###### Abstract  
Selective laser melting (SLM) is an additive manufacturing technique commonly used in the rapid prototyping of components. The complexity of the SLM microstructure poses a unique challenge to deriving effective mechanical properties at different length scales. Representative volume elements (RVEs) are often used to homogenize the material properties of composites. Instead of RVEs, we use statistical volume elements (SVEs) to homogenize the elastic and fracture properties of the material. This relates the inherent variation of a material's microstructure to the variation in its mechanical properties at different observation scales. The convergence to the RVE limit is examined from two perspectives: the stability of the mean value as the SVE size increases for the mean-based approach, and the tendency of the normalized variation in homogenized properties to zero as the SVE size increases for the variation-based approach. Fracture properties tend to make the RVE limit slower than do elastic properties from both perspectives. There are also differences between vertical (normal to printing plane) and horizontal (in-plane) properties. While the elastic properties tend to make the RVE limit faster for the horizontal direction, i.e., having a smaller variation and more stable mean value, the fracture properties exhibit the opposite effect. We attributed these differences to the geometry of the melt pools. selective laser melting (SLM); homogenization; statistical volume element; representative volume element +
Footnote †: journal: Applied Sciences  
0000-0001-5000-387X/0000-0001-5000-387X/0000-0001-50000-387X/0000-0001-5000-387X/00000-0001-50000-387X/00000-0001-50000-387X/00000-0001-50000-387X/00000-  
Melt pool boundaries change size and shape depending on the parameters used in the SLM process, such as laser power and laser scanning speed. These parameters greatly influence induced residual stresses, a hierarchical layout, and the severity of defects such as voids and cracks [4]. The inclusion of melt pools, however, dramatically increases the complexities of the microstructure of SLM materials, making it difficult to establish a correlation between microstructures and mechanical response [5; 6; 7; 8]. Current works have simulated this microstructure using Voronoi tessellation, approximating the polycrystalline geometry of the printed microstructure [5; 9; 10]. Notably, these studies share a focus on accurately representing the complex microstructural features inherent to AM processes. From [9], a modular methodology is used to obtain representative microstructural cells, encompassing feature-based representations and morphological shape analyses for different AM processes and materials. Analogously, additional works introduce a novel technique that models columnar and equiaxial grains, alongside melt pools, using crystal plasticity and finite element (FE) modeling for SLM components [5]. Additionally, a crystal plasticity-based fast Fourier transform (CP-FFT) framework captures microstructural influences on mechanical responses in SLM-fabricated materials, highlighting the role of grain features [10]. From this perspective, crystal plasticity furnishes the essential microstructural insight required for mechanical analysis, while FFT augments the ability to scrutinize and visualize the spatial distribution of microstructural features. Other crystal plasticity models are presented in [11], extending the focus to comprehend the impact of crack nucleation behavior on mechanical attributes, specifically the assessment of fatigue life in materials produced through SLM printing. This would suggest that process parameters leading to the formation of different pore types can significantly influence the initiation of fatigue cracks, which directly impacts the mechanical behavior of the material.