## 4 Discussion
It could be achieved by using conventional PM, only when temperature and pressure are in the limits of this technique (0 MPa and sintering temperatures 1000 \({}^{\circ}\)C and 1100 \({}^{\circ}\)C), although there is a notable loss of the mechanical strength (see below). However, the space-holder technique presents a great feasibility to get these values of total porosity and even to lower stiffness values (6-8 GPa at higher porosity), it being possible to replace the trabecular tissue by these obtained results. Concerning mechanical properties, two different analyses have been made, aiming at the evaluation of the role of the manufacturing route tested in the compression behaviour (Figure 5). Independent of the processing technique used, a parameter is fixed for each comparison: in Figure 5a, [PERSON]'s modulus close to the cortical bone is set in \(\sim\)29 GPa (porosity total range between 37.6-44.8%) and the influence of the processing technique on the yield strength (\(\sigma_{y}\)) of the porous specimens is studied. In order to reach the same Young's modulus, higher porosity is needed for a loose-sintering technique, its compression yield strength being committed (Table 3). This fact is related to the lack of powder compaction step and low sintering temperatures, without ensuring a good strength of the formed neck (also critical to fatigue and flexural requirements). Yield strength values are fixed in a range from 150 to 200 MPa meeting the requirements of the cortical bone tissue in Figure 5b, evaluating what occurs with the total porosity, the mean size of the pores (Table 2) and the Young's modulus (Table 3). A complete analysis of the results seen in Figure 5b allows for specifying that only samples processed by a space-holder technique with 40 vol.% could be implemented as substitute of the cortical tissue (bio-mechanical balance between stiffness \(\sim\)20-25 GPa and mechanical strength, \(\sim\)150-200 MPa). These specimens present a total porosity of \(\sim\)37%. Two behaviours of losing mechanical efficiency are observed related respectively to: decreasing compaction pressure by a conventional PM route (reduction of cold welding of titanium powders, weaker necks); and increasing the pore size in a space-holder technique. The decreasing trend of the relative strength observed in Figure 3a,b undergoes two different performances (see in the slope curves). A proportional and expected loss of the mechanical strength with the reduction of the load section is observed. Then, a part of the strength decrement regarding the pore content, is compensated by the titanium matrix strengthening (see in the lowest slope); this fact occurs in ratio \(P_{i}/P(\text{Arch})\geq 0.89\) (\(P_{i}=40\%\)) and it is related to the large stress triaxiality originated by more interconnected porosity, in addition to more roughness contour of pores. This strengthening is not representative to the porosity range achieved via conventional PM. The mechanical requirements of cortical bone tissue could be guaranteed in the shaded area in Figure 3b (175-211 MPa). These results are consistent with that proposed by [PERSON] [46]: before the mean stress reaches levels close to the yield strength (approx. 33%), in the surrounding area of the notch, it is produced a triaxiality stress state and local plastic strain. As a consequence in ductile material, the yield strength of a notched specimen is higher than the uniaxial one [47]. Therefore, the local plastic strain involves a macroscopic hardening reflected in the yield strength increment of the material [48]. This aspect was observed in Figure 4, where a localized effect of pores was made evident, but a good balance between the mechanical properties was achieved (Table 4), according to the results obtained by the FE model.