A Barba S A

A.-S Bonnet

P Lipinski

R Pesci

G Dubois

Development and mechanical characterization of porous titanium bone substitutes

Keywords:

Commercially Pure Porous Titanium (CPPTi) can be used for surgical implants to avoid the stress shielding effect due to the mismatch between the mechanica l properties of titanium and bone . Most researchers in this area deal with randomly distributed pores or simple architectures in titanium alloys. The control of porosity, pore size and distribution is necessary to obtain implants with mechanical properties close to those of bone and to ensure their osseointegration . The aim of the present work was therefore to develop and characterize such a specific porous structure. First of all, the properties of titanium made by Selective Laser Melting (SLM) were characterized through experimental testing on bulk specimens. An elementary pattern of the porous structure was then designed to mimic the orthotropic properties of the human bone following several mechanical and geometrical criteria . Finite Element Analysis (FEA) was used to optimize the pattern . A porosity of 53% and pore sizes in the range of 860 to 1500 µm were fi.nally adopted . Tensile tests on porous samples were then carried out to validate the properties obtained numerically and identify the failure modes of the sam_ples. Final!y, FE elasto_plastic ana!yses were yerformed on the porous samples in order to propose a failure criterion for the design of porous substitutes . .

1.

Introduction

200 MPa by [START_REF] Reilly | The elastic and ultimate properties of compact bone tissue[END_REF] and [START_REF] Reilly | The elastic modulus for bone[END_REF]. In long bones, the cortical tissue represents approximately 25%

In most cases, clinical failure of prosthetic solutions is due to the stress-shie lding generated by the mismatch of mechanical properties between bone and implant [START_REF] Karachalios | The long-term clinical relevance of calcar atrophy caused by stress shielding in total hip arthroplasty: a 10-year, prospective, randomized study[END_REF] . The mechanica l properties of bone depend on many factors such as anatomical part, sex and age. The global elastic properties of cortical bone are usually described by the orthotropic tensor of elastic moduli defined by nine constants. Its longitudin al compressive strength was estimated to be of the whole bone volume . Consequently, as a first order approximation an apparent compressive strength of 50 MPa is considered in this study.

The intrinsic properties of bulk titanium are significant ly higher than those of cortical bone. To minimize the negative impact of this stiffness incompatibility, substitutes with a controlled porosity can be introduced . [START_REF] Oh | Mechanical properties of porous titanium compacts prepared by powder sintering[END_REF] obtained the Young's modulus of porous titanium close to that of bone by changing the voids volume fraction fv . They reduced this property from 110 GPa (bulk titanium) to 10 GPa for fv = 0.35. Moreover, as demonstrated by many authors [START_REF] Otsuki | Pore throat size and connectivity determine bone and tissue ingrowth into porous implants: threedimensional micro-CT based structural analyses of porous bioactive titanium implants[END_REF]Heinl et al., 2008 ;[START_REF] Xue | Processing and biocompatibility evaluation of laser processed porous titanium[END_REF][START_REF] Hollander | Structural, mechanical and in vitro characterization of individually structured Ti-6Al-4V produced by direct laser forming[END_REF], the existence of porosity is also propitious for the substitute osseointegration, the essential factor of the longterm reliability of the implant . The question arises : do the size, shape, topology and volume fraction of voids have any influence on the substitute colonization? Only a few studies have addressed this crucial problem . There is no consensus in the literature about the optimal pore size to enhance bone ingrowth . In their pioneering work, [START_REF] Otsuki | Pore throat size and connectivity determine bone and tissue ingrowth into porous implants: threedimensional micro-CT based structural analyses of porous bioactive titanium implants[END_REF] showed that the pores of the structure have to be interconnected in order to ensure the bone ingrowth . These authors also compared the type of tissue formed as a function of time and implant internal architecture . They tested two levels of porosity (50% and 70%) combined with two ranges of pore sizes (between 250 and 500 µm and between 500 and 1500 µm) and concluded that the size of pores should range from 500 to 1500 µm for both levels of porosity to get a tissue of good quality. [START_REF] Xue | Processing and biocompatibility evaluation of laser processed porous titanium[END_REF] demonstrated that the bone colonization is impossible for a pore size under 100 µm . [START_REF] Chen | Fabrication of porous titanium implants with biomechanical compatibility[END_REF] tested the osteogenesis on structures with pores ranging from 100 to 400 µm but did not speak out against higher pore dimensions . [START_REF] Hollander | Structural, mechanical and in vitro characterization of individually structured Ti-6Al-4V produced by direct laser forming[END_REF] tested porous structure with pore dimensions of 500, 700 and 1000 µm and concluded that the growth of human osteoblast is possible for all these types of porosities . Those authors did not indicate a maximal pore size either. Generally speaking, no clearly identified rule exists to allow the optimal design of implants or bone substitutes in commercially pure porous titanium (CPPTi) .

Several manufacturing processes of porous titanium are known among which freeze casting [START_REF] Yook | Fabrication of porous titanium scaffolds with high compressive strength using camphene-based freeze casting[END_REF], space holder technique [START_REF] Niu | Processing and properties of porous titanium using space holder technique[END_REF], rapid prototyping [START_REF] Li | Porous Ti6Al4V scaffold directly fabricating by rapid prototyping : preparation and in vitro experiment[END_REF] or laser processing [START_REF] Parthasarathy | Mechanical evaluation of porous titanium (Ti6Al4V) structures with electron beam melting (EBM)[END_REF]Heinl et al., 2008;[START_REF] Krishna | Low stiffness porous Ti structures for load-bearing implants[END_REF] . Freeze casting and space holder processes mostly lead to randomly distributed pores whereas rapid prototyping and laser processing are adopted when a controlled architecture is required .

The freeze casting technique enables a porous material with a compressive strength close to that of bone to be obtained, but its main drawback underlined by [START_REF] Yook | Fabrication of porous titanium scaffolds with high compressive strength using camphene-based freeze casting[END_REF] is the pore size that does not exceed 300 µm for a long manufacturing time of 7 days . Higher pore sizes can be reached with the space holder technique but the mechanical properties obtained are lower than those of human bone [START_REF] Niu | Processing and properties of porous titanium using space holder technique[END_REF]. In both cases, the control of the elastic properties anisotropy seems to be difficult .

In the literature, rapid prototyping and laser processing are often reported to generate bulk titanium or porous titanium with simple pore architecture [START_REF] Parthasarathy | Mechanical evaluation of porous titanium (Ti6Al4V) structures with electron beam melting (EBM)[END_REF]Heinl et al., 2008;[START_REF] Krishna | Low stiffness porous Ti structures for load-bearing implants[END_REF][START_REF] Li | Porous Ti6Al4V scaffold directly fabricating by rapid prototyping : preparation and in vitro experiment[END_REF] . These techniques are generally used in the case of titanium alloys .

In this paper, the Selective Laser Melting (SLM) process was chosen to produce porous titanium with a particular periodic internal architecture . In a first part, the properties of titanium samples processed by SLM are studied and compared to the ISO Standard Specifications . Crystallographic texture and residual stress measurements are also examined to estimate the anisotropy of samples obtained by this technology.

In a second part, an elementary pattern is designed to approach the mechanical properties of human bone and to enable the optimal implant osteointegration . The final section is dedicated to the question of elastoplastic global properties and simple failure assessment for such porous implants .

2.

Materials and methods

2.1.

Criteria for elementary pattern de.finition

To design and optimize an elementary pattern for bone substitutes, several criteria had to be simultaneously taken into account . With biocompatibility, the criteria adopted in this study are as follows :

• Elastic (global) properties as close as possible to those of cortical bone (including the anisotropy) . • A maximal allowed apparent stress not exceeding 50 MPa .

• A maximal stress exerted at any point of the pattern smaller than aad = ay / k , where ay is the yield point of the CP Ti and k = 1.5 corresponds to a safety coefficient .

• Interconnected pores [START_REF] Otsuki | Pore throat size and connectivity determine bone and tissue ingrowth into porous implants: threedimensional micro-CT based structural analyses of porous bioactive titanium implants[END_REF] .

• A pore size greater than 100 µm to facilitate bone colonization [START_REF] Shiomi | Residual stress within metallic mode! made by selective laser melting process[END_REF][START_REF] Xue | Processing and biocompatibility evaluation of laser processed porous titanium[END_REF][START_REF] Chen | Fabrication of porous titanium implants with biomechanical compatibility[END_REF] . • A porosity in the range of 50% to 70% as defined by Otsuki et al. (2006) . • A pattern shape enabling the perfect periodic paving of 30 space.

To perform such an optimization, the mechanical properties of commercially pure titanium processed by SLM have to be identified first. A classical experimental procedure is adopted to characterize the elastoplastic properties of CP Ti.

2.2.

Characterization of CP Ti processed by SLM

Elastoplastic properties of CP Ti processed by SLM

To characterize the intrinsic properties of CP Titanium processed by SLM, three types of standard tensile test specimens (NF EN ISO 6892-1) have been manufactured with a SLM machine prototype . The direction of powder layer deposit varied for each type of specimen and was either longitudinal (L) , transverse (W) or through specimen thickness (T) . According to the standard, the dimensions of the gauge part of the samples have been fixed to 7 mm (L) x 3 mm (W) x 0.5 mm (T) . The actual raw gauge sections of the specimens were measured after fabrication with an optical 30 measurement device (InfiniteFocus, Alicona, Austria) .

The elastoplastic properties of the material have been determined using an Instron 5866 tension/compression testing machine equipped with a load-cell allowing a precise force measurement with an error less than 0.4% in the range of 0.1-10 kN . The Bluehill 2 software package was used to control the nominal stress rate during tests . A video tension device developed by Apollor ® enabled the strain measurement . All the tests have been carried out at room temperature and quasi-static strain rate (10-3 s-1) .

Crystallographic texture and resid ual stress measurement

Because of the high temperature gradient induced by SLM during material melting, residual stresses and pronounced crystallographic texture are often observed inside the parts produced with this fabrication process . These quantities generally lead to the appearance of an induced anisotropy of the material and influence its fatigue life.

In the present work, a four circles Seifert XRD 3003 PTS goniometer was used to determine the crystallographic texture of a 10 x 10 x 10 mm 3 cubic specimen fabricated by SLM. Since the alpha titanium is obtained by SLM, the {101} crystallographic planes were analysed on two faces of this sample and the corresponding pole figures were obtained .

The residual stresses were determined with a Proto IXRD goniometer equipped with a copper tube . In accordance with the European standard, the sin 2 t method was used considering the {213} planes . Tura 5 x 5 x 5 mm 3 cubic specimens were prepared for these tests . The geometry and face designation as well as the coordinate frame attached to the cubes are indicated in Fig. 1.

The measurement of residual stresses was performed on the six faces of bath cubes in order to study the influence of the powder deposit and melting directions . For each specimen, the deposit direction corresponded to axis 3 and started from face 6 (bottom) . After powder deposition, the external wall of the layer was melted followed by the filling of its core in the direction 1 or 2 . To avoid the generation of a preferred orientation, for each next deposited layer the melting direction was permuted .

2.3.

Design and fmite element improvement of the elementary pattern geometry

The elementary patterns were first designed in the software package Solidworks 2003 respecting the various criteria cited in Section 2 .1concerning the minimal pore size, porosity and perfect paving of 30 space. Elastic Finite Element analyses were performed to improve the design . The FE meshes for all patterns were created using MSC Marc Software . Because of the existence of three planes of symmetry, only one eighth of every elementary pattern was meshed using hexahedral and pentahedral elements . Periodicity conditions were applied to the model on the appropriate faces. An example of the FE mesh can be appreciated in Fig. 2. The same software was used to perform the finite element analyses. Tura types of Based on the results of Section 2 .2 , the elastic behaviour of the bulk CP grade 2 Ti was supposed to be isotropie . The average value of Young's modulus of 100 GPa was deduced from these tests . The commonly admitted value of the Poisson's ratio of 0.33 was also used, see [START_REF] Shiomi | Residual stress within metallic mode! made by selective laser melting process[END_REF] . For each geometric configuration, the concentration factor of von Mises stress on individual beams constituting the pattern was analysed and compared to the material allowable stress . After each design of the elementary pattern, numerical simulations were done in order to check the resulting elastic properties . The design improvement was performed in loop until the properties of the pattern fitted the mechanical criteria outlined previously in this paper.

2.4.

De.finition of porous tensile specimens for the determination of substitute elastoplastic properties

In order to verify the adequacy of the mechanical properties provided by the simulations on the optimized pattern with the ones of a porous structure generated by SLM, experimental tensile tests were carried out. The porous specimens used in this mechanical study are illustrated in Fig. 3 and were named X, Y and Z, in accordance with the coordinate system in Fig. 2 , depending on the orientation of the elementary pattern in the porous area with respect to tension direction . All specimens were manufactured using a SLM machine prototype . They were composed of a porous gauge area and two gripped ends in bulk titanium and were designed in such a manner that four elementary patterns were present in the tension direction and at least two patterns in the transverse directions, Fig. 3. For each direction tested, three samples were manufactured . The theoretical porous cross sections normal to the tension directions were 5.74 x 9.95 mm 2 , 4.2 x 9.95 mm 2 and 4.2 x 11.5 mm 2 , respectively for the X, Y and Z samples. The corresponding porous zone lengths were 8.4, 11.49 and 19.9 mm in the same order. The same experimental devices as those used for the mechanical tests on the bulk specimens were employed for these tensile experiments .

Concerning the effective elastic properties of these porous structures, only the Young's moduli were determined experimentally. The values of the remaining elastic constants (shear moduli and Poisson's ratios) were not characterized . The usual plastic properties of the porous titanium were identified, i.e. Rp 0 _ 2 , Rm and A% . The true global and local (pore) dimensions of all nine specimens were characterized a Phoenix Micro CT scan and compared with the theoretical ones.

To perform the measurement of the strain with the video-traction device, two points were marked on each specimen bulk part as illustrated in Fig. A .1 (Appendix) . To characterize the mechanical properties of the porous titanium, the experimental force-displacement curves had to be corrected subtracting the stiffness of the bulk parts of the specimen. The details of this procedure are provided in Appendix .

The aim of these tests was to investigate the apparent elastoplastic properties of the porous structure and to observe the failure modes as a fonction of the pattern orientation with respect to the tensile direction .

2.5.

Identification of porous implant dimensioning criterion

An analysis of fractured tensile porous specimens was carried out in order to propose simple criteria enabling the dimensioning of SLM made porous implants .

The method used to identify the failure criterion of bone substitutes consisted in comparing experimental and numerical global stress-strain curves of porous tensile specimens .

The finite element meshes of the three types of specimen were built respecting the true specimen dimensions measured via Micro CT scanning. Only one eighth of each sample was meshed with mainly hexahedral elements using

Results and discussion

3.1.

Elastoplastic properties of CP Ti grade 2 processed by

SLM

Three standard tensile test specimens of CP grade 2 Ti were tested for each direction of melting . The true stress-true strain curves were obtained using the actual specimen cross sections . As an example, Fig. 4 shows the three curves obtained for the tension direction (T) . It clearly appears that SLM process ensures a good repeatability as the maximum stress deviation with respect to the average curve does not exceed 2%. A similar conclusion can be drawn for the two other directions, not illustrated in this paper. Table 1 summarizes, for each melting direction, the average values of the usual elastoplastic material properties, i.e. Young's modulus E, conventional yield stress Rp _ , strength Rm and 0 2 elongation A% . Besides, the plastic strain Jm l ax corresponding to the maximum of stress-strain curve was also identified . The last column recalls the same characteristic, if available, provided by the ISO specification . This Table does not reveal any significant influence of the melting direction on the Young's modulus of SLM CP grade 2 Ti. The differences observed are mainly due to the precision of the experimental device which is not really adapted for measurement of elastic stiffness of bulk metallic materials. The conventional yield point and ultimate tensile strength are not influenced by this parameter either. However, the average elongation of the samples melted in (W) direction is significantly reduced compared to the two other directions . This is due to the mediocre quality of the sample surface after the removal of the sustaining structure. It is important to recall that all specimens were tested without any surface machining or mechanical treatment . The elongation value in (W) direction was discarded in the failure analysis presented in Section 3.5. The trends reported in our study are in agreement with the results of [START_REF] Vandenbroucke | Selective Laser melting of biocompatible metals for rapid manufacturing of medical parts[END_REF] on SLM grade 5 titanium . These authors observed that the SLM process increases the yield point and ultimate tensile strength by 50% and reduces the elongation by 25% .

3.2.

Crystallographic texture and residual stress measurement 100 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

True strain

The two pole figures obtained from the crystallographic analysis are illustrated in Fig. 5, showing maps of the iso-lines of the orientation intensity factor. It is commonly recognized that the tested material becomes textured when this intensity Compared with the ISO Standard Specification for unalloyed titanium 5832-2, the plastic properties of the SLM CP grade 2 Ti are higher except for the material elongation . Indeed, the conventional yield point and ultimate tensile strength are almost twice as high as the ISO specifications.

On the one hand the elongation is reduced by 15% in L, 27% in T and 75% in W directions . This important drawback can be partially attributed to the thickness of specimens tested (T = 0.5 mm -comparable with the diameter of porous pattern struts) which is relatively small with respect to the specimens roughness . Indeed a ten-point mean roughness of these specimens, obtained using Alicona InfiniteFocus microscope, was R2 = 45 µm . On the other hand however, the SLM process is commonly used to manufacture patientspecific implants to suit the patient morphology . As a consequence, no adjustment by plastic deformation of implant is needed during surgery contrary to conventional implants . In such a situation , the critical elongation of the material is not necessarily a dimensioning parameter.

factor is higher than 3. As the two pole figures indicate intensity factors not exceeding 2.3, it can be concluded that there is no preferred crystallographic orientation of grains constituting the sample . Consequently, the randomly distributed texture of this SLM-processed titanium leads to the isotropy of its elastic and plastic properties, at least initially.

The results of the residual stress analysis are reported in Table 2. The residual stresses have only been measured on the external faces of the cubes . This Table shows that five faces of the examined cubes are subjected to a bi-axial compressive stress state. Face 1, however, undergoes positive stresses . This result can, at least partially, be attributed to the cooling process of the samples studied . First of all, it must be noted that faces 6 and 1correspond respectively to the first and last deposited layers. During the SLM process, layer n is directly affected by the cooling of layer n +1consecutive to its melting. Indeed, the thermal contraction during the cooling of layer n + 1generates compression in layer n and tension in layer n + 1. Therefore face 1 is subjected to tension and face 6 to compression . These faces having the normal vector parallel to axis 3 of coordinate system attached , only a 11 and a22 stress components are different from zero. A similar explanation holds for the lateral faces. Indeed, as presented in Section 2.2, after the powder deposition, the external wall was first melted by the laser followed by the layer core. This means that the core of the sample cools down after the external specimen surface. This explains the development of negative residual stresses on lateral faces in directions 3 and 1or 2, as a fonction of the face considered (2, 3, 4 or 5) . The presence of negative values of stress on faces 2 to 6 of the SLM-made samples indicates that this process is well adapted to the fabrication of implants subjected to cyclic loads as residual compression stresses delay crack initiation . However since positive stresses are obtained on the last face of the cube, attention must be paid to the melting path chosen for bone substitute manufacture . A local heat treatment can be used to reduce this stress, for instance by heating the last melted layer, without any material deposit, by the laser beam used [START_REF] Shiomi | Residual stress within metallic mode! made by selective laser melting process[END_REF] .

Stress Sample 1 Sample 2 Mean component

It must nevertheless be emphasized that all the values appearing in Table 2 are relatively small (o-max = 180 MPa, OEmin = -115 MPa) compared to the material conventional yield stress ("'520 MPa).

As no work has been found in the literature concerning residual stress induced by SLM on CP grade 2 titanium, the results obtained in this paper have been qualitatively compared with those on steel provided by [START_REF] Shiomi | Residual stress within metallic mode! made by selective laser melting process[END_REF] . The generation of residual stresses by SLM has been studied on a metal composed of 69.6% of standard chrome molybdenum steel, 21.7% of Ni and 8.7% of CuP. The authors observed a tensile residual stress on the top surface of about 400 MPa . A significant gradient of residual stress was found near this top surface. Indeed, a value of 80 MPa was measured at a distance of 1 mm from this surface leading to the mean gradient of 320 MPa/mm . Tura comments can be formulated concerning this comparison . First, in our nondestructive tests only external surfaces have been examined . Consequently, the stress gradient obtained by Shiomi et al. cannot be discussed . Next, the relatively high values of residual stresses determined [START_REF] Shiomi | Residual stress within metallic mode! made by selective laser melting process[END_REF] are probably due to the specific SLM parameters used . If one compares this method with the welding process, it is well known [START_REF] Wohlfart | Residual stress as a consequence of welding[END_REF][START_REF] Lieurade | Effet de contraintes résiduelles et du rapport R sur la résistance à la fatigue des éléments soudés[END_REF] that the level of residual stresses, but also their sign, strongly depend on the welding parameters and especially on the energy flux transferred to the sample.

3.3.

Elementary pattern design

The leading idea in designing the elementary pattern was to use interconnected 30 irregular "asterisks" made of straight beams connected together. In order to obtain anisotropy of its elastic properties similar to that of human cortical bone, the length and orientation as well as the cross sectional area of these beams were adapted to respect all the criteria cited above . Let (0; ex , ey , ez) be the coordinate system attached to this pattern coinciding with its planes of orthotropic symmetry. It was decided to generate the highest stiffness in the X direction. To reach this aim, four of the straight beams were arranged parallel to this axis. To get lower properties in the Y and Z directions, the remaining beams form a six branch asterisk, see Fig. 4. They induce the theoretical pattern porosity of 53%. The pore length in X direction is 900 µm and its cross-section in Y-Z plane can be characterized by two diagonals of 860 and 1500 µm also indicated in this Figure .  Fig. 2 shows the von Mises stress field for the final pattern geometry, obtained in tension along the X axis. The applied global tensile stress is 50 MPa . The maximal value of this stress is concentrated at the base of the X-oriented beams and reaches 365 MPa . This value is lower than the SLM CP Ti conventional yield point and leads to a safety factor k = 1.45 .

The elastic moduli of the final pattern obtained by the numerical simulations are summarized in Table 4 and compared to those of human cortical bone reported in the literature . It appears from this Table that the bone orthotropy is well respected by the pattern . However, the theoretical longitudinal and transverse moduli are significantly higher than those of bone . For instance, the maximal ratio between the Young 's moduli of the pattern and mandibular bone reaches 1.56 in Z direction . This observation suggests that the beam cross-sections are too large. Nevertheless, one should remember that the size of beam cross-section results from the strength criterion and safety factor adopted . Consequently, any decrease of beam cross-section area will result in the increase of stresses and violation of this criterion as suggested by the results of Fig. 2. Even so, these moduli are much smaller than the elastic properties of the classical metallic materials used in surgical implants . Indeed, the bulk CP grade 2 titanium typically used in craniomaxillofacial implants leads to a ratio of longitudinal moduli approaching 10.00. These results underline also the remarkable properties of bone tissue compared to the metals such as titanium, wellknown for its high strength-to-weight ratio .

Measurements of actual dimensions of the pattern and estimate of the geometric tolerance of the samples obtained by SLM

Before carrying out the tensile tests allowing the determination of the elastoplastic properties of the porous structure, it was necessary to estimate the actual size of each specimen and to check the performance of the machine used to precisely reproduce their complex geometry. Measurements of the true dimensions of the gauge part of porous tensile specimens have been carried out using a Phoenix Micro CT scan. The voxel size of the 30 abjects obtained was 10 µm.

First of all it must be noticed that the melting process ensures good interconnectivity throughout the whole specimen volume ; no flaws were detected in all samples within the precision of the Micro CT scan employed . The comparison of the theoretical and typical real pattern geometries is illustrated in Moreover, one can observe an important ten-point mean dimensions are slightly greater than the theoretical ones .

For each sample, its external dimensions (PX , PY, PZ) were roughness of physical specimens with an R2 value of around characterized as well as the cross-sectional sizes of struts defined by dimensions A , B, C, D, E, and F indicated in the same Figure . Table 3 summarizes all values of the theoretical and average real pattern dimensions . Analysis of Table 3 indicates that an insignificant difference between the theoretical and real external pattern dimensions exists . The actual enveloping parallelepiped is smaller than the theoretical one. The biggest discrepancy is observed in Y direction and reaches -2.65% . However the cross section areas of the actual beams are significantly different from the theoretical ones . The largest mismatch concerns the struts' widths C and D where errors exceed 5% . The average ratio between the actual and theoretical cross sections was estimated to be 1.09 leading to an error of about 9% . Consequently, the actual specimen porosity was estimated (by volume measurement) to be 48% instead of the theoretical value of 53%. 45 µm estimated using Alicona InfiniteFocus optical device . The arithmetic roughness was evaluated to a value of Ra = 8.6 µm, see also Fig. 7.

Elastoplastic properties of the porous tensile samples. Failure assessment proposition

In vivo, bones are mostly loaded in compression and bending . Consequently bone substitutes should be tested under such loadings . However in the case of porous substitutes, this stress state induces locally tension, compression, bending or shearing stresses . Even if tension is one of the most critical loadings leading to the structure fracture, it also seems to be necessary to address the problem of the local buckling of struts during compression loading. In the Euler buckling theory the strut slanderness is defined by the ratio between the effective buckling length Le and the square root of the I/A quotient, where I is the moment of inertia and A the area of the strut cross-section . In our pattern the buckling phenomenon is the most likely to occur for the Z-oriented struts of dimensions 0.6 x 0.6 x 0.75 mm 3 . These struts can be considered as short columns with fixed-fixed boundary condition . In this case the slenderness ratio is equal to 2.15. It is commonly accepted that compression members having slenderness ratio smaller than 30 exhibit essentially no instability and fail by yielding or crushing. So, for the value of slanderness ratio of 2 .15 there is no risk of buckling . Consequently it seems adequate to test the implants in tension .

Tensile tests on porous specimens were carried out in the three principal directions X, Y and Z. Since the transversal displacements have not been measured and the hypothesis of volume conservation is not valid for porous materials, it was impossible to calculate the Cauchy's true stress. Consequently, the nominal stress and the true strain of the gauge part of the specimen were calculated, taking into account the real sample dimensions and the correction procedure presented in Appendix .

The apparent Young's moduli, conventional yield stress Rp 0 _ 2 , ultimate strength Rm and the corresponding elongation A% of the structures were identified in each direction . The results (average values from three tests) are reported in Table 5 and compared with the corresponding properties of the cortical tissue of long bones determined by Cowin (1989). The experimental data are provided for longitudinal and transverse directions in tension and compression .

On the one hand, it was observed in Table 4 of Section 2.4 that the Young's moduli provided by the numerical calculations the elementary pattern were significantly higher than those of bone . The same remark can be made concerning the experimental results, according to Table 5. On the other hand, the direct comparison of Tables 4 and5 shows that these experimental values in X and Y directions are greater than the theoretical ones. Differences of 32% and 10% are calculated respectively taking into account the mean experimental data .

This difference can be partially attributed to the porosity of the actual samples which is lower than theoretically determined . The highest discrepancy observed in X direction can also be explained by the ratio L/ l which is relatively high compared to the other specimens . Consequently, the strain measurement is strongly influenced in that case by the bulk parts and the apparent Young's modulus deduced is overestimated .

It can also be observed in Table 5 that the conventional yield point of the porous specimens is a fonction of the sample type . The lowest value of 96.2 MPa is obtained in Y direction and is even greater than the transverse strength of cortical bone of 51 MPa (Cowin, 1989). The highest value of 133.3 MPa is observed in X direction and is comparable with the tensile longitudinal strength of 133 MPa reported by the same author. Similar values were provided by other authors, see for instance [START_REF] Reilly | The elastic and ultimate properties of compact bone tissue[END_REF] and [START_REF] Reilly | The elastic modulus for bone[END_REF] .

The values of ultimate strength are also higher for the porous structure than for bone . The ultimate apparent elongation of porous samples is relatively weak but remains greater than that of bone for directions Y and Z. In X direction the low value of titanium samples elongation A% of 3.0 is partially due to the important roughness (Rz = 45 µm) of the specimens obtained by SLM compared to the crosssection size of struts (500 x 600 µm 2 ) . Each strut can thus be considered as a notched beam with stress concentrations decreasing the apparent ultimate elongation .

The elasto-plastic properties of human bone in compression are higher than those of the porous structure in tension .

.>-...:::::--. . such as von Mises stress, equivalent plastic strain, major principal stress and plastic strain were considered. After comparative analysis between numerical and experimental results, the von Mises equivalent plastic strain appeared to be the best candidate . Consequently the following criterion was proposed : otM 0 fr where ofr = ob-i ax corresponds to the equivalent plastic strain at the maximum stress value of bulk CP titanium produced by SLM. It is admitted that to be broken a whole strut section has to undergo this level of plastic strain . According to the results presented in Section 3.1 the following critical value However, to make a reliable comparison, compression tests on porous samples should be carried out.

The average nominal stress-true strain curves for each type of sample are drawn in Fig. 8. The same Figure shows the stress-strain curves deduced from the Finite Element simulations of porous sample tensile tests . The average actual dimensions of specimens reported in Table 3 were taken into account in these FE analyses .

A good agreement between numerical and experimental curves is obtained until the fracture point of the real specimens. Table 6 summarizes the usual elastoplastic characteristics obtained via these simulations . Instead of ultimate elongations determined experimentally, the total overall strain Emax corresponding to maximal nominal stress was identified . The remaining characteristics were defined in the standard manner.

It should be noted that FE analyses have been performed without introducing a fracture criterion .

Comparing Tables 5 and6, a very good agreement between experimental and numerical values was found except for the Young's moduli in X direction . However the value appearing in Table 6 remains consistent with the one of Table 4. Furthermore, the pattern defined in this work has a wireframe structure . Consequently, the individual struts are mainly under simple stress states such as tension -compression, shearing or bending . Moreover, the tensile tests performed on porous specimens have shown that all samples broke in a ductile manner. The good concurrence between these data enables the identification of a simple failure criterion for the dimensioning of porous bone substitutes . For these reasons a simple scalar failure criterion seemed to be sufficient to predict the fracture of such porous structures . Quantities was chosen : ofr = 0.11.

To illustrate the relevance of the criterion proposed, the loading at which the full strut section experiences the critical plastic strain has been identified and compared with the experimental fracture loads, for each numerical tensile test . The corresponding critical points are marked with a dotted square in Fig. 8. It appears from this Figure that the numerical and experimental fracture points are very close. Fig. 7 shows the comparison between the iso-surfaces of otM = 0.11 and the experimental fracture facies observed with an InfiniteFocus microscope . Pictures X, Y and Z concern respectively the three numerical and experimental tensile tests on X, Y and Z porous specimens . The left part of each picture provides the FE predictions of equivalent plastic strain and the right part shows the corresponding broken strut. One can conclude that for the three samples tested the shape and location of the fracture facies and the iso-surfaces of EtM = 0.11 concord . This comparison confirms the pertinence of such a simple criterion for the porous titanium wireframe bone substitutes processed by SLM.

Conclusions

An elementary pattern of a CPPTi structure mimicking the mechanical properties of bone and favouring bone colonization was developed in this study. This pattern is characterized by a porosity of 53% due to the periodic oblong pores of relatively important dimensions 0.9 x 0.86 x 1.5 mm 3 . Analyses performed on the bulk SLM processed samples seemed to reveal that this technology is well adapted to the manufacturing of implants . Indeed, the classical elastoplastic properties of CP Ti samples obtained via this method satisfied the international standards . Moreover, no anisotropy induced by the process was detected on the manufactured specimens . The high strength of the material tested and the existence of residual compression stresses suggested that cyclic loading can safely be applied to the SLM-made structures . To complete these observations, further analyses on the residual stresses existing in the porous structure developed in this study and on its fatigue behaviour would have to be carried out.

Mechanical tests performed on porous tensile samples at ambient temperature and under quasi static conditions led to the ductile fracture of individual struts. The critical strain and stress levels corresponded to the ultimate values of these quantities obtained via tensile tests carried out on bulk SLM-made specimens. Consequently, a simple scalar failure criterion was proposed, through experimental tests and their finite element simulations, for the design of SLMmade porous bone substitutes .

Fig. 1 -

 1 Fig. 1 -Scheme of a cubic specimen used for the residual stress measurements.

Fig. 2 -

 2 Fig. 2 -Equivalent von Mises stress on the elementary pattern submitted to an apparent equivalent stress of 50 MPa in X direction.

1Fig. 3 -

 3 Fig. 3 -Tensile specimens of CPPTi (downwards: X, Y and Z type specimens).

Fig. 4 -

 4 Fig. 4 -True stress-true strain curves of the (T) bulk specimens.

Fig. 5 -

 5 Fig. 5 -{101} pole figures of alpha titanium on two faces of a cubic sample made by SLM.

Fig. 6 -

 6 Fig. 6 -Front view of the elementary pattern superimposed on its CT scan image. Cross sections of X oriented beams are plotted using dashed lines.

  6. Several configurations were tested leading to the final pattern geometry illustrated by the same Figure . The main theoretical dimensions of this pattern are referenced in this Figure and their values are summarized in Table

Fig. 6 .

 6 Fig. 7 -Comparison between the iso-surfaces of etM = 0.11 from FE analyses (on the left) and the experimental fracture facies observed with an InfmiteFocus microscope (on the right) for the three tensile specimens X, Y and Z respectively.

Fig. 8 -

 8 Fig. 8 -Experimental and numerical tensile curves of porous specimens.

Table 1 -Comparison between the SLM CP grade 2 Ti elastoplastic properties and the ISO 5832-2 (ISO 5832-2, 1999) specifications (SD enclosed in parentheses).

 1

	Property	L	SLM CP grade 2 Ti T	w	ISO
	E(GPa)	91 (12)	100 (5.5)	101 (2.6)
	Rp 0 Rm (MPa ) (MPa ) . 2	522 (18) 654 (1.5)	518 (5.5) 640 (12.4)	533 (2.1) 617 (16.7)	230 345
	A%	17.0 (3.0)	14.7 (2.9)	5.1 (2.1)	20
	,! m ' ax	12.2 (1.7)	11.3 (1.3)	3.6 (1.4)

Hypermesh software . The number of elements and degrees of freedom varied respectively from 107,204 to 204,608 and from 366,000 to 700,000, in fonction of the specimen type . The h plastic flow theory was brought into play since only a monotonie loading was considered . The hardening curve of CP Ti made by SLM determined in this work was introduced, see Section 2.2. The loading was reproduced by applying a ramp displacement -rime fonction on the nodes corresponding to the grip end of the sample. These boundary conditions enabled easy simulation of unstable specimen behaviour.

Table 2 -Residual stresses measured on the external faces of cubic specimens (MPa). Ali the values for samples 1 and 2 are given ±10 MPa.

 2

Table 3 -Theoretical and real dimensions of the pattern proposed.

 3

	Theoretical Average ex -(µm) perimental	Relative error (%)

Table 4 -Elastic properties of the elementary pattern comp et al. (2002) and Ashman et al. (1984). red to those of human cortical bones reported by Castaiio

 4

	Elastic constants	Units	Pattern	Mandible (Casta:ii.o et al., 2002)	Long bones (Ashman et al., 1984)
	E x		28,615	22,900	20,000
	Ey	(MPa)	16,399	14,200	13,400
	Ez		16,402	10,500	12,000
	vxy		0.15	0.19	0.35
	vyz Vxz		0.48 0.15	0.31 0.29	0.42 0.37
	Gxy Gyz Gxz	(MPa)	14,087 8042 8339	6000 3700 4800	6200 4500 5600

Table 5 -Comparison of properties of porous t tanium samples and bone. Data concerning bones are taken from (Cowin, 1989). Standard Deviation is indicated in brac ets

 5 .

		X (Long.)	SLM CPPTi Y (Trans .)	Z (Trans .)	Long.	Cortical bone (Cowin, 1989) Tension Compression Trans. Long. Trans.
	E (MPa) Rp 0 _ 2 (MPa) Rm (MPa)	37,887 (1388) 133.3 (1.9) 143.6 {3.6)	17 ,987 {1227) 96.2 (5.3) 129.8 (2.5)	15,824 {566) 110.S {4.1) 141.i' {4.1)	17,400 115 133	9600 51	17,400 182 195	9600 121 133
	A%	3.0 (0.5)	7.8 {1.4)	7.7 {2.7)	2.93	3.24	2.20	4.62

Table 6 -Elastoplastic properties of the tensile samples obtained numerically.

 6

		X	Specimen y	z
	Young's modulu s (MPa)	29,461	17,004	17,083
	Rp 0 . 2 (MPa) Rm (MPa) Emax	125 143 3.0	88 136 12.S	101 140 9.1

Acknowledgement

The authors wish to thank Dr J.-M . Hiver from Institut Jean Lamour, Ecole des Mines de Nancy for his participation in the computed tomography analysis of the porous samples.

Appendix

Each tensile specimen can be represented by three distinct volumes with their own stiffness connected in series, see Fig. A.1. According to this scheme, the stretch of the porous part of the specimen can be estimated allowing the determination of its strain.

Let L 0 , L, ! 0 and lbe the initial and current lengths of gauge and porous part of the specimen, respectively, see Fig. A.1. Consequently, under the hypothesis of small strains of the bulk part of the gauge length, the stiffness to be taken into account in the correction procedure can be written as

where E is the Young's modulus of bulk titanium and So the initial cross section area of the specimen .

The equilibrium of the specimen submitted to the tension force F allows the calculation of the bulk part elongation .

F U = K "

The current length of the porous part can be calculated with the current distance between the measurement points and the applied tension force

Consequently the strain of the porous part can be expressed as:

Since the transversal displacements have not been measured and the hypothesis of volume conservation is not valid for porous materials, it was impossible to calculate the Cauchy's true stress .

Consequently the nominal stress defined as below, a = F/ So has been used to draw the stress-strain curves for each specimen .


G C Gu

R Pesci

E Becker

L Langlois

R Bigot

M Scheel

Quantification and localization of the liquid zone of partially remelted M2 tool steel using X-ray microtomography and scanning electron microscopy

Keywords: Semi-solid steel forming, Thermomechanical behavior, X-ray microtomography

Thixoforming of steels poses challenges due to the high temperatures involved and the lack of understanding of thermomechanical behavior. The volume fractions of the liquid and solid phases in the semi-solid state are the most important parameters for such a forming process, as they affect the viscosity and hence the flow behavior of the material. Two-dimensional observations might not always be sufficient, as the size distribution and the connectivity of phases cannot be obtained from associated measurements, which can only be determined by three-dimensional (3-D) investigation. This paper presents the first application of high-energy X-ray microtomography to the microstructure of steel in the semi-solid state. The microstructure of M2 high-speed tool steel was studied in both as-received and heated-and-quenched states. From the reconstructed images, 3-D information could be obtained and was compared with scanning electron microscopy and energy dispersive spectrometry observations. The volume fraction and the location of liquid phase in the semi-solid state were determined in particular, and the continuous solid skeleton was investigated.

Introduction

Semi-solid metal forming processing was first discovered by Flemings and his group at MIT in the 1970s [1]. As complex parts with high mechanical properties can be formed in a single forming operation, the thixoforming processforming at the semi-solid state by reheating the material -has been of great interest to engineers and scientists. Actually, the thixoforming of light alloys such as aluminum alloys has already been industrialized [2,3] and the thixoforming of steels has recently been studied by many researchers and industries as a potential manufacturing technology for industrial components [4,5]. During this process, an appropriate quantity of liquid is required. Fundamental knowledge on the formation, location and volume fraction of liquid during the reheating step is therefore of great importance. In partially liquid metals, the liquid fraction and its location, size and shape are indeed the main concerns because these parameters directly influence the microstructure development [6] and control the rheological behavior [7] and forming process [8].

Only under equilibrium conditions can the volume fraction of liquid in the semi-solid state be given for a certain temperature; in other cases, it depends on the previous thermal history. As for the determination of the volume fraction of liquid, various approaches have been applied either by direct definition of the liquid fraction or by means of the effect on special physical properties. Tzimas and Zavaliangos [9] studied three of the methods which are used to determine the volume fraction of liquid as a function of temperature for alloys in the semi-solid state, namely thermal analysis techniques, image analysis of samples quenched from the semi-solid state and thermodynamic data. Meanwhile, the accuracy, advantages and limitations of each method were assessed and recognized. Puttgen and Bleck [10] carried out extensive DTA (differential thermal analysis) experiments at various heating rates to determine the semi-solid area of different steels. The DTA results were combined with subsequent quenched microstructure parameters such as grain size, phase distribution, volume fraction, shape factor, matrix character etc. Omar et al. [11] performed DTA and partial remelting experiments on a high-performance HP9/4/30 steel, which is difficult to manufacture through conventional processes. The results of liquid fraction as a function of temperature obtained by differential thermal analysis and image analysis on the samples quenched from semi-solid were compared and discussed. They observed that liquation occurred initially at grain boundaries, then along the segregation bands. Omar et al. [12] studied the microstructures and phases of as-annealed M2 high-speed tool steel in the as-received condition and in the semi-solid state. The role of carbide dissolution in the grain boundary liquation of the steel was described and led to the production of a microstructure suitable for the thixoforming process. The above-mentioned microstructure observation and liquid fraction calculation were studied on two-dimensional (2-D) metallographic sections obtained after quenching the sample from the semisolid state; the 2-D image analysis may not give a complete image of the structure and can sometimes lead to invalid conclusions. Thus, three-dimensional (3-D) analysis is required. Rowenhorst et al. [13] used serial sectioning to observe the distribution of particle-particle contacts in semi-solid Sn-Pb alloys at various liquid fractions. Compared to the serial sectioning, X-ray microtomography, a non-destructive technique, offers a possibility to retrieve 3-D information from a given specimen. Maire et al. [14] presented the feasibility of obtaining the total liquid volume fraction, the volume distribution, the morphology of entrapped liquid and its 3-D location, for aluminium alloy A357 samples quenched from the semi-solid state. Limodin et al. [15] investigated the overall and local microstructural changes occurring during partial remelting of an Al-15.8 wt.% Cu alloy by in situ X-ray microtomography. However, such experiments have never been performed on steel grades.

The objective of this paper is to show that the 3-D and 2-D investigations of the microstructure of the M2 steel can provide useful information about the thixoforming process regarding the liquid zones in the semi-solid state. In the present work, two different states of M2 steel are investigated: as-received and quenched material from the semisolid state. The instrumental device and the experimental procedure are described and the microstructure evolution after quenching from the semi-solid state is analysed and discussed. By comparing the results obtained by various techniques, the former liquid zones are finally well identified and quantified.

Material and methods

Material

The M2 high-speed steel used was produced by hot rolling at a temperature of around 1100 °C. After quenching, it was then annealed three times for 1 h at 540 °C. This steel was selected because it has a reasonably large freezing range (more than 40 °C) compared to other steel grades. Moreover, its high content of alloying elements leads to a relatively low solidus temperature and is very important for 3-D observation using X-ray microtomography (phase contrast mode): especially the tungsten and molybdenum elements because of their high difference in X-ray absorption compared to iron. The chemical composition of M2 steel is given in Table 1.

Methods

X-ray microtomography experiments were carried out at room temperature on the high-energy ID15A beamline at the ESRF (European Synchrotron Radiation Facility) in Grenoble, France, where the X-ray energy ranges from 50 to 100 keV. For that purpose, a rolled bar 38 mm in diameter was first induction-heated into the semi-solid state and water-quenched, and then several samples 1.2 mm in diameter were taken from this bar using electrodischarge machining. In addition, the microstructure characterization in 2-D was performed using an optical microscope and a Jeol 7001FLV scanning electron microscope (SEM). Energy dispersive spectrometry (EDS) analyses were finally done with an Oxford INCA System to study the distribution of the different alloying elements. All samples observed in 2-D were etched using 2% Nital (2 ml HNO 3 + 98 ml ethanol).

Induction heating process

The rolled bar was induction-heated by a direct remelting route, that is, heating the slugs from the as-received condition directly to semi-solid state. In order to study the microstructure evolution, the M2 slug was partially heated to the semi-solid state: some zones were in the semi-solid state at high temperature while others remained 100% solid, similar to the as-received state. The temperature of the semi-solid zone was measured by a pyrometer. After 100 s of heating time, the slug reached 1250 °C ($20% of liquid phase) and was directly quenched into a water tank without any holding time to freeze the microstructure presented in the semi-solid state and prevent the diffusion of alloy elements in the steel. The schematic view of the set-up for the induction heating experiment is shown in Fig. 1. During the induction heating process, the slug was partially inserted into the induction coil with a part sitting on a ceramic holder, to ensure the coexistence of solid and semi-solid states. As illustrated in Fig. 2, due to the effect of penetration depth, a typical bell-shaped temperature profile was therefore obtained: temperature decreased with decreasing radius and height. The bottom of the slug was slightly colder due to a deficit of heat source in this area: it remained in the solid state during induction heating. Therefore, the temperature in zone B was below the solidus temperature, which will enable us to compare both solid and semi-solid states.

X-ray microtomography experiments

Samples were electrodischarge-machined from the quenched bar for the microtomography experiments. In these experiments, each sample was mounted on translation and rotation stages in order to achieve a good alignment with the X-ray beam before the measurement and a 360°rotation for 3-D observation. In the tests, a 15 lm thick LuAG:Ce scintillator was used to convert the X-ray light into visible light. The incident X-ray beam was directed onto the rotating samples with a constant energy of 60 keV. The transmitted beam was recorded using a fast DALSTAR Pantera 1M60 CCD detector, with an exposure time of $25 ms. The effective pixel size was $1.2 lm and 3600 projections were captured. The slices were then reconstructed and the different volumes obtained were processed and analyzed with the image analysis software, ImageJ.

Results

Material in the initial state

The scanning electron micrographs of the as-received M2 high-speed tool steel obtained on transverse and longitudinal sections are presented in Fig. 3a-c. Fig. 3ci sa close-up of the area outlined in Fig. 3b. In addition, Fig. 4 illustrates the EDS results of carbides marked in Fig. 3c. The average grain size is $10 lm and the carbide particles are distributed along the grain boundaries and in the matrix. The longitudinal surface (shown in Fig. 3b) bears evidence of microsegregation banding along the longitudinal direction of the slug. Two different types of carbides present in the material were confirmed by EDS analyses (shown in Fig. 4): the whiter particles are M 6 Ctype carbides, rich in tungsten and molybdenum, while the darker ones are MC-type carbides rich in vanadium, tungsten and molybdenum. Table 2 shows the chemical composition (wt.%) of these two types of carbides. High-energy X-ray microtomography experiments were also carried out using as-received samples. Thanks to the high content of heavy alloying elements, a good contrast between the matrix and carbides could be obtained. Fig. 5 shows two tomographic slices and a reconstructed stack of a cylindrical sample of as-received M2 steel. The carbide particles are present as white zones in all images; they are relatively small -a few micrometers -and are observed to be either isolated or distributed in bands. This is in good agreement with the SEM and EDS observations.

Microstructure of material quenched from the semi-solid state

Once directly induction-heated from its as-received state to the semi-solid state, the slug was then quenched to freeze the microstructure present in the semi-solid state. Micrographs of the quenched slug are shown in Fig. 6.

It is observed that M2 now exhibits equiaxed grains 40 lm in average grain size on the transverse section, and elongated grains on the longitudinal section with an average grain size of 40 lm  65 lm. One can also note that grain boundaries in transverse section and new carbides along grain boundaries in longitudinal section can form some interconnected networks. Two kinds of carbides with a high content of tungsten, molybdenum and vanadium surrounding the grains were detected by EDS analyses (Fig. 7): large MC-type carbides which are rich in tungsten, molybdenum and vanadium, as well as finer tungstenmolybdenum-rich M 6 C-type carbides. There were no such elements remaining inside the grains compared to the asreceived state: they were now concentrated in the grain boundaries. The microstructure differs from the one in the as-received state in grain size, distribution of carbides and morphology.

X-ray microtomography images were successively recorded in parallel after quenching at room temperature. Two reconstructed slices representing the transverse and longitudinal sections of partial remelted sample are presented in Fig. 8a andb, respectively. When compared to the SEM micrographs, the similarities of the structures are very clear. It is well observed that the material evolves dramatically during partial remelting. Compared to the original carbide particles, the morphology of these reformed carbides is different in both their dimensions and localization. During induction heating, as the temperature rises, alloying elements, such as vanadium, tungsten and molybdenum among others, diffuse to the liquid zones where the solubility is higher. These liquid zones, preferably developing from the grain boundaries, appear very clearly after quenching because of their high content in alloying elements. They form new interconnected carbide networks that make the definition of the new grain size obvious. It can be conjectured that M2 steel exhibits a microstructure combining both solid and liquid phases before quenching.

As the agreement between 2-D SEM observations and X-ray microtomography results is good, the real volume fraction of liquid can be obtained by the image analyses on reconstructed stacks as shown in Fig. 9; the connected carbide networks are white zones.

With the image processing software ImageJ, the total volume fraction of carbides as a function of height and diameter of samples taken from the initial slug are shown in Fig. 10. First, it can be seen that the fraction of carbides increases with height and radius, Fig. 10a andb, but at different rates. As illustrated in Fig. 10a, for sample 1, this fraction remains stable from the bottom up to the height of 12 mm, around 11 ± 1%. Then, it grows rapidly from 11 ± 1% to 15 ± 1% from 12 mm to 17 mm in height, and seems to remain constant until 24 mm in height. Finally, it increases until reaching the value of 21 ± 1%. The evolution of carbide fraction in sample 2 and in sample 3 is quite similar to that of sample 1, but with a discrepancy of $10 mm and 14 mm in height, respectively. The expected bell-shaped profile is here confirmed. Moreover, at the same height (>23 mm), the fractions of carbides in sample 3 are smaller than those in sample 2 by 2%. In Fig. 10b, the fraction in sample 4 increases with radius, while the one of sample 6 remains relatively constant. For sample 5, it increases to 14 ± 1% after remaining at 11 ± 1% from the core until the radius of 11 mm. In addition, for the same radius, the fraction of carbides increases with height in these three samples. Furthermore, as illustrated in Fig. 10a, the zones with a fraction of carbides of 11 ± 1% in samples 1, 2 and 3 exhibit the kind of carbides seen in Fig. 3, while the ones with a fraction of carbides more than 13 ± 1% show the newly formed carbides during quenching from liquid state as presented in Fig. 6. Finally, initial carbides and new ones coexist in the zones with a fraction of carbides between 11 ± 1% and 13 ± 1%.

The microstructures of sample 1 at different heights are presented in Fig. 11. Figures marked with an S are SEM micrographs while the ones marked with a T come from X-ray microtomography images. As shown in these images, the microstructure changes in grain size and morphology depending on the standoff distance. The greater the height, the higher the temperature. At 5 mm from the bottom, the obtained microstructure is similar to the one observed in the as-received material: the majority of the carbide particles have the same dimensions and are still distributed in the matrix and bands.

With increasing temperature, most of the original carbide particles are dissolved and the alloying elements in carbides along the microsegregation bands start diffusing to the liquid zones; new carbides are being created at the grain boundaries after quenching, as illustrated by the microstructure at the height of 15 mm. At the same time, the grains are growing. Then, higher in the sample, for instance at the height of 20 mm, the process is enhanced with the development of still larger interconnected liquid zones and grains. Finally, at the heights of 25 mm and 30 mm, the original carbides are completely dissolved, with the diffusion of the alloying elements to the liquid zones, forming very large new carbides after quenching because the fraction of liquid is $21%. Small carbides can also be present inside the grains, corresponding to the entrapped liquid zones at high temperature which represent $7% of total liquid, using image analysis. In addition, the SEM micrographs and X-ray microtomography results are in quite good agreement, when taking into account the resolution of the two techniques.

Discussion

In this study, two states of M2 steel have been investigated: as-received state and quenched from the semi-solid state.

Material in the as-received state

Concerning the initial as-received state, microsegregation bands parallel to the rolling direction are observed. They are typical for most commercially produced highspeed tool steels such as M2 grade, which contain a high amount of slowly diffusing elements [11]. When comparing the SEM micrographs (Fig. 3) and X-ray microtomography slices (Fig. 5), the correspondence is good; some very small differences in grain size and carbide distribution can be observed, which may result from the 3 lm resolution of X-ray microtomography. As seen in Fig. 3, the size of many carbide particles is smaller than 1 lm, which makes them impossible to distinguish with the lower resolution of X-ray microtomography. Moreover, when the distance between several isolated carbide particles is less than 3 lm, they will probably be considered only as one large particle. In any case, the global isolated carbide particles and the segregation bands can be observed in the X-ray microtomography results. With ImageJ, the volume fraction of carbides in the as-received state is 11 ± 1%, with a relatively homogeneous distribution.

Material in semi-solid state after quenching

In the micrographic study of M2 steel, the partially remelted and quenched material exhibits a microstructure that is different from the as-received material in morphology, grain size and carbide distribution. The grains are 40 lm in size compared to 10 lm in the as-received state, and surrounded with large carbides which correspond to the former liquid zones at high temperature, as shown in Fig. 6. Puttgen et al. [16] stated that with longer holding times, the average diameter of the grain increases steadily due to the ripening process, which results in a decreasing contiguity at high temperature. It is also found that a rise in remelting temperature will increase the grain sphericity level for AISI M2 [12] and for XW-42 [17].I n the present study, we have mainly focused on the semi-solid with a low volume fraction of liquid (F l < 20%). The shape of grains is not perfectly spherical due to the high heating rate and the absence of holding time.

As shown in Fig. 2, the typical bell-shaped temperature profile marks the boundary between the semi-solid zone (zone A) and pure solid ones (zone B). Thereby the initial carbides are shown in zone B with a fraction of 11 ± 1%. When they reach the solidus temperature, alloying elements in the original carbide MC first diffuse into the liquid zone and form large new carbides when quenched as presented in Fig. 12: microstructure of sample 1 at the height of 14 mm. With increasing temperature above the melting point of M 6 C, all original carbides at the grain boundary are dissolved and new carbides are created during the following quenching process as shown in Fig. 11S(d). As the temperature increases with height, the diffusion process is enhanced with the development of interconnected liquid zones in higher positions. Small carbides are also observed inside the grains, corresponding to the entrapped liquid zones at high temperature. This is due to the high heating speed and the short holding time that prevent all the alloying elements from diffusing completely to the liquid zones. Here, due to the resolution of X-ray tomography, few carbides allocated in grains are detected when comparing the images presented in Fig. 11 obtained by two techniques. Thus, based on the X-ray microtomography results, the fraction of carbides over 13 ± 1% is considered to be the real liquid fraction.

Since sample 6 was taken from zone B (solid state), the fraction of carbides is relatively constant, which means that the distribution of original carbides is homogeneous. Indeed, the temperature distribution in the radial direction is similar to that in the axial direction: temperature increases with increasing radius, the evolution of microstructure in the radial direction is similar to that in the axial direction. Fractions of carbides of sample 4 and 5 in zone A (semi-solid state) increase with the radius, with higher values on the surface than in the core of the slug. Meanwhile, temperature is also height-dependent: the higher the position, the higher the temperature. For the same position, fractions of carbides of different samples are compared in Table 3. By comparing these values, the axisymmetrical temperature field in the heated bar is confirmed.

When comparing the grain size at various heights, it is noted that the grains stop growing when large connected liquid bands are formed, which may be related to the carbide pinning of grain boundaries [12]. There is a significant grain growth during reheating when comparing the grain size of the as-received state and of quenched from the semi-solid state. In general, the grain grows with increasing temperature and holding time. It is important to study the grain growth during reheating, as large grains cannot flow into thin sections as easily as those of a finer size. Furthermore, the mechanical properties of the part will be weakened if the grain size is larger. One explanation for the grain growth was proposed by Omar et al. [18]: the grain growth and diffusion process are thermally activated. They are also related to the liquid fraction, because liquid provides a much faster diffusion path than solid, and once a continuous liquid path is present around the solid phase, coarsening can accelerate, which results in the grain growth. In addition, grain coalescence is also thought to be an important factor to the grain growth, as stated by Tzimas and Zavaliangos [19].

The obtained microstructure at high temperature is not exactly the most typical one for thixoforming -solid spherical grains surrounded by a liquid matrix -but the semisolid zone with a liquid fraction ranging from 16% to 20% interconnected at the grain boundaries makes it suitable for thixoforming, as discussed below.

First, although there is a significant grain growth from the as-received state, the grains are relatively equiaxial with a final grain size around only 40 lm. Then, the billet contains low liquid fraction in the semi-solid zone (15-25%) mainly developed from the grain boundaries. The advantages of such a microstructure have been introduced in Ref. [20]. Some M2 [21] and C38 [22] steels have been successfully thixoformed with such a liquid fraction. Finally, as shown in Fig. 11S(d), the microstructure at a height of 15 mm in sample 1 exhibits thin liquid films formed at grain boundaries, which may not be sufficient for grains to flow freely against each other. With the increasing height, the temperature increases too. The liquid films thicken with increasing temperature, as shown in Fig. 11S(a) and S(b). They will result in a reduction of solid skeleton consistency, which may be easier to fracture during thixoforming. Thus, these microstructures might behave in a thixotropic way, flowing when stressed and thickening under normal conditions. In our future work, it will be necessary to study the load-displacement curves of thixoforging process in order to better understand the relationship between the microstructure and the behaviour of the steel.

Conclusion

After being induction-heated and water-quenched, the microstructure evolution of an M2 steel was monitored and examined with various 2-D and 3-D techniques. While the as-received material showed microsegregation bands in longitudinal section and homogeneously distributed small carbides in transverse section, with MC-type and M 6 C-type carbides identified by EDS analyses, the partially remelted material exhibited a different microstructure. The grains were bigger, and the solid phase was surrounded with the new large carbides formed during quenching, which corresponded to the former liquid zones at high temperature. During heating, most of the liquid appeared in the microsegregation bands that can form interconnected networks. All this leads to the conclusion that the microstructures obtained at high temperature are suited to the thixoforming process, owing to the good liquid fraction (15-20%) and the interconnected networks.

Furthermore, the good agreement between 2-D SEM-EDS microstructures and 3-D X-ray microtomography results proves that both kinds of techniques are just as efficient in characterizing high-alloyed steels in the semi-solid state. This last point is of great importance because even though high-energy X-ray microtomography has proven to be a powerful tool, it is not as easy to use, nor as ubiquitous, as SEM and EDS techniques that are more readily accessible in laboratories and actually just as well-adapted for this kind of analysis.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Schematic view of (a) the set-up for induction heating experiments and (b) the position of samples for X-ray microtomography.

Fig. 3 .Fig. 4 .

 34 Fig. 3. SEM micrographs of as-received M2 steel on (a) cross-sectional surface and (b) longitudinal surface. (b) Shows the carbide segregation causedby forging. (c) Is a the area outlined in (b) with two kinds of carbide: M 6 C and MC.

Fig. 5 .

 5 Fig. 5. X-ray microtomographic results of as-received M2 steel. Carbides are shown as white zones in (a) transverse section, (b) longitudinal section and (c) reconstructed 3-D stack.

Fig. 6 .

 6 Fig. 6. SEM micrographs of the M2 steel quenched from semi-solid state. (a) Transverse and (b) longitudinal directions. (c) Is a close-up of the area outlined in (b) and shows two kinds of carbide. FL: former liquid phase; EL: entrapped liquid; S: solid phase.

Fig. 7 .

 7 Fig. 7. SEM-EDS mapping of the M2 quenched from the semi-solid state.

Fig. 8 .

 8 Fig. 8. 2-D reconstructions of partial remelted and quenched sample 1. (a) Transverse and (b) longitudinal sections. FL: former liquid phase; EL: entrapped liquid; P: porosity.

Fig. 9 .Fig. 10 .

 910 Fig. 9. 3-D representation of M2 steel in partial remelted and quenched state. Volume = 0.6 mm  0.6 mm  0.16 mm.

Fig. 11 .

 11 Fig. 11. SEM micrographs and X-ray microtomography slices observed at different heights in sample 1.

Fig. 12 .

 12 Fig. 12. Microstructure of sample 1 at the height of 14 mm.

Table 2

 2 The characteristic chemical compositions of the large and fine carbides.

	Elements	Carbide (wt.%)
		VC r	F e	M o	W
	Whiter particles	3.65	2.88	30.4	24.87	38.29
		2.55	3.19	34.2	22.37	37.69
		3.05	3.04	32.22	25.35	36.34
	Darker particles	34.72	4.76	9.3	23.98	27.25
		32.7	4.61	10.43	23.67	28.6
		35.32	5.06	10.06	20.72	28.88

Acknowledgements

The authors warmly thank Luc Morhain and Marc Wary (Arts et Me ´tiers ParisTech CER Metz) for their technical support.


A Kaissoine
email: abdou.kaissoine@telecom-paristech.fr

B Huyart
email: huyart@telecom-paristech.fr

K Mabrouk
email: 2kais.mabrouk@esigetel.fr

Demodulation of aggregated RF Signal in three Frequencies bands with a Unique Rx Chain

Keywords: spectrum aggregation, down converter, RF receiver, LTE-Advanced, Three phase demodulator, Zero-IF, Low-IF

Among the concerns of 4th generation wireless communication networks, there is the lack of desired bandwidth in a continuous manner in the frequency spectrum. The recommended solution is to transport the information on a Radio Frequency (RF) signal constituted of discontinuous frequency bands. Nowadays, the receiver architecture is generally constituted of n chains of receiver (Rx), n being the number of aggregated frequency bands. This paper demonstrates theoretically and practically that the demodulation of a RF signal having three discontinuous frequency bands can be made by a single Rx chain. The principle consists in down converting aggregated RF signal by mixing with a local oscillator (LO) signal constituted by n Continuous Wave (CW) signals. Using this technique the transposed signals occupy a narrow frequency band.

I. INTRODUCTION

The frequency band of RF signal used in 4th generation mobile communication networks, also known as LTE-A (Long Term Evolution Advanced), will reach values of the order of 100MHz in order to provide high data rate of 1 Gbits/s [START_REF] Shen | Overview of 3GPP LTEAdvanced Carrier Aggregation for 4G Wireless Communications[END_REF], [START_REF] Yuan | Carrier aggregation for LTE advanced mobile communication systems[END_REF], [START_REF] Najah | LTE, LTE-ADVANCED AND WIMAX[END_REF]. This bandwidth is available in the high frequency spectrum, but due to limits of the RF propagation channel, it is planned to transmit the information on different carrier frequencies. The spectrum of the RF signal is so composed of discontinuous frequency bands. Today, telecom operators like AT & T, for example, plan to use the aggregation of band 4 (1710-1785 MHz) and band 17 (734-746 MHz) [START_REF] Shen | Overview of 3GPP LTEAdvanced Carrier Aggregation for 4G Wireless Communications[END_REF]. The usual solution for designing the receiver is to double the number of Rx chain in order to simultaneously demodulate both frequency bands of the RF signal. In the case of 2 bands, another way is to use the architecture of the Weaver demodulator and a LO frequency equals approximately to the half of both carrier frequencies [START_REF] Wu | A 900-MHz/1[END_REF], [START_REF] Kitayabu | Implementation of Concurrent Dual-Band Receiver Using IF Undersampling[END_REF]. However, in the case where the number of aggregated frequency bands is upper than 2, these solutions become expensive or unworkable. In parallel to our research works, a team of NTT published in [START_REF] Kaho | A simultaneous receiving multi-band mixer with independent gain control[END_REF] practical results on the transposition by a mixer of a RF signal constituted of two frequency bands. The used technique is similar to that developed in this paper and consists in using a LO signal composed of two CW frequency tones.

In this paper, the technique of mixing with a multi-tone LO signal is applied directly to the demodulation of a RF signal which has spectral components distributed on three different frequency bands. The theoretical principle is given in section II and is validated by measurement results which are presented in section III.

II. THE PRINCIPLE OF THE DOWN CONVERSION OF FREQUENCY AGGREGATED SIGNALS

The technique is the mixing of the frequency aggregated RF signal with a LO signal composed of 3 CW signals. Let us consider a RF signal composed of three discontinuous frequency bands centered respectively at frequencies f 1 , f 2 and f 3 and of bandwidth BW 1 , BW 2 and BW 3 . The expression of the aggregated RF signal is defined as follows:

3 2 1 ( ) Re[ ( ) ] j j f t RF j j v t Z t e     (1) with, () ( )
( ) j jt j j Z t a t e  
j=1,2,3 the complex envelope of the three carrier frequencies f 1 , f 2 and f 3 .

In our case the objective is to lower the frequency bandwidth of the converted signals to relax the required performances of the Analog to Digital converter (ADC).

The strategy is consequently to convert the three frequency bands of the RF signal to Zero Intermediate Frequency (ZIF) for one, Low Intermediate Frequency (LIF) at frequency Δf 2 for the second one and LIF at frequency Δf 3 for the third.

In order to obtain these IF signals, the three CW frequencies of the LO signal are equal to f 1 , f 2 -Δf 2 and f 3 -Δf 3 with Δf 2 > BW 1 /2 and Δf 3 > BW 2 /2 + Δf 2 . Thus the expression of the LO signal is expressed as follows:

11 3 (2 ( ) ) (2 ) 2 ( ) Re[ ] j j ij i j f f t j f t LO LOi LOi j v t V e V e           (2)
with V LOi , the amplitude of the CW signals and angles φ ij , the phase shifts between LO and RF signals and i and j represent respectively the number of RF paths of the demodulator and of the RF signal frequency bands.

If the low-pass filter at the output of the mixer has a cutoff frequency:

3 3 /2 LPF f f BW   
(3) and that the following conditions are fulfilled:

3 2 1 2 1 3 1 3 2 LPF LPF LPF f f f f f f f f f f f f                (4)
The output signal of the mixer k of the demodulator is expressed as:

  1 1 1 1 3 2 v ( ) ( ) ( ) A a ( ) cos( ( ) ) V A cos( 2 )) k k LO RF k k LO kj j j j kj j t LPF v t v t t t a f t                        
(5) where A kj , j=1,2,3 are gains that include the conversion gain of the mixer and the losses of splitters, phase shifters and filters.

Regarding conditions (4) the six unwanted intermodulation products between RF signals and LO signals are eliminated.

The equation [START_REF] Kitayabu | Implementation of Concurrent Dual-Band Receiver Using IF Undersampling[END_REF] proves that the first frequency band is transposed directly to baseband around zero, it is a ZIF demodulation. The second band is transposed to the intermediate frequency Δf 2 , it is the first LIF demodulation. And the third band is transposed to the intermediate frequency Δf 3 , it is the second LIF demodulation.

Moreover the separation between the three baseband spectrums is possible if:

2 2 1 3 3 2 2 / 2 / 2 / 2 / 2 f BW BW f BW f BW            (6)

III. EXPERIMENTAL RESULTS

A. Description of the test bench

The Fig. 1 presents the measurement bench. Three sources E8267 (Agilent Technologies) generate modulated signals of carrier frequencies 2 GHz, 2.3 GHz and 2.6 GHz. These signals are added by a 3-way combiner (Anaren 043020). The output signal of the combiner is the RF signal aggregated in frequency bands. The I(p) and Q(p) numerical data are generated from a PC using Matlab software. The numerical frame is composed of a 16 symbols training sequence with Constant Amplitude Zero Autocorrelation (CAZAC) followed by a Pseudo Noise (PN9) data sequence. The carrier frequencies are modulated in different modulation format QPSK (Quadrature Phase Shift Keying), 8PSK (8-ary phase shift keying) or 16QAM (16 Quadrature amplitude modulation). However the modulation format is always QPSK in the case of the CAZAC sequence as the required signal to noise ratio is lower for this modulation format. Each numerical frame is filtered by a Square Root Raised Cosine filter (SQRC) with a roll-off equal to 0.35 which will be used also at the reception.

The filtered numerical frames are sent to the E8267 generators that operate in the mode ARB (arbitrary waveform generator) via the Local Area Network (LAN) constituted of a HP J2600A HUB.

On the other hand, the LO dedicated to the down conversion of the frequency aggregated RF signal have to be designed. According to II, we need to know the bandwidth of the three modulated signals.

In this demonstration, the symbol rate is low (100 kS/s) and is fixed by the components performances of the test bench (Low Frequency signal amplifier, data acquisition card, PC ...). To fulfill the condition (6), the lower frequency band centred to 2 GHz is down converted to ZIF and both upper frequency bands centred respectively to 2.3 GHz and 2.6 GHz are transposed to LIF around 200 KHz and 400 KHz. So the required LO signal is a combination of three CW signals of frequencies 2 GHz, 2.2998 GHz and 2.5996 GHz. In this experience, the power levels of CW signals are identical and equal to 7dBm. These three signals are respectively delivered by 3 sources (Agilent E4431B, Anritsu MMG369B and HP4432B). All these sources are synchronized by using the same clock signal at frequency 10 MHz. [START_REF] De La Morena-Álvarez-Palencia | Direct Baseband I-Q Regeneration Method for Five-Port Receivers Improving DC-offset and Second-Order Intermodulation Distortion Rejection[END_REF], [START_REF] Mabrouk | 3-D Aspect in the Five-Port Technique for Zero-IF Receivers and a New Blind Calibration Method[END_REF] demonstrate that if V 2 (t) output is symmetric in comparison with 2 others, the three output signals of the TPD can be added by an analog circuit of IQ regeneration (Fig. 3) performing the following operations:

1 2 3 ( ) [ ( ) 2 ( ) ( )] out I I t V t V t V t        (7) 1 3 ( ) [ ( ) ( )] out Q Q t V t V t     (

B. Measurement results

The spectrum of the baseband I out signal shows we obtain three different spectrums in baseband centered respectively between 0-67.5 KHz (ZIF configuration),133-267 KHz (first LIF configuration) and 333-467 KHz (second LIF configuration) (Fig. 4).

In the case where the 3 carrier frequencies are modulated in QPSK format, Fig. 5 shows the three demodulated QPSK constellations are recovered and centred. The power level for each band of the RF signal was equal to -30 dBm. The red points show that the synchronization CAZAC sequence functions correctly. The performance of the demodulation is measured by the Error Vector Measurement (EVM) metric in function of the input power level of the RF signal (Fig. 6). These results show that more the IF frequency is close to zero frequency more EVM value is high. This can be explained by secondorder inter-modulation distortion (IMD2). These spurious signals degrade more the ZIF converted band than both the LIF ones. Next, modulations QPSK, 8PSK and 16 QAM respectively were applied to signal carrier frequencies 2 GHz, 2.3 GHz and 2.6 GHz. For the same power level of -30 dBm for each frequency band of the RF signal three IQ constellations were measured. Fig. 7 shows that the symbols are centred and synchronized. As previously, the measured value of EVM of the signal demodulated in ZIF is higher than (Fig. 8) those in LIF. The result of the Fig. 9 shows that if the IF frequency is close to zero frequency, the intermodulation products are more significant. This is may be an explanation for the deterioration of the demodulated signal in ZIF than those demodulated in LIF, although the level of spurious lines is low.

IV. CONCLUSION

The technique presented in this paper makes it possible to demodulate a frequency aggregated RF signal with a single chain Rx. The RF signal was constituted of three discontinuous carrier frequencies modulated with the same modulation QPSK, or different modulations QPSK, 8PSK and 16QAM. The bandwidth of the down converted RF signal is limited to the interval (0, 500 KHz) that makes possible to use low cost ADC. In the case of a classical structure using a mono-ton LO signal the frequency bandwidth of the signal to sample would be (0, 600 MHz). This technique represents a good alternative in term of cost and volume to the usual one which uses as much of receiver Rx as the number of frequency band of the RF signal. The measurement results of the spectrums of the down converted signals, constellation and EVM validate the proposed theoretical method. In addition, our results also confirm that the signal demodulated in LIF configuration is less damaged than the signal demodulated in ZIF. Soon, the solution will be generalized and applied to n bands with high bandwidth of modulation according to the requirements of LTE-A.

Fig. 1

 1 Fig. 1 Test Bench for the demodulation of RF signal aggregated in frequency. The RF and LO signals is applied to the inputs of a Three Phase Demodulator (TPD) instead of the Classical In phase and Quadrature (CIQ) demodulator. Indeed, a previous paper [7] has shown TPD gives a gain of 20 dB in second-order inter-modulation distortion (IMD2) rejection in comparison with CIQ. The operation mode of TPD differs from the CIQ. The RF and LO signals are divided into three paths instead of two. The phase shift between the LO signals is equal to +-120° for the TPD instead of 90 ° for the CIQ. The CIQ delivers directly the IQ baseband signals. In the case of the TPD, the output signals are three low frequency signals, named V 1 (t), V 2 (t) and V 3 (t). The TPD (Fig. 2) was essentially realized using COTS components. The phase shifters were made with microstrip propagation lines. The phase shift varies from 60 ° to 150 ° in function of frequency in the range 2 to 4.2 GHz. The splitters insertion loss is 5

Fig. 2

 2 Fig. 2 Three Phase Demodulator

8 )

 8 Both μ I and μ Q constants are determined by a classical equalization procedure.

Fig. 3

 3 Fig. 3 Circuit of IQ regeneration The sampling frequency of the I out and Q out data (Spectrum data acquisition card MI3033) is equal to 1 MHz. The numerical data contain a mix of the information spread over 3 discontinuous frequency bands. A step of separation of the three bands is performed by a digital filter. Then equalization of I out and Q out data is performed using the CAZAC training sequence. Finally the transmitted I(t) and Q(t) signals are recovered .

Fig. 4 Fig. 5

 45 Fig. 4 Power Spectral Density in dBm/Hz of Iout signal in function of frequency in kHz.

Fig. 6

 6 Fig. 6 EVM in dB in function of RF input power level in dBm of the RF signal constituted of 3 carriers QPSK modulated.

Fig. 7

 7 Fig. 7 Phase constellation of 3 discontinuous frequency bands RF signal with QPSK, 8PSK and 16 QAM modulations.

Fig. 8

 8 Fig. 8 EVM in dB in function of RF input signal in dBm constituted of 3 carriers modulated by QPSK, 8PSK and 16QAM signals.Finally we realized the mixing of a RF signal constituted of three carrier bands unmodulated with a LO signal whose CW signals are shifted to 0 Hz, 200 Hz and 400 Hz compared to the aggregated frequency bands. In this measurement, the RF signal is constituted that CW signals at the frequency 2 GHz, 2.3 GHz and 2.6 GHz. The

Fig. 9

 9 Fig. 9 Power Spectral Density in dBm/Hz of the baseband Iout signal in function of frequency in kHz.

ACKNOWLEDGMENT

We thank the Islamic Development Bank (IDB) for its financial support.