Laurent Waltz

Delphine Retraint
email: delphine.retraint@utt.fr

Arjen Roos

Patrick Olier

Jian Lu

Combination of surface nanocrystallization and co-rolling: creating multilayer nanocrystalline composites

Keywords: Nanocrystalline materials, SMAT, Co-rolling, Multilayered structure, Mechanical properties

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Introduction

Materials presenting a microstructure in the nanometer grain size regime, i.e. characterized by a typical grain size of less than 100 nm, have generated widespread interest during the last decade. Actually, nanocrystalline materials possess fundamentally different physical and chemical properties compared to their traditional polycrystalline coarse grain counterparts, and numerous studies on different nanocrystallized metals like iron, titanium, copper or stainless steel have shown an improved mechanical strength as well as excellent tribological and corrosion properties [1][2][3][4][5][6][7][8][9][START_REF] Lu | Comprehensive Structural Integrity[END_REF][11]. However, despite a high yield and ultimate strength, nanocrystallized materials exhibit a significantly lower ductility than their traditional coarse grain counterparts, which is directly linked to the volume fraction of the nanostructure in a material. Different kinds of electrochemical and mechanical techniques have been developed for producing massive nanocrystallized bulk materials, such as inert gas condensation, electrodeposition and severe plastic deformation (SPD). However, nanocrystalline structures synthesized with most of these techniques are not free of porosities and contamination, which remains an obstacle for industrial applications. Several authors have shown that a recently developed Surface Mechanical Attrition Treatment (SMAT) technique, based on mechanisms of severe plastic deformation, may induce a grain refinement down to the nanometer scale in the top surface layer of metallic materials and alloys, without contamination or porosity [1,[2][3][4][5][6][7][8][9][START_REF] Lu | Comprehensive Structural Integrity[END_REF].

In the present paper, a method is presented which combines the superficial nanocrystalline treatment (SMAT) with the co-rolling process for the development of a semi-massive multilayered bulk structure. By optimizing the volume fraction of the nano-grains, this composite structure exhibits improved yield and ultimate tensile strengths, while conserving an acceptable elongation to failure. The alternating coarse grain layers and nanocrystallized layers are characterised by tensile tests and nanoindentations. Also, the microstructure is analysed by Transmission Electron Microscopy (TEM).

Experimental procedures

The material used in this investigation is a commercial 316L face-centered cubic (fcc) austenitic stainless steel. For the experimental tests, 120x120x1 mm 3 plates with the following chemical composition (in wt%) 0.025 C, 0.38 Si, 1.33 Mn, 0.027 P, 0.002 S, 16.70 Cr, 2.09 Mo, 10.20 Ni, 0.030 N, 0.40 Cu, 0.07 Co were used. The initial microstructure of the as-received material is characterised by a grain size ranging between 40 and 120 µm. The surface nanocrystallization of these sheets was obtained by SMAT. The SMA-treatments have been performed in air at room temperature during 30 minutes, with 3 mm stainless steel shot, and at a vibration frequency of 20 kHz.

The co-rolling has been carried out at CEA on a reversible rolling mill with a maximal capacity of 3500kN. The middle plate of the piling has been SMA-Treated on both sides, whereas the two other plates have been SMATed on their inner sides only (as depectited in Fig. 1). The choice of the rolling temperature (550°C) results in a compromise which preserves the nanostructured layers but allows a possible bonding at the interfaces. The stack of treated sheets was co-rolled in two passes with a total thickness reduction of 55% corresponding to a total equivalent strain of 0,88. Before each pass a preheating treatment was performed at 550°C during 90 minutes, and after the second pass, the material was water-cooled.

The microstructure of the co-rolled sample was characterized by means of TEM on a LEO 912 OMEGA microscope with an accelerating voltage of 120 kV. TEM plane-view specimens were cut from the co-rolled samples near the interface region. First, these specimens were mechanically polished down to a thickness of approximatively 90 µm. The electron transparency was then obtained by electropolishing using a twin-jet technique in a solution of 885 ml buthanol, 590 ml methanol and 90 ml perchloric acid at a voltage of 25V and a temperature of -16°C.

Tensile specimens with a total length of 36 mm, a gauge length of 19 mm and an average cross section of 1.4 x 3.6 mm² were electrodischarge machined from the co-rolled sample. Tensile tests were performed at room temperature on a screw-driven Kammrath & Weiss micro-tensile machine at a fixed strain rate of 10 -4 s -1 . After failure, the failure surfaces were analysed in a HITACHI S 3500 N scanning electron microscope (SEM).

In order to quantify the evolution of the local hardness through the cross-section of the co-rolled sample, nanoindentation measurements have been performed on a Nano Indenter XP TM fitted with a Berkovich diamond indenter. Furthermore, four indentations were put at the same distance from the upper surface in order to obtain a representative average value of the local hardness, as shown in the inset in Fig. 3. The indentation depths have been fixed at 600 nm, and in order to avoid erroneous hardness measurements due to the affected plastic zone around an indentation, neighbouring indentations are separated by a distance of 20 µm [START_REF] Hay | Instrumented Indentation Testing[END_REF]. Before testing, the samples have been mechanically polished with 1200 grid silicon carbide papers and polished to mirror finish with alumina.

Results and discussion

Fig. 2 displays a bright-field TEM micrograph showing the microstructure of the co-rolled sample interface at a depth of about 450 µm beneath the surface. By analysing this plane-view observation and its corresponding Selected Area Electron Diffraction (SAED) pattern, the microstructure in the interface region is characterized by ultrafine equiaxed grains with random crystallographic orientations. Taking into account several electron micrographs, the mean grain size is observed to range between 80 and 120 nm. Despite some difficulties caused by the thinning technique used in this work and by flatness defects of the co-rolled laminate, a TEM specimen could be obtained from the ultrafine grained layer.

The results of local hardness measurements obtained by nanoindentation through the cross-section of the co-rolled multilayer laminate are shown in Fig. 3. The inset at the top right hand corner gives an illustration of the distribution of the different indentations through the cross-section of the sample. In this figure it can be observed that the co-rolling process considerably enhances the local hardness of the coarse grain matrix layers to about 4.2 GPa. This value is approximately 1.8 times higher than the initial hardness of the coarse grain plate, and can be explained by the high work hardening occurring during the rolling process. Furthermore, the local hardness gradually increases and tends towards a maximum value of 9.2 GPa near the first interface of the laminate, at a depth of about 465 µm below the surface, which is approximately four times higher than the initial coarse grain hardness. This hardness level is comparable to the microhardness of nanocrystallized tungsten obtained by high-pressure torsion (about 11 GPa) [13], in severe plastic deformed steel [14] or in some hard ceramics. For comparison, nanoindentation measurements have been performed over the cross section of a co-rolled steak of three plates without SMAT rolled with the same reduction ratio and at the same temperature as the SMATed one. Despite a similar work hardening level, the distribution of the local hardness of this specimen stays more homogeneous. Indeed, a constant hardness value of about 4.2 GPa is obtained throughout the thickness of this specimen, and no significant hardness increase can be recorded near the interface regions or at the free edges. Accordingly to the studies of S.H. Lee et al [15][16] and B.L. Li et al [17] concerning the accumulative roll-bonding of aluminium, the absence of hardness increase in the interface region indicates that the work hardening induced by friction shear strain during co-rolling is negligible, and therefore, we can assume that no significant shear induced microstructural changes take place during co-rolling. So, the inhomogeneity of the hardness recorded for the co-rolled multilayer structure (Fig. 3) can be entirely attributed to the presence of a SMAT induced grain size gradient from the treated top surface to the deep matrix of the treated sample. As mentioned in the literature, this grain size gradient is directly linked with the distribution of the important SMAT-induced strain and strain rate throughout the thickness of treated specimens. The grain refinement underlying mechanism and hardening process occurring during SMA-Treatment are described in details by J. Lu et al [START_REF] Lu | Comprehensive Structural Integrity[END_REF] for different materials with different stacking fault energies (SFE). Furthermore, a linkage between the grain size and the hardness through a normal Hall-Petch relationship has been observed by T. Roland et al [7] and Jian et al [START_REF] Lu | Comprehensive Structural Integrity[END_REF]. Therefore, the hardness distribution of the co-rolled nanocrystallized multilayer structure indicates that the high hardness values in the interface regions can be explained by the presence of nanocrystallites, whose presence are confirmed by TEM images (see Fig. 2). However, the hardness level reached in the coarse grain matrix (≈ 4.2 GPa) is only an effect of the high work hardening induced during the process, since the average grain size recorded in this region remains unchanged from the coarse grain state (hardness of ≈ 2.4 GPa). The only difference is related to the morphology of the grains, which are more elongated in the co-rolled sample. Throughout the transition layer, the hardness increase an reach a maximum in the nanocrystallized layer which is characteristic of a grain size refinement in these regions, in accordance with the Hall-Petch law. So, referring to the TEM images obtained in this work and by T. Roland in his studies about 316L stainless steel [7], we can not a grain size reduction from several teens of micrometer in the coarse grain matrix to several teens of nanometer in the nanocristallized layer. In addition, it is noteworthy that a small part of the local hardness increase in the nanocrystalline layer at the top surface of SMATed samples, or at the interfaces of our co-rolled sample, may be attributed to the presence of a strain induced martensite phase [4][5][6][7].

The tensile engineering stress-strain curves of a co-rolled nanocrystallized multilayer laminate and of a co-rolled steak of three plates without SMAT (reduction ratio of 55% and rolled at 550°C) are shown in Fig. 4. For comparison, the stress-strain curve of an as-received coarse grain specimen with the same cross-section area is also included in this figure. Noteworthy observations from these plots are that the co-rolled multilayer structure shows significantly high values of yield and ultimate strength. The yield strength (0.2% offset) reaches a value as high as 750 MPa, which corresponds to an increase of about 154% compared to the coarse grain sample (295 MPa), and an ultimate strength of 860 MPa. One can also note that the strength levels of the co-rolled specimen are enhanced with respect to the co-rolled sample without SMAT, because yield and ultimate strengths are higher by about 13% and 15%, respectively. The high strength of the co-rolled multilayer laminate can be explained by an increased of the volume fraction of nano and ultrafine grains as described in the literature [1-2, 5-7], because nanocrystalline layers are able to sustain an important part of the load. Indeed, an increase of the volume fraction of nano grains of about 5% in the co-rolled structure SMATed at the interfaces leads thus to an appreciable yield strength increase of about 100 MPa in comparison of the co-rolled sample without SAMT. Furthermore, despite the increased volume fraction of nanograins and the strain hardening induced by the rolling process, the laminate shows an acceptable ductility of approximately 13%. Fig. 5 a) shows an example of the fracture surface of the co-rolled multilayer tensile specimen after the tensile test: the three sheets of the laminate stack can be clearly observed. It can be noted that this sample failed with an obvious macroscopic necking. Furthermore, the fracture morphology of this sample presents a significant feature, since on the two lateral sheets, initially SMATed on their inner sides, one can clearly distinguish two distinct failure structures. Indeed, Fig. 5 c) presents a high magnification SEM micrograph of this area, showing a clear and straight separation between the two regions, both characterized by a specific failure mode. It is interesting to note that the flat fracture surface region near the interface (Fig. 5 c) and 5 d)), which corresponds to the initially nanostructured and refined structure layer after SMAT [5][6][7][START_REF] Lu | Comprehensive Structural Integrity[END_REF], looks like a glassy brittle material. Chen et al. [18] reported a similar brittle failure mode in a 15 µm thick nanocrystallized 316L austenitic stainless steel tensile sample. Contrary to this, the outer side of this sheet presents a heavily dimpled and rough morphology (Fig. 5 b)), suggesting that this part of the specimen has been torn apart in a ductile manner and has been contributing actively to the observed plasticity in Fig. 4. Thus, as mentioned before, the difference in the underlying fracture mechanism, observed principally on the two outer plates, can be related to multilayer aspect of the microstructure in the specimen.

Conclusions

In the present study, generation of a high strength semi-massive structure by a combination of the surface mechanical attrition treatment (SMAT) and the co-rolling process at high temperature has been investigated. A multilayered composite laminate alternating nanocrystalline layers, transition layers and coarse grain layers was successfully developed. Process parameters used in this work have shown good interface welding of the co-rolled laminate, despite some boundary effects induced by the rolling process. TEM observations performed near the interface region and local hardness measurements by nanoindentation have shown that the nano-and sub-nanocrystalline layers are conserved after hot corolling, and that the grain growth remains limited. Furthermore, the new developed structure presents improved yield and ultimate strengths (710 MPa and 860 MPa respectively), while keeping an acceptable plastic strain to failure of approximately 13%. Finally, the fracture morphology of the corolled multilayer laminate suggests that the failure occurs in a combined ductile-brittle manner. This can be explained by the multilayer aspect of the microstructure in the cross-section of the laminate.

Fig. 1 :

 1 Fig. 1: Illustration of the co-rolling process of three SMATed plates.

Fig. 2 :

 2 Fig. 2: Bright-field TEM image and the corresponding SAED pattern of the sub-nanocrystalline layer near the interface at a depth of about 450 µm (rectangular box in Fig. 2).

Fig. 3 :

 3 Fig. 3: Local hardness evolution through the cross-section of the co-rolled multilayer sample.

Fig. 4 :

 4 Fig. 4: Uniaxial engineering tensile stress-strain curves of a co-rolled SMATed multilayer specimen, a cold rolled sample without SMAT and an as-received coarse grain sample.

Fig. 5 :

 5 Fig. 5: a) SEM micrographs of the fracture surface of the co-rolled multilayer tensile specimen; b), c) and d) high magnification SEM micrographs of selected regions.

Acknowledgements

The authors thank Prof. Pentti Karjalainen from the Materials Engineering Laboratory at the University of Oulu for supplying the transmission electron microscopy equipment and for helpful discussions.


Introduction

In this document we will study mirror surface specications for the Advanced Virgo Output Mode Cleaner (OMC). It is well known that atness defects and micro-roughness on mirror surfaces aect the resonant mode in a cavity. Here we would like to determine the mirror surface specications in order to have more than 99 % of transmission through the OMC for a perfect Gaussian input beam TEM 00 . To do this determination we will simulate the cavity with the code OSCAR [START_REF] Degallaix | OSCAR a Matlab based optical FFT code[END_REF]. Two kinds of losses will be characterised. The rst one is the part of resonant beam which go out of mirrors, such losses are called sometimes "diraction losses" or "clipping losses". The second, which can be the most important loss, is the reection of the incident beam which does not match the imperfect cavity.

Short elements of theory

The aim of this part is not to give the complete theory of optical cavity with defect surfaces but to give some denitions in order to be understandable, coherent and clear on what we are speaking about in this document. Surface defects correspond to small deviations of mirror surfaces from the ideal one. Even if such deviations are much smaller than the considered laser wavelength it can aect strongly results of optical systems. Usually these deviations are basically characterised by the Root Mean Scare (RMS) but can be detailed with the Power Spectral Density (PSD). The PSD correspond to the amplitude of defects as a function of its spatial frequency. There are several kind of PSD depending on which coordinate system we are dealing with. We will use in the document only the one dimensional PSD as a function of the radial frequency. In order to x variables and avoid mistakes we express the 1 dimensional PSD with the 2 dimensional PSD in the following equation 1.

P SD1D(f r ) = 2π 0 P SD2D(f r , θ) f r dθ [START_REF] Bonnand | Simulations for the specications of mirror atness for Advanced Virgo. Virgo Inernal Note[END_REF] with f r = f 2 x + f 2 y . Usually there are no angular dependence and we obtain the relation equation 2.

P SD1D(f r ) = 2π P SD2D(f r ) f r (2)
We remind the denition of the RMS and its relation with the PSD in equation 3 RM S 2 = h2 (x, y) dxdy

S = P SD1D(f r ) df r ( 3
)
where S is the area of the considered surface and h(x, y) is the deviation from the ideal surface. With the PSD it is possible to characterise the distinction between atness defects and microroughness. The rst one can be associated to the diculty to keep control of a surface on a large size for less than few nm. The second one is more associated to the local process of polishing.

With the PSD curve we can pass continuously from one kind of defects to the second kind but usually we dene a transition border between them at around f r ≃ 1000 m -1 . This distinction is really important since specication of polishing mirrors can be much dierent depending on the size of the mirror, as we will see. In our case of OMC mirrors, the diameter is supposed to be 5 mm, therefore the minimal frequency defects can not be less than

f rmin = 1 0.005 m -1 = 200 m -1 .
Such minimal frequency is close to the transition frequency and this optical system would be more sensible to micro-roughness specications than atness defects. [START_REF] Degallaix | OSCAR a Matlab based optical FFT code[END_REF] The simulation Simulations of OMC had been done with the FFT code OSCAR. Details about this code can be found in following references Degallaix 2010 [START_REF] Degallaix | OSCAR a Matlab based optical FFT code[END_REF] and on the web page dedicated to OSCAR [START_REF] Degallaix | an optical t code to simulate fabry perot cavities with arbitrary mirror proles[END_REF]. The main idea is to take the z axis for beam propagation and express all functions of x and y in a 2D matrix averaging values on each pixel. Propagation of any elds on z axis are computed by calculating two dimensional FFT on x and y axis in order to decompose such elds in a sum of plane waves. More explanation can be found in the manual associated to the code OSCAR [START_REF] Degallaix | an optical t code to simulate fabry perot cavities with arbitrary mirror proles[END_REF] or in the article of Vinet et al. [5]. For the real OMC cavity the beam follow the path gure 1. But for the simulation in OSCAR we will approximate the path of the beam as in gure 2. In this case no angles are taken into account, so no astigmatism can be studied here. Basically, the code works with input parameters such as the grid size N ( usually N = 256 or 512), the beam waist at entrance of the cavity w 0 and the diameters of mirrors d. Additionally to these basic input parameters it is possible to dene other characteristics of incoming beam such as taking an arbitrary position of the waist in the cavity. But the most important supplementary function of OSCAR is to add surface defects on mirrors from known maps or from created fake maps with a chosen PSD. We will use all of these functionalities to calculate resonant, transmitted and reected beams and losses for the OMC in order to study its optical properties.

VIR-0267A-12 -July 12, 2012 Preliminary pecications which we would apply to the OMC are a pick to valley less than λ/10 ≃ 100 nm for the atness defects. This specication correspond approximately to 20 nm RMS. We would have also a micro-roughness less than 0.3 nm RMS. In this section we will test the viability of these specications but since these specications are not enough to determine the PSD, we will take PSDs obtained for Virgo mirrors made by General Optics (GO) and LIGO mirrors made by CSIRO. We remark that PSDs are approximated on three range of frequencies by a power law P SD1D(f r ) = A f -n r and details about its parameters are given in the table 1. This is enough for a rst approach in our study. We did a simulation for 600 random fake VIR-0267A-12 -July 12, 2012 5/18 4 RESULTS FOR PRELIMINARY SPECIFICATIONS maps of GO and 1200 random fake maps of CSIRO for a RMS varying between 0 and 30 nm. The gure 3 show the power of transmitted beam in a fraction of the input beam power. We observe for the two PSD laws that transmission is dramatically low at 20 nm RMS and is already too much small even at few nm RMS. The decreasing is quite dierent for the two PSD laws but the conclusion about specications is the same, the chosen RMS is too high. We will give more details in the next section about how to dene specications for atness defects and micro-roughness. Next gures are still interesting since they help us to understand the VIR-0267A-12 -July 12, 2012 The reection can be interpreted as a consequence of the non matching of the input beam with the cavity. The more the RMS increases, the more the mirrors are deformed and the more the resonant mode moves away from a TEM 00 mode. The reection is exactly the dierence between the resonant mode and the input mode.To illustrate this phenomenon, the gure 5 show dierent elds calculated in OSCAR for a set of fake mirrors at 20 nm RMS with the GO PSD.

f r < 82.82 m -1 82.82 m -1 < f r < 400 m -1 400 m -1 < f r A GO 4.
The outgoing losses are mainly due to the diusion on mirror micro-roughness defects which is proportional to the square RMS [START_REF] Day | Inuence of mirror roughness on clipping losses in optical cavities[END_REF]. But as we can see on the gure 4 such losses are very small and reach few percent only for CSIRO PSD at high RMS. We point out the simulation has been done with a grid size of N = 256 for a mirror size of d = 5 mm, therefore the resolution is δd = 1.95 10 -5 m. This resolution is enough to consider micro-roughness eect in this simulation.

Mirror diameter eects

To be sure we are not dealing with size eects of mirrors we can study losses and transmission dependence on the mirror diameter. We did a 200 (resp. 400) simulations for a RMS of 10 nm (resp. 20nm) with a diameter varying between 0 and 1 cm. We took only GO PSD for mirror maps.

We observe on the top of the gure 6 that the transmission starts to increase dramatically when mirrors size is 2 times greater than the beam size. But for both RMS 10 nm and 20 nm we notice that we have reached optimal size for transmission at around 4 mm of diameter even if points are spread, therefore 5 mm of diameter is enough for the OMC. For outgoing losses we observe that they decrease with the increasing diameter. This results is coherent with the origin of such losses. Then at 5 mm of diameter we observe losses around 100 ppm for 10 nm RMS and 1000 ppm for 20 nm.

We conclude this section by assuming a diameter of 5 mm is optimal for the transmission and high enough to have small outgoing losses. This conclusion means the origin of very small transmission comes from low frequency spatial defects, which are too large for a specication of 20 nm RMS. We will explore more in details this problem in the following section. In this section we will try to dene new specications in order to obtain 99 % of transmission. To understand the cause of small transmission and dene good specications we will give generalities about the behaviour of PSD curves and what is done in OSCAR to create fake VIR-0267A-12 -July 12, 2012 9/18 5 REDEFINING SPECIFICATIONS maps of mirrors. On the gure 7 are shown PSD for several polishers and we observe in general Figure 7: PSD of mirrors for several polishers, Bonnand et al. 2011 [START_REF] Bonnand | Simulations for the specications of mirror atness for Advanced Virgo. Virgo Inernal Note[END_REF] a fast decreasing amplitude of defects with the spatial frequency. But the main point to be mentioned here is the very small amplitude of defects at high frequency f > 100m -1 , thus independently of the polishers and the resulting RMS. This means the PSD is dominated by atness defects and this part of the PSD determine the order of the RMS. The micro-roughness is sensibly independent of the resulting RMS. But we have to remind we create fake maps of mirrors for a given RMS in OSCAR by rescaling the PSD. Taking a mirror of 5 mm and assuming a 20 nm RMS for the fake map would say we have very very bad micro-roughness specications. This is the reason why we can easily take a much smaller RMS for OMC mirrors. Now, let us nely study the OMC specications. Since we observed the high impact of PSD on the simulation, the best thing would be to know the PSD shape expected for a given polisher. But unfortunately we have only maps of mirrors large of few hundreds of µm made in sapphire from the THALES-SESO factory, one of the candidate polisher. Therefore the best we could do is to take a simplied PSD as a function of only one power law and try to determine which is the limit for having 99% of transmission.

VIR-0267A-12 -July 12, 2012 5.1 Simplied PSD 10/18 5.1 Simplied PSD For this study we will take the following simplied PSD over all frequencies:

P SD1D(f r ) = A f n r (4)
Since the coecient A is not relevant for polishers and can be a complex function of the RMS [6], we will x this coecient and rescale fake maps in order to obtain a chosen RMS. We did 1300 simulations for the power law n ∈ [-0.5, 3] and the RMS ∈ [0.1 nm, 10 nm] randomly distributed on these intervals. On the gure 8 are presented the rate of transmission as a function of the the parameter n and the RMS. On this gure we observe that the smaller the RMS is or the higher the power n is, the more the transmission rate is high. The gure 9 show three bands of points (n, RMS) for 99%±0.2, 98%±0.2 and 94%±0.5 of transmission. This gure is much more interesting and gives a lot of information about how to dene new specications. First, we conrm the dependence of the transmission on parameters (n, RMS) we obtained in the previous gure. These bands are representing approximately the contour line for 99 %, 98 % and 94 % of transmission. A better VIR-0267A-12 -July 12, 2012 performance than a given percentage is obtained by taking parameters above the corresponding contour line. Then, we observe a threshold phenomenon on the RMS. At a RMS less than the threshold we have performance better than the corresponding percentage in any case of power law n. For example at around 0.3 nm RMS we have more than 99 % of transmission for any power law n. Such RMS correspond to the micro-roughness specication and is too excessive for the global RMS down to f rmin = 200 m -1 . A more acceptable specication would be 1 nm RMS for OMC mirrors. At this RMS, we can reach 99 % of transmission by taking a power law n upper than 1.5. Furthermore, with this RMS the threshold ensures us to have more than 94 % of transmission for any power law n. Referring to the gure 7 on the range of frequencies upper than f rmin = 200 m -1 , the power limit n = 1.5 is much less than the corresponding slope of PSD law for GO polisher or Tinsley polisher (n > 1.5) but the limit is higher than the corresponding slope of PSD law for CSIRO (n ≃ -0.5). This means PSDs of polishers don't respect systematically our limit. But we would like also to not require specications based on giving a power law to polishers. The way to do so is to give micro-roughness specications. As we will see in the next part, imposing a global RMS of 1 nm and micro-roughness RMS of 0.3 VIR-0267A-12 -July 12, 2012 5.2 Simplied PSD with micro-roughness specications 12/18 nm over f r = 1000 m -1 , the power law is forced to be higher than n = 1.5.

Simplied PSD with micro-roughness specications

We can understand easily when we require a small enough micro-roughness at a given global RMS, we will obtain a high enough power n. But determining precisely such quantities, moreover if we consider realistic PSD, is a dicult problem to solve. Here, we will try to do a simple analysis by taking the simplied PSD we used in equation 4. With this simplied PSD it will be possible to integrate analytically the equation 3 which give the RMS. In this study we will calculate the RMS on a frequency range, such as

[f 1 , f 2 ].
From equations 3 and 4 we obtain:

RM S 2 f 1 f 2 = f 2 f 1 A f n r df r = A -n + 1 f -n+1 2 -f -n+1 1 (5)
Three characteristic frequencies will be considered, the smallest f rmin , the cut-o frequency f c above which we are dealing with micro-roughness defects and the maximum frequency f rmax . The minimal frequency is limited by the size of mirrors and is given in the rst section, i. e. f rmin = 200 m -1 . A more elaborated theory would say the minimal frequency is higher but the one we choose correspond to the worst case.Then, the cut-o frequency f c is not well determine, often it is assumed f c = 1000 m -1 which correspond to defects of the order of the 1 mm. But we will take three other cut-o frequencies f c = 2000 m -1 , f c = 4000 m -1 and f c = 10000 m -1 in order to make complete this study. Finally, the maximum frequency should be innite but f rmax = 51200 m -1 , which is the maximum frequency considered in our conguration of OSCAR, is enough. We observed that higher frequencies do not change signicantly the results. We will now take the previously dened specications, so 1 nm RMS for mirror surfaces defects and 0.3 nm RMS for the micro-roughness. The rst specication corresponds to the whole integration, RM S 2 total = RM S 2 f rmin frmax = 1 nm 2 and the second corresponds to a partial integration RM S 2 micro = RM S 2 fcfrmax = 0.09 nm 2 . The aim of this part is to study the ratio RM S 2 total RM S 2 micro as a function of n in order to conrm that for the value RM S 2 total RM S 2 micro = 1/0.09 = 11.11 we have a power n > 1.5. On the gure 10 are represented the ratio RM S 2 total RM S 2 micro as a function of n for dierent cut-o frequencies. The smallest power n for the ratio at a value 11.11 correspond to the cut-o frequency f c = 10000 m -1 . In this case we have n = 1.47 which is close to the minimal limit for having 99 % of transmission. But we can say such frequencies are much higher than the limit for micro-roughness. At f c = 1000 m -1 we nd a value of n = 2.49 which is much higher than the minimal limit. The conclusion for this study based on a simple PSD is if we take a micro-roughness specication of 0.3 nm at higher than f c = 1000 m -1 and a global RMS defect of 1 nm we would ensure us approximately to have 99 % of transmission by the OMC.

VIR-0267A-12 -July 12, 2012

Extrapolation of SESO PSD

In this section we will try to take advantages of having mirror maps from the SESO factory, one of the candidate polisher. We are confronted to two diculties with these maps. First, the map for the plane mirror has a size of 800 µm and the map for the spherical mirror has a size of 200 µm which are much less than OMC mirrors and this will oblige us to extrapolate PSD obtained from these maps. The second diculty comes from the substrate of such mirror maps which is the sapphire. This is a much dierent substrate than the silica, i. e. the OMC substrate, but the SESO conrmed us their specications for polishing silica are better than for the sapphire. Therefore we will take such maps as an upper limit. The good point is even if we are dealing with very smal surfaces made of sapphire we have very small RMS for each mirror, i. e. 0.165 nm for the plane one and 0.214 nm for the sopherical one.

In the gure 11 are shown the PSD calculated from SESO maps for plane and spherical mirrors made in sapphire. We will interpolate these PSD with three segments for dierent range of frequencies and we will extrapolate the line for low frequencies down to 200 m -1 for OMC mirrors simulations. On the gure 12 are shown the PSD from SESO maps, the approximated VIR-0267A-12 -July 12, 2012 PSD and the PSD resulting from one example of fake map obtained with OSCAR, all of these for plane mirrors. And the same are shown on the gure 13 but for spherical mirrors. Only here the PSD is extrapolated for a larger range of frequencies than for plane mirrors. On the table 2 are summarised results for 20 simulation of OMC for approximated SESO PSD. We observe from these simulations the resulting RMS for mirrors is less than we would specify for the SESO polisher. The deviation of RMS between plane and spherical mirrors is not realistic and is caused for sure by the extrapolation. These RMS values should be regarded more as a order of magnitude as well determined values. The main result emerging from these simulations is the transmission rate which is no less than 99.4 %. We can conclude even if the VIR-0267A-12 -July 12, 2012 RMS change a little in the reality, we can expect to stay in our specication of more than 99 % of transmission. The outgoing losses are in any case very low and conrm to us that PSD give very good results.

RMS

To nish the study of surface specication we can rescale the approximate SESO PSD for a chosen RMS in order to estimate the transmission of the OMC as a function of the RMS.

We observe on the gure 14 a transmission around 99 % for a RMS ≃ 0.73 nm and a transmission around 98.6 % at 1 nm. This results should leads us to dene a less RMS than 1 nm for the specication but we should take care with this conclusion because the PSD used for the SESO maps are strongly extrapolated and for spherical mirrors we have a power law n = 1 which is less than the value dened in the previous section 5.2. We remind also the SESO can do a better polishing for silica. This mean, we can easily ask for polisher a specication which ensure us a higher transmission than 98.6 %.

Conclusion

The OSCAR software developed by Jérome Degallaix [START_REF] Degallaix | OSCAR a Matlab based optical FFT code[END_REF] had been a tool very helpful for simulate and study mirror surfaces of the Advanced Virgo OMC. The rst and general conclusion is global RMS specication for surfaces must be adapted to the size of the surface. Through our VIR-0267A-12 -July 12, 2012 study we redened initial surface specications in order to ensure a transmission of 99 % for the OMC with a TEM 00 mode at the entrance. We have found three kind of specications for this problem. The rst one is given in the section 5.1, the best way to get 99 % of transmission would be to impose a RMS of 0.3 nm on the whole mirror of 5 mm. This specication seems to be independent to the behaviour of the PSD but could be too much strong for polishers. The second specication is to take a higher RMS and impose to the polisher to have a PSD lower than a determined power law. As a realistic example we could impose a RMS of 1 nm on the whole mirror and a PSD lower than the power law P SD1D(f r ) = A f -1.5 r , i. e. n > 1.5. Since this specication is not usual for polisher we can force their PSD to be approximately lower than such power law by imposing micro-roughness specication. The previous example is reached by taking a RMS of 1 nm on the whole mirror and a micro-roughness RMS of 0.3 nm over the spatial defects frequency of f c = 1000 m -1 . Finally we can ask to the SESO to do an equivalent or better polishing than they have done for sapphire mirrors. In conclusion we can show the elds calculated by OSCAR for a fake map created with the simplied PSD for 1 nm RMS and a power law n = 1.5. On the gure 15 we can see the "gaussianity" of all elds except the reected eld of very small power because of defects on surfaces.

VIR-0267A-12 -July 12, 2012

Figure 1 :

 1 Figure 1: Path of the beam in the real OMC

Figure 2 :

 2 Figure 2: Path of the beam in the OSCAR OMC

Figure 3 :

 3 Figure 3: Transmission by the OMC for PSD of GO and CSIRO as a function of the RMS

Figure 4 :

 4 Figure 4: Reection and outgoing losses by the OMC for PSD of GO and CSIRO as a function of the RMS

Figure 5 :

 5 Figure 5: Fields calculated in OSCAR at 20 nm RMS with the GO PSD

VIR

  10 nm RMS Outgoing losses for 20 nm RMS

Figure 6 :

 6 Figure 6: Reection and outgoing losses dependence on the diameter of OMC mirrors for the GO PSD

Figure 8 :

 8 Figure 8: Rate of transmission as a function of the parameter n and the RMS

Figure 9 :

 9 Figure9: Band of points (n, RMS) for 99% ± 0.2, 98% ± 0.2 and 94% ± 0.5 of transmission.

Figure 10 : Ratio RM S 2 total RM S 2 micro

 1022 Figure 10: Ratio RM S 2 total RM S 2 micro as a function of n for several cut-o frequencies.

Figure 11 :

 11 Figure 11: SESO PSD for plane and spherical mirrors made in sapphire

Figure 12 :

 12 Figure 12: PSD, approximate PSD and fake mirror PSD for SESO plane mirrors made in sapphire

Figure 13 :

 13 Figure 13: PSD, approximate PSD and fake mirror PSD for SESO spherical mirrors made in sapphire

Figure 14 :

 14 Figure 14: Transmission rate of the OMC for approximated SESO PSD as a function of the RMS

[ 5 ]

 5 J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet. A high accuracy method for the simulation of non-ideal optical cavities. Journal de Physique I, 2:12871303, July 1992. [6] H. Yamamoto. 1D PSD of mirror maps. LIGO Inernal Note, September 2011. LIGO-T1100353-v1. VIR-0267A-12 -July 12, 2012

Table 1 :

 1 Parameters used for GO and CSIRO PSD.

		7897 10 -17	1.115 10 -19	1.4782 10 -16
	n GO	-2.8731	-1.5	-2.7
		f r < 53.43 m -1 53.43 m -1 < f r < 1089 m -1 1089 m -1 < f r
	A CSIRO	7.2452 10 -16	1.6678 10 -24	3.0188 10 -16
	n CSIRO	-4.5219	0.4775	-2.2415

Table 2 :

 2 Summary table of results for 20 simulations with extrapolated SESO PSD

		Plane RMS Spherical Transmission Outgoing losses
		(nm)	(nm)	(rate of input)	(ppm)
	Mean	0.58924	0.27131	0.99442	16.920
	Min	0.42171	0.24915	0.99428	16.248
	Max	0.80032	0.30853	0.99460	17.679

Acknowledgements

Many thanks to Jérome Degallaix for his adaptation of OSCAR to the Advanced Virgo OMC cavity and for his many interesting comments. Finally I'm grateful to Romain Gouaty and all the Virgo-LAPP team for their fruitful help and suggestions.


Laurent Waltz

Delphine Retraint
email: delphine.retraint@utt.fr

Arjen Roos

Claude Garnier

P Olier

Effect of interfacial oxidation occurring during the duplex process combining surface nanocrystallisation and co-rolling

Keywords: SMAT, Co-rolling, Grain refinement, Mechanical characterisation, Oxidation, Nanostructured materials

come

Introduction

Nanocrystalline and ultrafine-grained metals and alloys with average grain size of less than 500 nm have generated widespread interest during the last decade because of their remarkable mechanical properties as compared to their coarse-grained counterparts [START_REF] Lu | Comprehensive Structural Integrity[END_REF]. However, despite high yield and ultimate strengths, a significant number of these studies has shown a very limited tensile ductility, often caused by residual porosities, impurities and flaws arising from the elaboration process. The most common nanocristallisation processes are inert gas consolidation, electrodeposition, powder compaction and severe plastic deformation techniques such as ECAE (Equal Channel Angular Extrusion), HPT (High Pressure Torsion), ARB (Accumulative Roll-Bonding) and SMAT (Surface Mechanical Attrition Treatment). The recently developed SMAT technique can induce grain refinement down to the nanometer scale in the top surface layer of metals and alloys such as iron, titanium, copper or stainless steel [START_REF] Lu | Comprehensive Structural Integrity[END_REF][2][3][4]. Unfortunately the affected depth remains limited (≈ 250 µm for 316L stainless steel), which leads to a rapid saturation of the yield strength of SMATed bulk materials [5]. To overcome this problem, a novel process has been developed to increase the volume fraction of nano-grains. This duplex process combines the SMAT with a subsequent co-rolling process in order to produce multilayered bulk structures with improved yield and ultimate tensile strengths, while conserving an acceptable elongation to failure. The duplex process is described in detail in [5,6]. However, during the heat treatment before co-rolling, the impurities deposited on the surface of SMATed samples cause bonding imperfections due to interfacial oxidation during the process.

In the present work, nanocristallised 316L stainless steel multilayer structures were produced by the duplex process as described in [5,6]. Two different rolling temperatures, 550°C and 650°C, were imposed in order to quantify the effect of the heat treatment on the interface quality. The microstructures near the interface region of co-rolled samples were analysed by Optical Microscopy (OM). In addition, the oxide layers observed there were chemically characterised by Energy Dispersive X-ray spectrometry (EDX). Finally, uniaxial tensile tests were carried out at room temperature on the as-processed structures in order to study the influence of annealing on the macroscopic mechanical properties.

Experimental procedures

In this investigation a 316L face centered cubic (fcc) austenitic stainless steel with chemical composition as given in Table 1 was used. The initial microstructure of the as-received alloy after thermomechanical treatment and hyper-quenching, shown in Fig. 1, contains austenitic grains of 10 to 60 µm. A high density of mechanical and annealing twins can be observed within the grains. For the experimental tests, 120x120x1 mm 3 plates were used. The surface nanocrystallisation of these sheets was carried out by SMAT in air at room temperature during 30 minutes, with 3 mm stainless steel shot at a vibration frequency of 20 kHz. A complete description of the SMAT process is given in [START_REF] Lu | Comprehensive Structural Integrity[END_REF].

The co-rolling of the assembly of three SMATed plates was carried out on a reversible rolling mill with a maximum capacity of 3500 kN. In both cases, the middle plate was SMATed on both sides, whereas the two outer plates were treated on their inner side only. Then, the plates were co-rolled in two passes with a total thickness reduction of ≈ 55%, corresponding to a total equivalent strain of 0.88. To identify the effect of annealing on the mechanical behaviour of the co-rolled samples and on their interface bonding, two different heat treatments were carried out: the samples were respectively corolled at 550°C (sample T SMAT-550 ) and at 650°C (sample T SMAT-650 ). These annealing temperatures were deliberately chosen near the dechromisation temperature of the stainless steel. For comparison, laminates of three plates have been co-rolled without SMAT at the interfaces, with the same reduction ratio and at the same annealing temperature (samples T no SMAT-550 and T no SMAT-650 ).

The microstructure of the co-rolled samples was characterised by transmission electron microscopy (TEM) on a 120 kV LEO 912 OMEGA microscope. TEM plane-view samples were cut from the corolled samples near the interface region. A second TEM observation campaign was carried out on a PHILIPS CM200 FEG microscope with an accelerating voltage of 200 kV. For the latter, TEM samples were obtained from the co-rolled samples in the transverse plane defined by the rolling and normal directions (plane RD-ND). These samples allowed an adequate analysis of the microstructure near the interface, as well as the analysis of the chemical composition of the interface oxides by EDX.

Optical micrographs were obtained of the cross section (plane RD-ND) of samples T SMAT-550 and T SMAT-650 before and after electro-polishing at room temperature in a solution of 60% nitric acid and 40% water at a voltage of 1.5V. Moreover, the samples were polished to obtain a working surface near the plane defined by the rolling and transverse directions (RD-TD) as shown in Fig. 3 a).

In order to quantify the mechanical response of co-rolled structures, tensile tests were carried out at room temperature on a screw-driven Kammrath & Weiss micro-tensile machine at a fixed strain rate of 10 -4 s -1 . Tensile samples with a total length of 36 mm, a gauge length of 19 mm and an average crosssection of 1.4 x 3.6 mm² were machined by electrodischarge from the co-rolled samples.

Results and discussion

Preliminary OM observations were undertaken on co-rolled multilayer structures after mechanical polishing and without etching. The observations were principally carried out in the interface region as shown in the micrographs in Fig. 2 a) and b), which represent respectively the interface morphology and oxidation of the samples T SMAT-550 and T SMAT-650 . A significant difference between the oxide layers is observed. The laminate T SMAT-550 contains discontinuous oxide clusters with heterogeneous thickness. Between the oxide islets, a good metal/metal bonding is observed. The interface of sample T SMAT-650 is characterised by a continuous oxide layer with a uniform thickness of 1-2 µm. As shown by these micrographs, the higher annealing temperature for sample T SMAT-650 has a significant effect on the oxidation in the interface region, and probably on the oxidation kinetics, which may explain the difference observed between the two laminates.

To provide a better understanding and analysis of the oxides, metallographic samples were obtained by mechanical polishing in an inclined plane near RD-TD (see Fig. 3 a)). The micrograph obtained for sample T SMAT-550 thus prepared is given in Fig. 3 b). The oxide cluster shown in this figure contains several colorations (red, blue, brown, gray and black) indicating the presence of oxides such as hematite (α-Fe 2 O 3 ), magnetite (Fe 2 O 4 ) and different complex oxides resulting from the oxidation of various elements such as iron and chromium. In addition, a partial metal/oxide decohesion is noted, leading to the formation of cracks and micro-debonding in the interface region, which could be very harmful for the mechanical behaviour of co-rolled structures. This point will be discussed later.

Contradicting to some studies in the literature [7,8], who claim that SMAT does not contaminate the treated materials, the SMAT used in the duplex process is strongly suspected to contribute to surface pollution. The three principal sources of pollution in the SMAT process that have been identified are the shot, the ultrasonic resonator and the treatment chamber. Polluting particles put in motion and/or transported by the shot are deposited on the surface of the samples during the treatment. Such surface pollution has been reported before by Cemin et al. [9] on a 316L stainless steel after surface mechanical attrition by ball milling. In the present study, the pollutants oxidise in air before and during the heat treatment. During co-rolling, complex oxides are then formed at the interfaces of the multilayer structures.

As shown in Fig. 4 a), a TEM sample was prepared from the cross section (plane RD-ND) of sample T SMAT-550 . This sample was used for analysing the chemical composition of the oxide layer at the interface. The thickness of the oxide layer in this region is about 200 nm. The EDX measurements performed in the austenitic matrix show a chemical composition near to that given in Table I. The microanalyses of the oxidised interface region (Fig. 4 b)) show the presence of Fe, Cr, Mn and O elements in high proportion. This indicates that complex oxides are formed during the duplex process. Furthermore, the energy of the characteristic peak of the titanium emission spectrum is very atypical for the considered stainless steel alloy. The presence of titanium can be directly related to surface pollution by the TA6V titanium alloy ultrasonic resonator, and confirms the assumption that SMAT induces a surface pollution.

After the study of the interface region of the co-rolled multilayer structures without prior etching, a microstructural investigation was carried out after electro-polishing. Fig. 5 a-c) and a'-c') show the optical micrographs obtained for samples T SMAT-550 and T SMAT-650 respectively. It can be observed that the microstructure of these samples consists of deformed austenitic grains. Segregated bands developed during rolling, forming fibres in the middle of the three sheets composing the laminate, are also observed (Fig. 5 a) and a')). The shape of the grains through the cross-section of the laminates and the location of the fibres indicate that a large part of the plastic strain is accommodated in the middle of the sheets. These observations agree well with the local hardness measurements performed by Waltz et al. [6] on co-rolled laminates. There, the increase of the local hardness in the coarse grain matrix at the middle of the plates was entirely attributed to the work hardening during the rolling process. However, near the interface region, the γ→α phase transformation activated by work hardening during SMAT contributes to the increase of the local hardness [6]. More details about the martensite formation occurring during SMAT can be found in [10][11][12].

As can be observed in Fig. 5, the oxide islets for sample T SMAT-550 and the continuous oxide layer in the case of sample T SMAT-650 become clearly visible after electro-polishing. Shear bands are present near the interface region around the oxide islets in sample T SMAT-550 , as can be seen in Fig. 5 b) and c). A similar shear band formation was reported by Kolahi et al. [13] and Quadir et al. [14], respectively in a roll-bonded aluminium strip and ferrite processed by warm rolling and ARB. This indicates that the oxide islets significantly disturb the material flow during the rolling. The material cannot flow uniformly and flows around the obstacle, which gives rise to plastic strain localisation in shear bands.

No similar bands were observed for sample T SMAT-650 , because of the different morphology of the oxide layer. The underlying processes explaining the differences are not yet clearly understood. The fragility of the oxide layer, the deterioration of its mechanical properties by raising the annealing temperature, coupled to dissolution and migration of the oxides in the metal matrix might be at the origin of these differences [15][16][17][18][19]. It is conceivable that the brittle oxides cannot accommodate the plastic strain during co-rolling at 550°C. The result would be a multi-fissuration of the oxide layer during rolling. This hypothesis supports the one already expressed by Quadir et al. [14], who suggest that the bonding occurs by fracture of the oxide layers having a much lower ductility than the reference metal. At the origin of the fracture of the oxide layer is the formation of shear bands that break the oxide into single islets [14]. In this case, the underlying material, more ductile, could then diffuse into the cracks to form junctions by diffusion with the material extruded through the superficial oxide layer of the second sheet. This might explain the alternation of oxide islets and well-bonded areas between the sheets in sample T SMAT-550 (see Fig. 5 b-c)). For sample T SMAT-650 , the oxide layer remains continuous because of its increased ductility at the rolling temperature of 650°C.

Another significant difference can be noted in the microstructures near the interface. In the case of sample T SMAT-550 , the microstructure near the interface is characterised by deformation bands and a high density of mechanical sub-micrometric twins within equiaxed grains, whereas sample T SMAT-650 shows only micrometric grains elongated in the rolling direction. Twins observed in Fig. 5 c) are the result of the SMAT and are considered to be at the origin of a grain refinement in materials with low stacking fault energies (SFE), as discussed in [START_REF] Lu | Comprehensive Structural Integrity[END_REF]3,5]. These twins were eliminated by the thermomechanical treatment of laminate T SMAT-650 , and only a low density of annealing twins is visible.

Despite some difficulties caused by the thinning technique used in this work and by flatness defects of the co-rolled laminate, a TEM sample could be obtained from the ultrafine-grained layer. Fig. 6 displays a bright-field TEM micrograph showing the microstructure beneath the interface of the corolled laminate T SMAT-550 . By analysing this plane-view observation and its corresponding Selected Area Electron Diffraction (SAED) pattern, the microstructure in the interface region is characterised by a high density of dislocations, ultrafine equiaxed grains with nearly random crystallographic orientations, and sub-structures. Taking into account several electron micrographs, the mean grain size can be evaluated between 90 and 250 nm. This indicates that the effect of SMAT is not annihilated after annealing at 550°C, although the contribution of the deformation bands in the microstructural refinement remains currently unclear. TEM micrographs obtained near the interface of sample T SMAT-650 (not presented here) show no evidence of ultrafine grains and twins.

The tensile stress-strain curves of the samples T SMAT-550 and T SMAT-650 are given in Fig. 7 a) and b) respectively. For comparison, the stress-strain curves of the laminates co-rolled without SMAT (T no SMAT-550 and T no SMAT-650 ) and of an as-received coarse-grained sample are also included. It can be observed that the annealing temperature has a significant effect on the mechanical response. With respect to the sample T SMAT-550 , a yield strength reduction of 10% is recorded in both tensile directions (RD and TD) for the sample T SMAT-650 . In the rolling direction, sample T SMAT-550 reaches a yield strength of 750 MPa, corresponding to an increase of 154% as compared to the coarse grain sample (295 MPa). The benefit of the duplex process in terms of mechanical strength appears clearly by comparing the stress-strain curves of the laminates T SMAT-550 and T No SMAT-550 : SMAT at the interfaces increases the yield strength by approximately 14% for both directions. Since the laminates have been manufactured under identical conditions (reduction ratio, annealing temperature and the number of passes), the yield strength increase recorded in figure Fig. 7 can be entirely attributed to the presence of a SMAT induced refined microstructure near the interfaces. At 650°C, the increase is about 5%.

In accordance with the well known Hall-Petch relationship, the high strength of the co-rolled laminate T SMAT-550 can be explained by an increased volume fraction of nano-and ultrafine grains. As shown in several publications, nanocrystalline layers can sustain an important part of the load and greatly increase the mechanical strength of the material [3,5]. Therefore, raising the volume fraction of nano-grain boundaries in the material leads to a strength increase of the whole structure. In addition, and in agreement with the work of Christian et al. [20] and Chen et al. [21], submicrometric twins play a similar role to grains in dislocation blocking. Thus, in a SMA treated material, the effect of the high density of twins can be associated to the effect of the ultrafine and nano-grains [21][22][23]. An increase of the volume fraction of nano-grains and submicrometric twins of about 5% in T SMAT-550 thus leads to a significant yield strength enhancement of about 100 MPa with respect to T SMAT-650 . The lower yield strength of T SMAT-650 might be attributed to thermally activated recovery and partial recristallisation of the microstructure initiating dislocation and twin annihilation, as well as grain growth. Fig. 5 supports this hypothesis; it shows that the microstructural changes induced by SMAT are reversed for T SMAT-650 , contrarily to T SMAT-650 . Furthermore, increase of the tensile strain up to failure for this sample can be explained by the same phenomena. Of note in Fig. 7 a) is the drop in the stress-strain curve of sample T SMAT-650 , which is typical of debonding occurring during tensile tests. In that case, after debonding, two sheets of the multilayer structure have been torn apart and only the third one remains. During mechanical testing, no debonding has been observed for laminates co-rolled at 550°C, which suggests that the interface of the laminate annealed at 650°C is less resistant than that annealed at 550°C. The integrity of the oxide layer, i.e. the lack of contact areas between the fresh metal (metal-metal contact) of the two adjacent sheets, might explain this phenomenon.

The difference in tensile strain to failure between the samples loaded in their rolling direction (RD) or transverse direction (TD) is not clearly explained yet. Nevertheless, the rearrangement of dislocations leading to the formation of a crystallographic texture during the rolling process might be one possible cause. Furthermore, the heterogeneous material flow and the presence of uncompleted bonding near the interface region may modify the global mechanical response. Electron Backscattering Diffraction (EBSD) measurements and microstructural observations are currently under way to analyse the texture evolution during the process. The purpose is to correlate mechanical response (strength and strain to failure) with microstructural changes.

Conclusions

In the present study, the interface oxidation occurring during a recently developed duplex process combining the Surface Mechanical Attrition Treatment (SMAT) and the co-rolling process at high temperature has been investigated. Optical micrographs of the interface region of the co-rolled laminates have shown discontinuous oxide clusters with heterogeneous thicknesses for sample T SMAT-550 and a continuous oxide layer with a uniform thickness of 1-2 µm for sample T SMAT-650 . The surface nanocristallisation technique used in the duplex process is thought to cause surface pollution, and EDX microanalyses of the oxidised interface region show the presence of elements such as Ti, which points to the TA6V ultrasonic resonator as their main source.

The oxide islets in the laminate processed at 550°C significantly disturb the material flow during the co-rolling, leading to strain localisation in bands. Higher annealing temperatures reduce this effect, as no similar bands are observed for sample T SMAT-650 . However, annealing at 650°C eliminates SMATinduced mechanical twins. TEM micrographs taken beneath the interface of T SMAT-550 show a microstructure characterised by a high density of dislocations, ultrafine equiaxed grains at random crystallographic orientations, and sub-structures. This indicates that grain growth remains limited after co-rolling at 550°C, contrarily to 650°C.

Finally, a significant effect of the annealing temperature on the mechanical response is observed in tensile tests: a yield strength reduction of 10% is recorded for the sample T SMAT-650 with respect to sample T 550 (≈ 750 MPa). This decrease is thought to result from thermally activated recovery and recristallisation of the microstructure, initiating annihilation of dislocations and twins combined with grain growth. Moreover, the higher temperature causes a drop in the interface resistance, leading to interface debonding under stress.

  Chemical composition of the 316L austenitic stainless steel (Fe matrix).

Fig. 1 :

 1 Fig. 1: SEM micrograph showing the microstructure of the as-received 316L stainless steel.

Fig. 2 :

 2 Fig. 2: a-b) Optical micrographs showing the interfaces of samples T SMAT-550 and T SMAT-650 in the RD-ND observation plane.

Fig. 3 :

 3 Fig. 3: a) Sample preparation to obtain an inclined polishing plane (near RD-TD); b) Optical micrograph of an oxide islet with metal/oxide decohesion at the interface of sample T SMAT-550 .

Fig. 5 :

 5 Fig. 5: Optical micrographs of the cross section (plane RD-ND) of samples T SMAT-550 (a-c) and T SMAT-650 (a'-c').

Fig. 6 :Fig. 7 :

 67 Fig. 6: Bright-field TEM image, and the corresponding SAED pattern (inset) of the layer near the interface of sample T SMAT-550 .

Acknowledgements

The authors are grateful to D. Bouleau from the Research and Development Laboratory from ArcelorMitall Maizières-lès-Metz (France) for valuable experimental assistance and for helpful discussions.


L Waltz

Delphine Retraint
email: bdelphine.retraint@utt.fr

A Roos

P Olier

J Lu

HIGH STRENGTH NANOCRYSTALLIZED MULTILAYERED STRUCTURE OBTAINED BY SMAT AND CO-ROLLING

Keywords: Nanocrystalline materials, SMAT, Co-rolling, Multilayered structure, Mechanical properties

In the present study, a method is presented combining surface nanocrystalline treatment (SMAT) and the co-rolling process. The aim of this duplex treatment is the development of a 316L stainless steel semi-massive multilayered bulk structure with improved yield and ultimate tensile strengths, while conserving an acceptable elongation to failure by optimizing the volume fraction and distribution of the nano-grains in the laminate. To characterize this composite structure, tensile tests as well as sharp nanoindentation tests were carried out to follow the local hardness evolution through the cross-section of the laminate. Furthermore, transmission electron microscope (TEM) observations were carried out to determine the correlation between the microstructure, the local hardness and the mechanical response of the structure.

Introduction

Nowadays, ultrafine grain materials with mean grain size smaller than 100nm are actively studied and present a widespread interest because they exhibit enhanced mechanical properties, such as high strength, hardness and superplasticity properties. In order to achieve an ultrafine grain structure, several severe plastic deformation (SPD) processes have been proposed, such as accumulative roll-bonding (ARB), equal channel angular pressing (ECAP), high pressure torsion (HPT) or mechanical milling. In addition, numerous studies have shown that recently developed Surface Mechanical Attrition Treatment (SMAT) may induce a grain refinement up to the nanometre scale in the top surface layer of metallic materials, based on mechanisms of severe plastic deformation [START_REF] Lu | Surface nanocrystallization (SNC) of materials and its Effects on Mechanical Behavior, Encyclopedia of Comprehensive Structural Integrity[END_REF][START_REF] Roland | Generation of nanostructures on 316L stainless and its effect on mechanical behaviour[END_REF][START_REF] Roland | Fatigue life improvement through nanostructuring of stainless steel by means of surface mechanical attrition treatment[END_REF][START_REF] Roland | Enhanced mechanical behavior of a nanocristallised stainless steel and its thermal stability[END_REF][START_REF] Tao | Surface nanocrystallization of iron induced by ultrasonic shot peening[END_REF]. In the present work, a method is presented combining this SMAT process and the co-rolling process for the development of a semi-massive multilayer bulk structure with improved yield and ultimate tensile strengths, while conserving an acceptable elongation to failure. To characterize this new material, several tests and analyses were carried out on SMATed 316L stainless steel samples and on the resulting hot co-rolled laminate structure. A surface characterization of the treated samples, which was performed simultaneously with local hardness analysis, will be presented. Sharp nanoindentation experiments were performed in order to follow the evolution of the local hardness through the cross-section of specimens and to establish a relation with grain size distribution. Furthermore, complementary tensile tests highlight the effect of SMAT on the mechanical response of treated and co-rolled samples. The microstructures of SMATed but undeformed tensile specimens have been analysed previously by Transmission Electron Microscopy (TEM) [START_REF] Roland | Fatigue life improvement through nanostructuring of stainless steel by means of surface mechanical attrition treatment[END_REF][START_REF] Roland | Enhanced mechanical behavior of a nanocristallised stainless steel and its thermal stability[END_REF]. Finally, Scanning Electron Microscopy (SEM) micrographs show how the laminate samples are torn apart during tensile tests.

Experimental procedures

The material used in this investigation is commercial 316L face-centred cubic (fcc) austenitic stainless steel. For the experimental tests, 120x120x1mm 3 plates with the chemical composition (in wt%) 0.025 C, 0.38 Si, 1.33 Mn, 0.027 P, 0.002 S, 16.70 Cr, 2.09 Mo, 10.20 Ni, 0.030 N, 0.40 Cu, 0.07 Co were used. The initial microstructure of the as-received material is characterised by a grain size ranging between 20 and 80µm. The surface nanocrystallization of these sheets was obtained by SMAT. The spherical steel shot (material 100Cr6), with a diameter of 3mm, was placed in a reflecting chamber including an ultrasonic concentrator that was put in motion by an ultrasonic generator. Because of the high vibration frequency of the system (20KHz), the shot reaches the resonance regime and peens the entire surface of the sample with a high number of impacts in a short period of time. It is noteworthy that impacts during ultrasonic shot-peening are highly random and multidirectional, and the intensity induced by this technique is similar to that of conventional shot-peening processes. In this study, samples have been treated for 30 minutes in air at room temperature. Figure 1 shows the microstructure of a SAMTed sample after electropolishing in a solution of 90% methanol and 10% perchloric acid.

Fig. 1: SEM micrograph of the cross-section of a SMATed 316L stainless steel sample

The co-rolling process at high temperature consists of the hot rolling of three nanocrystallised sheets as illustrated in Fig. 2. The middle plate of the piling has been SMATed on both sides, whereas the two other sheets have been treated on their inner sides only (as depicted in Fig. 2). After preheating treatment at 550°C for 60 minutes, the stack of treated sheets was first co-rolled without lubrification. The reduction ratio set by pass was approximately 22%, which corresponds to a global reduction ratio of 66% after 3 passes. After the first and the second passes, the sample was preheated again for 20 minutes and then after the third pass is water-cooled. The co-rolling was carried out using semi-industrial STANAT reversible quarto rolling equipment under a typical load of about 3500kN.

Fig. 2: Global view of the co-rolling process of SMATed samples

The local hardness variation was determined on SMATed samples and on co-rolled laminate using a Nano Indenter XP TM fitted with a Berkovich diamond indenter. Furthermore, in order to obtain a precise hardness profile, four indentations were performed at the same distance (depth) from the treated surface. To avoid erroneous hardness measurements due to the affected plastic zone around an indent, the distance between two indentations was fixed to at least 20µm. The depth of the indentations themselves was fixed at 600nm. Before testing, the samples were mechanically polished to mirror finish with 1µm diamond polishing paste.

For a better understanding of the deformation mechanism and the properties of SMATed and corolled stainless steel samples, tensile tests were carried out at room temperature on a screw-driven Kammrath & Weiss micro-tensile machine at a fixed strain rate of 10 -4 s -1 . The dimensions of the tensile specimens were 36mm in total length, a gauge length of 19mm and an average cross-section of 1.2 x 3.6mm².

Results and discussion

In previous studies, microstructural characterizations of SMATed 316L austenitic stainless steel have been carried out [START_REF] Roland | Generation of nanostructures on 316L stainless and its effect on mechanical behaviour[END_REF][START_REF] Roland | Fatigue life improvement through nanostructuring of stainless steel by means of surface mechanical attrition treatment[END_REF][START_REF] Roland | Enhanced mechanical behavior of a nanocristallised stainless steel and its thermal stability[END_REF][START_REF] Liu | Surface nanocrystallization of 316L stainless steel induced by ultrasonic shot peening[END_REF]. Transmission Electron Microscopy observations (TEM) performed near the extreme top surface of the specimens have thus shown grains in the nanometre range characterized by highly random crystallographic orientations and exhibit an average grain size of approximately 20nm. SMAT parameters used in this work are similar to the parameters used in the previous studies.

Figure 3 shows the local hardness evolution along the depth of a specimen treated for 30 minutes with 3mm shot. It can be observed that the ultrasonic-assisted SMAT induces a considerable enhancement of the local hardness over the cross-section of the sample. The local hardness profile exhibits very high hardness values in the top surface layer of the specimen, values which decrease as the depth from the treated surface increases. For instance, at a depth of 3-5µm, we recorded a very high hardness around 8.5GPa which was more than 3.3 times higher than the coarse-grain hardness. Moreover, the hardness level reached near the treated top surface in this work was much higher than the hardness proposed by T. Roland et al [START_REF] Roland | Enhanced mechanical behavior of a nanocristallised stainless steel and its thermal stability[END_REF]. The difference can be explained by the position of the indents near the top surface and the depth of each indentation. Indeed, the maximal indentation depth fixed in this study was 600nm, so that indents could be performed very near the treated surface (between 3µm and 5µm), while keeping the plastic sphere created under the Berkovich indenter inside the material. Actually, accordingly to the strain and strain rate gradient induced by the SMAT process from the top surface to the strain free matrix, a grain refinement down to the nanometre range is observed in the surface layer. This grain refinement process follows a Hall-Petch-like trend combined with a strain hardening phenomenon of sub-layers and gives a simple explanation for the local hardness evolution. In fact, according to this, indents performed in this work at a depth of 3-5µm from the treated surface leads to a higher hardness, which provides a partial explanation for this hardness difference. Considering previous TEM observations, indents performed down to 25µm below the treated surface are supposed to be located in the nanostructured layer (see Fig. 3). However, as pointed out by T. Roland [START_REF] Roland | Fatigue life improvement through nanostructuring of stainless steel by means of surface mechanical attrition treatment[END_REF], the austenite phase transformation into martensite induced by SMAT has also to be taken into account, so that a part of the high hardness could be attributed to the presence of the hard martensite phase. In addition, it is interesting to note that the hardness recorded in the strain-free matrix of the SMATed sample is slightly higher than the coarse grain hardness, which is certainly a hardening effect induced by the distortion of the sample during SMAT.

Fig. 3: Local hardness measurements obtained by nanoindentation tests on a SMATed sample treated for 30 minutes with 3mm shot on one side

Fig. 4 shows engineering stress-strain curves of a co-rolled multilayer laminate, an as-received specimen and a SMATed sample (30 minute treatment with 3mm shot). It clearly shows that the SMAT process considerably affects the yield stress of the treated materials, whereas the ductility does not seem to be significantly changed, since an elongation to failure of 36% is reached. This sample exhibits a yield strength value as high as 525MPa, which corresponds to an increase of the yield strength of about 78% compared to the coarse grain sample (295MPa). This strength increase can be directly explained by the presence of SMAT-induced nanostructured layers on the top surface of both sides of the specimen, which are able to sustain a large part of the load. Furthermore, by analysing this figure, it clearly appears that SMAT combined with the co-rolling process leads to a high-strength co-rolled multilayer structure. Indeed, despite a reduction of the elongation to failure, the co-rolled laminate presents high yield and ultimate strengths reaching respectively 800MPa and 914MPa. We cannot claim, that compared to the SMATed sample, the corolled specimen provides a very high strength level, since we recorded a yield strength increase of 53%. It is noteworthy that the rolling process leads to the reduction of the ductility of the structure through work hardening of the material, which reaches an elongation to failure of 13%. Although this ductility reduction is induced by the combined SMAT-rolling process, the elongation to failure of the co-rolled specimen stays acceptable. The high strength of the multilayer structure can be explained by the combination of an increased volume fraction of nano and ultrafine grains, which are able to sustain a great part of the load, combined with a hardening effect induced by co-rolling. The SEM fractographs in Fig. 5 show an example of the fracture surface of the co-rolled multilayer tensile specimen after the tensile test. The fracture morphology of this sample presents a significant feature, since on the two lateral sheets, initially SMATed on their inner sides, two distinct failure structures can be clearly distinguished. Indeed, Fig. 5 b) presents a high magnification SEM micrograph of such an area showing a clear and straight separation between the two regions, both characterized by a specific failure mode. It is interesting to note that the flat fracture surface region near the interface (region A in Fig. 5) corresponds well with the initially nanostructured layers after SMAT [START_REF] Roland | Generation of nanostructures on 316L stainless and its effect on mechanical behaviour[END_REF][START_REF] Roland | Fatigue life improvement through nanostructuring of stainless steel by means of surface mechanical attrition treatment[END_REF][START_REF] Roland | Enhanced mechanical behavior of a nanocristallised stainless steel and its thermal stability[END_REF]. Furthermore, this flat failure surface is reminiscent of a glassy brittle material, whereas the outer side of the first sheet and the inner side of the middle sheet present a heavily dimpled morphology (region B in Fig. 5 b)), characteristic of a ductile material. These observations clearly indicate that this sample was torn apart in a non-trivial combined ductile-brittle manner. In addition, it is interesting to note that in the last stage of deformation during the tensile tests, local debonding occurs in the striction zone (Fig. 5 a).

Conclusion

In the present study, generation of a high strength semi-massive multilayer structure by a combination of Surface Mechanical Attrition Treatment (SMAT) and the co-rolling process at high temperature was investigated. To characterize SMATed and co-rolled laminate, local hardness measurements, tensile tests and electron microscopy observations were performed. It has been shown that the SMAT process has a significant influence on local hardness evolution through the cross-section of the sample and values recorded near the treated top surface are very high (≈ 8,5 GPa). The hardness increase near the surface can be attributed to the presence of an SMAT-induced nanocrystalline layer, which is confirmed by an enhanced yield strength obtained by tensile tests. Furthermore, the new co-rolled structure presents improved yield and ultimate strengths (800MPa and 914MPa respectively), while keeping an acceptable strain to failure of approximately 13%. Scanning electron micrographs of the failure surface obtained after tensile tests clearly show a separation between flat and dimpled areas, indicating that the specimen was torn apart in a ductilebrittle manner.

Fig. 4 :

 4 Fig. 4: Uniaxial engineering tensile stress-strain curves of (1) as-received coarse grain sample, (2) SMATed specimen, (3) SMAT + co-rolled specimen

Fig. 5 :

 5 Fig. 5: a) SEM micrographs of the fracture surface of the co-rolled multilayer tensile specimen; b) high magnification SEM micrographs of selected regions (white square)