Nicolas Arnaud

Paul Tapponnier

Roger Françoise

Maurice Brunel

Urs Schärer

Wen Chen

Xu Zhiqin

Evidence for Mesozoic shear along the western Kunlun and Altyn-Tagh fault, northern

come

Evidence for Mesozoic shear along the western Kunlun and Altyn-Tagh fault, northern Tibet (China).

N. Arnaud 1 , P. Tapponnier 2 , F. Roger 3 , M. Brunel 4 , U. Scharer 3 , Chen Wen 5 , and Xu Zhiqin 5 .

Large active faults of Northern Tibet may have accommodated a significant part of the deformation due to collision between India and Asia. The kinematics and magnitude of Cenozoic displacements along these faults have been the focus of abundant research [Tapponnier and Molnar, 1977, Peltzer and Tapponnier, 1988, Avouac and Tapponnier, 1993, Peltzer et al., 1988, Molnar and Kidd, 1988, Meyer et al., 1996, 1998, Van der Woerd et al., 1998], but these study have essentially not addressed the problem of pre-Cenozoic activity of these faults. Due to a lack of geological and reliable geochronological data, very little is known about the structural history of these faults prior to 30 Ma. Such a knowledge, however, is essential to reconstruct the geodynamic evolution of the Asian continent in Phanerozoic times as well as the Tertiary finite displacements induced by the India-Asia collision using older piercing points.

Here we present geochronological data along two segments of the Altyn-Tagh and Kunlun faults system, near 75° and 100°E respectively. We first briefly summarize the geology of the two regions sampled, then the ages and cooling histories both on a local scale and on a broader scale to document the existence of Mesozoic movement along both faults and the possible Tertiary offset of the metamorphic rocks on the Altyn-Tagh fault.

I/ Present geological setting.

Sampling area are located (figure 1) roughly parallel to the structural limits of the northern topographical limit of the Tibet Plateau. In the east, we sampled metamorphic rocks along the Kunlun fault south of Golmud over a distance of roughly 100 km. A geological description of the Golmud section is given in The geological evolution of Tibet, Phil. by the Royal Society of London (1998).

In the west we sampled metamorphic rocks along the Karakax valley, over a distance of c.a. 100 km following the south flank of the Kunlun mountains south of Yecheng. A geological and geochronological description is given in Matte et al. [1996] and Mattern et al. [1996].

1-The Kunlun fault in eastern Kunlun.

South of Naji Tal within the eastern Kunlun (figure 2), a step-over between overlapping segments of the Kunlun fault created the impressive Xidatan-Dongdatan pull-apart trough [ Van der Woerd et al., 1998]. North of this trough, Permian to Jurassic flysch and coal shales are intruded by calkalkaline granites and associated rhyolites. The granitic bodies just north of the fault appear to be largely of Triassic age [Harris et al., 1988, Mock et al., 1998]. South of the fault, the geology is dominated by the steep isoclinally folded slates and phyllites of the triassic series of Bayan Har terranes, the western equivalent to the famous Songpan Garze flysch sequence on Qiantang block. In the Xidatan valley, the fault bounds the southern flank of the Kunlun range and limits the Kusar Hu Neogene basin. It is marked by steep triangular facets indicating a normal component of throw. A belt of pegmatites, mylonites of granite and leucogranite, garnet schist phyllonites of various sedimentary origins, up to one kilometer wide, is intermittently exposed along the northern footwall of the Kunlun flank. The rocks show steep N100-110 striking schistosity planes roughly parallel to the fault, with horizontal lineations and clear sinistral shear indicators (figure 3). A petrographic study of the ductile deformation of quartz and the recrystallization of muscovites suggest peak deformation temperatures of ca 350-400°C [Brunel and Geyssant, 1978]. Such ductile fabrics are particularly well exposed to the west where the facets on the mountain sides are well developed and normal throw prominent.

2-Western Kunlun range: the Karakax valley.

The Karakax river follows the westernmost segment of the Altyn-Tagh fault about 80 km between Sanshili and Kanshiwar (figure 4). The river is offset about this amount by the fault which continues westward to the Muztagh Ata Tagh and Kongur Shan [Brunel et al., 1994]. The Karakax river then escapes towards the Tarim basin in a narrow gorge approximately at 78°E. The active trace of the fault is particularly clear in this area with glacial and post-glacial terrace rivers offsets, seismic mole tracks and kilometer-long pull-aparts and push-ups [Peltzer et al., 1996, Matte et al., 1996]. North of the fault, the southern flank of the western Kunlun range exposes a volcanic arc sequence sheared with other rocks along the fault. Tectonic slices of pyroxene cumulates, gabbros and basalts, granodiorites and granites, granulites and amphibolites, and Talc and jadeitic pyroxene are thus juxtaposed over a width of 2 to 3 km [Matte et al., 1996]. The highest summits of the range expose leucogranitic bodies. Regional U/Pb, Rb/Sr and Ar/Ar geochronological data indicate mid-Paleozoic, 380 Ma, suturing events [Matte et al., 1996, Arnaud, 1992, Xu et al., 1996]. The fault bounds a region of folded slates, to the south, with a facies similar to the Bayan Har slates. To the southwest of Kanshiwar, Triassic granites become progressively sheared toward the fault. Such mylonitic granites, together with garnet-muscovite schists and leucogranitic lenses in the highly sheared zone along the corridor bear evidence of syntectonic recrystallization (micas). Steep N100°-120° foliation planes bear horizontal lineations . The shear sense is sinistral in the micaschists but variable or less clear in other rocks [Mattern et al. 1996, Matte et al. 1996] and temperatures of deformation are of the order of 350-400°C.

II/ Geochronology.

1-Analytical techniques.

For U/Pb and Rb/Sr dating, mineral separates were obtained by processing 1-2 kg samples through crushing, the disk-mill, the Frantz magnetic separator and heavy liquids.

For each analysis, the fractions were selected grain-by-grain to represent the entire range of crystal types present in the population. Zirconswere mechanically abraded (Krogh, 1982) prior to dissolution in polytetrafluoroethylene (PTF) Teflon bombs with > 50% HF at 220°C for 2-3 days (Krogh, 1973), and feldspar, whole rock and micas were dissolved in two steps, using > 50% HF followed by 6N HCl, both at 150°C. U-Pb and Rb-Sr analyses were performed by the isotope dilution method using a 205 Pb-235 U-233 U and a 85 Rb-84 Sr mixed isotope tracer, respectively, and isotope ratios were measured on a Cameca TSN 206 mass spectrometer, equipped with a single Faraday collector and a secondary electron multiplier for U, Pb and Rb, and a double Faraday collector for Sr. The decay constants used for U and Rb are those recommended by IUGS (Steiger and Jäger, 1977). For Sr standard NBS 987 an average value of 87 Sr/ 86 Sr = 0.71024 ± 3 (2σ, n = 25) was obtained. Analyses of the NBS 983 standard yield a mean mass fractionation value of 0.1 ± 0.05% amu-1 for both the Faraday and secondary electron multiplier systems. Sr ratios were normalized to 86 Sr/ 88 Sr = 0.1194.Total blanks lie around 10-15 pg for Pb and at < 1pg for U, whereas blanks for Rb and Sr are negligible. All zircon analyses were also corrected for initial common Pb, the isotopic compositions were determined from Stacey and Kramers (1975) at 384 Ma. Calculations were made using the Isoplot 200 program of Ludwig (1987). Analytical uncertainties are listed as 2σ and uncertainties in ages as 95% confidence levels.

For 40 Ar/ 39 Ar dating purposes, high purity aliquots were separated using heavy liquid, magnetic separator, and hand-picking methods. Minerals in the range 180-250µm were always used. Because samples were sampled and analysed at different times between 1990 and 1996 they were irradiated at different periods, but always in the site 69 of the Siloée reactor in the Grenoble facility of the Commissariat à l'Energie Atomique (France). They were shielded by cadmium foil to reduce neutron interactions on 40 K, with CaF 2 and K 2 SO 4 to account for interfering nuclear reactions, and flux monitors in the upper and lower positions in each vessel.

Most of the time the Caplongue hornblende (344.5 Ma, Maluski and Schaeffer, 1982) was used as a flux monitor. Step heating analysis was performed at the 40 Ar/ 39 Ar laboratory in Clermont-Ferrand on a VG3600 mass spectrometer. The major characteristic of our facility is that analyses are carried out successively on two collectors: a Faraday cup of 10 11 ohm in axial position and a photomultiplier that receives the signal of a Daly plate interceptor. Using both collectors allows for greater amounts of gas to be analysed when 36 40 Ar range from 1.3x10 -15 moles STP at low temperature to 4.7x10 -15 moles STP at 1200°C on both furnaces and have been reproducible along the years. Blanks for other masses are usually under detection level or so low that they have large uncertainties. Age spectrum calculations are given at 1σ on each step and include all correction factors, as well as 2% errors on blanks taken for correction. Individual steps do not include error on J factor, while plateau and isochron ages do so, with an average of 1.5%. Comparison of several isotopes allows qualitative analysis of K/Ca ( 39 Ar/ 37 Ar) and Cl/K ( 38 Ar/ 39 Ar) ratios. Note that for simplicity K/Ca and Cl/K will be used in the text while no strict calculations have been made and those terms only reflect the isotope ratios. Results are given in table 1. Plateau ages and isochrons are calculated following the criteria of Dalrymple et al. [1981] and Roddick [1980].

2-Age of deformation events.

Because argon systematics show evident losses in the temperature range 300 to 450°C it is often difficult to distinguish the dating of deformation from that of cooling subsequent to the peak of deformation. In our case the characteristics of plastic deformation of quartz show features of dynamic recrystallization such as sub-basal deformation lamellae [White, 1976], typical of low temperatures of deformation in the range 300-350°C [Brunel and Geyssant, 1978]. U/Pb dating will thus yield the emplacement age as an upper limit for the thermal history of these rocks. Rb/Sr and Ar/Ar ages will be only partially retained by magmatic muscovite, but will be very close to the deformation age on syntectonic muscovites since their closure temperatures are on the order of the highest bracket [Lister andBaldwin, 1996, Hames andBowring, 1994]. Finally the Rb/Sr and 40 Ar/ 39 Ar ages of biotites however will date subsequent cooling since their closure temperature is lower [Harrison et al., 1985].

a. The Kunlun fault in eastern Kunlun. Only limited data is available for magmatic ages of the widespread plutonic activity. Harris et al. [1998] show dominantly Mesozoic ages and more rarely Paleozoic ones. We dated one deformed granite (QGS17, figure 5 and table 1) from the belt of metamorphic rocks on the northern side of the fault (figure 2). The deformation of this rock has resulted in an orthogneiss in which magmatic biotites and muscovites are not recristallized. The U-Pb data for the Xidatan orthogneiss (QGS 17) are shown on a Concordia diagram [Wetherill, 1956] in figure 5. The zircons selected for U-Pb analysis were euhedral, unbroken, crackfree crystals, translucent and inclusion free. Eight fractions were made using color, shape (euhedral or rounded) and size criteria ; their weight ranges from 0.059 mg to 0.1 mg. The data define a reverse discordia, with a lower intercept at 384 ± 9 Ma and an upper intercept at 2.4 ± 0.2 Ga, when plotted on a concordia. The most discordant fraction corresponds to rounded fractions and demonstrates inheritance from an old basement.

Rb/Sr dating of the same rock (figure 6a and table 2) on whole rock, K-feldspar, and three different size fractions of biotite and muscovite are analyzed for Rb-Sr, define two scattered isochrons. Data for whole rock, Kfeldspar, and muscovite fractions define an isochron of 197 ± 3 Ma (± 2σ) with an initial 87 Sr/ 86 Sr ratio of 0.7312 ± 0.0006 while the whole rock, K-feldspar and biotite fractions array yield a date 114 ± 2 Ma (± 2σ) and an initial Sr ratio of 0.7359± 0.0002. This indicates one or two successive isotopic remobilisation and therefore thermal events.

Another rock, a deformed pegmatite, was also dated by Rb/Sr (QGS 16, figure 6b). Feldspar and 4 muscovites yield an array with an date of 192 ± 12 Ma and an initial ratio 87 Sr/ 86 Sr of 0.7138 ± 0.0001 (± 2σ).

Note that in both samples the initial Sr ratios are similar. The highly radiogenic initial 87Sr/86Sr ratios for biotite and muscovite isochrons, show that the major source lithology of the granite was derived from highly evolved continental crust. 40 Ar/ 39 Ar dating has been carried out on several facies (figure 7 and table 3) from the metamorphic band north of the fault. Because most of the deformed granites are calk-alkaline in chemistry and thus have no primary muscovites, the latter are associated only with syn-tectonic recrystallization. Though biotites probably predate the deformation, most appear to have recrystallized in shear bands along the shear S/C planes, and are plastically deformed suggesting they recorded post-emplacement tectonic events. Sample K93G30 comes from the highly sheared edge of a granite intrusion in the middle of Xidatan trough. Sinistral mica-fish shaped muscovites yield a climbing age spectrum, from ages of ca. 51 Ma up to a plateau at 120 ± 2 Ma covering 75% of the total 39 Ar. The last steps are a little older at 128 Ma probably as a result of undercorrection of 40 Ar high temperature blanks. No sign of excess argon or unusual behavior was noted in this sample, though amounts of radiogenic argon (more than 90% in most degassing steps) precludes the use of isotope correlation plots [Roddick, 1980].

The other samples, K93G36, K93G37 and K93G42 were sampled further west in a steep and narrow orthogneiss band just north of the active fault trace. The gneisses bear clear sinistral indicators on vertical foliation planes with horizontal lineation and sinistral shearing indicators. Sample K93G36 contains both biotites and muscovites, both underlining the metamorphic foliation. We obtain simple spectra with a large plateau at 126.8±3.5 Ma for the muscovite and a much younger one for the biotite at 93.4±1.1 Ma. A difference in age between micas is not unusual as the biotite closure temperature is probably at least 50°C below that of muscovite, but this one is particularly large, suggesting very slow cooling. This is consistent with the first step of the muscovite spectra being younger than the plateau. Sample K93G37 is a leucocratic mylonite and in which both the muscovite and biotite yield very well developed plateaus at 122 ± 1 Ma and 111 ± 2 Ma, with the first step younger than the plateau for the muscovite. Again biotite is younger than muscovite. Finally, sample K93G42 is a sheared pegmatite with a plateau age on muscovite of 120.1 ± 3.5 Ma, with again a younger first step.

All together, these results suggest that middle Paleozoic plutons were at roughly 350-400°C during Cretaceous time. Keeping in mind the relative closure temperature for muscovites and biotites for Rb/Sr (500°C and 300 °C) [Cliff, 1985] and 40 Ar/ 39 Ar (400°C, 325°C) [Lister and Baldwin, 1996;Hames and Bowring ,1994] and the temperature of deformation as deduced from petrography (350-400°C) it appears that this set of ages can be interpreted in two ways. On the one hand the various ages represent a cooling curve sampled at several moments in an otherwise rather monotonic cooling history after a tectonometamorphic event at least as old as the oldest ages, thus triassic. On the other hand, those distributed ages can represent disturbance of the geochronometers, first closed during at least Triassic times, by a post-triassic deformation event along the fault, possibly as young as the youngest ages, thus cretaceous Although ages in the range 190-200 Ma are reported elsewhere [Delville et al., 2001; Mock et al., 1999; Roger et al., submitted] for deformation as well as magmatic activity it is not possible to at present to choose between those equally plausible solutions.

b. The western Altyn-Tagh fault. Direct dating of the shear deformation along the fault was possible on garnet-muscovite micaschists (K89G217) bearing horizontal lineation and sinistral indicators clearly associated to fault movements. Syn-tectonic muscovites in the shearing planes were dated (8a and 8b). A well-defined plateau appears on more than 90% of total 39 Ar released with an age of 119±2 Ma. The first steps have significantly lower ages from 83 to 95 Ma associated to lower though not unusually so K/Ca ratios though. The last step shows a higher age that is probably due to under correcting of blanks at 1400°C accounting for almost 40% of the total 40 Ar released at that step.

In order to place constraints on the thermal conditions of the deformation, rocks near the shear zone along the fault that did not completely recrystallize corridor were sampled. Closing toward the fault, biotites from a foliated granodiorite (sample K89G204) taken a few hundreds of meters north of the fault yields a disturbed spectrum with, at the beginning, ages increasing from 166 Ma to ca. 400 Ma, then a median bulge at 450 Ma, and finally a small pseudo-plateau at 420± 4 Ma with 50% of the total 39 Ar. The bulge is older than most Paleozoic intrusives in the western Kunlun range (350 to 400 Ma on average [Matte et al., 1996, Arnaud, 1992]. Moreover, this bulge correlates with a negative spike in the K/Ca ratio and a positive one for the Cl/K ratio. This situation matches that described by Ruffet et al. [1991], who conclude to the presence of chlorite interlayered with the biotite, in agreement with our petrographic observations. It is thus likely that the minimum ages at the beginning of the spectrum are partially due to excess 39 Ar in low retentivity sites of the biotite lattice. However, the magnitude of the drop in ages at the beginning being more pronounced than the excess ages in the middle, a real age gradient probably exists in this sample, with an argon loss at a time younger than 200 Ma ago.

Farther east, muscovites from leucogranitic boudins within schists just south of the active fault trace, and with the same fabric (K89G44), have an even more complex spectrum (figure 8a). The first two steps are clearly affected by excess argon (increasing Cl/K ratio), then ages climb from 94 Ma to a broadly defined plateau at 150±3 Ma (for 58% of released 39 Ar) before finally climbing to 177 Ma. The last much higher step must be regarded with caution because it is probably affected by blank correction. Variations in age seem to correlate with K/Ca variations which suggest mineralogical heterogeneity. The inverse isochron plot is scattered but not correlated enough to distinguish between a possible excess component and a real age gradient. Overall, this spectrum suggests that the argon system was partially reset around 100 Ma from a much older sample. The illdefined plateau age and the highest age, however are both coherent with the Mesozoic history in this area.

Finally sample K89G42 (figure 8b) is a undeformed granite taken a few kilometers south from the fault in the middle of the Songpan Garze flysch. Muscovites and biotites show almost undisturbed spectra at 190 ± 8 Ma and 177 ± 3 Ma respectively suggestive of slow undisturbed cooling.

These results are most simply interpreted in a way similar to the eastern Kunlun in Xidatan. It appears that a major thermotectonic event occurred during Triassic times, and that rocks along the fault have recorded either monotonic and slow cooling between the Trias and the Cretaceous, or alternatively that deformation at Cretaceous times along the Altyn-Tagh fault in the Karakax induced resetting of geochronometers along the fault. It is noteworthy that apparent progressive resetting of ages when nearing the fault favors the latter interpretation.

3-Thermal history and cooling along the faults.

To unravel in more detail the thermal history associated to the ductile fabrics, whatever its age, and subsequent cooling, simple diffusion models were tested on partially reset micas to bracket the magnitude and duration of the thermal event associated with Cretaceous fault movement. Analysis and modelling of K-feldspar data was conducted following the method developed by Lovera et al. [1989Lovera et al. [ , 1991]]. To compute theoretical argon losses we used published data from diffusion studies on micas. For the biotite, we took the values chosen by Harrison et al. [1985] with a cylindrical geometry (activation energy E= 47 kCal/mol, frequency factor D o =0.077cm 2 /s, and characteristic diffusion radius r =150µm which leads to an average closure temperature of 325°C). For the muscovite, recent contributions by Lister and Baldwin [1996] and Hames and Bowring [1994] disagree on diffusion geometry and kinetic values resulting in a 50°C difference in the closure temperatures. For the coherence of the data with biotites we took values of the latter authors (E= 52 kCal/mol, D o =0.04 cm 2 /s and r=150 µm which transfer into a closure temperature of 398°C). a. The Kunlun fault. Petrology and dating imply conditions of 350-400°C to have prevailed at ca. 120 Ma. Some muscovites spectra show apparent argon loss shapes, with the first steps significantly younger than the plateau. In many cases those decreasing age steps seem associated with decreasing K/Ca ratios but optical examination did not reveal severe alteration at rims or in defects, nor any reaction rims. Moreover the K/Ca ratios are always greater than 10 and up to 100 even in the beginning of the spectra. Consequently those spectra were used as indicative of temperature/time conditions. It is noteworthy that the biotites that appear to be kinematically coeval with the muscovites are systematically younger implying thatcooling in biotites was systematically delayed c.a. 20 Ma before compared to muscovites. This delay is particularly long and suggests abnormal cooling conditions or even thermal stasis after muscovite closure. Those conditions were calculated by comparing the integrated total 40 Ar/ 39 Ar ratio on muscovites (corresponding to the total fusion age) and the plateau age defined on high temperature steps and assumed to be close to the original age. For example sample K93G36 shows 1.8% loss and sample K93G30 2.6% loss. Moreover biotites 40 Ar/ 39 Ar ages are always significantly younger than the muscovites though significant variations among their ages are observed. It is easy to calculate possible losses induced by varying (temperature time) pairs (figure 9) and this leads to estimations of temperatures roughly 250-300°C lasting for 5 to 20 Ma. Therefore, one concludes that a significant thermal regime was maintained in the fault zone for the period 120-100 Ma.

The data from K-feldspars appear compatible with those conclusions. On both samples K93G36 (figure 10a) and K93G30 (figure 10b), the feldspars age spectra show increasing ages to maxima of 86 to 89 Ma. With use of the multidomain theory, several authors have suggested that the most retentive diffusion domains in feldspar have a closure temperature close or even higher than that of biotites. Similar ages of the biotites and feldspars in our case further support this idea. Moreover, even if a broader estimate of closure temperature for feldspars is taken roughly around 250°C, the maximum age of the feldspars leads to the idea of a long lasting thermal event when compared to that of the muscovites. If both spectra show increasing ages they differ from one another, as K93G30 is monotonously increasing while K93G36 shows a small plateau in the first 40% of 39 Ar release at 26 Ma. In each case the first steps are associated to very low ages of less than 10 Ma. Several studies [Arnaud and Kelley, 1997;Parsons et al., 1988] have suggested possible artifacts in the early stages of degassing of feldspars, in which complex subsolidus textures are likely to express in the first percents of gas released. Thus the first 5% of the ages spectra are not taken into account in our modeling. The inverse isotope diagram fails to show any systematic behavior and suggests that the age range is real. Overall, K/Ca and Cl/K plots show a remarkable homogeneity, particularly the near absence of plagioclase mixing or fluid inclusion degassing. Therefore, such spectra are most likely the result of partial 40 Ar loss by a secondary heating event or continuous loss associated with slow cooling. No metamorphic or magmatic phase is reported in this region of the Eastern Kunlun during the Cenozoic and Mock et al. [1999] indicate that feldspar spectra similar to those presented here are common in the Eastern Kunlun and are not spatially linked with any pluton or visible structural feature. It is likely therefore that such argon loss spectra are indicative of slow cooling superimposed on a multidomain structure as experimental degassing reveals on associated arrhenius plots. The model of K93G36 suggests an increasing but overall slow cooling rate of ca 2°C/Ma during the Cenozoic with a rapid change to cooling rate of more than 40°C at roughly 25 Ma. This cooling history is the same as the one obtained from the modelling of the spectra of the K-feldspars from sample K93G30 and is fully compatible with with the mica argon data as well as with fission track regional ages on apatites at 20 Ma [Lewis, 1989] though one must note that the latter were not acquired on the same samples.

b. The western Altyn-Tagh fault. The muscovite from K89G44 from (leucogranitic boudins) shows a distinct loss spectra which implies about 5% of radiogenic 40 Ar loss, if one compares the total fusion age (158 Ma) with a possible estimate of initial age for the protolith at 160 Ma. Calculating temperature/time pairs for such a loss with muscovite diffusion data leads to a minimum temperature of 260°C and a probable range of 280-300°C for a heat duration of 0.5-10 Ma. Doing the same with the biotite from K89G204 leads to a similar average loss of 5%. But because the biotite is less retentive for argon than the muscovite, temperatures of 230-240°C are deduced for the same time range. This is in good agreement with the fact that the K89G204 granodiorite is deformed but shows no sign of recrystallization. It is also structurally farther from the most ductile zone than is K89G44.

With that temperature range in mind we now turn toward the garnet-micaschist sample K89G217 (figure 11) which was completely recrystallized during ductile shear along the fault. This sample also shows decreasing ages at the beginning of the spectra which can easily be modeled if one assumes that the sample stayed hot for a long time as was hypothesized for the deformed units near Xidatan. In fact it is easy to model the resulting age spectra if a temperature of 300°C is maintained for at least 5 Ma after a closure onset at 120 Ma. Alternatively slow cooling from 300°C at 120 Ma to 200°C at 80 Ma would also be adequate. K-feldspars were studied on samples K89G204 and K89G50 (figure 12), the latter a less deformed granodiorite taken east of K89G204. K89G50 spectrum is very complex. After 5% of gas release, clearly dominated by excess argon, the next 20% of 39 Ar release gives a small plateau at ca. 38 Ma, then a rapid increase to ages of 350 Ma and finally a decrease to a poorly defined plateau at 250 Ma. The presence of the hump in the middle strongly suggests the presence of excess argon [Forster et al., 1990]. However the age of the final steps are coherent with the 350 Ma age of most plutonic bodies in southern Kunlun. Moreover, the first plateau is associated to systematic low values of the K/Ca ratio, and therefore is likely to reveal the degassing of perthitic features from that feldspar. Applying multidomain theory to such a sample might therefore lead to large errors in the deduced cooling history. Thus, though diffusion data in laboratory was satisfactorily modeled, only a trivial cooling history is suggested. But it is worth noting that then end of the modeled cooling shows a suggested temperature of ca. 220°C at 50 Ma, which implies further cooling during the Cenozoic. The same kind of remark applies to sample K89G204 (Kfeldspar). The effect of excess argon is even clearer at the beginning of the spectra and probably at the end, even if the highest ages agree with the biotite ages given that closure temperature is likely to be lower. Modeling is close to the original spectra and would also suggest a trivial history with very slow cooling since the granodiorite emplacement. However because the biotite showed traces of partial resetting we believe the spectrum is in fact revealing of a complex partial loss event and maybe slow cooling to explain the lowest ages.

Of course these models are non unique as an infinity of temperature/time pairs can be invoked, but all spectra seem consistent with a rather high temperature of ca 300°C that lasted at least several millions of years if not more in late Cretaceous.

III/ Discussion.

The comparison between the between the Karakax segment of the Altyn-Tagh fault and the Xidatan-Dongdatan segment of the Kunlun fault indicates late cretaceous thermal conditions identical in both regions, although spaced by almost 1500 kilometers. Moreover the rocks studied show a strong deformation event. The two simplest explanations are: (1) that deformation occurred at the oldest recorded times, in the Trias or even earlier and that every other data only record surprisingly coeval cooling over a very wide area, or (2) that deformation happened in late Cretaceous superimposed on plutonic rocks emplaced during Triassic or Paleozoic times..

If slow cooling alone brought the rocks along older faults at the same temperature at ca 120 Ma this implies that exhumation along most of what is now northern Tibet has been fairly homogeneous through the Mesozoic, and particularly that ongoing continental accretion further south, such as the Jurassic accretion of the Lhassa and Qiantang terranes did not disturb this equilibrium. In fact, ongoing work on magmatism and cooling during the Mesozoic in northern Tibet (Roger et al., submitted) shows that cooling is broadly homogeneous along northern Tibet after the Trias. However such an homogeneous cooling is rarely maintained except in cratonic areas. Moreover, along the Karakax valley, it appears that samples are progressively and regularly reset when one closes the fault, suggesting a resetting effect associated with the fault corridor (see for example differences between 40 Ar/ 39 Ar ages from micas on K89G44 and K89G217). We thus favor the idea that indeed cretaceous deformation was superimposed on older plutonic and metamorphic rocks.

1-Origin of a Cretaceous sinistral shear event along the Kunlun and western Altyn-Tagh faults.

The origin of the possible Cretaceous sinistral shear in northern Tibet is unclear. Major orogenic events of late Mesozoic age in Tibet include the accretion of the the Qiantang and Lhasa blocks, a collision that was over prior to that of India with Asia. Xu et al. [1984] interpret a U/Pb age of 171 ± 6 My on gneisses from the northern Lhasa block as dating the accretion of Qiantang and Lhasa blocks. South of Longmutso, in western Tibet, small leucogranitic bodies have been dated at 100 Ma [Arnaud, 1992, Matte et al., 1996]. Xu et al. [1984] also report ages of 121 Ma for leucogranitic bodies south of Anduo. Various studies [England and Searle, 1986;Murphy et al., 1995;Yin et al., 1995, Matte et al., 1996] confirm that some shortening occured in southern Tibet before the India-Asia collision, and there is evidence for overthrusting at 150 Ma in the north-eastern Pamir [Arnaud et al. 1993]. Also, the Mongol-Okhotsk ocean closes in northern Mongolia closes around the beginning of the Cretaceous [Khramov, 1958, Enkin et al., 1992]. New paleomagnetic evidence [Gilder andCourtillot, 1997, Nadir et al., 1998] suggests that by 120 Ma, this ocean was closed. Finally there is growing evidence for late Mesozoic suturing and deformation in the Qinling range. It is possible that such events triggered block reorganisation and strike-slip movements along more ancient welding zones within the part of Asia that had already been accreted, much as the collision between India and Asia now does. However, most of the Mesozoic geological history in Tibet is thought of as resulting from « weak » collisions without much continental deformation.

Alternatively, oblique subduction along the Cretaceous active margin of Asia, several hundred kilometers south of either the Kunlun or western Altyn-Tagh faults, might have dragged the southern part of Tibet much as oblique motion of the Pacific plate relative to North-America now drags slices of the western North-American collage.

It has already been mentioned that age data show a systematic delay between muscovite and biotite closure following the peak deformation. Although this may be due to slow unroofing, the ages of the biotites are highly scattered implying heterogeneous exhumation on a very local scale. Alternatively a high and heterogeneous thermal flux lasting for 20 Ma as modeled could be a better explanation.

The existence of thermal anomalies along major strike slip faults is debated. Although there is only a broad, modest rise in the isotherm across the San Andreas fault [Lachenbruch andSass, 1980, Scholz, 1980], there is evidence for fairly large heat anomalies along the Red River Fault [Leloup et al., 1993, 1998, Schärer et al., 1994], the Alpine fault [Grapes, 1995, Scholz et al., 1979] and the Altyn-Tagh fault [ Van der Woerd et al., 1998]. Shear heating can produce a significant amount of heat [Fleitout and Froidevaux, 1980, Thatcher and England, 1998, Leloup et al., 1998] and in addition large scale strike-slip fault may provide easy path for convection of fluids in the shallow crust thus leading to heat advection. Finally, along the Red River fault the presence of alkaline magmas indicates partial melting in the mantle beneath the fault. Whatever the intimate, if any, connection between strike slip faulting and mantle melting, those magmas provide a supplementary plausible source for upward advection of heat.

2-Cenozoic cooling along the Xidatan-Dongdatan segment of the Kunlun fault.

Cooling, as revealed by the feldspar cooling curves, seems to have been rather slow until the Miocene. In the eastern Kunlun, a severe increase in the cooling rate occurs at 25 Ma, lasting until 10 Ma. Such a cooling rate of 40°C/Ma is not easily reconciled with simple conductive cooling and requires exhumation, either because of enhanced erosion or due to a vertical component of faulting along the faults. Although telling thrusting from normal faulting by the cooling path alone is not possible, normal faulting clearly occurs now along the fault [ Van der Woerd et al., 1998] and may have brought the ductily deformed rocks to outcrop. Since similar studies [Mock et al, 1999] in the eastern Kunlun generalize a similar cooling event to the whole region north of the Kunlun fault, we infer that limited normal faulting along the Kunlun fault accommodated regional uplift of the range beginning 25 Ma ago.

IV/ Conclusion.

Firstly our observations confirm that at least some segments of the large Tertiary faults of Tibet follow more ancient features. Similar work in north-eastern Tibet and the Qilian shan suggest that NE trending faults might also locally reuse older structures [Delville et al., 2001]. That both E-W the Xidatan and Karakax segments of the Kunlun and Altyn-Tagh faults are reactivated implies that they were favorably oriented within the stress field generated by the India-Asia collision [Peltzer et al., 1988]. The amount of Cretaceous shear along both shear zones is unknown, but since such movements happens to have taken place in the same sense as the posterior Tertiary slip, part of the finite offset on the faults is clearly unrelated to the India-Asia collision. Offsets based on pre-Cretaceous percing points will therefore be larger than those due to Cenozoic motion resulting from the India-Asia collision.

Second, the great resemblance in rock types, ages, structure and geodynamic environment along both the Karakax and Xidatan shear zones suggest that they may have formed a continuous belt from western to eastern Kunlun. If it was the case, and if the Xidatan zone can be documented westwards to the Ayakum -Kol region, then restoration of the present day offset between the Karakax and Xidatan zones might indicate on order of several hundreds of kilometers of post-Cretaceous slip along the N70°E trending stretch of the Altyn-Tagh fault zone between the Eastern and Western Kunlun, a value in agreement with independent recent estimates [Ritts and Biffi, 2000]. Much of the offset of this transcrustal marker could have resulted from the India-Asia collision. Data from various minerals are indicated on the isochrones as follows: Ms: muscovite, Bt: biotite, Fd: feldspar, WR: whole rock. Number in parenthesis behind initial ratio shows error on the last digit of the ratio. Figure 7: 40 Ar/ 39 Ar age spectrum from micas in Xidatan. The plateau age is given at 1σ and includes error on J factor. It is indicated with the corresponding steps used in its calculation.. TF age is the total fusion age. Lettering refers to the type of mineral dated, muscovites, biotites. Figure 8a and b: 40 Ar/ 39 Ar age spectrum from micas in the Karakax valley. Same conventions apply as in figure 7. When age spectra are complex 39 Ar K / 37 Ar Ca and 38 Ar Cl / 39 Ar K are shown as proxies for K/Ca and Cl/K ratios. They are discussed in the text to derive the most meaningful ages. Figure 9: Model of argon loss calculated for Xidatan mica samples following several kinetic parameters solutions. The three sets of lines indicate equal argon loss models for various sets of diffusion data and various values of argon losses. The dashed box shows the range of temperatures for a plausible heating event lasting for 5-10 Ma. Figure 10a andb: Cooling histories modeled on K-feldspars from Xidatan valley gneisses using the multi-domain theory of Lovera et al. (1989Lovera et al. ( , 1991)). A: age spectra; B: diffusion data with laboratory heating schedule as inset; C: resulting cooling model. In A and B experimental data curve is thin while model is bold. Data from micas and apatite (fission tracks from Lewis, [1989]) are shown as a confirmation of the model consistency for sample K93G36. Unsupported part at the end of thermal model for K93G30 is shown as dashed (see text for details). Both models suggest a significant change in cooling rate at ca 25-28 Ma. Figure 11: Model of argon loss in the micas from Karakax gneisses. Two hypothesis allow modeling: A/ thermal disturbance at ca 300°C lasting 5 to 15 Ma, or B/ slow cooling from 300°C to 250°C between 120 Ma and 80 Ma. H a X G Te a 4 X 4 &4 d ¢¡ £ ¥¤ ¢i £ @¡ S p © q ( 4 &4 &4 R A 9 &% 3 p © q 6 A 9 &% 3 © © r 6 1 2 £ @i s 3 F 5 8 6 t ¢V u( g H &H f( uv C A £ @9 &A @A 9 &% 3 p 9 © 9 &q 6 V fR 4 X e &g 0 9 cb q t3 f U9 A9 3 q sb 3 e Ae 9 cb Uq Y9 9 Yb 9 A9 A9 9 cb 9 A9 A9 9 cb 3 T d cb e r S e sb d S 3 q sb 3 e 3 e sb 9 r 9 cb q r f U9 A9 3 r b 3 e Yp 9 cb t3 ¤p 9 Yb 9 A9 A9 f Yb f r q 9 cb 9 Yf p cb 3 ¤d p S b 9 Up 3 ¤d cb f T 3 S b 3 T 9 cb e S f Af U9 q Y9 cb d r q 9 cb Uq ¢3 9 Yb 9 A9 A9 r b 9 Ap T 9 cb 9 S r b T f r e sb e Ad 3 r b T e q ¢3 )b q Aq 9 cb e Ue f Af U9 q ¢3 )b p Ue ¢3 9 cb Uq Y9 9 Yb 9 A9 A9 p cb p r uT 9 cb 9 Ap S b T AT r 9 cb q r 3 S b e r q Aq sb f T 9 cb f )e d A9 A9

Bibliography

Captions of figures.

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Figure 1 :

 1 Figure 1: Sketch map of active tectonic features associated to the Indian collision in Asia. Classical patterns for faults have been used. Small dashed open squares show the locations of detailed geological maps of figure 2 and 4. Inset shows a schematic terrane map of Asia from Yin and Nie [1996] modified.Figure 2: Geological sketch map of eastern Kunlun along the Xidatan valley. The map is adapted from the chinese 1:1500000 Geological map (Liu, Z. Q., editor, 1988 modified , the Royal Society geotraverse observations and personal observations. Samples numbers are shown with their complete names.Figure 3: Field and micro photographs of orthogneisses from the Xidatan segment of the Kunlun fault. A-B: field view of the deformation on planes roughly perpendicular to the foliation (S1 on photo A), with dip of the foliation toward reader (dashed arrow); C: close photograph of augen feldspars showing sinistral shear planes; D: microphotograph in

Figure 2 :

 2 Figure 1: Sketch map of active tectonic features associated to the Indian collision in Asia. Classical patterns for faults have been used. Small dashed open squares show the locations of detailed geological maps of figure 2 and 4. Inset shows a schematic terrane map of Asia from Yin and Nie [1996] modified.Figure 2: Geological sketch map of eastern Kunlun along the Xidatan valley. The map is adapted from the chinese 1:1500000 Geological map (Liu, Z. Q., editor, 1988 modified , the Royal Society geotraverse observations and personal observations. Samples numbers are shown with their complete names.Figure 3: Field and micro photographs of orthogneisses from the Xidatan segment of the Kunlun fault. A-B: field view of the deformation on planes roughly perpendicular to the foliation (S1 on photo A), with dip of the foliation toward reader (dashed arrow); C: close photograph of augen feldspars showing sinistral shear planes; D: microphotograph in

Figure 3 :

 3 Figure 1: Sketch map of active tectonic features associated to the Indian collision in Asia. Classical patterns for faults have been used. Small dashed open squares show the locations of detailed geological maps of figure 2 and 4. Inset shows a schematic terrane map of Asia from Yin and Nie [1996] modified.Figure 2: Geological sketch map of eastern Kunlun along the Xidatan valley. The map is adapted from the chinese 1:1500000 Geological map (Liu, Z. Q., editor, 1988 modified , the Royal Society geotraverse observations and personal observations. Samples numbers are shown with their complete names.Figure 3: Field and micro photographs of orthogneisses from the Xidatan segment of the Kunlun fault. A-B: field view of the deformation on planes roughly perpendicular to the foliation (S1 on photo A), with dip of the foliation toward reader (dashed arrow); C: close photograph of augen feldspars showing sinistral shear planes; D: microphotograph in

Figure 4 :

 4 Geological sketch map of western Kunlun along the Karakax valley. The map is adapted fromMatte et al., 1996. Samples numbers are shown without the prefix "K89G" that should be added to every sample to be compared with text and other figures.

Figure 5 :

 5 U/Pb dating of sample QGS 17 from Xidatan valley.

Figure 6 :

 6 Rb/Sr dating of a/ sample QGS 17 and b/ sample QGS 16 from Xidatan valley.

Figure 12 :

 12 Cooling histories modeled on Kfeldspars from the Karakax valley using the multi-domain theory. Same rules as in figure 10. Both feldspars are almost certainly affected by excess argon and thus yield only crude trivial model. They nevertheless indicate a significant Cenozoic thermal disturbance or very slow cooling.

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  Ar signals are low, while bigger signals for 39 Ar and 40 Ar are taken on the Faraday cup. This decreases the errors on the low signals. Duplicate analyses of 39 Ar during each run allows to calculate the gain between Faraday and photomultiplier signals.

	For signals of more than 20mV (with a
	sensitivity of 3.15x10 -17 mole/mV) on the
	Faraday cup, statistical analysis of more than
	2000	gain	analyses	shows	good
	reproducibility at 92.5 with an estimated error
	of 2% maximum. This error is taken into
	account during age calculation. Average
	blanks for

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Cosmochim. laser dating of biotites from the North Ar conventional and Ruffet, G., G. Feraud, and M. Amouric, Lett., 48, 185-208, 1980. -a 40 Ar/ 39 Ar analysis. Earth Planet. Sci. China, 94-123, 1996 evolution of excess argon in alpine biotites Yusheng ed., Seismological press, Beijing, Roddick J.C., R.A. Cliff, and D.C. Rex, The the Karakoram and Kunlun mountains, P. 2000. granitoids rocks, in Geological evolution of America Bulletin, 112 (no.1), pp.61-74, Vidal and N. Arnaud Geochemistry of Northwest China, Geological Society of Yuquan, Z., X. Yingwen, X. Ronghua, Ph. on the central Altyn Tagh fault system, 27, 6, p. 335, 1995. Middle Jurassic (Bajocian) displacement Programs, Geological Society of America. Ritts, B.D., and U. Biffi, Magnitude of post-America annual meeting, abstracts with Geophys. Res, 93: 7793-7812, 1988. Asian collision. Geological Society of earthquakes on the Chang Ma fault. J. 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Cantagrel, An early unroofing in eastern Kunlun revealed by 40 Ar/ 39 Ar thermochronology. Earth Planet. Sci. Lett. submitted. 326, 1956. ages. Trans. Am. Geoph. Union 37, 320-Wetherill G. W., Discordant uranium lead 1998. (Qinghai, China), Geology, 26,8 695-698, Xidatan segment of the Kunlun fault by cosmogenic surface dating on the Qunlu, Holocene left-slip rate determined Mériaux, M. Caffee, Z. Guoguang and H. Tapponnier, Y . Gaudemer, R. Finkel, A.S. Van der Woerd, J., F.J. Ryerson, P. London, A 327, 1-413, 1988 of Tibet, Phil. Trans. of the Roy. Soc. The Royal Society, The geological evolution Qinghai, lithospheric mantle subduction, 891-905, 1998. and Z. Chen, Crustal thickening in Gansu-Andreas fault zone, J. Geophys. Res., 103, Métivier, Y. Gaudemer, G. Peltzer, S. Guo, implications for the mechanics of the San Meyer, B., P. Tapponnier, L. Bourjot, F. zones beneath strike-slip faults : 1996. Thatcher, W., and Ph. England, Ductile shear Mesozoic, Geol. Runsch, 85, 805-822, p.192, 1993. implications for the Paleozoic and Meet. 4-6, Montpellier, Ed. BRGM, 21, (Xinjiang, China): tentavive geodynamic Belts, Malavieille and Seranne (eds), Int. traverse through the western Kunlun In : Late Orogenic extension in Mountain Mattern, F., W. Schneider, Y. Li, and X. Li, A crustal shortening : an updated overview. 330, 1996 or denudation" faulting in regions of Indus. Earth Planet. Sci. Lett., 142, 311-Tapponnier, P., Mechanisms of "extensional western Tibet, between the Tarim and the 157, 1986. P. Yusheng and Y. Wang. Tectonics of of London special publication, 19, 115-Boujot, J.P. Avouac, Ph. Vidal., L. Qing, Coward and Ries (eds), Geological Society

Geol. Surv., Prof. Paper 1176, 1981.

Delville N., Arnaud N., Montel J. M., Roger F., Brunel M., Tapponnier P. and Sobel E., Paleozoic to Cenozoic deformation along the Altyn-Tagh Fault in the Altun Shan massif area, Eastern Qilian Shan, NE Tibet

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Claude Verdier
email: verdier@ujf-grenoble.fr

Guillaume Ravilly

Peeling of Polydimethylsiloxane Adhesives : the Case of Adhesive Failure

Keywords: adhesion, interfaces, thin films

The adhesion properties of high molecular weight Polydimethylsiloxane adhesives are measured using 90°-peel adhesion tests, in the high velocity range. Such adhesives undergo mainly adhesive failure in this regime. The influence of viscosity (non-Newtonian), adhesive thickness, peeling velocity, and backing properties are studied, and new unexpected behaviours are shown.

The role of rheology and peeling velocity can be explained by an extension of a model already presented for cohesive failure, by using a power-law fluid for the adhesive. On the other hand, the influence of the backing rigidity reveals to be coupled with the adhesive elastic properties, this effect being correlated to the introduction of a new parameter in the model, the Weissenberg number for viscoelasticity.

INTRODUCTION

The adhesive properties of pressure-sensitive adhesives (P.S.A.) have been studied by a large number of researchers over the years, using different methods for predicting adhesive failure in particular using peeling tests 1,2 and probe-tack tests 3,4 but also other various approaches such as the JKR (Johnson-Kendall-Roberts) technique 5 . Prediction of the adhesive properties in terms of interfacial and rheological properties is still a challenge, and although several studies already focused on such correlations [6][7][8][9] , there is still a lack of prediction of the effect of such properties as well as geometrical effects. Recently, model polymers (Polydimethylsiloxanes, PDMS) were used 10 to investigate the peeling properties of Newtonian adhesives. Although this analysis was found to predict well experimental data, it was only obtained in a rather limited range of velocities which corresponds to two-dimensional adhesive flow of the cohesive peeling branch.

Indeed, previous studies reported on the complex flow behaviour of the adhesive in both cohesive and adhesive regimes, close to the peeling front 2,11 . After a certain threshold velocity is reached, both cohesive and interfacial flow or deformation regimes show the appearance of instabilities leading to three-dimensional deformations corresponding to stable regimes for the energy release rate G (N/m) or Force per unit width ( b F G = , F is the force required to peel the adhesive strip, and b is the adhesive strip width).

To model the effect of the adhesive and rheological properties on the energy release rate G, several studies 12,13,14,15 focused on the possible decomposition of G into the product of two different terms, W a , the Dupré adhesion energy, and a rheological parameter (V) φ to be determined. (V) φ contains the viscoelastic contribution of the adhesive in terms of rheological properties and the velocity of peel V, and is intimately related to the rate dependence of the microscopic motions of elements (polymer chains, networks, particles, etc.), within the adhesive :

(V) W G a φ = (1)
It has been a source of interest to try to model this function, which can be assumed to contain both shear and elongational deformation types. Still the use of the Dupré energy of adhesion in formula ( 1) is under debate and might be related to more complex microscopic phenomena, due to the presence of polymer chains of different molecular weights M w for example 13 . Finally, the geometry of the system plays a role which renders the use of (1) difficult.

In the present work, we pay attention to the adhesive (interfacial) regime of failure in a 90°-peel test and try to analyse the effect of the governing parameters, i.e. the adhesive thickness, the velocity of peel, the influence of the backing rigidity as well as the rheological adhesive properties. In the first part, experimental results are presented [START_REF] Ravilly | Adhésion et pelage bidimensionnel des polymères[END_REF] , illustrating the dependence of the energy release rate as a function of the governing parameters described above. The interfacial parameters are also described and their importance is mentioned in terms of interfacial energies, determined through wetting measurements. In the second part, an explanation is proposed through the use of a power law fluid, which is typical of the PDMS adhesive used in this study.

The model predicts fairly well the importance of the governing parameters in terms of the peeling velocity. To explain these results further, a new explanation is proposed in the last part, accounting for the viscoelasticity effects which appear in the high velocity regime where adhesive failure occurs. Dimensionless numbers are introduced through an empirical model. The model is in good agreement with the experimental data and might be used for other systems.

The transition from cohesive to adhesive mode of failure is also discussed.

EXPERIMENTAL MEASUREMENTS Experimental set-up and adhesive properties

In a previous study 10 , model PDMS adhesives have been investigated using a peeling experiment.

The set-up has been already described and is briefly recalled here. An adhesive is coated thanks to a blade coating system (thickness in the range 30-400 µm) onto an initially treated backing. In the present study, different backings are used (stainless steel of different thicknesses, 10µm and 20µm, and PolyEthylene-Terephtalate PET, 23 µm). After the coating is achieved, the system is rapidly set into contact with the substrate, i.e. a High density Polyethylene (HDPE). This system was selected because it enables to obtain adhesive failure at the polymer-substrate interface which is required for practical applications. The peeling system consists of two micrometric tables X and Z moving at the same velocity V, this enabling to obtain a fixed point for observations of the peeling front 2,7,8 . The adhesive strip (adhesive and backing) is attached on the force transducer located on the vertical micrometric table moving in the Z-direction with velocity V. The substrate is located in the X-Y plane and moves in the X direction with velocity V. The whole set-up is located in a controlled chamber (fixed temperature T=20°C ± 0.1°C, and relative humidity 10% ± 2%). As the experiment is started, corresponding to simultaneous motion of the two micrometric tables, a transient regime is found which will lead to a stable regime after a certain time, depending on the geometry as well as the viscoelastic parameters of the adhesive.

The adhesive which was selected is a long molecular weight linear PDMS (Rhodia silicones, 47V 2500,000), its zero-shear viscosity is η 0 =2500 ± 100 Pa.s and its surface tension γ = 21 ± 1 mN/m at 20°C (measured by the pendant drop technique, Digidrop GBX, France). A more complete rheometrical study [START_REF] Kissi | [END_REF] (rotational rheometer RMS, cone-plate geometry) shows the following shear-rate dependence for this polymer (figure 1): This polymer has the advantage to present a large viscosity, followed by a strong shear-thinning behaviour at high shear rates, and to exhibit viscoelastic effects when the time scales are smaller than the relaxation time λ, which is the case (as will be shown later) for high peeling velocities.

λ, the longest relaxation time, can be found at the onset of decrease on the viscosity curve (figure 1), corresponding to a critical shear rate of about 0.3 s -1 , therefore λ =1/0.3 ≈ 3s.

The elongational properties of such a polymer have not been measured here, but do not exhibit strain hardening [START_REF] Mestadi | Caractérisation en élongation de polymères fondus et en solution : comparaison entre essais à force constante et à vitesse de déformation constante[END_REF] . This behavior was shown when pulling a PDMS sample at constant stretch rate (Ref. 18, stretch rates from 0.03s -1 to 3 s -1 ). The transient elongational viscosity undergoes a slow increase followed by a plateau (defining the elongational viscosity), but shows no strain hardening effects. On the contrary, hardening has been observed when using branched polydimethylsiloxanes [START_REF] Mestadi | Caractérisation en élongation de polymères fondus et en solution : comparaison entre essais à force constante et à vitesse de déformation constante[END_REF] at the highest velocity rates (around 3 s -1 ).

When peeling is achieved, at the smallest velocities, cohesive failure is possible, but the most general behaviour corresponds to interfacial failure, i.e. the adhesive is being detached from the substrate.

Surface energy measurements and surface treatment

In order to obtain the desired peeling regimes, different backings were used and only one substrate (HDPE). The free surface energies of all materials were determined following wetting measurements using the contact angle technique coupled with a vizualisation technique (Digidrop, GBX, France). Fluids with known surface energy components were used . Two kinds of free surface energies decompositions were used, the one based on the Owens-Wendt [START_REF] Owens | [END_REF] decomposition, as in equation ( 2) a , and the second one -equation (2) b -based on the acido-basic concept by van Oss et al. 20 (Lewis concept): This leads to the Dupré adhesion energy expression W a given by : ( )

P D γ γ γ + = (2) a AB LW γ γ γ + = (2)
P S P L D S D L L a γ γ 2 γ γ 2 cosθ 1 γ W + = + = (3) a ( )
+ - + + + = + = S - L S L LW S LW L L a γ γ 2 γ γ 2 γ γ 2 cosθ 1 γ W (3) b )
where θ is the wetting angle between the drop (L) and a substrate (S), and L γ is the liquid surface tension. The surface tension or free energy components of the liquids and the solids are denoted with a subscript L or S respectively, and the superscripts LW and AB are used for the van Oss decomposition 20 , whereas D and P are used for the Owens-Wendt method [START_REF] Owens | [END_REF] .

Four different liquids were used for the study, water, glycerol, formamide, and diiodomethane.

They span the whole range of fluids going from dispersive to polar liquids, which is useful in particular for the first decomposition (Owens-Wendt). Their components, as described previously [START_REF] Owens | [END_REF]20 , are shown in Table 1:

Acido-basic 20 Polar-dispersive [START_REF] Owens | [END_REF] From these measurements, it appears that the PDMS adhesive is more likely to develop affinities with respect to Stainless steel and PET, as compared with the substrate (HDPE). This is for this reason that such a substrate and backings were used. In fact, to obtain such data, we also had to use a primer for increasing the adhesion towards the PET backing. The primer which was used (typical thickness 20 µm, using a blade coating system) is an industrial one, containing acrylic copolymers filled with titanium dioxide and chloride charges. Its main effect is to increase surface roughness of the PET backing, as shown in figures 2a and 2b. The roughness is clearly increased by etching, as seen on the SEM photograph corresponding to the PET surface, after the primer was used.

To summarize this analysis, the systems used will tend to be in favour of an adhesive regime of failure at the interface between the adhesive and the HDPE substrate, and this is what is discussed next.

Peeling experiments

The peeling measurements were obtained at T=20°C using the peeling experiment described above [START_REF] Ravilly | Adhésion et pelage bidimensionnel des polymères[END_REF] . The influence of the following parameters has been studied: adhesive thickness, peeling velocity and backing rigidity. In figure 3, we present the peeling properties of the PDMS adhesive coated onto the HDPE substrate. adhesive regimes occurs at a certain critical velocity V c and will be discussed in the final part.

We will now pay more attention to the second regime, appearing in the velocity range 0.1 cm/s < V < 1 cm/s, i. The peeling curves of the different strips, corresponding to the three backings are shown in figure 6. Again, the velocity dependence is the same (typical slope 0.25) for the three adhesive strips.

Only in the case of the Polyester backing (PET), a cohesive branch was obtained at the lower velocities, whereas in the other cases, the only regime observed is the interfacial one. From this curve, we deduce the influence of the backing rigidity EI. Figure 7 shows that the dependence is a power law with a negative slope of -0.2, in the regime of velocities and thicknesses studied. This result might seem unusual, but we may note that it is in agreement with Bikerman's formula 21 . To sum up these results, we finally we obtain the dependence of the energy of restitution rate G in terms of the three parameters V, e, and 3 Eh .

( )

2 . 0 3 33 . 0 25 . 0 - ≈ Eh e V G (2(2)(2 ) (4)
We will now try to explain these results in the next part.

THEORETICAL PEELING MODEL FOR A POWER LAW FLUID

To propose an explanation of the results previously obtained, we consider figure 8, as the starting sketch representing the locus of failure in the adhesive regime. The adhesive is brought to the contact failure zone (point A) where it detaches from the substrate.

During such a motion, the flow of the adhesive can be considered, according to lubrication theory, to be a homogeneous flow with its major component u = u(z) e z , where e z is a unit vector.

According to lubrication theory, the z-component of the momentum equation is written by

z dx dp xz ∂ ∂ = - σ (5)
where p is the pressure and xz σ the relevant shear component. Equation ( 5) can be integrated

) ( ) ( x B z x A xz + - = σ (6) where 0 ) ( < - = dx dp x A
is the non-zero pressure gradient, and B(x) a function of x to be determined. We follow the analysis carried out in previous work 10 but we use a power-law relationship for the fluid [START_REF] Bird | Dynamic of polymeric liquids. I. Fluid Mechanics[END_REF] , i.e. . Accordingly, the solution of ( 6)-( 7) will be divided into two parts, to preserve the correct signs:

• z< h 0 (x) z x A x B dz du m n ) ( ) ( - =       - (8) a • z> h 0 (x) ) ( ) ( x B z x A dz du m n - =       (8) b
The solution of (5) can easily be obtained and the integration yields:

• z< h 0 (x) ) ( 1 1 1 ) ( 1 / 1 z C m Az B n A m z u n - + - +       - + = (9) a • z> h 0 (x) ) ( 1 1 1 ) ( 1 / 1 z C m B Az n A m z u n + + + +       - + = (9) b ) (z C - and ) (z C +
are integration constants to be determined.

Using the proper boundary conditions, i.e.,

V u = - ) 0 ( , V H u = + ) ( , ) ( ) ( 0 0 h u h u + - = and ) ( ) ( 0 0 h dz du h dz du + = - =0 (
this last one is satisfied because it corresponds to the critical line where

• γ =0), we obtain the unknown constants ) (z C - , ) (z C + and ) ( 0 x h : 1 1 2 1 1 1 ) ( ) ( + + -       + - = = n m AH n A m V z C z C (10) 2 ) ( ) ( 0 x H x h = (11)
We note here that the line for which the shear rate changes sign corresponds to the "mid-line"

2

) (x H
between the substrate and the backing. We next compute the flow rate Q:

∫ ∫ ∫ + + = = = - ) ( 2 / ) ( 2 / ) ( 0 ) ( 0 ) ( ) ( ) ( x H x H x H x H dz z u dz z u dz z u Q eV ( 12
)
After a few simplifications, the integration is used to obtain the pressure gradient: (13) This result can be checked with previous work 10 , where it was found that The pressure drop across a typical length scale L (see figure 8) is now expressed by: (14) This integral can only be evaluated when a typical function is used for H(x). In the present analysis, we use:

n n n H e H V H m dx dp x A       + - = - = 1 2 ) ( 2 2 ) ( 2
dx n n H e H V H m dx dx dp p n L L       + - - = = ∆ ∫ ∫ 1 2 ) ( 2 2 2 0 0
R x e x H 2 ) ( 2 + = ( 15
)
where R is a radius. This radius is in fact the initial radius of curvature R (for x=0), and can be measured in our experiments, as seen for example in figure 9. Further careful analyses of the shape of the backing confirms that this shape is in very good agreement with experimental data [START_REF] Ravilly | Adhésion et pelage bidimensionnel des polymères[END_REF] . Finally, equation ( 14) can be integrated formally, using Matlab™, and the result is found to yield the following scaling laws, provided that eR L > , which is satisfied in our experiments (typically R=2mm, e=80µm, and L=2mm, so eR

≈0.4 mm) e R e V m p n       ≈ ∆ (16)
Again, these results are checked with a previous analysis 10 where it was found that e R e V p η ≈ ∆ for a Newtonian adhesive (n=1, m=η). The influence of the shear-thinning index n is therefore demonstrated to act through the power n of a typical shear rate e V . Proceeding further, the pressure is assumed to match the force applied at the ends of the ribbon, after considering the geometry of a small beam element:

F R b = ∆p ( 17
)
where b is the bond width and F is the applied force measured in the experiments. The radius of curvature also appears and is taken to vary as

F EI R ≈
. Finally, we obtain:

EI b F e F EI e V m p n 2 / 3 4 / 1 1 ≈             ≈ ∆ (18)
This leads to the energy of restitution rate spent to peel the adhesive strip (using 3

2 3 bh I = ): ( ) 7 / 3 3 7 / ) 2 4 ( 4n/7 7 / 4 e V Eh m b F n+ ≈ (19)
This final result demonstrates the ability of the model to account for rheofluidification with index n, the case of the Newtonian fluid being recovered by setting n=1 and m=η (the Newtonian viscosity).

In our experiment, the velocity ranges from 10 -3 m/s < V < 10 -2 m/s, whereas the thickness is of the order of 100µm. The typical shear rate e V varies between 10 and 10 2 s -1 . This means, that, referring to figure 1, the viscosity behaviour is like

6 . 0 - • ≈ γ η m
, so n can be taken to be 4 . 0 ≈ n .

Inserting this into (19) leads to the relationship for the force per unit width:

( ) 43 . 0 3 51 . 0 0.23 e V Eh b F - ≈ (20)
The model is therefore quite accurate for predicting the velocity dependence but fails to describe the behaviour in terms of the backing rigidity and adhesive thickness. Still it is helpful for putting the basis of a more careful analysis presented next.

DISCUSSION

Cohesive-adhesive transition

We first investigate the transition between cohesive and adhesive failure modes in figure 3.

According to a previous study [START_REF] Lakrout | [END_REF] , elastic effects have been shown to play an important role in the deformation processes involved in probe-tack experiments, as suggested by the introduction of a Deborah number. At small Deborah numbers (De < 1), the viscous effects dominate, whereas for high Deborah numbers (De > 1), elasticity becomes important. Such effects (deformations) can be relevant here because mechanisms involved during probe-tack experiments are comparable to the ones in peel tests 24 . We will rather introduce the Weissenberg number W i =λV/e (λ = 3s, V is the velocity of peel, and e the adhesive thickness), as in our previous study 8 . This number is equivalent to the Deborah number described above [START_REF] Lakrout | [END_REF] . For the transition from cohesive to adhesive failure, inspection of figure 3 gives the following transition velocities V c = 0.5 10 -3 m/s, 1.5 10 -3 m/s, 4.0 10 -3 m/s corresponding to thicknesses of 40, 80, 160 µm. They correspond to the first unstable velocities of peel. In fact, in some cases, there is a wide region of instability. Such transition velocities can be related to the equivalent Weissenberg number. They correspond respectively to values of W i = 37.5, 56.2 and 75, slightly smaller than the ones found previously [START_REF] Lakrout | [END_REF] . According to this data, the transition velocity varies approximately with thickness (e) like a power law e 2/3 . This is in favor of the idea that the Weissenberg number cannot alone distinguish between the cohesive and adhesive regimes, but may come out in combination with another dimensionless parameter like one based on surface energies 8 . Further studies are still needed to provide such evidence. In any case, the values found for the Weissenberg number are typical of an elastic behavior, and they fall in the range of the ones indicated previously [START_REF] Lakrout | [END_REF] in the case of acrylic adhesives (between 100 and 1000 at the cohesive to adhesive transition). This enforces the fact that peel and tack experiments are clearly related.

Model for predicting interfacial failure

According to various authors, the peeling energy is closely related to the influence of the backing curvature 21,25 , because the flow induced within the adhesive generates stresses, which conversely modify the backing curvature changing again stresses inside the adhesive; finally an equilibrium is found with a complex interdependence of all the parameters, as just shown above. In practice, Bikerman 21 proposed with the following expression :

* 4 . 0       = E E h e b F σ (21)
Where 0 σ is a typical stress, and E* is the adhesive's Young modulus, when it is considered as a linear elastic solid. This expression also has the problem of the absence of velocity, and the wrong dependence on adhesive thickness (although better) and backing thickness. On the other hand, the dependence on the adhesive modulus E is rather accurate (power law -0.25 instead of -0.2 in the experiments). This formula is difficult to use here and we will rather rely on the analysis from the previous part, based on the following ideas.

1) The correct dependence in terms of the velocity V (shown to be close to 0.25) has shown the relevance of the power law index n, which should be used for modelling adhesive stresses and viscosity.

2) Dimensional analysis 8 shows the importance of the relevant numbers. The first one is the Weissenberg number for viscoelasticity i W . Indeed, simple models using either viscous or elastic adhesives fail to describe the problem. The Weissenberg number W i has been defined previously as :

e V W i λ = (22)
ξ is the second dimensionless number accounting for the competition between curvature effects and viscous stresses. where σ is a typical stress within the adhesive. Here a typical stress [START_REF] Ravilly | Adhésion et pelage bidimensionnel des polymères[END_REF] is

n n e V m m       = = • γ σ , therefore 3 3 Eh e e V m n       = ξ (23)
3) Finally the force per unit width G=F/ l will depend on these numbers in a combined manner, and we may look for a solution of the kind :

a Wi l F G ξ ≈ = (24)
Using a=0.2 takes care of the backing rigidity influence, and we are left with the effect of the velocity V and thickness effects. Choosing the velocity V, we need to insure from ( 4) and ( 24)

that 25 . 0 = + b an
. Since n=0.4 from figure 1, we find that b=0.13. The power law dependence in terms of the adhesive thickness e is deduced to be e (3-n)a-b = e 0.39 , which gives a very nice comparison with experiments (slope 0.33). Finally, we find :

( ) 2 . 0 3 39 . 0 25 . 0 13 . 0 2 . 0 3 3 13 . 0 2 . 0 - =                         ≈ ≈ = Eh e V k e V Eh e e V m W l F G n i λ ξ (25)
The dimensionless coefficient k in front of (25) has been found experimentally [START_REF] Ravilly | Adhésion et pelage bidimensionnel des polymères[END_REF] to be around k=500. This analysis has not taken into account the surface energy properties, since one substrate (HDPE) and one adhesive only were used, therefore (25) does not contain the surface energy parameters. Following the work of Gent and Schultz 12 and other authors 13,14,15 , we suggest a possible extension of the model in terms of the surface parameters, in particular the Dupré work of adhesion W a :

) 1 ( b i a a W k W l F G ξ + = = (26)
The parameters k, a and b are very likely to be different depending on the adhesives. In our case, for the present adhesive (PDMS), in the range of parameters used (velocity of peel, thickness, backing rigidity), we found that k≈500, a=0.2 and b=0.13. Note that the Dupré work of adhesion W a might, in some cases, be replaced by other modified expressions, as suggested in previous works 5,13 . To summarize, this analysis is based on the shear rheological properties of the adhesive only and is therefore relevant to the linear PDMS polymer studied here, but would need to be modified when elongational effects become relevant (branched polymer adhesives [START_REF] Lakrout | [END_REF] , or strain hardening materials, as in previous studies 2,[7][8] ). This would probably affect the values of the parameters k, a and b determined above.

CONCLUSIONS

In the present analysis, it has been shown that modelling the peeling behaviour of viscoelastic adhesives is still a challenge. After obtaining peeling data corresponding to a variety of parameters, it has been shown that the competition between backing rigidity and viscous behaviour is of importance, as shown in previous studies 10,21 , and leads to the introduction of a dimensionless parameter ξ, modified to take into account the shear-thinning behaviour of the adhesive. A detailed analysis showed indeed that the peeling force model predicts very well the velocity dependence when a power-law fluid dependence is used. This non-Newtonian effect is typical of the most common adhesives.

On the other hand, to predict correctly the dependence of the peel force in terms of adhesive thickness and backing rigidity, an empirical model has been proposed, based on the use of another dimensionless number for viscoelasticity, the Weissenberg number i W . Although the peel force depends slightly on i W (small power law exponent), it is necessary to introduce it in order to derive a correct description of the results for viscoelastic adhesives 5,13 .

Figure 1 .

 1 Figure 1. Shear rheometry of the PDMS adhesive polymer (T= 20 °C). Determination of the longest relaxation time of the polymer gives approximately λ = 3 s.

  b where the surface tension γ has two components, a dispersive one ( D γ ) and a polar one ( P γ ) in the first case, and a Lifshitz-van der Waals ( LW γ ) one and an acido-basic component ( AB γ ) in the second case. The AB γ component (acido-basic) is defined in terms of the electron donator (Lewis base, - γ ) or acceptor (Lewis acid, + γ ) character of the fluid or solid and is written as

Figure 2 .

 2 Figure 2. PET surface visualized with a SEM (X200). a) before treatment b) after treatment

1 Figure 3 .

 13 Figure 3. Peeling curve. Influence of the peeling velocity and adhesive thickness (T= 20 °C, PET backing). Cohesive to adhesive failure transition corresponds to changing from open to filled symbols

Figure 4 .Figure 5 .

 45 Figure 4. Photographs of the peeling front (PET backing, adhesive thickness e=80 µm). a) cohesive failure with formation of regularly spaced filaments, V=0.1 cm/s. b) adhesive two-dimensional peeling regime, V=0.75 cm/s.

Figure 6 .

 6 Figure 6. Peeling curve. Influence of the peeling velocity and backing rigidity (T= 20 °C, e=80µm)

2 Figure 7 .

 27 Figure 7. Influence of the backing rigidity for different velocities (T= 20 °C, e=80 µm).

Figure 8 .

 8 Figure 8. Sketch of the adhesive regime of failure. Z=H(x) is the backing shape. u(z) is the xcomponent of the velocity field. The velocity gradient dz du is > 0 or < 0 depending on z. z=h 0 (x) is the critical line where 0 = dz du . L is a typical length scale of the region of deformation.

γ

  is the shear rate (s) (taken >0 here), n is the rheofluidification fraction exponent, typically 0 < n < 1, and m is a constant. This will allow to obtain different adhesive behaviours according to the power-law index n. Depending on the shear rate, the viscosity curve n≈1 at low shear rates, and a value of n of the order n ≈ 0.4 at the higher shear rates, by inspection of figure1.

  the Newtonian behaviour corresponding to the limiting case m=η and n=1.

Figure 9 .

 9 Figure 9. Shape of backing showing initial radius of curvature R (stainless steel, 2h=10 µm).V=10 -2 m/s. T=20°C

  b

Table 1 :

 1 Liquid components as given by van Oss et al.20 and Owens-Wendt[START_REF] Owens | [END_REF] (mN/m).

			γ	LW L	γ	+	γ	-	γ	P	γ	D
	Water	72.8	21.8	25.5	25.5	51	21.8
	Glycerol (99% pure)	64	34	3.9	57.4	30	34
	Formamide (99.5% pure)	58	39	2.3	39.6	19	39
	Diiodomethane ( 98% pure)	508	50.8	0	0	0	50.8
	Contact

Liquids L γ angles have been measured for each liquid on the two different backings (stainless steel and PET) and also for the HDPE substrate. Table 2 gives the values of the Dupré adhesion energies between a substrate and the PDMS adhesive, obtained using the two methods of decomposition, and follow equations (3) a and (3) b . S γ (van Oss et al.)

Table 2 :

 2 Free energies S γ (mN/m) and Dupré adhesion energies W a (mN/m) using the two methods.

Table 3 .

 3

	Backing type	Thickness (2h)	Rigidity (EI)
	PET	23 µm	3.8 10 -7 Pa.m 4
	stainless Steel	10 µm	1 10 -6 Pa.m 4
	stainless Steel	20 µm	7.1 10 -6 Pa.m 4

Table 3 :

 3 Different backing characteristics. E is Young's modulus, 3

	I =	2 3 bh	, b=strip width,

ACKNOWLEDGMENTS

The authors are grateful to N. El Kissi for providing the PDMS adhesive as well as its rheometrical properties.