Computational modelling of defects in additively manufactured lattice structures

Inclusion of manufacturing defects in computational models of additively manufactured lattice structures enables improved simulation accuracy. A computational model of a cellular or lattice structure¿s mechanical response often starts with a defect-free computer-aided design (CAD) geometry, which is discretised for finite element analysis. Such idealised CAD geometries neglect imperfections that occur during the additive manufacturing process of lattice structures, resulting in model oversimplification. This dissertation discusses a series of novel methodologies proposed for the analysis of defects produced on the fundamental strut and node elements of a lattice structure during AM processing, as well as methods of including these defects in computational models.

The first proposed method generates AM representative strut CAD models using geometrical data obtained from micro-computed tomography (μCT) analysis of struts manufactured by selective laser melting (SLM). A series of elliptical cross-sections with the same geometrical properties as the SLM manufactured struts are used to generate the AM representative strut and lattice CAD models. A significant error reduction is achieved by using the AM representative strut models in finite element analysis over the idealised strut models, from approximately 50% to 8%. AM representative lattice models displayed improved size converging behaviour and more realistic strut deformation behaviour under compressive loads. The method of generating AM representative strut models is built upon in the second proposed methodology and allows for a stochastic modelling approach to the prediction of a lattice's mechanical response. The µCT-derived geometric properties of the manufactured struts provided statistical information which allowed for digital CAD realisations of AM struts to be generated. The digital realisations are then used as input for a combined Monte Carlo - finite element method procedure for an investigation into the distribution of an AM struts effective mechanical properties. The 300-micron diameter struts built at 35.6, 45 and 90 degrees to the build platform displayed a mean effective diameter of 310, 262 and 248 microns, respectively. Strut effective diameter distributions were used in lattice scale beam element FE models to find ranges of possible lattice mechanical properties. Stretch-dominated lattices fell within their experimental moduli and yield stress ranges, though reduced predictive capability was seen in bending-dominated lattice models. This was found to be attributed to the lack of accounting for increased material accumulation at nodal intersections.

The third and fourth methods proposed are the measurement and study of the mechanical response of individual nodes within a fabricated lattice structure. The literature regarding this is relatively lacking, a simple algorithm is proposed which exploits the periodicity of a lattice structure to isolate manufactured nodal geometries from lattice µCT scans. In some node types, the cross-sectional area was shown to vary from design by greater 10% on average and principal moments of inertia greater than 20%. Maximum and minimum Feret diameters, at the centre of the most common node in an FCCZ lattice structure, were both shown to vary from design by approximately 3-4% on average. However, in some of these manufactured nodes of the same type this variation was almost 10%. A large automated image-based finite element study was conducted on the mechanical response of every single strut which intersects every single node within a manufactured lattice structure. The intra-lattice variation in stiffness is reported, as well as the deviation from the design's mechanical response. The most common FCCZ node type has only 45-degree struts intersecting it, their minimum simulated axial stiffness (63.4 kN/mm) differs from the maximum (73.6 kN/mm) axial stiffness by approximately 15%. This indicates a spread of defects throughout nodes which affect each nodes structural response differently. The deviation between the simulated average stiffness from µCT over their idealised voxel, solid and beam representation was approximately 5%, 4.5% and 13%, respectively. Overall, the methodologies and analysis techniques discussed in this dissertation are aimed at allowing more informed decisions during the design of an AM lattice structure.