Mathieu Rodriguez
email: rodriguez@geologie.ens.fr

Nicolas Chamot-Rooke

Philippe Huchon

Marc Fournier

Delescluse

The Owen Ridge uplift in the Arabian Sea: implications for the sedimentary record of Indian 3 monsoon in Late Miocene 4

The pelagic cover of the Owen Ridge in the Arabian Sea recorded the evolution of the Indian 17 monsoon since the Middle Miocene. The uplift of the Owen Ridge resulted from tectonic 18 processes along the previously unidentified Miocene India-Arabia plate boundary. Based on 19 seismic reflection data tied with deep-sea drilling to track the Miocene India-Arabia plate 20 boundary, we propose a new timing for the uplift of the Owen Ridge and highlight its impact on 21 the record of climate changes in pelagic sediments. The new dataset reveals a fracture zone east 22 of the Owen Ridge corresponding to the fossil plate boundary, and documents that the main 23 uplift of the Owen Ridge occurred close to ~8.5 Ma, and is coeval with a major uplift of the east 24 Oman margin. Late Miocene deformation at the India-Arabia plate boundary is also coeval with 25 the onset of intra-plate deformation in the Central Indian Ocean, suggesting a kinematic change 26 of India and surrounding plates in the Late Miocene. The uplift of the Owen Ridge above the lysocline at ~8.5 Ma accounts for a better preservation of Globigerina bulloides in the pelagic 28 cover, previously misinterpreted as the result of a monsoon intensification event. 29

Introduction 31

The pelagic sedimentary cover of the Owen Ridge contains the past records of the Asian summer 32 monsoon since the Middle Miocene (Shipboard Scientific Party, 1974, 1989). The ridge itself consists 33 of a series of bathymetric highs sub-dividing the Arabian Sea into an abyssal plain to the east and a 34 shallower Owen basin to the west (Fig. 1). The Arabian Sea is located on the migration path of the 35 Inter Tropical Convergence Zone, which controls the seasonality of the Asian monsoon. The apparent 36 increase in the abundance of the foraminifera Globigerina bulloides within the Owen Ridge's pelagic 37 cover, commonly interpreted as a proxy for monsoon-driven upwelling [START_REF] Kroon | Onset of monsoonal related upwelling in the western 617 Arabian Sea as revealed by planktonic foraminifers[END_REF], suggests 38 that the evolution of astronomical parameters alone cannot be responsible for the observed monsoon 39 intensification in the upper Miocene [START_REF] Molnar | Mantle dynamics, uplift of the Tibetan Plateau, and the 636 Indian monsoon[END_REF]Molnar, 2005;[START_REF] Sun | How old is the Asian monsoon system? Palaeobotanical records from 705 China[END_REF]Huang 40 et al., 2007;[START_REF] Clift | Correlation of 535 Himalayan exhumation rates and Asian monsoon intensity[END_REF][START_REF] Steinke | East Asian summer 701 monsoon weakening after 7.5 Ma: Evidence from combined planktonic foraminifera Mg/Ca and 702 δ18O (ODP Site 1146; northern South China Sea)[END_REF]. A Late Miocene uplift of the Himalayan-Tibetan 41 Plateau [START_REF] Harrison | Raising Tibet[END_REF] was proposed as a forcing mechanism over the climatic system, high 42 elevation inducing a reorganisation of the atmospheric circulation and hence, monsoon intensification 43 [START_REF] Molnar | Late Cenozoic uplift of mountain ranges and global climatic change: 634 chicken or egg?[END_REF][START_REF] Molnar | Mantle dynamics, uplift of the Tibetan Plateau, and the 636 Indian monsoon[END_REF]Ann et al., 2001). However, a growing set of 44 observations showed that the Himalaya mountain belt reached its present-day elevation at least ~15 45 Myrs ago, and probably earlier [START_REF] Spicer | Constant elevation of southern Tibet over the past 15 million years[END_REF]Molnar, 2005;[START_REF] Harris | The elevation of the Tibetan Plateau and its impact on the monsoon[END_REF]Rowley and Currie, 46 2006;[START_REF] Dupont-Nivet | Tibetan uplift prior to the Eocene-Oligocene climate 559 transition : Evidence from pollen analysis of the Xining Basin[END_REF][START_REF] Wang | Two-phase growth of high topography in eastern Tibet during Cenozoic[END_REF][START_REF] Yuan | The growth of northeastern Tibet and its relevance to large-scale continental 728 geodynamics: a review of recent studies[END_REF]. 47

A re-analysis of marine sediments drilled at the Owen Ridge questioned the record of an apparent 48 monsoon intensification at ~8.5 Ma [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF]. Selecting foraminifera of large size to 49 remove the effect of variations in carbonate dissolution in the abundance records, [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF] 50 document only a minor change in the fraction of G. bulloides near 10 Ma. The latter is consistent with 51 a constant decrease in weathering of India during the Late Miocene (Clift et al., 2001;[START_REF] Spicer | Constant elevation of southern Tibet over the past 15 million years[END_REF]2008). 52 [START_REF] Steinke | East Asian summer 701 monsoon weakening after 7.5 Ma: Evidence from combined planktonic foraminifera Mg/Ca and 702 δ18O (ODP Site 1146; northern South China Sea)[END_REF] even suggested that the Late Miocene was a period of summer monsoon 53 weakening over India, rather than intensification. 54

The timing of seafloor uplift in the Indian Ocean is critical to the understanding of the sedimentary 55 record of climate during the Cenozoic. The commonly accepted tectonic framework of the Arabian 56

Sea is that the uplift of the Owen Ridge was coeval with the beginning of accretion at the Sheba Ridge 57 in the Gulf of Aden 20 Ma ago (Fig. 1) [START_REF] Whitmarsh | The Owen Basin off the south-east margin of Arabia and the evolution of the 723 Owen Fracture Zone[END_REF] and with the shift of the India-Arabia plate-58 boundary from the Oman continental margin to its present-day location [START_REF] Mountain | A multiphase plate tectonic history of the southeast continental 644 margin of Oman. The Geology and Tectonics of the Oman Region[END_REF]. 59 However, structural and kinematic studies show that the Owen Fracture Zone (the current plate 60 boundary) is no older than 3 to 6 Ma (Fournier et al., 2008a;[START_REF] Bonatti | this framework, the 3-6 Ma-old Owen Fracture Zone[END_REF][START_REF] Rodriguez | Neotectonics of the Owen Fracture Zone (NW Indian Ocean): structural 670 evolution of an oceanic strike-slip plate boundary[END_REF]2013b). As 61 a result, the location of the India-Arabia plate boundary during the Miocene, as well as its relationship 62 with the uplift of the Owen Ridge, remain unknown. 63

Here we present a new set of seismic reflection data that documents a Late Miocene tectonic uplift at 64 the edges of the Owen Basin, including the Owen Ridge. We identify the Miocene India-Arabia plate 65 boundary and highlight the tectonic processes at the origin of the Owen Ridge uplift. We finally 66 discuss how the latter impacted the record of climate evolution in the pelagic sediments of the Arabian 67 Sea. 68 69

Materials and methods 70

The dataset presented in this study was acquired onboard the French Navy oceanographic vessel 71

Beautemps-Beaupré during the OWEN and OWEN-2 surveys run in 2009 and 2012 respectively. 72

Multibeam bathymetry was collected using a Kongsberg-Simrad EM 120 echo-sounder (Fig. 1,2). 73 Seismic reflection profiles were acquired at 10 knots using two GI air-guns (one 105/105 c.i. and one 74 45/45 c.i., fired every 10 seconds at 160 bars in harmonic mode, resulting in frequencies ranging from 75 15 to 120 Hz) and a 24-channel, 600 m-long streamer, implying a common mid-point spacing of 6.25 76 m. A sub-surface penetration of about 2s two-way travel time (TWT) was achieved throughout the 77 survey. The processing consisted of geometry setting, water-velocity normal move-out, stacking, 78 water-velocity F-K domain post-stack time migration, bandpass filtering and automatic gain control. 79

All profiles are displayed with a vertical exaggeration of 8 at the seafloor. The seismic dataset is tied 80 with Deep Sea Drilling Project (DSDP) and Ocean Drilling Project (ODP) drillings available in the 81 Arabian Sea (Shipboard Scientific Party, 1974;1989) to provide the stratigraphic framework (Fig. 3, 82 inset). Reflectors picked on seismic profiles have been selected based on seismic discontinuities that 83 reflect lithological changes, stratigraphic hiatuses or tectonic deformation. 84 85 3. Geological framework of the Arabian Sea and the Owen-Murray Ridge System 86

Present-day morphology of the Arabian Sea 87

The Owen Fracture Zone is an 800-km-long strike-slip fault system, which runs along the Owen Ridge 88 (Fig. 1). The southern Owen Ridge is a 300 km-long, 50-km wide, and up to 2000 m-high relief that 89 appears as a vast tilted slab (Fig. 2b). It contrasts with the uneven topography of the 220 km-long, 90 50 km-wide, and up to 1700 m-high central ridge (Fig. 2a), and the guyot morphology of the Qalhat 91

Seamount further to the north. The Owen Fracture Zone connects seafloor spreading at the Sheba mid-92 oceanic ridge with the Makran subduction zone (Fig. 1). At its northern end, the Owen Fracture Zone 93 forms a complex stepover basin known as the Dalrymple Trough [START_REF] Edwards | Extension across the Indian-Arabian plate 565 boundary: the Murray Ridge[END_REF]Gaedicke et 94 al., 2002), which is flanked to the east by the Murray Ridge. Seafloor spreading at the Sheba Ridge 95 started around 20 Ma [START_REF] Fournier | Arabia-Somalia plate kinematics, evolution of the Aden-Owen-Carlsberg 589 triple junction, and opening of the Gulf of Aden[END_REF], whereas subduction in the Makran area began in the Late 96

Cretaceous [START_REF] Mccall | The geotectonic history of the Makran and adjacent areas of southern Iran[END_REF]. The modern accretionary wedge developed since the Tortonian (7.2-11.6 97 Ma) [START_REF] Mccall | The geotectonic history of the Makran and adjacent areas of southern Iran[END_REF][START_REF] Burg | A giant catastrophic mud-and-debris 511 flow in the Miocene Makran[END_REF][START_REF] Smit | Effects of mass waste events on thrust wedges: 695 Analogue experiments and application to the Makran accretionary wedge[END_REF]. Seafloor morphology does not display any 98 trace of the Miocene India-Arabia plate boundary [START_REF] Rodriguez | Neotectonics of the Owen Fracture Zone (NW Indian Ocean): structural 670 evolution of an oceanic strike-slip plate boundary[END_REF]. 99 100

Substratum of the Owen-Murray Ridge System 101

Several seismic lines run as pre-site surveys for DSDP and ODP reached the basement of the southern 102 and the central ridges. Their uneven substratum, drilled at DSDP Sites 223 and 224 (Fig. 2), is basaltic 103 in composition and of Late Paleocene age (Shipboard Scientific Party, 1974;1989). These 50-55 Ma-104 old reliefs might either be tilted slivers of oceanic crust or volcanic highs (Fig. 3b), and are hereafter 105 referred as the "pre-Owen Ridge". The history of the Murray Ridge basement is not clearly 106 established, since it has never been drilled. Based upon seismic refraction data, the Murray Ridge has 107 been interpreted as a small piece of continental crust inherited from the Gondwana break-up (Edwards 108 et al., 2000;2008). 109

Uplift of the Owen Ridge 111

In its present-day configuration, the southern Owen Ridge is formed at its top by Upper Oligocene-112

Lower Miocene turbidites coming from the Indus deep-sea fan and the subsequent pelagic cover (Fig. 113 3b) (Shipboard Scientific Party, 1974;1989). Lower Miocene turbidites at the top of the Owen Ridge 114 indicates an episode of uplift during the Miocene, rejuvenating the topography of the proto-Owen 115

Ridge. 116

So far, the uplift of the Owen Ridge has been dated at 20 Ma based on two sets of arguments. The first 117 set of arguments deals with the progressive burial of the proto-Owen Ridge and its pelagic cover by 118

Upper Oligocene-Lower Miocene Indus turbidites, which forms a diachronous angular unconformity 119 (picked in light purple) (Fig. 3) biostratigraphically dated at 19.6 Ma and ~14 Ma at the southern (Fig. 120 3b) and central (Fig. 3c) Owen Ridge, respectively (Shipboard Scientific Party, 1974). In fact, this 121 angular unconformity is unrelated to any tectonic uplift of the Owen Ridge, in contrast with previous 122 interpretation by Whitmarsh et al. (1974;[START_REF] Whitmarsh | The Owen Basin off the south-east margin of Arabia and the evolution of the 723 Owen Fracture Zone[END_REF]. Second, the transition from Indus turbidites to 123

Miocene pelagic deposits drilled on the southern Owen Ridge at DSDP Site 224 and ODP Sites 721, 124 722, 731 (top of Unit 4, Fig. 3) has been considered by [START_REF] Mountain | A multiphase plate tectonic history of the southeast continental 644 margin of Oman. The Geology and Tectonics of the Oman Region[END_REF] as an indicator of 125 uplift above the level of turbiditic deposition. The transition is marked by a mixed pelagic-turbiditic 126 sequence biostratigraphically dated at 14-15 Ma, composed of thin detrital particles, interpreted as the 127 uppermost part of the turbiditic plume being deposited during the first stages of ridge uplift (Mountain 128 and Prell, 1990). The latter argument will be revised in the light of our new dataset. 129 130

Past locations of the India-Arabia plate-boundary 131

Past location of the India-Arabia plate boundary prior to the Owen Fracture Zone is currently 132 unknown. Early paleogeographic reconstructions by [START_REF] Whitmarsh | The Owen Basin off the south-east margin of Arabia and the evolution of the 723 Owen Fracture Zone[END_REF] suggested that the India-133 Arabia plate boundary was already at its present-day location when India started to move northwards 134 at ~90 Ma. An alternative paleogeographic reconstruction [START_REF] Mountain | A multiphase plate tectonic history of the southeast continental 644 margin of Oman. The Geology and Tectonics of the Oman Region[END_REF] postulates that 135 the India-Arabia plate-boundary initially ran along the Oman continental margin, while the Mascarene 136

Basin opened between Madagascar and Seychelles (between ~90-60 Ma) (Bernard and Munschy, 137 2000) and the Carlsberg Ridge developed (since ~63 Ma; [START_REF] Dyment | Evolution of the Carlsberg Ridge between 60 and 45 Ma: Ridge propagation, 562 spreading asymmetry, and the Deccan-Reunion hotspot[END_REF]. The India-Arabia plate-138 boundary would then have jumped to its present-day position in the Early Miocene (~20 Ma), 139 triggering the uplift of the Owen Ridge [START_REF] Mountain | A multiphase plate tectonic history of the southeast continental 644 margin of Oman. The Geology and Tectonics of the Oman Region[END_REF]. A Paleogene location of the India-140 Arabia plate-boundary in the Owen Basin is also supported by paleogeographic reconstructions based 141 on the record of magnetic anomalies over the Arabian Sea (Royer et al., 2002). 142 143

Results 144

Late Miocene deformation and contourites on the East-Oman margin 145

Seismic profiles crossing the edge of the continental platform reveal a large, ~20-km-wide anticline 146 affecting Lower to Upper Miocene sediments composed of calcareous turbidites according to the 147 nearby ODP Site 730 (units U2 and U3, Fig. 3a and4) (Shipboard Scientific Party, 1989). A dense 148 network of faults affects the anticline and is sealed by upper Miocene to Plio-Pleistocene deposits 149 (unit U1, Fig. 3a and4). The folded unit contains planktonic faunas typical of a deep-sea environment 150 (Shipboard Scientific Party, 1989). An erosive surface sealing the top of the anticline (Fig. 3a and4) 151 (Shipboard Scientific Party, 1989). This set of 158 observations documents a major uplift episode along the Oman margin around 8.5 Ma. 159

Bottom currents influenced the architecture of the sedimentary unit U1 sealing the fold (Fig. 3a). Unit 160 1 displays a complicated set of imbricated, sigmoid to undulating geometries, all non-parallel to the 161 accumulation surface that moved preferentially upslope through times. This description corresponds to 162 a confined drift according to the classification of [START_REF] Faugères | Seismic features diagnostic of contourite 576 drifts[END_REF], and is very similar to drifts 163 observed along the Algarve Margin (Portugal) (Marchès et al., 2010;[START_REF] Brackenridge | A Pliocene mixed 479 contourite-turbidite system offshore the Algarve Margin, Gulf of Cadiz: Seismic response, margin 480 evolution and reservoir implications[END_REF]. 164

An E-W seismic line was acquired close to ODP Site 722 on the Southern Owen Ridge, where the 167 most complete sequence has been drilled (Fig. 3b). A fanning configuration characterizes the lower 168

Miocene turbidites on top of the Owen Ridge (Fig. 3b,5a,5b,6a). The seismic profile crossing ODP 169 Site 722 (Fig. 3b) shows that the 14-15 Ma-old turbiditic-pelagic facies has been drilled on the levee 170 of a fossil turbiditic channel. The ~40-m-deep channel axis is identified by a typical lens-like 171 architecture and discontinuous, high-amplitude reflections. The associated levees display a 172 characteristic wedge shape with high-amplitude, transparent seismic facies (Fig. 3b). 173

The sedimentary cover overlying the last turbiditic channel (units U3 to U1) is composed of pelagic 174 deposits (Fig. 3,5,6). Pelagic Unit 3 displays slight lateral thicknesses variations (<0.1 s TWT), which 175 results either from MTDs coming from the proto-Owen Ridge that still stood above the seafloor 176 before the uplift, or from fanning related to a moderate tectonic activity (Fig. 5 a,b). 177

The transition between units 3 and 2 is marked by an increase of the sedimentation rates (from 15 to 178 54 m.Ma -1 ) (Shipboard Scientific Party, 1989). Unit 2 is also marked by the appearance of submarine 179 failures around ~8.5 Ma according to the nearby ODP Sites 721 and 731 (Fig. 2,3,[START_REF]Origin of the Late Miocene deformation in the Owen Basin 295 The 15-20 Ma uplift of the Owen Ridge used to be related with the onset of seafloor spreading at the 296[END_REF]. The age of ~8.5 180 Ma corresponds to the age of the Foraminifera (Discoaster hamatus) immediately overlying the 181 sedimentary hiatus (formed by the submarine failure) drilled at ODP Site 721. The configuration of 182 submarine failures observed in the uppermost part of the pelagic sequence shows that the sediment 183 failed and were transported in the direction of the Owen Basin (Fig. 3,5), which indicates that the 184 Owen Ridge was already uplifted at ~8.5 Ma. The thickness of Unit 2 increases in the southernmost 185 part of the Owen Ridge, where it displays a conspicuous fanning pattern (Fig. 6a), starting at ~10 Ma, 186 and ending at 8.5 Ma (first pelagic layer over the MTD that seals the fanning). The sedimentary 187 sequence at the top of the Owen Ridge is faulted throughout its entire thickness (Fig. 3b and5a) by a 188 dense network of faults very similar to what is observed on the Oman margin (Fig. 3a). These faults 189 display very irregular offsets and do not root into the basement (Fig. 6a). We interpret these faults as 190 the result of fluid circulation (i.e. polygonal faults as defined in Cartwight, 1994). The change of 191 sedimentary setting induced by the uplift of the southern ridge and the margin sealed fluid circulation 192 in most places. At the southern ridge, fluid circulation may have controlled the distribution of 193 submarines failures [START_REF] Rodriguez | Mass 673 wasting processes along the Owen Ridge (NW Indian Ocean)[END_REF].

Several folds are observed in the Indus abyssal plain at the eastern foot of the southern Owen Ridge,195 and south of the Beautemps-Beaupré Basin (Fig. 5c,6). A sharp and vertical fault plane, interpreted as 196 a fracture zone, crosscuts the eastern side of the Owen Ridge at depth (Fig. 6b, 6c; 7a). A system of 197 fossil folds buried under Indus deposits and MTDs coming from the ridge is observed east of the 198 southern ridge. The growth anticline displayed in Fig. 6c shows that compressive deformation is still 199 active at the Owen Fracture Zone [START_REF] Rodriguez | Neotectonics of the Owen Fracture Zone (NW Indian Ocean): structural 670 evolution of an oceanic strike-slip plate boundary[END_REF]. The series of folds observed south of the 200 Beautemps-Beaupré Basin (Fig. 6d) display an isopach pattern at depth. The overlying deposits show 201 angular unconformities indicating several discontinuities in episodes of folding. Unfortunately, the 202 penetration of the nearby ODP Site 720 (location on Fig. 1) is too shallow to provide confident dating 203 of the initiation of this compressive episode. These folds could correspond either to the Owen Ridge 204 uplift at 8.5 Ma or to the emplacement of the Owen Fracture Zone between 3-6 Ma. 205 206

Late Miocene deformation at the Central Owen Ridge and mass transport deposits 207

Seismic profiles crossing the eastern side of the Central Owen Ridge document an angular 208 unconformity within the Indus deep-sea fan (blue in Fig. 7). The angular unconformity becomes 209 laterally concordant with the overlying sediments from the Indus fan. This key reflector is about 1 s 210 TWT deep in the undeformed area, which roughly corresponds to a Late Miocene age according to the 211 nearby DSDP Site 222. A sub-vertical fracture zone is identified at the eastern edge of the central 212 ridge (Fig. 7a). 213 DSDP Site 223 is located west of the central segment of the Owen Ridge, where the Early Miocene 214 unconformity was first determined (Shipboard Scientific Party, 1974;[START_REF] Whitmarsh | The Owen Basin off the south-east margin of Arabia and the evolution of the 723 Owen Fracture Zone[END_REF]. A second, 215 younger unconformity is observed both in the Owen Basin (Fig. 5d) and at the top of the central Owen 216

Ridge (Fig. 7), where it is underlined by MTDs composed of upper Miocene sediments (Fig. 3c) 217 overlying diatoms-rich sediments dated at 10 Ma (Shipboard Scientific Party, 1974). The reflector 218 corresponding to the top of the MTDs is correlated with sediments at the top of the Central Owen 219

Ridge. The overlying pelagic layer is 0.3 s (TWT) thick at the top of the central ridge, and devoid of 220

MTDs. The thickness of 0.3 s (TWT) is the same as Unit 1 on the Southern Owen Ridge in areas 221 undisturbed by submarine failures (Fig. 3). Assuming a pelagic sedimentation rate similar to the one 222 estimated at the southern ridge [START_REF] Bourget | Late 499 Quaternary megaturbidites of the Indus Fan : origin and stratigraphic significance[END_REF] The Late Miocene episode of deformation (~8-9 Ma) described above contrasts with the 15-20 Ma age 232 previously assessed for the major uplift of the Owen Ridge [START_REF] Whitmarsh | The Owen Basin off the south-east margin of Arabia and the evolution of the 723 Owen Fracture Zone[END_REF]Mountain and Prell, 233 1990). The main argument in favour of a 15-20 Ma-old uplift of the Owen Ridge was the 14-15 Ma-234 old mixed turbiditic-pelagic facies drilled at ODP Sites [START_REF] Mountain | A multiphase plate tectonic history of the southeast continental 644 margin of Oman. The Geology and Tectonics of the Oman Region[END_REF]. Because of its 235 location on a turbiditic levee (Fig. 3), the mixed facies cannot be interpreted by itself as the first stage 236 of the southern ridge uplift. During their deposition along turbiditic channels, turbiditic plumes 237 frequently undergo flow-stripping or overspilling processes [START_REF] Piper | Turbidite depositional patterns and flow characteristics, Navy 657 Submarine Fan, California Borderland[END_REF]Hiscott et al., 238 1997). These processes imply that the uppermost part of the turbiditic plume, composed of the thinner 239 detritic particles, overflows throughout the channel axis, leading to the deposition of mixed turbiditic-240 pelagic sequence on turbiditic levees similar to the one described at ODP Site 722. The overlying 241 pelagic deposits (Units 2-3) simply reflect a shift in the locus of turbidites deposition. The lysocline is currently at a depth of ~4000 m in the area [START_REF] Kolla | Calcium Carbonate distribution in the surface sediments 613 of the Indian Ocean[END_REF] The ~8.5-9 Ma onset of major submarine failures is a striking feature of both the southern and the 252 central Owen Ridges [START_REF] Rodriguez | Mass 673 wasting processes along the Owen Ridge (NW Indian Ocean)[END_REF]2013a). The large expansion of the failure-related 253 erosive surface over both ridge segments, together with the erosive surface observed at the top of 254 buried reliefs in the Owen Basin and the synchronicity with the formation of anticlines along the 255

Oman margin strongly suggest that they all relate to a common regional tectonic event. 256

The 8-9 Ma age of deformation in the Owen Basin fits with the estimated Tortonian age (7.2-11.6 Ma) 257 of the post-rift uplift episode observed along the Dhofar margin in the Gulf of Aden (Platel and Roger, 258 1989;[START_REF] Lepvrier | Cenozoic extension in coastal Dhofar (southern 621 Oman): Implications on the oblique rifting of the gulf of Aden[END_REF][START_REF] Fournier | Oblique rifting and segmentation of the NE 578 Gulf of Aden passive margin[END_REF][START_REF] Petit | Tectonic and climatic controls on rift escarpments: Erosion 654 and flexural rebound of the Dhofar passive margin (Gulf ofAden, Oman)[END_REF]Gunnel et al., 2007;Bache et al., 259 2010). Several local processes have been invoked for the uplift episode in the Dhofar (Bache et al., 260 2010;[START_REF] Leroy | From rifting to oceanic spreading in the Gulf of Aden: a synthesis[END_REF], but the Late Miocene episode of deformation identified in the Owen Basin 261 could better account for this uplift as rifted areas are prone to be reactivated by intra-plate deformation 262 (e.g. Cloetingh et al., 2008). On the other hand, the reassessed age of deformation in the Owen Basin 263 contrasts with the age of uplift of the Murray Ridge estimated at ~20 Ma (Clift et al., 2001;Gaedicke 264 et al., 2002). This discrepancy may reflect either the lack of good stratigraphic control of the 265 deformation in the vicinity of the Murray Ridge, or a different tectonic episode. Recent ties with 266 industrial drillings [START_REF] Calvès | Tectonostratigraphic and climatic record of the NE Arabian Sea[END_REF] shows that the youngest turbidites tilted by the uplift of the Murray 267Ridge are actually 8-10 Myr-old. 268 269

2. Uplift of the Owen Ridge and the Early-Middle Miocene India-Arabia boundary 270

The fracture zone segments observed at the eastern edge of the Owen Ridge (Fig. 6b,6c) likely 271 correspond to the fossil India-Arabia plate-boundary in Early-Middle Miocene times, prior to the onset 272 of the Owen Fracture Zone. The system of buried fold observed on Fig. 5c probably marks the 273 deformation related to the Owen Ridge uplift. The fossil plate boundary must have been very weak to 274 allow the >2000 m uplift of the Owen Ridge. Based on free-air gravimetry and seismic profiles 275 analysis, [START_REF] Weissel | Extensional and Compressional Deformationof the 720 Lithosphere in the Light of ODP Drilling in the Indian Ocean.Synthesisof Results from Scientific 721 Drilling in the Indian Ocean[END_REF] showed that the uplift of the Owen Ridge may have occurred as a 276 flexural response to either an extensional or a compressive event, making the tectonic interpretation of 277 the ridge ambiguous. Vertical deformation within the oceanic lithosphere is mainly controlled by the 278 lithospheric strength, which is a direct function of the thermal state -and therefore the age -of the 279 lithosphere [START_REF] Weissel | Extensional and Compressional Deformationof the 720 Lithosphere in the Light of ODP Drilling in the Indian Ocean.Synthesisof Results from Scientific 721 Drilling in the Indian Ocean[END_REF]. Consequently, even a slight change in the stress field can generate 280 prominent seafloor uplift (>1000 m) of flexural origin in areas of strong rheological contrasts (i.e. the 281 2008a; [START_REF] Bull | Reconciling plate 508 kinematic and seismic estimates of lithospheric convergence in the central Indian Ocean[END_REF]. Age of the intraplate extension, counterpart of the intraplate compression, is 306 also compatible with a beginning of widespread deformation within the Indo-Australian plate around 307 10 Ma [START_REF] Henstock | Localized rifting at Chagos bank in the India-Capricorn plate 605 boundary zone[END_REF]. It suggests that the entire plate was subjected to a kinematic change 308 around 8-10 Ma, affecting both the plate interior and its boundaries. 309

The origin of the kinematic change responsible for the Indo-Australian intraplate deformation is a 310 matter of debate. [START_REF] Clark | Continental collision slowing due to viscous mantle lithosphere rather than 526 topography[END_REF] proposed a convergence of India with respect to Eurasia smoothly 311 decreasing through time since the very beginning of the collision, as a result of the viscous resistance 312 exerted by the lithospheric mantle in the collision zone. The latter does not explain the origin of the 8-313 10 Ma kinematic change. [START_REF] Molnar | Slowing of India's convergence with Eurasia since 20 Ma and its 640 implications for Tibetan mantle dynamics[END_REF] proposed that the growth of the Himalayas 314 increased the gradient of gravitational potential energy, resulting in an increase in stress applied on the 315 Indian plate and its boundaries. However, the Himalaya-Tibet reached its present-day altitude some 15 316 Ma, and probably earlier [START_REF] Yuan | The growth of northeastern Tibet and its relevance to large-scale continental 728 geodynamics: a review of recent studies[END_REF]. Late Miocene deformation at India's plate boundaries 317 may have occurred once the stress induced by gravitational potential energy exceeded some threshold 318 value. Onset of widespread deformation in the Indian Ocean may relate to strength loss of the oceanic 319 lithosphere in relation with fault selective abandonment (Delescluse et al., 2008a) and further 320 serpentinization (Delescluse and Chamot-Rooke, 2008b). [START_REF] Delescluse | Instantaneous deformation and kinematics of the India-546 Australia Plate[END_REF] and 321 [START_REF] Copley | India-Asia collision and the Cenozoic slowdown of the 543 Indian plate: implications for the forces driving plate motions[END_REF] alternatively proposed that the driving forces resulted from changes in the slab-322 pull forces at Sunda subduction. Whatever the driver, the 8-9 Ma episode of deformation within Indo-323 Australian plate modified the kinematics at all surrounding plate's boundaries. 324 325

4. Implications for the Indian monsoon and environmental changes 326

The seafloor of the Owen Ridge was significantly uplifted at ~8.5 Ma above the lysocline, inducing 327 the apparent dominance of G. bulloides since 8. 5 Ma (Shipboard Scientific Party, 1989;Kroon et al., 328 1991) unrelated to monsoon intensification [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF]. The Late Miocene change in 329 Foraminifera abundances therefore reflects a change in their conditions of preservation rather than a 330 climatic change. 331

In absence of any monsoon intensification at 8.5 Ma, the origin of the coeval environmental change in 332 the Siwalik sequence in Pakistan is enigmatic. This environmental change is characterized by a shift 333 from the dominance of C 3 to C 4 plants in the vegetation (C 3 and C 4 plants using a different 334 photosynthesis pathway) [START_REF] Quade | Development of Asian monsoon revealed by marked 665 ecological shift during the latest Miocene in northern Pakistan[END_REF][START_REF] Cerling | Global vegetation change through the Miocene/Pliocene boundary[END_REF]Molnar, 2005). The estimated 335 decrease in annual precipitation (~120 mm), the increase in annual temperature (+3°C), as well as the 336 decrease in atmospheric CO 2 [START_REF] Cerling | Global vegetation change through the Miocene/Pliocene boundary[END_REF] at ~8-9 Ma cannot account for the ecological 337 transition alone [START_REF] Nelson | Isotopic reconstructions of habitat change surrounding the extinction of 647 Sivapithecus, a Miocene hominoid, in the Siwalik Group of Pakistan[END_REF][START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF]. [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF] propose that the ecological 338 transition resulted from a large-scale hydrological change over Pakistan and he Himalayan foreland, 339 but the origin of this hydrological change is unknown. 340 Tectonic processes involved in surface uplift act at a different time-scale and are less precisely dated 341 than ecological and climatic changes, making any relationship based on synchronicity difficult to 342 assess. However, the environmental change is coeval with several indicators of surface uplift in 343

Pakistan that might have helped the environmental transition through Indus River avulsion (Fig. 8), 344 which provides a likely origin for the hydrological change pointed out by [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF]. Indeed, 345 the Makran underwent a structural reorganization in Late Miocene while the frontal thrust migrated 346 southward. Folds reaching altitudes of 1000-2000 m according to field works [START_REF] Mccall | The geotectonic history of the Makran and adjacent areas of southern Iran[END_REF]Ellouz 347 Zimmerman et al., 2007) triggered a huge submarine olistostrome (~42 000 km 3 ) [START_REF] Burg | A giant catastrophic mud-and-debris 511 flow in the Miocene Makran[END_REF]. 348

The Kirthar, Sulaiman and Salt ranges also underwent complex structural reorganizations during the 349 Late Miocene. These structural reorganizations favoured a complex episode of avulsion of the Indus 350 River over more than 400 km [START_REF] Waheed | Changes in paleocurrents during the development of an obliquely 707 convergent plate boundary (Sulaiman fold-belt, southwestern Himalayas, west-central Pakistan)[END_REF][START_REF] Cochran | Bull and Scrutton[END_REF], which is at its present-day location 351 since only 5 Ma (Clift and Blusztajn, 2005). Surface uplift in Pakistan reduced monsoon precipitation 352 coming from the ocean and increased aridity, without affecting the seasonality (consistently with 353 environment reconstructions of [START_REF] Nelson | Isotopic reconstructions of habitat change surrounding the extinction of 647 Sivapithecus, a Miocene hominoid, in the Siwalik Group of Pakistan[END_REF]. Surface uplift also explains the greater fraction of 354 precipitation coming from continental sources in the Siwalik area, revealed by geochemical studies of 355 [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF]. The complex interplay between precipitation source changes (Huang et al., 2007) 356 and Indus avulsion (Waheed andWells, 1990, 1992) triggered by surface uplift over Pakistan induced 357 successive fragmentations of habitats and the related ecological stresses that lead to the environmental 358 change (Barry et al., 2002). 359

The Owen margin, basin and ridge have undergone a significant episode of deformation in the Late 362 Miocene, leading to the uplift of the east Oman margin and the Owen Ridge. The best-dated 363 deformation is the anticline structure on the Oman margin, bracketed between 8.2 and 8.8 Ma. This 364 episode of deformation corresponds to the transition from the Early-Middle Miocene India-Arabia 365 plate boundary to the Owen Fracture Zone. The Late Miocene episode of deformation at the India-366 Arabia plate boundary is coeval with intraplate deformation in the Central Indian Ocean, suggesting a 367 possible common cause. 368

The uplift of the Owen Ridge induced changes in the condition of preservation of Foraminifera, 369 which confirms the previous assumption of [START_REF] Huang | Large-scale hydrological change 610 drove the Late Miocene C4 plant expansion in the Himalayan foreland and Arabian Peninsula[END_REF] that the apparent increase in G. 370 Bulloides at 8.5 Ma is not related to a climatic change. The monsoon might have already been strong 371 at 10 Ma, then decreasing over the Arabian Sea until ~5 Ma [START_REF] Clift | Correlation of 535 Himalayan exhumation rates and Asian monsoon intensity[END_REF]Prasanta and Sinha, 372 2010;[START_REF] Sakai | Climate shift 691 recorded at around 10 Ma in Miocene succession of Samburu Hills, northern Kenya Rift, and its 692 significance[END_REF]. Proxies recording changes in summer monsoon intensity east of India, i.e. 373

Chinese loess, abundances of N. dutertrei in South China Sea, windblown record in northeast Pacific 374 [START_REF] Molnar | Orographic controls on climate and paleoclimate of 642 Asia: thermal and mechanical role of the Tibetan Plateau[END_REF][START_REF] Steinke | East Asian summer 701 monsoon weakening after 7.5 Ma: Evidence from combined planktonic foraminifera Mg/Ca and 702 δ18O (ODP Site 1146; northern South China Sea)[END_REF], may reflect a shift in the trajectory of atmospheric eddies 375 involved in the Indian monsoon that did not affect the western Indian Ocean. Contouritic drifts lay on 376 the Late Miocene highs (Fig. 7), leading to the hypothesis that the uplift of the Owen Basin edges may 377 also have changed the conditions of record of deep-sea current activity. The arising working 378 hypothesis is that the general increase in carbonate preservation recorded in the Indian Ocean 379 [START_REF] Peterson | Cenozoic carbonate accumulation 650 and compensation depth changes in the Indian Ocean[END_REF]) may be the result of the 8-9 Ma-old episode of seafloor uplift rather than the 380 expression of a major climatic or deep-sea circulation change. 381

The questioning of the 8.5 Myrs monsoon intensification suggests that surface uplift in the Pakistan 382 may be responsible for the coeval environmental change recorded in the Siwalik sequence. This 383 environmental change influenced the evolution of mammals in the Late Miocene (Barry et al., 2002;384 Elton, 2008), including Sivapithecus, a likely ancestor of Pongo pygmae [START_REF] Andrews | The relationships of Sivapithecus and Ramapithecus and the 470 evolution of the orang-utan[END_REF], 385 who disappeared in Pakistan following the ~8.5Ma ecological change [START_REF] Begun | Sivapithecus is east and Dryopithecus is west, and never the twain shall meet[END_REF]. 386

We are grateful to Captain Rémi De Monteville, officers and crew members of the BHO Beautemps-389 Beaupré, and to the GENAVIR team and the hydrographer D. Levieuge for their help in data 390 acquisition. Processing of the Owen-2 dataset was carried out using the Geocluster 5000 software 391 from CGGVeritas.We thank A. Rabaute who helped the organization of the Owen-2 cruise, J. Smith 392 for scientific discussions, and P. Dubernet and N. Bacha for technical assistance. J. Bull, T. Henstock 393 and an anonymous reviewer provided very constructive and careful comments that helped us to 394 improve the manuscript and clarify our thoughts. This study was supported by SHOM, IFREMER, 395 INSU-CNRS, and CEA (LRC Yves-Rocard). 396 397

Figure captions 398

Figure 1 : Bathymetric map of the Arabian Sea, with location of ODP and DSDP drilling sites. The 399 multibeam bathymetric coverage is draped over SRTM-PLUS topography (Becker et al., 2009). Inset 400 shows the regional tectonic setting of the India-Arabia plate boundary, and the position of the summer 401 Ma, the Owen Ridge and the Oman margin uplifted, inducing a better preservation of pelagic 457 foraminifera on their top. This event is coeval with general plate reorganization recognized overall the 458 Indian Ocean. The Makran Subduction Zone underwent a major structural reorganization during 459

Tortonian [START_REF] Mccall | The geotectonic history of the Makran and adjacent areas of southern Iran[END_REF], marked by olistostromes [START_REF] Burg | A giant catastrophic mud-and-debris 511 flow in the Miocene Makran[END_REF] and a geographic isolation of 460 paleontological species with regards to the area east of the Kirthar Ranges (Ellouz-Zimmerman et al., 461 2007). The precise location of the frontal thrust in Tortonian is currently unknown. Since 3-6 Ma, the 462 Miocene India-Arabia plate boundary jumped to the Owen Fracture Zone emplaced with large 463 stepover basins along strike. The Oman margin subsided down below the sea level. The Indus river is 464 at its present-day location since ~5-6 Ma (Clift and Blusztajn, 2005). 465

  indicates local uplift of the platform during the folding episode. At the location of the ODP Site 730, 152 the fold then subsided down below the sea level in early Pleistocene times, as indicated by the age of 153 the first overlying sediments (1.3 Ma). Thick chaotic bodies interpreted as Mass Transport Deposits 154 (MTD hereafter) on Fig. 3a and 4 are observed down the eastern flank of the fold, indicating sudden 155 slope over-steepening related to the formation of the fold. The youngest calcareous turbidites affected 156 by the deformation are ~8.8 Ma-old according to correlations with ODP Site 730. The fold is overlaid 157 by ~8.2 Ma-old sediments according to ODP Site 728

  implies a Late Miocene age of the unconformity 223 (~8 Ma), consistent with the MTDs drilled downslope at DSDP Site 223. A similar unconformity 224 sealed by 0.3s (TWT) of pelagic sediments is observed at the top of most of the bathymetric highs 225 buried by the Indus fan and sediments from the Oman margin in the Owen Basin (Fig. 5 c). These 226 observations suggest a regional tectonic deformation at the origin of the ~8 Ma-old unconformity and 227 the uplift of the central Owen Ridge. Age of uplift of the Owen Ridge and Late Miocene deformation in the Owen Basin 231

  Thick pelagic 242 layers (>100 m-thick) are common features of the Indus deep-sea fan (DSDP Site 222, Shipboard 243 Scientific Party, 1974; ODP Site 720, Shipboard Scientific Party, 1989), where the alternation of 244 turbidites within pelagic sequences is controlled by avulsion processes, and not by seafloor uplift. 245

  and its Miocene depth 246 is unknown, making it difficult to discriminate whether fluctuations in the conditions of microfossils 247 preservation throughout Unit 3 reflect the first stage of uplift of the Owen Ridge or oscillations in the 248 lysocline depth. Slight lateral thickness variations (~ 0.1 s (TWT)) of Unit 3 (10.4 to 14-15 Ma) may 249 indicate nearby tectonic activity (Fig. 3; 5a,b), but with no major topographic building during the 250 deposition of Unit 3. 251

Figure 2 :Figure 3 :Figure 4 :Figure 5 Figure 6 :

 23456 Figure 2 : Bathymetric maps of the central (a) and southern (b) portions of the Owen Basin, and 404

Figure 7 :Figure 8 :

 78 Figure 7 : Seismic profiles crossing the eastern side of the Central Owen Ridge. Profile a) shows an 447

  Figure1

Fig. 2a

  Fig.2a

  Figure2Southern Owen Ridge

2. Late Miocene deformation at the Southern Owen Ridge

Molnar, P., 2005. Mio-Pliocene Growth of the Tibetan Plateau and Evolution of East Asian Climate.

Palaeontologia Electronica 8, 1-23.

Acknowledgements

388


Gaëtan Leurent
email: gaetan.leurent@inria.fr

Tag Second-preimage Attack against π-cipher

The π-cipher is one of the candidates of the CAESAR competition. One of the advertised features of the π-cipher is tag second-preimage resistance: it should be hard to generate a message with a given tag, even for the legitimate key holder (insider attack). In this note, we show that the generalized birthday attack of Wagner gives a practical tag second-preimage attack against the π-cipher.

Introduction

The π-cipher [START_REF] Gligoroski | Submission to CAESAR[END_REF] is an authenticated encryption algorithm submitted to the CAESAR competition. One of the extra features advertised by the designers is tag secondpreimage resistance: it should be hard to produce second-preimages of a given tag, even for an adversary who knows the secret key (most authenticated encryption algorithm do not have this feature, and an insider can easily generate tag secondpreimages).

As written in [2, 4.1], the tag generation of an m-block message with the π-cipher can be written as:

T = T ′′ ⊞ 8 e(1, M 1 ) ⊞ 8 e(2, M 2 ) ⊞ 8 • • • ⊞ 8 e(m, M m )
where e denotes a keyed function known to the key holder (the e-triplex), ⊞ 8 is a component-wise addition of vectors of 8 elements in Z 2 ω , and T ′′ is the associated data tag (known to the insider). The word-size ω is 16, 32, or 64, depending on the security level. In a tag second-preimage attack, an insider wants to build a message M reaching a fixed tag T . Witout loss of generality, we assume T ′′ = 0 and T = 0.

In the submission document of π-cipher, the tag second-preimage problem is seen as a knapsack problem, and the main attack considered is a variant of an attack by Camion and Patarin [START_REF] Camion | The knapsack hash function proposed at crypto'89 can be broken[END_REF]. However, the generalization of this attack due to Wagner [START_REF] Wagner | A generalized birthday problem[END_REF] can break the problem more efficiently.

Wagner's Generalized Birthday Attack

The generalized birthday attack of Wagner is an attack against the m-sum problem: given m lists L 1 , L 2 , . . . , L m of n-bit words, one find values l 1 ∈ L 1 , . . . , l m ∈ L m such that m i=1 l m = 0. If each list contains at least 2 n/m elements there is a good probability that a solution exists, but the best known algorithm is a simple birthday attack in time and memory O(2 n/2 ). One would first build two lists L A and L B with all the sums of elements in L 1 , ...L m/2 and L m/2+1 , ...L m respectively, then sort L A and L B , and look for a match between the two lists (L A and L B contain 2 n/2 elements each).

Wagner's algorithm has a lower complexity, but it requires more elements in the lists. For instance, with m = 4, it uses lists of size 2 n/3 in order to find one solution using O(2 n/3 ) time and memory. The basic operation of the algorithm is the general join ⊲⊳ τ : L ⊲⊳ τ L ′ consists of all the elements of L × L ′ that agree on their τ least significant bits. More precisely, the operation can be defined over list of values with associated data:

L ⊲⊳ τ L ′ = l ⊕ l ′ , (a, a ′ ) (l, a) ∈ L, (l ′ , a ′ ) ∈ L ′ , low τ (l ⊕ l ′ ) = 0 .
The join operation is computed efficiently by sorting the lists L and L ′ according to the lower τ bits, and stepping through the lists simultaneously in order to find values that agree on their low bits. Moreover, the sorting can be done in linear time using a hash table, or a radix sort. The generalized birthday algorithm for m = 4 is described by Figure 1. We first build the lists L 12 = L 1 ⊲⊳ n/3 L 2 and L 34 = L 3 ⊲⊳ n/3 L 4 , containing about 2 n/3 elements. Next, we build L 1234 = L 12 ⊲⊳ 2n/3 L 34 . Since the elements of L 12 and L 34 already agree on their n/3 lower bits, we are only matching bits n/3 to 2n/3, so we still expect to find 2 n/3 elements. Finally, we expect one of the elements of L 1234 to be zero. This can be generalized to any m that is a power of two, using a binary tree: if m = 2 a , we need m lists of 2 n/(a+1) elements and the time and memory used by the algorithm is 2 a • r2 n/(a+1) . The algorithm for m = 8 is shown by Figure 2.

Application to the π-cipher

In order to apply this attack to the π-cipher, we need to solve the m-sum problem for the word-wise modular addition ⊞ 8 , instead of the exclusive-or ⊕. Wagner showed how to solve the generalized birthday problem with a modular addition, and his trick also works for the word-wise modular addition. More precisely, we have to modify the join operator to:

L ◮◭ τ L ′ = l ⊞ 8 l ′ , (a, a ′ ) (l, a) ∈ L, (l ′ , a ′ ) ∈ L ′ , low τ (l ⊞ 8 l ′ ) = 0 .
Since the word-wise modular addition ⊞ 8 only has carries from the low order bits to the high order bits, when x and y have their τ low-order bits set to zero, x ⊞ 8 y also has τ low-order bits set to zero. Moreover, the join ◮◭ can still be computed efficiently. We first negate the list L and define -L = {(-l, a) | (l, a) ∈ L}, where -l is the additive inverse with regard to the word-wise addition, i.e. l ⊞ 8 (-l) = 0. Then we sort -L and L ′ according to their lower τ bits, and step through the lists in parallel. When an element of -L and an element of L ′ agree on their low bit, the corresponding sum will have its low bits equal to zero. Therefore, this variant of Wagner's algorithm is suitable for a tag second-preimage attack on the π-cipher.

We give a full description of an attack with ω = 16 in Algorithm 1; this attack uses 8 lists of size 2 32 (illustrated by Figure 2), i.e. we consider an 8-block message, with 2 32 possibilities for each block. This gives a complexity of 2 35 . More generally, we can apply Wagner's attack to different versions of π-cipher (i.e. with different values of ω), and several trade-offs between the message length and the attack complexity are possible. We give some parameters in Table 1.

3 L34⊲⊳ n/ 3 L1234⊲⊳ 2n/ 3 4Fig. 1 .

 3331 Fig. 1. Wagner's algorithm for m = 4

Table 1 .

 1 Attack parameters

				Optimal parameters		Short messages
			ω	m	|L|	Complexity	m	|L|	Complexity
		16	2 11	2 11	2 22		2 3	2 32	2 35
		32	2 16	2 15	2 31		2 7	2 32	2 39
		64	2 22	2 23	2 45		2 15	2 32	2 47
	L1	L2	L3	L4	L5	L6	L7	L8	8 lists of 2 n/4 elements
		⊲⊳ n/4		⊲⊳ n/4		⊲⊳ n/4		⊲⊳ n/4
	L12			L34		L56			L78	4 lists of 2 n/4 elements with 2 n/4 zeros
		⊲⊳ 2n/4				⊲⊳ 2n/4
		L1234					L5678		2 lists of 2 n/4 elements with 2 2n/4 zeros
					⊲⊳ 3n/4
				L12345678					1 list of 2 n/4 elements with 2 3n/4 zeros
				Fig. 2. Wagner's algorithm for m = 8

Algorithm 1 Short message attack with ω = 16 and m = 8.

for all (l, (((a1, a2), (a3, a4)), ((a5, a6), (a7, a8))


J Belchior
email: jeremy.belchior@insa-rennes.fr

L Leotoing
email: lionel.leotoing@insa-rennes.fr

D Guines

E Courteille
email: eric.courteille@insa-rennes.fr

P Maurine

A Process/Machine coupling approach: application to Robotized Incremental Sheet Forming

Keywords: incremental sheet forming, FE simulation, robot machining, off-line compensation

In this paper, a Process/Machine coupling approach applied to Robotized Incremental Sheet Forming (RISF) is presented. This approach consists in coupling a Finite Element Analysis (FEA) of the process with an elastic modelling of the robot structure to improve the geometrical accuracy of the formed part. The FEA, assuming a rigid machine, is used to evaluate the forces at the interface between the tool and the sheet during the forming stage. These forces are used as input data for the elastic model, to predict and correct the tool path deviations. In order to make the tool path correction more effective, the weight of three numerical and material parameters of the FEA on the predicted forces is investigated. Finally, the proposed method is validated by the comparison of the numerical and experimental tool paths and geometries obtained with or without correction of the tool path.

Introduction

The Incremental Sheet Forming (ISF) is an innovative process for small series production and prototyping. The sheet is deformed locally by successive paths of a simple tool, usually a hemispherical punch. Complex shapes can be realized without dies which represents a significant cost benefit. In order to reduce manufacturing costs and improve production versatility, serial robots can be used for industrial processes like the ISF. For example, Meier et al. [2009a] have coupled two industrial robots to perform two point incremental forming. The first robot moves the forming tool in depth direction and along the contour path. The second robot drives a supporting tool to hold the sheet on the backside. For the same purpose [START_REF] Vihtonen | Comparing two robot assisted incremental forming methods: incremental forming by pressing and incremental hammering[END_REF] have used a serial robot and an appropriate clamping device. Nevertheless robot serial structure presents high compliances and a low absolute positioning accuracy. The process forces acting on the tool lead to robot structure deflection and then to tool path errors. To compensate the tool path errors induce by the machine (robot) and/or the process compliance different approaches are available in the literature. [START_REF] Bres | Simulation of robotic friction stir welding of aerospace components[END_REF] give a solution that consists in the dynamic elastic modelling of the machine or the robot structure in order to compensate by a linear or non linear feedback control the elastic deformations of the structure that degrade the TCP (Tool Center Point) pose accuracy. Outputs of such control consist in modifying the actuator torques. However [START_REF] Bigras | New formulation for an industrial robot force controller: Real-time implementation on a kuka robot[END_REF] have shown that its implementation is difficult in actual industrial robots where only the TCP pose is controlled. Moreover, the dynamic parameters (inertia, center of gravity, gear ratio) must be identified by dedicated methodologies such as proposed by [START_REF] Khalil | Modeling, Identification and Controls of Robots[END_REF] or de [START_REF] Canudas De Wit | Theory of Robot Control[END_REF].

For flexible processes as ISF a promising solution consists in using a robust closedloop control of the machine. For those processes, dedicated sensors as stereovision cameras, lasers, etc. can be involved to perform an on-line feedback control of the part geometry during the process. However the setup of the machine control parameters requires an appropriate and realistic process model that can be difficult to obtain. This can be done for example from a set of spatial impulse responses measured by linearization around a pre-planned tool path as explained by Allwood et al. [2009] and by [START_REF] Music | The use of spatial impulse responses to characterise flexible forming processes with mobile tools[END_REF]. As proposed by [START_REF] Rauch | Tool path programming optimization for incremental sheet forming applications[END_REF] it is also possible to use on-line measurements available directly on the machine itself (values of the encoders and/or torques) as a feedback to achieve a real time closed-loop control. To overcome the difficulties related to the previous approaches, one solution is based on realistic parametric models of machines and robots to predict the elastic deformations. The methodologies proposed in the literature are based either on lumped-parameter model in [START_REF] Dumas | Joint stiffness identification of six-revolute industrial serial robots[END_REF] or more realistic Finite Element models as in [START_REF] Marie | Elasto-geometrical modelling of closed-loop industrial robots used for machining applications[END_REF]. Since outputs of these models are TCP pose errors, the term elasto-geometrical model is used. As a result, a correction of the tool path deviations is possible and can be easily implemented in the native programming language of the controller (real-time or off-line programming).

With this second approach, the knowledge of the forces acting on the TCP is essential. Several studies, such as [START_REF] Ambrogio | Some considerations on force trends in incremental forming of different materials[END_REF], [START_REF] Jeswiet | Forces in single point and two point incremental forming[END_REF], [START_REF] Petek | Forces and deformations analysis of in-cremental sheet metal forming[END_REF], have analysed the influence of experimental setup parameters on the prediction of the forming forces. Duflou et al. [2007a] proposed a force prediction model applied during the forming of a cone as a function of the step-down amplitude, the wall angle, the tool diameter and the sheet thickness. This model, based on a simple regression equation, could predict the peak, steady-state and in-plane forces with a high degree of confidence. Nevertheless this analytical model is only valid for simple geometries.

For more complex geometries, [START_REF] Aerens | Force prediction for single point incremental forming deduced from experimental and fem observations[END_REF] involve the previous model. A strategy, based on experimental measurements, is proposed to identify the model parameters. Several materials were tested. For each material, an analytical formula able to predict level of the steady-state tool force is fitted for various parts. The ultimate tensile strength of the considered material seems to govern the level of the steady-state force. Due to the complex tool path in the ISF process, the most common way to estimate these forces is based on a FEA of the process. [START_REF] Meier | A model based approach to increase the part accuracy in robot based incremental sheet metal forming[END_REF] have proposed a model-based approach in which a MBS (Multi Body System) model of the robot is coupled with a FEA of an ISF operation. In the MBS model, the links are assumed rigid and the elastic behavior of the robot structure is described considering only the joint stiffness. In fact this coupling approach has not been really carried out since measured forces during a first run without any compensation have been defined as the input data of the robot model instead of using the predicted forces calculated with FEA model.

To avoid errors due to possible inaccuracies in the force prediction from analytical or numerical models, [START_REF] Verbert | Obtainable accuracies and compensation strategies for robot supported spif[END_REF] have chosen the same strategy. As explained by the authors, the main drawback of this procedure is that the forming of a dummy part is required. The hypotheses used in the FEA of the process made by Meier et al. [2009b] can explain the inaccuracies of the numerical model and finally the choice of this strategy. With these hypotheses the simulated forces through the forming of a straight groove present a maximum overestimation of 30% compared to the measured ones. This result underlines the difficulty to accurately compute the forces induced by the process.

The FEA of the ISF operation is commonly applied to predict the final geometry of the part. Most studies on the simulation of the ISF like the one from [START_REF] Ambrogio | Influence of some relevant process parameters on the dimensional accuracy in incremental forming : a numerical and experimental investigation[END_REF] are based on the same hypotheses: thin shell elements, frictionless conditions between the tool and the sheet, rigid tool, hardening power law, encastre boundary conditions for the clamping system... These models are usually effective to predict the final shape but when results of force prediction are presented, they are systematically overestimated. In the literature, this overestimation is usually justified by three main factors described below:

• The first one concerns the deformation mechanisms during the process which are not well identified. [START_REF] Eyckens | MK Modelling of sheet formability in the incremental sheet forming process, taking intoaccount through-thickness shear[END_REF] have shown that Through-Thickness Shear (TTS) appears by measuring small deformed holes in cone wall angles. [START_REF] Emmens | An overview of stabilizing deformation mechanisms in incremental sheet forming[END_REF] have demonstrated that this shear can delay the onset of necking and may explain the high levels of deformation in ISF (strain levels of about 70%-120% can be reached). [START_REF] Allwood | The increased forming limits of incremental sheet forming processes[END_REF] demonstrate, in a simplified version of incremental forming, that the throughthickness shear is significant in the direction of the tool movement. In [START_REF] Allwood | Generalised forming limit diagrams showing increased forming limits with non-planar stress states[END_REF], TTS is incorporated into Marciniak-Kuczynski model and it is shown that the forming limit curve increases with increasing TTS. [START_REF] Henrard | Forming forces in sin-gle point incremental forming: prediction by finite element simulations, validation and sensivity[END_REF] have recently studied the ability of FEA to predict the correct tool force during a Single Point Incremental Forming (SPIF) operation. The forming of two frustum cones with different wall angles (20°and 60°) has been simulated to compare the effects of various numerical and material parameters. TTS can be neglected for the 20°cone, while it is significant for the 60°cone. Two different types of element were chosen for the simulation of each geometry: shell elements neglecting TTS, and brick elements modelling TTS. For the 60°cone, the error between the experimental and simulated values is reduced from 40% to 20% when the TTS is considered with the brick elements.

• The second factor which can influence the level of the simulated forming forces is the modelling of the plastic behavior of the sheet material. The calibration of the hardening law is one of the most influent on the force level. Indeed hardening laws are typically identified from tensile test until a level of strain which is about 20% whereas the level of strain reached during the process can be 2 or 3 times greater. In [START_REF] Flores | Model identification and fe simulations: Effect of different yield loci and hardening laws in sheet forming[END_REF], a strong discrepancy between the simulation force prediction based on an elastic-plastic law with isotropic or kinematic hardening model is observed. For a AA3003-O, a decrease of 20% of the predicted forces is observed when kinematic hardening is introduced in the FE simulation of a frustum cone with a wall angle of 50°. But recently, [START_REF] Henrard | Forming forces in sin-gle point incremental forming: prediction by finite element simulations, validation and sensivity[END_REF] have also compared the influence of several plastic behavior (Swift and Voce hardening laws, isotropic or kinematic hardening models, isotropic von Mises and the anisotropic Hill yield criteria) on the force prediction. The forming material is also an aluminium alloy (AA3003-O). It is shown that, for this material and for important wall angle (60°) cone, leading to accumulated equivalent engineering strain of about 200%, the choice of isotropic or anisotropic yield locus is negligible. Moreover, an isotropic saturating law such as Voce's seems the most suitable hardening behavior. A difference of about 20% on the axial force is observed between the Voce and Swift hardening laws. An other conclusion of this study, is that the kinematic hardening behavior appears to have only a little effect on the force prediction for this material. As one can see it, this point remains debatable but for the 5086 aluminum alloy considered in this study, the hardening is mainly isotropic and the contribution of the kinematic hardening is low and will be neglected in this study.

• Finally the boundary conditions applied to the simulation (modelling of the clamping system) can also lead to an artificial stiffening of the model as it has been remarked by [START_REF] Bouffioux | Development of an inverse method for identification of materials parameters in the single point incremental forming process[END_REF]. To avoid the force overestimation due to encastre boundary conditions, the clamping system has been modeled by springs distributed along the sheet edges. The nodes of the edges are fixed in rotation and in translation following the axial tool direction while the displacements in the sheet plan are possible and depend on the stiffness springs. To correlate with experimental force values, a unique spring stiffness has been computed using an inverse method based on an indentation test.

With the aim to reduce the process time and to propose a simplified method, an offline compensation procedure based on an elastic modelling of the machine structure coupled with a FEA of the process, is proposed in this work. The SPIF procedure and the process parameters are firstly described. An experimental investigation studies the robot ability during the forming of a frustum cone by comparing the experimental results from a three axis milling machine and the robot. Due to the high stiffness of its structure, the measured forces on the milling machine are defined as a reference.

Then, a FE model of the process is proposed and the force prediction of this model is numerically investigated. Finally, the predicted force is used as an input data of the robot elastic model in order to compute tool path correction of the robot. The effectiveness of the proposed method is verified by comparing the nominal and the measured tool path. This approach is finally validated on a non-symmetrical geometry: a twisted pyramid.

Process description

Part and tools

The part consists of a frustum cone of 45°wall angle centered on a sheet of 200 × 200×1 mm 3 (Figure 1). The depth of the frustum cone is 40 mm. The chosen material is an 5086 H111 aluminum alloy. The forming tool is a hemispherical punch with a 15 mm diameter. The feed rate value of the tool is 2 m/min and the tool rotation is locked. Grease is not an ideal lubricant but it has been used to reduce the friction coefficient between the sheet and the tool. The clamping system is composed of a blank holder screwed on a rigid frame (Figure 2).

Process parameters

The incremental step direction is along z p (Figure 3). The trajectory consists of successive circular tool paths at constant z p . The incremental step size value (∆ Z ) is 1 mm per loop. Different strategies to perform a frustum cone in SPIF are available in the literature (multi-pass, begin the forming at the center of the sheet...) and their application leads to different results in term of geometrical accuracy. However, our first objective is to correct the errors due to the low stiffness of serial robots. These errors will appear whatever the forming strategy. In consequence, a classical strategy has been chosen for the study in order to build a generic method applicable for all the forming strategies.

Measurement systems

The forces acting on the tool are measured using a six-component force cell (ATI Omega 190). The three orthogonal components of the forming force F x , F y , F z (see This system has a pose measuring accuracy of ± 37 µm for a single point. After the forming process the part geometry is measured by a coordinate-measuring machine (CMM). The tactile measurement of the machine presents an accuracy of ± 3.5 µm for a single point.

Forming machines

In order to evaluate the ability of an industrial serial robot (Fanuc S420iF) to form a part with ISF process, a comparison of the experimental results obtained from a three axis milling machine (Famup MCX500) and the robot is made. The milling machine is a three axis cartesian structure. It can develop up to 7000 N at the extremity of the tool with a precision of ± 15 µm. Due to the high stiffness of the cartesian structure of the milling machine, the errors on the tool path induced by the elastic deformations of the machine can be neglected. Consequently, the experimental results obtained with this machine will be considered as the reference. The robot has a payload capacity of 1200 N . Its kinematic closed loop increases the global stiffness of the structure.

Its maximum accuracy error with a load of 650 N applied on the TCP is about 3.2 mm. The clamping system is fixed on a rigid table near the robot base to maximize the stiffness of the robot during the process (Figure 4).

To show the weight of the robot stiffness on the forming force, the static equilibrium of the tool, during the process, is presented. Because feed rates are closed to 1 m/mn

F S/R = K S .(P R -P 0 ) (1) F R/S = K R .(P R -P T ) (2)
Where: ,xp,yp,zp) is the initial pose of the contact point between the tool and the sheet (Figure 5).

• P 0 = [P 0x ,P 0y ,P 0z ,R 0x ,R 0y ,R 0z ] T (Op
• P R is the pose actually reached by the TCP without correction.

• P T is the targeted pose.

• K S is the stiffness matrix (6 × 6) of the sheet and clamping device which depends on the position and the type of the clamping system, and on the sheet material and process parameters.

• K R is the stiffness matrix (6 × 6) of the robot structure, which depends on the joint configuration of the robot and on its geometrical and mechanical parameters (joint stiffness, quadratic moments of links,...).

The static equilibrium, at the contact point between the tool and the sheet, gives: It means that the lowest stiffness between K R and K S will have the major impact on the forming force F S/R and finally on P R .

F S/R = K S .K R K S + K R .(P 0 -P T ) (3

Results

The measured force along the tool axis for both the milling machine and the robot is

FE simulation: Improvement of the force prediction

To limit the path error through a coupling approach, a precise force prediction is required. In the literature, the main factors identified like the most important in the forming force prediction by FE simulation are: (i) the choice of the element type, (ii) the consideration of the through thickness shear, (iii) the plastic behavior model of the tested material and finally (iv) the modeling of the boundary conditions applied to the sheet. These different key parameters have been clearly identified in particular in two complete studies on this subject [START_REF] Henrard | Forming forces in sin-gle point incremental forming: prediction by finite element simulations, validation and sensivity[END_REF], [START_REF] Bouffioux | Development of an inverse method for identification of materials parameters in the single point incremental forming process[END_REF].

In sections 3.1 to 3.4, the parameters listed above are presented and discussed and their influence on the force prediction is evaluated through three different FE models numerically investigated in section 3.5.

Model description

All the numerical simulations are done with the ABAQUS © software using an implicit formulation. A 45°pie model is chosen to minimize the computation time (Figure 9). This approach has been first described by [START_REF] Henrard | Forming forces in sin-gle point incremental forming: prediction by finite element simulations, validation and sensivity[END_REF] and it has been shown that the results of a whole blank and a 45°pie models are very close. In particular, the axial force F z computed by the partial model is generally lower than the one calculated with the full model but the difference doesn't exceed 10 %. Symmetry boundary conditions are applied on the 0°and 45°sections. The tool path of the 45°pie model is computed with a CAD software (Figure 10). The starting points of each incremental step are defined on the same side. The same z level strategy as the one previously described in section 2.2 is applied.

Element type and mesh

The meshing size is smaller at the contact point between the tool and the sheet over the trajectory. Two types of elements are compared (S4R and C3D8I). The S4R element is a 4-node, quadrilateral, stress/displacement shell element with reduced integration and a large-strain formulation. It is particularly dedicated for stamping processes of thin shells and allows reduction of the computation time. The C3D8I element Sheet Boundaries of the 45° pie model

Tool

Shell elements

Brick elements

Figure 11: Description of the mix model

Boundary conditions

In the literature the clamping system is usually modeled as an encastre boundary condition. However sliding between the sheet and the clamping system can appear and reduce the predicted force level. To quantify the clamping system modelling two types of boundary conditions are investigated. The first one consists in defining encastre boundary condition on the four edges of sheet in contact with the clamping system.

For the second case the clamping system is modeled by pressure areas applied on the contact zone between the sheet and the blank holder (Figure 12). The pressure (4.3 M P a) applied on each tightening areas, is estimated from the experimental torque applied on each screw (20 N m) and measured by means of a torque wrench. The contact between the frame and the sheet is modeled with a friction coef-ficient of 0.05.

Material behavior

Based on previous works of [START_REF] Zhang | Experimental and numerical study on effect of forming rate on AA5086 sheet formability[END_REF], an elasto-plastic model with an isotropic von Mises yield criterion is used to describe the behavior of the 5086 H111 aluminum alloy. It has been shown previously that this material exhibits a quasiisotropic plane behavior and a low transversal thickness anisotropy. The elastic behavior of the material is defined by the Young modulus E=66 GP a and the Poisson's ratio ν=0.3.

Two different hardening laws are implemented on the model. First a Ludwick law is chosen:

σ = σ e + K 1 .ε p n ( 4
)
where σ is the equivalent stress, σ e the initial yield stress (σ e = 125.88 M P a), ε p is the equivalent plastic strain, K 1 = 447.08 M P a, n = 0.413.

Secondly a Voce law described by [START_REF] Diot | Forming Process of a 5083 Aluminium Alloy. Constitutive Model Covering a Large Range of Temperature[END_REF] to model saturation or softening effects of aluminum alloys is applied. The formulation is given by:

σ = σ e + K 2 . 1 -e (-B.εp) (5)
with σ e = 130.2 MPa, K 2 = 330.37 MPa, B = 3.94.

The constants of the two hardening laws defined above are determined from the experimental stress/strain curve of a tensile test made in the rolling direction. This experimental curve and the identified laws are presented in Figure 13.

Due to the high level of deformation reached in the process, the hardening law must be chosen carefully. Figure 13 shows the strain range reached in ISF (up to 120%) in comparison with the strain level reached in the uni-axial tensile test (about 20%). For high levels of deformation, it is difficult to identify accurately the hardening behavior with only a database from a uni-axial tensile test. The choice of the Voce law leads to a constant stress for strain higher than 60%. On the contrary the Ludwick law presents a stiffer behavior for large strains.

Models

Finally, to quantify the influence of each parameter discussed above on the force prediction three different modelling configurations are proposed. The table 1 sums up the different assumptions for each model. Model 0 is built with the same hypotheses of the literature. Model 1 uses brick elements to model accurately the through thickness shear. Model 2 represents a more realistic clamping system with pressure areas applied on the contact zone between the sheet and the blank holder. Based on Model 2, the weight of the hardening law (Ludwick or Voce) is evaluated. For each model, the predicted force along the tool axis is compared with the experimental force value from the milling machine. This value is defined as the reference since the milling machine is assumed to be perfectly rigid.

The mean force at each loop of the trajectory is computed when the TCP crosses the middle axis of the 45°pie model.

Influence of TTS

The importance of TTS on the force prediction is evaluated through the comparison of results from Model 0 and Model 1. It is verified that the force reaches a maximum steady state value according to the work of Duflou et al. [2007b]. The Figure 14 shows that the choice of thin shell elements does not give a good agreement between experimental and predicted force. A maximum difference between Model 0 and experiments of approximately 750 N is identified which represents 40% of the final value. The predictions of Model 1 give better results. With TTS consideration the improvement of the force prediction is about 30%. For that purpose, brick elements have to be considered. Nevertheless the prediction of the final geometry of the part is very close for both elements (Figure 15).

Influence of boundary conditions

To measure the effect of the boundary conditions, results of Model 1 and Model 2 are compared. The Figure 16 shows a comparison between the simulated forces from the two different boundary conditions. As expected, the more realistic model with the pressure (Model 2) gives a predicted force level lower than Model 1 and closer to the experiments. This modelling improves the force prediction of 55% compared to the Model 1. However, before a value of 20 mm for ∆ Z the predicted forces is lower than the measured one. This difference is linked with a slight sliding during the simulation.

Conclusion

From FE investigations presented above, an accurate estimation of both the force magnitude along the tool axis F z and the xy-plane force F xy has been obtained. This force prediction could be used before performing the coupling approach instead of a force estimation obtained from an analytical model or a first test run made on a stiff machine. The calculation time is about 1 hour for the first model and 6 hours for the last one (Simulation was made using a computer with a 2.33Ghz CPU -16GB of Ram). If we compare the time and the cost needed to perform the test on a milling machine this strategy can be a good alternative. This method offers also the possibility to be easily included on an optimization loop to improve the forming strategy in order to enhance the geometrical accuracy of the process. Obviously the time calculation increases when a more complex part which cannot be represented by a symmetrical model is studied but [START_REF] Giraud-Moreau | Comparison between an advanced numerical simulation of sheet incremental forming using adaptive remeshing and experimental results[END_REF] have shown that remeshing techniques could be an interesting alternative to reduce the computational times. One must be noted that a comparable degree of confidence between experimental and predicted forces has been observed previously by Henrard et al. on a different aluminium alloy.

Elastic model of the robot

The elastic modelling of the robot is performed using the analytical method proposed by [START_REF] Deblaise | A systematic analytical method for pkm stiffness matrix calculation[END_REF]. This modelling has been already described in the RISF context by [START_REF] Belchior | Offline compensation of the tool path deviations on robotic machining: Application to incremental sheet forming[END_REF]. It consists in describing the elastic behavior of the robot as a unique elastic beam. The resulting analytical model can be written by:

0 ∆ R = 0 K R -1 0 F R/S (6)
0 ∆ R , 0 F R/S and 0 K R are expressed within the robot base frame (O 0 , x 0 , y 0 , z 0 ).

0 F R/S is a 6 × 1 vector 0 [F x F y F z M x M y M z ]
which represents the equivalent wrench acting at the TCP. The components F x , F y and F z are computed by the FE simulation (cf. section 3.8) and M x =M y =M z =0 because the TCP corresponds to the forming tool tip and a point contact with the sheet is assumed. 0 ∆ R stands for the elastic displacements and 0 K R is the equivalent 6 × 6 stiffness matrix that describes the whole elastic behavior of the robot structure. As explained in [START_REF] Belchior | Offline compensation of the tool path deviations on robotic machining: Application to incremental sheet forming[END_REF] for each pose of the tool path the joint variables of the robot are computed with its inverse geometrical model and their values are then used to calculate the components of 0 K R .

To identify the stiffness parameters of the FANUC S420iF structure within the workspace corresponding to the forming application, a set of 150 TCP poses have been generated. A complete characterization of the robot has been obtained by stressing all its joints by means of a cable-pulley device used to generate forces at the end-effector along all axis of the reference frame R 0 . The magnitude of the loads applied during this

0 E p R = 0 ∆P c,p R -0 ∆P m,p R (7)
The joint stiffness values gathered in the vector Γ are identified by minimizing, for a set of n p poses and loads, the following function:

C (Γ) = np i=1 ( 0 E p R ) 2 (8)
For the forming of the frustum cone previously described the mean computed values of three main components of K R are K xx = 937 N/mm, K yy = 597 N/mm and K zz = 898 N/mm. During the forming trajectory, the variation of these ones are respectively ±1.1%, ±2.3% and ±3.2%. If the stiffness of the robot is kept constant during the process, these fluctuations can represent at the end of the trajectory a variation of the predicted displacement of ± 0.2 mm. Obviously these variations will increase for larger parts which shows the necessity to compute K R at each point of the robot tool path.

The identified elastic model allows to predict the TCP displacements induced by elastic behavior of the robot structure over the workspace whatever the load applied on the tool. The prediction maximum and mean errors respectively of ±0.3 mm and ±0.15 mm remain compatible with the process requirements.

Coupling approach Process/Machine

This approach consists in coupling the FEA of the forming process and the elastic modelling of the robot. To perform this approach a post-processor is adopted (Figure 20) according to the approach described by [START_REF] Meier | A model based approach to increase the part accuracy in robot based incremental sheet metal forming[END_REF]. Using the assumption of a quasi static process, only the elastic behavior of the mechanical structure is considered. Measurements of the TCP elastic displacements have been conducted with the controller on and off (actuators blocked) and have shown exactly the same elastic behavior of the robot. As a result, it has been assumed that the robot controller does not compensate the elastic displacements and do not have to be integrated in the elastic model. The needed data are the process and material parameters and the values of the robot stiffness matrix. The approach is a total off-line method without feedback loop. The absolute errors between the nominal and measured tool paths before and after correction, in the plane (O p , x p , y p ), are depicted in Figure 21. As one can see:

• Without correction: a significant TCP deviation can be noticed. The maximum value of the error norm is about 7 mm at the end of the trajectory and the mean value is about 3.1 mm. The error is not uniformly distributed along the path because of the direction of the resulting forces. When the force direction is mainly along x p it produces resulting torques on robot joints.

• With correction: The maximum value of the error norm is about 0.9 mm and the mean value is about 0.5 mm. The final TCP error that can be observed after the tool path compensation is mainly induced by the residual identification errors due to the elastic calibration. However, the TCP pose accuracy can be improved about 85% during the forming of this part. For the final shape, the difference along the cut axis obtained respectively with the milling machine and the robot is less than 1 mm when a correction is applied against approximately 4 mm without correction (Figure 22). The shape of the frustum cone made by the robot shows an inward bulging of the unprocessed bottom central area with or without compensated path (Figure 22) whereas this phenomenon is not observed for milling machine made parts (Figure 7). As explained in [START_REF] Belchior | Offline compensation of the tool path deviations on robotic machining: Application to incremental sheet forming[END_REF], this effect is due to the non-symmetrical behavior of the robot during a loop of the tool path. Because the correction is not exactly the same for the points close to the x p axis and for the ones close to the y p axis, it causes this geometrical error. Despite this, these experimental results show the method relevance.

Twisted pyramid

By using the same procedure, a twisted pyramid is formed with the same aluminum alloy sheet. Its non-symetrical geometry will confirm the robustness of both the process FE analysis and the elastic calibration of the FANUC robot (Figure 23). The tool path • With correction: the pose accuracy is considerably improved. The maximum value of the error norm is about 1 mm and the mean value is about 0.6 mm. The effect of the inclination of each face of the pyramid is well compensated thanks to the good prediction of the FE forming forces (Figure 26) and to the realistic identification of the elastic behavior of the FANUC robot structure. The final TCP error after the tool path compensation is mainly induced by the residual identification errors after the elastic calibration. They introduce a difference between the predicted and measured forces which grows up with the incremental step size value (Figure 26). For more readability the presented forces are given as an average per loop. Nevertheless, the reduction of the TCP pose error compared to the milling machine results is about 80% during the forming of this part.

General conclusion

In this paper a correlation between numerical and experimental forces of a SPIF operation was performed. The prediction accuracy of the force needed to form a classical frustum cone was improved with the study of three influent parameters: finite element type, boundary conditions and hardening law. With Model 1, brick elements have been used to model accurately the TTS. An improvement of 30% of the force prediction has been obtained compared to the Model 0 built with the classical hypotheses of the literature. With Model 2, a more realistic clamping system with pressure areas applied on the contact zone between the sheet and the blank holder has been defined. This modelling has increased the accuracy of the force prediction of 55% compared to Model 1. Based on Model 2, the influence of the hardening law (Ludwick or Voce) has been evaluated. A better correlation with experiments has been obtained using the Voce law instead of the Ludwick law. Using the more realistic FE modelling to compute forces, the coupling approach Machine/Process was applied to correct the tool path errors of RISF operations. The frustum cone and a non-symmetrical part (a twisted pyramid) were formed with this methodology. The experimental results show the method relevance since the errors due to the unstiffness of the serial robot for the both formed parts have been reduced with approximately 80%.

  Figure 1: Shape of the frustum cone (45°wall angle)

Figure 3 :

 3 Figure 3: Target tool path -successive circular paths -∆ Z =1 mm

Figure 4 :

 4 Figure 4: Fanuc robot S420iF with the experimental set-up

Figure 5 :

 5 Figure 5: Schematic view of the forming configuration

shown Figure 6 .Figure 6 :

 66 Figure 6: Comparison of the measured force in function of the theoretical depth of the cone (∆z).

Figure 7 :Figure 8 :

 78 Figure 7: Comparison of the final shape along the cut axis

FigureFigure 10 :

 10 Figure 9: Description of the 45°pie model

  and modelling of the clamping system

Figure 13 :

 13 Figure 13: Hardening laws implemented in the simulation

Figure 14 :

 14 Figure 14: Effect of the finite element type on the force

Figure 15 :Figure 16 :Figure 17 :Figure 18 :

 15161718 Figure 15: Effect of the finite element type on the final geometry prediction

Figure 19 :

 19 Figure 19: FANUC S420iF modelling

Figure 20 :

 20 Figure 20: Post-processor scheme

Figure 21 :

 21 Figure 21: Norm of the error measured between the nominal and tool paths during the forming of the frustum cone (a) without correction and (b) with correction

Figure 22 :Figure 23 :Figure 24 :

 222324 Figure 22: Measurement of the final shapes along the cut axis

Figure 25 :

 25 Figure 25: Norm of the error measured between the target and tool paths during the forming of the twisted pyramid (a) without correction and (b) with correction

Figure 26 :

 26 Figure 26: Measured and predicted forces (Fz) on the twisted pyramid

Table 1 :

 1 Description of the compared models

		Elements	Boundary conditions	Hardening laws
	Model 0	Shell	Encastre	Ludwick
	Model 1	Brick + Shell	Encastre	Ludwick
	Model 2	Brick + Shell	Realistic	Ludwick or Voce


Denis Miclet

Emmanuel Piron

Soil compaction: track induced soil stress isn't so positive in comparison with tyre

This study concludes that, from the soil compaction point of view, using tracks does not confer an advantage, because of irregular contact pressure induced by the roller presence and the overall higher load of the track system. Conversely, tyres distribute uniformly the load on all the contact area and induce overall less stress on the soil.

Introduction

As agricultural machines sizes and weights are always greater, rubber tracks are often presented as an alternative equipment to maximise the power transmission to the soil, but also to reduce the stress applied on soils. Considering the easy to obtain contact area surface of the track -or tyre-with the soil, the interface pressure is supposed to be less important for tracks than for tyres. However, this study shows that the reality is different, as true as there aren't a lot of studies in the literature.

The objective of this study was to measure the stress induced by tracks and tyres on the soil, when a combine harvester is used. The contact pressure with a hard soil is investigated, as well as the increased hardness of an agricultural soil. Protocol used is first explained, before giving major results of the study.

Used protocol

The same combine harvester has been used alternatively equipped with tyres and tracks, and stress induced at the soil interface was evaluated on two different soil types: hard soilas it could be on a road for example during transport-and agricultural soil -as it is the case during the harvester works in the field.

Stress induced on a hard soil

In order to evaluate the contact pressure at a hard soil interface, the linear force along the contact area has been measured, considering the force distribution along the transverse direction was uniform. A great weighing system, equipped with electronic load cells allowing 50 grams of precision, has been used. During a slow displacement -measured using a laser telemeter-of the harvester from its initial horizontal place to the weighing horizontal device, the force and position values were recorded using a 100 Hz frequency rate. Ten successive measurements were repeated allowing a mean value calculation of the interface pressure. Perpendicularly to the combine harvester following parallel runs, a soil hardness resistance measurement has been performed using a specific Irstea device. Displaced into the field, this device allows measuring the hardness force opposed to each of three different steel blades cutting the soil at three depths (10, 20 and 30 cm). Values were registered using 100 Hz frequency.

Both of these field operations were geo-localized using a dGPS allowing a very precise spotting of 1 cm. Three different modalities were investigated, using a combine harvester with a total weight of 28 tons: 900/60 R38 Michelin tyre successively inflated with 2,2 and 1,4 bar, and a 3 roller track. Rear tyres inflation was 1.4 bar.

Globally, 100 repetitions for each of the 3 tested modalities were performed, using the random distribution in the field.

Results and discussion

Stress induced on a hard soil

The registered values are computed with the dimensional information of the tyres and tracks.

The graph (cf. fig. 4) represents the contact pressure with the soil for the 3 different modalities. This graph demonstrates that a tyre, with its air inflation, distributes more uniformly the stress under the whole contact area. The soil stress decreases when inflation decreases, due to the tyre deformation which can be seen by a longer contact zone on the graph. Contact pressure peaks are respectively around 5,7 and 4,3 bar for 2,2 and 1,4 bar tyre inflations.

At the opposite, soil pressure contacts for the track system are not uniformly distributed at all.

3 pressure peaks can be seen, which are located exactly at the vertical position of the track rollers. The contact pressure peak is around 9 bar, which is twice the pressure measured for the tyre inflated with 1,4 bar. It also demonstrates that the contact interface with the soil isn't the commonly used value simply obtained by multiplication between length and width of the track.

Stress induced on agricultural soil

As a precise dGPS was used to geo-localize the following steps of the experiment, the soil compaction induced by the combine harvester successive runs have been computed and added together in order to obtain the soil hardness distribution transversely, and along 7 metre distributed on each part of the centre of run (cf. fig. 5). The scattering hardness is represented in daN along the 7 meter. It allows calculating, for each modality, 3 witness values of the soil hardness (not impacted by the vehicle runs) and 2 packed area (one for each of the right and left tyre). As 100 similar distributions are measured for each of the 3 modalities, the standard deviations for these different mean values have been calculated.

The ratio between the mean hardness in the packed area and in the witness area represent the modality impact on the soil (cf. fig. 6). Even if a lot of repetitions have been performed in order to minimise the random soil and experiment effects, standard deviation are very important (see the error bar on the fig. 6). As a consequency, the obtained visible differences between modalities mean values were not significant. Consequently, the impact of the track wasn't observed as so interesting regarding the hardness modification impact on the soil, as it's commonly expressed.

Conclusion / perspectives

This study demonstrates that the tracks systems are not better than tires in terms of compaction. On hard soil like a road for example, the differences between tires and tracks are the more significant. Indeed, for tracks, the efforts of the vehicle are only transmitted to the ground by rollers unlike tires which distribute the stress more uniformly on the contact area. The contact pressure peaks for tracks can be twice the pressure measured for tyres in these conditions. On agricultural soil, no significant difference has been measured between the tires and the tracks though a visual constant tendency show a slight benefit for the tires on the soil compaction.

Next step is to measure more accurately the distribution efforts of the machine on agricultural soil and better understand what really happens. The goal of this study is to limit the variability we meet for measures on agricultural soil and help to conclude for the benefit of one system over the other in terms of compaction.

Fig. 1 :

 1 Fig. 1: Measurement schema for hard soil interface pressure evaluation.

Fig. 2 :

 2 Fig. 2: Field organisation of the agricultural compaction evaluation following combine harvester work.

Fig. 3 :

 3 Fig. 3: Scattering device used to measure the soil hardness everywhere in the field.

Fig. 4 :

 4 Fig. 4: Soil contact pressure distribution obtained for the 3 different modalities on hard soil. Data are given in bar using an uniform pressure distribution along the transverse axis. The abscisse 0 is the vertical position for the harvester front axle.

Fig. 5 :Fig. 6 :

 56 Fig. 5: Soil hardness mean values measured transversely to the harvester runs. The graph represents 7m measurement.