Random field modelling of spatial variations in additively manufactured lattice structures

Lattice structures are known as structures that consist of a network of interconnected strut members. The design of these lattice structures in the material at micro and millimeter scales have become prevalent in the literature worldwide to attain lightweight and strong engineering applications. However, due to the complex network of strut members designed at small scales, the fabrication of these lattice structures is either very difficult or not possible using the conventional manufacturing technologies. The fabrication of these lattice structures is only possible by using the recently advanced additive manufacturing Technologies. On the other hand, because of the layer-by-layer manufacturing strategy, there exist micro- and milli-meter scale variations and uncertainties on the geometry and material properties of the strut members in the designed lattice structures when fabricated. Therefore, differences and uncertainties are occurred between the computer-aided design (CAD) model and fabricated strut members of lattice structures in terms of both geometrical and mechanical properties. In literature, several research works has been performed to characterize AM induced uncertainties of lattice structures with using random variable approach. However, random variable approach ignores spatial variations, therefore differences occurs between mechanical performance of designed lattice structures and corresponding AM fabricated structures. The aim of this study is random field modelling of geometrical and Material uncertainties caused by fabrication of lattice structures with FFF process which is an AM technique. In order to evaluate differences between designed and AM fabricated lattice structures, strut members of lattice structures are fabricated using material extrusion technique with different build angles and built diameters. The specimens are examined by a digital light microscope and the measurements are done for the fabricated diameter variations. These variations are characterized using advanced istatistical methods, based on the spatial dependency and investigating their inclussion to the simulation models. In this context, experimental data are modeled by the Random Field Method (RFM) which is commonly used for modeling the spatially dependent variations. These variations modeled by the RFM are integrated into the finite element (FE) models by using voxel mesh elements. In house scripts are developed to represent fabricated strut members of lattice structures with these voxel elements. FE simulations of voxel models are performed with tensile boundary conditions. Eficient geometrical and Material properties are specified with the results of the FE analysis. The developed model can be extended to different AM techniques and the variations observed in the fabricated geometry and material properties can be characterized.