1. Introduction
Cast irons are usually categorized into different groups based on their microstructure due to the crucial effect of their microstructural features [
1]. Compacted graphite iron (CGI) is broadly used in the automotive industry, for example, in brakes, exhaust manifolds, cylinder heads, and cylinder blocks, thanks to its good combination of thermal conductivity and mechanical properties [
2,
3]. The volume fraction, shape, size, and spacing of graphite particles in CGI significantly affect its mechanical properties and fracture mechanism [
4,
5]. Changes in chemical composition are insufficient to meet specific requirements to improve engine performance. The most efficient approach is to modify the microstructure of cast-iron materials, thereby enhancing their performance and extending their operational lifespan.
As graphite particles are the weakest of CGI’s main constituents, cracks always tend to initiate inside such inclusions or at the interface between them and the matrix [
6,
7]. With scanning electron microscopy (SEM), Hieber [
8] found that fractures usually occurred within graphite flakes as well as at their interfaces. It was concluded that the fracture patterns in both particles and the matrix were unaffected by the strain rate, as similar features were observed for both traditional tensile tests and impact loading. Lopez-Covaleda et al. [
9] investigated crack initiation by using a semi-in situ technique. They found that a cyclic plastic zone of graphite particles at interfaces exceeded that for bulk particles. This could explain the enhancement of crack initiation by the presence of graphite clusters. Yang et al. [
10] established that the stress–strain distribution in a cutting region of CGI was affected by graphite particles with different sizes and distributions. Tensile strength, fracture toughness, and impact properties of CGI were evaluated by Gregorutti et al. [
11] for various microstructures. Still, experimental analysis of CGI cannot predict the strain at the damage onset for each graphite particle, thus lacking a deep insight into its fracture behaviours. Furthermore, the effects of particle spacing on effective plastic strain and equivalent stress during the deformation are hard to obtain experimentally. At the same time, since the crack growth rate of CGI is high, it is difficult to capture details of the fracture process with SEM. Hence, numerical methods can be used to complement experimental studies. Generally, there are two main approaches used in continuous microstructure-based numerical models: representative volume elements (RVEs) [
12,
13,
14] and unit cells [
15,
16]. There are three main types of micromechanical methods used for cast irons: (i) direct introduction of real microstructure obtained from SEM or CT (computed tomography) images [
17]; (ii) utilisation of idealized shapes of graphite particles with their regular arrangement [
18]; and (iii) modelling based on random distribution of particles (e.g., to capture the mechanical response or fracture response by considering the interactions between inclusions [
19]).
Modelling based on the microstructure is a crucial initial step for the simulation of the mechanical properties of materials. The next step is the introduction of damage into numerical schemes. Cohesive zone models (CZMs) have been extensively employed to analyse debonding between the matrix and particles as well as crack growth in CGI at the micro level, especially with the unit cell approach [
20]. A Johnson–Cook damage model could also predict the initiation and propagation of cracks in CGI with less computational effort and good predictions of the crack path for realistic graphite morphology [
21]. Yang et al. [
22] developed a simple but effective approach for a relation between graphite morphology and the mechanical properties of CGI. They also found that 2D slices of a 3D graphite microstructure can reasonably depict the spatial morphology of CGI. The effect of graphite particle size, orientations, and volume fraction on tensile properties was investigated by Zhang et al. [
23], which revealed a quantitative relation between the tensile properties of CGI and graphite morphology.
However, the influence of the distance between graphite particles on cracks was not considered, although the interaction between inclusions can cause stress concentration in the matrix. This occurs mostly in areas bridging the neighbouring particles, accelerating the crack-propagation process in them. The narrow matrix bridges facilitate the concentration of high stress [
17]. Palkanoglou et al. [
18] investigated the interaction between two neighbouring particles with a 2D unit cell with two graphite inclusions. He et al. [
24] considered a microstructure with circular particles of different sizes randomly distributed in the matrix. Yang et al. [
10] generated four microstructural models with various sizes and distributions of particles. Their findings revealed that such microstructures affected stress–strain distributions in the material. However, only a circular shape of graphite particles was used in their models.
In this paper, the interaction between a graphite particle and its nearest neighbour as well as with the four closest particles is analysed in terms of respective distances. The effect of such distances on crack-initiation strain is studied numerically, also considering the effects of the size and orientation of inclusions. The focus is mainly on the effect of nodularity, the distance between graphite particles, and their orientation in CGI. Analysis was limited to graphite particles with an aspect ratio below 10:1, which is suitable for most inclusions in CGI (the effect of higher aspect ratios will be studied separately). The random microstructure-based models were generated using an in-house Python script to achieve particle distributions close to the real ones. The elastoplastic behaviour and cracking of the matrix, along with decohesion at the graphite–matrix interface and particle fracture, are simulated using the Johnson–Cook damage model. These findings contribute to understanding the fracture mechanism of CGI.