Investigation of Spatial Variability on Strut Diameters of Additively Manufactured Lattice Structures

Lattice structures that consist of connected strut members have become prevalent in engineering applications due to lightweight but strong characteristics. Additive manufacturing (AM) is an effective manufacturing technique to fabricate the lattice structures which has complex geometries and topologies without using additional tools. Besides the essential advantages of the AM, defects can occur due to uncertainties in the layer by layer deposition strategy of AM process. Quantification of the geometric uncertainties plays a key role for the accuracy of the numerical predictions of lattice structure behavior. The spatial uncertainty is especially critical since the uncertain parameters at each layer can be dependent to the parameters at the other locations. However, the existing solutions to quantify the uncertainties on the strut members of the lattice structures ignore the spatial uncertainty and treat it as random variables.

In this study, the influence of the spatial variability of geometric uncertainties on the strut members of the lattice structures fabricated by AM are investigated by considering the random field theory. Individual struts are fabricated with various printing angles and diameters using a material extrusion process, the so-called fused filament fabrication (FFF) process, and PLA material and are characterized using random field discretization methods for developing efficient representation models of the spatial uncertainties. Diameter values of the fabricated samples are measured for this purpose along the printing direction and the radial direction of the cross-section at each layer under an optical microscope. Spatial correlations are characterized based on the measurements using experimental autocorrelation function. Four different candidate autocorrelation functions are also fitted to the mesured data to identify the best fitted ones for each diameter parameter considered as the random field and the corresponding correlation lengths are evaluated. The results show that the diameters of the strut members at each layer are spatially dependent. Two random field discretization methods, namely Karhunen-Loève expansion (KLE) and Expansion Optimal Linear Estimation (EOLE) methods are investigated to reduce the dimensionality of the random field discretization. The KLE method was found to give better accuracy in terms of variance error means while EOLE can produce better local accuracy. The voxel-based strut models are generated with the diameter parameters modeled by the proposed random fields discretization framework and compared by the existing approach with random variables. Thus, the common issue of the spatial variability at each layer in additive manufacturing is addressed in this study. To reveal the response of the lattice structures, achieved results can be incorporated into the lattice modeling and design stages.