21 In the case of the loading (Figure 6b), the fast martensite nucleation leads to local heating of surrounding not yet transformed material thus increasing locally the transformation stress approximately by a factor of 6 MPa.K -1 . Consequently, the propagation of martensite band fronts into their surrounding is hindered since the stress required for the forward transformation has been locally increased in this volume. As a result, a new nucleation site is created at a distant location not affected by released latent heat. These processes of nucleation bursts and transformation arrests proceed along the axis of the wire as seen in Figure 6d where the reconstructed heatsources 1-10 represent the nucleation sites. The nucleated martensite bands bring about the transformation strain, which adds up to the elastic strain and increases the measured strain rate, as confirmed by strain measurement overlapped in Figure 6d. As a result of the sequence of 10 transformation nucleation events, the temperature of the sample is homogeneously increased by 12 K, which leads to an increase of transformation stress by 72 MPa. With the applied loading rate of 8 MPa.s -1 (see Table 3), 9s were necessary after the first burst to reach the increased transformation stress. During this period of time, the martensitic transformation was indeed suppressed as indicated in Figure 6b by the absence of heatsources and a decrease in strain rate. Finally, when the increased transformation stress was reached pairs of martensite band fronts from adjacent nucleation sites start to propagate until they merge. This proceeded again sequentially in locations 11-20 due to the effect of local temperature changes as in the case of the nucleation sequence.
Elastomers are materials that exhibit a specific ther- mal sensitivity related to numerous properties such as entropic elasticity, viscosity, stress softening, as well as strain-induced crystallisation under certain conditions. As regards fracture mechanics in rubbers, the main approach which is developed in the litera- ture is based on the tearing energy (Rivlin & Thomas 1953). However, the mechanical energy which is involved at the crack tip can be in part mechani- cally dissipated into heat because of damage, viscous effects and possibly local stress softening, which is not taken into account in the tearing energy. The local measurement of the heatsources produced or absorbed in the crack tip zone can therefore provide information of paramount importance for fracture mechanics in rubber. Such measurements can be performed using full-field measurement techniques (Le Cam 2012, Toussaint et al. 2012).
A B S T R A C T
During cyclic loading of a cracked metallic alloy at room temperature, heatsources are generated and produce a heterogeneous temperature ﬁeld around the crack tip. Those heatsources are: (i) the thermo-elastic coupling source, (ii) the intrinsic dissipation due to microplasticity in the material, and (iii) the cyclic plasticity dissipated into heat in the reverse cyclic plastic zone (RCPZ) ahead of the crack tip. The thermoelastic source is computed by ﬁnite element analysis in agreement with classic linear thermoelasticity theory. The intrinsic dissipation due to microplasticity is experimentally estimated by carrying out self-heating fatigue tests on uncracked specimens, and then approximating its values in the cracked specimens by using self-heating curves. The cyclic plastic strain energy dissipated into heat in the RCPZ is also experimentally quantiﬁed by carrying out fatigue crack growth tests and using infrared measurements. The temperature ﬁelds, generated by the three types of heatsources, are separately computed by using the linearity of the heat di ﬀusion equation. Afterward, the stress ﬁelds, associated with each thermal eﬀect and induced by the material thermal expansion, are computed by considering the hypothesis of the linear elastic fracture mechanics (LEFM). Thus, the mode I stress intensity factor is calculated by taking into account the thermal eﬀect associated with each heat source. The consequences on K , Δ K and
Infrared thermography (IRT) is a technique that enables the thermal image of a sample observed in a spectral range of the infrared to be obtained. However, while tomography is now prevalent in various domains, which enables volumetric measurements (x-ray, magnetism resonance imaging, etc.), it is still not possible to measure the temperature in a 3D volume; in other words, it is not possible to realize thermal tomography. The challenge is then to reconstruct 3D heatsources in a volume from the 2D field measured at the surface by thermal imaging cameras. This inverse situation is an ill-posed problem mainly due to the diffusive nature of temperature. To circumvent this problem, classical regularization methods or statistical ones can be used. Interested readers can refer to [ 1 , 2 ], which provides some examples with a rather general overview of the existing inverse methods.
entropic coupling. The fact that a dissymmetry is observed if the maximum stretch ratio applied is superior to 4 shows that the heatsources are not caused only by entropic coupling. During unloading, the heatsources are first lower than during loading (between points 3 and 2) and then higher (between points 2 and 1). Nevertheless, the area under the curves during loading and unload- ing is equal, meaning that no heat is produced due to mechanical dissipation. Consequently, the only explanation for the dissymmetry is the occurrence of crystallization during loading, and a difference in the kinetics of crystallization and crystallite melting (the latter during unloading). This is in a good agreement with studies reported in the literature (Toki, Fujimaki, & Okuyama 2000). Concerning the stress-strain curve, a hys- teresis loop begins to form. It is associated with the crystallization/melting phenomenon, and not with mechanical dissipation.
The asymmetric nature of the distribution of radiogenic heatsources on the lunar surface was ﬁrst made abundantly clear by data obtained from the Lunar Prospector gamma-ray spectrometer (Lawrence, 2003). The observed concentration of heat-producing elements on the nearside hemisphere of the Moon in a region that encompasses the Imbrium impact basin and Oceanus Procellarum, the Procellarum KREEP Terrane (PKT; Jolliﬀ et al., 2000), had a major inﬂuence on the global interior evolution of the Moon, including, but not limited to, volcanic activity, magnetic ﬁeld generation, impact processes, and true polar wander (Hess & Parmentier, 2001; Laneuville et al., 2013; Miljkovic et al., 2013; Siegler et al., 2016; Wieczorek & Phillips, 2000; Zhang et al., 2013; Zhong et al., 2000). We reevaluate the global distribution of heat-producing elements in the Moon and the Moon’s thermal evolution using new constraints based on crustal thickness, the size of a nearside province with low magnetization, surface composition from orbit, Apollo samples, and mass balance considerations. Earlier models of the Moon’s bulk composition (e.g., Longhi, 2006) recognized that the Moon was depleted in the element K compared to Earth, but these studies varied in the estimates of refractory element abun- dances, including U and Th. Estimates fell into two groups: Earth-like bulk refractory silicate contents and enrichments with respect to the bulk-Earth values by up to 50% (e.g., Taylor et al., 2006). The enriched values
2 LUNAM Université, ONIRIS, CNRS, GEPEA, UMR 6144, site de la Géraudière, 44322 Nantes, France
Received: 10 January 2017 / Accepted: 22 August 2017
Abstract. This work describes the implementation of a simple procedure that helps to easily position the heating elements in press plates used in high-temperature composites thermoforming process. The developed method permits to obtain desired temperature pro ﬁles on the surface of the press plates through two main steps. The ﬁrst step consists in ﬁnding out an appropriate parametric curve that deﬁnes the spatial location of the heating sources into the thickness of the press heating plates. The second step uses an inverse method that combines a stochastic optimization algorithm in conjunction with ﬁnite element simulations. This second step serves for the adjustment of the position curve parameters to obtain a simulated temperature pro ﬁle as close as possible to the expected one at the press plates surface. This easy-to-implement approach is shown to be very effective to rapidly obtain a suitable location of the heatsources that minimizes energy consumption. Keywords: press heating plates / composite thermoforming / ﬁnite element analysis / parameter optimization / efﬁcient positioning
ef ﬁcient tool to model heat transfer in mulilayered with heatsources located in one or several layers. These applications demonstrate the ability of the technique to deal with broad ranges of time and thicknesses of the layers. Our methodology presents a real advantage considering what could have happened with a classical ﬁnite elements simulation because we can model prob- lems with different scales. This accurate formulation has been already applied in thermal characterization problems even if it is tricky to have an explicit analytical solution when the number of layers becomes very important.
5 Ecole Centrale de Nantes, GeM, firstname.lastname@example.org
Résumé — Many industrial processes involve transient heat transfer problems where the heat source moves over the domain. For instance, the Automated Tape Placement (ATP) in the context of composites manufacturing may be considered. In this process, the composite piece is built up by adding different layers successively, which are welded on the substrate by means of a local heat source, typically a laser, which moves all over the boundary. If one is interested in monitoring or controlling the process, some thermocouples need to be installed where knowing the temperature is of interest. However from a nu- merical point of view, having a moving heat source poses several problems. Classically, even when the problem remains linear, it would be needed to solve the transient problem by performing an appropriate time stepping, needing for the solution to solve many algebraic problems. In order to overcome these limitations, this work proposes solving the problem in the frequency domain because in this case it can be proved that the reciprocity principle is satisfied. Then, a unitary heat source may be applied where the temperature measurement is performed giving place to a transfer function which relates the measurement point and the boundary, where the heat flux applies. However this transfer function is only valid for a single frequency, and thus if the heat flux signal contains several frequencies, many transfer functions need to be computed. Instead, we prefer to compute a generalized transfer function by using the PGD method, i.e. the frequency is included as an extra-coordinate, like the physical space. Once this gener- alized transfer function has been computed, a simple and computationally cheap postprocessing suffices for obtaining the temperature response at the point of interest, for any heat source path on the boundary. Mots clés — monitoring, processes, heat transfer, PGD, transient problem
Par le rejet du recours pour excès de pouvoir, l’arrêt du Conseil d’Etat affirme donc, avec fermeté, la compétence du pouvoir réglementaire en matière de déontologie des avocats. Il nous donne aussi des indications sur la méthode suivie. D’abord, l’absence d’une consultation formelle des professionnels concernés, qui n’était certes pas prévue par les textes : « aucune disposition législative ou réglementaire n’imposait que fussent consultés le Conseil national des barreaux et la conférence des bâtonniers préalablement à l’adoption du décret contesté ». Les textes ne sont pourtant pas tout. Les pratiques préalables, le respect d’engagements informels et la participation des intéressés aux dispositions qui les concernent ont leur importance. Inutile de rêver, il est vrai, à l’instauration d’une déontologie applicable aux faiseurs de décrets. Les gouvernants ne sont pas connus pour s’encombrer : la déontologie, c’est pour les autres. Ensuite, le décret compile, sous la bannière de la déontologie, des dispositions dont les sources sont diverses. Les principes essentiels de la profession d’avocat -destinés à « guider son comportement en toutes circonstances » (art. 1)- regroupent des exigences –de la dignité à la courtoisie- relatives à l’exercice des fonctions d’avocat (art. 3) et le respect du secret de l’instruction (art. 5), par ailleurs formulé dans le code de procédure pénale. Faut-il considérer la déontologie décrétale comme un ramassis de dispositions éparses visant à rappeler les avocats à leurs devoirs ? Ce serait excessif et désobligeant, même si le procédé a de quoi agacer pour venir d’en haut. Toujours est-il que s’il existe une répartition de la compétence normative en matière déontologique, elle est déterminée par le pouvoir réglementaire, qui, selon les termes de l’arrêt du Conseil d’Etat (à propos de l’article 19 al 1 du décret), a pu légalement investir le bâtonnier d’une mission en ce sens.
C A R AC T É R I S T I Q U E S D E S S O U R C E S L U M I N E U S E S
Une source lumineuse est caractérisée en par- tie par sa puissance, qui est l’énergie débitée par unité de temps exprimée en watts (W) ou joules par secondes (J/s). La deuxième caractéristique physique est la luminance énergétique (L) ou éclairement énergétique représentant le flux énergétique par unité de surface émettrice (m 2 ) et par unité d’angle solide d’émission (sr, stéra- dian). Elle s’exprime en W/m 2 /sr. Pour les sources polychromatiques, la luminance dépend de la nature des photons. La luminance spectrale (L λ) caractérise le rayonnement dans chaque portion des longueurs d’onde du spectre. La variation de L λ en fonction de λ représente le spectre de la source.
Theorem 4. When the diffusion is asymptotically strong Feller at c 0 and the stability condi-
tion ( 5 ) is satisfied, the heat conduction network can have at most one invariant measure. Notice that this condition does not dependent on the temperatures of the heat baths. We will discuss the asymptotic strong Feller condition in Appendix A . We will prove that this regularity condition is satisfied in the harmonic setting as soon as the graph is asymmetric. We could not reach the generality of anharmonic potentials but we expect that this property is still true in this setting.