Ti6Al4V alloy is widely used to fabricate many components of orthopaedic implants, such as the femoral stem or the acetabulum component of a total hip joint replacement [1
]. Titanium alloy offers many favourable properties, such as good biocompatibility, no allergenicity and a moderate elastic modulus (~110 GPa) [3
], which, however, is still much higher than that of the adjacent bone stock (typically, 10–20 GPa [4
]). This phenomenon known as stiffness mismatch can result in stress shielding [5
], which has been identified as a cause for the aseptic loosening of orthopaedic implants, the main cause of their failure [7
]. In order to reduce the risk of stress shielding, metal alloy implant components can be fabricated for instance with open-porous structures that provide an elastic modulus low enough for this specification [9
Open porous structures were generated and tested as irregular [15
] and regular or non-stochastic scaffolds [9
]. Since trabecular bone is irregular, irregular structures may be a more authentic imitation than regular ones. Imwinkelried et al. [15
] described an open-porous titanium foam with a stiffness comparable to that of cortical and trabecular bone depending on the porosity that ranged from 50% to 80%. Due to the non-spherical shape of the space holder particles, their scaffolds showed an anisotropic behaviour.
In contrast, Li et al. [16
] investigated a sponge-like titanium scaffold with a macrostructure similar to that of cancellous bone with nearly no anisotropic behaviour. However, due to this irregularity, controlling the mechanical properties and geometrical parameters, e.g., pore size or defined structural modulus, is complicated. Pore sizes in the range of 100–600 µm were found in one specimen [18
]. Therefore, as it seems, irregular structures are less suited for fabricating load bearing implants with defined mechanical properties.
Additive manufacturing (AM) methods, such as selective laser melting (SLM), are widely used for fabricating open-porous metals and alloys [22
]. They afford the means for the development and manufacturing of structures with defined mechanical and geometrical properties, e.g., with an elastic modulus in the range of that of human bone [4
]. Furthermore, the properties of the fabricated scaffolds can be directly controlled by the geometrical shape and the composition of different parameter sets [31
]. However, the material used [22
], the variation in geometry [38
] as well as the additive manufacturing technique (EBM—electron beam melting or SLM—selective laser melting), all have an important impact on the properties of a scaffold.
Important for the evaluation of the mechanical properties of open-porous structures is, moreover, the accuracy of the fabricated scaffolds. Marin et al. [40
] demonstrated that a cellular solid with a porosity of 63% and 72% can be used in biomedical applications to enhance osseointegration. Geetha et al. [33
] discussed the biomechanical compatibility, thermomechanical processing and surface conditions of many metallic materials. In reference [41
], the author cultured human osteoblasts under static and dynamic conditions with results that confirmed the suitability of open-porous structures for biomedical applications.
Particularly, the employed additive manufacturing technologies are critically characterized by the effects of the process. The microstructure and also mechanical properties are affected by the process parameters [42
] as well as by the thermal after-treatment [44
] of structures. In the evaluation of open-porous structures, strut orientation and loading angles [24
] as well as the functional correlation between porosity and elastic modulus [19
] play a critical role.
To avoid stress shielding of the adjacent bone tissue around stiff implants, the modification and reduction of the scaffold stiffness is necessary [7
]. The mechanical properties of bone vary considerably and can be several times higher [49
]. For successful application of an additively manufactured structure, its mechanical properties must be adjusted to match that of human bone. Such adjustment offers the opportunity to overcome the interfacial difference between the elastic properties of human bone and metallic implants. In this way, bone stress shielding problems caused by the extreme stiffness of the metal implant could be solved. For this purpose, it is necessary to adapt the mechanical properties according to patient-specific requirements. This includes e.g., a similar elastic modulus to human cortical bone (i.e., 15–20 GPa) [4
The aim of the present study therefore was to determine experimentally the influence exerted by the design and the configuration of a scaffold’s unit cell on its porosity and compressive modulus. Three design variations of additively manufactured scaffolds, each with at least three configurations, were investigated.
Studies are known that provide a characterization of porous structures, including geometric or material-specific factors [46
]. Often in the foreground is the comparison of the moduli of porous models with full-body models, which only partially reflects the possibilities of a structure. In this study, characterization includes also the identification of the functional relationship between experimentally determined porosity and modulus of elasticity. This characterization method provides a possibility to directly compare different geometric cell variants and dimensions as well as to classify the attainable strengths. Specific yielding is of particular importance here, offering an excellent opportunity to establish a direct correlation between porosity and elastic modulus. A special benefit is derived through the classification of structures, which, in order to avoid failure, must offer adequate structural rigidity at a low weight and sufficiently high porosity. The evaluation of specific yielding as a magnitude of influence on the failure behaviour of a component equally takes into account the influence of porosity and material parameters (elastic modulus), i.e., design and material. This new approach is of great practical importance with regard to implant engineering. As the determining factor for the characterization of deformation resistance, specific yielding (depending on the elastic properties of materials and the geometrical conditions of the component) offers an invaluable benefit when assessing the suitability of a given geometry/structure for medical applications (implant). The consideration of specific yielding not only allows a comparison between different structures and porosities but also a direct comparison with human bone parameters. Specific yielding can facilitate the presentation of different bone parameters. Based on this relationship, structures can be directly classified in respect to their biomedical application.
By using additive manufacturing methods, open-porous scaffolds can be fabricated in a wide range of design variations with specific properties that fulfil both mechanical and biological requirements [10
In this study, the influence of the structural design was investigated. The generated designs varied with respect to geometry, dimension and porosity. The latter exhibited values between 43% and 80% that correspond to porosities found in the literature that are interesting for the application of porous structures [25
]. Accuracy of the fabricated scaffolds is mandatory for the evaluation of the mechanical properties of open-porous structures. The porosities for scaffolds made by us were calculated and revealed high accordance with the porosities derived from CAD data with deviations less than 3.2%.
Apart from the build parameters (Table 3
), it is also the orientation of individual struts within the structures (scaffold) that has an influence on porosity. Build parameters such as laser power, scan speed and hatch distance [58
], which influence surface morphology, macro- and micro-porosity, can be predominantly excluded here due to the identical parameters used.
All scaffold designs were manufactured in the same building direction. Because it is known that subsequent post-processing (sand-blasting, ultrasonic cleaning, chemical etching, etc.) has an influence on the surface and therefore on porosity, post-treatment steps were avoided.
What is much more interesting here is the orientation of struts during the building process. As Suard et al. [61
] described, the surface roughness and the resulting strut shape depend on the orientation during the building process. Whereas vertically oriented struts display uniform roughness values, a horizontal or oblique orientation leads to an increased roughness of struts which is mainly attributable to energy flows into the powder bed. Due to this energy flow, powder particles repeatedly tend to adhere to the strut underside (Figure 4
). This phenomenon causes deviations from the present geometry as well as porosity deviations. The effect of powder adhesion is also described in [62
The structures made in the course of this study exhibit vertical and horizontal struts in the models C1–C5. The pyramid-shaped structural elements display, apart from horizontal struts, struts with an oblique orientation, while torsional structures are exclusively built up with obliquely oriented struts. The lower porosity of pyramidal structures determined by way of experiment is attributable to the orientation of the struts. The scaffolds consisting of cubes show lower experimentally determined porosities, especially when it comes to struts with larger cross-sections (C1—2.2 mm, C2—1.8 mm). Apparently, the diameter and thereby, indirectly, the required energy input too, play a role in the cube structures with horizontal and vertical struts. Since the torsional structure is also inconsistent (T1, T3—lower porosity; T2—higher porosity), there seems to be an influence here.
These facts offer the possibility for scaffold fabrication with mechanical properties that can be predetermined by CAD design analysis or by numerical simulations [63
] before manufacturing. All samples showed a failure behaviour, which is known from the literature. A shear deformation at an angle of ca. 45° is shown in Figure 5
for the twisted and pyramidal design. The cubic design showed a layer-by-layer failure mechanism. This is in accordance with the results of Cheng et al. [64
], Xiao et al. [65
] and Li et al. [23
]. Using computationally predicted deformation models, Kadkhodapour et al. [66
] show that a layer-by-layer failure mechanism applies to stretch-dominated structures (i.e., cubic unit cell) while bending-dominated structures (i.e., twisted, pyramidal) show shear bands at 45°. Due to the geometrical variation of the structural design, the elastic modulus could be varied between 7 GPa and approximately 22 GPa for the cubic design, between 3 GPa and approximately 7 GPa for the pyramidal design and between 17 GPa and 26 GPa for the twisted design. Thus, we could demonstrate the possibility of generating scaffolds with specific mechanical properties within the reported range for human cortical bone [4
]. Moreover, modification and reduction of scaffold stiffness is necessary to prevent stress shielding of the adjacent bone tissue around stiff implants [7
Based on uniaxial compression testing for the three investigated design variations, linear correlation with a high coefficient of determination of the elastic modulus with scaffold porosity (Figure 7
) and compressive strength (Figure 9
) were found. The correlations between elastic modulus and porosity and between elastic modulus and geometrical parameters were very similar.
The influence of the length of the individual load-bearing bars on the achievable mechanical properties is directly connected to the load-bearing section. As shown in Figure 8
, this correlation can be described as the ratio of the width of unit structure (a
) and strut diameter (d
). The existing pyramid and cubic unit cell structures, which are geometrically similar, here describe a different stiffness level than the structures of the twisted unit cells. Similarly, there is a bigger quotient of unit cells with higher porosities. The ascertained functional linear connection thus offers another possibility to influence the mechanical qualities by providing specific geometrical constraints.
Cell size has a significant influence on the mechanical behaviour of open-porous structures or cellular materials [50
]. A characterization of the effect of cell size on the mechanical properties is possible using the length ratio λ. λ is defined as λ = L
, where L
is the cell size and LS
is the size of the specimen. Results of this study show that the design with the smaller λ achieves higher results in the elastic modulus. This relationship does not apply universally and to all tested design types. However, in general, this knowledge can be confirmed. Accordingly, the results for the cubic design range from 0.188 to 0.133 and from 0.32 to 0.3 for the pyramidal design. The E moduli for the cubic design are between 7.2 and 21.6 MPa, and those for the pyramidal design are between 3.4 and 6.9 MPa.
This shows that a lower value corresponds to λ with higher values for the E modulus. A comparison of the pyramidal design with the twisted design (λ = 0.166–0.222 and elastic modulus 16.7–26.2 MPa) confirmed this relationship. When comparing the cubic and the twisted design, this connection is not generally valid. Differences found with regard to the E modulus can be explained by the buckling length of individual struts and the position of the strut to the acting force. Thus, when comparing T2 with C2, the elastic modulus of the twisted design types is higher than that of the cubic design in spite of the reduced cross section. The structure has rigidity advantages over the cubic structure. The bars of the cubic design are aligned directly perpendicular to the acting force (larger free buckling length), and there is no mutual support as in the twisted design.
These partially valid relationships that are difficult to overlook in their complexity require a simple way of characterization. Core aspects for describing porous structures include, of course, the porosity and the obtained mechanical properties—specifically of the elastic modulus. With the application of such structural elements in medical fields or in particular in implants, where porous structures are intended to fulfil bone-like functions, rigidity in the context of porosity plays an essential role. Characterization of the specific yielding of structures as a measure of the stiffness of porosity offers an immediate option to assess the suitability of structure types and their geometric variations for their envisaged field of application. As shown in Figure 10
and Figure 11
, the individual design types differ clearly with respect to their mechanical properties.
To determine the mechanical properties, a uniaxial compression test was conducted. Based on these tests, a correlation between the elastic modulus and the scaffold porosity and elastic modulus ratio could be verified and described in the power law (5). This power law (5) could be verified for different structures (Figure 11
) manufactured with SLM using TI6AL4V [10
]. Specific yielding indicates how well a structure (geometrical variation) fulfils the requirements in terms of stiffness and porosity. It describes the resistance that is put up by the structure against deformation caused by the acting force. The active cross-sectional area, the material and the influencing manufacturing factors have a direct impact on the characterization of specific yielding. Density is typically taken into account in order to describe specific technology parameters. In the power law (4), the porosity of the structure, or in other words, a macro density is used for evaluation.
Factor ϑ describes this relationship very well, thus combining the requirements placed on components for medical applications, i.e., the description of a sufficiently high porosity, to ensure the secondary stiffness required for the successful retention of the implant and on mechanical stiffness necessary for the absorption of the acting loads to avoid stress shielding.
The investigated structures compared with values from the literature as well as our own investigations are shown in (Figure 11
). These results are used in reference to the characteristic values for human bones. An evaluation and comparison with the listed structures is possible by looking at the porosity of cortical bone (between 6%–13%) [67
] and cancellous bone (between 38%–43%) [68
] in relation to known literature values for the elastic modulus (cancellous bone—2.5–3.5 GPa; cortical bone—15–18 GPa).
impressively underlines that human bone is superior with regard to specific yielding for each generated elastic modulus. It also shows that there is a need to develop structures with properties that can compete with the characteristics of the human bone. Specific yielding as the determining factor for characterizing the resistance against deformation offers an invaluable benefit in the assessment of the suitability of a given structure for medical applications (implant). Since specific yielding is directly related to the volume of structures, it is possible to selectively decide which geometries, i.e., which structures, are to be preferred. The simple and comparative description of mechanical properties in the context of porosity offers another important means to assign structures to specific areas of application (cortical or trabecular bone areas) and functions (hips, knees). In a further step, it would be interesting to determine how the detected regularities manifest themselves under dynamic load.