J Biteau

E Prandini

L Costamante

M Lemoine

P Padovani

E Pueschel

E Resconi

F Tavecchio

A Taylor

A Zech

Typeset using L A T E X twocolumn style in AASTeX62 tweeked for nat

Keywords: acceleration of particles, astroparticle physics, cosmology: diffuse radiation, galaxies: jets, radiation mechanisms: non-thermal

The most powerful persistent accelerators in the Universe are jetted active galaxies. Blazars, galaxies whose jets are directed towards Earth, dominate the extragalactic γ-ray sky. Still, most of the highest-energy particle accelerators likely elude detection. These extreme blazars, whose radiated energy can peak beyond 10 TeV, are ideal targets to study particle acceleration and radiative processes, and may provide links to cosmic rays and astrophysical neutrinos. The growing number of extreme blazars observed at TeV energies has been critical for the emergence of γ-ray cosmology, including measurements of the extragalactic background light, tight bounds on the intergalactic magnetic field, and constraints on exotic physics at energies inaccessible with human-made accelerators. Tremendous progress has been achieved over the past decade, which bodes well for the future, particularly with the deployment of the Cherenkov Telescope Array.

INTRODUCTION

The luminosity of most galaxies is dominated by thermal emission from stars. For the remaining 1%, emission from the active galactic nucleus (AGN), which hosts a super-massive black hole (10 6 -10 10 M ), can outshine the billions of stars in the galaxy [START_REF] Padovani | Active galactic nuclei: what's in a name?[END_REF]. Up to ∼ 10% of AGN develop two-sided relativistic jets that emit nonthermally over the whole electromagnetic spectrum [START_REF] Urry | Unified Schemes for Radio-Loud Active Galactic Nuclei[END_REF]. The emitting region in the jet moves away from the super-massive black hole with a relativistic bulk velocity that, for small viewing angles (θ < 10 -15 • ), shifts the luminosity of the source to higher frequencies by a bulk Doppler factor δ D = O [START_REF] Giommi | Detection of exceptional X-ray spectral variability in the TeV BL Lac 1ES 2344+514[END_REF], and amplifies the bolometric emission by δ 4 D . Such an AGN is called a blazar. The broad-band spectral energy distribution (SED) of blazars is characterized by two distinctive humps. The first hump, peaking at infrared to X-ray wavelengths, is commonly explained as synchrotron emis-sion from electrons accelerated in the jet. The second hump, peaking above MeV energies, is often attributed to inverse-Compton scattering, possibly of the same electrons on their own synchrotron emission (synchrotron self-Compton or SSC model, e.g., [START_REF] Tavecchio | TeV BL Lac objects at the dawn of the Fermi era[END_REF]). The peak frequency of each hump, ν, arises from a break in the spectrum of the emitting particles, probing the comparative strength of acceleration, cooling, and escape mechanisms.

Blazars form a continuous sequence from low-to highenergy peaked objects, with an overall correlation of the two peak frequencies. The end of the sequence is dominated by high-frequency-peaked BL Lac objects (HBL, [START_REF] Padovani | The connection between x-rayand radio-selected BL Lacertae objects[END_REF]), i.e., blazars with weak emission lines and radiatively inefficient accretion disks. HBLs are characterized by synchrotron emission peaking at νx 10 15 Hz (∼ 4 eV), with the most extreme blazars showing larger values by at least two orders of magnitude [START_REF] Ghisellini | Extreme blazars[END_REF].

Standard models predict a γ-ray peak below 1 TeV for HBLs, either because of the limited maximum energy of the electrons, traced by νx , or of a reduced scattering cross-section (Klein-Nishina regime). The discovery of extreme blazars with a γ-ray peak up to 10 TeV therefore came as a surprise. Only 3 out of 10 extreme blazars with TeV emission were detected in the GeV range a decade ago [START_REF] Tavecchio | TeV BL Lac objects at the dawn of the Fermi era[END_REF]. Their intrinsic properties were bound by upper limits on absorption by the extragalactic background light (EBL, [START_REF] Aharonian | A low level of extragalactic background light as revealed by γ-rays from blazars[END_REF]). A new window on extreme blazars was opened by the growth of γ-ray astronomy. Observational progress promoted not only developments of elaborate acceleration and radiative schemes but also the investigation of ties with cosmic magnetism, ultrahigh-energy cosmic rays (UHECRs), and physics beyond the Standard Model.

EXTREME OBSERVATIONAL PROPERTIES

Multi-wavelength observations of extreme blazars

Extreme blazars come in two flavours: extremesynchrotron sources show a synchrotron peak energy hν x ≥ 1 keV (2.4 × 10 17 Hz); extreme-TeV sources have a γ-ray peak energy hν γ ≥ 1 TeV (2.4 × 10 26 Hz) (e.g., [START_REF] Costamante | Extreme synchrotron BL Lac objects. Stretching the blazar sequence[END_REF][START_REF] Costamante | The NuSTAR view on hard-TeV BL Lacs[END_REF]). This is revealed by a hard spectrum in the soft X-ray band with photon index Γ x < 2, or in the 0.1 -1 TeV band, Γ γ < 2. The intrinsic spectrum is recovered from the observed spectrum by accounting for absorption, namely photoelectric absorption in intervening gas for X-rays and γ-EBL interactions at GeV-TeV energies (see Sec. 4.1).

In the optical band, measurements of the flux and polarization of extreme blazars are generally hampered by the thermal emission of the giant elliptical host galaxy. These sources show radio properties similar to other HBLs, but their flux is generally very low. Indeed, a high X-ray to radio flux ratio is a very effective way to select extreme-synchrotron sources among normal HBLs (see Sec. 2.2). The combination of an extreme-synchrotron nature with a hard GeV spectrum appears to be a multiwavelength marker favoring the selection of extreme-TeV sources.

Extreme blazars were discovered in 1996-97, with BeppoSAX observations of flares from Mkn 501 [START_REF] Pian | BeppoSAX Observations of Unprecedented Synchrotron Activity in the BL Lacertae Object Markarian 501[END_REF] and 1ES 2344+514 [START_REF] Giommi | Detection of exceptional X-ray spectral variability in the TeV BL Lac 1ES 2344+514[END_REF]. Mkn 501 reached synchrotron peak frequencies hν x > 100 keV, with an increase of the luminosity by a factor of 20 in a few days and a typical "harder-when-brighter" behaviour (Fig. 1, left). BeppoSAX also discovered in 1999 the first example of extreme source in low or quiescent state, with 1ES 1426+428 displaying a hard and straight power-law spectrum over three decades in energy [START_REF] Costamante | Extreme synchrotron BL Lac objects. Stretching the blazar sequence[END_REF]. With ob-served hν x 100 keV, Mkn 501 and 1ES 1426+428 can be considered prototypical of the extreme-synchrotron subclass.

The first extreme-TeV blazars were discovered in 2006 with H.E.S.S. [START_REF] Aharonian | A low level of extragalactic background light as revealed by γ-rays from blazars[END_REF]. The intrinsic spectra of 1ES 1101-232 and H 2356+304 were unusually hard even after accounting for absorption with the lowest possible EBL intensity, locating the γ-ray peak definitively above 1-3 TeV. With the present knowledge of the EBL, eleven blazars with measured redshift can be classified as extreme-TeV objects, as listed in Table 1 (see also TeVCat [START_REF] Wakely | An online catalog for Very High Energy Gamma-Ray Astronomy[END_REF] and references therein). Three other blazars have shown extreme-TeV properties but only temporarily, namely Mkn 501, 1ES 1727+502, and 1ES 1426+428. Extreme-TeV properties were also found in IC 310, a peculiar nearby AGN (z = 0.0189) whose jet might be misaligned by 10 -20 • from the line of sight [START_REF] Ahnen | First multi-wavelength campaign on the gamma-ray-loud active galaxy IC 310[END_REF]. The record for the highest γ-ray peak energy observed is held by the prototypical extreme-TeV blazar 1ES 0229+200 (see Fig. 1), with hν γ 10 TeV and an intrinsic spectrum with Γ γ 1.5 [START_REF] Aharonian | New constraints on the mid-IR EBL from the HESS discovery of VHE γ-rays from 1ES 0229+200[END_REF].

Most extreme-TeV sources appear steady over years at TeV energies, although large statistical uncertainties make it difficult to rule out flux variations such as those seen in X-rays over similar timespans. The only firm evidence was found in 1ES 1218+304, with a fast flare over a few days reaching ∼ 20% of the Crab nebula flux [START_REF] Acciari | Discovery of Variability in the Very High Energy γ-Ray Emission of 1ES 1218+304 with VERITAS[END_REF]. There are also indications of a factor of 2 -3 variations in 1ES 0229+200 on year timescales [START_REF] Aliu | A Three-year Multi-wavelength Study of the Very-high-energy γ-Ray Blazar 1ES 0229+200[END_REF]. In both cases, the TeV spectrum remained hard, indicating no change in the extreme-TeV character of these objects. On the contrary, during a long active phase in 2012, Mkn 501 showed both synchrotron and γ-ray peaks shifted from normal to extreme energies, by ∼ 3 and ∼ 1 decade in energy respectively [START_REF] Ahnen | Extreme HBL behavior of Markarian 501 during 2012[END_REF]. The synchrotron peak of 1ES 1727+502 similarly shifted between 2011 and 2013 [START_REF] Archambault | VERITAS Detection of γ-Ray Flaring Activity From the BL Lac Object 1ES 1727+502 During Bright Moonlight Observations[END_REF].

The relationship between extreme-synchrotron and extreme-TeV blazars is not well established. There are 24 extreme blazars with firm redshift and published TeV spectrum (see Table 1), all of which are now detected at GeV energies by Fermi -LAT [START_REF]Fermi Large Area Telescope Fourth Source Catalog[END_REF]. Twenty three of these are extreme-synchrotron sources, at least half of which (13/23) are also extreme-TeV blazars. On the other hand, thirteen of the fourteen known extreme-TeV blazars are also extreme-synchrotron in same-epoch observations or in other epochs. This suggests that extreme-TeV sources may have a greater tendency to display extreme-synchrotron behaviour at some point in time than the other way round. b) display the SEDs of two extreme-synchrotron blazars, during short-lived large flares and long-lasting quiescent states, respectively. The SED of an extreme-TeV blazar is shown in panel c). Observed γ-ray spectra are corrected for EBL absorption [START_REF] Franceschini | The extragalactic background light revisited and the cosmic photon-photon opacity[END_REF]. Nearlycontemporaneous historical data are shown with the same colour and labelled accordingly. Grey points correspond to archival data. Error bars denote 1 σ statistical uncertainties. Arrows denote upper limits at the 95% confidence level (CL). Guideline SSC models are presented as dash-dotted lines. Dotted lines show the host-galaxy emission, modelled with the template spectrum of a giant elliptical galaxy [START_REF] Silva | Modeling the Effects of Dust on Galactic Spectral Energy Distributions from the Ultraviolet to the Millimeter Band[END_REF], scaled to match the magnitude of the host galaxy [START_REF] Scarpa | The Hubble Space Telescope Survey of BL Lacertae Objects. I. Surface Brightness Profiles, Magnitudes, and Radii of Host Galaxies[END_REF]. Data and models are from [START_REF] Pian | BeppoSAX Observations of Unprecedented Synchrotron Activity in the BL Lacertae Object Markarian 501[END_REF][START_REF] Aharonian | The time averaged TeV energy spectrum of MKN 501 of the extraordinary 1997 outburst as measured with the stereoscopic Cherenkov telescope system of HEGRA[END_REF][START_REF] Tavecchio | Theoretical Implications from the Spectral Evolution of Markarian 501 Observed with BeppoSAX[END_REF] for Mkn 501, [START_REF] Ghisellini | Low power BL Lacertae objects and the blazar sequence. Clues on the particle acceleration process[END_REF] for 1ES 1426+428 and [START_REF] Costamante | The NuSTAR view on hard-TeV BL Lacs[END_REF] for 1ES 0229+200.

As illustrated in Fig. 1, the emerging picture is that there are three distinct extreme behaviours:

1. becoming extreme during large flares, when both peaks shift to higher energies (Mkn 501-like). These objects revert back to their standard HBL state;

2. showing a steady, hard synchrotron spectrum up to 10 -100 keV (1ES 1426+428-like), which is not accompanied by a persistently hard TeV spectrum;

3. showing a persistently hard γ-ray spectrum with a peak above several TeV, which remains mostly unchanged across flux variations (1ES 0229+200like). Their synchrotron spectrum tends to peak in the X-ray band.

Catalogues and population studies

Population studies of extreme blazars are currently restricted to the extreme-synchrotron subclass, due to the lack of an unbiased extragalactic survey at TeV energies.

The largest catalogue of extreme blazars to date is the 3HSP, which builds on the 1WHSP and the 2WHSP (see [START_REF] Chang | The 3HSP catalogue of Extreme High Synchrotron Peaked Blazars[END_REF] and references therein). The 1WHSP catalogue assembled a large sample of HBLs starting from the ALLWISE infrared survey and applying further restrictions on their infrared slope, as well as on their infrared/radio and infrared/X-ray flux ratios. The 2WHSP abandoned the infrared slope criterion, as it excluded sources dominated by the host galaxy. The 3HSP catalogue complemented the 2WHSP sample with Fermi -LAT γ-ray sources with hard spectra (Γ γ < 2) and with objects with a high X-ray to radio flux ratio, thus selecting HBLs. The final sample includes 2,011 HBLs, with redshift information for 88% of them (including photometric estimates), out of which 199 qualify as extreme-synchrotron blazars. All presently known extreme-TeV blazars are part of the 3HSP.

Fermi -LAT has now detected half of the ∼ 340 3HSP sources with νx ≥ 10 17 Hz [START_REF] Paliya | Fermi-LAT Stacking Analysis Technique: An Application to Extreme Blazars and Prospects for their CTA Detection[END_REF]. Only a sub-sample of the studied 3HSP sources, with a higher νx and harder Γ γ , constitute the extreme-TeV blazar population, whose size and properties remain to be determined.

The 3HSP catalogue is flux-limited in the radio and X-ray bands for sources with νx > 10 16 Hz. Radio number counts are displayed in Fig. 2, together with the number counts of other BL Lac samples from the Deep X-ray Radio Blazar Survey [START_REF] Padovani | The Deep X-Ray Radio Blazar Survey. III. Radio Number Counts, Evolutionary Properties, and Luminosity Function of Blazars[END_REF]. The slopes of the subsample distributions are similar, implying that the fraction of high-ν x blazars is roughly independent of radio Radio number counts of extremesynchrotron blazars and of different samples of BL Lacs. Green squares denote BL Lacs from the Deep X-Ray Radio Blazar Survey (DXRBS), red trapezoids the HBLs from DXRBS, blue circles the HBLs from 3HSP, and orange circles the extreme-synchrotron blazars from 3HSP. Error bars denote 1 σ statistical uncertainties. The solid line represents the number counts predicted from the luminosity function of BL Lacs [START_REF] Urry | Unified Schemes for Radio-Loud Active Galactic Nuclei[END_REF]. Figure adapted from [START_REF] Chang | The 3HSP catalogue of Extreme High Synchrotron Peaked Blazars[END_REF], courtesy of Yu-Ling Chang.

flux. Extreme-synchrotron blazars represent about 10% of HBLs, which in turn correspond to 10% of all BL Lacs.

Above a radio flux of 3.5 mJy at 1.4 GHz, the surface density of ∼ 4.5 × 10 -3 deg -2 inferred for extreme blazars corresponds to a total number of extremesynchrotron sources over the sky of ∼ 200. The maximum observed radio luminosity tends to be lower for extreme blazars than for regular HBLs. This is consistent with the inferred anti-correlation between power and ν often denoted as the "blazar sequence" [START_REF] Ghisellini | The Fermi blazar sequence[END_REF], which can also be explained by selection effects [START_REF] Giommi | A simplified view of blazars: clearing the fog around long-standing selection effects[END_REF]. The rareness of extreme-synchrotron sources suggests the latter, as these sources, which are at the low end of the luminosity function, would otherwise be expected to represent the most common subclass along the blazar sequence.

THE CHALLENGE OF MODELING EXTREME BLAZARS

The simplest one-zone SSC models generally represent well the stationary SED of most HBLs with hν γ < 1 TeV [START_REF] Tavecchio | TeV BL Lac objects at the dawn of the Fermi era[END_REF], including purely extreme-synchrotron sources. This suggests that extreme-synchrotron sources are the high-energy tail of the blazar population. On the other hand, the origin of the extreme-TeV emission is still unknown, as it presents two essential challenges:

1. explaining the peak of radiation at TeV energies: hν γ > 1 TeV.

2. explaining the hard intrinsic spectrum of the component radiated at sub-TeV energies: Γ γ < 2.

A hard intrinsic spectrum at TeV energies, F ν /ν ∝ ν -Γγ with Γ γ 1.5, typically implies a hard accelerated particle spectrum, dN/dγ ∝ γ -p with spectral index p < 2, so that most of the energy is carried by the highest-energy particles, an unusual case in astrophysics. The spectral index derives from a competition between energy gains and escape or energy losses in the acceleration region. In shock acceleration, this competition leads to spectral indices p 2 ( [START_REF] Blandford | Particle acceleration at astrophysical shocks: A theory of cosmic ray origin[END_REF]; [START_REF] Sironi | Relativistic Reconnection: An Efficient Source of Non-thermal Particles[END_REF] for relativistic shocks). Additional effects, such as non-linear backreaction of the accelerated particles, could harden the spectra to p < 2. Both p > 2 and p < 2 appear to be possible in other acceleration scenarios, e.g., turbulent acceleration [START_REF] Schlickeiser | Cosmic-Ray Transport and Acceleration. I. Derivation of the Kinetic Equation and Application to Cosmic Rays in Static Cold Media[END_REF], shear acceleration (e.g., [START_REF] Rieger | An Introduction to Particle Acceleration in Shearing Flows[END_REF]), or reconnection (e.g., [START_REF] Kagan | Relativistic Magnetic Reconnection in Pair Plasmas and Its Astrophysical Applications[END_REF]), since energy gains and loss rates depend on additional parameters. Ab-initio reconnection simulations have in particular now shown hard particle spectra for a large ratio of magnetic to rest-mass energy density [START_REF] Kagan | Relativistic Magnetic Reconnection in Pair Plasmas and Its Astrophysical Applications[END_REF].

The observations of most blazars are matched by phenomenological models, which leave the acceleration scenario unspecified and fit the environmental parameters and the accelerated particle spectrum to reproduce SEDs. These models are separated into two classes: leptonic for electrons and positrons, hadronic for protons and nuclei.

Leptonic scenarios

In simple one-zone SSC models, TeV radiation results from inverse-Compton scattering of electrons or pairs with comoving-frame energy e . A peak emission beyond 1 TeV imposes δ D e > 1 TeV in the Klein-Nishina regime, which implies high Lorentz factors for the electrons, γ e = e /m e c 2 > 2×10 5 × (δ D /10) -1 . Both the high νγ and hard Γ γ of extreme-TeV blazars are matched by such models provided the electron distribution shows a minimum Lorentz factor with a sufficiently large value, sometimes up to γ min 10 4 -10 5 (e.g., [START_REF] Katarzyński | Hard TeV spectra of blazars and the constraints to the infrared intergalactic background[END_REF]). These models require an unusually low radiative efficiency and conditions out of equipartition by several orders of magnitude. A sub-TeV spectrum as hard as Γ γ = 2/3 can be obtained in an environment with a very weak magnetic field (B 1 mG) where spectral softening due to synchrotron cooling is reduced.

A different approach within the leptonic framework considers additional inverse-Compton components from external photon fields. Models with a sheath surrounding an inner jet [START_REF] Ghisellini | Structured jets in TeV BL Lac objects and radiogalaxies. Implications for the observed properties[END_REF][START_REF] Chhotray | On radiative acceleration in spine-sheath structured blazar jets[END_REF] struggle to reproduce a high νγ , due to the intense target photon field. However, up-scattering of photons from the broad-line region in a compact emission zone [START_REF] Lefa | Formation of Very Hard Gamma-Ray Spectra of Blazars in Leptonic Models[END_REF] or from the cosmic microwave background (CMB) in the extended kpc-jet [START_REF] Böttcher | The Hard VHE γ-Ray Emission in High-Redshift TeV Blazars: Comptonization of Cosmic Microwave Background Radiation in an Extended Jet?[END_REF] could produce hard spectra up to TeV energies. These scenarios require either a sufficiently luminous broadline region, which is not expected for extreme blazars and other BL Lacs, or a very energetic particle distribution over kpc scales. The latter would lead to steady TeV emission over thousands of years, in contradiction with flux variations detected in 1ES 1218+304.

The most successful leptonic models applied to extreme-TeV blazars thus appear to be simple SSC models that involve electron distributions with either a large minimimum Lorentz factor, γ min 1, or hard particle spectra, p < 2, as well as a magnetic field strength well below equipartition [START_REF] Lefa | Formation of Very Hard Gamma-Ray Spectra of Blazars in Leptonic Models[END_REF][START_REF] Tavecchio | The hard TeV spectrum of 1ES 0229+200: new clues from Swift[END_REF]. As an example, the model for 1ES 0229+200 in Fig. 1 and Fig. 3 assumes a moderate γ min = 100, a very hard particle spectrum with index p = 1.4, a high Doppler factor δ D = 50 and a low magnetic field of 2 mG. The electron energy density dominates over the magnetic one by a factor of ∼ 10 5 .

The requirement of weak magnetization that limits spectral softening from radiative cooling appears to disfavour reconnection scenarios, which may otherwise produce high γ min values (e.g., [START_REF] Tavecchio | The hard TeV spectrum of 1ES 0229+200: new clues from Swift[END_REF]). Stochastic acceleration could result in narrow pseudo-Maxwellian particle distributions with high peak energies (e.g., [START_REF] Tramacere | Stochastic Acceleration and the Evolution of Spectral Distributions in Synchro-Self-Compton Sources: A Self-consistent Modeling of Blazars' Flares[END_REF]), although a magnetic field well below equipartition implies a slow acceleration process in this case.

(Lepto-)hadronic models

Typical hadronic scenarios for extreme blazars are based on the co-acceleration of protons and electrons and attribute the TeV emission to proton synchrotron radiation or to the decay of pions from pγ interactions, possibly mixed with SSC emission from secondary pairs (e.g., [START_REF] Cerruti | A hadronic origin for ultra-high-frequency-peaked BL Lac objects[END_REF]). Proton synchrotron scenarios require ultra-high-energy particles with p > 10 19 eV × (B /100 G) -1/2 in a strong comoving-frame magnetic field, B [START_REF] Aharonian | TeV gamma rays from BL Lac objects due to synchrotron radiation of extremely high energy protons[END_REF]. Mixed models propose instead an energy budget dominated by the kinetic energy of protons. Such models require hard particle injection spectra, with p from 1.3 to 1.7, as well as large jet energetics, typically close to the Eddington limit of the central black hole.

If extreme blazars accelerate very-high-energy cosmic rays, the observed TeV emission might even result from secondary radiation produced outside the source, through an electromagnetic cascade triggered by photopion or photo-pair production on the EBL and CMB (e.g., [START_REF] Murase | Blazars as Ultra-high-energy Cosmic-ray Sources: Implications for TeV Gamma-Ray Observations[END_REF][START_REF] Essey | Secondary Photons and Neutrinos from Cosmic Rays Produced by Distant Blazars[END_REF][START_REF] Taylor | Extragalactic magnetic fields constraints from simultaneous GeV-TeV observations of blazars[END_REF][START_REF] Dzhatdoev | Electromagnetic cascade masquerade: a way to mimic γ-axion-like particle mixing effects in blazar spectra[END_REF]). The original version of this scenario assumed protons or nuclei with energies ∼ 10 16 eV, well below the ankle of the UHECR spectrum (at a few 10 18 eV). However, nuclei at these energies are deflected Figure 3. Phenomenological models of the observed SED of the extreme blazar 1ES 0229+200. γ-ray data are not corrected for EBL absorption. Error bars denote 1 σ statistical uncertainties. Arrows denote upper limits at the 95% CL. Representative leptonic (SSC, [START_REF] Costamante | The NuSTAR view on hard-TeV BL Lacs[END_REF]) and hadronic (proton synchrotron, [START_REF] Cerruti | A hadronic origin for ultra-high-frequency-peaked BL Lac objects[END_REF]) models are shown as black and magenta lines, respectively. The cyan line covering only the γ-ray range depicts the external cascade model [START_REF] Murase | Blazars as Ultra-high-energy Cosmic-ray Sources: Implications for TeV Gamma-Ray Observations[END_REF]. The orange dashed line shows the emission from the host galaxy.

by magnetic fields associated to structures of the cosmic web (voids, clusters, filaments, with magnetic fields up to 10 nG), which broadens the beam and increases the luminosity required to reproduce the observed γray spectra [START_REF] Tavecchio | On the hadronic cascade scenario for extreme BL Lacs[END_REF]. Such models predict slower variability than that observed, although synchrotron radiation from secondary pairs in magnetic fields extending on Mpc scales could account for variability down to year timescales [START_REF] Oikonomou | Synchrotron pair halo and echo emission from blazars in the cosmic web: application to extreme TeV blazars[END_REF].

As an example, Fig. 3 shows a one-zone proton synchrotron model and an external cascade model applied to 1ES 0229+200. The proton synchrotron model requires a much larger magnetic field (B 20 G) than the leptonic model, a comparable value for γ min 100 and a smaller Doppler factor, δ D 30. The particle spectra are again very hard and the considerable energy of the protons leads to a jet power at the Eddington limit.

This illustrative proton synchrotron model predicts a peak neutrino flux of ∼ 10 -15 erg cm -2 s -1 around 10 19 eV. Such fluxes are beyond the reach of currentgeneration neutrino observatories. On the other hand, the recent indication of a link between a neutrino track event and the blazar TXS 0506+056 [START_REF]Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922[END_REF][START_REF] Aartsen | Neutrino emission from the direction of the blazar TXS 0506+056 prior to the IceCube-170922A alert[END_REF], which is not an extreme source, can be successfully modelled if a sub-dominant component of the γ-ray emission arises instead from pγ or pp interactions [START_REF] Gao | Modelling the coincident observation of a high-energy neutrino and a bright blazar flare[END_REF][START_REF] Cerruti | Leptohadronic single-zone models for the electromagnetic and neutrino emission of TXS 0506+056[END_REF][START_REF] Keivani | A Multimessenger Picture of the Flaring Blazar TXS 0506+056: Implications for High-energy Neutrino Emission and Cosmic-Ray Acceleration[END_REF][START_REF] Liu | Hadronuclear interpretation of a high-energy neutrino event coincident with a blazar flare[END_REF]. These two hadronic channels are not expected to dominate the emission of extreme-TeV blazars, but other classes of the blazar population have been proposed to contribute to the neutrino and cosmic-ray background up to the ankle (e.g., [START_REF] Tavecchio | Structured Jets in BL Lac Objects: Efficient PeV Neutrino Factories?[END_REF][START_REF] Padovani | A simplified view of blazars: the neutrino background[END_REF]).

Whether AGN jets can accelerate UHECRs above the ankle remains unresolved. Interestingly, the high νx of extreme sources suggests that they are the most efficient accelerators of the AGN population. Neglecting energy losses, the ratio of the acceleration timescale, t acc , to the gyration time, t L , is constrained by the peak synchrotron frequency in the comoving frame, as t acc /t L 150 MeV/hν x [START_REF] Guilbert | Spectral and variability constraints on compact sources[END_REF][START_REF] Arons | Pulsar Wind Nebulae as Cosmic Pevatrons: A Current Sheet's Tale[END_REF]. Therefore, the higher ν x , the smaller t acc /t L . If this property can be extrapolated to ultra-high energies, faster acceleration points to a larger maximum energy in extreme blazars than in other AGNs [START_REF] Hillas | The Origin of Ultra-High-Energy Cosmic Rays[END_REF]. This seems in line with phenomenological models of the UHECR spectrum and composition observables above the ankle, which suggest particle spectra with p < 1 escaping from the sources [START_REF] Aab | Depth of maximum of air-shower profiles at the Pierre Auger Observatory. II. Composition implications[END_REF], or p 1.5 -2 for source populations with a negative evolution [START_REF] Taylor | Indications of negative evolution for the sources of the highest energy cosmic rays[END_REF], as inferred for HBLs and in particular extreme blazars [START_REF] Chang | The 3HSP catalogue of Extreme High Synchrotron Peaked Blazars[END_REF][START_REF] Ajello | The Cosmic Evolution of Fermi BL Lacertae Objects[END_REF].

At even higher energies, interactions with the EBL and the CMB constrain the sources of UHECRs at ∼ 10 20 eV to lie within 100 Mpc, or even closer for nuclei lighter than iron and heavier than protons [START_REF] Hillas | The Origin of Ultra-High-Energy Cosmic Rays[END_REF][START_REF] Taylor | Need for a local source of ultrahigh-energy cosmic-ray nuclei[END_REF]. Although the nearest extreme blazar, Mkn 501, is at a luminosity distance of ∼ 150 Mpc, misaligned counterparts viewed as radio galaxies could satisfy the local proximity constraint. Because of a tight lower bound on the magnetic luminosity (e.g., [START_REF] Lemoine | Anisotropy vs chemical composition at ultra-high energies[END_REF], or [START_REF] Matthews | Centaurus A, and other radio galaxies as sources of ultrahigh energy cosmic rays[END_REF] for lowerfrequency-peaked radio galaxies such as Cen A), only luminous sources should be able to reach the highest energies, so that nearby ones may be identifiable in recent electromagnetic surveys [START_REF] Alves Batista | Open questions in cosmic-ray research at ultrahigh energies[END_REF]. The γ-ray spectra of blazars are softened by pairproduction interactions with the EBL above ∼100 GeV, in an energy-and redshift-dependent fashion shown in Fig. 4 (e.g., [START_REF] Hauser | The Cosmic Infrared Background: Measurements and Implications[END_REF]). The first component of EBL, peaking at optical frequencies, is now well determined thanks to both direct modeling (e.g., [START_REF] Franceschini | The extragalactic background light revisited and the cosmic photon-photon opacity[END_REF]) and γ-ray constraints (e.g., [START_REF] Biteau | The Extragalactic Background Light, the Hubble Constant, and Anomalies: Conclusions from 20 Years of TeV Gamma-ray Observations[END_REF][START_REF] Desai | A GeV-TeV Measurement of the Extragalactic Background Light[END_REF]). Emission from extreme-TeV blazars detected around 10 TeV provides constraints on the EBL intensity up to ∼ 50 µm. The limited number of extreme- The steady emission of 1ES 0229+200 [START_REF] Aharonian | New constraints on the mid-IR EBL from the HESS discovery of VHE γ-rays from 1ES 0229+200[END_REF] and the active phase of Mkn 501 in 1997 [START_REF] Aharonian | The time averaged TeV energy spectrum of MKN 501 of the extraordinary 1997 outburst as measured with the stereoscopic Cherenkov telescope system of HEGRA[END_REF] are shown in panels a) and b), respectively. γ-ray data are not corrected for EBL absorption. Error bars denote 1 σ statistical uncertainties. Arrows denote upper limits at the 95% CL. The solid black line shows the expected spectra after interaction with the EBL, assuming the intrinsic emission shown by the dotted grey line. The modifications induced by Lorentz invariance violation [START_REF] Tavecchio | On the detectability of Lorentz invariance violation through anomalies in the multi-TeV γ-ray spectra of blazars[END_REF] are shown by the long-dashed green, dashed blue and dash-dotted red lines for ELIV = 3 × 10 19 , 10 20 and 2 × 10 20 GeV, respectively. The magenta solid line shows the spectrum modified by mixing with axion-like particle [START_REF] Galanti | VHE spectral alterations induced by photon-ALP oscillations[END_REF].

TeV sources has thus left the second hump of the EBL (mid-to far-infrared) poorly constrained.

EBL measurements based on blazars with a firm redshift rely on assumptions about the intrinsic emission prior to absorption. In the absence of full SED modelling, intrinsic spectra are assumed to be well-described by power-law or log-parabola functions with the flux decreasing at the highest energies. The lack of bright thermal components associated to a strong broad line region or a dusty torus supports a minimal absorption within the source (jet and galaxy nucleus).

A major step forward came with the H.E.S.S. spectral measurements of 1ES 1101-232 and H 2356+304 in 2006 [START_REF] Aharonian | A low level of extragalactic background light as revealed by γ-rays from blazars[END_REF]. Their hard spectra provided the first strong constraints to the maximum intensity of the EBL. Since the discovery of the EBL imprint [START_REF] Ackermann | The Imprint of the Extragalactic Background Light in the Gamma-Ray Spectra of Blazars[END_REF][START_REF] Collaboration | Measurement of the extragalactic background light imprint on the spectra of the brightest blazars observed with H[END_REF], state-of-theart TeV measurements have relied on observations of both steady and temporary extreme-TeV blazars to constrain the longest wavelengths [START_REF] Collaboration | Measurement of the EBL spectral energy distribution using the VHE γ-ray spectra of H.E.S.S. blazars[END_REF][START_REF] Acciari | Measurement of the extragalactic background light using MAGIC and Fermi-LAT gamma-ray observations of blazars up to z = 1[END_REF].

Cosmology: Intergalactic Magnetic Field

With their hard and high-energy emission, extreme-TeV blazars offer a unique possibility to constrain the presence of cascades in the intergalactic magnetic field (IGMF). The strength of the IGMF is not well constrained, despite its relevance (e.g., [START_REF] Durrer | magnetic fields: their generation, evolution and observation[END_REF] for a review). It may have provided the seed field for magnetic fields in galaxies and galaxy clusters, and measurement of its strength and correlation length could distinguish between generation scenarios (in the early Universe or after the formation of the first galaxies).

An electromagnetic cascade can develop when electronpositron pairs generated by γ-EBL interactions upscatter CMB photons to GeV energies. All the energy flux absorbed at TeV energies is reprocessed into the GeV band. The cascade develops when inverse-Compton scattering proceeds faster than plasma cooling of the pair beam, which depends on the primary γ-ray spectrum, Γ γ [START_REF] Vafin | The Electrostatic Instability for Realistic Pair Distributions in Blazar/EBL Cascades[END_REF]. The deflection of electrons and positrons in the IGMF angularly broadens the cascade and introduces a time delay with respect to primary γ-rays, thereby affecting the low-energy γ-ray component.

The first limits, which depend on the assumed source variability and duty cycle, came from γ-ray observations of 1ES 0229+200 (e.g., [START_REF] Neronov | Evidence for Strong Extragalactic Magnetic Fields from Fermi Observations of TeV Blazars[END_REF]). Spectral observations in the GeV-TeV range constrain the strength of the IGMF to be larger than a few femto-Gauss, while searches for angular broadening have constrained intervals of even higher magnetic field [START_REF] Ackermann | The Search for Spatial Extension in High-latitude Sources Detected by the Fermi Large Area Telescope[END_REF][START_REF] Collaboration | Search for extended γ-ray emission around AGN with H.E.S.S. and Fermi-LAT[END_REF][START_REF] Archambault | Search for Magnetically Broadened Cascade Emission from Blazars with VERITAS[END_REF]. The predicted cascade component at GeV energies is particularly large for extreme blazars, due to their hard intrinsic spectra, and to the relative stability of their flux, which reduces uncertainties introduced by arrivaltime delays. The strongest individual lower limits from Fermi -LAT come from 1ES 0229+200 and 1ES 0347-121, while the VERITAS and H.E.S.S. exclusion regions make use of observations of 1ES 1218+304, 1ES 1101-232 and 1ES 0229+200.

Fundamental physics

Due to their emission at multi-TeV energies, extreme blazars have been identified as prime candidates for the search for TeV spectral anomalies, as theorized for Lorentz invariance violation [START_REF] Liberati | Tests of Lorentz invariance: a 2013 update[END_REF] or mixing with axionlike particles [START_REF] De Angelis | Relevance of axionlike particles for very-high-energy astrophysics[END_REF].

Phenomenologically, Lorentz invariance violation leads to modifications of the dispersion relations of particles and photons, implying in particular the alteration of the pair production threshold above a γ-ray

energy E mod [(2m e c 2 ) 2 E n LIV /(1 -2 -n )] 1/(n+2)
, where n is the order of the correction and E LIV is the energy scale at which Lorentz invariance is violated [START_REF] Biteau | The Extragalactic Background Light, the Hubble Constant, and Anomalies: Conclusions from 20 Years of TeV Gamma-ray Observations[END_REF]. Above E mod , pair production is virtually forbidden and the Universe becomes transparent. The first quantitative limits have emerged from the very-high states of Mkn 501 [START_REF] Biteau | The Extragalactic Background Light, the Hubble Constant, and Anomalies: Conclusions from 20 Years of TeV Gamma-ray Observations[END_REF][START_REF] Abdalla | Temporal and Spectral Constraints on Lorentz Invariance Violation[END_REF]. Complemented by the approach based on time-of-flight, extreme blazars constrain E LIV to be above the Planck scale (1.2 × 10 19 GeV) for n = 1 [START_REF] Lang | Improved limits on Lorentz invariance violation from astrophysical gamma-ray sources[END_REF], indicating that effects would potentially be detectable only above E mod 50 TeV.

Axion-like particles are generically predicted by several extensions of the Standard Model (such as string theory). They are expected to be light, neutral, and to couple to two photons, implying conversion of γ-rays to axion-like particles in a magnetic field. The particlephoton oscillation during propagation could lead to ripples in the γ-ray spectra [START_REF] Abramowski | Constraints on axionlike particles with H.E.S.S. from the irregularity of the PKS 2155-304 energy spectrum[END_REF] and to a substantial reduction of the effective opacity at the highest energies [START_REF] De Angelis | Relevance of axionlike particles for very-high-energy astrophysics[END_REF], as illustrated in Fig. 4. For moderate redshifts, the reduction of the opacity is particularly relevant above few TeV. Extreme-TeV blazars are therefore natural candidates for these studies [START_REF] Galanti | VHE spectral alterations induced by photon-ALP oscillations[END_REF]. The current knowledge of the extreme-blazar population is based on surveys from radio wavelengths to X-rays. eROSITA will further enlarge the extremesynchrotron population with the first imaging all-sky survey up to 10 keV [START_REF] Merloni | eROSITA Science Book: Mapping the Structure of the Energetic Universe[END_REF]. IXPE will open the X-ray polarimetric window, probing the magnetic fields and jet content of extreme blazars [START_REF] Krawczynski | Science White Paper: Using X-Ray Polarimetry to Probe the Physics of Black Holes and Neutron Stars[END_REF]. At higher energies, future MeV telescopes such as AMEGO and e-ASTROGAM (e.g., [START_REF] De Angelis | Science with e-ASTROGAM. A space mission for MeV-GeV gamma-ray astrophysics[END_REF]) have the potential to observe the high end of the extreme-synchrotron population.

As the next-generation γ-ray observatory, the Cherenkov Telescope Array (CTA, [START_REF]Science with the Cherenkov Telescope Array[END_REF]) will play a central role in establishing a census of extreme-TeV sources. Thanks to its sensitivity, CTA will likely discover numerous extremely hard objects, including sources that are too faint to be detected with Fermi -LAT and current TeV instruments. The CTA survey of a quarter of the extragalactic sky, complemented in the multi-TeV range by LHAASO [START_REF] Bai | The Large High Altitude Air Shower Observatory (LHAASO) Science White Paper[END_REF] and SWGO [START_REF] Albert | Science Case for a Wide Field-of-View Very-High-Energy Gamma-Ray Observatory in the Southern Hemisphere[END_REF], will provide for the first time an unbiased view on the extreme-TeV population, blazars and their off-axis counterparts. This latter subclass of radio galaxies constitutes a promising field of research both for AGN population studies and for the search of the origin of UHECRs.

The physics of particle acceleration in extreme environments has benefited from the emergence of ab initio numerical simulations that focus on the microscopic scales of acceleration, at the expense of idealizing on macroscopic scales (see [START_REF] Kagan | Relativistic Magnetic Reconnection in Pair Plasmas and Its Astrophysical Applications[END_REF][START_REF] Sironi | Relativistic Shocks: Particle Acceleration and Magnetization[END_REF][START_REF] Wong | First-principles demonstration of diffusive particle acceleration in kinetic simulations of relativistic plasma turbulence[END_REF] for recent advances). Conversely, phenomenological modeling often integrates out the microphysics to deal with the macroscopic scales of the source. A major challenge of the coming years lies in bridging this gap, including e.g., a realistic description of relativistic jets and of their environment, as well as propagation in intervening magnetic and photon fields. In particular, an improved knowledge of the IGMF would benefit both the study of cosmic-ray sources and tests of external cascade scenarios.

A productive interplay between theory, phenomenology and observations will be fostered by the broadrange measurements from ∼ 30 GeV to hundreds TeV offered by CTA. The improved sensitivity with respect to current-generation instruments by a factor of 5 -20 depending on energy will make it possible to test emission and propagation models with unprecedented accuracy. The enhanced γ-ray sensitivity and energy resolution of CTA will also make deep observations of extreme blazars a formidable probe of fundamental physics. With the long-term monitoring program of CTA dedicated to AGN, we expect to access for the first time to time-resolved, broad γ-ray spectra of extreme-TeV blazars. TeV observations will be complemented by X-ray monitoring with Swift-XRT and future satellites like SVOM [START_REF] Paul | The Chinese-French SVOM mission for gamma-ray burst studies[END_REF].

As very-high-energy extragalactic accelerators, extreme blazars are prime candidates to investigate multimessenger correlations with neutrinos and cosmic rays. Significant improvements in the statistics of these astroparticles and in their composition are expected from next-generation astroparticle observatories, including IceCube-Gen2 [START_REF] Aartsen | IceCube-Gen2: A Vision for the Future of Neutrino Astronomy in Antarctica[END_REF], KM3NeT [START_REF] Adrián-Martínez | Letter of intent for KM3NeT 2.0[END_REF], for the neutrino sector, and AugerPrime [START_REF] Pierre | The Pierre Auger Observatory Upgrade -Preliminary Design Report[END_REF] and TA×4 [START_REF] Sagawa | Telescope Array extension: TAx4[END_REF] for the cosmicray sector. The detection of astroparticle flux excesses associated with electromagnetic sources remains a most promising avenue to understand acceleration, radiative and escape mechanisms at energies beyond the reach of human-made accelerators.

DATA AND CODE AVAILABILITY

All data presented in this study are included in this published article (and its supplementary information files).

The authors declare no competing financial interests.

Correspondence should be addressed to Jonathan Biteau <biteau(at)in2p3.fr> and Elisa Prandini <elisa.prandini(at)pd.infn.it>. JB and EPr coordinated the work and mostly contributed to Sec. 1 and 5. LC and PP mostly contributed to Sec. 2. ML, ER, AT, and AZ mostly contributed to Sec. Table 1. Salient properties of the 24 extreme blazars with firm redshift that are presently detected at TeV energies. The X-ray and γ-ray spectra are labelled as: H = hard spectrum (extreme behaviour); S = soft spectrum; HS = mostly hard spectrum, sometimes soft; SH = mostly soft spectrum, becoming hard when flaring. As-yet uncertain classifications are annotated with a question mark. Fluxes at 1 keV and 100 GeV are rounded to half a dex.

Figure 1 .

 1 Figure1. Prototypical SEDs illustrating the three types of extreme behaviours. Panels a) and b) display the SEDs of two extreme-synchrotron blazars, during short-lived large flares and long-lasting quiescent states, respectively. The SED of an extreme-TeV blazar is shown in panel c). Observed γ-ray spectra are corrected for EBL absorption[START_REF] Franceschini | The extragalactic background light revisited and the cosmic photon-photon opacity[END_REF]. Nearlycontemporaneous historical data are shown with the same colour and labelled accordingly. Grey points correspond to archival data. Error bars denote 1 σ statistical uncertainties. Arrows denote upper limits at the 95% confidence level (CL). Guideline SSC models are presented as dash-dotted lines. Dotted lines show the host-galaxy emission, modelled with the template spectrum of a giant elliptical galaxy[START_REF] Silva | Modeling the Effects of Dust on Galactic Spectral Energy Distributions from the Ultraviolet to the Millimeter Band[END_REF], scaled to match the magnitude of the host galaxy[START_REF] Scarpa | The Hubble Space Telescope Survey of BL Lacertae Objects. I. Surface Brightness Profiles, Magnitudes, and Radii of Host Galaxies[END_REF]. Data and models are from[START_REF] Pian | BeppoSAX Observations of Unprecedented Synchrotron Activity in the BL Lacertae Object Markarian 501[END_REF][START_REF] Aharonian | The time averaged TeV energy spectrum of MKN 501 of the extraordinary 1997 outburst as measured with the stereoscopic Cherenkov telescope system of HEGRA[END_REF][START_REF] Tavecchio | Theoretical Implications from the Spectral Evolution of Markarian 501 Observed with BeppoSAX[END_REF] for Mkn 501,[START_REF] Ghisellini | Low power BL Lacertae objects and the blazar sequence. Clues on the particle acceleration process[END_REF] for 1ES 1426+428 and[START_REF] Costamante | The NuSTAR view on hard-TeV BL Lacs[END_REF] for 1ES 0229+200.

Figure 2 .

 2 Figure 2.Radio number counts of extremesynchrotron blazars and of different samples of BL Lacs. Green squares denote BL Lacs from the Deep X-Ray Radio Blazar Survey (DXRBS), red trapezoids the HBLs from DXRBS, blue circles the HBLs from 3HSP, and orange circles the extreme-synchrotron blazars from 3HSP. Error bars denote 1 σ statistical uncertainties. The solid line represents the number counts predicted from the luminosity function of BL Lacs[START_REF] Urry | Unified Schemes for Radio-Loud Active Galactic Nuclei[END_REF]. Figure adapted from[START_REF] Chang | The 3HSP catalogue of Extreme High Synchrotron Peaked Blazars[END_REF], courtesy of Yu-Ling Chang.

4 .

 4 EXTREME BLAZARS AND TESTS OF γ-RAY PROPAGATION 4.1. Cosmology: Extragalactic Background Light

Figure 4 .

 4 Figure 4. Observed TeV spectra of two extreme blazars including different γ-ray propagation models. The steady emission of 1ES 0229+200[START_REF] Aharonian | New constraints on the mid-IR EBL from the HESS discovery of VHE γ-rays from 1ES 0229+200[END_REF] and the active phase of Mkn 501 in 1997[START_REF] Aharonian | The time averaged TeV energy spectrum of MKN 501 of the extraordinary 1997 outburst as measured with the stereoscopic Cherenkov telescope system of HEGRA[END_REF] are shown in panels a) and b), respectively. γ-ray data are not corrected for EBL absorption. Error bars denote 1 σ statistical uncertainties. Arrows denote upper limits at the 95% CL. The solid black line shows the expected spectra after interaction with the EBL, assuming the intrinsic emission shown by the dotted grey line. The modifications induced by Lorentz invariance violation[START_REF] Tavecchio | On the detectability of Lorentz invariance violation through anomalies in the multi-TeV γ-ray spectra of blazars[END_REF] are shown by the long-dashed green, dashed blue and dash-dotted red lines for ELIV = 3 × 10 19 , 10 20 and 2 × 10 20 GeV, respectively. The magenta solid line shows the spectrum modified by mixing with axion-like particle[START_REF] Galanti | VHE spectral alterations induced by photon-ALP oscillations[END_REF].

5 .

 5 PERSPECTIVESThree main research lines should guide future observations of extreme blazars: (i) population studies, featuring the characterization of a large number of extreme blazars at TeV energies; (ii) emission mechanisms, including the measurement of variability timescales in the TeV band; (iii) jet hadronic content, connecting extreme blazars and multi-messenger observations.

  3. EPu and FT mostly contributed to Sec. 4. All authors discussed the material and contributed to the writing of the manuscript. EPr has received funding from the European Union's Horizon2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no 664931. EPu acknowledges the Young Investigators Program of the Helmholtz Association. FT acknowledges contribution from the grant INAF CTA-SKA "Probing particle acceleration and γ-ray propagation with CTA and its precursors" and the INAF Main Stream project "High-energy extragalactic astrophysics: toward the Cherenkov Telescope Array". This review is the result of several fruitful discussions raised during the meeting eXtreme19 (22-25 January 2019, Padova, Italy). The authors, as chairs of the scientific committee and review speakers, wish to thank all the participants to the meeting: C. Arcaro, B. Balmaverde, U. Barres de Almeida, E. Benítez, D. Bernard, E. Bernardini, M. Boettcher, S. Boula, A. Caccianiga, C. Casadio, I. Christie, A. De Angelis, L. Di Gesu, A. di Matteo, I. Donnarumma, M. Doro, T. Dzhatdoev, V. Fallah Ramazani, R. Ferrazzoli, I. Florou, L. Foffano, L. Foschini, N. I. Fraija, A. Franceschini, G. Galanti, M. Gonzalez, O. Gueta, O. Hervet, S. Kerasioti, F. Krauss, M. Kreter, G. La Mura, R. Lico, R. Lopez Coto, M. Lucchini, M. Mallamaci, M. Manganaro, A. Marinelli, M. Mariotti, K. Nalewajko, E. Nokhrina, F. Oikonomou, L. Olivera-Nieto, S. Paiano, V. Paliya, D. Paneque, Z. Pei, C. Perennes, S. Rainò, P. Romano, A. Sharma, G. Sigl, C. Sinnis, P. Soffitta, A. Spolon, B. Sversut Arsioli, A. Tramacere, S. Vercellone, V. Vittorini, and H. Xiao.

  Source Name redshift X-ray spectrum γ-ray spectrum Flux at 1 keV Flux at 100 GeVz [erg cm -2 s -1 ] [erg cm -2 s -1 ]

	Mkn 421	0.031	SH	S	10 -12 -10 -9	10 -10
	Mkn 501	0.034	SH	SH	10 -11 -10 -10	10 -10.5
	1ES 2344+514	0.044	SH	S	10 -11.5 -10 -10.5	10 -11
	1ES 1959+650	0.048	SH	S	10 -11 -10 -10	10 -11
	TXS 0210+515	0.049	H	H	10 -11	10 -12
	1ES 2037+521	0.053	H	H?	10 -11.5	10 -12
	1ES 1727+502	0.055	HS	SH	10 -11	10 -11.5
	PGC 2402248	0.065	H	S?	10 -11.5	10 -12
	PKS 0548-322	0.069	H	H	10 -11	10 -12
	RGB J0152+017	0.08	H	S	10 -11.5	10 -12
	1ES 1741+196	0.084	H	H	10 -11.5	10 -11.5
	SHBL J001355.9-185406	0.095	H	S	10 -11	10 -12
	1ES 1312-423	0.105	H	S	10 -11	10 -12
	RGB J0710+591	0.125	H	H	10 -11	10 -12
	1ES 1426+428	0.129	H	SH	10 -11	10 -11.5
	RX J1136.5+6737	0.1342	H	S	10 -11.5	10 -12
	1ES 0229+200	0.1396	H	H	10 -11.5	10 -12
	1ES 1440+122	0.163	H	S	10 -11	10 -12
	H 2356-309	0.165	H	H	10 -11	10 -12
	1ES 1218+304	0.182	HS	H	10 -11	10 -11
	1ES 1101-232	0.186	HS	H	10 -11	10 -11.5
	1ES 0347-121	0.188	H	H	10 -11	10 -12
	RBS 0723	0.198	H	S	10 -11.5	10 -12
	1ES 0414+009	0.287	S	H	10 -11	10 -11.5


LABORATORY ASTROPHYSICS

Miniature supernova shock waves

A laser-plasma experiment has recreated shock waves in collisionless, weakly magnetized conditions and evidenced electron acceleration to relativistic energies, offering unprecedented insight into a long-standing problem in astrophysics. In highly rarefied space plasmas, supersonic motion spawns collisionless shock waves, that is, shocks whose dissipative properties proceed from particle scattering in self-generated electromagnetic fields rather than Coulomb collisions. This remarkable feature turns those structures into efficient particle accelerators à la Fermi [1], in which particles gain energy from repeated bounces in the electromagnetic turbulence across the shock front. Accordingly, cosmic phenomena glow with non-thermal radiation from highly relativistic particles and the very origin of cosmic rays can be traced to the collisionless shock fronts of supernova remnants. Evidence for particle acceleration up to energies well above 1 TeV in these objects has accumulated over the years [2] as illustrated in Fig. 1. More generally, collisionless shock waves and their phenomenological consequences are thought to shape much of the high-energy, multi-messenger Universe. Thus, generating a collisionless shock in the laboratory, and one that can give rise to particle acceleration as reported now by Federico Fiuza and co-authors [3] in Nature Physics represents an experimental feat.

Laurent Gremillet & Martin Lemoine

In itself, the structure of a collisionless shock is a famous problem of plasma physics [4]. It depends on both the shock velocity and the Mach numbers, in particular the so-called Alfvénic Mach number (ratio of the shock velocity to the speed of the incompressible normal modes of the magnetized plasma) that scales inversely to the magnetization degree of the unshocked medium. Shock waves of moderate magnetization (Alfvénic Mach numbers around ten) abound in interplanetary space. For those, spacecrafts have provided a wealth of in situ data up to the edge of the Solar system. However, supernova shock waves are not only faster (thousands of kilometres per second), they are also significantly less magnetized (Alfvénic Mach numbers of several hundreds). In this regime, the turbulence that initially sustains the shock transition is believed to result from the electromagnetic Weibel instability [5] that generates microscopic random electromagnetic fields out of momentum space anisotropy. Here, the anisotropy stems from the counterstreaming of the ambient plasma and the particles reflected off the nascent shock surface. Thereon, the Weibel instability fragments the plasma into magnetized filaments whose nonlinear evolution mediates the shock transition [6]. As this process takes place on scales orders of magnitude below what can be resolved from observations, the structure of these shock waves has remained elusive. How a particle is extracted from the thermal ambient plasma and injected with sufficient energy into shock acceleration represents yet another puzzle, pivotal to our understanding of the radiative properties of collisionless shocks. This problem is more acute for electrons than for ions, as their mean (thermal) energy would scale proportionally to their mass, should both species cross the shock without being influenced by the other. Observations indicate that electrons draw extra energy from the shock but how so remains under debate. This is where the experiment of Fiuza and co-authors finds special importance.

Conducted with the world's largest laser at the National Ignition Facility (NIF), this experiment consisted of irradiating two deuterated carbon foils, placed a few centimetres apart facing each other. More than a hundred laser beams delivered a total energy of about 1 MJ in 3 ns, vaporizing the targets into plasma plumes, which then expanded and interpenetrated at high velocities (of about 2000 km/s). The Weibel instability that ensued in the counterstreaming region generated magnetic fields on sub-millimetric ion skindepth scales that were strong enough to halt and thermalize the ions, thereby generating a double-shock system representative of supernova remnants. Laser ablation permeated the pre-shock plasmas with a net, large-scale magnetization, but at a level sufficiently low to preserve weakly magnetized conditions with an Alfvénic Mach number of around 400. Shock formation was demonstrated by measuring a fourfold plasma compression around the contact plane, together with bulk electron heating to tens of millions of Kelvins.

Remarkably, the shock was sustained long enough to accelerate electrons to relativistic energies about two orders of magnitude above the thermal shocked plasma. This achievement builds upon a decade of experimental and theoretical progress in the field [7]. The key to success in the experiment of Fiuza and co-authors was to ensure that the turbulence developed rapidly enough during the interaction, and that the overlapping plasma region remained substantially larger than the scattering length of the ions in the turbulence -yet much smaller than their collisional mean free path. Dense plasmas were thus needed to speed up the turbulence growth, but not excessively so lest collisions affect the system dynamics. The high flow speeds that are desired to hasten the instability also require strong laser heating and sufficient spacing between the targets -conditions attainable with a NIF-class laser drive. It should be noted that collisionless shock waves have been produced before using lower-energy lasers, but at higher magnetization and smaller velocities [8]. While no longer underpinning the shock formation, some Weibeldriven turbulence may then still arise to generate suprathermal electrons as observed recently [9].

Albeit impressive, the study of Fiuza and co-authors remains limited in its ability to diagnose the self-induced fields, the degree of ion heating and the very mechanisms through which electrons are accelerated. The data are interpreted through kinetic numerical simulations but these are forced -as is standard -to use a reduced dimensionality, an artificially low ion mass and scaled-up ion velocities, which precludes direct comparison with the measurements. These simulations indicate that the electron acceleration occurs through repeated encounters with moving structures in the shock transition layer, in general agreement with theoretical views [10]. However, the measured electron spectrum does not exhibit the power-law seen in the simulations, and the reason for this deserves further scrutiny.

Finally, a nagging question regarding such experiments is whether Coulomb collisions, which are neglected in kinetic simulations, may alter the electron dynamics and also, to some extent, the turbulence growth. At stake is the true similarity between the experimental and actual supernova remnant shock waves. While ion-ion collisions between the interpenetrating beams can be safely neglected, electron-ion collisions remain frequent on the experimental timescale, at least for electrons with near-thermal energies. Appraising their impact on the properties of laser-driven shocks, and particularly on the electron energization processes, will undoubtedly spur further experimental and simulation studies.

Laurent Gremillet

Commissariat à l'Énergie Atomique et aux Énergies Alternatives, Arpajon, France, email: laurent.gremillet@cea.fr

Martin Lemoine

Institut d'Astrophysique de Paris, Centre National de la Recherche Scientifique -Sorbonne Université, Paris, France, email: lemoine@iap.fr

Figure 1 :

 1 Figure 1: Zooming in on a supernova shock wave: Tycho's supernova remnant, revealing soft Xray emission from the interior shocked gas (in red), and hard X-rays from electrons accelerated to TeV energies at the shock wave (in blue). The inset shows a zoom (not to scale) on the structure of the collisionless shock. © X-ray: NASA/CXC/Rutgers/K.Eriksen et al.; Optical: DSS; numerical simulation: CALDER/L. Gremillet; photomontage: C. Henneguez. source file: https://chandra.harvard.edu/photo/2011/tycho/


P Rahme

P Moussa

F Lachaud

Y Landon

Effect of adding a woven glass ply at the exit of the hole of CFRP laminates on delamination during drilling

Keywords:

Composite materials are increasingly used in the aeronautical field. The assembly of structures requires usually drilling of composite parts. Drilling of composite materials generates defects, mainly delamination at the exit of the hole. This major defect diminishes the structure strength. Delamination is directly related to the drilling thrust force. Minimizing this force reduces the defects. Adding a woven glass ply at the exit of the hole is found to be another adequate solution to reduce the defects. In this paper, the drilling of carbon/epoxy thick composite structures with a woven glass ply at the exit of the hole is considered. An analytical model is developed to determine for a given tool geometry the critical delamination forces as function of the number of non-drilled plies remaining beneath the tool. The results are validated experimentally. These results show that adding a woven glass ply at the exit of the hole reduces delamination.

Introduction

The bolted assembly of two composite carbon/epoxy plates (or one composite and another metallic) requires drilling of holes using cutting tools. The twist drill is the most widely used drilling tool, with its main parts: the chisel edge (dead center) and the cutting edges. The drilling by removing material of the composite structures generates defects at the entry of the hole, on the wall and at the exit of the hole [START_REF] Rahme | Delamination-free drilling of thick composite materials[END_REF][START_REF] Rahme | Drilling of thick composite materials using a step gundrill[END_REF][START_REF] Rahme | Study into causes of damage to carbon epoxy composite material during the drilling process[END_REF]. These defects detract from the strength of the structure. The major defect, called delamination, caused by the drilling is located at the exit of the hole [START_REF] Rahme | Delamination-free drilling of thick composite materials[END_REF][START_REF] Rahme | Drilling of thick composite materials using a step gundrill[END_REF][START_REF] Rahme | Study into causes of damage to carbon epoxy composite material during the drilling process[END_REF][START_REF] Piquet | Experimental analysis of drilling damage in thin carbon/epoxy plate using special drills[END_REF][START_REF] Hocheng | The path towards delamination-free drilling of composite materials[END_REF]. The chisel edge of the twist drill cannot cut the material, due to its sharpening and zero cutting speed at the center, but it extrudes it [START_REF] Rahme | Drilling thick composite materials using large diameter drills[END_REF]. This creates a normal stress on the plane of the plate which leads to the separation of the plies and therefore delamination at the exit of the hole [START_REF] Hocheng | Comprehensive analysis of delamination in drilling of composite materials with various drill bits[END_REF]. The delamination of a composite structure corresponds to a cohesive failure of the matrix and a separation of the plies. Delamination of fibers is an important problem when machining a composite material. Hocheng et al. [START_REF] Hocheng | The path towards delamination-free drilling of composite materials[END_REF] defined the critical delamination force as the smallest force which causes the appearance of the first delamination. Then, to eliminate delamination when drilling, the applied thrust force must not exceed the critical thrust force of the nondrilled thickness for the composite plate. When drilling, the used cutting conditions must be less than the critical conditions corresponding to the critical delamination force.

At the exit of the hole, the axial force of penetration imposed by the tool (F Z ) tends to bend the last plies. This can cause the cohesive failure of the matrix until the tearing of the last ply and the breaking of the fibers, causing delamination of the last plies [START_REF] Hocheng | Delamination during drilling in composite laminates[END_REF]. This delamination at the exit of the hole, which is considered to be the major defect, is therefore influenced by the thrust force (F Z ) [START_REF] Tsao | The effect of chisel length and associated pilot hole on delamination when drilling composite materials[END_REF][START_REF] Langella | A torque and thrust prediction model for drilling of composite materials[END_REF]. Several studies [START_REF] Piquet | Experimental analysis of drilling damage in thin carbon/epoxy plate using special drills[END_REF][START_REF] Hocheng | The path towards delamination-free drilling of composite materials[END_REF][START_REF] Rahme | Drilling of thick composite material with a small-diameter twist drill[END_REF][START_REF] Rahme | Analytical models of composite material drilling[END_REF][START_REF] Velayudham | Effect of point geometry and their influence on thrust and delamination in drilling of polymeric composites[END_REF] have been carried out on the modeling of the critical axial force of delamination at the exit of the hole. As per Piquet et al. [START_REF] Piquet | Experimental analysis of drilling damage in thin carbon/epoxy plate using special drills[END_REF], different tool geometries can effectively reduce delamination by decreasing the thrust force (F Z ). Also, the axial force and the delamination depend significantly of the state of wear of the tool [START_REF] Fernandes | Investigation of hole quality on drilling carbon composites with a 'one shot' drill bit[END_REF]. This state of wear is strongly dependent on the material of the drill. Finally, the use of special tools as well as the adjustment of drilling and reaming conditions can greatly reduce delamination [START_REF] Hocheng | Analysis of delamination in drilling composite materials using core-center drill[END_REF][START_REF] Furet | Milling and drilling of composite materials for the aeronautics[END_REF][START_REF] Gouleau | Faisabilité du perçage d'empilements multimatériaux de type aluminium/composites[END_REF]. Moreover, Rahme et al. [START_REF] Rahme | Contribution à l'Etude de l'Effet des Procédés de Perçage-Alésage sur l'Apparition du Délaminage dans les Structures Composites Epaisses[END_REF][START_REF] Rahme | Perçage carbone[END_REF] state in their experimental observations that defects at the exit of the plate are considered as being the major defects and the length of cracks between the last plies is always important. They showed that the cracks are first initiated under the chisel edge and propagated through the plies under the cutting edges. The critical delamination forces are then these which correspond to the initiation and propagation of cracks at the exit of the plate. According to Fernandes et al. [START_REF] Fernandes | Drilling of carbon composites using a one-shot drill bit. Part II: empirical modeling of maximum thrust force[END_REF] and Won et al. [START_REF] Won | Drilling of aramid and carbon fiber polymer composites[END_REF], the delamination at the exit results in the separation of the last plies according to the cracks opening mode I. On the other hand and for the effect of anisotropy on the critical force, https://doi.org/10.1016/j.compositesa.2019.105731 ⁎ Corresponding author. E-mail address: prahme@ul.edu.lb (P. Rahme).

the isotropic material has a higher delamination resistance than the orthotropic material, according to Rahme [START_REF] Rahme | Contribution à l'Etude de l'Effet des Procédés de Perçage-Alésage sur l'Apparition du Délaminage dans les Structures Composites Epaisses[END_REF]. The anisotropic composite material can then be delaminated by applying a lower axial force. Therefore, the anisotropy has a significant influence on the critical delamination effort. That is why, a solution to minimize the delamination is to add a taffeta fabric ply at the entrance and the exit of the composite plate.

In this paper, the drilling of carbon/epoxy thick composite plates with a woven glass ply at the exit of the hole is considered. A taffeta woven glass fabric is used. This glass fabric has a better resistance to delamination and eliminates, at the same time, the galvanic couple between the composite and the metal structure during assembly, if any. The study of drilling composite materials with a woven glass ply at the exit of the hole has not been developed yet. An analytical model that takes into account the added glass fabric ply at the exit of the hole is presented in this work. This model calculates the critical thrust force for a given number of non-drilled plies remaining under the drill, when drilling composite plate with a glass fabric ply at the exit. Finally, experimental tests are performed to validate both models and the results are compared and discussed.

Modelling of the critical thrust force at delamination

When drilling a laminate, the last plies at the exit of the hole should be modeled to determine the critical thrust force at delamination. In this paper, at the exit, the remaining non-drilled plies including the glass/epoxy woven fabric are modeled as thin circular orthotropic laminate, without back-up support at the exit. This laminate should be subjected to the load induced by the drill. This loading is directly related to the cutting tool action on the material during drilling. This loading is considered axisymmetric since the cutting speed is much bigger than the feed rate speed of the drill. In this paper, a conventional twist drill of diameter 16 mm, made of tungsten (K15), is used. It is a tapered relief twist drill without thinning of the chisel edge [DIN 1897]. The length of the chisel edge of this drill is 3.9 mm. According to Rahme et al. [START_REF] Rahme | Study into causes of damage to carbon epoxy composite material during the drilling process[END_REF][START_REF] Rahme | Drilling thick composite materials using large diameter drills[END_REF], the cracks are initiated under the chisel edge and propagated under the cutting edges. More, based on the observations presented by Rahme et al. [START_REF] Rahme | Perçage carbone[END_REF], a visible deflection of the plate located under the drill is shown in the direction of the drill axis. This deflection results of absence of any resistant moment. Consequently, when the chisel edge is approaching the exit of the plate, the part remaining under the drill is modeled by a simply supported thin circular laminate, of diameter equal the length of the chisel edge (2a), subjected to a uniformly distributed load, as shown in Fig. 1. When the chisel edge exits out of the plate, the effect of the cutting edges is modeled by a simply supported laminate, of diameter slightly greater than the length of the chisel edge (2b), with a pilot hole at the center of diameter equal the length of the chisel edge, as shown in Fig. 2. A diameter (2b) of 6 mm is taken in this study. Indeed, an assumption of propagation of cracks is taken at the beginning of the cutting edges, around the boundaries between the chisel edge and the cutting edges. This assumption has been taken based on observations of cracks propagation using a high speed camera [START_REF] Rahme | Perçage carbone[END_REF].

Using the principle of conservation of the energy for the plate and the theory of plates and shells developed by Timoshenko and Woinowsky-Krieger [START_REF] Timoshenko | Theory of plates and shells[END_REF], the critical thrust force at delamination corresponding to the considered loading and boundary conditions, for the effect of the chisel edge without pilot hole, is found as:

= + F π D ϑ G D 8 ( 1) 2 ' C r θ IC 1 (1)
With:

= + + + D D D D D 1 8 (3 2 4
3 )

11 12 66 22 (2)
And

= + + - + + D D D D D (ϑ 14ϑ 13) 3( 2 ) rθ rθ ' 2 11 12 22
(3)

ϑ rθ is the poisson's ratio in polar coordinates and D ij are found to be function of the stiffness matrix of the laminate as:

∑ ⎜ ⎟ = ⎛ ⎝ - ⎞ ⎠ = - D Q Z Z | | ( ¯) 3 ij k n ij k k k 1 3 1 3 ( 4
)
where Q ij are the stiffness coefficients of the laminate located under the drill. Z k is the position of the ply k through the thickness from the mean plane of the laminate. The critical energy release rate corresponding to crack opening in mode I, G IC , is experimentally found using the double cantilever beam (DCB) of international standard [START_REF]Fibre-reinforced plastic composites -Determination of mode I interlaminar fracture toughness, GIC, for uni[END_REF]. This energy corresponds to the interface glass woven and carbon unidirectional lamina (GFRP/CFRP) for the last ply (G ICCG ) and to the interface carbon/carbon (CFRP/CFRP) for the plies above (G ICCC ).

The same method is used to determine the effect of the cutting tools when the cracks start to propagate. The critical thrust force is analytically also found as:

= + - - + + F πD a b a b ϑ aG K L M 8 ( ) ( ) ( 1) 3 (
)

C rθ IC 2 2 2 2 (5)
where: (8)

⎜ ⎟ ⎜ ⎟ = ⎛ ⎝ ⎛ ⎝ -⎞ ⎠ + -+ ⎞ ⎠ + ⎛ ⎝ ⎞ ⎠ K a Db Da b a Z b b a 72 2 3 ( ϑ 1) 4 3 (ϑ 1) (1 ϑ
= + - + - - + + M a b a b C b C b C b C b C b a C ( ) ( ) ( 2 )
= - -+ + + Z D D D D (ϑ 2ϑ
3) 2

(9) (10) (15)

= - -+ + + Z D D D D ' (ϑ 2ϑ
= - ⎛ ⎝ + + + + + ⎞ ⎠ C D D D D 7 2 (ϑ 1) (ϑ 2ϑ

Experimental results

Composite carbon/epoxy laminates of thickness 10.33 mm are used in this section in order to experimentally validate the models. One lamina of glass/epoxy woven fabric is added to the carbon/epoxy laminate at the exit of the hole. The stacking sequence of the used quasiisotropic laminate is [90°, 45°, 0°, -45°] S5 . The glass woven fabric lamina has a thickness of 0.13 mm and the unidirectional carbon/epoxy lamina (T700/M21) has a thickness of 0.255 mm and a surface mass of 268 g/m 2 , as shown in Fig. 3. Adding a woven glass ply at the exit of the laminate may reduce the delamination. At the same time, and in the case of the assembly of carbon composite laminate with another metallic plate (like aluminum alloys), adding this glass ply may also reduce the galvanic corrosion. Finally, this glass ply contributes to isolate and protect the airplanes against the lightning strikes.

The critical energy release rate is needed in the modelling part. For this purpose, experimental tests are conducted according to international standard [START_REF]Fibre-reinforced plastic composites -Determination of mode I interlaminar fracture toughness, GIC, for uni[END_REF] using double cantilever beam (DCB) specimen. The critical energy release rate in mode I (opening mode) is found for all cases: (i) cracks between unidirectional carbon/epoxy, (ii) cracks between glass/epoxy woven and (iii) cracks between unidirectional carbon/epoxy and glass/epoxy woven (GFRP/CFRP, Fig. 4). As shown in Fig. 4, the initiation phase is identified in the beginning of the cracks growth. However, after the initiation phase of the crack, the propagation of the crack is shown with a constant value of the energy (i.e, the plateau on the figure). As shown, the values of the critical rate energy corresponding to the initiation and propagation of cracks between unidirectional carbon/epoxy CFRP and glass/epoxy woven GFRP are 338 J/m 2 and 402 J/m 2 , respectively.

The mechanical properties of the used unidirectional carbon/epoxy and woven glass/epoxy are also experimentally found and presented in Table 1.

To validate the proposed analytical model in the previous section, experimental tests have been realized. To measure the critical thrust force, punching tests are performed. These static punching tests are considered to be the suitable method to experimentally identify delamination as a function of the remaining non-drilled plies. Indeed, it is very difficult to identify delamination during drilling. Several blind holes are drilled to be used for the punching tests. The number of nondrilled carbon plies remaining under the drill varies from zero to six. When the number of non-drilled carbon plies is zero, the glass woven fabric ply is only punched. A standard conventional twist drill, without web thinning, of diameter 16 mm and of point angle 132°, is used to drill the blind holes. The length of the chisel edge of this drill is 3.9 mm. A cylindrical punch of 3 mm diameter is used for the punching tests without pilot hole. Also, to validate the effect of the cutting edges, a pilot hole of diameter 3.9 mm is taken and another cylindrical punch of 6 mm diameter is used for the punching tests. This diameter is taken based on the experimental observations showing that the cracks propagate just after they have been initiated under the chisel edge.

The pilot holes and the blind holes are drilled using a 5-axis CNC Machine with a rated power of 25 kW and a maximum spindle speed of 18,000 RPM. Also, the punching tests are performed using the same machine. The punching force is recorded using a Kistler dynamometer 9257B, operated with a frequency of 1000 Hz and a maximum supported axial load of 15 kN. Fig. 5 shows the used experimental setup for punching tests, as well as the used laminate, the twist drill, the load cell and the punch. The following sequence is taken to perform the punching test for a given number of non-drilled plies: (i) fix the laminate on the used setup, (ii) drilling a blind hole with a given number of non-drilled plies using a twist drill, (iii) replace the twist drill by the punch, and (iv) punching quasi-static test using a speed of 1 mm/min. The process is repeated by changing the expected hole location and the number of non-drilled plies.

Results and discussion

Fig. 6 shows an example of the thrust force graph recorded during a punching test for four non-drilled carbon laminae remaining under the drill, without pilot pole. As shown on the figure, the corresponding critical thrust force at delamination measured experimentally is 880 N. This value is identified as the first point where the curve starts to lose its linearity. This corresponds to the initiation of cracks under the chisel edge. However, based on the non-linearity method, it is not easy to identify, in an accurate way, the critical thrust force due to the initiation of cracks. An ultrasonic sensor may be used in future works to identify the initiation of cracks. The significant drop in force corresponds to the failure of fibers due to bending, at the exit of the hole. Varying the number of non-drilled laminae remaining under the drill from zero to six carbon/epoxy plies, the critical thrust force at delamination is experimentally recorded for each test, in the same manner. The critical thrust force at delamination is plotted as function of the delaminated laminae remaining under the drill, for both analytical and experimental cases, as shown on Fig. 7. On the figure, a zero lamina under the drill corresponds to the punching of the glass woven ply only. The maximum relative error found between the analytical model and the experimental results is about 20% for the carbon laminate. This maximum error can be considered acceptable since the analytical model is conservative. However, for the punch of the woven glass ply, a relative error of about 75% is found. This high error could be due to the non-accurate method of the identification of the cracks initiation, which is based on the identification of the beginning of the non-linearity of the punch force curve. More, the developed analytical model is sensitive to the thickness and the critical energy release rate. Any error in the determination of these two parameters results an amplification of the error in the critical thrust force.

Several punching test have been also performed to verify the repeatability of the tests. Fig. 8 shows five punching repeatability tests for five specimens corresponding to two non-drilled laminae remaining under the drill. A maximum relative error of 3% is found. This error is small and is assumed to be acceptable. The same punching tests are repeated on another blind holes with pilot hole. Pilot holes of diameter 3.9 mm, equal to the length of the chisel edge, are pre-drilled. Fig. 9 shows an example of the recorded punching thrust force on blind hole with pilot hole for two delaminated plies remaining under the punch. Same, the critical thrust force corresponding to the propagation of cracks under the drill is identified by the non-linearity of the force curve. For the taken example, a critical thrust force of 290 N is found. More, a plateau of the propagation of cracks is found on Fig. 9. This plateau shows the propagation of cracks far from the punch. The assumption of the initiation of cracks under the chisel edge and the propagation of cracks under the cutting edges is validated. Fig. 10 shows the comparison of the analytical and the experimental critical thrust force, for a number of carbon plies varying from 1 to 6. A maximum relative error of 13% is found for the carbon laminate when two plies are remaining under the punch. When the woven glass ply is only remaining under the punch, an error of 60% is found. For the same reasons explained before for the case without pilot hole, the high value of the relative error can be explained. However, the critical thrust forces of the analytical model are always conservative with respect to the experimental results.

The effect of adding a glass woven ply at the exit of the hole is however shown when comparing the critical thrust force at delamination. Fig. 11 shows the analytical ratio of the critical thrust forces with a woven glass ply and without this ply, as function of the number of delaminated plies. The figure shows that when adding a woven glass ply at the exit of the hole, the critical thrust force at delamination is amplified. The ratio of amplification varies for this case between 1. 5 and 1, approximately, for both cases of drilling with and without a pilot hole. This result shows the importance of adding a woven glass ply on the critical thrust forces at delamination. Increasing the critical thrust force at delamination reduces the defects at the exit of the hole. In future works, the critical cutting conditions at delamination should be found and experimental tests using these values should be performed to validate these results, for a given couple of laminate/tool.

Fig. 1 .

 1 Fig. 1. Equivalent model of the laminate with glass ply at the exit for the part located under the chisel edge.

Fig. 2 .

 2 Fig. 2. Equivalent model of the laminate with glass ply at the exit for the part located under the cutting edges.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Stacking sequence and thickness of each lamina of the used laminate.

Fig. 5 .

 5 Fig. 5. Experimental punching tests using CNC machine and load cell.

Fig. 6 .

 6 Fig. 6. Example of recorded punching thrust force corresponding to the initiation of cracks for 4 delaminated plies without pilot hole, beginning of non-linear curve, value = 880 N.

Fig. 7 .

 7 Fig. 7. Comparison of the critical thrust force of the analytical model with the experimental results without pilot hole.

Fig. 8 .

 8 Fig. 8. Repeatability punching tests for two plies under the drill, a max relative error of 3%

Fig. 9 .

 9 Fig. 9. Example of recorded punching thrust force corresponding to the propagation of cracks for 2 delaminated plies with pilot hole, beginning of non-linear curve, value = 290 N.

Fig. 10 .

 10 Fig. 10. Comparison of the critical thrust force of the analytical model with the experimental results with pilot hole.

Fig. 11 .

 11 Fig. 11. Effect of adding a woven glass ply at the exit of the hole on the critical thrust force at delamination.

Table 1

 1 Mechanical Properties of the used composite materials.

	Material	E 11 (GPa)	E 22 (GPa)	E 33 (GPa)	G 12 (GPa)	G 13 (GPa)	G 23 (GPa)	ν 12	ν 13	ν 23	G 1CI (J/m 2 )	G 1CP (J/m 2 )
	Carbon/epoxy UD (CFRP)	135	8	8	4.8	4.8	3.2	0.31	0.31	0.36	400	430
	Glass/epoxy woven (GFRP)	21	21	10	4.8	4.8	3	0.05	0.05	0.3	373	530
	Interface CFRP/GFRP	-	-	-	-	-	-	-	-	-	338	402
			Punch
	Composite
	laminate		Twist drill
	Load cell

Acknowledgements

This work was carried out within the context of the working group Manufacturing 21 which gathers 18 French research laboratories. The topics approached are:

• The modelling of the manufacturing process, • The virtual machining, • The emerging of new manufacturing methods. This project has been funded with support from the Lebanese University.