Introduction

The current trends in aerospace, automotive and bio-medical industries involve the development of optimized light-weight structures providing high strength as close as possible to that of conventional bulky structures1. Also, foam based cellular materials have been extensively used in energy absorption applications. However, one of the limitations to use these structures is the poor availability of control on the parameters such as pore size and wall thickness which determine their properties. The development of lattice based cellular materials with repetitive unit cells has been helping to tailor the mechanical properties based on the loading requirements. Cellular materials are termed as true cellular materials when their relative density is less than 0.32.
Cellular materials become a rising star in the biomedical industry and are a prospective replacement for fully solid implants. The use of solid implants which have higher stiffness compared to the surrounding bone results in stress shielding phenomenon, which might cause bone resorption. This eventually results in implants loosening which requires implant replacement3,4. The use of porous cellular materials helps to adapt the implants stiffness to that of the surrounding bone. Also, the presence of pores in the structure improve bone regeneration which provides better fixation5,6. Metal alloys being the first choice for implants, Titanium alloys such as Ti6Al4V have been widely used in implants manufacturing due to their high strength, corrosion resistance and bio-compatibility7–9.
Additive manufacturing (AM) technologies such as Laser powder bed fusion (LPBF) facilitates the production of intricate complex structures in a short period of time. The same technique is employed in the current study. LPBF is widely used in the production of cellular materials to obtain higher precision compared to other AM techniques5,10. The LPBF fabricated parts have certain issues such as quite low surface finish, internal porosity, geometrical deviation, residual stress and brittle material phases, which negatively affectthe mechanical properties of the structures. Various studies have concluded that the above-mentioned issues are highly influenced by process parameters such as laser power, hatching distance, scanning speeds and building direction11–16. Furthermore, heat treatment processes such as stress relief and hot-isostatic pressing significantly improves the mechanical performance by transforming the microstructure to a more stable ductile α+β phase with the additional advantage of eliminating residual stresses and internal porosity17–21.
The mechanical properties of cellular materials are mainly characterized by material type, cell topology, and relative density. Their characterization is generally carried out through static and fatigue compression tests. Cheng et al.22 compared compressive properties of foam based and lattice based cellular structures with different relative densities, indicating that the lattice based structures had higher specific strength. Additionally, various studies focusing on the influence of different types of unit cell and relative density on the compressive behavior of cellular materials were carried out23–30. It was reported that the strength and stiffness of the structures enhances with increasing the relative density in well agreement with Gibson-Ashby law2. This increase depended on the morphology of the unit cell as well. Depending on the local loading conditions in the struts, the unit cell topologies can be grouped into two different categories of bending dominated and stretching dominated structures. Stretching dominated structures are characterized by high strength and stiffness since the struts are subjected to axial loading conditions. On the other hand, bending dominated structures do not possess any struts along the loading direction and hence fail due to bending loads in the struts. Bending dominated structures are more compliant compared to stretching dominated structures which failed mainly due to buckling. The compressive behavior of bending dominated structures consist of three regions, elastic region, flat plateau region where strain increases with constant stress followed by densification. However, in stretching dominated structures, the plateau region consists of oscillating stress followed complete densification of the structure despite cell morphology29–34.
Cellular materials used in biomedical applications as well as aerospace applications are exposed to cyclic loads. Therefore, understanding the fatigue behavior of these materials has gained strategic importance in the recent years. Various studies have indicated that the compression-compression fatigue properties are dependent on various parameters such as cell topology, stress ratio (R-ratio), heat treatment and the presence manufacturing defects from AM process20,29,35–42. Zhao et al.36and Yavari et al.31 have investigated the effect of cell topology and porosity on the compression-compression fatigue behavior. The studies have clearly shown that if the deformation in the structure is bending dominated, plastic strain is progressively accumulated, leading to the final fatigue failure. While the fatigue crack growth is decelerated in structures that fail due to buckling. The S-N curves normalized with respect to the yield stress indicate that a single power law is followed by a particular cell topology despite the difference in porosity. The effect of fatigue the stress R-ratio has been studied using diamond unit cells. Specifically, it was found that the higher the stress R-ratio the lower the fatigue strength at a given number of cycles to failure43. The effect of post manufacturing thermal and chemical treatments on fatigue properties were also studied. Yuan et al.44 used two heat treatment temperatures (750ºC and 950ºC) and showed that samples treated at 950ºC had a broader plateau under static loading indicating better performances under plastic strains. The fatigue endurance ratio was increased by 0.5 – 0.6 times with heat treatment at 950ºC. Hot-Isostatic pressing (HIP) and Chemical Etching (CE) treatments have improved the fatigue strength of cellular materials by increasing the ductility, eliminating some internal defects and improving the surface finish20. The fatigue failure of cellular materials can be divided into strain accumulation, crack initiation and crack propagation. The strain accumulation in the structures is mainly due to cyclic ratcheting as indicated in various studies36. The crack propagation takes place in two steps, a first propagation in the struts followed by propagation through the unit cells45. Applied stress level and surface defects such as roughness, defects and waviness have a greater influence on the fatigue properties compared to internal porosity in the crack initiation stage. On the other hand, parameters such as material, microstructure and internal porosity influence the crack propagation phase38,46.
The porous material used for bone implants should have mechanical properties in range of the human bone for better fixation. Therefore, mechanical properties of the implants are of primary importance at the initial stage of implant fixation; once the bone regeneration is complete, higher fatigue life from the implant may not be necessary35. Hence, it is necessary to study a variety of structures with varying cell topologies, irregularities, and pore shape to understand the material properties. Benedetti et al.47 analyzed the compressive behavior of various types of cellular materials in presence of different porosity levels. That study has shown that the properties of the different analyzed structures range between the two extremities of a cubic structure and a cross shaped cellular structure. Also, despite the absence of vertical struts, cross shaped samples had the highest strength for the given stiffness. Therefore, the below mentioned seven different topologies are considered in the present study to explore their suitability to be used as an osteo-integrative coating for solid implants. Since this porous coating is commonly placed in the contact region between bone and solid implant, the resulting load is entirely compressive. Therefore, the knowledge of monotonic properties and fatigue strength under compressive loads is fundamental for their proper design. For this purpose, cellular lattice specimens were manufactured via LPBF using the titanium alloy Ti6Al4V. Their cell architecture includes three regular structures ((#1) Cubic, (#2) Star and (#3) Cross, three irregular structures obtained by skewing the junction of regular structures ((#4) Cubic irregular, (#5) Star irregular and (#6) cross irregular); a(#7) trabecular consisting of random arrangement of struts mimicking trabecular bone topology structure. The samples were analyzed for assessing porosity and struts dimensions. Compression tests have been carried out using monotonic and cyclic loading conditions to obtain the strength and stiffness properties (under loading and unloading) of the considered structures The specimens have been subjected to compression-compression fatigue loading with an R-ratio of 0.1 and loading between 0.1-0.8 yield load. One specimen from each topology has been employed to visually detect the deformation pattern in the different investigated structures. Fracture surface analysis has been carried out to show the failure mechanisms under quasi-static loading and cyclic loading. The effect of geometrical irregularity on the fatigue performance has been explicitly shown in the normalized S-N curves. The results of the regular and irregular topologies have been carefully compared with the trabecular based topology for a better understanding of their behavior with the future optic of possible systematic employment in biomedical applications.