## 2 Background: Steps of RVE Simulation for Fracture Analysis at the Microscale
### Representative Volume Element (RVE)-Based Simulations  
Systems based on RVEs ensure the measurement of material properties effectively while incorporating scalable capabilities [11; 12; 13; 14; 15; 16; 17; 18]. An RVE is the smallest volume of material that encompasses the bulk properties. An RVE may be defined as a volume that shows the same overall material properties irrespective of the boundary conditions applied [19; 20; 21; 22; 23]. RVE-type models typically involve a microstructure at only one length-scale, but these microstructures provide effective material properties, as well as local microstructural responses. RVEs of metals like steel and aluminum have been developed and imported into FE software in order to examine how the microstructure affects the nonlinear elastoplastic stress-strain behavior of the material [6; 24]. Studying decohesion at the interface between the matrix and particles by incorporating cohesive elements in RVEs is crucial. [PERSON] et al. [25] recently created a script that inserts cohesive elements at the grain boundary interfaces in a crystalline material. However, to the best of the authors' knowledge, no similar work involving the insertion of cohesive elements at the matrix/precipitate interfaces of 2D RVEs for metals has been described in the literature. This is especially relevant for those created using OOF2 software, and most importantly, the script is publicly accessible. There are several software programs that allow one to generate the RVE for materials, such as CEMHYD3D for cement past materials [26], Dream.3D [27], and Neper [28] for metals. There is software available for generating RVEs based on actual metal images, such as OOF2, which was developed by the National Institute of Standards and Technology (NIST) [29]. OOF2 generates the RVE containing multiple phases, and the resulting output can be imported into the FE software ABAQUS. Every phase is assigned to a separate element set with specific material properties. The RVE in OOF2 can be meshed using rectangular elements with four nodes or triangular elements with three nodes [29]. In order to obtain accurate outcomes, it is necessary to have experimental microstructure data, which helps in constructing the RVE. In addition, it is also necessary to consider the responses of the matrix and its constituent particles. The separation at the boundary between the matrix and particles, along with the fracture of particles, results in the void coalescence and eventually the final fracture of metals [30; 31]. The phenomenon has been clearly demonstrated in a typical sheet made of an AA2 xxx series aluminum alloy [32]. However, information regarding the behavior of individual microstructural components and the interface between the matrix and constituents in aluminum sheet materials is scarce in the existing literature. Moreover, experimenting to accurately define this behavior can be more difficult. It may be necessary to estimate it by taking into account additional theoretical considerations. Figure 1: Debonding occurs at the interface between the matrix and particle in the AA7075-T6 alloy. The formation of microcracks is caused by the separation between the Mg2 Si particle and the matrix in AA7075-T6 [9]. Figure 2: Characteristics of the AA7075-T73 alloy: (**a**) SEM image of inclusions in the AA7075-T73 alloy; (**b**) stress–strain curves comparing inclusions and the matrix [10]. ABAQUS/ CAE offers more advanced features. The shape of the geometry can be changed by using extrusions of various shapes, and it is possible to put together multiple parts to create a model; thus, samples with arbitrary shapes can be reproduced. The mesh generation capabilities of ABAQUS/CAE are also more advanced. Different element types and meshing algorithms can be used [25]. Therefore, performing FE analysis of the RVE created using the software OOF2 and importing it into ABAQUS is an ideal approach to comprehend and accurately depict the elastic-plastic behavior of metals, as well as the fracture process [24].