Elodie Péronnet

Marie-Laetitia Pastor

Hélène Welemane

Non destructive testing of artificial defects in composite

structures by thermal full field measurement methods

  This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 10126 To cite this version: Péronnet, Elodie and Pastor, Marie-Laetitia and Welemane, Hélène and Huillery, Richard Non destructive testing of artificial defects in composite structures by thermal full field measurement methods. (2013) In: PhotoMechanics 2013, 27 May 2013 -29 May 2013 (Montpellier, France).Open Archive Toulouse Archive Ouverte (OATAO)OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.Any correspondence concerning this service should be sent to the repository administrator: evaluation by pulsed phase thermography : depth retrieval with the phase NDT&E International


Renaud Ansart

Mehrdji Hemati

Herv É Neau

Olivier Simonin

3D numerical simulation of Circulating Fluidized Bed: comparison between theoretical results and experimental measurements of hydrodynamic

This work was realized in the frame of the European GAYA project supported by ADEME. This paper presents a description of the hydrodynamic into a CFB according to experimental measurements of gas pressure and solid mass flux. These experimental data are compared to three dimensional numerical simulation with an Eulerian approach. The obtained numerical results show that the applied mathematical models are able to predict the complex gas-solid behavior in the CFB and highlight the large influence of the particle wall boundary condition. Indeed, it is shown that free slip wall boundary condition gives a good prediction a solid mass flux profile in comparison with experimental measurements nevertheless a convex shape. Moreover, the numerical solid hold-up is underestimated compared to the experimental data. On the contrary, a no-slip boundary condition improves the profile shape of solid mass flux but highly overestimates its intensity and the solid hold-up. A compromise appears to be a friction particle-wall boundary condition such as Johnson and Jackson (1) but the model parameters have to be chosen very carefully especially the restitution coefficient.

INTRODUCTION

Circulating fluidized beds are used in a wide range of industrial applications such as Fluidized Catalytic Cracking (FCC), Chemical Looping Combustion, and biomass gasification. Since few years, the development of computational ability and Computational Fluid Dynamic (CFD) allows 3-dimensional realistic simulations of industrial configurations by using eulerian multi-fluid approach. In the application of CFD models, careful validation with experimental measurements is needed. Indeed, the several complex phenomena involved in industrial circulating fluidized bed, such as particle-turbulence interaction, particle-particle and particle-wall collisions or heat and mass transfer, and the large dimensions of industrial plants are challenging for numerical modeling. This study addresses the effects of particle wall boundary conditions in circulating fluidized bed. Benyahia et al. [START_REF] Benyahia | Evaluation of boundary conditions used to model dilute, turbulent gas/solids flows in a pipe[END_REF] pointed out different boundary conditions and showed that they significantly affect the predicted dilute gas/solid flow in pipe. Moreover according to comparisons with PEPT measurement in dense fluidized bed, Fede et al. [START_REF] Fede | 3D numerical simulation and pept experimental investigation of pressurized gas-solid fluidized bed hydrodynamic[END_REF] have shown that free slip wall boundary condition overestimates the downward mean particle velocity in the near wall region and no-slip conditions improve this velocity profile.

MODELING OF THE GAS-SOLID TWO-PHASE FLOW

Three dimensional numerical simulations are carried out using an Eulerian n-fluid mod-eling approach for poly-dispersed fluid-particle flows implemented in NEPTUNE CFD software which is developed by IMFT (Institut de M écanique des Fluides de Toulouse). This software is a multiphase flow code developed in the framework of the NEP-TUNE project, financially supported by CEA (Commissariat à l' Énergie Atomique), EDF ( Électricit é de France), IRSN (Institut de Radioprotection et de S ûret é Nuc éaire) and AREVA-NP. The multiphase eulerian approach is derived from a joint fluid-particle Probability Density Function equation allowing to derive transport equations for the particle velocity's moment. In the proposed modeling approach, transport equations (mass, momentum and fluctuating kinetic energy) are solved for each phase and coupled through interphase transfer terms. The momentum transfer between the phases is modeled using the drag law of Wen & Yu limited by Ergun equation for the dense flows (4). The collisional particle stress tensor is derived in the frame of the kinetic theory of granular media [START_REF] Bo Ëlle | Second-order prediction of the prediction of the particle-phase stress tensor of inelastic spheres in simple shear dense suspensions In Gas-Particle flows[END_REF]. The fluid turbulence modeling is achieved by the two equations k ´ε model extended to particle-laden flows (accounting for additional source terms due to the inter-phase interactions) [START_REF] Vermorel | Numerical Study and Modelling of Turbulence Modulation in a Particle Laden Slab Flow[END_REF]. For the dispersed phase, a coupled transport equation system is solved on particle fluctuating kinetic energy and fluid-particle fluctuating covariance (q 2 p ´qfp ). The effect of the particle-particle contact force in the very dense zone of the flow are taken into account in the particle stress tensor by the additional frictional stress tensor [START_REF] Srivastava | Analysis of a frictional-kinetic model for gasparticle flow[END_REF]. In this paper, three kinds of wall particle boundary conditions were evaluated. The Johnson and Jackson (1) wall boundary conditions are written:

$ ' ' ' ' & ' ' ' ' % ˆνp BUp,τ Bn ˙wall " ´φπg0 2 ? 3α max p Up,τ c 2 3 q 2 p ˆKp Bq 2 p Bn ˙wall " φπg0 2 ? 3α max p U 2 p,τ c 2 3 q 2 p ´?3πg0 `1 ´e2 w 4α max p ˆ2 3 q 2 p ˙3 2 , (1)
where ν p and K p are the particle viscosity and diffusivity, U p,τ the wall tangential component of particle velocity. The parameter φ is the specularity coefficient which varies from zero (smooth wall) to one (rough wall). The dissipation of solid turbulent kinetic energy by collisions with the wall is specified by the particle-wall restitution coefficient e w which ranges from 0 (deposition) to 1 (elastic bouncing). The particle fluctuating kinetic energy flux exchanged with the wall has two contributions: a positive one which represents the production of agitation by wall roughness (through a energy redistribution from the mean motion) and a second term of dissipation due to inelastic bouncing. φ " 0 corresponds to a smooth wall with inelastic rebound without friction. Different specularity coefficients φ were applied in the literature with high values (« 0.5) for dense fluidized bed [START_REF] Li | Study of the wall boundary condition in numerical simulations of bubbling fluidized beds[END_REF], whereas low values (« 10 ´4) were recommended for circulating fluidized bed. Benyahia et al. [START_REF] Benyahia | Study of the ability of multiphase continuum models to predict core-annulus flow[END_REF] reported that the specularity coefficient strongly affected the core-annular flow in dilute gas-solid system: the higher specularity the lower is the concentration at the wall. Li and Benyahia [START_REF] Li | Revisiting Johnson and Jackson Boundary conditions for granular flows[END_REF] derived the specularity coefficient dependence on the particle-wall restitution and wall frictional coefficients and gave an analytical expression of φ for a flat, frictional surface with a low frictional coefficient. However as the authors explained, it is difficult to incorporate such a model into the boundary conditions for two-fluid model, as the individual collisional angle is not tracked. In this study, free slip wall boundary conditions are corresponding to φ " 0 and e w " 1 and no-slip conditions are corresponding to pU p,τ q wall " 0 and ´Kp

Bq 2 p
Bn ¯wall " 0. The free slip and no-slip wall boundary conditions for solid phase are used as the upper and lower bounds of partial-slip.

EXPERIMENTAL SETUP CONFIGURATION

The experimental setup is a cold Fast Internal Circulating Fluidized Bed Biomass Gasifier (FICFB) designed and built in the LGC (Laboratoire de Gnie Chimique). The basic concept of the FICFB gasifier is to separate the fluidized bed into two zones, a gasification zone and a combustion zone (Figure 1). Between these two zones, a circulating loop of Heat Carrier Particles (HCP) is created but the gases remain separated [START_REF] Hofbauer | Six years experience with the FICFB-Gasification Process[END_REF]. The HCP, usually Sand or Olivine, influence the thermodynamic and hydrodynamic behavior of the system. During circulation, the HCP transfer the heat generated in the combustion zone to the gasification zone where the overall reaction process is endothermic and thus, influence the thermodynamic behavior of the system. The fluidized HCP also has an important role to play in controlling the hydrodynamics of the system. Indeed, it is very difficult to fluidize the relatively large sized-biomass particles in the absence of the media particles. In this paper, we focus on the hydrodynamic of the HCP behavior into the combustion zone at ambient temperature. The geometry of the combustor is 10.4 cm diameter and 7 m high. A uniform gas inlet condition is considered at the fluidization grid. Particles are introduced through the L-valve with a diameter of 5.5 cm, placed 12.25 cm above the distributor and inclined with an angle of 30 0 . 25 cm above the fluidization grid, a secondary inlet gas injection is set according to a tube of 3.8 cm diameter to reach superficial gas velocity higher than the terminal settling velocity of the particles. Thus, a dense fluidized and a transported bed are generated respectively below and above this secondary gas injection. The particle size distribution of the HCP (sand) particles is d 50 " 378 µm, d 32 " 269 µm and span " 2.

Pressure probes spread along the riser, provide axial pressure profiles. An iso-kinetic sampling probe, based on Rhodes and Laussman [START_REF] Rhodes | A simple non-isokinetic sampling probe for dense suspension[END_REF], provides local upwards and downwards solid mass flux. Figure 3 illustrates the probe used. Two iso-kinetic probes of different diameters (4 mm and 8 mm) were tested to measure the solid mass flux. The integrated local solid flux over the riser cross-section measured with the 4 mm diameter probe are higher than the averaged solid fluxes obtained by measuring solid height in the standpipe when the particle transfer from the standpipe to the gazeifier is cut off. With the 8 mm diameter probe the integrated local solid flux is in a good agreement with a averaged solid flux measured in the standpipe. It is widely accepted that core-annulus structure is the typical structure existing in CFB risers: a dilute central solid region with high velocities for both fluid and solids and a high solids concentration near the walls. Salvaterra et al. [START_REF] Slavaterra | Solid flux in a circulanting fluidized bed riser[END_REF] have shown that the profile of solid mass flux was parabolic and that flow distribution could be considered to be symmetrical. It can be observed from Figure 4 that the solid mass flux measured with 8 mm diameter probe follows a parabolic trend and the mean solid mass flux increases as the secondary gas flow rate rises. Moreover, this measurement technique gives reproducible results with an accuracy of 10 %.

NUMERICAL PARAMETERS

The 3D mesh is composed of 858,000 hexahedra, based on O-grid technique with approximately ∆ r " 2.5 mm and ∆ z " 6 mm (Figure 2). The numerical simulations have been performed on parallel computers with 64 cores. The fluidization grid and the secondary inlet gas injection are an inlet for the gas with imposed gas mass flow rate. These same sections correspond to walls for particles. At the top of the column, a free outlet for both gas and particles is defined. The wall-type boundary condition is friction for the gas. The Table 1 summarized the phase properties and mass flow rate retained for the simulations. We have to underline that the particles are assumed to be spherical and monodispersed. A numerical simulation is divided into two step: a transitory step to reach a predicted total mass of particle constant in the column and an established regime during which the statistics are computed for 30 s. The timeaveraged radial profiles will be presented by circumference averaging. φ " 0, e w " 0.9

2.90 kg free-slip (φ " 0, e w " 1) 2.87 kg exp. measurement 3.06 kg

RESULTS

Table 2 shows the solid mass predicted according to the integration of the pressure profiles from Figure 5(a). We note that the riser solid loading is strongly dependent on the wall particle boundary condition. We found that the higher the friction, the higher the predicted solid mass. The no-slip condition largely overestimates the solid mass. For φ " 10 ´4, the inelastic bouncing (e w " 0.9) provides a very high solid mass larger than the one predicted by no-slip condition. As observed by He and Simonin ( 14), Sakiz and Simonin (15) for dilute particle-laden high velocity flow, the particle velocity fluctuation anisotropy is very important close to the wall and must be accounted for in the derivation of the wall boundary condition. As a matter of fact the particle kinetic energy dissipation effect is controlled by the wall-normal velocity fluctuation which can be much lower than the longitudinal one. Thus, the isotropic description of the inelastic bouncing through mean fluctuation may be not appropriated by leading to an overestimation of the fluctuating kinetic energy dissipation by the inelastic bouncing at the wall. Moreover, a slight increase of the predicted mass is observed for inelastic bouncing applied to φ " 0. Consequently for high velocity transport flow as observed in CFB process, this description of inelastic bouncing looks not appropriated. In contrast, for the case assuming elastic bouncing (e w " 1) and φ " 10 ´4, which underestimates the particle fluctuation wall dissipation effect, a much reasonable value of solid-hold-up is predicted.

Figures 5(b) and 5(c) present the predicted solid mass flux. Free slip wall condition provides profile close to experimental measurements despite a convex form. Indeed, the maximum of solid flux is observed near the wall. On the contrary, no-slip condition gives the good trend of the flux but largely overestimates its intensity. Moreover, we note a downward flow that is not observed in the experiments. For partial slip with, the solid mass flux presents a minimum at the center and a maximum at the wall without downward flow. Figure 6(a) presents the vertical component of solid velocity. The maximum, reached at the center, is almost the same for all the boundary conditions. An increase of particle-wall friction results in a reduction of solid velocity at the wall until negative value. This solid velocity reduction at the wall induces a gas velocity reduction, Figure 6(b). Thus, the gas velocity increases at the center with the increase of wall-particle friction. The time-averaged solid volume fraction (Figure 6(c)) presents the core-annulus structure with a high concentration near the wall. Both, the solid volume fraction and the concentration gradient near the wall increase with the wallparticle friction boundary condition. Figures 6(d), 6(e) and 6(f) show the predicted granular agitation and solid velocity fluctuations. We can note that an increase of particle-wall friction results in an increase of granular agitation.

CONCLUSION

In this paper, three dimensional numerical simulations of circulating fluidized bed with an Eulerian approach were realized and the effects of particle wall boundary condition were evaluated. The comparison between numerical results and experimental measurements of gas pressure and solid mass flux have shown the strong influence of the boundary conditions. Indeed, a particle free slip condition produces a relative good solid hold-up and solid mass flux slightly underestimated but without a parabolic trend. On the other side a no-slip condition predicts a parabolic trend of solid mass flux but with an intensity strongly overestimated and a downward flow close to the wall, that is not observed experimentally. A relative compromise seems to be a partial slip condition such as Johnson and Jackson wall boundary condition. This condition needs two entree parameters which have to be chosen properly. On the contrary to dense fluidized, where the value of this parameter has to be close to the unit, for a circulating fluidized bed the specularity coefficient must be very low (φ « 10 ´4) and the effective restitution coefficient e w very close to 1. The development of wall particle boundary conditions in dilute flow with high transport velocity is presently under way: bouncing of irregular particle on smooth wall (extension of Sakiz and Simonin's work [START_REF] He | Non-Equilibrium Prediction of the Particle-Phase Stress Tensor in Vertical Pneumatic Conveying[END_REF]) and bouncing on rough wall [START_REF] Sakiz | Development and Validation of Continuum Particle Wall Boundary Conditions Using Lagrangian Simulation of a Vertical Gas-Solid Channel Flow[END_REF].

Figure 1 :

 1 Figure 1: Overall design of FICFB pilot plant.

Figure 2 :

 2 Figure 2: Mesh of circulating fluidized bed.

Figure 3 :Figure 4 :

 34 Figure 3: Suction iso-kinetic probe.

  Zoom on solid mass flux.

Figure 5 :

 5 Figure 5: Comparison between experimental measurement and time-averaged numerical results for the solid hold-up and the solid mass flux. (˝): no-slip; ( ): Johnson and Jackson φ " 10 ´4, e w " 1; (♦): free-slip, ('): experimental measurements.

  Variance of vertical component of solid velocity.

  Variance of radial component of solid velocity.

Figure 6 :

 6 Figure 6: Effect of different boundary conditions for the particle phase on the timeaveraged flow variables radial profiles at z " 4.9 m. (˝): no-slip; ( ): Johnson and Jackson φ " 10 ´4, e w " 1; (♦): free-slip.

Table 1 :

 1 Parameters for numerical simulations.

	Parameter	Value
	Gas density ρ g	1.18 kg ¨m´3
	Gas viscosity µ g	1.85.10 ´5 Pa	¨s
	Particle diameter d p	269 µm
	Particle density ρ p	2700 kg ¨m´3
	Fluidization grid gas flow rate Q g,I	12 kg ¨h´1
	Secondary inlet gas flow rate Q g,II	120 kg ¨h´1
	Solid mass flow rate injected Q p	300 kg ¨h´1

Table 2 :

 2 Solid hold-up.

	Boundary conditions	Mass
	no-slip	9.32 kg
	φ " 10 ´4, e w " 0.9	ą 13 kg
	φ " 10 ´4, e w " 1	2.87 kg

ACKNOWLEDGMENTS

This work was granted access to the HPC resources of CALMIP under the allocation 2013-P11032 and CINES under the allocation 2013-gct6938 made by GENCI.


Viscoplastic behavior of diamond die attach subjected to high temperature conditions S. MSOLLI, A. BAAZAOUI, O. DALVERNY, J. ALEXIS, M. KARAMA Université de Toulouse ; INP/ENIT ; LGP ; 47, avenue d'Azereix ; F-65013 Tarbes, France smsolli@enit.fr, ahlem.baazaoui@enit.fr, olivier.dalverny@enit.fr, joel.alexis@enit.fr, Moussa@enit.fr

Abstract

In power electronic applications, diamond based semiconductors appears to be a new way to widely increase the capabilities of power electronic converters [START_REF] Brezeanu | On-state behaviour of diamond Schottky diodes[END_REF][START_REF] Lostetter | An overview to integrated power module design for high power electronics packaging[END_REF]. The main prospective expected is an increasing in system integration and power capabilities. The Diamonix project concerns the elaboration of a single-crystal diamond substrate with electronic quality and its associated packaging. The designed structure has to resist to temperatures varying between -50°C and +300°C. This paper deals with an experimental and numerical study of the diamond die attach solution. The development of a packaging for diamond component relies in particular on a specific choice of solder's alloys for the junction die/substrate. To carry out this junction, AuGe and AlSi eutectic alloys were chosen and characterized; the choice of these two kinds of solders i.e. AuGe and AlSi is motivated by the practical elaboration process and the restrictions of hazardous substances (RoHS). The first solder has a melting temperature of 356°C; the second has a higher melting point of 577°C. In this paper, we present some numerical results obtained from FE simulations of two 2D configurations of simplified electronic packaging. The power electronic packaging is composed of a diamond die and a copper metallized Si 3 N 4 ceramic substrate which are brazed together with either AuGe or AlSi solder alloy. To predict the thermomechanical behavior of the solders, a particular constitutive behavior law was implemented as a User MATerial subroutine which is based on a viscoplastic unified McDowell formulation, coupled with porous damage equations. The mechanical law can describe precisely the viscoplastic damage phenomenon of solder subjected to high thermal cycling and to optimize the thermo-mechanical modeling for advanced package development.

Experimental characterizations of solders

For temperatures of about 300°C, the solder materials exhibit viscoplastic mechanical behavior. In order to identify the dependency on temperature and strain rates for the two solders, a set of experimental results, such as simple shear, creep and cycling tests are realized at 25, 200 and 300°C using specific shear specimens [START_REF] Msolli | Mechanical characterization of an Au-Ge solder alloy for high temperature electronic devices[END_REF]. The specimens are mounted into a material testing machine equipped with a thermal enclosure for test temperatures up to 300°C. For creep tests, applied forces vary between 100 and 250 N. The database obtained is used for identification of material parameters of the viscoplastic damage model [START_REF] Fu | Time Integration Procedures For A Cyclic Thermoviscoplasticity Model for Pb-Sn Solder Applications[END_REF][START_REF] Haghi | A constitutive model for isotropic, porous, elastic-viscoplastic metals[END_REF]. We used finite element model for the lifetime prediction of the packaging under thermal or power cycling. The obtained results in 2D and 3D basic packaging configurations allow us to prepare for a design of experiment (DOE) of the diamond die packaging to find the optimal geometrical configuration for the new diamond packaging.

Experimental results analysis

In Fig. 1, we present some results from creep, simple and cyclic shear tests for the two solders. In the case of AuGe solder, Fig. 1(a) shows the results of shear tests realized at various temperatures and displacement rates. The maximal applied force does not exceed 200 N whatever the imposed temperature. See that AuGe shows more sensitivity to strain rate at temperature of 300°C. This is due to the activated viscous mechanisms in the microstructural level such as dislocation climb and dislocation glide. Mechanical behavior of AlSi solder alloy is presented in Fig 3 . For the simple shear tests, AlSi solder demonstrates a weak sensitivity to displacement rate even at high temperature. Moreover, it was mainly elastic behavior for temperatures up to 200°C and the applied forces reach a high value of 300 N. At 300°C, the yield stress decreases and plasticity is reached (Fig. 3(a)). A fast saturation level is reached due to the high material ductility. The AlSi mechanical behavior stills very close to Aluminium hardening behavior. In the cyclic case, there is also a weak amount of plasticity either for a temperature of 200°C. Contrarily to AuGe mechanical behavior, there is no Bauschinger effect for the AlSi solder but the material shows cyclic softening for the first cycle whatever the displacement and temperatures imposed. This softening behavior is combined to force saturation (200 N) at 300°C. Fig. 4 illustrates the failure profile of the AlSi specimen. There are small shear bands oriented to the load direction. This bands show high ductility of AlSi material and prove that failure produces on the solder volume. There is no apparent voids present in the solder layer after the reflow process of the solder.

Modeling and damage prediction of 2D simplified packaging architecture

The simplified structure of a 2D power electronics packaging is showed is Fig 5(a). A half model is considered in this study. The packaging consists on a diamond die brazed to a Copper metallized Si 3 N 4 ceramic substrate using a solder layer which can be either AuGe or AlSi. The packaging is subjected to thermal cycling decomposed into two steps: the first step consists on the reflow cycle included in the manufacturing process. The second step is the thermal cycling imposed for a temperature range of -50°C to 300°C with a temperature ramp of 20°C/min. There is a hold period of 30 min at both 300°C and -50°C. The whole thermal cycle is illustrated in the Fig. 5(b). The model is integrated using a semi-implicit Euler scheme combined with a line search strategy [START_REF] Msolli | Implicit integration scheme for porous viscoplastic potential-based constitutive equations[END_REF]. The complete model parameters are identified using simple shear and creep experimental data. Damage parameters are identified using cyclic data giving maximal force versus number of cycles. Note that no interfacial behavior is considered between solder and die deposits. There is no consideration of the effects of intermetallic compounds which implies that failure produce purely in solder layers. Only voids nucleation and growth are taken into account in the damage model [START_REF] Gurson | Plastic Flow and Fracture Behaviour of Ductile Materials Incorporating Void Nucleation, Growth And Coalescence[END_REF]. Coalescence of voids is not considered in the modeling.

Simulations are conducted using the finite element code Abaqus®. The stress and strain values are extracted on the solder layer for comparison purposes between the two solder solutions. Damage profiles produced for 10 thermal cycles are plotted and compared for the two packaging configurations. Fig. 6(a) shows the stress distribution on the AuGe solder layer after heating and cooling. Stress is higher in the cooling step near the interface between die and solder. This is obvious because diamond has the highest rigidity among the whole assembly materials. The solder is more solicited in the die side and hardens during cycling. The effective stress reaches a value of 83 MPa. Note that AuGe behavior is monitored by combined kinematicisotropic hardening behavior.

In the other hand, AlSi solder shows much less hardening in such way that the maximal stress in the solder is concentrated on the middle of the layer fillet. The value of the effective stress is about 30 MPa at the heating stage of the thermal cycling (Fig. 6(b)). AlSi behavior presents many similarities to Aluminium because it describes pure isotropic hardening and a stabilization of stress at advanced stage of loading.

(a) (b)

Figure 7: Hysteresis loops at the end of the thermal cycling. Hysteresis loops representing shear stress versus shear strain are extracted at an integration point of the layer where shear stress is maximal. These responses illustrated in Fig. 7 demonstrate the hardening characters of the two solders. In fact, for the AuGe solder, shear stress increases from 25 to 130 MPa and stabilizes at this value at the end of the cycling stage (Fig. 7(a)). The total shear strain reaches 2.5% at the first cycle of loading then it decreases progressively to 1.5% at the end of loading. However, for AlSi solder, there is a stress softening decreasing the stress from 22 MPa to 15 MPa and the stress response stabilizes in the 7 th cycle. The shear strain is more important than AuGe shear strain and increases from 4% to a value of about 6%. Then the two solders show completely opposite mechanical behaviors and are expected to describe different damage profiles.

(a) (b) Figure 8: Evaluation of damage in the two solder layers, (a) FE results of damage distribution, (b) damage variation with respect to number of cycles for the two

solders. Looking at the damage profile in Fig. 8, we see that in the case of AuGe-based assembly, damage tends to be stable at the end of loading and takes a maximal value of 7.4E-3 in the solder layer. This amount of damage is higher than that observed in the AlSi solder layer which stabilizes at 5.7E-3 for a total number of thermal cycles equal to 10. Thus, for high thermal loading, AlSi seems to accumulate much less damage than AuGe. That is obvious because AlSi is subjected to cyclic softening and the stress produced in the solder still less important than that produced in AuGe solder. Regarding the evolution of damage in the two solders, we can conclude that the AlSi based packaging, represents a quite good prospective for high temperature high power applications in comparison with AuGe based assemblies.

3D Modeling and damage prediction of AlSi based test vehicle

A 3D power electronics test vehicle was designed for thermal and power cycling. The vehicle is disposed as a "sandwich" structure and consists on diamond die brazed using AlSi solder alloy on Mo metallized Si 3 N 4 ceramic substrate. The distance between the two vehicle halves are controlled using a molybdenum guide brazed to the die and the Mo metallization. The molybdenum guide is used to minimize the breakdown voltage risk and as a link between the two packaging parts. Four cylindrical Molybdenum bumps are brazed to the Mo metallization for mechanical support of the system. Thus, AlSi solder is used for both die/Mo, and Mo/Mo assemblies. Two connection leads in Molybdenum ensure electrical power conduction. The test vehicle is subjected to the same thermal cycling illustrated in Fig. 5(b). The composition of the 3D vehicle test is detailed in Fig. 9. For all cases, stress softening is viewable in all regions.

Concerning damage evolution, Fig. 11 illustrates damage profiles in the four regions. As expected, damage in the bumps solder is nearly twice higher than the other values and keeps increasing until 6% at the 10 th cycle. For the damage, stabilization (essentially due to voids nucleation) is not reached and may take many computations efforts. But a conservative prediction consists on assuming a continuous linear evolution of damage and extrapolating the damage profiles to determine the numbers of cycles N f which permit to have a volumic fraction of damage of 50%. This limit is fixed by the "Standard Military Handbook" and represents the criteria for the packaging validity [START_REF]Military Standard Handbook[END_REF].

Following this method, the failure is expected to start in bumps solders after a minimum period of about 62 cycles (1 in Fig( 10(

Conclusions

Two diamond-based packaging configurations designed for high temperature and high power applications are studied. The packaging are composed with two kinds of high temperatures solders AuGe and AlSi. The experimental data permitted to approve the viscoplastic mechanical behavior of the two solder alloys and gives a database to identify the material parameters for a coupled porous damage and viscoplastic model. The last is used for the FE modeling of 2D and 3D packaging architecture. The FE modeling permitted to demonstrate that AlSi based packaging represents a good prospective for extreme temperature power electronics applications. The model shows that failure may happen in the bumps solders for the 3D test vehicle which must be proved experimentally. Studies of the test vehicle under power cycling must be explored to identify and evaluate failure.

Figure 1 :

 1 Results of realized mechanical tests using AuGe shear specimen, (a) simple shear, (b) cyclic shear, (c) creep.

Fig. 1 (

 1 b) also demonstrates that AuGe solder exhibit cyclic hardening and Bauschinger effects due to shear. Fig .1(c) represents the creep behavior of AuGe solder at various temperatures and loads. At 300°C, effect of creep is preponderant. Failure produces fast for the chosen forces 100 N, 150 N and 200 N.

Figure 2 :

 2 Figure 2: Micrographs of AuGe specimen failure profiles: initial voids fraction due to reflow process.

Fig. 2 Figure 3 :

 23 Fig.2shows specimen failure profiles after simple shear loading at 200°C and a displacement rate of 6.10 -2 mm/min. The failure profiles are heterogeneous but show that deformation hardening produces in the shear direction. However, we can notice the presence of an initial voids fraction with spherical form. These voids have an average diameter of 100 µm. The presence of voids is essentially due to the solder reflow process during specimen manufacturing and have to be optimized to reduce their volumic fraction.

Figure 4 :

 4 Figure 4: Micrographs of AlSi specimen failure profiles: shear bands in the load direction.

Figure 5 :

 5 Figure 5: Modeling of 2D power electronics packaging, (a) simplified packaging architecture, (b) imposed temperature profile.The diamond and Si 3 N 4 ceramic are taken as pure elastic materials. Copper metallization is considered to have elastoplastic mechanical behavior with combined hardening. The die attach exhibit viscoplastic behavior which follows the coupled viscoplastic McDowell law and potential based damage rules. The model is integrated using a semi-implicit Euler scheme combined with a line search strategy[START_REF] Msolli | Implicit integration scheme for porous viscoplastic potential-based constitutive equations[END_REF]. The complete model parameters are identified using simple shear and creep experimental data. Damage parameters are identified using cyclic data giving maximal force versus number of cycles. Note that no interfacial behavior is considered between solder and die

Figure 6 :

 6 Figure 6: Stress distribution in the solder layers after thermal cycling of the two configurations, (a) AuGe, (b) AlSi.

Figure 9 :

 9 Figure 9: 3D geometric configuration of the power electronics test vehicle.

  Evaluation of stress in the solder layers, (a) FE results of stress distribution, (b) stress variation with respect to number of cycles in various solder regions.Fig.10shows the difference of stress amplitudes in the various regions of solder layers (denoted 1,2,3 and 4 in Fig.10(a)). Following this figure, stress in the bumps solders (1 in Fig.10(a)) are much more important than the other regions stress. It takes a value of 40 MPa in the first heating stage and a maximal value of 43 MPa in the first cooling stage. The other stress profiles still the same degrading stress from 37 MPa tending to a stable value of 20 MPa.

Figure 11 :

 11 Figure 11: Progression of damage in four solder regions of the test vehicle.

  a)), in Die/Mo solder layers (2 and 3 in Fig. 10(a)) after 110 cycles and in Mo/Mo solder layers (4 in Fig. 10(a)) after 130 cycles.