Three-dimensional (3D) microstructure-based modeling of crack growth in particle reinforced composites

The mechanical properties of particle reinforced composites are largely dependent on the reinforcement particle distribution and volume fraction [1, 2]. Crack growth in particle reinforced metal matrix composites (MMCs), such as SiC particle reinforced aluminum (Al/SiCp), is very much dependent on the reinforcement microstructure [1, 3] as well as the matrix characteristics [4, 5]. A robust numerical model to simulate crack growth must incorporate the true particle geometry, orientation, size distribution, and spatial distribution [6]. Ayyar and Chawla [6] modeled the crack growth behavior in an Al/SiCp composite, using 2D microstructures obtained from optical microscopy. The results of these models showed that the incorporation of the ‘‘actual’’ microstructural attributes significantly affected the simulated crack growth response. Of course, 2D models must be conducted under simplified stress states, such as plane stress or plane strain conditions. Thus, 2D simulations do not provide as complete a picture of the crack growth processes as 3D simulations. In reality, the stress state in 3D is quite complex. This is particularly true of composite materials, where the geometry of the SiC particle in the third dimension and the matrix around the particle play an important role. Because the geometry of the SiC particle is very complex, a 2D representation of the microstructure cannot adequately capture the behavior of the composite. Chawla et al. [7–9] have shown that predictions from 3D microstructure-based models simulating the tensile behavior of heterogeneous materials correlated well with experimental results. Most of the 3D microstructure-based modeling efforts have focused on predicting the elastic modulus and simulating the elastic-plastic behavior of the composite in tension. The onset and evolution of damage by particle fracture has been studied by a few researchers [10–14], although the reinforcement particles are modeled as simple spheres. Crack growth in 3D has not been modeled in particle reinforced metal matrix composites. In this paper, crack growth in a SiC particle reinforced Al composite was simulated, using the actual 3D microstructure of the composite. A serial sectioning process was used to capture the complex geometry of the SiC particles from a series of micrographs of a SiC particle reinforced 2080 Al matrix composite [7, 8]. The SiC particles had a volume fraction of approximately 20%, average particle size of about 8 lm, and an average aspect ratio of 2. The serial sectioning process allows one to capture the realistic microstructure of the particles, including the geometry, orientation, and distribution of the particles. A typical flow chart of the serial sectioning and 3D reconstruction process is shown in Fig. 1. Details of this process can be found in reference [7]. The sample was cut and mounted for polishing and a ‘‘representative’’ region of the microstructure was selected. The term ‘‘representative’’ is somewhat subjective as it is dependent on the size of the SiC particles, spatial distribution, etc. As the number of particles increases, however, the computational demands also increase. For the Al/SiCp composites modeled in this paper, a volume of about 32 particles was included in the model (which is about half of the total particles reconstructed after serial sectioning), because of reasonable limits on computational efficiency. Fiducial marks were made by Vickers indentation. These A. Ayyar Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-8706, USA