Conventional Powder Metallurgy Process and ...

Conventional Powder Metallurgy Process and Characterization of Porous Titanium for Biomedical Applications Y. TORRES, J.J. PAVOŃ, I. NIETO, and J.A. RODRI´GUEZ Commercially pure titanium (c.p. Ti) is one of the best metallic biomaterials for bone tissue replacement. However, one of its main drawbacks, which compromises the service reliability of the implants, is the stress-shielding phenomenon (Young’s modulus mismatch with respect to that one of the bone). Several previous works attempted to solve this problem. One alternative to solve that problem has been the development of biocomposites implants and, more recently, the fabrication of titanium porous implants. In this work, porous samples of c.p. Ti grade 4 were obtained using conventional powder metallurgy technique. The influence of the processing parameters (compacting pressure and sintering temperature) on the microstructure features (size, type, morphology, and percentage of porosity), as well as on the mechanical properties (compressive yield strength, and conventional and dynamic Young’s modulus) were investigated. The results indicated that there is an increment in density, roundness of pores, and mean free path between them as compacting pressure and/or sintering temperature is increased. The Young’s modulus (conventional and dynamic) and yield strength showed the same behavior. Better stiffness results, in the central part of cylindrical samples, were obtained for a uniaxial compression of 38.5 MPa using a sintering temperature of 1273 K and 1373 K (1000 C and 1100 C). An evaluation of porosity and Young’s modulus along a cylindrical sample divided in three parts showed that is possible to obtain a titanium sample with graded porosity that could be used to design implants. This approach opens a new alternative to solve the bone resorption problems associated with the stress-shielding phenomenon. DOI: 10.1007/s11663-011-9521-6 The Minerals, Metals & Materials Society and ASM International 2011

I.

INTRODUCTION

TISSUE degradation associated with traumas and diseases and its replacement is currently an important public health problem. For the bone tissue, degradation is evident in the bone density reduction of patients as young as 30 years old, which implies a strength reduction up to 40 pct that could be increased by both the cyclic load degradation and the surface wear of joints. Of all biomaterials used for bone replacement, it is recognized that both commercially pure titanium (c.p. Ti) and Ti6Al4V alloy, medical grade, are the materials that show the best in vivo behavior because of their excellent balance between mechanical, physical-chemical, and biofunctional properties. However, they have the following three disadvantages that, in many cases, compromise the implants and prosthesis liability: (1) The stiffness of titanium is higher than the bone, which produces the stress shielding phenomenon, promoting the bone resorption around the implant; (2) despite its high osteointegration capability, titanium is surrounded Y. TORRES and J.A. RODRI´GUEZ, Associate Professors, and I. NIETO, Fellowship, are with the Departmento de Ingenierı´ a Mecańica y de los Materiales, E.T.S. de Ingenierı´ a, Universidad de Sevilla, 41092 Sevilla, Spain. Contact e-mail: [email protected] J.J. PAVOŃ, Associate Professor, is with Grupo BIOMAT, Programa de Bioingenierı´ a, Universidad de Antioquia, Medellı´ n, Colombia. Manuscript submitted September 29, 2010. Article published online May 3, 2011. METALLURGICAL AND MATERIALS TRANSACTIONS B

by a fibrous tissue because of its bioinert behavior, which is related with many loosening events; and (3) more studies are needed about its liability from damage prevention criteria because this is the only admissible criteria for biomaterials design. Regarding the stressshielding problem, some developments of both biocomposites and porous titanium implants still do not reach suitable equilibrium between mechanical and biofunctional properties.[1–4] Several previous works showed that is possible to match the stiffness of cortical bone using different techniques to fabricate porous titanium samples.[5–15] However, there is a lack of studies about the real effect of this porosity on other important mechanical properties, i.e., mechanical strength and fatigue life, and about the relationships between both the porosity and microstructure with the mechanical properties. Porosity percentage must be controlled to reduce the implant stiffness without any undesirable influence in mechanical resistance. From a powder metallurgy (PM) point of view, this could be reached by controlling compacting pressure, sintering temperature, and even using some special additives as space holders. To improve both bone ingrowth and osteointegration, the pores size and morphology must be controlled, especially in the surface, which will be also critical for the fatigue resistance of the implant. In this work, porous samples were obtained by a PM conventional technique. The influence of the main sintering conditions, compacting pressure and temperature, on both microstructural and mechanical properties of VOLUME 42B, AUGUST 2011—891

porous c.p. Ti samples was investigated. This work was developed in the framework of a project in which the aim is to evaluate the improvement of the equilibrium between biofunctional and mechanical properties of porous titanium implants. This article is arranged in the following sequence. A description of the samples fabrication, characterization techniques, and mechanical testing is presented in Section II. The microstructural, density, and porosity characterization results are showed in Section III–A. The mechanical testing results and stiffness measurements by ultrasound technique are presented in Section III–B. The discussion and analysis about the relations between porosity and mechanical properties is presented in Section III–C, as well as the analysis of the possibilities to manufacture porous graded samples by this method. The article concludes with a summary of the salient findings of this work in Section IV.

II.

EXPERIMENTAL PROCEDURE

A. Samples Processing The powder metallurgy technique used to manufacture the samples consisted of a conventional process of compaction followed by sintering of grade 4 c.p. Ti powder fabricated by a hydrogenation/dehydrogenation process. The particle size distribution, according to the supplier SE-JONG Materials Co. Ltd. (Seoul, Korea) showed a size lower that 9.7 lm (10 pct), 23,3 lm (50 pct), and 48.4 lm (90 pct), with a chemical composition equivalent to Grade 4 c.p. Ti ASTM F67-00.[16] To obtain porosities between 30 and 50 pct and to ensure the desired stiffness,[4,17,18] the compacting pressures used were 38.5, 89.7, 147.7, and 211.5 MPa (from the compressibility curve of the powder), and the sintered temperatures were 1273 K, 1373 K, 1473 K, and 1573 K (1000 C, 1100 C, 1200 C, and 1300 C) for 2 hours (Table I). The powder mass used to obtain samples with dimensions suitable for testing compression (height/diameter = 0.8) was 5.14 g. The compacting step was carried out using an Instron 5505 universal machine (Instron, Norwood, MA) to apply the pressure needed for the desired porosity. The compacting loading rate was 6 kN/s, the dwelling time was 2 minutes, and the unloading time was 15 seconds for decreasing load up to 150 N. The sintering process was performed in a

Table I. Die compaction

Sintering

B. Density, Porosity, and Microstructural Characterization Density measurement was carried out using Archimedes’ method with distilled water impregnation because of its experimental simplicity and reasonable reliability (ASTM C373-88[19]). This method basically consisted of the following steps: (1) weigh the dry sample, (2) warm the sample in distilled water for 5 hours, (3) settle down the sample for 24 hours (to ensure that water penetrates through the porosity), (4) remove the sample and let the outer water out, (5) weigh the sample again (mass of saturated sample), and (6) weigh the sample again, immersed in water. The total and interconnected porosity were calculated from density measurements. The porosity evaluation by image analysis was performed using an optical microscope Nikon Epiphot (Nikon, Tokyo, Japan) coupled with a camera Jenoptik Progres C3 (Jenoptik, Jena, Germany), and suitable analysis software (Image-Pro Plus 6.2, Mediacibernetic, Bethesda, MD). Initially, this analysis was performed only in the middle part of the cylinders because it presents the most homogeneous pores distribution. Afterward, the same analysis was extended along the whole cylindrical sample by dividing it in three parts (top, middle, and bottom) to verify any possible graded behavior. Before the image analysis, the sectioned parts were prepared properly by a sequence of conventional steps (resin mounting, grinding, and polishing) followed by a mechanochemical polishing with magnesium oxide and hydrogen peroxide. The main porosity characteristics estimated by this method were as follows: (1) the pore shape factor (Ff = 4pA/PE2, where A is the pore area and PE is the experimental perimeter of the pore); (2) the mean free path between the pores (k, measure of the mean size of titanium matrix); (3) the equivalent diameter (Deq); (4) the pore contiguity, Cpore (this parameter is a measurement of the pore interconnectivity and it is calculated in the same way that cemented carbide[20]); and (5) the porosity itself. Conventional optical microscopy (OM) was also used for the basic observation of the microstructural features of the samples.

Powder Metallurgy Process: Experimental Matrix

compacting pressures pressing direction deformation rate temperature tooling lubrication temperatures heating rate to temperature hold time at temperature atmosphere

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Carbolite STF 15/75/450 ceramic furnace (Carbolite, Derbyshire, UK) with a horizontal tube using high vacuum (5 9 104 mbar).

38.5, 89.7, 147.7, and 211.5 MPa 1 High (6 kN/s) Ambient Tool steel Ethylene-bis-stearamide 1273 K, 1373 K, 1473 K, and 1573 K (1000 C, 1100 C, 1200 C, and 1300 C) 0.25 K/s (15 C/min) 2h High vacuum (5 9 104 mbar)

METALLURGICAL AND MATERIALS TRANSACTIONS B

C. Mechanical Testing For mechanical compression testing, the specimen dimensions were fixed to standard recommendation from ASTM E9-89a (height/diameter = 0.8).[21] The tests were carried out with a universal electromechanical Instron machine 5505 by applying a strain rate of 0.005 mm/mmÆmin. All tests finished for a strain of 50 pct, and afterward, it was estimated both Young modulus, E, and yield strength, ry. The Young’s modulus estimation from the compression stress–strain curves was corrected with the testing machine stiffness (87.9 kN/mm). The dynamic Young’s modulus measurement using the ultrasound technique was performed with a KRAUTKRAMER USM 35 equipment (GE Measurement & Control Solutions, Minden, NV), which was used to estimate both the longitudinal and transverse propagation velocity of acoustic waves. To evaluate longitudinal waves, a Panametrics S-NDT (Olympus, Tokyo, Japan) probe of 4 MHz and an ultrasonic couplant fluid (Sonotrace grade 30) was used. On the other hand, for cross-sectional waves, a Panametric S-V153 probe of 1 MHz/.5 and a shear wave couplant (Panametric S-NDT) was used. For nonporous c.p. Ti samples, the velocities of longitudinal and cross-sectional waves were 6100 m/s and 3120 m/s, respectively.[22] Once the acoustic wave velocities were measured, the dynamic Young’s modulus calculation was made using a proper mathematical expression.[23] Finally, the Young’s modulus of porous samples was estimated from both porosity and pores shape factor measurements, using the models proposed by Knudsen[24] and Spriggs,[25] Pabst and Gregorova´,[26] Gibson and Ashby,[27] and Nielsen.[28]

III.

showed any presence of oxidation and contamination of titanium, which is a clear indicator of the role played by the vacuum during sintering. As mentioned previously, all characterization and mechanical testing was focused, initially, in the central part of the cylinders because of its uniform porosity according to theoretical stress distribution. Afterward, the analysis was also performed in the other two parts, top and bottom, to evaluate some graded material behavior. B. Density, Porosity, and Microstructural Characterization Figure 2 shows the dependence of both total and interconnected porosity, in terms of both compacting pressure and sintering temperature. As expected, the lower values of total porosity and higher density were obtained for the higher values of both compacting pressure and sintering temperature. Regarding the guide value of total porosity to reach the desired stiffness (30 pct to 50 pct), this was obtained for compacting pressures between 38.5 MPa and 89.7 MPa, and sintering temperatures between 1273 K and 1473 K (1000 C and 1200 C) (Figure 2). From that figure, it is deduced that for a total porosity range of 30 to 40 pct

RESULTS AND DISCUSSION

A. Samples Processing Figure 1 shows an example of the sample aspect after the sintering process for a compacting pressure and sintering temperature of 38.5 MPa and 1573 K (1300 C), respectively. None of the sintered samples

Fig. 1—Porous c.p. Ti material at 38.5 MPa, 1573 K (1300 C) and split in three pieces. METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 2—Porosity behavior as a function of both compacting pressure and sintering temperature: (a) total porosity and (b) interconnected porosity. VOLUME 42B, AUGUST 2011—893

and a sintering temperature range of 1273 K to 1473 K (1000 C to 1200 C), a compacting pressure range of 38.5 MPa to 89.7 MPa can be used. These conditions allow higher porosity values for both lower compacting pressure and sintering temperature. Interconnected porosity was always lower than the total and showed a similar trend as that found in this study. However, in this case, there is not a defined desired range because it depends on the elastic properties of the material to be used as filler compound (bioactive glass, high-density polyethylene, etc.). In fact, this kind of porosity should be most properly controlled to be only at the surface to promote the bone ingrowth, considering the risk of reducing both mechanical strength and fatigue resistance. In regard to the evaluation of the graded behavior of the porous samples, Figure 3 presents the porosity behavior along the cylindrical sample represented by measurements performed in three parts of the original sample: top, middle, and bottom. It can be observed that there is a porosity increment from the top to the bottom of the sample, showing a continuous change that can be considered as a graded change of porosity. Furthermore, this figure shows that the porosity behavior is reasonably consistent with the theoretical pressure distribution in a cylindrical sample under uniaxial compressive stress, which was the criterion used to study initially only the middle part of the sample. It is well known that the density of the nonporous sample is higher within the part where was pressure applied; therefore, it is reduced as we move far from the top. It is also known that that there is an effect of the radial pressure; i.e., the outer pressure is different with respect to core pressure. In that sense, we have focused our work in samples machined from the central part for the cylindrical samples, where the material is more homogeneous. However, according to Figure 4 (not corresponding to Ti), it seems that the heterogeneity problem and the pressure differences are more significant between the central part and the bottom; this observation could explain the highest slope. Nonetheless, it is necessary to make the same analysis for Ti density. Note that the comparison of porosities for increasing compacting pressures and two different sintering temperatures, 1373 K and 1473 K (1100 C and 1200 C) shows that the porosity is lower for the highest temperature, as expected. However, it is more remarkable that the higher porosity sensitivity to compacting pressures increments for the lowest temperature: Compaction curves are closer in the drawing for the highest sintering temperature. This result, besides being interesting for controlling both stiffness and mechanical strength, is also related to the sensitivity of these properties when the compacting pressure is changed for a fixed temperature. This result is discussed later in this article. Regarding the relation between the porosity guide to obtain the desired stiffness and the results in Figure 3, it is clear that the better results correspond to both the lowest sintering temperature and compacting pressure (1373 K [1100 C] and 38.5 MPa). However, in this case, it would be advisable to use the continued change of porosity, from top to bottom, to grade the change 894—VOLUME 42B, AUGUST 2011

Fig. 3—Porosity behavior along the cylindrical porous sample measured on three parts: top, middle, and bottom: (a) 1373 K (1100 C) and (b) 1473 K (1200 C).

Fig. 4—Density compact.[29]

distribution

in

a

cylindrical

nickel

powder

between a titanium core and cortical bone. This will be discussed subsequently in the article in terms of the Young’s modulus change. Figures 5 and 6 summarize the most important pore morphology parameters in terms of both compacting METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 5—Effects of the temperature and compacting pressure in characteristic of the pores.

pressure and sintering temperature in the middle part of the cylindrical sample. From these results it can be noticed, as expected, that the most important parameters, pore shape factor (Ff) and free-mean path or distance between pores (k), increased for higher values of both compacting pressure and sintering temperature. As a logical consequence, porosity was reduced (higher stiffness), especially by compacting pressure effects, whereas sintering temperature has a stronger influence in Ff. However, the most important feature of the pore morphology behavior is the different trend of both Ff and k parameters for lower and higher compacting pressure. It is observed that for a fixed, low compacting pressure (38.5 MPa), an increasing sintering temperature has a stronger effect in both Ff and k, with a acceptable porosity reduction. It should be pointed out that the porosity measurement using the Archimedes method was reasonably coherent with porosity estimation by an image analysis after optimization of the samples preparation before they were observed (see data in Figure 5). In addition, as long as compaction pressure and/or sintering temperature are increased, it is observed that the porosity distribution is more homogeneous; i.e., the wide bell shape of the curve is decreased (see the curves of Figure 5). This trend implies that to improve both mechanical and fatigue resistance with a small effect in the desired porosity (stiffness), it is advisable to work with small increments of sintering temperature for the lowest METALLURGICAL AND MATERIALS TRANSACTIONS B

compacting pressure. These conditions are consistent with the stronger effect in Ff because of an increasing sintering temperature. However, sintering-temperature increments for the highest compacting pressure produce the largest pores and a reduction of the pore shape factor (i.e., pores with more irregular shape correspond to lower temperature conditions) because of the coalescence of the smallest ones present at the lowest temperatures. Regarding the interconnected porosity, it is observed that Cpore behavior (0 for null interconnectivity and 1 for maximum) matches perfectly the measurements from Archimedes’ method, which implies that the Cpore parameter is reasonably good for the estimation of this kind of porosity. This parameter is also related to the distribution of the equivalent diameter: For the highest values of Cpore (closer to one, a higher interconnectivity), there will be the largest pores, which implies that the pore size distribution will be wider. C. Mechanical Testing The compression stress–strain curves of the middle part of the cylindrical samples for the different processing conditions are depicted in Figure 7. From this figure, it is verified that an increment in sintering temperature, for a fixed compacting pressure, implies higher values of both Young’s modulus and yield strength. It is interesting VOLUME 42B, AUGUST 2011—895

Fig. 6—Different OM images for all conditions studied in this work.

to remark that the influence of changing processing conditions on E y ry is more important when those conditions generate a higher heterogeneity of both the distribution (see cumulative curves of Figure 5) and the shape factor of total porosity. However, it is important also to evaluate the changes of yield strength with the interconnected porosity. This issue is also observed in other PM materials and has been related normally to a different level of matrix constraint(deformation capacity decreased[30]); it should be studied in future works. The results obtained in this article indicate that Ff and k can affect not only the plastic properties (yield and mechanical strength, and fatigue resistance) but also the elastic properties of the titanium porous sample. Therefore, this has to be considered to improve the mechanical properties of porous titanium without affecting the stiffness of the sample. Note from the same figure that the compacting pressure increments for the lowest and highest sintering temperatures show the same E and ry sensitivity: They are more sensible for compacting pressure increments at the lowest sintering temperature. From Figure 7, it is also observed that the yield strength 896—VOLUME 42B, AUGUST 2011

values are always lower than the nonporous titanium value (approximately 600 MPa[5]), except for the highest sintering temperatures. However, it is more important to make this comparison with respect to yield strength of the cortical bone (approximately 150 MPa[5]), in which case the experimental values are always higher. This is especially remarkable for the lowest values of both compacting pressure and sintering temperature (38.5 MPa and 1273 K [1000 C]) because these conditions correspond to the more suitable stiffness results, which are provided subsequently in this article. Regarding the stiffness value for cortical bone replacement (approximately 20 GPa), Figure 8[2,10,14,31–34] shows that the best results (20 to 25 GPa) were obtained for the lowest compacting pressure (38.5 MPa) with sintering temperatures of 1273 K and 1373 K (1000 C and 1100 C). These conditions correspond to the highest porosity (roughly 30 pct) in the middle part of the cylindrical samples. Tthe trends obtained by other authors are provided in this figure also, and it is observed that their results fix reasonably well with those obtained in this work. From Figure 8, the influence of METALLURGICAL AND MATERIALS TRANSACTIONS B

Fig. 7—Compression stress–strain curves of the samples for the different processing conditions: (a) 38.5 MPa, (b) 211.5 MPa, (c) 1273 K (1000 C) and (d) 1573 K (1300 C).

Fig. 8—Behavior of compression tests in terms of total porosity. Relation between the compression Young’s modulus and porosity.

Fig. 9—Relation between the dynamic Young’s modulus and porosity.

using the stiffness correction of the testing machine in Young’s modulus evaluation is clear: The corrected values are higher than those obtained by other authors for the same porosity. However, these values remain lower than those obtained with the ultrasound technique, as will be observed and discussed subsequently.

The Young’s modulus measurements obtained by ultrasound technique (dynamic Young¢s modulus) showed higher values than those estimated from the compression stress–strain curves of the middle part of the cylindrical samples (Figures 8 and 9). However, for the lowest Young’s modulus values, the results are more similar. These differences could be explained by the


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normal uncertainties of the compression test measurement and by the higher well-known reliability of the ultrasound technique. The theoretical curves, which are included in Figure 9, correspond to the following mathematical models: Knudsen,[24] Pabts and Gregorova´,[26] and Gibson and Ashby.[27] These models relate Young’s modulus by ultrasound technique with porosity and they are only valid up to 66 pct of porosity.[35] The authors have found several theoretical models that were reviewed by Zhu et al.,[35] and their conclusions have been applied to our experiments. Therefore, starting from both c.p. titanium and Ti6Al4V powders, they prepared specimens using the PM method, which consisted of mixing, pressing, and heat treating steps. However, pores were generated after the fugitive space holders (urea) as the second phase were removed during the heat treatment. They showed that a general expression of the Young’s modulus as a function of porosity for the porous medium was of the following form: E ¼ E0 fðPÞ

½1

where E is the Young’ modulus of the porous material, E0 is the Young’s modulus of the fully dense material, and P is the porosity. f(P) is a function that correlated the Young’s modulus to the porosity and was obtained usually by fitting the experimental data. In particular, Knudsen[24] and Spriggs[25] had proposed the following relation: E ¼ E0 ebP

½2

where b is a material constant and related to particles stacking. This expression has been used widely to predict the Young’s modulus of porous materials with low P, but it could not satisfy the boundary condition that E equals zero for P = 1. Phani and Niyogi[36] proposed another expression for the Young’s modulus: P n E ¼ E0 1 ½3 PC where PC was the critical porosity at which E = 0, i.e., the material loses integrity. PC depends on the stacking geometry of particles, and the material constant n also depends on pore distribution geometry, such as shape, connectivity, etc. Pabst and Gregorova´[26] had presented a much simple relation, which can be written as: P E ¼ E0 ð1 aPÞ 1 ½4 PC When PC = 1, Eq. [4] reduces to the Coble-Kingery relation.[26] Thus Pabst and Gregorova´ relation can be observed as the general form of the Coble-Kingery relation. In the same paper, Zhu et al.[35] fit the Phani–Niyogi relation and the Pabst–Gregorova´ relation with two adjustable parameters to the porosity dependence of Young’s modulus for porous c.p. titanium and Ti6Al4V over a wide range of porosity. Although these two relations worked well for the porosity dependence of 898—VOLUME 42B, AUGUST 2011

Young’s modulus, the adjustable parameters (PC, n, or a) showed the dependence on the selected porosity ranges, which limited their applicability. However, if they used n = 2 and a = 1, these two relations correctly accounted for the porosity dependence of Young’s modulus, and the left adjustable parameter PC was nearly independent of the selected porosity ranges. Thus, they could conclude that both Phani–Niyogi relation and Pabst–Gregorova´ relation with the only adjustable parameter PC and with fixed values of n = 2 or a = 1 were applicable to the dependence of Young’s modulus on porosity for porous materials. Figure 9 presents the dynamic Young’s modulus behavior of the middle part of the cylindrical samples, in terms of compacting pressure, sintering temperature and porosity. As in the case of the compression test measurement, the better stiffness results correspond to both lowest compacting pressure and sintering temperature (38.5 MPa and 1273 K to 1373 K [1000 C to 1100 C]) with a porosity of approximately 40 pct. Note that the relation between measurements through both methods and porosity are in concordance with those reported in previous works[2,14,26,35]: 20 to 25 MPa for 50 pct porosity. Although the better stiffness results obtained in this work were for the lowest sintering temperature, this finding does not imply any loss of mechanical strength as could be expected from the literature. In fact, the authors have new results in which they use a lower compacting pressure (13 MPa) and a loose sintering technique, with results of 50 pct porosity and 14.3 GPa for 1273 K (1000 C) and 45 pct porosity and 21.7 GPa for 1473 K (1200 C). Similar stiffness values for lower porosity could be explained by some measurement uncertainties in the previous works (all compression test measurements in this work were corrected with the testing machine stiffness); in addition, the ultrasound technique in this study was carried out carefully and with detail. In fact, the reliability and certainty of the ultrasound measurements were contrasted and validated by a comparison with a well-known and accepted pore-elasticity model, such as the Nielsen model.[28] Figure 10 shows the

Fig. 10—Comparison between experimental Young’s modulus and estimated by the Nielsen’s equation. METALLURGICAL AND MATERIALS TRANSACTIONS B

other hand, the highest Young’s modulus value appears in the top for the highest compacting pressure. This behavior implies that we could make an implant with a cross-sectional gradient porosity from the top to the bottom of the sample: (1) the top of the sample with the highest Young’s modulus (~90 GPa) to be in contact with a titanium core; (2) the bottom part, with the lowest Young’s modulus, to be in contact with cortical bone; and (3) the middle part that could be obtained for a compacting pressure between 90 MPa and 150 MPa, with a middle Young’s modulus value (~60 GPa) corresponding to the central part of the sample. It is evident that this analysis is just a first approach to implement a graded behavior of a cylindrical sample in a definitive titanium implant. Therefore, it requires additional studies and refinements that will be done in future works.

IV.

CONCLUSIONS

According to this study, the following salient findings were drawn about the influence of conventional powder metallurgy conditions in both microstructural and mechanical properties of porous c.p. Ti for bone replacement:

Fig. 11—Young’s modulus along the cylindrical porous sample measured on three parts: top, middle, and bottom: (a) 1273 K (1000 C) and (b) 1373 K (1100 C).

correlation between the both Young’s modulus experimental measurements and the calculation using the Nielsen model including the porosity parameter experimentally determined. From that figure, it is evident that the Young’s modulus measurements from the ultrasound technique present the best fix with respect to calculations from Nielsen model, for the complete range of both compacting pressure and sintering temperature. However, the measurements obtained from compression tests show an important deviation for the highest Young’s modulus values. The results of the graded behavior of porous cylindrical samples, in terms of the Young¢s modulus, are presented in Figure 11. As expected from the porosity behavior, the low slope change of Young’s modulus was observed from the bottom to the top of the samples. With respect to the desired Young’s modulus for bone replacement, the more suitable results for the three parts belong to the lowest compacting pressure for both sintering temperatures. However, it is more important for the application to use the graded concept from the global analysis of the compaction curves behavior. According to these curves, on the one hand, it is clear that the lowest Young’s modulus value (~20 GPa) can be obtained, in the bottom, for the lowest compacting pressure. On the METALLURGICAL AND MATERIALS TRANSACTIONS B

1. The better stiffness results of porous grade 4 c.p. Ti samples for cortical bone replacement (20 to 25 GPa against ~20 GPa of bone) were obtained for the lowest values of both compacting pressure and sintering temperature, 38.5 MPa and 1273 K to 1373 K (1000 C to 1100 C), with a porosity of approximately 40 pct. These results correspond to the central part of cylindrical samples initially fabricated because of its highest porosity uniformity. 2. The main porosity parameters, which include form factor and mean free path, presented a highest sensitivity to sintering temperature increments for a lowest compacting pressure. This trend was consistent with the behavior exhibited by both the Young’s modulus and yield strength from compression tests: highest sensitivity for sintering temperature increments at lowest compacting pressures as well as for compacting pressure increments for lowest sintering temperatures. The knowledge of this sensitivity could be determinant to improve both mechanical strength and fatigue life with a low influence in the porosity and, therefore, in the stiffness of the samples. 3. The ultrasound technique used for dynamic Young’s modulus estimation of porous c.p. Ti samples has shown to be a suitable tool for studying this kind of material. This was verified by a comparison of the measurements obtained by this technique with the values calculated from a theoretical model the Nielsen model, which include porosity parameters experimentally determined. 4. According to the Young’s modulus values that were measured along the cylindrical samples obtained by uniaxial compression and divided into three samples, it could be expected that it will open an indirect route to manufacture Ti implants with a cross-sectional, graded porosity. VOLUME 42B, AUGUST 2011—899

ACKNOWLEDGEMENTS This work was supported by the MICINN (Spain) through project Reference number MAT2010-20855. Furthermore, the authors thank to J. Pinto and S. Lascano for carrying out the microstructure characterization and mechanical testing.

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