Micromechanical simulations of microstructure-sensitive Stage I fatigue crack growth

Keywords: Stage I, multiaxial fatigue, short cracks, grain boundaries, dislocations

AB S T R AC T Simulations of dislocation dynamics at the tip of a Stage I crack are performed, taking into account the influence of the normal stress on the friction of the crack flanks and on the condition for dislocation emission at the crack tip. The interactions of the emitted dislocations with microstructural obstacles are analysed. The repeated decelerations and sometimes arrests that characterize Stage I crack growth are properly described by the model, and the differences in Stage I kinetics observed in reversed torsion and push-pull are analysed in terms of crack tip-grain boundary interactions.

INTRODUCTION

crack growth, which appears to be a major shortcoming for the analysis of multiaxial fatigue, as, e.g. nothing In the first stage of their development, fatigue cracks are driven by cyclic shear, but their growth rate is influenced discriminates push-pull and reversed torsion as concerns Stage I kinetics. This is why the simulations of discrete by the normal stress: it is increased by an opening stress and reduced by a compressive one. In a previous paper, 1 dislocations emission and glide ahead of a crystallographic mode II crack mentioned above were extended, simulations of dislocation dynamics at the tip of a crystallographic mode II crack, ignoring at first the so as to incorporate the interactions of the dislocations with microstructural obstacles. In the present paper, the influence of microstructural obstacles, have been presented. The crack growth rates were deduced from the results of this approach are compared to those obtained by Tanaka et al. 2 or Navarro and De Los Rios. 3 dislocation flux at the crack tip. The normal stress was assumed to affect the growth kinetics through its influence on friction of the crack flanks and on the condition A BRIEF DESCRIPTION OF THE MODEL FOR for dislocation emission at the crack tip. Preliminary UNCONSTRAINED SLIP results were qualitatively consistent with experimental data: a threshold stress intensity factor below which no

The principle of the simulations is only briefly recalled here. More details can be found in Ref. 1. Stage I fatigue propagation occurs for lack of cyclic plasticity at the crack tip was found, and for unconstrained slip, the cracks grow along localized slip-bands and can be submitted to mode I+II+III loading, but plasticity, i.e. growth of crystallographic mode II cracks was predicted to be slower in torsional fatigue than in push-pull for dislocation nucleation and glide, is related only to the shear components and is restricted to the slip band equivalent stress ranges.

In reality, due to interactions of the emitted dislo-colinear to the crack, otherwise (i.e. if non-coplanar slip is activated) there is a transition towards Stage II cations with microstructural obstacles, Stage I crack growth is characterized by repeated decelerations and propagation.

In the present simulations, only mixed mode I+II sometimes arrest that have to be properly modelled if the fatigue life and fatigue limit of structures containing loading has been considered for the sake of simplicity. This means that the dislocations that are emitted and short cracks is to be predicted. Models based on the continuously distributed dislocation theory were pro-glide along the coplanar slip plane have a pure edge character. This was also the case in the recent work by posed by Tanaka et al. 2 and Navarro and De Los Rios. 3 These models have some success in describing the Wilkinson et al., 4 who envisaged an influence of mode I on Stage I crack growth (blunting would enhance slip irregularities in Stage I kinetics. However, they do not irreversibility), but did not explicitly integrate it into Experimental information concerning crack flanks frictional interactions for long cracks loaded in mode II, in their simulations, while Pippan 5 and Caracostas et al. 6 consider mode III, and thus screw dislocations, but the presence of a static normal stress, has been obtained through combined tension and torsion tests performed underline the similitude with mode II.

The possibility of cross-slip is not envisaged here. inside a scanning electron microscope on precracked tubular specimens of maraging steel. 1 In the present This means that the present simulations are pertinent essentially for low stacking-fault-energy FCC alloys (or study, an attempt is made to reproduce qualitatively these experimental data using empirical equations. The medium SFE alloys at low temperature) as well as for short-range ordered alloys. The possible splitting of effective mode II stress intensity factor is thus calculated, assuming that a uniform, normal stress-dependent fric-dislocations into partials is, however, not represented.

Figure 1 shows the algorithm of the calculations. The tion stress, c, exists along the crack flanks: cyclic loading path is followed by incremental time steps,

K eff II =K nom II ±cǰpa
(2) Dt, small enough for the velocity of each dislocation to be considered constant over Dt. Two successive cycles with only need to be simulated, because the second cycle is representative of the steady-state. The nominal stress ficient of the material. The simulations described below where s ncp and t cp are the current values of the normal have been performed with values of c 0 between 5 and stress and shear stress on the critical plane. Because real 20 MPa, k + =0.057, k -= 0.014 (this means that c is Stage I cracks are not straight, allowance has to be made divided by 100 for s n =80 MPa, but is multiplied only for asperity-induced friction that tends to reduce the by three for s n =-80 MPa, consistent with experimencrack driving force, and is either enhanced or reduced tal data reported in Ref. 1). by a compressive (respectively tensile) normal stress.

c=c 0 Ωexp(-k + Ωs ncp )i f s ncp 0 c=c 0 Ωexp(-k -Ωs ncp )i f s ncp ∏0 (
The critical mode II stress intensity factor for the emission of a coplanar edge dislocation from the crack tip, which depends on the mode mixity parameter Y= arctan(K II /K I ), is then calculated, using the expression given by Sun et al.:

7 K nucl II = S 2m (1-n) C c r us -aΩ(c u us -c r us ) A p 2 -Y BD (4)
where a, c u us and c r us are material parameters estimated by atomic models (density functional theory or embedded atom method) and tabulated in Ref. 7 for a few materials, among which are iron, nickel and aluminium. Because c u us >c r us , Eq. (4) predicts a lower threshold stress intensity factor for dislocation nucleation when Y decreases, i.e. when an opening stress is present. Figure 2 illustrates this effect for the values of a, c u us and c r us given in Ref. 7 for nickel and used in the simulations.

The shear stress on each dislocation in the plastic zone is then evaluated as: constants. For the simulations described below, t f varied between 20 and 90 MPa. Typical values of v 0 and m for FCC metals (13 ms -1 and 0.88, respectively) taken from the velocity measurements made on edge dislocations in pure copper by Jassby and Vreeland 8 were chosen.

t i = K eff II √ 2px i - mb i 4p(1-n)x i -∑ j≠i mb j 2p(1-n) S x j x i Ω 1 x j -x i +t cp (5)
The new position of each dislocation is then deduced, and annihilation criteria are checked: if a dislocation comes close enough to the crack tip (less than 1 A ˚), or if the distance between two dislocations with opposite signs becomes less than 16 nm, they are removed from the simulation.

The real mode II stress intensity factor, with allowance made for crack tip shielding by the dislocation stress field, is then evaluated as:

K tip II =K eff II -∑ n i=1 mb i (1-n) √ 2px i (7)
The dislocation emission criterion:

K tip II ∏-K nucl II or K tip II K nucl II (8)
is then checked to decide whether a negative or positive dislocation can be emitted. This sequence is repeated until the second cycle is completed. Then, the crack growth rate per cycle is deduced from the dislocation flux as follows. The crack a pair of positive-negative dislocations has been emitted at the crack tip, or when a positive (or negative) dislocation returns to the crack tip. In the latter case, it is in which the first three terms represent, respectively, the assumed that even though the crack tip geometry before crack tip stress, image stress and stress of other dislothe dislocation nucleation is, in principle, recovered cations. The last term, which had been omitted in Ref. 1, when this dislocation comes back, the free surface is the far-field term, negligible for dislocations located increment created at nucleation, that has been exposed very close to the crack tip, but more important for to environment and gas adsorption in the meantime, leading dislocations, when the size of the plastic zone is cannot be rewelded afterwards. Anyway, both events a relatively large fraction of the crack size, as will be the correspond to some cyclic plastic flow at the crack tip case for the short cracks considered below. In the followand should thus contribute to its growth. ing, however, the size of the plastic zone will never An example set of data used for the simulations, in exceed 0.2a, so that Eq. ( 5) may be considered a reasonaddition to the shear modulus and Poisson's ratio able approximation. In the author's view, anyhow, the (70 000 MPa and 0.3, respectively), is given in Table 1. crudest approximation is perhaps not the use of an elastic Figure 3 (published in Ref. 1 with a misprint on the stress field (somewhat corrected for plasticity through abcissa scale) shows the mode II crack growth rates dislocations contributions) but rather the direct use of calculated, for unconstrained slip, in push-pull and the external loading for the calculation of t cp and reversed torsion, for Tresca equivalent stress ranges, K nom II , without any account for internal stresses as yet. drawn in a bilogarithmic plot, as a function of the This might be a way for future improvement of the nominal DK II , for various values of the crack flanks model.

friction stress, c 0 . In reversed torsion, where the effective The velocity of each dislocation is then calculated as: loading is fully reversed and where no opening stress affects the threshold for dislocation emission, the calcu-

v 1 =v 0 Ωsign(b i )Ωsign(t i )Ω|t i |-t f m
where x is zero if x∏0 and x otherwise (6) lated growth rates follow a very simple equation:

t f is the resistance to dislocation glide when slip is not da dN = (1-n) 4ΩmΩbΩt f Ω(DK eff 2 II -4ΩK nucl 2 II ) (9)
constrained by a grain boundary, v 0 and m are two thus considered to stop [if Eq. ( 8) was still applied, the simulation would diverge, i.e. an endless process of emission-annihilation would occur, which is meaningless]. Strictly speaking, the last position of the tip for which the crack growth rate can be obtained from the simulations is at a distance x 0 from the obstacle, where x 0 is the abscissa of the unstable equilibrium position of a dislocation at a crack tip calculated by Ohr, [START_REF] Ohr | An electron microscope study of crack tip[END_REF] below which the dislocation is attracted back to the tip

k + k - t f v 0 c r us c u us t GB (MPa) (MPa -1 ) (MPa -1 ) (MPa) (ms -1 ) m (Jm -2 ) (Jm -2 ) a (
A x 0 = (K II √ 1-n-√ K 2 II Ω(1-n)-2ΩmΩbΩt f ) 2 8ΩpΩ(1-n)Ωt 2 f B
that is a few Angstro ¨m for the parameters considered here. If the obstacle has not yet been overcome by dislocations when the crack tip is closer than x 0 , the crack is considered to stop.

Simulations of stage I growth for two constant stress ranges (Dt/2=36.95 MPa and Dt/2=37.8 MPa) and 30 MPa, and the crack flanks friction stress, c 0 , was 20 MPa. Figure 4 shows the evolution of the calculated growth rate. It can be shown that when the maximum in which K nucl II is the emission threshold in pure shear. applied shear stress is less than t f , the crack accelerates, The threshold for propagation is thus 2K nucl II in that case.

as long as its plastic zone does not reach the obstacle,

INTERACTIONS WITH MICROSTRUCTURAL OBSTACLES

Influence of an impenetrable obstacle

If there is an impenetrable obstacle ahead of the crack tip, the dislocations emitted by the crack pile up there, and as the crack propagates towards the obstacle, the shielding effect due to the pile up is stronger and stronger [see Eq. ( 7)]. The increment of K eff II necessary for the emission of a new dislocation is thus higher and higher. As a result, there are fewer and fewer dislocations emitted, even though DK nominal II increases, so that the crack decelerates. When the crack tip is finally so close to the obstacle (e.g. less than the core radius of a dislocation) that there is not enough space for a single dislocation loop to expand from the tip, and anyway the as emission becomes physically impossible. The crack is and then slows down until it stops. But for both cases the crack when it changes sign [see Eq. ( 5)]. Below a certain distance between the obstacle and crack tip, illustrated in Fig. 4, t cp,max >t f , so that the crack tip plastic zone hits the obstacle for each crack length however, the pile-up shielding effect becomes dominant and the crack growth decreases, as in torsion. Figure 5 considered. But for the smallest stress range considered, the number of dislocations emitted is small, so that down also shows that for equal crack lengths and equivalent stress ranges, the range of interaction with the obstacles to 5 mm distance from the obstacle, the rise of the shielding term in Eq. ( 7) is slower than the increase in (which is identical to the size of the plastic zone) is longer in push-pull than in reversed torsion. K eff II , and the crack is able to accelerate in spite of its constrained plastic zone. For the highest stress range considered, on the contrary, the rise of the shielding Influence of grain boundaries term approximately compensates that of K eff II at the beginning, and then exceeds it, therefore the constant Slip transfer beyond a grain boundary and then decreasing growth rate.

The influence of an impenetrable obstacle on Stage I Grain boundaries (GBs) are generally not impenetrable to dislocations. They can be sinks for incident lattice kinetics is more complex in push-pull. Figure 5 compares the evolution of the calculated crack growth rates as a dislocations as well as effective sources of dislocations.

Ohr [START_REF] Ohr | An electron microscope study of crack tip[END_REF] has made direct observations of crack tip-GB function of the distance to the obstacle in push-pull and reversed torsion (here, the obstacle is moved, not the interactions in thin foils loaded in a transmission electron microscope. He reports dislocations annihilating in GBs, crack tip, and DK nominal II is constant). The maximum applied shear stress, t cp,max was 27.2 MPa (which is less while others were emitted at the GBs into the neighbouring grain. than the friction stress chosen here, t f =90 MPa) and c 0 was 10 MPa. Whereas in torsion the growth rate in the In the present simulations, if the plastic zone at the crack tip reaches a GB, dislocations are assumed to pile presence of an obstacle is always smaller than for unconstrained slip, the obstacle can accelerate the crack growth up there until the shear stress on the leading dislocation reaches a value allowing it to enter the GB and a new in push-pull, provided it is not too close. This paradoxical result can be understood in the light of the simu-one to glide into the next grain, on a slightly misoriented plane. The geometrically necessary dislocations left at lations detailed in Ref. 1. It was shown that in push-pull the return of emitted dislocations to the crack tip, the GB by the incorporation reaction are not taken into account, nor is, explicitly, the tilt of the crack path necessary for crack advance, was made difficult by enhanced crack flanks friction in the compressive stage beyond the GB. But some of it is modelled through the roughness-induced friction stress [Eqs (2) and ( 3)]. The of the cycle: the effective loading was therefore not fully reversed. But if an obstacle limits the size of the plastic same criterion is then applied to the following dislocations. This scenario, consistent with Ohr's obser-zone and keeps the dislocations closer to the crack tip, they are attracted back more easily by the stress field of vations, has an additional advantage: it avoids introducing an ill-defined position for a dislocation source in the next grain, as is done in some short crack models. 3 Similar conditions for grain boundary crossing were introduced by Pippan, 5 and Li and Li 10 in their simulations. The critical shear stress for slip transfer, t GB , should depend on the crystallographic misorientation of the adjacent grains and on the angle of incidence of the slip plane on the GB plane. Here it is considered as independent of the slip direction (the GBs are also obstacles for dislocations gliding back towards the crack tip at unloading). Figure 6 shows the positions of the dislocations emitted by a crack tip located 1 mm away from a first GB and 16 mm from a second one, at various points of a load ramp, in torsion. Two cases are considered: t cp,max <t f [30 and 90 MPa, respectively, in Fig. 6(a)], where c 0 = 10 MPa and t GB =350 MPa; and t cp,max >t f [41 and from the moment when the condition for slip transfer is Tanaka et al., 2 according to which the dislocation density is infinite on both sides of the GB.

Irregularity of Stage I kinetics

Simulations of Stage I growth at a constant stress range (Dt/2=36.5 MPa) have been performed, in reversed torsion, for a crack of initial half-length, a=105 mm, in a polycrystal with a 15-mm mean grain size and a 30-MPa friction stress. The friction stress along the crack flanks was c 0 =20 MPa. The calculated crack growth rates are plotted versus the crack length in Fig. 7, for various values of the critical stress for slip transfer at grain boundaries, t GB . These values of t GB are small enough to allow the crack to cross the grain boundaries, but slip transfer is achieved when the crack tip is very close to the GB (#0.1 mm), so that the corresponding points merge with those corresponding to the entry of the crack tip into the next grain. For t GB =300 and 400 MPa, the size of the plastic zone, in microns, is indicated above (or below) each point of the curve. It can be seen that the condition for slip transfer beyond the first GB is met earlier and earlier in successive grains because of the increase in DK nom II associated with an increase in the number of dislocations emitted and piled up against the GB. But this does not produce a sudden acceleration, as slip transfer is progressive: the plastic zone may well extend over the GB, but a substantial fraction of the emitted dislocations may still be withheld by the GB and have a strong shielding effect. For first met, plasticity extends progressively into the next grain (in this example it does not even reach the next grain boundary). In the second case, although dislocations that individually pass the first GB glide at once to the next one, slip transfer is more progressive than in the model of Navarro and De Los Rios 3 for which the blocked slip band, with all its dislocations, jumps to the next GB when a critical stress concentration is reached. It also appears that, due to the strong repulsive force of the pile up that pushes leading dislocations away, a second dislocation-free zone (in addition to that present dislocation distribution for a 'propagated slip band' of three of the emitted dislocations have been transmitted to the second GB and eight of them remained stacked in a 1-mm-wide zone ahead of the crack tip. Unlike the case of unconstrained slip, there is therefore no correlation between the size of the plastic zone and the crack growth rate. It also appears that each time the crack tip enters a new grain there is a sudden acceleration. The magnitude of this acceleration depends on t GB . Figure 8 compares the distribution of emitted dislocations at K max for crack half-lengths, a, of 149 and 150 mm, for various values of t GB . It is clear that the stronger the t GB , the higher the fraction of emitted dislocations withheld by the first GB for a=149 mm (6/13 for t GB =300 MPa, 7/10 for 350 MPa and 7/7 for 400 MPa), and thus the larger the decrease in dislocation shielding when the crack passes the GB, this allows the emission of a larger number of dislocations.

Influence of the loading mode on GB crossing

It had been observed on a Co45Ni alloy, that for equivalent stress ranges it takes approximately twice as long for microcracks, once initiated, to cross the first GB encountered in reversed torsion than in push-pull, [START_REF] Doquet | Crack initiation mechanisms in torsional fatigue[END_REF] but it was not clear whether this came merely from a slower transgranular growth rate, or if the interaction between microcracks and GBs was stronger in torsion. The present simulations throw some light on that point. Figure 9(a) compares the calculated stress concentrations length a=100 mm propagating toward a GB, initially 50 mm away, for reversed torsion and push-pull loadings of equivalent stress ranges. First, it can be noticed that past a given crack length, the stress concentration in the next grain decreases because there are fewer dislocations emitted due to their increased shielding of the crack tip stress field. This is in contrast with the models of Tanaka et al. 2 and Navarro and De Los Rios, 3 according to which the stress concentration varies monotonically with the crack length until it reaches the GB. Anyway, the stress concentration in the next grain, as well as the shear stress on the leading dislocation, are both much higher in push-pull, because the opening stress increases K eff II and decreases K nucl II , so that many more dislocations would be able to shield the mode I singularity, contrary to coplanar slip. The explanation for the slower develop-uted dislocation models quoted above, relating the growth rate to the vector CTD (total crack tip displacement, ment of microcracks in torsion lies thus probably in the interaction with microstructural obstacles as well as in taking into account an opening component) evaluated by LEFM. This equation also contains an empirical pro-the slower transgranular growth rate predicted in Ref. 1 and illustrated in Fig. 3. portionality constant that is not calculated. Moreover, this model is not yet able to deal with the influence of a compressive normal stress that does not induce any K I DISCUSSION term or any CTOD, but is well known to make Stage I crack growth slower, as the influence of such a stress on The interest of this approach compared to existing models based on continuously distributed dislocations is the mode II 'closure' term is not specified. The influence of grain boundaries is also ignored (although interesting now discussed.

In previous work on Stage I cracks, 2,3 once the crack work on this aspect has been performed by Li, using a finite element method). tip sliding displacement (CTSD) was deduced from the dislocation flux, growth laws of the type:

The present simulations have to be considered as a tool for the understanding and analysis The present approach, based on a simulation of discrete dislocation emission, glide and annihilation, at the tip of were adopted, in which the constants B and m were unknown and could not be deduced from calculations Stage I crack, assuming an influence of the normal stress on crack flank friction and dislocation emission was performed on continuously distributed dislocations. These models do not, in fact, predict the crack growth shown to reproduce important experimental facts.

(1) The existence of a normal stress-dependent rates. By contrast, the present approach is fully quantitative. However, it has to be recognized that the present threshold stress intensity factor, below which no propagation can occur, even in a single crystal, for lack of model requires some data available only from sophisticated measurements (c 0 , k + , k -, v 0 , m, t f , t GB ) or cyclic plasticity at the crack tip (2) The variations in the crack growth rate or even calculations (c u us , c r us , a) that make it unsuitable, for the time being, for engineering practice.

the arrest of a crack due to interactions with microstructural obstacles which characterize Stage I crack growth. A second important difference is that the models mentioned above do not predict any threshold for Stage I A dual explanation for the slower development of Stage I cracks in reversed torsion compared to push-pull crack growth when slip is not constrained. This is not consistent with experimental data on precracked single was also proposed, i.e. a slower transgranular propagation for unconstrained slip, mainly due to crack flanks friction, crystals, showing the existence of a finite, normal stressdependent threshold stress intensity factor for crystallo-and a smaller stress concentration induced by constrained crack tip plasticity in the next grain. graphic crack growth. 12 In the present approach, due to the consideration of a threshold stress intensity factor for dislocation emission at the crack tip, this experimental REFERENCES fact is predicted, whereas in the two other models, the dislocations necessary for the complete shielding of the

  3) intensity factors for a Stage I crack of length 2a lying along the critical plane (i.e. the plane where the shear stress range is maximum) are calculated at each timec 0 is a constant which characterizes the friction stress in step as: the absence of any normal stress and is thus related to the tortuosity of the crack path. k + and k -are two K I =s ncp Ωǰpa when s ncp 0K nom II =t cp Ωǰpa constants, the latter connected with the friction coef-(1)

Fig. 1

 1 Fig. 1 Algorithm of the simulations.

Fig. 2

 2 Fig. 2 Evolution of the dislocation nucleation threshold with mode

Fig. 3

 3 Fig. 3 Comparison of the calculated crack growth rates versus

Fig. 4

 4 Fig. 4 Evolution of the growth rate for a Stage I crack (initial half-

Fig. 5

 5 Fig. 5 Influence of an impenetrable obstacle on the Stage I crack

Fig. 6

 6 Fig. 6 Positions of the dislocations emitted by a crack tip located

Fig. 7

 7 Fig. 7 Evolution of the growth rate for a Stage I crack (initial half-

Fig. 9

 9 Fig. 9 Shear stress evaluations in reversed torsion and push-pull,

Fig. 8

 8 Fig. 8 Distribution of dislocations at K max , at the tip of a Stage I

  1 V. Doquet (1998) A first stage in the development of microcrack singularity are considered as naturally available. mechanical simulations of the crystallographic propagation of This assumption does not seem appropriate for small fatigue cracks under multiaxial loading. Fatigue Fract. Engng stress ranges. Mater. Struct. 21, 661-672. 2 K. Tanaka, Y. Akinawa, Y. Nakai and R. P. Wei (1986) Modelling But the main difference between the present approach of small fatigue crack growth interacting with grain boundary. and pre-existing models is the attempt to capture the Engng Fracture Mech. 24, 803-819. influence of the normal stress on crack tip plasticity and 3 A. De Navarro and E. R. Los Rios (1988) Short and long on the 'true' Stage I crack growth (as opposed to the fatigue crack growth: a unified model. Phil. Mag. A 57, 15-36. 'extended' Stage I, involving secondary as well as coplanar 4 A. J. Wilkinson, S. G. Roberts and P. B. Hirsch (1998) Modelling slip, considered by Li 13 ) which is believed to be essential the threshold conditions for propagation of Stage I fatigue for the analysis of multiaxial fatigue. Li derived an equacracks. Acta Mater. 46, 379-390. 5 R. Pippan (1992) The condition for the cyclic plastic defor-tion, of the same type as those from continuously distrib-

Table 1

 1 Example set of data used in the simulation c 0


The reproductive cost of Drosophila melanogaster : effects on cold tolerance

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The reproductive cost of Drosophila melanogaster : effects on cold tolerance

Results : fecundity

Take home message

In order to survive, species often make trade-offs between reproduction and survival, often resulting in reduced reproduction. During the cold and stressful winter months Drosophila melanogaster, like a lot of freeze avoidant insects, enters a reproductive dormancy. There could be a trade-off between reproductive activity and cold stress tolerance.

romane.gout@univ-rennes1.fr

Drosophila's winter strategy

The responses to overwintering by oogenesis stop suggests a cost of reproduction and/or an increased cold tolerance by reduced reproductive activity in Drosophila melanogaster.

We compared fecundity and cold tolerance of gravid versus virgin females. We then attempted to artificially stop oviposition by pharmacological treatments : Rapamycin and Phloroglucinol. Our hypothesis was that virgin flies and chemical treated flies will lay respectively less or no eggs and this would affect cold tolerance.

Fecundity

Cold tolerance

We put about 120 flies in a refrigerating column set with a ramping rate of -0.5 C/min.

Recovered Coma

1

  Université de Rennes 1, France, UMR ECOBIO CNRS 6553 -CNRS : 6553 France Romane Gout 1 , Hervé Colinet 1

••

  Generally, mated flies laid more eggs than virgins • The flies' temporal oviposition profile differs, there's a delay in peak egg laying activity for mated females compared to virgin ones 1. We put either one female (virgin/mated) or a pair of females (chemical treatments) in falcon tubes 2. Every 24h for 7 days we changed the charcoal medium filled caps and counted the eggs treated flies had better cold tolerance than control ones in both assays • Virginity did quantitatively reduced egg ovipostion, but it did not confer an advantage in cold thermal stress. • Control flies laid eggs normally • Phloroglucinol treated flies gradually stopped laying eggs after the second day • Phloroglucinol completely stopped oviposition which confered an advantage in cold thermal stress *We only show data for the phloroglucinol set as rapamycin showed no sinificant result Phloroglucinol is considered a polyol, and thus might have some cryoprotective propreties which are currently unknowned * 0.032


Jean-François Mull
email: jeanfrancois.mull@ensam.eub

Camille Durand
email: camille.durand@ensam.eu

Cyrille Baudouin

Régis Bigot

Marc Borsenberger

Validation Of A Purely Elastic Model And A Finite Element Model For A Screw Press

The increasing use of superalloys in the industry brings new issues to forging manufacturers concerning Finite Element analysis of the forming process. Once we consider high performing materials, significant differences can occur between numerical and experimental results. The lack of knowledge about materials and thermal exchanges explains a part of these differences but it has been shown that the machine behavior has a significant impact on the forging process. Press modelling is a way to quantify the energy dissipated in the machine structure and improve simulations. This study is a first step in the screw press modelling. Starting from an approximation of the press geometries, a purely static elastic (PSE) model is developed and a numerical simulation considering only uprights is performed. Uprights stiffness predictions from the PSE model and the FE simulation are compared and the PSE model is validated. Then, the press is approximated by a portal frame and FE simulation is realized to determined uprights stiffness by considering links effects and bending behaviors in the structure. Comparison with experimental results validates the approximation.

INTRODUCTION

Forging processes are often developed with the help of numerical simulation to determine the best sequence and process parameters. However, for high performing materials, significant differences are observed due to the elastic collision between tools and billet caused by the high resistivity of the material [START_REF] Durand | 17th International Conference on Metal Forming[END_REF]. Thus, an important part of the stroke energy is returned to the machine and must be properly considered to improve simulation's prediction.

During a forging operation, a part of the stroke energy is dissipated as elastic energy in the machine itself. A first approach is to quantify this loss by modelling the press as an equivalent spring [2]. It is possible to consider an equivalent spring in the three directions, axially and in rotation. With the stiffness associated with these springs, the loss of energy in the machine deformations can be calculated. Another way to consider the press behavior is to introduce the flexibility matrix, whose coefficients express the deformation of the axis i in rotation or axially due to a moment or a load applied on the axis j. This matrix can be completed with a clearance's vector to consider the non-linearity of the force due to the guidance clearances. This model is commonly used and was applied for the case of hydraulic, eccentric and screw presses [START_REF] Chodnikiewicz | [END_REF][4][5]. Press stiffness identification methods are an important subject of research because of the difficulties to stress machines in the adapted way. Indeed, determining stiffness experimentally, demands to develop complex tools able to generate the needed deformation to be able then to calculate stiffness. A loading of a machine in a specific direction can be realized through two mains methods: either we use the machine in its normal functioning mode and a stroke is exploited as load generator [6,7] or external device like hydraulic cylinder placed on the press table can be used to apply load directly to the ram [8]. Otherwise some studies propose to perform FE simulation to avoid experimental errors and simplify mechanical loading [9]. Then, experimentally or numerically, deformations obtained allows to calculate press stiffness. Several authors proposed to predict the equivalent press stiffness by modelling the press as a succession of springs [5,10]. Each spring represents an element of the press with its proper stiffness. The equivalent press stiffness is expressed according to the press elements stiffness and the type of elements connection defined as series or parallel. So far, this method considers a limited number of press elements and do not provide a specific way to obtain press parts stiffness. This paper presents a purely static elastic (PSE) model for a screw press based on the elastic behavior of materials and an approximation of the press geometries. This model allows to predict the press uprights stiffness. Moreover, the CAD of the uprights is developed, and FE simulation are performed to obtain stiffness. Then, the CAD is completed with the crosshead to approximate the press by a portal frame. FE simulation is realized and the stiffness value obtained is compared with experimental investigations with the aim to validate the approximation of the press by a portal frame.

MATERIAL

The screw press of our study is the LASCO SPR 400 from the VULCAIN platform in Metz, in France (Fig. 1 a)). The structure of the machine is a portal frame made of four uprights constituted of pre-stressed steel tie rods embedded in a cast iron case. A bedplate bears the four uprights which support the crosshead. The press ram is linked to the screw with a nut fixed to the ram. The screw being linked to the frame by a pivot linkage, this assembly allows a translation motion for the ram. The rotation of the screw is ensured by the flywheel on the top of the press, alimented by a direct electric drive motor. The motor can be reversed to allow downstroke and upstroke. Concerning materials, the screw and the ram are made with steel whereas the nut is made with bronze. The press integrates strain gauges fixed on the press crosshead to measure the evolution of the load during strokes. Furthermore, the position of the ram in comparison with its bottom dead point is recorded with a magnetic coding system.

VALIDATION OF THE PSE MODEL Purely static elastic model

Press geometries are approximated by using standard forms defined in TABLE 1. The schema of the approximation of the machine is shown in Fig. 1 b).

FIGURE 1. a) Face view of the press LASCO SPR400 b) The geometrical approximation of the press elements

The standard forms chosen to discretize the press are defined with a surface S and a length l0. Considering one press part, according to the Hooke's law:

𝜎 = 𝐸. 𝜀 (1)
With σ the stress applied on the surface S,  the equivalent strain and E the Young's modulus of the material. By substituting the stress and the equivalent strain by their definitions in the Eq. ( 1), an expression of the load applied on the surface S can be obtained as in the Eq. (2).

𝐹 = 𝐸.𝑆 𝑙 0 . (𝑙 -𝑙 0 ) (2)
With F the load applied on the surface S and l-l0 the true stain of the element. Given the Eq. ( 2) and the relation between load and deformation for a spring Eq. ( 3), the stiffness of the element can be identified Eq. ( 4) then calculated according its material and its geometry.

𝐹 = 𝑘. (𝑙 -𝑙 0 ) (3)
𝑘 = 𝐸.𝑆 𝑙 0 (4)
For each one of the forms defined in the TABLE 1, it is possible to calculate an associated stiffness thank to the Eq. ( 4). Thus, it is possible to determine the stiffness of each press part considered.

TABLE 1. Stiffness of standard forms

By studying the connections between each element, the press can be modeled as a succession of springs. In the Fig. 2, each line represents an element whereas points show the type of connection, series or parallel. For each one of these elements is associated a proper stiffness. Crosshead and bedplate are not yet modelled. This study focuses on the calculation of equivalent uprights stiffness. Each upright is constituted of one prestressed steel tie rod and a cast iron case common between two uprights, as it is shown in the Fig. 2. According to the type of connections and the stiffness of each spring composing the uprights, the equivalent stiffness of the four uprights is calculated: KPSE = 2.39*10 10 N/m.

Finite element simulation

The CAD is developed with CATIA V5 to realize FE simulations with the module Generative Part Structural Analysis. The mesh is defined as regular and a 50mm size parabolic tetrahedron element is chosen. First, the uprights are modeled considering the steel tie rods and the cast iron case (Fig. 3 a)). In the FE simulation a tensile load of 5000kN is applied on the top of the uprights, the base of the uprights is fix. The stiffness of the uprights is calculated according to the Eq. ( 3) with the vertical elongation of the uprights from the results of the FE simulation: KUprightsFE = 2.45*10 10 N/m. The PSE model and the simulation shows a good agreement. Indeed, the relative deviation between kPSE and KUprightsFE is equal to 2.4%. This small deviation can be explained by the approximations done in the geometries and materials definition of the press elements in the models. Thus, in the case of axial load, the PSE model is a good way to predict press part stiffness, even for complex structure as the uprights. It might be possible to extend this approach for other press elements.

Results

VALIDATION OF THE PORTAL FRAME APPROXIMATION

Finite element simulation

The CAD of the uprights is completed with the crosshead to approximate the behavior of the whole press by a portal frame (Fig. 3 b)). A FE simulation is realized with the same mesh definition as the first simulation. A load of 5000kN is applied on a circular surface centered on the inferior part of the crosshead, corresponding to the screw surface, this simulating the stress caused by a forging operation. Then, the stiffness of the uprights is calculated in the same way as previously: KPortalFrameFE = 1.40*10 10 N/m.

Experiments

The determination of the uprights stiffness necessitates the measurement of the uprights elongation during a stroke. For this purpose, a 3D tracking point system following reflecting stickers placed on the upright was used (Fig. 4 a-b)).

Moreover, in order to measure a significant elongation of the upright, load applied on the frame must be maximal and the forming time must be long enough to allow the recording of enough data. Inelastic collision on C17 carbon steel billet implying a maximal force of 6414 kN was chosen. This load is closed to the maximal load allowed by the machine. In addition, the billet is designed with a high length/diameter ratio to increase forging time and record more data.

Experiment was repeated twice, load and elongation curves are overlapping for both. Thus, the stroke is considered repeatable and only the first experiment is shown for clarity reason (Fig. 4 c)).

However, data recorded by PONTOS cannot be used directly. Indeed, PONTOS measures the distance between two stickers but not the total elongation of the upright. A linear deformation of the upright is assumed to calculate the total elongation.

Knowing the load applied and the elongation, the uprights stiffness is calculated with the Eq. ( 3) for each measurement. Then, the mean of these values is calculated: kExp = 1.31*10 10 N/m. We notice that the FE simulation of the portal frame agrees well with the experimental results, indeed the relative deviation between KPortalFrameFE and KExp is equal to 6.9%. Sensors accuracy and approximations on the geometries and materials definition of the press elements can explain this slight difference. Despite the simplicity of the portal frame approximation to model the screw press, the FE simulation provides a good prediction of the experimental uprights behavior. The use of portal frame approximation in FE simulation could be a way to predict vertical load and moments applied to the uprights by considering the links effects in the structure and the bending behavior of the crosshead. A coupled approach between FE simulation and analytical modelling could be a way to improve the PSE model by considering links effects and bending behavior.

CONCLUSIONS

Considering a screw press as a succession of springs, this study proposed to predict upright stiffness with a purely static elastic model based on press geometries and materials. FE simulations for the press uprights and the whole press approximated by a portal frame were performed. The results of simulations and experimental investigations allowed us to determine several uprights stiffness values. The following conclusions were drawn:

1. PSE model is sufficient to explain uprights behavior without the consideration of the crosshead. If links effects and bending behavior can be neglected, it might be possible to predict stiffness of other press elements with the PSE model; 2. An approximation of the press by a portal frame allows good predictions of the press uprights stiffness with FE simulation. It may be an appropriate solution to predict moments and load applied to the uprights; 3. A step forward to improve the prediction of the PSE model will be to consider the crosshead bending behavior and links effects in the press structure. FE simulation of the screw press by a portal frame could be a way to study these effects and complete PSE model.

FIGURE 2 .

 2 FIGURE 2. a) The structure of the screw press LASCO SRP400 b) Purely static elastic model of the press system

FIGURE 3 .

 3 FIGURE 3. a) Result of the finite elements simulation of the press uprights b) Result of the finite elements simulation of the press approximated by a portal frame

FIGURE 4 .ResultsTABLE 3 .

 43 FIGURE 4. a) 3D tracking point system PONTOS b) Stickers placed on the press upright c) Upright elongation and load during a stroke on carbon steel C17

TABLE 2 .

 2 Stiffness obtained by PSE model and uprights FE model PSE

Model (N/m) *10 10 Upright FE (N/m) *10 10 Standard deviation

	2.39	2.45	2.4%


Sarah Fodil-Cherif
email: fodilcherif@chu-montpellier.fr

Rachel Desailloud

Thierry Brue

UPDATES IN NEUROENDOCRINE NEOPLASMS : FROM MECHANISMS TO THE CLINIC

Keywords: Neuroendocrine neoplasm, neuroendocrine tumor, neuroendocrine carcinoma, pituitary, pancreas, pheochromocytoma, paraganglioma, personalised medicine, precision medecine

Scientific advances constantly improve our understanding of the mechanisms underlying tumorigenesis, allowing us to now analyse cancer in a more precise manner and to identify at an earlier stage the tumours that have an increased risk of aggressive behaviour.

Understanding theneuroendocrine neoplasms at a molecular level has permitted us to provide increasingly targeted treatments to our patients, which safety and efficacy have been validated by large randomised trials. Moreover, the first studies to examine the benefits of using targeted therapies after molecular profiling of neuroendocrine neoplasms, have shown encouraging results, allowing us to foresee more and more personalised medical treatments in the future. This literature review aims to summarise recent advances in neuroendocrine neoplasms and to show how the identification of new mechanisms underlying tumorigenesis can be of benefit for the management of patients in clinical practice.

In 2000, Hanahan and Weinberg published a highly-cited paper, 'The Hallmarks of Cancer' [START_REF] Hanahan | The Hallmarks of Cancer[END_REF] , which suggested that the majority of cancers have acquired the same group of functional capacities during their development. They identified six major characteristics responsable for tumour progression, including the escape from apoptosis, the ability to metastasise and the induction of angiogenesis. A decade later, significant progress had been made in our understanding of the mechanisms underlying tumour development, allowing the hallmarks to be updated in 2011 [START_REF] Hanahan | Hallmarks of Cancer: The Next Generation[END_REF] , to highlight new characteristics, including the capacity to avoid immune surveillance, the role of inflammation and role of genomic instability. The large number of recent discoveries finally led to a new version of cancer hallmarks being published in 2022, which notably includes the impact of epigenetic modifications and role of the microbiome in tumour development [START_REF] Hanahan | Hallmarks of Cancer: New Dimensions[END_REF] . As well as increasing our understanding of tumour development, the identification of underlying mechanisms has provided new biomarkers for detection and surveillance, and new potential therapeutic targets, notably in the field of oncoendocrinology. This literature review aims to summarise recent developments in the field of neuroendocrine neoplasms and to show how identification of new genetic and epigenetic mechanisms, developments in histolopathology and identification of new proteins underlying tumour development, can have benefits for diagnosis, treatment and prognosis of patients in clinical practice.

IDENTIFICATION OF NEW MECHANISMS INVOLVED IN ONCOENDOCRINOLOGY

The place of 'omics' 'Omics' approaches have become ubiquitous in basic research, however they are now also an integral part of clinical practice and routine patient management. In endocrine and neuroendocrine cancers, the identification of new mechanisms involved in tumorigenesis, new genes linked to cancer predisposition and new target proteins is continuously expanding [START_REF] Tarazona | Undisclosed, unmet and neglected challenges in multi-omics studies[END_REF] . However, the growing place of bioinformatics, genomics, epigenomics and proteomics, as well as the study of clinical data and population analysis, is of interest to the clinician only if these make concrete improvements to patient management, result in the identification of new biomarkers, assist in disease prediction or provide new, more precise, and more personalised, therapeutic targets.

Advances in genetics

Cancer is characterised by abnormal and uncontrolled cell proliferation, principally caused by mutations in so called driver genes [START_REF] Stratton | The cancer genome[END_REF][START_REF] Stratton | Exploring the Genomes of Cancer Cells: Progress and Promise[END_REF][START_REF] Martínez-Jiménez | A compendium of mutational cancer driver genes[END_REF] , which affect a group of key cellular functions and confer selective advantages on some cells in an organ or tissue compared to their neighbours [START_REF] Hanahan | The Hallmarks of Cancer[END_REF] . Since the beginning of the study of molecular biology, one of the principal aims of cancer research has been the identification of these driver genes [START_REF] Martínez-Jiménez | A compendium of mutational cancer driver genes[END_REF] , which would allow the development of targeted anticancer therapies and the discovery of prognostic biomarkers, as well as provide improvements in therapeutic follow up [START_REF] Hanahan | Hallmarks of Cancer: The Next Generation[END_REF][START_REF] Hanahan | Hallmarks of Cancer: New Dimensions[END_REF] .

Adrenocortical carcinoma and adenoma

Prior to the arrival of genomics, driver genes were generally discovered due to their presence in familial predisposition syndromes. In the case of adrenocortical carcinoma, the main anomalies which were identified were inactivating mutations of TP53 in Li-Fraumeni syndrome, alteration of the 11p15 region and overexpression of IGF2 in Beckwith-Wiedemann syndrome, and alteration of the beta-catenin signalling pathway and loss of APC expression in familial adenomatous polyposis [START_REF] Assié | Integrated genomic characterization of adrenocortical carcinoma[END_REF][START_REF] Jouinot | Genomics of adrenocortical tumors: from molecular classification to identification of driver genes[END_REF] .

There are now several ways to identify new driver genes, including exome sequencing, chromosomal alterations profiling, and integrated genomic characterization. This last method allowed the identification of ZNRF3 as a new driver gene in adrenocortical carcinomas [START_REF] Assié | Integrated genomic characterization of adrenocortical carcinoma[END_REF][START_REF] Jouinot | Genomics of adrenocortical tumors: from molecular classification to identification of driver genes[END_REF] .

ZNRF3 is a tumour suppressor gene that is a negative regulator of the Wnt/-catenin pathway and has been found to be the gene most frequently altered in adrenocortical carcinomas (20-25% of cases) [START_REF] Jouinot | Genomics of adrenocortical tumors: from molecular classification to identification of driver genes[END_REF][START_REF] Wilmouth | A metastatic ACC mouse model: Combined inactivation of Znrf3 & Tp53 results in consistent adrenocortical carcinoma formation[END_REF] . A group in Clermont-Ferrand (France), has recently shown that combined inactivation of ZNRF3 and TP53 by gene knockout (KO) in mice, leads to the formation of aggressive adrenocortical carcinomas with a 36.8% rate of metastasis in 6 month-old KO mice. This result was not reproduced in mice that had a single gene, either p53 or ZNRF3, inactivated [START_REF] Wilmouth | A metastatic ACC mouse model: Combined inactivation of Znrf3 & Tp53 results in consistent adrenocortical carcinoma formation[END_REF] .

Apart from the identification of ZNRF3 deletions being responsable for activation of the Wnt/-catenin pathway in adrenocortical carcinomas, recent studies have also identified changes in ion channels and intracellular calcium signalling in aldosterone-secreting adenomas, mutations in PRKACA resulting in activation of the AMPc/PKA pathway in cortisol-secreting adenomas, and identified the genes ARMC5 and KDM1A as being responsible for germinal predisposition to primary macronodular adrenal hyperplasia [START_REF] Jouinot | Genomics of adrenocortical tumors: from molecular classification to identification of driver genes[END_REF] .

Pituitary carcinoma

In a similar way, a number of germinal and somatic mutations have been identified in aggressive pituitary neuroendocrine tumours. The great majority of pituitary tumours are adenomas but in rare cases (<2% of macroadenomas [START_REF] Dekkers | The epidemiology of aggressive pituitary tumors (and its challenges)[END_REF] ) these tumours can be more aggressive. Aggressive pituitary neuroendocrine tumours are defined by invasion of neighbouring tissue, rapid growth, resistance to conventional treatments and multiple recurrences. The term pituitary carcinoma is used where there is a metastatic disease [START_REF] Raverot | Aggressive pituitary tumours and pituitary carcinomas[END_REF][START_REF] Burman | Aggressive pituitary tumours and carcinomas, characteristics and management of 171 patients[END_REF] .

Germinal mutations identified in aggressive pituitary tumours are mostly the same as those seen in predisposition to Lynch syndrome (MLH1, MSH2, MSH6, PMS2), being associated with microsatellite instability (DNA mismatch repair) [START_REF] Burman | Aggressive pituitary tumours and carcinomas, characteristics and management of 171 patients[END_REF] . Four cases of aggressive pituitary tumours have been described in the literature: a corticotroph carcinoma carrying an MSH2 mutation [START_REF] Bengtsson | Corticotroph Pituitary Carcinoma in a Patient With Lynch Syndrome (LS) and Pituitary Tumors in a Nationwide LS Cohort[END_REF] , an aggressive corticotroph tumour with MLH1 mutation [START_REF] Uraki | Atypical pituitary adenoma with MEN1 somatic mutation associated with abnormalities of DNA mismatch repair genes; MLH1 germline mutation and MSH6 somatic mutation[END_REF] , an invasive corticotroph tumour and an invasive macroprolactinoma both with MSH2 mutations [START_REF] Burman | Aggressive pituitary tumours and carcinomas, characteristics and management of 171 patients[END_REF][START_REF] Teuber | Aggressive pituitary adenoma in the context of Lynch syndrome: a case report and literature review on this rare coincidence[END_REF][START_REF] Loughrey | Invasive ACTH-producing pituitary gland neoplasm secondary to MSH2 mutation[END_REF] . Somatic analyses has also shown mutations in TP53, ATRX, PTEN in corticotroph tumours and CDKNA2A/CDKNA2B mutations in lactotroph and somatotroph tumours [START_REF] Burman | Aggressive pituitary tumours and carcinomas, characteristics and management of 171 patients[END_REF][START_REF] Tanizaki | P53 Gene Mutations in Pituitary Carcinomas[END_REF][START_REF] Casar-Borota | Corticotroph Aggressive Pituitary Tumors and Carcinomas Frequently Harbor ATRX Mutations[END_REF][START_REF] Guo | Identification of Novel Genes Involved in the Pathogenesis of an ACTH-Secreting Pituitary Carcinoma: A Case Report and Literature Review[END_REF][START_REF] Duhamel | Immunotherapy in Corticotroph and Lactotroph Aggressive Tumors and Carcinomas: Two Case Reports and a Review of the Literature[END_REF][START_REF] Shah | Complete Response of a Patient With a Mismatch Repair Deficient Aggressive Pituitary Adenoma to Immune Checkpoint Inhibitor Therapy: A Case Report[END_REF] .

In 2020, Casar-Borota et al [START_REF] Casar-Borota | Corticotroph Aggressive Pituitary Tumors and Carcinomas Frequently Harbor ATRX Mutations[END_REF] identified somatic mutations in the ATRX gene (which is involved in heterochromatin remodelling and telomere maintenance) in a sub-group of aggressive pituitary neuroendocrine tumours, more frequently found in those that were corticotroph tumours. Mutations in ATRX were confirmed by immunohistochemistry showing the loss of immunoexpression in 9 tumours (5 pituitary carcinomas (28%) and 4 aggressive pituitary tumours (13%)) out of 48 tumours examined, suggesting the utility of immunohistochemical staining for ATRX to identify thos patients at high risk of developing aggressive tumours or pituitary carcinomas. In addition, TP53 mutations were obsereved in 6 of these tumours [START_REF] Raverot | Aggressive pituitary tumours and pituitary carcinomas[END_REF][START_REF] Burman | Aggressive pituitary tumours and carcinomas, characteristics and management of 171 patients[END_REF][START_REF] Casar-Borota | Corticotroph Aggressive Pituitary Tumors and Carcinomas Frequently Harbor ATRX Mutations[END_REF] .

Pheochromocytoma paraganglioma

The main epigenetic and transcriptional genetic changes that were found in a study on 128 samples of pheochromocytomas and paragangliomas were listed as nucleotide polymorphisms (Single Nucleotide Polymorphism), DNA methylation, differences in mRNA expression, miRNA sequences and sequences of known driver genes (identified by targeted sequencing). The clinical characteristics associated with particular molecular groups have also been analysed [START_REF] Castro-Vega | Multi-omics analysis defines core genomic alterations in pheochromocytomas and paragangliomas[END_REF] . The samples have been classified according to the mRNA group that they belong to and this integrative genomic characterization of pheochromocytomas and paragangliomas has allowed five principal clusters of tumours with specific genetic, epigenetic or clinical characteristics to be identified. Pheochromocytomas and paragangliomas of cluster 1A are notably the more aggressive tumours, more often metastatic, and often associated with a mutation in SDHx genes [START_REF] Castro-Vega | Multi-omics analysis defines core genomic alterations in pheochromocytomas and paragangliomas[END_REF] .

Progress in epigenetics

The development of pituitary tumours is strongly dependent on epigenetic mechanisms such as promoter methylation [START_REF] Ezzat | Epigenetics of pituitary tumors: Pathogenetic and therapeutic implications[END_REF][START_REF] Asa | Pituitary carcinoma: reclassification and implications in the NET schema[END_REF] , modification of histone tails and of non-coding RNAs [START_REF] Bahreini | The role of noncoding RNAs in pituitary adenoma[END_REF] .

The CpG dinucleotides are usually grouped in islands, generally localised in the promoter region of genes, and are normally protected from methylation. When they are methylated, these CpG islands lead to silencing of the gene in question [START_REF] Ezzat | Epigenetics of pituitary tumors: Pathogenetic and therapeutic implications[END_REF] . Studies have shown different somatic mutation and methylation profiles between adenomas, aggressive pituitary neuroendocrine tumours and pituitary carcinomas. Notably, altered methylation appears to be an early event that favours aggressive tumour behaviour and progression towards carcinoma, in a direct or indirect way, by inducing gene mutation [START_REF] Guaraldi | Epigenomic and somatic mutation profile of pituitary adenomas (PAs)/ pituitary neuroendocrine tumors (PitNETs)[END_REF][START_REF] Mete | Overview of the 2017 WHO Classification of Pituitary Tumors[END_REF][START_REF] Chang | Genetic and Epigenetic Causes of Pituitary Adenomas[END_REF] . Epigenetic analyses have shown a reduction in protein expression by gene silencing of PARP15, LINC00599, MIR137HG and MIR193a, when they are hypermethylated, in pituitary tumours and carcinomas. These data confirm previous observations that the expression of these genes is reduced in aggressive pituitary tumours [START_REF] Guaraldi | Epigenomic and somatic mutation profile of pituitary adenomas (PAs)/ pituitary neuroendocrine tumors (PitNETs)[END_REF][START_REF] Chang | Genetic and Epigenetic Causes of Pituitary Adenomas[END_REF] .

Tumour microenvironment

Pituitary tumour microenvironment

Apart from non-tumoral cells that are resident or have infiltrated the tumour, the tumour microenvironment consists of blood vessels and lymphatics, as well as extracellular matrix molecules and numerous cytokines and chemokines, which makes it an attractive target both for therapy and for use as a prognostic tool [START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF] . The immune system, in particular tumourassociated macrophages and lymphocytes in the tumour microenvironment, is the most studied aspect of the pituitary tumour microenviroment [START_REF] Raverot | Aggressive pituitary tumours and pituitary carcinomas[END_REF] .

Significant reciprocal communication exists between pituitary tumour cells and their microenvironment. Pituitary tumour cells secrete cytokines into the tumour microenvironment which stimulate the recruitment and migration of immune cells into the tumour. These immune cells then modify the behaviour of tumoural cells, particularly stimulating their proliferation. Tumour-associated fibroblasts are equally able to secrete cytokines including IL-6 into the tumour microenvironment, which also results in increased invasion by pituitary tumour cells [START_REF] Raverot | Aggressive pituitary tumours and pituitary carcinomas[END_REF][START_REF] Ilie | The Microenvironment of Pituitary Tumors-Biological and Therapeutic Implications[END_REF][START_REF] Marques | The role of the tumour microenvironment in the angiogenesis of pituitary tumours[END_REF] .

Treatments targeting the pituitary tumour microenvironment need to take into account the different components that it contains (tumour and non-tumour cell, cytokines, chemokines, extracellular matrix and hormones), all of which are interdependent, thus targeting one component will inevitably have an impact on others [START_REF] Raverot | Aggressive pituitary tumours and pituitary carcinomas[END_REF] . Angiogenesis and immune cells have so far been the preferred therapeutic targets, but targeting the pituitary tumour microenvironment also needs to consider the significant influence of pituitary and hypothalamic hormones produced by either tumour cells or healthy cells. For example, it has been shown that prolactin has a stimulatory role in angiogenesis [START_REF] Yang | A Positive Feedback Loop Between Prolactin and Stat5 Promotes Angiogenesis[END_REF] , and that growth hormone (GH) can stimulate epithelial-mesenchymal transition in several tumour types [START_REF] Brittain | Growth Hormone and the Epithelial-to-Mesenchymal Transition[END_REF] . Additionally, it has been reported that GHRH receptor antagonists can inhibit the growth and progression of some tumor types, particulalry in prostate and thyroid tumours [START_REF] Pópulo | Inhibitory Effects of Antagonists of Growth Hormone-Releasing Hormone (GHRH) in Thyroid Cancer[END_REF][START_REF] Muñoz-Moreno | Growth hormone-releasing hormone receptor antagonists modify molecular machinery in the progression of prostate cancer[END_REF][START_REF] Rekasi | Isolation and sequencing of cDNAs for splice variants of growth hormone-releasing hormone receptors from human cancers[END_REF] .

Pancreatic neuroendocrine tumours microenvironment

The tumour microenvironment has become a subject of interest in endocrine and neuroendocrine cancers as a whole. Cuny et al published a study examining the effect of stromal fibroblasts on proliferation in human cell lines from pancreatic neuroendocrine tumours. They confirmed a stimulating role of stromal fibroblasts on the growth of human pancreatic NET cell lines and a reciprocal effect of NET cell lines on fibroblasts [START_REF] Cuny | Reciprocal Interactions between Fibroblast and Pancreatic Neuroendocrine Tumor Cells: Putative Impact of the Tumor Microenvironment[END_REF] . These biochemical, molecular and histological advances are of interest to clinicians only if they can be useful in clinical practice. Therefore, it is important to identify the diagnostic and prognostic improvements that have arisen due to these mechanistic discoveries.

NEW DIAGNOSTIC AND PROGNOSTIC TOOLS Next Generation Sequencing (NGS)

Thanks to the possibility of sequencing many thousands of DNA sequences at a time, NGS allows routine constitutional or somatic analysis of tumour samples. After extraction of tumour DNA from tissue or cell samples, regions of interest are specifically amplified and sequenced. Thus, identification of specific mutations now allows some patients to benefit from targeted therapies, for example anti-RET or anti-BRAF treatment in the case of thyroid tumours. The identification of specific biomarkers is also absolutely necessary for the regulatory approval of numerous targeted therapies.

Though the condition Multiple Endocrine Neoplasia type 1 (MEN1) is a hereditary syndrome linked to an autosomal dominant mutation in the gene MEN1, the frequency of mosaicism is likely under-estimated in patients with suspected MEN1 as it is not the subject of systematic screening. However, though NGS favours the detection of mosaicism, classic methodologies do not dependably distinguish between true mosaicism and sequencing artefacts. Lagarde et al established a targeted digital NGS, including unique molecular identifiers allowing rare molecular events to be detected in somatic DNA. They searched for MEN1 mosaicism in a cohort of non-resolved cases identified between 2017 and 2019. Three new cases of mosaicism were identified by targeted digital NGS, favouring the routine use of this technique to reduce the number of false-positives detected [START_REF] Lagarde | Systematic detection of mosaicism by using digital NGS reveals 3 new MEN1 mosaicisms[END_REF] .

New potential biomarkers

Pancreatic neuroendocrine tumours and CELF4

The identification of new biomarkers would be beneficial for both the diagnosis and prognosis of neuroendocrine tumours, particularly digestive tumours, and these would ideally be more specific than chromogranin A, and more sensitive than urinary 5-hydroxyindoleacetic acid (5HIAA). Indeed, new tumour biomarkers are currently being studied. Notably, CELF4 an RNA splicing factor that is dysregulated in pancreatic neuroendocrine tumours, and alterations of which contribute to both tumour development and a more aggressive phenotype via an action on the mTOR signalling pathway. CELF4 is associated with relevant clinical parameters and could have significant predictive potential. Under-expression of CELF4 has notably been associated with an increased frequency of metastases and an increase in abdominal pain symptoms [START_REF] Garcia Vioque | Unveiling the role and contribution of CELF4 to the malignant features of PanNETs[END_REF] .

Pheochromocytoma, paraganglioma and INSM-1

Similarly, though assays for plasma or urinary metanephrines are satisfactory in routine clinical practice, a study has examined the potential of proteins of the Granin and INSM-1 family in diagnosis of patients with pheochromocytoma. Of the potential biomarkers studied, INSM-1 had the best diagnostic value in patients with pheochromocytoma and this marker may thus be of interest, in particular in cases where assay of metanephrines leads to a doubtful diagnosis [START_REF] Glinicki | Granin family peptides and INSM-1 (Insulinoma-associated protein 1) in the biochemical diagnosis of pheochromocytoma[END_REF] .

Functional imaging

Neuroendocrine tumours are characterised by the expression of specific hormone receptors on the cell membranes of tumour cells, making them ideal targets for radio-labelled peptides.

The most commonly-expressed receptors on neuroendocrine tumour cells are somatostatin receptors and the molecular imaging method of choice uses a number of radiolabelled somatostatin analogues (Pentetreotide [Octreoscan], 68Ga-DOTATATE, DOTATOC, DOTANOC), or somatostatin antagonists (68Ga-OPS202) which have given the best imaging quality [START_REF] Refardt | Molecular Imaging of Neuroendocrine Neoplasms[END_REF] . Positron emission tomographie (PET) using 18F-DOPA has become the second choice imaging modality in neuroendocrine tumours, with the exception of pheochromocytomas-paragangliomas. Neuroendocrine carcinomas which show low expression of somatostatin receptors (because of dedifferentiation) are best visualised using classical imaging techniques based on glucose metabolism (18F-FDG-PET), a method also useful in prognosis [START_REF] Refardt | Molecular Imaging of Neuroendocrine Neoplasms[END_REF][START_REF] Pacak | Functional Imaging of Neuroendocrine Tumors: Stacking the Odds in a Patient's Favor[END_REF] . Lastly, for visualisation of insulinomas, which are often small-sized, GLP-1 receptor imaging has become the ideal choice [START_REF] Refardt | Molecular Imaging of Neuroendocrine Neoplasms[END_REF] .

Pheochromocytomas, which are derived from chromaffin cells, can be imaged using 18F-DOPA PET as they over-express type L amino acid transporters (LAT1 and LAT2). An Italian study from 2022 confirmed the over-expression of LAT1, LAT2 and phenylethanolamine Nmethyltransferase (PNMT) mRNA in pheochromocytomas compared to normal adrenal tissue, and provided the first experimental evidence of a quantitative correlation between 18F-DOPA signal and the expression level of LAT1 [START_REF] Manso | Overexpression of miR-375 and L-type Amino Acid Transporter 1 in Pheochromocytoma and Their Molecular and Functional Implications[END_REF] .

Liquid biopsy

Liquid biopsies are a diagnostic method becoming increasingly important in cancer diagnosis, particularly for neuroendocrine neoplasms, and are already in routine use in several French centres. Genetic alterations associated with cancer, such as point mutations, copy number variation and chromosomal rearrangements can be detected in samples of circulating cellular DNA. Tumour cells release small fragments of acellular DNA through multiple mechanisms. Through the analysis of this circulating DNA, the aim of liquid biopsy techniques is the early and non-invasive detection of cancers [START_REF] Di Nicolantonio | Precision oncology in metastatic colorectal cancerfrom biology to medicine[END_REF][START_REF] Siravegna | How liquid biopsies can change clinical practice in oncology[END_REF][START_REF] Diaz | Liquid Biopsies: Genotyping Circulating Tumor DNA[END_REF] .

Liquid biopsies have several potential clinical uses. Aside from their diagnostic benefit, they can be used to monitor the therapeutic response in real-time, and to quantify residual disease [START_REF] Di Nicolantonio | Precision oncology in metastatic colorectal cancerfrom biology to medicine[END_REF] . A study that is currently underway in Italy aims to evaluate minimal residual disease using liquid biopsies (the PEGASUS study), as well as the benefit of measuring circulating DNA to monitor the therapeutic response in real time and to evaluate the benefit of retreatment using a targeted therapy ('rechallenge') according to the tumour stage and the evolution of liquid biopsy results (the CHRONOS study) [START_REF] Siravegna | How liquid biopsies can change clinical practice in oncology[END_REF] .

Metabolomic profile of pheochromocytomas-paragangliomas as a prognostic tool

In 2021, a German team studied the clinical signs and symptoms linked to catecholamine secretion in patients with pheochromocytomas-paragangliomas (PPGL). The severity of symptoms was found to be correlated with the level of endocrine activity. However, though signs and symptoms were associated with norepinephrine production in patients with metastatic PPGL, and epinephrine in patients carrying non-metastatic PPGL, there was no difference in clinical presentation between the two groups. Thus, clinical signs and symptoms do not appear to be useful in identifying patients who are more or less likely to develop metastases [START_REF] Li | Metastatic pheochromocytoma and paraganglioma: signs and symptoms related to catecholamine secretion[END_REF] .

Additionally, though a study on a large group of more than 600 patients with PPGL allowed the identification of factors favouring the development of metastases, such as the diagnosis of a tumour in older age, in terms of individual patients it is impossible to predict the development of metastases at the time of PPGL diagnosis [START_REF] Pamporaki | Determinants of disease-specific survival in patients with and without metastatic pheochromocytoma and paraganglioma[END_REF] .

Finally, histopathology may be useful in predicting the development of metastases in patients carrying PPGL. A study of 143 patients showed that a higher GAPP score (Grading System for Adrenal Pheochromocytoma and Paraganglioma) was associated with more aggressive PPGL while the PASS score (Pheochromocytoma of the Adrenal Gland Scaled Score) was not associated with metastases and also showed a high inter-observer variability [START_REF] Wachtel | Predicting Metastatic Potential in Pheochromocytoma and Paraganglioma: A Comparison of PASS and GAPP Scoring Systems[END_REF] .

PHEOCHROMOCYTOMAS-PARAGANGLIOMAS: FROM MOLECULAR UNDERSTANDING TO TREATMENT TARGET

Three clusters with specific pathophysiological and phenotypic characteristics

Pheochromocytomas-paragangliomas are an excellent example of the application of advances in genetics and molecular mechanisms for the diagnostic and therapeutic management of patients. They can be divided into several molecular clusters, defined by the germinal or somatic mutations that underlie their pathophysiology. These clusters have specific clinical, biochemical and imaging characteristics that can be used to direct their treatment and follow up [START_REF] Nölting | Personalized Management of Pheochromocytoma and Paraganglioma[END_REF] . Indeed, each cluster reflects alterations in several genes that have common signalling pathways. Regardless of the tumour cluster, surgery remains the firstintention treatment of choice, however in the short to medium term, more and more targeted and specific treatments of the different clusters that have been identified can be envisaged.

Cluster 1 tumours present with a more aggressive phenotype, with a greater risk of metastasis, and are more frequently secreting and symptomatic. The severity of these tumours warrants closer monitoring.

Looking in greater detail, pheochromocytomas and paragangliomas arising due to mutation in genes of cluster 1 are associated with a phenomenon of cellular pseudohypoxia. Cluster 1A includes mutations in genes associated with the Krebs cycle, such as SDHx genes.

Cluster 1B includes mutation in genes linked to the hypoxia pathway, associated with the VHL gene. These mutations lead to stabilisation of HIF-2 and favour angiogenesis, tumour progression, cell migration, invasion and development of metastases. Such mutations result in tumours with a noradrenergic/dopaminergic phenotype and are best evaluated by assays of free plasma normetadrenaline or 3-methoxytyramine. The most sensitive functional imaging method for screening in cluster 1A tumours is Gallium-68 PET, while 18F-DOPA PET is the most sensitive functional imaging technique for PPGL of the other groups [START_REF] Nölting | Personalized Management of Pheochromocytoma and Paraganglioma[END_REF] .

Cluster 2 PPGL tumours are associated with mutations in genes including RET, NF1 and MAX. These mutations lead to activation of signalling pathways associated with tyrosine kinases, RAS/RAF and mTOR. As with group 1, these mutations are also associated with increased HIF-2A expression, cell proliferation, cell survival and tumour formation.

Lastly, cluster 3 consists of mutations associated with over-activation of Wnt/-catenin signalling, leading to (amongst other effects) angiogenesis, proliferation, cell survical, invasion, metastasis and metabolic dysregulation. Cluster 3 PPGL tumours are principally localised in the adrenal, they present most frequently with somatic mutations and have an increased risk of recurrence and metastasis. Overexpression of chromogranin A is also higher than in the other groups.

Belzutifan: a new therapeutic option

The molecular analyses described above allow us to foresee more and more targeted treatments, and the existence of these PPGL clusters is a perfect example of the potential of personalised medecine.

Von Hippel Lindau disease results from inactivation of the VHL gene, which causes constitutive activation of the transcription factor, hypoxia-inducible factor-2 (Hif-2), leading to several hypervascular lesions including renal clear cell carcinoma. An open-label, singlegroup phase 2 trial was published in 2021, studying the safety and efficacy of belzutifan, a HIF-2 inhibitor, in patients with renal clear cell carcinoma associated with VHL disease [START_REF] Jonasch | Belzutifan for Renal Cell Carcinoma in von Hippel-Lindau Disease[END_REF] .

The principal evaluation criterion was the objective response of the renal carcinoma (complete or partial response). The secondary evaluation criteria were the response to belzutifan in patients with other neoplasms related to VHL disease. After a median follow up of 21.8 months, 49% of patients showed an objective response in terms of their renal carcinoma. Responses were also observed in 30% of patients who had pancreatic lesions or hemangioblastomas in the central nervous system. All those with retinal lesions showed improvement over the course of treatment [START_REF] Jonasch | Belzutifan for Renal Cell Carcinoma in von Hippel-Lindau Disease[END_REF] .

In view of these encouraging results, in particular for non-renal lesions associated with VHL disease, an international phase 2 trial has commenced, which will evaluate the safety and efficacy of belzutifan as monotherapy in patients with an advanced PPGL, a pancreatic neuroendocrine tumour, or any other neoplasm linked to VHL disease.

FIRSTMAPPP trial

Results from the FIRSTMAPPP (First International Randomized Study in Malignant

Progressive Pheochromocytoma and Paraganglioma) study were presented at the European Society of Medical Oncology (ESMO) conference in 2021 [START_REF] Baudin | 567O First International Randomized Study in Malignant Progressive Pheochromocytoma and Paragangliomas (FIRSTMAPPP): An academic double-blind trial investigating sunitinib[END_REF] . This randomised trial recruited 78 patients with a malignant progressing PPGL, in 15 centres across 4 European countries.

Participants were randomised (1:1) to receive sunitinib (37.5 mg/day) or placebo. 35.9 % of patients who received sunitinib reached the principal evaluation criterion of progression-free survival at 12 months. Fourteen patients of the 39 treated with sunitinib showed no tumour progression for at least one year. The median progression-free survival was 8.9 months in the sunitinib group versus 3.6 months in the placebo group. The results of this study suggest that sunitinib should be considered as first-line treatment for malignant PPGL [START_REF] Baudin | 567O First International Randomized Study in Malignant Progressive Pheochromocytoma and Paragangliomas (FIRSTMAPPP): An academic double-blind trial investigating sunitinib[END_REF] .

PERSONALISED MEDECINE IN REAL LIFE

Molecular profiling for target actionability and clinical benefit

In 2018, a working group on translational research and precision medicine of the European Society for Medical Oncology (ESMO) proposed a classification system for molecular alterations based on the available evidence to support their validity as clinical targets. A first version of the ESMO Scale of Clinical Actionability for molecular Targets (ESCAT) was produced, defining six levels of clinical evidence for molecular targets according to their involvement in patient management: from level I, targets ready to be used in routine clinical decision making; level II, experiemental targets requiring further data; to level X, absence of evidence of actionability. The ESCAT defined criteria that are based on clinical evidence, to rank genomic alterations as markers allowing patients to be selected for targeted therapies [START_REF] Mateo | A framework to rank genomic alterations as targets for cancer precision medicine: the ESMO Scale for Clinical Actionability of molecular Targets (ESCAT)[END_REF] .

It is believed that 50-66% of patients with a neuroendocrine tumour have actionable mutations (that can be targeted with existing treatments). Boilève et al retrospectively analysed the molecular profile of tumours from 114 patients with thoracic neuroendocrine neoplasms, digestive system tumours, ENT tumours or others. Forty eight percent of analysed lesions showed a genetic alteration that was potentially actionable, amongst which 35% had received a personalised treatment and 78% of these patients had shown a clinical benefit.

Genomic Medicine Plan for France 2025

Genomics is at the centre of the 21st century medecine. In view of this fact, a national plan -'Plan France Médecine 2025', has been established. This has three principal objectives: to prepare for the integration of genomic medecine into current management of disease; to put in place a pathway so that genomic medecine can be a force for scientific and technological innovation; and to ensure that France is one of the major countries engaged in personalised medecine. This will require scientific, clinical, technological, economic and population aspects to be taken into consideration.

Certainly, thanks to great advances in our scientific knowledge, we are now well-placed to analyse cancer pathologies in a more and more precise manner and to differentiate at an increasingly early stage those tumours with an increased risk of aggressive behaviour.

Understanding tumours at the molecular level now allows us to propose increasingly targeted therapies to patients. While large randomised trials will permit the validation of the safety and efficacy of these treatments on a large scale, the first studies analysing the benefit of the specific association of an actionable mutation with a targeted therapy have shown promising results, allowing us to foresee the use of increasingly personalised medecine in the future.

This article had institutional support from Ipsen Pharma, the first author having participated in the Must Endocrinology conference, 2022.

Figure 1 .

 1 Figure 1. From mechanisms to the clinic. A. New epigenetic and molecular mechanisms shown in neuroendocrine neoplasms B. Clinical applications: diagnostic, prognostic and