Valter Carvelli
email: valter.carvelli@polimi.it

Vanni Neri Tomaselli

Stepan V Lomov

Ignaas Verpoest

Volker Witzel

Bjorn Van Den Broucke

FATIGUE AND POST-FATIGUE TENSILE BEHAVIOUR OF NON-CRIMP STITCHED AND UNSTITCHED CARBON/EPOXY COMPOSITES

Keywords: (A) Laminate, (B) Fatigue, Mechanical Properties

An experimental study is described in this paper dealing with the tensile-tensile fatigue and the quasistatic post-fatigue tensile behavior of a structurally stitched multi-ply carbon composite and the unstitched counterpart. The influence of the stitching on the fatigue life and on the residual post-fatigue quasi-static properties in two principal direction is investigated. The fatigue behavior of both composites is represented by Wöhler-like diagrams. The damage imparted during fatigue is studied by X-ray analyses.

The residual mechanical properties of the fatigued composites after different number of cycles are compared in term of stiffness and strength. The post-fatigue quasi-static tensile tests include acoustic emission (AE) registration and full-field surface strain mapping (SM) to investigate the damage onset and

INTRODUCTION

Laminate composites have a broad range of application in several industrial fields (aircraft, marine, automobile, civil infrastructure, etc.) [START_REF] Tong | 3D Fibre Reinforced Polymer Composites[END_REF]. Their main drawback are the reduced out of plane mechanical properties. Among the techniques to increase the through-thickness properties, in the last decades, stitching of multi-ply preforms and of occasionally prepreg laminates attracted a large interest [START_REF] Bogdanovich | Three-Dimensional Reinforcements for Composites[END_REF][START_REF] Mouritz | Review of applications for advanced threedimensional fibre textile composites[END_REF]. The stitching benefits are the improvement of: delamination resistance, impact damage tolerance and out-ofplane stiffness of the laminate [START_REF] Dransfield | Improving the delamination resistance of CFRP by stitching a review[END_REF][START_REF] Mouritz | A review of the effect of stitching on the in-plane mechanical properties of fibre-reinforced polymer composites[END_REF]. Other attractive benefits of the stitching are the robotically controlled multi-needle sewing machines and the cost-effective joining of multi-layer preforms which improve the ease of handling prior to liquid moulding [START_REF] Mouritz | A review of the effect of stitching on the in-plane mechanical properties of fibre-reinforced polymer composites[END_REF].

The interest in stitching technologies for the reinforcement of polymer matrix composites led to a considerable number of studies devoted to the influence of the stitching on the mechanical properties of the laminates (see e.g. the review papers [START_REF] Mouritz | Review of applications for advanced threedimensional fibre textile composites[END_REF][START_REF] Dransfield | Improving the delamination resistance of CFRP by stitching a review[END_REF][START_REF] Mouritz | A review of the effect of stitching on the in-plane mechanical properties of fibre-reinforced polymer composites[END_REF][START_REF] Mouritz | A mechanistic approach to the properties of stitched laminates[END_REF]). Some conclusions, in the mentioned review papers, on the large amount of experimental data appeared in the literature suggest:

-a benefit of the stitching is an improvement of the delamination resistance increasing the interlaminar fracture toughness under mode I and II loading conditions [START_REF] Dransfield | Improving the delamination resistance of CFRP by stitching a review[END_REF]; -stitching improves the impact resistance and the post-impact mechanical properties [START_REF] Tong | 3D Fibre Reinforced Polymer Composites[END_REF]; -the stiffness and strength of laminates loaded in quasi-static tension can be unaffected, increased or more common reduced by the stitching [START_REF] Mouritz | A mechanistic approach to the properties of stitched laminates[END_REF][START_REF] Beier | Mechanical performance of carbon fibre-reinforced composites based on stitched preforms[END_REF];

-the influence of stitching on fatigue life of laminates was examined mainly under cyclic compression loads [START_REF] Tong | 3D Fibre Reinforced Polymer Composites[END_REF] and only few study appeared for tensile fatigue (see e.g. [START_REF] Beier | Mechanical performance of carbon fibre-reinforced composites based on stitched preforms[END_REF][START_REF] Aymerich | Static and fatigue behaviour of stitched graphite/epoxy composite laminates Composites[END_REF][START_REF] Vallons | Carbon composites based on multi-axial multiply stitiche preforms -Part 6. Fatigue behaviour at low loads: Stiffness degradation and damage development[END_REF] for CFRP and [START_REF] Shah Khan | Fatigue behaviour of stitched GRP laminates[END_REF][START_REF] Aono | Fatigue damage of GFRP laminates consisting of stitched unit layers[END_REF] for GFRP).

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Despite the knowledge of the results presented in literature, a deep understanding of the fatigue endurance of stitched composite is still request because of their potential application in structural elements subject to long-term fluctuating loads, especially under tension [START_REF] Mouritz | A mechanistic approach to the properties of stitched laminates[END_REF].

The present work aims to provide a contribution to understanding of tensile fatigue and post-fatigue behavior of a structurally stitched multi-ply carbon composite. To assess the influence of the structural stitching on the mechanical response of the stitched composite the experimental data are compared to the ones of the unstitched carbon composite counterpart. The term 'structural' means that the stitching yarn does not only consolidate the plies (as the non-structural one does) but forms also a through the thickness reinforcement. The quasi-static mechanical response of the considered stitched carbon composite, produced in a different batch, were experimentally investigated in [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF].

The first part of the paper presents the characteristics of the two composites and the description of the experimental techniques applied. In the second part, the tensile-tensile fatigue life is presented and compared by Wöhler-like diagrams. Pictures obtained by X-ray device are used to investigate the damage patterns produced during fatigue after different number of cycles for a stress amplitude. The last part of the paper is dedicated to the post-fatigue residual mechanical properties of composites undergone different number of cycles. During the post-fatigue quasi-static tensile tests, the techniques described in detail in [START_REF] Lomov | Experimental methodology of study of damage initiation and development in textile composites in uniaxial tensile test[END_REF] (acoustic emission registrations and optic full-field surface strain measurements) were used to investigate the damage onset and development.

MATERIALS

The stitched and unstitched preforms (see Figure 1 and Figure 2) are laminated using two Seartex ® non-crimp fabrics (NCFs) made of Tenax HTS carbon fibres:

-the fabric with the plies construction +45º/-45º, areal weight of the plies of 267 g/m 2 (total areal weight of the fabric of 540 g/m 2 ); -the 0º/90º fabric with areal weight of the plies of 283/267 g/m 2 (total areal weight of the fabric 556 g/m 2 ).

/ 23

Each NCF has a polyester sewing thread (8.3 tex, 2.6 x 5 mm tricot + chain knitting pattern, 6 g/m 2 ) that knits together the carbon plies. The fabrics are stacked to form a symmetric laminate [45/-45/0/90/45/-45] S and has a total thickness of about 4.2 mm before impregnation. 90º direction corresponds to the non-structural sewing direction (see Figure 2).

The structurally stitched composite has a 5 x 5 mm square piercing pattern made with a 1 K carbon rowing and tufting method (KL RS 522 stitching head mounted on a KUKA-robot). The stitching direction coincides with 0º. Typical appearance of the stitched preforms is shown in Figure 1. It is shown [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF] that the knitting device for the stitching process produces openings in the composite and these openings are naturally oriented along the global fibres orientation in the ply. Characteristics of the reinforcement, stitching yarn and non-structural sewing thread are listed in Table 1.

The impregnation of unstitched and stitched preforms is obtained through VAP (Vacuum Assisted Process) using RTM-6 epoxy resin (HexFlow ® -Hexcel ® ). The final thickness of the cured laminates of 3.2÷3.5 mm shows a significant densification in comparison with the dry state. The volume fraction (V f ) was ≈54%.

EXPERIMENTAL SETUP

The tensile fatigue and the tensile quasi-static post-fatigue tests were performed using prismatic specimens having width 25mm and total length 250mm. Aluminium tabs (1.5mm thick) glued in the grip zones gave a free length of 150mm. Each specimen was preliminary checked by C-scan device (HFUS 2000 -Ingenieurbüro Dr. Hillger) to detected defects or damage imparted during the production of the laminates and the preparation of the specimens.

Tensile-tensile fatigue tests

Two hydraulic MTS testing machines were adopted for fatigue investigation. Tests were performed under constant stress amplitude, sinusoidal wave-form tensile-tensile loading and assuming the ratio R = 0.1 (ratio of the minimum σ min to the maximum σ max stress in the cycle). The stress was evaluated by the specimen cross-section area averaged from three measurements. In the direction 0 o and 90 o of both composites, four different maximum stress levels were considered (see Table 2) in order to have a complete characterization, from values close the static strength (see [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF]), to the stress level which did not lead to a complete failure before 2 million cycles. Complete failure means separation in two parts of the specimen during cyclic loading. To avoid the influence of tabs zones and grips pressure, a cyclic test was considered "valid" if the specimen broke at a distance greater than 2 cm from the tabs. At least three valid specimens were tested for each considered stress level. The loading frequency was in the range 4÷8Hz according to the applied maximum stress, as detailed in Table 2.

Quasi static post-fatigue tensile tests

The post-fatigue experimental activity included quasi-static tensile loading up to failure with acoustic emission (AE) registration, full-field surface strain mapping (SM). The specimens dedicated to postfatigue tractions were scanned by X-ray to assess the damage imparted during the cyclic test (see section 6). The post-fatigue tensile tests were performed using an INSTRON 4505 machine setting the crosshead speed of 2 mm/min. Each specimen was equipped with two acoustic emission (AE) sensors placed at the boundaries of the gauge length region. The energy of AE events registered by the AE system (AMSY-5, Vallen Systems GmbH, see details in [START_REF] Lomov | Experimental methodology of study of damage initiation and development in textile composites in uniaxial tensile test[END_REF]) and the associated loading level provide the cumulative energy for each stress level. Signals occurred outside the sensors are filtered out by the AE system by means of a suitable calibration procedure. The processing of the acoustic emission data allows to determine stress levels corresponding to characteristic damage thresholds (see section 7.2).

An optical extensometer was adopted to have the true values of strain components. The employed system measures the surface strain in the centre of the specimen (about 30 mm long gauge region) by means of the correlation of subsequent digital images taken during loading. The strain maps (SM) were obtained by the Vic2D software (LIMESS Messtechnik und Software GmbH); parameters of the strain mapping device are reported in [START_REF] Lomov | Experimental methodology of study of damage initiation and development in textile composites in uniaxial tensile test[END_REF].

Fatigue tests can be split in two different groups: fatigue until failure or 2 million cycles to generate a Wöhler-like diagram and a series of fatigue tests with fixed stress level stopped to different number of cycles. The second group of specimens were scanned by X-Ray after fatigue to detect the damage imparted and then tested under quasi-static load to determine the degradation of the mechanical properties increasing the number of cycles.

Qualitative damage considerations

The usual damage pattern of the specimens after 2 million cycles (no failure) reveals an extremely diffused delamination on the unstitched composite and limited delamination on the stitched counterpart, see Figure 3. The failure mechanism is also qualitatively different when complete failure was obtained in the cyclic tests (see Figure 4); the layers of the stitched laminate remains rather in contact, while the layers in the unstitched one had complete separation. Both in 0º and 90º loading direction, cracks appear in the external layers after few thousands cycles with higher stress levels: 350 MPa for unstitched and 400 MPa for stitched composite. The structural stitching prevents macro delaminations in particular for 90º loading direction.

The development of the damage during the cyclic tests could be studied comparing the variation of the shape of fatigue stress-displacement cycles (further called "cycle curve") and of the maximum and minimum displacement vs. the number of cycles. The displacement is in the loading direction as recorded by the tensile device. Considering tests with maximum stress 200 MPa and 0º load direction, Figure 5 shows how the damage develops differently in the stitched and unstitched composites. Most of the damage occurs within 1 million cycles for the unstitched specimens (see Figure 5a). The slope of the cycle curve, segment passing through the points of maximum and minimum stress (called "cycle slope"), continuously decreases up to one million cycles (reduction of the cycle slope of ≈34% for specimen in Figure 5a). Above one million cycles, the slope remains nearly constant (cycle slope decreases of ≈5% in the range 1÷2 million cycles). These statements are confirmed also by observing the evolution of the maximum and minimum displacements for increasing number of cycles (see Figure 5a). The stitched laminate shows (see Figure 5b) the maximum reduction of the cycle slope within 250k cycles (≈12% for sample in Figure 5b), a considerable lower reduction in the range 250k ÷ one million cycles (≈5%) and nearly stable shape of the cycles above one million cycles (reduction of the cycle slope of ≈2% between 1 and 2 million cycles). The above analysis confirm a different damage initiation and development behaviour of the two considered composites.

Wöhler-like diagrams

In Figure 6, the valid tests of the unstitched composite loaded in 0 o and 90 o are collected to depict a Wöhler-like diagram, i.e. maximum stress in the cycle (σ max ) vs. the number of cycles to failure N. The results of the valid tests for the stitched composite in 0 o and 90 o direction loading are shown in Figure 7, respectively. In each diagram the average static tensile strength, obtained in a previous work for a different production batch [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF], is also indicated as corresponding to the number of cycles N=1.

A summary and comparison of average number of cycles to failure for the stress levels considered, for each composite and loading direction is given in Figure 8.

The stitched composite shows a longer fatigue life when loaded in 0º direction than in 90º, for any stress level considered. The opposite behaviour is observed for the unstitched composite, i.e. loading in 90º direction provides an higher average number of cycles to failure with respect to 0º direction for any considered stress level.

The stitching has a positive effect in term of fatigue life when the load is applied along the 0º fibres i.e. the stitching direction (see Figure 6a, Figure 7a). For the stress levels in Figure 8a,b, the average fatigue life of stitched composite is 140% and 322% higher for maximum stress 240 MPa and 320 MPa, respectively, with respect to the unstitched counterpart. On the other hand, the stitching has a negative effect on the tensile fatigue life when load is applied in 90º direction, i.e. orthogonal to the stitching direction (see Figure 6b and Figure 7b). In this case, the reduction of the average fatigue life (see Figure 8a,b), is 52% and 73% for 240 MPa and 320 MPa, respectively. All these differences are statistically significant at least at 95% confidence level.

The above mentioned results show: 8 / 23 [START_REF] Tong | 3D Fibre Reinforced Polymer Composites[END_REF] The unstitched composite has the best fatigue performance if loaded in the direction of the polyester sewing thread (non-structural), i.e. 90 o , while has reduced fatigue life when loaded orthogonally to this direction (i.e. 0 o ).

(2) The structural carbon stitching provides an improvement of the fatigue performance when the tensile cyclic load is applied in the carbon stitching direction (0 o in the present study), on the contrary the fatigue life decreases when loading is orthogonal to the structural stitching direction.

POST-FATIGUE X-RAY DAMAGE ANALYSIS

The damage imparted during fatigue tests was investigated using an X-ray device. In particular, the damage analysis was focused on specimens fatigued up to three fixed number of cycles (1k, 10k, and 100k) ('k' means thousand) with maximum stress of 240 MPa.

In order to make the cracks and other damages visible, the specimens were maintained under the effect of a reactant for 12 hours. The reactant was a 99% diiodomethane solution. Using the Micro Focus Computer Tomography AEA Tomohawk system, 2D images of the specimens were produced. The specimens were irradiated with a Phillips ® HOMX 161 X-ray source setting: voltage 89kV, current 0.38mA and iris position 91.9%. Typical appearance of unstitched specimens is shown in Figure 9 and Figure 10: cracks in ±45º directions are evident and mostly affecting the external layers. Density of cracks increases with the number of cycles and after 100k cycles the unstitched composite shows large delamination zones (dark/black areas in Figure 9c). The delamination is mainly concentrated at the interface between the ±45º external layers and the rest of the lay-up. Debonding and cracks are also visible in the central part of the cross-section (Figure 10). Figure 11 and Figure 12 show stitched specimens after fatigue. A large density of cracks appear in ±45º direction, and as expected the density increases with increasing number of cycles. After 10k cycles marked openings appear on the specimen according to the stitching pattern. The damage observation in the cross-section shows the stitching effect in reducing the delamination. Some delaminations appear after 100k cycles (Figure 12c) but extremely reduced in comparison to the unstitched composite (Figure 10c). 9 / 23

POST-FATIGUE QUASI-STATIC TENSILE TEST RESULTS

The influence of the fatigue loading on the residual mechanical properties was measured by quasistatic tensile tests of specimens fatigued with maximum stress 240 MPa after different number of cycles (1k, 10k and 100k). The post-fatigue tensile tests were equipped with the strain mapping device and AE sensors. The quasi-static tensile tests of unstitched composite fatigued in 90º direction after 100k cycles could not be performed due to the elevate damage imparted during the fatigue tests.

Residual Mechanical Properties

The residual mechanical properties of the two composites in both loading direction are summarized in the histograms of Figure 13 in term of stiffness (elastic modulus) and strength (ultimate stress). For each composite and loading direction, one specimen has been tested for each pre-defined number of cycles.

The comparison of the obtained mechanical properties (Figure 13) provides only a trend of the fatigue influence on the residual mechanical properties, but cannot be considered exhaustive due to the limited number of specimens. A larger set of experimental data will be collect in future work.

The residual elastic moduli in Figure 13a show an invariance of the stiffness up to 10k cycles, while a significant dropping is observed after 100k cycles, especially for the unstitched composite in 0 o direction (reduction of 30% with respect to the value for 1k cycles). Only the stitched composite tested in 90º direction maintains the stiffness even after 100k cycles, while in 0 o direction a reduction of 13% was recorded with respect to the modulus after 1k cycles.

The comparison of average ultimate stress (see Figure 13b) shows rather stable values of the strength after 10k cycles, a maximum reduction of 9% was recorded for the unstitched composite in 90 o direction.

A significant drop of 40% is notable after 100k cycles for the unstitched composite in 0º, while the stitched showed only a reduction, with respect to the strength after 1k cycles, of 11% and 6% in 0º and 90º direction, respectively.

It must be highlighted that this comparison does not use the quasi-static data in [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF] (which were measured on different batch), but is fully related to the composites in the present study.

Strain maps and Acoustic Emissions recordings

The optical extensometer provides maps of the strain components on the external surface of the specimen. The picture frame (25 mm x 30 mm), placed in the centre of the specimen, was painted with spackle pattern for digital image correlation and was dedicated to the study of the strain distribution. The stitched composite, after 10k cycles, provide the two maps of the strain component in the load direction in Figure 14 ((a) loading in 0 o direction and (b) in 90 o ) for a stress level of 220 MPa. In Figure 14, both strain maps show a regular pattern of concentrations in the stitching points, i.e. the zones where the damage starts to develop. It is reminded that the optical extensometer device takes pictures of the external layers (±45º).

The acoustic emission (AE) equipment records acoustic events and provides the cumulative energy. In Figure 15 and Figure 16, typical AE diagrams are depicted for a specimen of each composite and for each loading direction considered. The processing of these results allowed to determine: the AE Threshold Stress (AETS) σ min , above which relatively low energy acoustic events start to occur; the First Damage Threshold Stress (FDTS) σ 1 at the first increase of the slope of the cumulative AE energy curve; the Second Damage Threshold Stress (SDTS) σ 2 at the second "knee" on the AE cumulative energy curve [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF]. In Table 3 the value of average threshold σ 1 and σ 2 are collected for the specimens fatigued after different number of cycles. The graphs in Figure 15 and Figure 16 and the values of first damage threshold stress σ 1 in Table 3 show a significant amount of events recorded close to the maximum stress formerly set during fatigue tests (240 MPa), below this threshold the amount of noise is barely significant.

The damage detected during quasi-static tensile tests in [START_REF] Koissin | Structurally Stitched NCF preforms: Quasi-static response[END_REF], below the stress level of 240 MPa, was not recorded in the present work because completely imparted during cyclic tests. The large part of the damage (AE events) appears in the present quasi-static tensile loading for stress levels above the maximum stress applied during fatigue.

The experimental study, presented in this work, deals with the fatigue and the post-fatigue quasi-static tensile mechanical response of a structurally stitched multi-ply carbon composite and its equivalent unstitched counterpart. The mechanical response was investigated in two orthogonal directions and the main results are summarized in the following.

The fatigue tests showed:

-unstitched composite has the best performance in the direction of the non-structural polyester sewing (90 o ) and the worst in 0 o , for each stress level considered; -X-ray images of unstitched composite show, for the considered stress level, a diffuse delamination after the early stage of the cyclic tests (after 10k cycles) in both loading directions; -structural stitching increase the fatigue life in the sewing direction (0 o ) and reduce the one in the direction orthogonal to the stitching (90 o ); -fatigue life in 0 o direction of the stitched and in 90 o of the unstitched composite are similar.

The post-fatigue quasi-static tests demonstrate:

-unstitched composite shows invariance of the stiffness in the early stage of the cyclic loading (after 10k cycles), and a significant reduction after 100k cycles ; -stitched composite tested in 90º direction did not have a significant decrease of the stiffness even after 100k cycles; -ultimate stress has stable values if unstitched composite is fatigued for 10k cycles in direction 0º, while has significant drop after 100k cycles ; -the influence of the cyclic loading on the ultimate stress of the stitched composite is considerable lower than on the unstitched counterpart.

LIST OF FIGURE CAPTIONS

LIST OF TABLE CAPTIONS

Table 1. Some properties of the components (data from Seartex® and Walker Wilhelm GmbH). Table 2. Stress levels and frequencies adopted in cyclic loading. Table 3. Damage threshold σ1 and σ2 of fatigued specimens after different number of cycles and maximum stress 240MPa.

Figure 1 .

 1 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.Figure 2. (a) Face side and (b) back side of unstitched preform.Figure 3. Fatigue tests maximum stress 200 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after 2 million cycles.Figure 4. Fatigue tests maximum stress 320 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after complete failure. Figure 5. Cyclic tests load in 0º direction, maximum stress 200 MPa. Some stress vs. displacement curves; maximum and minimum displacement vs. number of cycles. (a) unstitched and (b) stitched composite. Figure 6. Maximum stress σµαξ vs. number of cycles to failure N for unstitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).Figure 7. Maximum stress σµαξ vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles). Figure 8. Average number of cycles to failure for the applied maximum stress levels (± means standard deviation). Figure 9. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 10. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 11. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 12. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles. Figure 14. Mapping of the strain component in the load direction, for stress level ≈220 MPa. Load direction is horizontal. Specimens of stitched composite in (a) 0o and (b) 90o direction after 10.000 cycles with maximum stress 240 MPa. Figure 15. Unstitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]). Figure 16. Stitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]).

Figure 2 .

 2 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.Figure 2. (a) Face side and (b) back side of unstitched preform.Figure 3. Fatigue tests maximum stress 200 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after 2 million cycles.Figure 4. Fatigue tests maximum stress 320 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after complete failure. Figure 5. Cyclic tests load in 0º direction, maximum stress 200 MPa. Some stress vs. displacement curves; maximum and minimum displacement vs. number of cycles. (a) unstitched and (b) stitched composite. Figure 6. Maximum stress σµαξ vs. number of cycles to failure N for unstitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).Figure 7. Maximum stress σµαξ vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles). Figure 8. Average number of cycles to failure for the applied maximum stress levels (± means standard deviation). Figure 9. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 10. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 11. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 12. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles. Figure 14. Mapping of the strain component in the load direction, for stress level ≈220 MPa. Load direction is horizontal. Specimens of stitched composite in (a) 0o and (b) 90o direction after 10.000 cycles with maximum stress 240 MPa. Figure 15. Unstitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]). Figure 16. Stitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]).

Figure 3 .

 3 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.Figure 2. (a) Face side and (b) back side of unstitched preform.Figure 3. Fatigue tests maximum stress 200 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after 2 million cycles.Figure 4. Fatigue tests maximum stress 320 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after complete failure. Figure 5. Cyclic tests load in 0º direction, maximum stress 200 MPa. Some stress vs. displacement curves; maximum and minimum displacement vs. number of cycles. (a) unstitched and (b) stitched composite. Figure 6. Maximum stress σµαξ vs. number of cycles to failure N for unstitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).Figure 7. Maximum stress σµαξ vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles). Figure 8. Average number of cycles to failure for the applied maximum stress levels (± means standard deviation). Figure 9. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 10. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 11. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 12. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles. Figure 14. Mapping of the strain component in the load direction, for stress level ≈220 MPa. Load direction is horizontal. Specimens of stitched composite in (a) 0o and (b) 90o direction after 10.000 cycles with maximum stress 240 MPa. Figure 15. Unstitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]). Figure 16. Stitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]).

Figure 4 .

 4 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.Figure 2. (a) Face side and (b) back side of unstitched preform.Figure 3. Fatigue tests maximum stress 200 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after 2 million cycles.Figure 4. Fatigue tests maximum stress 320 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after complete failure. Figure 5. Cyclic tests load in 0º direction, maximum stress 200 MPa. Some stress vs. displacement curves; maximum and minimum displacement vs. number of cycles. (a) unstitched and (b) stitched composite. Figure 6. Maximum stress σµαξ vs. number of cycles to failure N for unstitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).Figure 7. Maximum stress σµαξ vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles). Figure 8. Average number of cycles to failure for the applied maximum stress levels (± means standard deviation). Figure 9. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 10. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 11. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 12. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles. Figure 14. Mapping of the strain component in the load direction, for stress level ≈220 MPa. Load direction is horizontal. Specimens of stitched composite in (a) 0o and (b) 90o direction after 10.000 cycles with maximum stress 240 MPa. Figure 15. Unstitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]). Figure 16. Stitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]).

Figure 7 .

 7 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.Figure 2. (a) Face side and (b) back side of unstitched preform.Figure 3. Fatigue tests maximum stress 200 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after 2 million cycles.Figure 4. Fatigue tests maximum stress 320 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after complete failure. Figure 5. Cyclic tests load in 0º direction, maximum stress 200 MPa. Some stress vs. displacement curves; maximum and minimum displacement vs. number of cycles. (a) unstitched and (b) stitched composite. Figure 6. Maximum stress σµαξ vs. number of cycles to failure N for unstitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).Figure 7. Maximum stress σµαξ vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles). Figure 8. Average number of cycles to failure for the applied maximum stress levels (± means standard deviation). Figure 9. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 10. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 11. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 12. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles. Figure 14. Mapping of the strain component in the load direction, for stress level ≈220 MPa. Load direction is horizontal. Specimens of stitched composite in (a) 0o and (b) 90o direction after 10.000 cycles with maximum stress 240 MPa. Figure 15. Unstitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]). Figure 16. Stitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]).

Figure 9 .

 9 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.Figure 2. (a) Face side and (b) back side of unstitched preform.Figure 3. Fatigue tests maximum stress 200 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after 2 million cycles.Figure 4. Fatigue tests maximum stress 320 MPa, load direction 90o. Cross-section view of (a) unstitched and (b) stitched specimen after complete failure. Figure 5. Cyclic tests load in 0º direction, maximum stress 200 MPa. Some stress vs. displacement curves; maximum and minimum displacement vs. number of cycles. (a) unstitched and (b) stitched composite. Figure 6. Maximum stress σµαξ vs. number of cycles to failure N for unstitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).Figure 7. Maximum stress σµαξ vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles). Figure 8. Average number of cycles to failure for the applied maximum stress levels (± means standard deviation). Figure 9. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 10. Typical X-Ray of unstitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 11. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Front view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 12. Typical X-Ray of stitched specimens after cyclic traction in 0º direction, maximum stress 240 MPa. Cross-section view of specimens stopped at: (a) 1k; (b) 10k and (c) 100k cycles. Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles. Figure 14. Mapping of the strain component in the load direction, for stress level ≈220 MPa. Load direction is horizontal. Specimens of stitched composite in (a) 0o and (b) 90o direction after 10.000 cycles with maximum stress 240 MPa. Figure 15. Unstitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]). Figure 16. Stitched composite: post-fatigue tensile test in 0º direction after: (a) 1.000 cycles and (b) 10.000 cycles, maximum stress 240 MPa. Acoustic Emission events and cumulative energy ([a.u.] means [arbitrary unit]).

Figure 1 .Figure 2 .Figure 3 .Figure 4 .Figure 5 .Figure 6 .

 123456 Figure 1. (a) Face side and (b) back side of 5 x 5 mm structural stitched preform.

Figure 7 .Figure 8 .Figure 9 .Figure 10 .Figure 11 .Figure 12 .

 789101112 Figure 7. Maximum stress σ max vs. number of cycles to failure N for stitched composite loaded in: (a) 0º direction; (b) 90º direction. ('→' means no failure after 2 million cycles).

Figure 13 .Figure 14 .Figure 15 .Figure 16 .

 13141516 Figure 13. (a) elastic modulus and (b) ultimate stress of fatigued specimens (maximum stress 240 MPa) after different number of cycles.

Table 1 . Some properties of the components (data from Seartex ® and Walker Wilhelm GmbH).

 1

	Tenax® HTS	Tenax® HTA (stitching yarn)	Polyester 83 dtex SC
	Filament
	Linear Density [Tex]	800	67		8,3
	Number of fibres	12000	1000		12
	Twisting [m -1 ]	0	S 1 5		Z 2 4
	Fiber
	Diameter [ µ m]	7	7		2,1
	Density [g/cm 3 ]	1,77	1,76		1,38
	Maximum Stress [MPa]	≥ 350	320	240	200
	Frequency [Hz]	4	4	6	8

Table 2 . Stress levels and frequencies adopted in cyclic loading.

 2

		1000 cycles	10000 cycles	100000 cycles
	Samples	σ1	σ 2	σ1	σ 2	σ1	σ 2
		[MPa]	[MPa]	[MPa]
	unstitched 0 o	223,7	246,7	237,9	272,9	213,4	250,6
	unstitched 90 o	230,0	246,3	233,8	250,4	n/a	n/a
	stitched 0 o	236,1	247,2	242,0	254,6	248,9	255,0
	stitched 90 o	240,8	247,5	242,5	269,9	235,1	242,1

Table 3 . Damage threshold σ 1 and σ 2 of fatigued specimens after different number of cycles and maximum stress 240MPa.

 3

Acknowledgements

The research reported here has been carried out in the framework of the Erasmus Master program of Vanni Neri Tomaselli in K.U. Leuven and Politecnico di Milano. The help of laboratory staff of the Department MTM -Bart Pelgrims, Kris van der Staey and Johan Vanhuist -is gratefully acknowledged


N L Beveridge
email: n.beveridge@physics.gla.ac.uk

A A Van Veggel

M Hendry

P Murray

R A Montgomery

E Jesse

J Scott

R B Bezensek

L Cunningham

J Hough

R Nawrodt

S Reid

S Rowan

Low temperature strength tests and SEM imaging of hydroxide-catalysis bonds between silicon

Silicon is under consideration as a substrate material for the test masses and suspension elements of gravitational wave detectors of improved sensitivity. Hydroxide catalysis bonding is a candidate technique for jointing silicon elements with the potential for both high strength and low mechanical loss. A future detector with quasi-monolithic silicon final stages may operate at cryogenic temperatures. Here we present the first studies of the strength of siliconsilicon bonds at 77 K (liquid nitrogen temperature) and show characteristic strengths of ∼ 44 MPa are achieved. When comparing cryogenic to room temperature results no significant difference is apparent in the strength. We also show that a minimum thickness of oxide layer of 50 nm is desirable to achieve reliably strong bonds. Bonds averaging 47 nm in thickness are achieved for oxide thicknesses greater than 50 nm.

Introduction

Hydroxide catalysis bonding is a technique that was developed and used successfully for the telescope construction in the Gravity Probe B space mission [?]. This technology has successfully been adapted for use in the construction of the mirror suspensions of laser interferometric gravitational observatories. A network of six detectors has been constructed to search for gravitational waves from astrophysical events that involve the asymmetric acceleration of significant mass. There are three detectors (two 4 km detectors and one 2 km detector) forming the US LIGO system [?, ?], a French-Italian detector, Virgo [?], the German-UK GEO 600 detector [?] and the TAMA300 instrument [?] in Japan. These detectors aim to measure the change in separation of mirrors suspended as pendulums caused by astrophysical gravitational radiation.

The technique of hydroxide catalysis bonding was applied in the GEO 600 detector in order to create a quasi-monolithic suspension of the fused silica mirrors. Fused silica fibres were welded to fused silica interface pieces, called 'ears' which provide suitable welding points onto the sides of the mirror, [?] bonded onto the sides of the mirror using the hydroxide catalysis bonding technique [?]. The technique will be used in a similar way in upgrades to the suspensions of the LIGO [?]and Virgo [?] detectors to form 'Advanced' detector systems which aim to be operational around 2014. These Confidential: not for distribution. Submitted to IOP Publishing for peer review 2 March 2011 advanced instruments should have a factor of 10 to 15 times better sensitivity than first generation detectors. The reason for using 'monolithic' fused silica mirror suspensions is to reduce as much as possible the thermal noise in the operating frequency band of the detectors between ∼ 10 Hz and a few kHz, which can be achieved by reducing the number of contact points of the suspension fibres to the test masses or making any interfaces low loss. Fused silica is a material that shows suitably low thermal noise at room temperature [?, ?, ?]. The hydroxide catalysis bonding technique adds very little to the noise, because of a combination of its level of mechanical loss [?, ?], small bond thickness and high mechanical strength [?]. Additionally it is vacuum compatible and allows for precision alignment of pieces.

Plans are also developing for the design of potential 'third generation' detectors (such as the Einstein Telescope (http://www.et-gw.eu)) [?, ?]. These detectors may well operate at cryogenic temperatures to further reduce thermal noise. Silicon is a prime candidate material for use in the test masses and their suspensions because of its desirable thermo-mechanical properties in the cryogenic regime [?, ?, ?, ?]. With some adaptation, hydroxide catalysis bonding may also be a viable technique for use in third generation detectors; however, to evaluate its suitability it is essential to quantify both the strength of silicon-silicon bonds at cryogenic temperatures and the thickness of such bonds as the bond thickness has a direct effect on the contributions of the bond to the overall thermal noise of a bonded suspension.

We have previously investigated the strength of silicon-silicon bonds at room temperature under shear [?] with some investigation into the effect of the oxide layer. Other authors [?] have studied the effect of the effective flatness of silicon and sapphire bonds on bending strengths of hydroxide catalysis bonds at room temperature. In this paper investigations of the strength of silicon-silicon hydroxide catalysis bonds are presented applying for the first time the same strength testing technique as was used in [?] both at room temperature and at ∼ 77 K, allowing studies of the strength of the bonds to be carried out as a function of the thickness of the thermal SiO 2 layer grown on the surface to be bonded.

Hydroxide Catalysis Bonding

The hydroxide catalysis bonding technique allows bonding between a variety of materials if a silicatelike network can be formed at the material surfaces, which is the case for most oxide materials, e.g. silica, Zerodur, fused silica, ULE glass or granite [?]. The two materials are bonded using an alkaline bonding solution; e.g. sodium hydroxide (NaOH), potassium hydroxide (KOH) or sodium silicate (Na 2 SiO 3 ) dissolved in water.

For application to the suspensions of the gravitational wave detectors the bonding surfaces ideally have global surface figures that match to within 60 nm peak-to-valley to create very thin bonds with a hydroxide solution; the final thickness of the bond is important in minimizing the mechanical loss and associated thermal noise. Both bonding surfaces are cleaned in a clean room environment to remove any chemical or particulate contaminants. The bonding solution is filtered with a 0.2 µm pore size filter and a volume of typically a few tenths of µl/cm 2 is deposited on one bonding surface (facing upwards). The other substrate is then placed gently on top of the first substrate and can be compressed slightly to aid successful bonding. When the bonding solution comes into contact with the bonding surfaces the hydroxide catalysis commences. This consists of three steps; hydration and etching, polymerization, and dehydration [?]. These steps have been described in detail in previous papers [?, ?].

The time taken for a bond to form can be controlled by altering temperature and/or pH of the bonding solution used [?, ?] . The bond thickness between fused silica surfaces is found to be approximately 40 nm -100 nm [?, ?].

To make bonding of silicon components possible, the bonding surfaces must ideally have a thin coating of SiO 2 , with which the hydroxide can react to form the bond. This layer can be formed, for example, through thermal oxidation by placing the cleaned pieces in a quartz tube furnace at typically 800 -1200 • C in a dry air or a wet environment using air, nitrogen or oxygen as a carrier gas [?]. Previous studies of bonding silicon and silicon carbide [?] seemed to suggest that the nature of the silicon oxide layer plays a role in the success of the bonding process. In [?] it was postulated that if hydrogen formed during the bonding process due to direct contact between silicon and hydroxide this might have an effect on strength.

In practical configurations in the suspensions of gravitational wave detectors the forces applied to bonds are not purely shear; 'peel' stresses are also present, thus the strength of bonds under different types of loading conditions are of interest.

Strength Testing

For the strength tests rectangular silicon blocks (20 mm × 10 mm × 5 mm) from two different silicon ingots were used. Both ingots were manufactured by Prolog; ingot one had a <111> crystal orientation, ingot two had a <100> crystal orientation, as shown in Figure 1. Both were boron doped P-type silicon ingots with an unknown doping level. The bonding surface was one of the 5 mm × 10 mm surfaces, so that after bonding a sample was created with dimensions 40 mm × 10 mm × 5 mm. The bonding surfaces of all samples were polished to a nominal flatness of λ/10 where λ=633 nm. The flatness of each side was measured before oxidation using a Zygo GPI XP/D ‡ interferometer at 633 nm. All samples were marked with identification numbers, to allow the bonds to be characterized and tracked throughout the experimental process.

Sample Preparation

In order to remove any organic residue on the bonding surfaces prior to oxidation an acid clean, using a 1:7 volumetric ratio of hydrogen peroxide and sulphuric acid, was performed on all samples. The samples were placed in a tube furnace at ∼ 1000 • C for periods of time between 5 and 55 minutes to grow thermal SiO 2 layers of various thicknesses. A wet nitrogen method was used; nitrogen gas saturated with water vapor was passed through the furnace for the duration of the oxidation.

During the process of oxidising some of the blocks, it was discovered that the oxide layers grown were not as thick as originally intended. As a result, it was necessary to re-oxidise some of the samples. The oxidised blocks were put back into the tube furnace (in the same environment as before) to 'top-up' the oxide layer. The resulting oxide layer was measured and assumed to be a single oxide layer.

The bonding surfaces were made hydrophilic prior to bonding through a regime of polishing with cerium oxide in de-ionised water followed by cleaning with sodium bicarbonate. Immediately before the bonding solution was deposited, the surface was wiped with methanol as a final cleaning step.

The bonding solution was pipetted onto the surfaces using 0.4 µl of solution per cm 2 (0.2 µl for the strength test samples). The bonding solution was produced by diluting a commercially available sodium silicate solution (14% NaOH and 27% SiO 2 ) with de-ionized water at a volumetric ratio of 1:6, a solution used previously [?].

All samples were left to cure at room temperature for a minimum period of 4 weeks and were categorized by the minimum oxide layer, t min , of the pair of surfaces to be bonded, the difference between the thickness of each of the two oxide layers, t diff and the ingot pairing.

Strength Testing Procedure

The bond strength was determined using a four point bend test as shown in Figure 2 and is in line with ASTM standard C 1161-2C [?]. The samples were placed on the setup and a force, F , was applied through a loading arm and measured until the sample broke. If the supports underneath the sample are placed at a distance L the force is applied equally through two points on top of the sample at a distance L/2 apart, with both distances centered at the bond.

The samples were tested on Zwick-Roell static 2 kN and 200 kN machines, and the strength was calculated using (1) below where F is the force, L is the distance between the bottom supports, b is the width of the sample and d is the thickness of the sample.

σ max = 3F L 4bd 2 (1)
Measurements were performed at room temperature and at ∼77 K. The latter cryogenic measurements were performed by submerging the samples in liquid nitrogen and waiting for thermal equilibrium by observing the settling of the nitrogen after boiling before conducting the strength test. ‡ http://www.zygo.com/?/met/interferometers/gpi/ 109 samples were strength tested; 49 at room temperature and 86 at ∼77 K. A photograph of the strength testing is shown in Figure 3.

Results

Figure 4 shows how the strength of the samples varied with the minimum oxide layer thickness (t min ) found on the surface of each sample and three main features can be identified. Firstly, when looking only at the cryogenic temperature results, there is a clear trend of decreasing strength once the minimum oxide layer is less than 50 nm. Secondly, when comparing cryogenic to room temperature results at comparable oxide layer thicknesses there appears to be no significant difference apparent in strengths indicating that the strength of the bonds is not negatively influenced by thermal loading due to expansion differences between the bond material (silicon dioxide and siloxane chains) and the bulk material (silicon). Lastly, there appears to be a grouping of samples that lie in 75 nm < t min < 260 nm that have somewhat lower strength (less than 30 MPa) than the remainder The bond strength at cryogenic temperature shows a similar average strength as at room temperature, but a wider range of strengths is apparent. The absence of correlation between oxide layer thickness and bond strength at thicknesses above ∼ 50 nm shows an opportunity to minimize potential thermal noise by reducing the oxide layer thickness as much as possible without compromising bond strength.

of the samples.

Due to the brittleness of the samples, a statistical variation could be expected to be seen in their strengths. This occurs because a fracture may originate at flaws in the material itself and therefore the strength will depend upon the probability of there being a flaw that is large enough to cause a fracture normal to the direction of the maximum tensile stress.

The variations in strength of such materials are generally modeled by a Weibull distribution [?] rather than, for example, a Gaussian. The Weibull distribution is commonly used in modeling extreme or critical phenomena or in survival and reliability analysis where one wishes to estimate the 'time to failure' of an industrial or mechanical process. In particular the Weibull distribution can be strongly skewed and is thus appropriate for modeling statistical variations which are not symmetric with respect to some given characteristic behaviour -such as one may encounter when considering the distribution of breaking strengths.

The two-parameter Weibull distribution has a probability density function (pdf) given by (2):

P (F ) = m F 0 F F 0 m-1 exp - F F 0 m (2)
where the Weibull modulus, m, provides a measure of the variability of the material properties -with increasing Weibull modulus indicating a smaller range of variability. The parameter F 0 represents a characteristic strength for the distribution. The combination of these two parameters permits comparison between data sets acquired from similar experiments, in order to explore and identify factors that might influence the strength of the data sets.

In previous literature (see [?]) estimation of m and F 0 has generally been carried out in terms of the cumulative distribution that corresponds to the pdf of (2). The measured strengths and estimated cumulative probabilities for the data set are transformed into new variables related to m and F 0 via a simple straight line dependence. Fits to these parameters are then obtained via, for example, linear regression. However this approach generally assumes that the scatter about the regression line is Gaussian -an assumption that may be questionable given the highly skewed nature of the original Weibull distribution.

In this paper instead a Bayesian analysis was carried out that simultaneously estimates m and F 0 directly from the Weibull pdf and requires no such Gaussian assumption. Moreover we use a Markov Chain Monte Carlo method [?] to obtain confidence regions for our fitted Weibull parameters. Figure 5 shows 68% confidence regions for the joint parameter fits to the full cryogenic data set and room temperature data set. Note that these regions are not elliptical in shape, as the Gaussian assumption would require.

Figure 6 shows estimates of the m parameter (top figure) and F 0 parameter (bottom figure) for all data sets, determined by marginalizing the joint posterior distribution of m and F 0 . Here the markers indicate the mode of the marginalized posterior and the error bars indicate the central 68% of the distribution. It can be seen that the values for the Weibull modulus and characteristic strength vary when different factors are taken into account. The low value of m for the full data sets indicates that there may be several factors affecting the strength of the samples. Some possible factors were identified during the experiment and filters were applied in order to identify which of these factors influence the characteristic strength and spread of results. Initially, a minimum oxide layer thickness filter was applied. The value of 50 nm was selected after inspection of Figure 4 as discussed earlier, in which a clustering of low strength samples for oxide thicknesses below 50 nm can be seen. There appears to be no correlation between the minimum oxide layer thickness on the pair of bonding surfaces for each sample and the strength of the sample when the minimum oxide layer thickness on the bonding surfaces is between 50 nm and 250 nm. This is of importance because the goal is to minimize the thickness of the overall oxide and bond layer as much as possible for application in third generation gravitational wave detectors, due to the direct relationship between the thickness of the oxide layer and bond and the thermal noise caused by the bond [?].

A significant limitation with this analysis is the small number of data points after certain filters are applied. However, a clear effect is seen in Figure 6 when removing samples with a minimum oxide layer thickness of less than 50 nm at cryogenic temperatures: both the characteristic strength and Weibull modulus increase. This is not seen at room temperature, possibly because only a very small portion of the room temperature samples had oxide layers below 50 nm. The complete sample set size having oxide thicknesses lower than 50 nm was too small to allow statistically significant results to be obtained at both room and low T, thus measurements were predominantly made at cryogenic temperature for this group of samples.

The samples broke in two different ways; in a 'bond' break, where the fracture was along the bond of the sample, or in a 'diagonal' break, where the fracture went through the bulk material. It was observed that the majority of the samples with a minimum oxide layer of less than 50 nm had a bond break in comparison to the samples with thicker oxide layers mostly having a diagonal break pattern, suggesting that when the bonds were weak the sample would break along the bond. This confirms suspicions that there is a minimum oxide layer needed.

Looking further at Figure 6 it was observed that when the difference between the oxide layers on the bonding surfaces of each sample was greater than 20 nm, although the characteristic strength (F 0 ) only increases at room temperature (it remains the same at cryogenic temperature) the value of m increases by a significant amount at both temperatures, showing a reduction in the spread of strengths. The low grouping seen in Figure 5 is also eliminated. It is hypothesized that there may The key describing the filters applied to each data set is shown in Table 1.

be a geometrical effect resulting from the large difference in oxide layer that is influencing these results. Finite Element Analysis may shed light on this.

The effect of re-oxidation does not consistently change the characteristic strength, however the value of m decreases when the samples were re-oxidised suggesting that the value of the characteristic strength is less reliable when the samples have been re-oxidised. This could be caused by an increased likelihood of contamination of samples before bonding or a weak interface between layers.

There is a marked difference between the room temperature results for characteristic strengths and Weibull modulus of samples from the same ingot in comparison to those from different ingots; both the strength and modulus increase when samples are from mixed ingots. At cryogenic temperature, the strength does not appear to change. However, the Weibull modulus does increase significantly for samples from mixed ingots. A possible explanation is a difference in mechanical behaviour in samples from mixed ingots due to differences in the density of the oxide layer. A slowly grown thermal oxide layer will be denser than one grown rapidly [?]. Silicon of orientation < 111 > will grow a thermal oxide layer at a faster rate to silicon of orientation < 100 > and will therefore have a slightly less dense thermal oxide layer. However, the exact mechanism causing the improved value of m and the increase in characteristic strength at room temperature is not yet known.

Bond Thickness

Sample Preparation

For the measurements of bond thickness 10 silicon discs were used, each of diameter 12.6 mm and thickness 6.3 mm, from the same ingot as the samples discussed in [?] (<111>, purity >99.999%, resistivity >1 Ohm cm).

These samples were oxidized using the same wet oxidation technique as for the strength tests, with two samples oxidized for each oxidation time of 10, 20, 30, 40 and 50 minutes, respectively. After oxidation the thicknesses of the oxide layers on each of the silicon samples were measured at several points on the bonding surfaces using a Sentech SE850 Ellipsometer §, and the results averaged. The flatness measurements of the samples were repeated using the Zygo interferometer and the results averaged.

Table 2 shows the measured oxide thicknesses for the discs used in the bond thickness investigation.

Scanning Electron Microscope imaging

From the bonded 12.6 mm diameter disc samples, two 3 mm cross sections were sawn in such a way that the bond and oxide layers lay perpendicular to the cut face. The slices cut from the silicon substrates were then polished with progressively finer polishing grits (16 µm, 9 µm, 3 µm, and sub-micron grits) on a Logitech Precision Polishing Machine . The surface roughness after polishing is in the order of Ra ∼5 nm after polishing. This makes it possible to image the bonds using scanning electron microscopy.

The samples were cleaned and studied using a Hitachi TM-1000 Tabletop Electron Microscope ¶ and images of the bond and oxide region were captured. This gave a clear indication of the total thickness of the bond and oxide layers. However, when viewed using the maximum magnification of the electron microscope (10,000) it is impossible to readily distinguish between the oxide and bond layers themselves in each of the cross sections. A selection of the cross sections were then imaged using a more powerful FEI Nova 200 Dual beam FIB system Scanning Electron Microscope + at the Kelvin Nanocharacterisation Centre at the University of Glasgow.

Results of the SEM imaging

Using the Hitachi tabletop electron microscope it was possible to measure the overall thickness of the bond and oxide layers for all samples mentioned above. With the Nova scanning electron microscope this was possible as well. The results are shown in Table 3. The averages are taken over more than 20 measurements per sample from both the Nova and Hitachi SEMs. The error is the error of the mean of these measurements along the entire length of the sample, and indicates that there was a relatively small amount of variation of thickness along the length of the sample. By subtracting the thicknesses of oxide layers measured prior to bonding (see Table 3), the bond thickness can be determined. The bond thickness is plotted against oxide layer thickness in Figure 7. There is very little variation in the bond thicknesses with oxidation time or thickness and the average bond thickness was found to be 47 ± 15 nm. The average peak to valley flatness of the samples after oxidation, measured before bonding was 43 ± 3 nm.

Figure 8 shows an image of a cross section of a bond between two oxide layers created after a 30 minute oxidation made with the NOVA scanning electron microscope at 75 000 x magnification.

http://www.logitech.uk.com/PM5.asp ¶ http://www.hht-eu.com/cms/7929.html + http://www.knc.gla.ac.uk/index.php?L1=content&L2=Equipment&L3=FIB The image is typical for images made of the other samples. With the NOVA SEM it was also possible to discern the oxide and bond layers. The oxide thickness measurements with the SEM are very comparable (to ±10 nm) to the thicknesses measured before bonding using ellipsometry (compared to Table 2). It is interesting to note that the oxide layers have not thinned significantly due to any hydroxide etching.

Discussion and Summary

Bend strength tests have been performed on silicon-silicon bonds that incorporated thermal oxide layers of varying thicknesses. The bond strength reduces significantly with oxide layer thicknesses below 50 nm at cryogenic temperature. Strength test results show a characteristic strength of approximately 49 MPa at 77 K and 42 MPa at room temperature for samples with a minimum oxide layer of 50 nm.

Van Veggel et al [?] showed bending strengths averaging 23MPa in silicon carbide-silicon carbide bonds. Those experiments were performed with similar sample geometry and with a very similar 4-point bending set-up. The strengths for silicon-silicon bonds reported by van Veggel et al [?] averaged 3.9 MPa at room temperature. Those strengths are a factor of 10 lower than those reported in this paper. The experiments done by van Veggel et al [?] were however performed under different loading conditions; i.e. they were shear experiments that were thought to be limited by the way the samples were clamped. Performing shear strength experiments that will be less dominated by the sample and loading geometry should shed light on the isotropy of the bond strength under different loading conditions. The results in this paper support the postulation by van Veggel et al [?] that an oxide layer which is too thin can negatively influence the bond strength.

The bending stress in silicon-silicon bonds have previously been measured by Dari et al [?] to be approximately 8.7 ± 3.7 MPa at room temperature. The results presented here use a different sample geometry and are significantly higher, also demonstrating the need for an oxide layer to be present for a successful bond to form.

In summary, it can be seen that the characteristic strength of all the samples studied at both cryogenic and at room temperature lies above 20 MPa, and there is ample opportunity for this to increase along with the Weibull modulus once factors negatively affecting the bond can be identified and removed. It has been shown that repeated oxidation, differences in oxide thickness and ingot pairing can have effects on bond strength that would benefit from further investigation.

The bond thickness measurements show that when the oxide layers on both sample substrates are intact and the oxide layers are at least 50 nm, the bond is uniform in thickness as opposed to wedged (as reported in [?]). This may be because the bonding solution did not come into direct contact with the underlying silicon material, and therefore could not create hydrogen gas bubbles that may induce 'wedging'. The average bond thickness was found to be 47 nm. This value is comparable to the minimal values found in the wedged silicon-silicon samples in [?] and also comparable to values reported by [?] and [?] for silica-silica samples. The fact that the average flatness of the samples after oxidation was 43 nm, a value very close to the average bond thickness, might indicate that there is a direct relation between the flatness of the samples and the obtained bond thickness. This would need to be investigated further.

Further investigation of the factors that affect the bond strength is of interest. The influence of different types of oxidation e.g. dry oxidation and sputtering, and the effect of differences in the oxide layer thickness on bond strength of samples will be considered. The influence of the crystallographic orientation of silicon on the bond strength will also be examined.

his technical support for the SEM imaging.

We would like to thank the Royal Society of Edinburgh, the Science and Technology Facilities Council, the Scottish Funding Council, the EC under contract no. FP7-211743, the Royal Society of London, the Wolfson Foundation and the University of Glasgow for financial support.

Finally, we would like to thank our colleagues in the GEO600 and LSC-Virgo collaborations for their interest in this work.

Figure 1 .

 1 Figure 1. Diagram showing a 'mixed' ingot pairing. The bonding surface on each block is 5 mm x10 mm, and for a mixed ingot pairing, a < 111 > block is bonded to a block of orientation < 100 >

Figure 2 .Figure 3 .

 23 Figure 2. 3D and detail CAD images of the bending strength set-up. The sample holder slides underneath the loading arm to reduce time needed between testing samples.

Figure 4 .

 4 Figure 4. Graphical representation of all results.The bond strength at cryogenic temperature shows a similar average strength as at room temperature, but a wider range of strengths is apparent. The absence of correlation between oxide layer thickness and bond strength at thicknesses above ∼ 50 nm shows an opportunity to minimize potential thermal noise by reducing the oxide layer thickness as much as possible without compromising bond strength.

Figure 5 .

 5 Figure 5. Joint 68% confidence regions for the Weibull parameters m and F 0 , obtained from a Bayesian analysis of all cryogenic (left) and room temperature (right) strength results.

Figure 6 .

 6 Figure 6. Graphs showing the values for the Weibull modulus (top) characteristic strength (bottom) for each data set, with error bars indicating the 68% confidence limits.The key describing the filters applied to each data set is shown in Table1.

Figure 7 .

 7 Figure 7. Plot of calculated bond thickness versus total oxide layer thickness for each of the oxidized and bonded silicon samples.

Figure 8 .

 8 Figure 8. 75,000x magnified Scanning Electron Microscope image of polished cross-section of a 30 minute oxidized hydroxide-catalysis bonded silicon sample.

Table 1 .

 1 Data set sizes used in Figure6

	Temperature	Filter 01	Filter 02	Data Set Size
	77 K			86
	293 K			49
	77 K	t min > 50 nm		33
	293 K	t min > 50 nm		37
	77 K	t min > 50 nm	t dif f > 20 nm	7
	293 K	t min > 50 nm	t dif f > 20 nm	17
	77 K	t min > 50 nm	Diagonal Break	29
	293 K	t min > 50 nm	Diagonal Break	33
	77 K	t min > 50 nm	Bond Break	4
	293 K	t min > 50 nm	Bond Break	5
	77 K	t min > 50 nm	Re-oxidised	16
	293 K	t min > 50 nm	Re-oxidised	14
	77 K	t min > 50 nm	Not Re-oxidised	17
	293 K	t min > 50 nm	Not Re-oxidised	24
	77 K	t min > 50 nm	Same Ingot	25
	293 K	t min > 50 nm	Same Ingot	20
	77 K	t min > 50 nm	Mixed Ingot	8
	293 K	t min > 50 nm	Mixed Ingot

Table 2 .

 2 Oxide thicknesses of silicon discs measured using ellipsometry investigation into bond thickness.

	Oxidation Time (mins)	Oxide Thickness of	Oxide Thickness of
		Side 1 (nm)	Side 2 (nm)
		(ellipsometry)	(ellipsometery)
	10	46 ± 3	4 9 ± 2
	20	60 ± 3	9 0 ± 3
	30	104 ± 5	1 3 4 ± 5
	40	196 ± 4	1 5 2 ± 4
	50	259 ± 4	1 7 2 ± 4
	§ http://www.sentech.de/index.php?st id=15&itid=219

Table 3 .

 3 Summary of the total bond and oxide thicknesses for the differing oxidation times measured using electron microscopy

	Oxidation Time Total Thickness
	(mins)	(± standard error) (nm)
	10	131 ± 9
	20	209 ± 14
	30	287 ± 16
	40	388 ± 18
	50	479 ± 14

Acknowledgments

We would like to thank John Davidson from the University of Glasgow School of Engineering for his help with the strength measurements, Donald Nicholson from the University of Glasgow School of Engineering for his help with the thermal oxidation of the silicon samples and William Smith for