Controlling the mechanical behaviour of stochastic lattice structures: The key role of nodal connectivity

Abstract

Additive manufacturing has enabled the fabrication of lattice structures with controlled micro-architectures and mechanical properties. These structures are particularly attractive in the orthopaedic industry where their osseointegration capability and bone-matching mechanical properties are ideally suited for use in implants and bone scaffolds. The broad range of mechanical properties required for this application is a challenge – it typically requires a range of periodic lattice structures, each of which require separate characterisation. An alternative approach is to use a stochastic lattice structure, where a single relationship between the lattice design parameters (connectivity, strut density and strut thickness) and resulting mechanical properties should be possible. To investigate this, we manufactured stochastic lattices in pure Titanium with connectivity from 4 to 14, strut density from 3 to 7 [struts/mm3] and strut thickness of 230 and 300 µm. Specimens were compression tested in quasi-static and fatigue loading. In static loading, the low connectivity structures displayed bend-dominated deformation while the high connectivity structures displayed stretch-dominated deformation. The structures had a stiffness ranging from 0.1 to 8 GPa and different Gibson-Ashby stiffness/relative density relationships were required for high and low connectivity structures. A unified multivariable linear regression model was found to predict relative density from the connectivity, strut density and strut thickness of the structure. In fatigue loading, increasing the connectivity from 4 to 14 increased the fatigue strength by 60% for a fixed relative density. These findings provide important design information when creating structures using stochastic lattices to maximise strength for a desired relative density or stiffness. The single integrated model presented in this study can define a structure to achieve a broad range of design requirements, even as gradient within the same component. To achieve the same with periodic lattices would require different unit cell, with individual regression models for each unit cell used.