these disadvantages, with which the general situation (both fiber and matrix carry applied stress and also act as stress transfer media) can be described and residual stresses can be incorporated, to a first approximation. In the present study, the modified shear lag analysis mentioned above will be combined with the Monte Carlo method and be applied to 2D model, to simulate the tensile behavior of unidirectional weakly bonded brittle matrix composites. MODELING AND SIMULATION METHOD A two-dimensional model composite employed in the present work is shown in Fig.1. The components (fiber and matrix) were numbered as 1,2,…i,... to N from left to the right side. Each component was regarded to be composed of k+1 short component elements with a length Dx. The position at x=0 was numbered as 0 and then 1, 2, 3,...j... k+1 downward, in step of Dx.. The "i" component from x=(j-1) Dx to jDx was named as the (i,j)-component-element, and the interface from x=(j-1/2) Dx to (j+1/2) Dx between "i" and "i+1" components as the (i,j)-interface-element. The displacement of the (i,j)-component-element at x=jDx was defined as Ui,j. Two parameters (ai,j and gi,j) were introduced to express whether (i,j)-interface is debonded (ai,j=0) or not (ai,j=1) and whether (i,j)-component is broken (gi,j=0) or not (gi,j =1). From the spatial distribution of debonded interface-elements with ai,j=0 and broken component-elements with gi,j=0, the damage map was expressed. The values of ai,j and gi,j were determined at each occurrence of damage. The values of Ui,j were calculated by the procedure elsewhere [3,4], from which the tensile stress si,j of each component and shear stress ti,j at each interface were calculated . The simulation of the stress-strain behavior was carried out in the following procedure. (1)The strength of each component Si,j was determined by generating a random value based on the Monte Carlo procedure using the Weibull distribution. (2)Two possibilities arise for the occurrence of damage; one is the fracture of the component which occurs when the exerted tensile stress si,j exceeds the strength Si,j and another is the interfacial debonding which occurs when the exerted i j-1 j j+1 Ui,j-1 Ui,j Ui,j+1 Displacement Interface element •@•@•@(i-1,j) •@•@•@(i,j) Component element (i,j) (i,j+1) Matrix Fiber 2 j=0 •E •E •E •E j-1 j •E •E •E •E k+1 i=1 •E •E •E •E •E i•E •E •E •E •E •E•E N Dx j+1
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