,~ = t~(z ) + f~(z ) + (-z-z )t~'(z ) 2kt ~---~ (ux -iu,) = ~c~(z ) = f2(z ) -(7-z )df (z )(i) For the edge dislocation in an infinite body, shown in Fig. 1, ~p(z) and f~(z) are [6] ~t B -rci(1 + k) (bx + iby) where b and b are the two components of the edge dislocation, and li is shear modulus, ~ = 3-'4v for plane strain and (3-v)/(l+v) for plane stress. Int Journ of Fracture 68 (1994) R 4 8Simulating the semi-infinite crack (main crack) and microcracks (see Fig. 2) with arrays of dislocation, and supposing the length of all microcracks is 2 unit without generality, we have a singular integral equation of the main crack asTo make the transform u --1 ~--u + l ' ( -1 % u % 1)t --1 ~= t + l ' ( -l < t < 1)(2) is put into a suitable form for numerical solution 7 _(,m ~._(,,m u2 t ^ u.. ( u ) + o~, , .( u ) = E " " ) ( t ) d t + where 2(u -+-1) h(u,t) --t ÷ l 2ilm(z --s)

The 'radius' of the plastic zone at a crack tip is an important parameter that has numerous applications in fracture mechanics. The solutions that have been obtained were only under the plane stress and plane strain conditions; with the increase in engineering application requirements, obtaining the form and size of the plastic zone under the three-dimensional stress state will be very important. The aim of this paper is to research the shape and size of the crack tip plastic zone of various thickness specimens using the parameter "Tz".In order to estimate the spread of plasticity ahead of a crack (of length 2a) it is first necessary to know the stress distribution in that region, this can be found by making use of the Westergaard stress function (see for example, Knott [1]):S is the applied stress and z is a complex variable but, since the dependence of stress on both distance (r) and angular position (0) from the crack tip ( Fig. 1) is required, the following substitution is made: a+rei°=z. The near crack tip stresses (normal $1,$2,$3; shear $12,Sz3,$13) at a point A determined by the vector r and angle 0, can then be found from the relationships:The unwritten stresses are zero except that in plane strain $3=v($1+$2); v is Poisson's ratio. In order to arrive at the familiar equations for the near crack tip stresses [2], only the first term of each series is used. Hence the following equations are approximate and valid only for small stresses (i.e. r<

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