PSI - Issue 52

Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 52 (2024) 366–375 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The properties of particle-reinforced composites can be affected by modifying parameters such as particle distribution, size, and orientation. This is because the mechanical behavior of any material is dependent on the microstructure, and the introduction of the reinforcement particles into a monolithic material modifies its microstructure and changes its mechanical properties. The addition of stiff reinforcement particles in the matrix improves the monotonic properties, such as Young’s modulus and tensile strength, as well as the fatigue crack growth threshold of the composite (Ayyar and Chawla (2006)). It is interesting to note that coarser particles provide better fatigue crack growth resistance, than finer particles, because of roughness-induced crack closure (Shang et al. (1988)). Since crack growth mechanisms are dependent on the microstructure, any modeling approach to understanding crack formation must incorporate the microstructure. Analytical methods such as the Hashin – Shtrikman by Hashin and Shtrikman (1963)) and Eshelby’s model for ellipsoidal inclusion by Eshelby (1957) are typically used to calculate the elastic properties of composite materials. These analyses cannot be used for composites with irregular particle geometries and complex microstructure. Even if the particle geometries were regular, the solution for composites containing more particles is complex, because the distribution of particles also affects the mechanical behavior. In reality, the particle microstructure is complex and varies significantly in size, shape, and aspect ratio. Particle distribution is important since a specific microstructure may contain clusters of particles. Thus, in order to understand the mechanical behavior of the composite and its failure, the complex microstructure of the composite has to be examined. The Finite Element Method (FEM), with the ability to capture the complex geometry of the reinforcement particles, hence, was used for such modeling. It has been shown in Sun et al. (2020), that there are three typical failure mechanisms during composite deformation, i.e., debonding at the particle/matrix interface, cracking of the matrix, and brittle fracture of the particles. In this study, the particle was treated as an isotropic elastic solid. The growth and linking of microcracks and the aggregation of micropores led to formation of macroscopic cracks which finally led to the fracture of the material (Shen et al., 2020). The present paper utilizes numerical modeling to study crack propagation in particle-reinforced composites by considering the complex geometry of the reinforcement particles and their distribution. The obtained results can be applied to any particle-reinforced composite, where the particle is much stiffer than the matrix. The influence of reinforcement particle size, particle shape, and particle distribution on crack growth is also studied. 2. Analytical damage model 2.1. Elastic-Plastic Deformation of Damaged Material In the case of elastic-plastic deformation, the material’s st rain-hardening theory of plasticity can be described by isotropic-hardening (Murakami, 2012). The damage starts when the plastic strain attains a limit , and the damage variable increases with the increase in . The value is called a threshold plastic strain for the damage initiation. The damage variable can be interpreted as the fraction of decrease in the effective area due to damage development and is specified by =0 as initial undamaged state and =1 as final fractured state. 2.2. Constitutive and Evolution Equations of Elastic-Plastic Isotropic Damage The elastic-plastic constitutive equations with isotropic damage are given as follows: ij = i e j + i p j , = 1+ E ν ̃ ij − E ν ̃ kk ij , ̇ = 3 2 ̃ ̃ ,̇ where and i p j are the components of the elastic and the plastic strain tensors, while ̃ and ̃ denote the