## 2 Background: Steps of RVE Simulation for Fracture Analysis at the Microscale
### Determination of Cohesion Properties  
In order to achieve realistic results, experimental microstructure data are required to create the RVE and the constitutive responses of the matrix and associated constituent particles. Furthermore, cohesive properties are required between the matrix/interface, and maximum stress is necessary for particle cracking and matrix failure. It is important to note that the study conducted by [PERSON] et al. [24] focuses on dual-phase (DP) steels, which exhibit a significant volume fraction of martensite and experience extensive damage that is often easily quantified. For instance, the accumulation of damage in the tensile test for DP600 dual-phase steels has been studied and presented in [34]. The high-strength aluminum sheet materials used in the automotive sector have a much smaller fraction of second-phase particles distributed within the aluminum matrix phase. The constitutive response of the individual microstructural components and the matrix/constituent interface for aluminum sheet materials is often not available in the literature, and characterizing it experimentally is more challenging. It may be necessary to estimate it by taking into account additional theoretical considerations. In aluminum-based metal-matrix composites, which have a much higher volume of particles compared to automotive aluminum sheet materials, it has been mentioned that the stage of void nucleation starts when particles fracture or when there is decohesion at the interface between the matrix and particles [32]. Decohesion between the matrix and particles, along with particle breakdown leading to coalescence, is clearly observed in a typical sheet of AA2 xxx series aluminum alloy, as depicted in Figure 5[32]. It is stated that stress does not exceed a critical level in the soft matrix, and particle decohesion from the matrix takes place. Furthermore, it can be deduced that the principal damage mechanism in a soft matrix is the separation of particles from the matrix caused by tensile loading. On the other hand, particle cracking is the primary damage mechanism observed in hard matrix systems. This type of cracking mainly occurs along surfaces that are approximately perpendicular to the tensile axis. However, particle/matrix decohesion is also observed in hard matrix materials, but it occurs at a significantly lower level of plastic strain. Furthermore, it has been observed that the proportion of particles that have become detached tends to decrease as the volume fraction of reinforcement increases. In another study [35], it was discovered that as the temperature increases, the main cause of damage changes from particle cracking to the  
Figure 4: The results of a uniaxial tension test using a microstructure-based FE model: (**a**) identification of strain localization and damage; (**b**) comparison between experimental and simulated stress–strain curves [24]. The amount of damage was determined in the areas indicated by the red circles. separation of the matrix and particles when the matrix becomes softer. On the contrary, it is also observed that the strength of the particles remains the same in both the soft and hard matrix materials [36]. However, determining the accuracy of this assumption for the strength of the matrix/particle interface is quite challenging [36]. The process of particle breakdown is controlled by the stress level, whereas the debonding of interfaces depends on the plastic strain that has accumulated in the matrix near the interface. The particle/matrix interface can only fail due to the accumulation of damage caused by the proximity of plasticity to the particle [36]. The results regarding the cracking of particles are relatively easy to explain and are primarily associated with the transmission of a load from the matrix to the particle. Overall, the complexity of the stress/strain fields surrounding the particle makes it difficult to reach a unanimous agreement on decohesion [32]. It is noticeable that once decohesion is initiated, it begins to expand [37].