PSI - Issue 52

368 Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 52 (2024) 366–375 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000 – 000 3 components of effective stress tensor and its deviatoric part. The symbol ̇ and ν in these relations denote the accumulated plastic strain rate and the Poisson's ratio, respectively. In order to characterize the degradation of the matrix during the deformation process, the continuum damage mechanics approach is used in this study. The evolution equation of damage variable is given as Ḋ = ( ) ̇ ( − ), (1) = ( ̃ ) 2 2 , = 23 (1 + ) + 3(1 − 2 ) ( ) 2 , where ̃ denotes the effective equivalent stress and is calculated as ̃ = /(1− ) , and Young's modulus = 0 (1− ) . The symbols and denote the threshold value of the accumulated plastic strain for the damage initiation and a material constant, while () signifies the Heaviside function. When the accumulated strain reaches the threshold value , the Heaviside function becomes 1 and the differential equation (1) can be solved analytically. The equation of the damage variable at step as a function of ̇ is given as: ( ) = 1− √1−(2 +1){ ( 2 ) 2 0 (1− ( −1) ) [23 (1 + ) + 3(1 − 2 ) ( ) 2 ]} ̇ 2 2 2 +1 . (2) If the damage variable D is assigned a value of 1, the plastic strain rate at the fractured state can be predicted as: ̇ =√(2 2 +1){ ( 2 ) 2 0 (1− ( −1) ) [23 (1 + ) + 3(1 − 2 ) ( ) 2 ]} − . Furthermore, the unknown material parameters and can be estimated with the experimental results. First, we can limit the value of by dividing it into three intervals <−1; −1≤ ≤0; >0 and substituting it into equation (2). The corresponding three damage development curves are shown in Figure 1, whereby it can be seen that the second curve best describes the usual behavior of the damage variable. Thus, we can adopt the interval of ∈ [−1; 0].

Fig. 1. Damage development based on different intervals of .

3. Modeling For the preparation of a parametric study, various 2D models are created and verified as filler-matrix composites. In order to influence the tensile strength of the matrix, particles are introduced into the matrix, which can initiate cracking under tensile stress. Moreover, the influence of the parameters such as particle size, particle shape, and particle distribution are also considered.