J Du

T Höschen

M Rasinski

S Wurster

W Grosinger

J-H You
email: you@ipp.mpg.de

Feasibility Study of a Tungsten Wire Reinforced Tungsten Matrix Composite with ZrO x Interfacial Coatings

Keywords: A. Metal-matrix composites, B. Fracture toughness, B. Interfacial strength, B. Debonding, Fiber push-out test

Brittleness problem imposes a severe restriction on the potential application of tungsten as high-temperature structural material. In this paper, a novel toughening method for tungsten is proposed based on reinforcement by tungsten wires. The underlying toughening mechanism is analogous to that of fiber-reinforced ceramic matrix composites. Strain energy is dissipated by debonding and frictional sliding at engineered fiber/matrix interfaces. To achieve maximum composite toughness fracture mechanical properties have to be optimized by interface coating.

In this work, we evaluated six kinds of ZrOx-based interface coatings. Interfacial parameters such as shear strength and fracture energy were determined by means of fiber push-out tests.

The parameter values of the six coatings were comparable to each other and satisfied the criterion for crack deflection. Microscopic analysis showed that debonding occurred mostly between the W filament and the ZrO x coating. Feasibility of interfacial crack deflection was also demonstrated by a three-point bending test.

Introduction

Tungsten is currently the most favored candidate for the plasma-facing material of nuclear fusion reactors due to its refractory nature, excellent surface erosion resistance and good thermal conductivity. On the other hand, inherent brittleness and further embrittlement to be caused by neutron irradiation or recrystallization are the most critical drawbacks limiting its structural application. In this context, enhancement of the tungsten toughness has been one of the paramount R&D issues in the fusion reactor materials community. In general conventional metallurgical methods have been applied in order to improve the toughness including alloying with rhenium to increase ductility and severe plastic deformation or mechanical alloying followed by HIP to form a nanometer-sized microstructure [START_REF] Lässer | Structural materials for DEMO: The EU development, strategy, testing and modeling[END_REF][START_REF] Rieth | Limitations of W and W-1%La 2 O 3 for use as structural materials[END_REF][START_REF] Faleschini | Fracture toughness investigations of tungsten alloys and SPD tungsten alloys[END_REF][START_REF] Kurishita | Development of ultra-fine grained W-TiC and their mechanical properties for fusion applications[END_REF]. Oxide particles dispersion could increase the creep strength but reduced the tensile elongation [START_REF] Rieth | Limitations of W and W-1%La 2 O 3 for use as structural materials[END_REF]. There is a strong restriction in the chemical composition of plasma-facing tungsten, because the requirements of plasma compatibility and reduced activation have to be fulfilled. This limitation impeded flexible application of various metallurgical options. In spite of intensive research efforts, the hitherto achieved progress is still distant from the design specifications. Microstructural instability at high temperatures and damage under intense neutron irradiation are the main challenges. Therefore, there is an urgent need to explore a novel toughening mechanism which is able to function under such fusion-relevant loading environment.

Since last two decades, active research efforts have been conducted to develop long fiberreinforced ceramic matrix composites (FCMCs) for high-temperature structural applications.

Toughness of FCMCs has been notably improved and overall mechanical performance was successfully approved in several industrial applications (e.g. brake disks of an aircraft or a racing car) [START_REF] Chawla | Ceramic Matrix Composites[END_REF][START_REF] Evans | Design and life prediction issues for high-temperature engineering ceramics and their composites[END_REF][START_REF] Evans | Perspective on the development of high-toughness ceramics[END_REF]. The working principle of a high toughness FCMC is the non-plastic energy dissipation caused by controlled interfacial cracking and subsequent frictional sliding at the debonded fiber/matrix interface [START_REF] Chawla | Ceramic Matrix Composites[END_REF][START_REF] Evans | Design and life prediction issues for high-temperature engineering ceramics and their composites[END_REF][START_REF] Evans | Perspective on the development of high-toughness ceramics[END_REF][START_REF] Budiansky | Fiber-matrix debonding effects on cracking in aligned fiber ceramic composites[END_REF]. When a propagating primary matrix crack meets an array of fibers standing perpendicular to the crack faces, the primary crack can deflect along the vertical interfaces, provided a specific fracture mechanical condition is satisfied. Then the strong fibers collectively bridge the primary crack suppressing its dynamic extension. As the applied load is increased, the interfacial debonding may continue followed by fiber pull-out and the matrix crack opens further in a controlled manner. The total amount of the consumed energy is the measure of apparent toughness. The toughening mechanism of a FCMC is by now well understood in terms of fracture mechanics where fracture mechanical properties of interface are the determining parameters. This toughening mechanism of FCMCs would also have validity for brittle tungsten provided that reinforcing fibers are strong enough and their interfaces are suitably engineered. Tungsten wire-reinforced tungsten matrix composite (W f /W) is a candidate. Commercially available tungsten wires are generally very strong (tensile strength: >2.7 GPa) and quite ductile. This beneficial property is ascribable to extremely textured fine-grained structure. Hence the original toughness of tungsten wires can be utilized until the wires become fully embrittled during fusion operation. The amount of its contribution to the total toughness of a W f /W composite will depend on the volume fraction of the wires. On the other hand, the overall chemical purity will be just slightly modified by interface coating because only thin (<1µm) films are used. To author's knowledge there is no previous publication in literature dealing with this kind of tungsten composites prior to authors'. The idea of a novel W f /W composite based on a fundamentally different toughening mechanism was the motivation of the present work [START_REF] Du | Interfacial fracture behavior of tungsten wire/tungsten matrix composites with copper-coated interfaces[END_REF][START_REF] Du | Shear debonding behavior of a carbon-coated interface in a tungsten fiber-reinforced tungsten matrix composite[END_REF].

As in the FCMC technology, one of the major engineering challenges is how to optimize the interface coating. To this end, integrated evaluation of fracture mechanical and metallurgical behavior of the engineered interface is needed. A fiber push-out test can provide relevant material data and information on microscopic failure feature of an interface. In this paper we present the results of extensive fiber push-out experiments conducted on W f /W composites either with ZrO x single-layer or Zr/ZrO x multi-layer interface coating. Single-filament minicomposite specimens were used. Interfacial parameters were determined by calibrating with theoretical equations. Microscopic analysis of the internal interface domains was carried out before and after a push-out test by means of scanning electron microscopy (SEM) and focused ion beam (FIB) preparation.

Experiment

Fabrication of composite specimens

A commercial tungsten (W) wire with diameter of 150 µm was used as fiber reinforcement.

The W wire was wound on two square stainless steel frames (edges: 10 cm) with interval of a couple of millimeters and put into a magnetron sputtering device for coating the wire surface.

Six different ZrO x coatings were prepared as follows (see Figure 1): ZrO x single-layer films with three different average thicknesses (150, 400, 900 nm, respectively), a ZrO x single-layer film (140 nm) with a W protection film (140 nm), a Zr/ZrO x multi-layer film (35 nm/55 nm each) and a W/ZrO x multi-layer film (90 nm/90 nm each). Both multi-layer coatings consisted of five ZrO x films and five Zr or W films in an alternating way. Each of these coating layers shall form an engineered filament/matrix interface. The coated filaments were further coated with tungsten by CVD process using tungsten hexafluoride at 550°C to form a dense matrix mantle on the coated filaments. The fabricated single-filament W f /W composite rods had a diameter of 2.5 mm and length of 35 mm. To produce push-out test specimens the cylindrical rods were carefully sliced into thin discs with four different thicknesses ranging from 50 to 300 µm and finished by fine-polishing. It is generally expected that cutting of a composite rod into thin specimens would partially relax the residual stress. But this effect did not appear in our case since there was no residual thermal stress in the W f /W composite. Figure 1 shows the longitudinal sections of the four different as-fabricated interface coatings. The micrographs exhibit intact adhesion between the individual layers. Porosity was found in the W protection film whereas the zirconium oxide layers were dense.

Push-out test

Fiber push-out test has been widely applied to probe the interface properties of various fiberreinforced composites. At the same time theoretical models of push-out mechanics has been developed to interpret measured push-out responses and to calibrate interface parameters [START_REF] Greszczuk | Theoretical studies of the mechanics of fiber-matrix interface in composites. Interface in composite[END_REF][START_REF] Shetty | Shear-lag analysis of fiber push-out (indentation) tests for estimating interfacial friction stress in ceramic-matrix composites[END_REF][START_REF] Parthasarathy | Extraction of interface properties from a fiber push-out test[END_REF][START_REF] Liang | Mechanics of the fiber pushout test[END_REF][START_REF] Kalton | Measurement of interfacial fracture energy by single fiber push-out testing and its application to the titanium-silicon carbide system[END_REF][START_REF] Kerans | The role of the fiber-matrix interface in ceramic composites[END_REF][START_REF] Jero | The contribution of interfacial roughness to sliding friction of ceramic fiber in a glass matrix[END_REF][START_REF] Kerans | Theoretical analysis of the fiber pull-out and push-out tests[END_REF]. In this study we used an instrumented macro-indentation device (< 2kN) for push-out test.

Details of the device, specimen and test procedure are found elsewhere [START_REF] Du | Interfacial fracture behavior of tungsten wire/tungsten matrix composites with copper-coated interfaces[END_REF][START_REF] Du | Shear debonding behavior of a carbon-coated interface in a tungsten fiber-reinforced tungsten matrix composite[END_REF].

In Figure 2 a typical push-out curve measured on a ZrO x single-layer coating (140 nm) is plotted. The original load-displacement curve (no.1) is compared with the calibrated one (no.2) which was obtained by subtracting the machine compliance. The corresponding pushed-out filament is also shown in the box. The area below the curve indicates the total amount of work done by the applied load. The other coatings showed also similar characteristics in overall push-out responses.

In the initial loading phase the response was nearly linear elastic until it reached the maximum Beyond the maximum friction load fr p at D frictional resistance decreased gradually as the remaining contact area diminished. In this regime the applied work is mostly dissipated by cracking and frictional sliding at the interfaces. Push-out test was repeated five times for each specimen thickness.

Calibration of material parameters

The estimated material parameters of the interfaces are shear strength d τ , radial roughness stress r σ , friction coefficient µ , (roughness-induced) frictional shear stress r τ and fracture energy (toughness) i Γ . These parameters were calibrated by means of numerical regression using the theoretical equations of selected shear-lag models (cf. Appendix) [START_REF] Du | Interfacial fracture behavior of tungsten wire/tungsten matrix composites with copper-coated interfaces[END_REF][START_REF] Du | Shear debonding behavior of a carbon-coated interface in a tungsten fiber-reinforced tungsten matrix composite[END_REF]. d τ is defined as the maximum value average shear stress attains at push-out load d P before an interface begins to fail. d τ was calibrated by fitting the measured d P vs. H data with eq.(A1),

where H denotes the specimen thickness.

During the shearing motion of a debonded filament the asperity mismatch between two contacting faces generates strain oriented normal to the interface. We call the corresponding stress radial roughness stress r σ . r σ and friction coefficient µ were calibrated by fitting the measured fr P vs. l data with eq.(A2), where l denotes the embedded filament length at fr P

( o d H l - =
). The frictional shear stress r τ was calculated using the relation

Results and discussion

Interfacial parameters

In Figures 3,4 τ of the ZrO x single layer and the W/ZrO x single-/multi-layer coatings ranged from 360 to 440 MPa whereas i Γ ranged between 3 and 6 J/m². Apart from the Zr/ZrO x multi-layers, there seems to be no definite evidence of any multi-layer effect or thickness dependence. i Γ of the ZrO x single-layer was also calibrated using eq.(A5). The two values agreed well with each other within 2.4 % error.

All ZrO x -based coatings exhibited rather uniform and large values of µ (>1) indicating a significant contribution of roughness. One of its physical origins is the small debris of the coating film attached on the broken interfaces as shown in Figure 6. In addition, the tungsten filaments have inherent surface asperity produced by the wire drawing process. Normally the interface of a FCMC has smaller µ values ranging between 0.1~0.6 because ceramic fibers have a smooth surface.

In the case of the carbon coating, its d τ , r τ and µ were significantly smaller compared to the ZrO x -based coatings but its i Γ was larger. This feature indicates a lubricating property of the carbon film.

As to the copper-based coatings, the W/Cu multi-layers showed a similar range of parameter values as the ZrO x single layer coatings. The Cu single layer (170 nm) with two W protection films on both sides (50 nm) had particularly large values of i Γ and r σ whereas its d τ and µ were comparable to those of the ZrO x -based coatings. Electron micrograph revealed that the thin Cu films ruptured without any notable plastic flow in contrast to the thicker counterpart (420 nm) which underwent extensive plastic deformation [START_REF] Du | Interfacial fracture behavior of tungsten wire/tungsten matrix composites with copper-coated interfaces[END_REF]. The brittle rupture behavior of the thin copper film is due to the limitation of dislocation glide path. The parameters of the thicker Cu film could not be evaluated within the linear elastic shear-lag models.

One important implication of the estimated i Γ data is that they satisfy the fracture-mechanical criterion for crack deflection at the interface. According to the pioneering work of He and

Hutchinson [START_REF] He | Crack deflection at an interface between dissimilar elastic materials[END_REF], interfacial cracking in a bi-material bond joint under tension requires that the ratio f i Γ Γ be smaller than a specific value depending on elastic mismatch between the two bonding partners. Here, f Γ denotes the fracture toughness of the material in front of an approaching crack. If the elastic mismatch is negligible as in the present case where both fiber and matrix are tungsten, then the critical value is reduced to 0.25. But it is noted that this value was originally derived for a flat interface. The f Γ value of a commercially available tungsten wire is typically about 300 J/m² [START_REF] Conner R D | Mechanical properties of tungsten and steel fiber refinforced Zr 41.25 Ti 13.75 Cu 12.5 Ni 10 Be 22.5 metallic glass matrix composites[END_REF]. Substituting this value and the i Γ data into the criterion above, one finds that the requirement of crack deflection along interface is obviously satisfied ( f i Γ Γ : 0.01~0.02). It is well known that the capability of energy absorption (a measure of toughness) of a FCMC is actually determined by this ratio. τ value of the ZrO x /filament interface has to be interpreted as effective shear strength averaged over the length. The bonding at the W film/ZrO x interface and the W film/W matrix interface was fully intact.

Microscopic investigation

Figure 8 shows the pushed-out filaments of the ZrO x single-layer coatings with three different thicknesses (a: 150 nm, b: 400 nm, c: 900 nm) together with the longitudinal sections of the corresponding interface domains. It is seen that the filament surface with the 150 nm ZrO x coating was only partly covered indicating that the bond strength at both sides of the ZrO x film were comparable. On the contrary, the thicker ZrO x coatings (b, c) showed a debonding feature identical to the aforementioned W/ZrO x single-layer coating case. However, the measured parameters of the 900 nm coating did not coincide well with those of the W/ZrO x single-layer coating in spite of the similarity in their microstructural fracture feature. On the other hand, the analogy of the parameters between the 150 nm coating and the W/ZrO x singlelayer coating was a rather unexpected outcome since the failure features of the two coatings were quite different. A columnar grain structure is visible at the matrix side of the 900 nm coating. Figure 10 shows the pushed-out filament of the W/ZrO x multi-layer coating (a) and magnified views of the multi-layer at the ruptured interface (b: cross section, c: longitudinal section). A part of the coating remained attached to the filament near the edge, but the filament surface was mostly uncovered. The multi-layer coating was still bonded to the W matrix side even after the filament/coating(ZrO x ) interface was separated. It is also found that the multi-layer itself and the coating(ZrO x )/matrix interface were partly fractured. But the bond interfaces within the W/ZrO x multi-layer coating seem to be intact.

Incidentally, stability of the microstructure at high temperatures or under neutron irradiation is an open issue needing further clarification. Recently authors' group is performing extensive push-out tests on selected oxide coating interfaces after annealing at 800 °C for 10 hours to investigate thermal impact. Yet, the result of this ongoing work is not included in the present article.

Direct validation of interfacial crack deflection

In previous section it was demonstrated that the calibrated i Γ values of the tested coatings satisfied the fracture-mechanical criterion of interfacial crack deflection. For direct visual validation of this prediction a 3-point mini bending test was conducted under in-situ SEM observation using a miniaturized single-filament specimen. To trace the crack propagation, the originally rod-shaped model composite (with Zr/ZrOx multi-layer coating) was cut along the longitudinal axis. For stable supporting of the half cylinder specimen during bending test, the two lateral edges were cut out to produce parallel side faces. The surface of the cut sections was fine polished. A sharp notch was introduced on one lateral face to define the crack initiation site.

Figure 11 shows the cut section of a half-cylindrical mini specimen set up in a testing device after bending test. A schematic illustration is also attached. Until the applied load reached 110 N there was no sign of any failure. At 110 N a transverse crack was abruptly produced from the notch root and propagated rapidly in opening mode perpendicular to the specimen axis but without cutting the filament. The sharp crack plane extended though the matrix surrounding the wire. Figure 12 shows the cracked interface domain with higher magnification. The two micrographs clearly reveal that the primary matrix crack was deflected along the interface leading to controlled debonding at the interface while the filament bridged the opening crack.

This cracking feature coincides exactly with the typical toughening mechanism of a CMC.

This result may be a direct evidence to support our approach to realize a high-toughness tungsten composite material.

Conclusions

1. The fracture energy and shear strength of the filament/matrix interface in W f /W composites could be determined using the measured push-out test data and numerical fitting to theoretical equations.

2. The values of the interfacial parameters obtained for six different ZrO x -based coatings were comparable with each other. In the cases of the ZrO x single layer and the W/ZrO x single-and multi-layer coatings, the calibrated shear strength d τ ranged from 360 to 440 MPa whereas the fracture energy i Γ ranged between 3 and 6 J/m². On the other hand, the Zr/ZrO x multilayer coating showed notably smaller magnitude for both parameters. ( d τ : 330 MPa, i Γ : 1.2 J/m²) The estimated i Γ values satisfied the fracture mechanical criterion for interfacial crack deflection.

3. The cracking and separation occurred mostly at the filament/ZrO x coating interface while both the ZrO x coating and the W film remained attached to the W matrix side. On the contrary, in the Zr/ZrOx multi-layer case, debonding occurred equally either at the filament/coating or the coating/matrix interface.

4. The exposed surface of the pushed-out filament was fully uncovered suggesting absence of any strong chemical bonding between the ZrO x film and the W filament.

where, d P : the applied load at the onset moment of interface debonding, f r : the filament radius, α : the shear-lag parameter depending on the elastic properties of the fiber and the matrix and L : the initially embedded filament length. This equation can also be used for a push-out test case by replacing L with the specimen thickness H because eq.(A1) assumes rapid crack extension at d τ in a thin specimen.

A.2. Roughness stress r σ and friction coefficient µ

According to the shear-lag model of Shetty [START_REF] Shetty | Shear-lag analysis of fiber push-out (indentation) tests for estimating interfacial friction stress in ceramic-matrix composites[END_REF], fr P can be correlated with l as follows:

) , where ν and E are the Poisson ratio and the Young's modulus, respectively. The subscripts f and m stand for filament and matrix. r σ is thermal expansion mismatch which is negligible in the present case.

On the other hand, Liang and Hutchinson [START_REF] Liang | Mechanics of the fiber pushout test[END_REF] argued that r τ was a constant friction term arising from an asperity mismatch at a broken interface. They suggested Alternatively, Clyne suggested a model for the interface fracture toughness [START_REF] Kalton | Measurement of interfacial fracture energy by single fiber push-out testing and its application to the titanium-silicon carbide system[END_REF] based on an energy balance approach. This model yielded a relationship between i Γ and p as

ACCEPTED MANUSCRIPT

-13 -where th z σ represents the axial thermal residual stress and o r τ the total shear stress consisting of the contributions from roughness and thermal strain. Again, the contribution of thermal stress vanishes. Eq. (A5) has exactly the same form as eq. (A4) except for the factor B 2 . [START_REF] Du | Interfacial fracture behavior of tungsten wire/tungsten matrix composites with copper-coated interfaces[END_REF], the presented data are modified one using an improved fitting algorithm.

Figure captions

  load d P at the point B. Upon reaching d P , interface cracking was initiated triggering rapid (40 ms) brittle shear rupture. At the same time, the stored elastic strain energy was released in sudden bursts causing a dynamic push-out movement from B to C until the filament was decelerated by frictional resistance. The displacement ( o d ) generated by this dynamic event was 32 µm. A slight load jump was observed from C to D prior to the quasi-static progressive sliding stage which was caused by the delay of feedback signal to the load cell controller.

  Γ (mode II) was calibrated by fitting the measured p vs. H data with eq.

Figure 7 (

 7 Figure 7 (a) shows a part of the pushed-out filament which was originally coated with the W/ZrO x single-layer coating. In the box (b) the coating film detached from the filament is shown in higher magnification. (c) shows the longitudinal section of the debonded interface domain after test. The base part of the exposed filament was locally excavated by FIB as shown in the box (d) to observe the interior domain of the interface. In both micrographs it is seen that the separation occurred articulately at the W filament/ZrO x interface. Both the ZrO x coating and the W film remained attached to the W matrix side. The exposed surface of the pushed-out filament looked completely uncovered. Such a clear debonding feature suggests absence of chemical bonding between the ZrO x film and the filament. The load carrying capability of the interface under shearing was controlled by interlocking of roughness as well as adhesion. The calibrated d

Figure 9 (

 9 Figure 9 (a) shows the exposed surface of the pushed-out filament with the ZrOx/Zr multilayer coating. Also shown are the longitudinal interface sections at two different locations (b, c). The micrographs reveal that debonding occurred either at the filament/multilayer interface or at the multilayer/W matrix interface with similar failure probability. Hence the calibrated parameters are actually averaged properties of the two adhesion interfaces. The dual cracking behavior may explain the particularly smaller magnitude of d τ and i Γ . The number of favored failure sites was approximately doubled increasing the failure probability and thus decreasing the strength. The multi-layer coating itself and the multi-layer/W film bonding remained intact.

4 .

 4 Interfacial fracture toughness i Γ Liang and Hutchinson[START_REF] Liang | Mechanics of the fiber pushout test[END_REF] developed a model to calibrate the interfacial fracture toughness i Γ (mode II) from a push-out test data which is expressed as axial thermal residual stress and thus becomes null for the present case. It is noted that the third term of the right hand side is identical to eq. (A3). The second term stands for the contribution of the interfacial fracture energy to the debonding resistance.

Figure 1 .

 1 Figure 1. Longitudinal sections of the as-fabricated interfaces with four different coatings. (a) ZrO x single-layer film, (b) ZrO x single-layer film with a W protection film, (c) Zr/ZrO x multi-layer film and (d) W/ZrO x multi-layer film.

Figure 2 .

 2 Figure 2. A typical push-out curve measured on a ZrO x single-layer coating (140 nm) together with a SEM image of the pushed out filament. Curve 1: original load-displacement curve, Curve 2: after correction of machine compliance.

Figure 3 .

 3 Figure 3. Collected d P vs. H data obtained from the push-out curves of ZrO x single-layer coating together with the corresponding regression curve based on eq.(A1).

Figure 4 .

 4 Figure 4. Collected fr P vs. l data obtained from the push-out curves of ZrO x single-layer coating together with the corresponding regression curve based on eq.(A2).

Figure 5 .

 5 Figure 5. Collected p vs. H data obtained from the push-out curves of ZrO x single-layer coating together with the corresponding regression curve based on eq.(A4).

Figure 6 .

 6 Figure 6. Small debris of the coating film attached on a broken interface.

Figure 7 .Figure 8 .

 78 Figure 7. (a) A part of the pushed-out filament which was originally coated with W/ZrO x single-layer coating, (b) coating film detached from the filament in higher magnification, (c) longitudinal section of the debonded interface layer, (d) locally excavated filament base and exposed interior interface domain (FIB preparation)

Figure 9 .

 9 Figure 9. (a) Exposed surface of the pushed-out filament with ZrOx/Zr multi-layer coating, (b, c) longitudinal interface sections at two different locations.

Figure 10 .

 10 Figure 10. (a) Pushed-out filament of W/ZrO x multi-layer coating, magnified views of the multi-layers at the ruptured interface (b: cross section, c: longitudinal section).

Figure 11 .

 11 Figure 11. Cut section of a half-cylindrical mini specimen with Zr/ZrOx multi-layer interface coating set up in a testing device after bending test. The vertical crack was initiated at the applied load of 110 N.

Figure 12 .

 12 Figure 12. Interface domain of the half-cylindrical bending specimen with higher magnification. Interface debonding crack is clearly seen.

  Figure6

Figure12

  Figure12

  and 5 the experimental data of the W/ZrO x single-layer coating are plotted as an example to illustrate a generic feature of the parameter calibration procedure. All other As a whole the calibrated parameter values of the ZrO x -based coatings were comparable with each other except for the Zr/ZrO x multi-layers. The latter produced essentially smaller d

	τ
	and i Γ values ( d τ : 330 MPa, i Γ : 1.2 J/m²) than the other coatings. d
	coatings also exhibited a similar feature, thus are not presented separately. Each graph shows
	the d P vs. H , fr P vs. l and p vs. H data, respectively, together with the corresponding
	regression curves produced using eqs.(A1), (A2) and (A4). The final result of calibration is

summarized in Table

1

. In addition, recently published literature data of other coating systems for W f /W composite are also listed. The literature data include carbon single-layer film, copper/tungsten single-layer film and copper/tungsten multi-layer film. It is noted that the scattering errors were relatively small for all data.

1.

Acknowledgement

The author J. Du is grateful to Chinese Scholarship Council (CSC) for the financial support.

5. The capability of the interfacial ZrO x coating to allow controlled crack deflection along the interface under tensile load could be demonstrated in a 3-point bending test on a miniaturized single-filament specimen. This crack bridging behavior of the coated filament can be regarded as more direct evidence supporting the W f /W toughening concept.


J C Lloyd

E Neubauer

J Barcena

W J Clegg

Effect of Titanium on Copper-Titanium / Carbon Nanofibre Composite Materials

Keywords: A. Metal-matrix composite (MMCs), A. Carbon Nanofibre, B. Thermal properties, D. Raman Spectroscopy, D. Transmission Electron Microscopy (TEM)

Copper/carbon nanofibre composites containing titanium varying from 0.3wt% to 5wt% were made, and their thermal conductivities measured using the laser flash technique. The measured thermal conductivities were much lower than predicted. The difference between measured and predicted values has often been attributed to limited heat flow across the interface. A study has been made of the composite microstructure using x-ray diffraction, transmission electron microscopy and Raman spectroscopy. It is shown in these materials, that the low composite thermal conductivity arises primarily because the highly graphitic carbon nanofibre structure transforming to amorphous carbon during the fabrication process.

Introduction

Effective thermal management in modern power electronics requires a heat sink material with as high a thermal conductivity as possible [START_REF] Zweben | Thermal materials solve power electronics challenges[END_REF]. Carbon based materials such as diamond and carbon nanofibres exhibit high thermal conductivity values, 1500 -2000 [START_REF] Tavangar | Assessing predictive schemes for thermal conductivity against diamond-reinforced silver matrix composites at intermediate phase contrast[END_REF] and 1200 W m -1 K -1 [START_REF] Denko | Vapour grown carbon fibre (VGCF-H[END_REF], respectively.

High thermal conductivity composites, for example synthetic Ib-type diamond inclusions embedded in a silver-11at%silicon matrix, have been fabricated exhibiting high thermal conductivity values of 970 W m -1 K -1 at an inclusion volume fraction of 0.76 [START_REF] Weber | Diamond-based metal matrix composites for thermal management: Potential and limits[END_REF]. Unfortunately, these composites are difficult to machine due to the high hardness of diamond [START_REF] Khalid | Microstructure and interfacial characteristics of aluminium-diamond composite materials[END_REF]. Therefore, composites containing carbon nanofibre inclusions potentially combine high thermal conductivities with the ease of machinability.

In studies of metal matrix composites containing carbon-based inclusions, the main area of concern has been the quality of interfacial bonding between the metal matrix and carbon inclusion [START_REF] Khalid | Microstructure and interfacial characteristics of aluminium-diamond composite materials[END_REF][START_REF] Schubert | Interfacial characterization of Cu/diamond composites prepared by powder metallurgy for heat sink applications[END_REF]. This is because inert metals, such as copper and silver, do not wet carbon and no physical bond is formed at the interface [START_REF] Schubert | Interfacial characterization of Cu/diamond composites prepared by powder metallurgy for heat sink applications[END_REF]. Wetting has been enhanced by alloying with carbide forming additives, such as chromium and titanium, which diffuse to the carbon surface and react to form a thin, continuous carbide interlayer [START_REF] Mortimer | The wetting of carbon by copper and copper alloys[END_REF].

In this work, copper/carbon nanofibre composites were fabricated using a powder metallurgical route where titanium was added to enhance interfacial bonding. The aim of this work was to study the effect of varying the concentration of titanium and to correlate the microstructure of these composites with the measured thermal conductivities.

Experimental Techniques

Composite Fabrication

The composites were fabricated using a powder metallurgy technique [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF], which involves coating Showa Denko carbon nanofibres [START_REF] Denko | Vapour grown carbon fibre (VGCF-H[END_REF] with copper, using an electroless deposition technique. Different chemical solutions are used to sensitise (SnCl) and activate (PdCl) the surface of the carbon nanofibres, before plating with copper [START_REF] Ang | Decoration of activated carbon nanotubes with copper and nickel[END_REF]. The amount of copper deposited yielded composites with a fibre volume fraction of 0.2, assuming a fibre density of 2.0 g cm -3 . After the copper deposition process, the copper coated carbon nanofibres was washed and dried. Following this, titanium powder (50 nm and 45 m, contains 0.05 -0.4 wt% oxygen) was admixed and the final powder mixture was hot pressed in a graphite die at 900 -1000 o C under a pressure of 35 MPa. This results in a composite with a 2-D random fibre arrangement.

Further details of the composite fabrication process can be found in [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF]. The composites were identified using the following notation CuTi(Xwt%)/CNF where X denotes the amount of titanium introduced to the system.

Thermal Measurements

The room temperature thermal diffusivity, D, of these composites were measured in the transverse direction, parallel to the hot-pressing direction, using a transient thermal flash technique (Netzsch LFA 457 Microflash TM ).

Measurements were made on cylindrical discs 6 mm in diameter and 4 mm thick. Composite thermal conductivity, κ, was determined from measurements of composite density, ρ, and specific heat capacity, C, using the relationship [START_REF] Salazar | On thermal diffusivity[END_REF] κ = DρC. Specific heat capacity was measured using differential scanning calorimetry (TA-Instruments Q100) on cylindrical discs 4 mm in diameter and 0.5 mm thick. Composite density was determined using the Archimedes technique, using perfluoromethyldecalin (Flutec PP9, ρ = 1.96 g cm -3 ) as the fluid medium.

Characterisation of Composite

Phase-identification

The phases in the composite were determined using X-ray diffraction.

Standard -2 traces were recorded on a diffractometer (Phillips PW1820) from 20 -90 o , using a Cu K radiation source operated at 40kV accelerating voltage and 40 mA filament current. The beam was narrowed using 1/2 o divergence and anti-scatter slits, and a 0.2 mm receiving slit. The signal was recorded at a step size of 0.025 o and a dwell time of 12.5 s. Phase identification was carried out on the Xpert Highscore Plus programme and quantification was achieved by Rietveld analysis.

Microstructural Characterisation

The overall composite microstructure was observed in the dual beam FIB (Helios Nanolab SEM/FIB), where focused ion beam (FIB) milling was used to prepare the sample surface for viewing in the scanning electron microscope (SEM).

Teansmission electron microscopy (TEM) samples were prepared using the trench technique in the FIB (FEI 200 FIB workstation) and studied in the transmission electron microscopes (CM30 and Tecnai FEI20), using acceleration voltages of 300 and 200 keV, respectively. Elemental analysis was performed, where elemental mapping of titanium, copper and carbon was carried out using energy filtered TEM (EFTEM). The K-and L-edges of copper and titanium from electron energy loss spectroscopy (EELS) was used to determine the bonding nature of these elements. EELS spectra were acquired at 1 nm intervals along the line of interest. Quantitative analysis was then carried out using the ES Vision FEI software.

Raman spectroscopy was used to determine the level of graphitization in the carbon nanofibre, using a micro-Raman system (Ramascope-1000) with a 633 nm red laser monochromator source. All spectra were collected through a 50× objective lens, whereby the laser spot size was approximately 10 m in diameter. The Raman spectra exhibits three characteristic peaks: the D-peak arising from defects and disorder, for example grain boundaries, broken sp 2 C bonds and sp 3 C); the G-peak is a result of the graphitic structure within the sample; and the G peak is due to long range order [START_REF] Tuinstra | Raman spectrum of graphite[END_REF][START_REF] Dileo | Purity assessment of multiwalled carbon nanotubes by Raman spectroscopy[END_REF]. Relative changes in defect concentration was monitored using the D/G peak ratio, where a small ratio corresponds to an ordered and highly crystalline material.

Results and Discussion

Composite Thermal Conductivity

The thermal conductivity of the Cu/CNF composite, in the transverse direction, was 255 ± 35 W m -1 K -1 . Figure 1 shows the variation in composite thermal conductivity, in the transverse direction, with titanium concentration.

The introduction of 0.3 wt% titanium (50 nm) resulted in a 22% increase in composite thermal conductivity (311 W m -1 K -1 ). Further additions of titanium to the copper coated carbon nanofibres reduced the composite thermal conductivity. At 5 wt% titanium (200 W m -1 K -1 ), a reduction of 35% from peak value was observed. These low composite values are comparable to other previously studied copper-alloy/CNF composites, where the resultant composite thermal conductivity lies below that of copper [START_REF] Edtmaier | Carbon Nanotubes as Highly Conductive Nano-Fillers in Metallic Matrices[END_REF][START_REF] Neubauer | Copper based composites reinforced with carbon nanofibres[END_REF], which is expected in randomly arranged fibre composites containing highly anisotropic fibres [START_REF] Lloyd | Effect of Fibre Anisotropy on Composite Thermal Conductivity[END_REF].

Predictions were made for a 0.2 volume fraction 2-D randomly aligned fibre composite, using the relationships in [START_REF] Lloyd | Effect of Fibre Anisotropy on Composite Thermal Conductivity[END_REF], assuming perfect thermal conduction at the interface (infinite interface thermal conductance), a matrix thermal conductivity of m = 400 W m -1 K -1 and various fibre properties. For a composite containing isotropic fibres, f = 1200 W m -1 K -1 , the composite was expected to have a thermal conductivity of 526 W m -1 K -1 (in-plane) and 489 W m -1 K -1 (transverse). Most carbon fibres are anisotropic, taking an anisotropy ratio comparable to K1100 carbon fibre (Cytec [START_REF]Thornel K-1100 Continuous Pitch-Based Fibre[END_REF]), f long = 1200 W m -1 K -1 and f trans = 3 W m -1 K -1 , the composite thermal conductivity was estimated to be 401 W m -1 K -1 (in-plane) and 268 W m -1 K -1 (transverse). When f = 0 W m -1 K -1 there was no difference in the transverse direction properties (267 W m -1 K -1 ).

The Cu/CNF and CuTi(Xwt%)/CNF composite thermal conductivities (200 -311 W m -1 K -1 ) are very similar to predictions where the fibres are have low transverse thermal conductivity.

Taking into consideration poor transverse fibre properties (a few W m-1 K -1 ) the variations in composite thermal conductivity with titanium content arises from changes in matrix properties, as it is known that alloying reduces the thermal conductivity of copper. Figure 2 shows the thermal conductivity of copper rapidly reduced from 400 Wm -1 K -1 to 175 Wm -1 K -1 after alloying with 1 wt% titanium [START_REF] Neubauer | Interface optimisation in copper-carbon metal matrix composites[END_REF]. It is observed that the composite thermal conductivity does not fall as drastically with titanium content as that of copper. This is a due to the removal of titanium from the matrix as a result of titanium carbide formation. At high addition of titanium powders, the remains of titanium particles could still be observed, which reduces the effective matrix thermal conductivity and thus the composite thermal conductivity.

Study of Composite Microstructure

Results presented are primarily on the CuTi(5wt%)/CNF material, where there is an ease in identifying phases and at reasonable quantities. The CuTi(5wt%)/CNF composite microstructure is very inhomogeneous, Figure 3, consisting of both well-dispersed and agglomerated carbon nanofibres, titanium agglomerates and voids. In regions with a high titanium content, see top right of micrograph, the carbon nanofibres are coated with a titanium carbide interlayer.

Carbon nanofibres at a distance greater than the diffusion distance of titanium in copper under the consolidation conditions, 35 µm, from any titanium powder will not have this interlayer, as shown by the carbon nanofibre agglomerate at the bottom left corner of the micrograph. It should be noted that a more homogeneous structure was observed in the CuTi(0.3wt%)/CNF composite.

Phase-Identification

From the X-ray diffraction profile, Figure 4, the main phase in the composite was copper. The observed trace also confirmed the presence of Cu 2 O (2 wt%), TiC (5 wt%) and -CuPd (2 wt%). Oxygen analysis of the composites complements the XRD analysis, as the average oxygen content was 0.35 wt% [START_REF] Barcena | Microstructural study of vapour grown carbon nanofibre/copper composites[END_REF]. Both the Cu 2 O and -CuPd are impurities arising from the composite fabrication process. Measurements on other composite samples show that -CuPd was not uniformly distributed throughout the composite material, as it was only observed in 10% of the samples.

Elemental mapping of carbon, copper and titanium using EFTEM, Figure 5, confirms the diffusion of titanium to the copper/carbon nanofibre interface to form titanium carbide. The titanium carbide layer is approximately 80 to 140 nm thick. This is quite a severe reaction, as a majority of the fibres have a diameter of 150 nm and would be totally converted into titanium carbide. The intrinsic thermal conductivity of titanium carbide is approximately 30 Wm -1 K -1 [START_REF] Radosevich | Thermal conductivity of transition metal carbides[END_REF][START_REF] Williams | Physics of transition metal carbides[END_REF] .

Therefore thick layers of titanium carbide are undesirable, as they act as a physical thermal barrier to heat flow across the interface. The extent of titanium carbide formation can be limited by reducing the amount of titanium.

From the near edge structure of EELS spectra, the bonding nature of the elements was probed, where in Figure 6b and 6c the carbon K-edge corresponds to a mixture of sp 2 and sp 3 bonded carbon, and carbon bonded to titanium, respectively. The collection of EELS spectra at the titanium carbide/carbon interface, Figure 6a, was quantitatively analysed giving titanium to carbon ratio of 0.94 to 1 in the titanium carbide layer.

Further study of the EELS spectra, Figure 6d, revealed that titanium diffused 14 nm ahead of the titanium carbide/carbon nanofibre interface without bonding to carbon. Titanium was first detected at 27 nm, whilst titanium carbide was only observed at 40 nm. The titanium content in the carbide layer increases to a constant ratio over a distance of 47 nm.

Carbon Nanofibre Structure

In the TEM, the surface of the carbon nanofibre in contact with the titanium carbide layer was observed to be amorphous, Figure 7. This was determined using electron diffraction. Two patterns were recorded, one at the centre of the carbon nanofibre (position Y), Figure 7b, and the other close to the carbide interface layer (position X), Figure 7c. The electron diffraction pattern at the centre of the carbon nanofibre, indicates that there is long range order, as sharp (002) diffraction spots are observed. Amorphous halo rings are observed in Figure 7c. In the fibre studied, the amorphous carbon layer is approximately 430 nm thick, where two-thirds of the fibre is no longer graphitic.

The high thermal conductivity of carbon fibres arise from their highly graphitic structure [START_REF] Piraux | The temperature variation of the thermal conductivity of benzene-derived carbon fibres[END_REF]. Therefore, the transformation of graphitic carbon to amorphous carbon results in a reduction in the thermal conductivity. A qualitative study of the variations in graphite content between the fabricated composites was carried out using Raman spectroscopy by studying the D/G peak ratio. The measured values have been summarized in Table 1.

The D/G peak ratio for the as-received fibre was very low at 0.12. Upon consolidation in the composite without any additive material, the D/G peak ratio increased to 0.97. Composites with titanium exhibit similarly high D/G peak ratios. The Raman results confirm observation in the TEM, that the carbon fibres have lost their highly crystalline structure.

Conclusions

Raman spectra from the carbon nanofibre material in the composites show a loss of fibre crystallinity, where graphitic carbon undergoes an amorphous transformation. This crystalline to amorphous transformation reduces the effective thermal conductivity of the carbon nanofibres and thus accounts for the low composite thermal conductivities observed. Observations of the composite microstructure reveal that the titanium additives diffuse to the carbon nanofibre surface and reacts to form titanium carbide, Ti 0.94 C. In the case of high titanium contents, the reaction is severe where whole carbon nanofibres are converted into titanium carbide, which corresponds to the Raman D/G peak ratios. The presence of titanium particles in the copper matrix, as well as other impurity phases, such as copper oxide and copper palladium, reduces the effective thermal conductivity of the matrix, further diminishing the composite thermal conductivity.

In order to achieve high thermal conductivity composites from these materials, the graphitic nature of the carbon nanofibres needs to be preserved.

Further work, would be to determine when in the fabrication process and how this transformation takes place. It is suggested that this occurs by:

1. Interaction between titanium atoms which have diffused into carbon vacancy sites. The formation of the Ti-C bond disrupts the ordered graphitic structure, as the Ti-C bond lengths (2.17 Å) is dissimilar to the C-C bond (1.42 Å) and graphite interplanar (3.394 Å) distance.

2. The carbon nanofibre material acts as a reducing agent for copper and titanium oxides during the hot-pressing process, consuming the carbon nanofibre.

Figure captions

Figure 1 :

 1 Figure 1: Measured composite thermal conductivity values plotted against titanium additive content. Black circles denote composites made with 50 nm titanium powders whilst blue triangles are for 45 m powders.

Figure 2 :

 2 Figure 2: Thermal conductivity of copper falls with titanium additive content.Adapted from[START_REF] Neubauer | Interface optimisation in copper-carbon metal matrix composites[END_REF].

Figure 3 :

 3 Figure 3: Overall microstructure of CuTi(5wt%)/CNF composite material observed in the SEM. The vertical lines observed is known as curtaining, which is an artifact from FIB milling.

Figure 4 :

 4 Figure4: X-ray diffraction pattern from CuTi(5wt%)/CNF composite. Phases were identified as *copper (91 wt%), copper oxide (2 wt%), titanium carbide (5 wt%), copper palladium (2 wt%), and carbon.

Figure 5 :

 5 Figure 5: Elemental maps obtained using energy filtered transmission electron microscopy of (a) carbon; (b) copper and (c) titanium from the CuTi(5wt%)/CNF composite.

Figure 6 :

 6 Figure 6: Quantitative elemental analysis at the titanium carbide/carbon nanofibre interface using electron energy loss spectroscopy (EELS), where (a) the scanning transmission electron micrograph, showing the line in which EELS spectra was collected; (b) the EELS spectra from position Y, where the C-K and Ti-L edges are observed; (c) the EELS spectra of carbon; and (c) plot of normalized carbon and titanium content with distance.

Figure 7 :

 7 Figure 7: TEM micrograph of CuTi(5wt%)/CNF composite, showing (a) a single CNF embedded in the copper matrix; (b) diffraction pattern from the centre of the fibre, position Y, exhibiting sharp (002) diffraction spots; and (c) diffraction pattern from the surface of the fibre, position X, consisting of diffuse halo rings from amorphous carbon.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7

 1234567 Figure 1

Table 1

 1 Raman spectra D/G peak ratio from as received carbon nanofibre and composite materials.

	Material

Acknowledgements

This work was supported by the FP6 EU project STRP 031712 INTERFACE and AGAPAC Project, REF: 218851 / FP7-SPACE-CALL-1. The authors would like to thank Dr Mary Vickers, Dr Richard Beanland and Dr Jonathan Barnard for their assistance in this work.


Joseph N Grima
email: joseph.grima@um.edu.mt

Brian Ellul

Daphne Attard

Ruben Gatt

Michael Attard

COMPOSITES WITH NEEDLE-LIKE INCLUSIONS EXHIBITING NEGATIVE THERMAL EXPANSION: A PRELIMINARY INVESTIGATION

Keywords: B: mechanical properties, B: thermal properties, C: Finite Element Analysis (FEA), OTHER: negative thermal expansion

In this work a simple cylindrical structure with a stiff needle-like inclusion embedded within a much softer matrix is presented and analysed with the aim of obtaining a system with tuneable thermal expansion properties. It is shown that by the correct combination of the thermal and mechanical properties of the matrix and inclusion, it is possible to design a system which can be tailor-made to exhibit particular values of the coefficient of thermal expansion (CTE) in the radial direction and also negative thermal expansion (NTE). In particular an analytical model to quantify the radial strain with changes in temperature is derived and verified through finite element analysis. The model is used to find correct property combinations which lead to particular values of thermal expansion which could also be negative or zero.

Introduction

It is a well known fact that most materials which we encounter in everyday life expand on heating and contract when cooled, a property which may be explained by looking at interatomic distances [START_REF] White | Properties of materials[END_REF][START_REF] Taylor | Thermal Expansion of Solids[END_REF]. This subject of thermal expansion is one of great practical importance and has been studied for many years since miscalculations of the temperature effects may lead to disastrous consequences.

Expansion in a material may be one of two forms: isotropic or anisotropic. In isotropic expansion, the material expands by the same extent in any direction (isotropically) upon heating whilst if the extent of expansion is dependent on the particular direction where the measurement is taken, then the expansion is referred to as anisotropic expansion. To quantify thermal expansion in some particular direction one may make use of the linear coefficient of thermal expansion, henceforth referred to as CTE which may be defined as α which relates the resultant strain ε as a result of a change in temperature of dT through dT ε α = As noted above, in most cases, materials expand when heated, i.e., ε is positive for a positive dT (i.e. as T increases) with the result that the CTE is positive. However, it should be noted that materials which defy common expectation and contract when heated do exist [START_REF] Evans | Negative thermal expansion materials[END_REF][START_REF] Barrera | Negative thermal expansion[END_REF][START_REF] Grima | Xjenza[END_REF][START_REF] Sleigh | Negative thermal expansion materials[END_REF][START_REF] Grima | Preface to[END_REF][START_REF] Kelly | Controlling thermal expansion to obtain negative expansivity using laminated composites[END_REF][START_REF] Kelly | Composite material of controlled thermal expansion[END_REF][START_REF] Lakes | Cellular solid structures with unbounded thermal expansion[END_REF][START_REF] Landert | Negative thermal expansion of laminates[END_REF][START_REF] Mary | Negative thermal expansion from 0.3 K to 1050 K in ZrW 2 O 8[END_REF][START_REF] Miller | A generalised scaleindependent mechanism for tailoring of thermal expansivity: Positive and negative[END_REF][START_REF] Milton | The theory of composites[END_REF][START_REF] Sigmund | Composites with extremal thermal expansion coefficients[END_REF][START_REF] Sigmund | Design of materials with extreme thermal expansion using a three-phase topology optimization method[END_REF][START_REF] Vandeperre | Tailoring Strains Through Microstructural Design[END_REF][18][START_REF] Smith | Mechanism for Negative Thermal Expansion and its links to Negative Poisson's Ratio[END_REF]. It should also be noted that for anisotropic systems, different values for the CTE will exist, depending on the direction of measurement and it is possible that a system exhibits negative thermal expansion (NTE) in some but not all directions. Over the years, there have been various studies aimed at designing, analysing, manufacturing and/or testing of materials and structures having very particular CTE values, in particular, studies looking at systems, including composites exhibiting NTE [START_REF] Evans | Negative thermal expansion materials[END_REF][START_REF] Barrera | Negative thermal expansion[END_REF][START_REF] Grima | Xjenza[END_REF][START_REF] Sleigh | Negative thermal expansion materials[END_REF][START_REF] Grima | Preface to[END_REF][START_REF] Kelly | Controlling thermal expansion to obtain negative expansivity using laminated composites[END_REF][START_REF] Kelly | Composite material of controlled thermal expansion[END_REF][START_REF] Lakes | Cellular solid structures with unbounded thermal expansion[END_REF][START_REF] Landert | Negative thermal expansion of laminates[END_REF][START_REF] Mary | Negative thermal expansion from 0.3 K to 1050 K in ZrW 2 O 8[END_REF][START_REF] Miller | A generalised scaleindependent mechanism for tailoring of thermal expansivity: Positive and negative[END_REF][START_REF] Milton | The theory of composites[END_REF][START_REF] Sigmund | Composites with extremal thermal expansion coefficients[END_REF][START_REF] Sigmund | Design of materials with extreme thermal expansion using a three-phase topology optimization method[END_REF][START_REF] Vandeperre | Tailoring Strains Through Microstructural Design[END_REF][18][START_REF] Smith | Mechanism for Negative Thermal Expansion and its links to Negative Poisson's Ratio[END_REF][START_REF] Grima | A system with adjustable positive or negative thermal expansion[END_REF][START_REF] Lakes | Solids with tunable positive or negative thermal expansion of unbounded magnitude[END_REF]. Some of these studies have considered the possibility of generating very low or negative thermal expansion in structures constructed from conventional materials. These systems, which are constructible at any lengthscale, include those proposed by Clegg et al. [START_REF] Vandeperre | Tailoring Strains Through Microstructural Design[END_REF][18][START_REF] Smith | Mechanism for Negative Thermal Expansion and its links to Negative Poisson's Ratio[END_REF][START_REF] Grima | A system with adjustable positive or negative thermal expansion[END_REF] and Lakes et al. [START_REF] Lakes | Solids with tunable positive or negative thermal expansion of unbounded magnitude[END_REF] and have the advantage that they are relatively easy to construct at reasonable costs and thus have excellent potential for commercialisation. Alderson et al. [22] have also proposed a method for achieving these effects using auxetic materials (i.e. materials exhibiting negative Poisson's ratio). Normally, such systems also offer the added advantage that they can be tailor-made to exhibit any desired thermal expansion properties (positive, negative or near zero) through careful choice of the geometric parameters and/or materials used in the construction. Furthermore, such systems are also of interest in view of the fact that they can be engineered to exhibit other interesting macroscopic properties, e.g. negative Poisson's ratio [START_REF]CHISMACOMB Special Issue[END_REF][START_REF] Alderson | Elastic constants of 3-, 4-and 6-connected chiral and antichiral honeycombs subject to uniaxial in-plane loading[END_REF][START_REF] Grima | Connected triangles exhibiting negative Poisson's ratios and negative thermal expansion[END_REF] with the result that one achieves multifunctional systems with obvious added value.

In this paper we propose and discuss a novel system constructible at any lengthscale including the microscale from conventional components having different mechanical and thermal properties which may be combined to form composite systems which exhibit any desired CTE values, in particular negative ones (NTE).

The Concept

For simplicity, to illustrate how systems operating through the proposed mechanism can be designed to exhibit NTE, we shall first consider a simple and basic system and predict the optimal requirements for it to exhibit this effect. The system which is shown in Fig. 1 consists of a cylindrical rod of length l and radius r made of a material B which is embedded inside another cylindrical shell of thickness t made from a material A having different thermal and mechanical properties with all dimensions being measured at a reference temperature T.

---Insert Fig. 1 here ---Assuming that materials A and B are perfectly bound to each other at the interface and that they are isotropic with respect to their thermal and mechanical properties, when the system is subjected to a change in temperature ∆T, both materials expand or contract in volume accordingly, each at a different rate. Since the materials are bound to each other, they cannot expand freely and as a result, each of them exerts forces on the other. In particular, the material with the higher CTE exerts a tensile force in the longitudinal direction on the material having the lower CTE and conversely the latter exerts a compressive force on the former resulting in a mechanical strain. This strain in turn gives rise to an additional strain in the radial direction, the magnitude of which is dependent on the Poisson's ratio (henceforth referred to as the Poisson's effect). This causes a contraction (or an expansion) in this direction and unless the Poisson's ratio of the materials is zero, this Poisson's effect may have significant contributions to the overall radial strain and therefore should not be neglected.

In addition, to further simplify our analysis, we shall also assume that:

(1) the inclusion has a needle shape, i.e. the length is much larger compared to its thickness so that changes in dimension arising from the Poisson's effect due to expansion in the radial direction can be ignored since they are negligible when compared to that resulting from a longitudinal expansion;

(2) the Young's modulus of the outer cylinder (i.e. the matrix) is much smaller than that of the inclusion and thus additional mechanical strains in the radial direction arising due to mismatch of the CTEs can be neglected.

(3) No necking effects occur during deformation.

Thus, in the analytical model it is being assumed that the strain at the interface is only dependent on the thermal expansion and Poisson's effect of material B i.e. the inner circumference of material A expands accordingly to accommodate the changes in the outer circumference of material B thereby satisfying the boundary condition of the interface (and therefore eliminating gaps or unrealistic overlaps).

In this way, it is possible to derive a simple expression for the radial strain by taking into consideration only the radial thermal strain and the additional radial mechanical strain arising from the Poisson's effect due to expansion in the longitudinal direction.

Taking first the longitudinal strain l ε into consideration, it can be quantified through the following equation:

A B l A B A A B B F F dT dT a E a E ε α α = + = + ( 1
)
where α is the CTE of the material, E its Young's modulus, a its area, F the force exerted by the other material and the subscript refers to the material (material A and B).

At equilibrium, B

A F F F = -= so that solving for F, the following expression is obtained:

( ) A B A B A B B B A A a a E E F dT a E a E α α - = + (2)
The mechanical strain on material A arising from this force is therefore:

( ) l B B A B A A A B B A A a E F dT a E a E a E α α ε - - = = - + (3)
so that the induced radial strain arising from the Poisson's effect can be given by: ( )

r A B B A B A B B A A a E dT a E a E ν α α ε - = + (4)
and similarly for material B:

( ) r B A A A B B B B A A a E dT a E a E ν α α ε - = - + (5)
Therefore, the total strain r ε in the radial direction, taking also into account the thermal expansion of both materials can be given by:

( ) ( ) ( ) ( )( ) ( )( ) 2 2 2 2 d r r A B A B r A B A B B B A A A B B B A A t r dT t r r t t a E r a E t r T t r a E a E t r α α ε ε ε α α ν ν α α + + + = + - - + = + + + + (6)
Thus defining r α as the thermal expansion coefficient in the radial direction, we note that:

( ) ( )( ) ( )( ) A B A B B B A A A B r B B A A t a E r a E t r t r a E a E t r α α ν ν α α α - - + = + + + + (7)
Since i a , i E , t and r are all positive quantities, it follows that the r α and the radial strain is negative if:

( )

1 A A A B B B A A B B t r t a E r a E α α ν ν α α + < - - (8)
This inequality suggests that for a system with A B E E < as in our earlier assumptions the NTE effect can be enhanced by decreasing A B α α . This ensures that thermal expansion in the radial direction of the thicker material is minimal so that the main contribution comes from the Poisson's effect which can be enhanced by using a soft matrix with a high Poisson's ratio and a much stiffer inclusion with a low or negative Poisson's ratio.

In this way, the matrix has very little effect on the inclusion, i.e. the degree by which material A is stretched is much higher than that by which B is compressed. This in turn means that the decrease in thickness of A is much larger than the increase in thickness of B (if

0 B ν > ) making NTE possible.
If the inclusion is auxetic, the change in its radial dimension due to compression will further contribute to a more negative thermal expansion (and also have the additional advantage of a larger pull-out resistance [START_REF] Alderson | The effect of processing parameters on the mechanical properties of auxetic polymeric fibers[END_REF][START_REF] Simkins | Single Fibre Pullout Tests on Auxetic Polymeric Fibres[END_REF]). For example for a system with

Simulations

In an attempt to obtain further evidence that what is proposed here can indeed result in a method for controlling the thermal expansion in the radial direction which could also lead to NTE, we used the Finite Elements (FE) software package ANSYS Academic Research V. 12.0 to construct this most basic system. In the simulation, we used two elastic materials A and B which were perfectly bonded together and meshed using the 2-D, 8-node, coupled-field PLANE223 plane element with axisymmetric behaviour where the z-axis is the axisymmetric axis while symmetric boundary conditions were applied along the r-axis (Fig. 2). The nodal degrees of freedom (DOF) are translations in the zand r-directions and temperature where Table 1 lists the nodal constraints. As regards loading, a uniform temperature rise of 100K was applied on all the nodes.

---Insert Fig. 2 here ------Insert Table 1 here ---Two sets of simulations were performed. In the first, this system was solved linearly for the geometry corresponding to l = 500mm, t = 50mm and r = 0.5mm. The material was modelled as perfectly elastic and isotropic with E A = 0.01 GPa, E B = 200 GPa, B = 0.3, A = 15 × 10 -6 K -1 and B = 324 × 10 -6 K -1 while the Poisson' s ratio of the matrix ( A ) was varied from -1.0 < A < 0.5 subjected to a temperature rise of 100 K. In the second set, A was set at 0.49 whilst the thickness t was allowed to vary from 100 > t > 0 with all the other parameters set as before. It should be emphasised that although the simulations performed here are in the mm range, the effect is scale independent and can also be exhibited at smaller or larger scales.

As post-processing, for both sets of simulations, the radial strain r was recorded as A or t were varied from which we calculated the thermal expansion coefficient α r in the radial direction as α r = r ∆T -1 . The results of these two sets of simulations are shown in Fig. 3 and Fig. 4 which compare the FE results with those predicted by the analytical model.

---Insert Fig. 3 here ------Insert Fig. 4 here ---These results clearly show that in accordance to what is predicted by the analytical model, the systems presented here can exhibit a wide range of thermal expansion properties which can be varied by varying either the types of materials used (something which may be limited by the availability of materials having the required properties) or the geometric parameters, such as the thickness of the outer material. In particular, the simulations confirm that in the radial direction, the system can indeed exhibit not only negative linear thermal expansion, a property which is exhibited best when the outer material (the matrix) has high positive Poisson's ratios but also zero linear thermal expansion. This property is highly desirable in applications where a system has to maintain its structural integrity while subjected to significant changes in temperature which would otherwise lead to changes in the geometrical features of the structure, for example, in the construction of railway tracks, bridges, Bragg gratings [START_REF] Vandeperre | Application of negative thermal expansion to optical fibres[END_REF] and satellites [START_REF] Collins | Linear-Quadratic-Gaussian-based Controller-Design for Hubble Space-Telescope[END_REF]. It is also interesting to note when auxetic materials are used, the Poisson's ratio (mechanical properties contribution) makes it possible to get volumetric thermal expansion which is higher than what could have been achieved when one considers only thermal expansion effects. All this is very significant as it confirms that the setup proposed here may indeed be used as a mechanism to achieve any pre-desired thermal expansion properties.

Let us now intercompare the predictions made by the analytical and FE models. Both Fig. 3 and Fig. 4 show that the analytical model does indeed predict, to a first approximation, the magnitude of the thermal expansion in the radial direction, thus adding confidence in the analytical model. In particular we note that in cases when t >> r, the analytical model predicts the thermal expansion in the radial direction to a high degree of accuracy. Also interesting to note is that both analytical and FE models suggest a similar profile for the variation of α r vs. t which suggest that there is an optimal thickness t of the outer material (for a fixed inclusion thickness r) which optimises the magnitude of NTE.

The main discrepancies between the analytical and FE models seem to occur at low values of t and these are evident in the plots of α r against the thickness t of the surrounding material where at low values of t, the analytical model underestimates the extent of NTE. The most likely reason for this underestimation is due to the fact that at small values of t, the Poisson's effect as a result of an increase in the thickness r (and hence the circumference) of the needle shaped inclusion are not insignificant. Such increase in the circumference will cause an additional thinning of the outer material, which thinning has not been accounted for in the analytical model. All this suggests that although there is a need to fine-tune the analytical model so as to take into account this effect (something which unfortunately will decrease the simplicity of the analytical model), the analytical model as presented here already can already provide a reasonable estimate of the thermal expansion properties of such systems Before we conclude, it is important to note that the concepts presented here may be used in the design and manufacture of real composites exhibiting such NTE properties or for controlling the thermal expansion of composites (which may not necessarily have to exhibit NTE). For example, an easily constructible but more complex system based on the same mechanism is illustrated in Fig. 5 which shows a cross-section of a possible composite where the highly expanding and hard needle shaped inclusions are moulded inside the matrix in a random but aligned manner. Other systems which could be modified to exhibit these effects include fibre-reinforced composites which if constructed using the right component materials would also be able to exhibit these unusual properties. In such systems, one would assume that the CTE will also be affected by other factors such as the degree of perfection in the alignment of the needle shaped inclusions, the packing, etc., but the principles which may lead to the unusual thermal effects presented in this paper, including the ability to exhibit NTE, remain the same. It is also important to note that although materials which have the thermal and mechanical properties required to achieve this NTE effect in a very significant manner are not currently in abundance, the effect may be obtained by building micro mechanical systems (e.g. using syringe-like structures filled with a highly expanding fluid embedded within a soft material) or having the components themselves being manmade composites which are tailor-made to have the required properties.

---Insert Fig. 5 here ---

Conclusion

This work presented a concept for controlling the thermal expansion through the introduction of highly expanding and hard needle shaped inclusions into a soft matrix.

In particular, we derived an analytical model for a simple cylindrical system containing a needle-like inclusion which can be tailor-made to exhibit any pre-desired positive or negative thermal expansion coefficient in radial directions. In fact, the derived expression for the radial strain showed that by the correct combination of the materials' thermal and mechanical properties, NTE and zero thermal expansion in the radial direction are possible, with the NTE effect being further enhanced by the use of auxetic inclusions. The validity of the model under the made assumptions has also been verified using finite element analysis.

We hope that the models presented and discussed here will encourage experimentalists to manufacture and commercialize new materials which can be tailor-made to have properties to fit particular practical applications based on the concepts presented here.

Given the simplicity of our systems and their adjustability, we envisage materials based on what is proposed should find extensive use in many practical applications where negative or zero thermal expansion is required, or where the thermal expansion needs to controlled in a cost-effective manner. Fig. 5: An example of a realistic but more complex system which can be built to exhibit particular CTE properties using the principles presented here.

Table Captions:

Table 1. Translational nodal constraints applied on the nodes lying on the lines shown in Fig. 2, where U r and U z denote displacements in the r-and z-directions respectively.

Fig. 1 ACCEPTED MANUSCRIPT

  ) is used. It is also interesting to note that zero thermal expansion is also predicted if

Fig. 1 :

 1 Fig. 1: (a) A cylindrical structure consisting of a needle-like inclusion of material B

Fig. 2 :

 2 Fig. 2: (a) Line numbers showing the respective nodes. (b) 3/4 of the composite in 3D.

Fig. 3 :

 3 Fig. 3: Plot of the radial CTE α r versus the Poisson' s ratio of the matrix A for both the

Fig. 4 :

 4 Fig. 4: Plot of the radial CTE α r versus the matrix thickness t for both the FE and

Fig. 2 Fig

 2 Fig. 2

Fig 5

 5 Fig 5

Table 1 :

 1

		DOFs Constraints
		U r	U z
	1	0	-
	2	-	0
	3	Coupled a	-
	4	-	Coupled a
	5	-	Coupled a

a The DOF is equal for all the nodes

Acknowledgments

This work is financed by the Malta Council for Science and Technology (MCST) through their 2006 R&I programme.