Search

The model of diffusional deformation is revisited by accounting for the dependence of the diffusion potential on grain boundary curvature. The issue is developed through the analysis of two case-studies: the deformation of a lattice of columnar grains in conditions of Coble creep, and the rotation of a grain embedded in a polycrystal in conditions of either Nabarro-Herring creep or Coble creep. The analysis reveals that, unless grain boundary mobility is infinite, grain boundary curvature is dynamically induced by strain rate. A link is established between the curvature distribution and the transfer of diffusion fluxes across grain boundaries. For the two case-studies, the equation expressing the balance of grain boundary motions at steady-state is solved for calculating, within a range of grain boundary mobilities, the grain boundary profiles, the diffusion fluxes, and the contributions to power dissipation arising from curvature. The latter contributions are found to scale closely as the square of grain size. It follows that the dissipation contribution due to curvature is larger in conditions of Nabarro-Herring creep. In conditions of Coble creep, the dissipation contribution due to curvature translates into a lower bound for the apparent boundary viscosity parameter to be used in numerical simulations. This lower bound is consistent with previous identifications of the parameter in the literature. The classical model assuming flat grain boundaries with transfer of fluxes via triple junctions emerges as a particular case involving the implicit assumption of an infinite grain boundary mobility.

According to the principles of diffusional creep, the normal and tangent components of the velocity jumps be- tween adjacent grains arise from, respectively, the climbing and sliding of disconnections along grain boundaries. Stationary deformation thus implies a balance between nucleation and recovery of moving disconnections. The model considers a periodic lattice of hexagonal grains with nucleation of disconnection multipoles at triple junc- tions. The strain energy coupled to the population of climbing disconnections is calculated by inferring that the internal strain field associated to disconnection pile-ups brings a distribution of tractions along GBs that is consis- tent with the field of diffusion potential gradient that drives disconnection climb. It follows that the distribution of the density of climbing disconnections is parabolic and that the dissipation due to the nucleation and recovery of climbing disconnections is equal to 50% of the dissipation arising from diffusion fluxes. These results hold for both Nabarro-Herring creep and Coble creep. The analysis of the disconnection nucleation process highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.

Modeling of bulk sintering viscosity usually neglects the contribution of pore surface diffusion with respect to grain‐boundary diffusion. This approximation is questionable at the high densification rates used today in advanced fast sintering techniques. A two‐dimensional analysis of the problem shows that the influence of surface diffusion on bulk viscosity at high strain rate can be decomposed as the sum of two terms: a term linked to the change in pore surface curvature and a term linked to the change in grain‐boundary size. The computational procedure relies on the partition of pore profile evolution into a transient component accounting for non‐densifying phenomena and an asymptotic component accounting for strain‐rate‐controlled phenomena. The largest impact of surface diffusion is found to arise from the change in grain‐boundary size. It follows a transition from Newtonian viscosity at low strain rate to non‐Newtonian viscosity which, during densification, increases nearly linearly with strain rate. In some conditions, viscosity can then reach more than twice the value estimated when neglecting pore surface diffusion. Reversely, expansion is accompanied by a decrease in grain‐boundary size which causes a decrease in viscosity and can lead to grain separation at high strain rate.

The toughness of Al-to-steel welds decreases with increasing thickness of the intermetallic (IM) layer formed at the interface. Co plating has been added as interlayer in Al-to-steel Friction Melt Bonded (FMB) welds to control the nature and thickness of the IM layer. In comparison to a weld without interlayer, Co plating brings about a reduction of the thickness of the IM layer by 70%. The critical energy release rate of the crack propagating in the weld is used as an indicator of toughness. It is evaluated via an adapted crack propagation test using an energy conservation criterion. For a weld without interlayer, critical energy release rate is found to increase when the thickness of the intermetallic layer decreases. When the intermetallic layer is thick, the crack propagates in a brittle manner through the intermetallic whereas, at low layer thickness, the crack deviates and partially propagates through the Al plate, which causes an increase of toughness. The use of a Co interlayer brings about an increase of toughness by causing full deviation of the crack towards the Al plate.

Voir fichier attaché

At high homologous temperature, plastic flow of a polycrystalline material can be mediated by self-diffusion and grain boundary sliding, rather than by dislocation glide. The effective viscosity of the polycrystal depends on the underlying mechanisms as well as on the microstructure. Simple expressions relating the shear viscosity to lattice and grain boundary diffusion coefficients were proposed in pioneering contributions by Nabarro (1948), Herring (1950) and Coble (1963). While these models remain widely used today to deduce the dominant mechanism based on the observed dependence of viscosity on grain size, a number of questions remain open. The present work revisits Nabarro–Herring–Coble creep using a micromechanical approach and variational principles. We focus on a random polycrystal of equiaxed grains deforming by coupled lattice and grain boundary diffusion and grain boundary sliding. We show that the classical results of Herring and Coble correspond to upper bounds on the shear viscosity, and obtain complementary lower bounds. Our results shed new light on these classical results and question the validity of the common interpretation of the dependence of viscosity on grain size.

The basic science underneath the phenomenon of thermal expansion in composite materials is presented on the basis of a comprehensive review of literature. Owing to the high yield strength of the matrix, the effective thermal expansion of metal matrix composites depends on an intricate manner on the highly anisotropic internal stresses that are induced by the mismatch between the thermo-elastic constants of the phases. Three cases are discussed successively: (1) pure elastic behavior of the phases; (2) plastic yielding in the matrix; (3) role of porosity and damage.

Dissimilar welding consists in joining materials presenting large differences of properties. This is the case of the aluminium-steel assemblies, of particular interest in the automotive industry due to the lightness of the former and the strength of the latter. The large differences in melting temperatures, mechanical properties and the formation of brittle Al/Fe intermetallic phases at the interface constitute major challenges. Friction melt bonding (FMB) is a novel process, developed and patented at UCL, to join dissimilar materials showing large differences in melting temperatures. A rotating cylindrical tool pressed against the upper steel plate generates heat by friction. The temperature rise brings the melting of the underneath aluminium plate. The reaction between solid steel and liquid aluminium leads to the formation of a continuous thin intermetallic layer that keeps both plates welded. The mechanical strength of FMB joints was characterised in the present work. Hot tear defects in the aluminium plate leads to the premature failure of welds. They were thus suppressed with the control of the thermo-mechanical cycles during welding. The toughness of the joint was assessed using single lap joint testing and compared to friction stir welds (FSW). The microstructure observations and finite element modelling revealed that the weld failure is controlled by the initiation and fast propagation of a crack through the intermetallic layer. To improve the mechanical performance of the weld, the nature of the intermetallic layer was changed with addition of electroplated layers of Ni and Co at the reacting interface. It was revealed that the toughness depends on both the thickness and the nature of the intermetallic layer. The Co plating showed the largest toughness since the crack is forced to propagate through the aluminium plate instead of the intermetallic layer. Finally, the residual stresses after welding were characterised using neutron diffraction. Their distrib, (FSA - Sciences de l'ingénieur) -- UCL, 2018

Un polycristal à grains fins peut se déformer par un mécanisme de glissement aux joints de grain accommodé par un transfert de matière par diffusion. Ce mécanisme est censé gouverner le « fluage diffusionnel », dont on distingue le fluage « Nabarro-Herring » et le fluage « Coble », selon que la diffusion s’opère de façon prépondérante à travers le réseau ou le long des joints de grain. À l’état pur, le mécanisme de glissement aux joints de grain accommodé par diffusion se traduit par un exposant de contrainte égal à 1, ce qui justifie que ce mécanisme soit considéré dominant également dans la mise en forme superplastique. Opérant de façon identique en présence de pores, le même mécanisme est sous-jacent à la viscosité de cisaillement de l’agrégat au cours du frittage par diffusion aux interfaces. Malgré l’abondante littérature sur le sujet, de nombreux points restent mal-compris : parts de la contribution de la déformation des grains et du glissement aux joints de grain dans la déformation macroscopique ; nature physique de la friction aux joints de grain et valeur du coefficient de friction associé ; raison du maintien d’une distribution sensiblement uniaxe des grains même après grande déformation ; valeur effective de l’exposant de taille de grain. En vue d’élucider ces points, nous avons établi des principes variationnels qui nous ont permis de définir des bornes supérieure et inférieure de la limite d’écoulement plastique (c’est-à dire de la viscosité) sous un cisaillement pur. En particulier, ces bornes apportent un éclairage nouveau sur le rôle du coefficient de friction. Une méthode auto-cohérente est proposée pour établir le meilleur estimateur entre les bornes. Les résultats sont comparés avec les diverses estimations proposées dans la littérature. La méthode permet également de prédire l’influence de la fraction de porosité sur la viscosité de cisaillement en frittage.

Les modèles visant à prédire la viscosité hydrostatique d’un agrégat au cours du frittage gouverné par diffusion aux interfaces utilisent habituellement l’approximation de quasi-équilibre qui consiste à négliger la part de dissipation due à la diffusion en surface des pores. Cette approximation est valide tant que la diffusivité le long des joints de grain est suffisamment plus faible que la diffusivité en surface des pores. Elle peut devenir invalide au cours d’un frittage à haute température avec une vitesse de densification élevée. Une analyse en deux dimensions montre que l’effet de la diffusion en surface sur la viscosité est alors la somme de deux termes : un terme lié à l’augmentation des gradients de courbure en surface et un terme lié à l’augmentation de la taille du joint de grain. L’évaluation de ces deux termes nécessite la simulation de l’évolution du profil du pore au cours de la densification. Nous avons développé une méthode permettant de séparer, dans cette évolution, la composante transitoire, reflétant les mécanismes de transport non-densifiants, de la composante asymptotique, reflétant les phénomènes liés seulement à la vitesse de densification. Les calculs montrent que l’effet le plus important est dû au changement de taille du joint de grain. Lorsque la vitesse de densification augmente, il en résulte une transition entre une viscosité Newtonienne et une viscosité non-Newtonienne qui augmente presque linéairement avec la vitesse. Dans certaines conditions, la viscosité peut atteindre le double de la viscosité prédite via l’hypothèse de quasi-équilibre. A l’inverse, une expansion du système peut induire une réduction de la taille du joint de grain entraînant une diminution de la viscosité et pouvant mener à une séparation des grains à haute vitesse.

Short C fibres–Mg matrix (AZ91D) composites have been produced by friction stir processing sandwiches made of a layer of C fabric stacked between two sheets of Mg alloy. The process parameters have been optimized to ensure a good fiber distribution. 3D X-ray tomography reveals that the fibers orient like onion rings. Thermal treatments have allowed to modify the flow stress level of the matrix material. Tensile testing inside the scanning electron microscope have revealed the decohesion at the fiber/matrix interface if the fibers are preferentially oriented perpendicularly to the loading direction. Modelling allows to estimate the stress needed to initiate this decohesion is about 250 MPa, i.e. appearing early in heat treated samples. To compare with different loading conditions, micro-compression and instrumented micro-indentation testing have also been performed. The consequence of the loading path on the decohesion is discussed.

The role of liquid phase and grain growth during the intermediate stage of sintering is investigated by comparing the isothermal densification rate of the tungsten skeleton in two systems: solid-state sintered W and liquid-phase sintered W-10wt%Cu. Densification curves at 1380 C, i.e. well after completion of capillary rearrangement in W-Cu, are confronted to the predictions of a model that considers a single representative grain size with quasi-equilibrium interfaces and a monotonic increase in grain size and coordination with density. In both systems, the densification mechanism is taken to be governed by W diffusion along grain boundaries. For system W-Cu, a phenomenological law is proposed to allow accounting for the decrease in liquid surface curvature during funicular filling of the pores by the liquidphase. The kinetics of grain growth is described via current literature model. Good agreement is demonstrated between experimental measurements and model predictions when relying on material parameter values given in literature. In system W-Cu, the detrimental effect of the decrease in dihedral angle is, at the beginning of the funicular stage, compensated by the contribution to sintering stress brought about by the concave curvature of liquid/vapour interface. The sensitivity of computational results to model hypotheses and material parameters is assessed. The most influential parameters are diffusivities along W grain boundaries and along W/vapour and W/Cu interfaces.

Composite plates in which the low CTE phase has the shape of a honeycomb are anticipated to present optimum anisotropy of thermal expansion and thermal conductivity for baseplates in electronic packaging. This design is explored by choosing an invar alloy for the low CTE phase. In order to allow the formation of a passivation layer protecting from reaction with liquid Al during squeeze casting, the honeycomb is made of the Cr-rich alloy commonly called “stainless-invar”. Composite plates containing 20 vol.% and 38 vol.% stainless invar were processed using honeycombs with the same thickness over cell side ratio. Experimental CTE values are significantly lower than the predictions of three different thermo-elastic models. The very limited amplitude of the strain hysteresis precludes the occurrence of global plastic yielding in the matrix. It appears that, owing to the high contiguity of the lowCTE phase, the lowvalue of the experimental CTE results fromvoid closing and opening by localised plastic flow. A honeycomb volume fraction of 38% is necessary for bringing the average CTE down to the level suitable for packaging applications. The ratio of transverse thermal conductivity to density then amounts to about half of the performance of the best Al/SiC composites. © 2015 Elsevier Ltd. All rights reserved.

Short C fibres-Mg matrix composites have been produced by friction stir processing sandwiches made of a layer of C fabric stacked between two sheets of Mg alloy AZ31B or AZ91D. This novel processing technique can allow the easy production of large-scale metal matrix composites. The paper investigates the microstructure of FSPed C fibre-Mg composites in relation with the fragmentation of the C fibres during FSP and their influence on the tensile properties. 3D X-ray tomography reveals that the fibres orient like onion rings and are more or less fragmented depending on the local shear stress during the process. The fibre volume fraction can be increased from 2.3% to 7.1% by reducing the nugget volume, i.e. by using a higher advancing speed in AZ31B alloy or a stronger matrix alloy, like AZ91D alloy. A higher fibre volume fraction leads to a smaller grain size which brings about an increase of the composite yield strength by 15 to 25%. However, a higher fibre volume fraction also leads to a lower fracture strain. Fracture surface observations reveal that damage occurs by fibre/matrix decohesion along fibres oriented perpendicularly to the loading direction.

The influence of dihedral angle and particle coordination on the evolution of densification rate is investigated throughout the intermediate and final stages of sintering. From a review of literature data, heuristic expressions are proposed for representing different trajectories of evolution of coordination from the onset of skeleton formation up to full density. The influence of dihedral angle and coordination on the threshold density for pore closure is established by revisiting the Plateau–Rayleigh instability criterion. The intermediate and final stages are modeled using representative volume elements that do not restrict coordination to integer values. Computational results enlighten the interplay between coordination and dihedral angle on the evolution of sintering stress, bulk viscosity, and sintering rate. The results allow quantifying the amplitude of the drop of densification rate at pore closure transition. The monotonous increase of coordination with relative density brings about a monotonous increase of sintering rate at constant particle size. Simulations emphasize the beneficial effect of higher initial density and coordination in the green part.