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Discrete Network (DN) models are a useful tool to investigate structure-property relationships in rubbery networks such as elastomers and hydrogels. In a DN model, polymer chains are represented by entropic springs connected at crosslinking points, and the partitioning of stretches among the chains is dictated by the condition of mechanical equilibrium at each crosslink. A key feature of these models is that springs have a zero natural length, and are therefore pre-stretched in the reference configuration. However, the role of chain pre-stretch distribution on the emerging mechanical properties has often been overlooked. In this work we investigate the elastic properties of DNs where the average chain pre-stretch, chain density and chain length distribution can be prescribed independently via a novel network generation algorithm. We show that increasing the average pre-stretch increases the network stiffness and decreases its extensibility limit. We also compare predictions of semi-analytical micromechanical models of rubber elasticity to DN predictions taken as reference. Deviations between analytical model and DN predictions are attributed to the combination of two factors: the loss of affinity at large strain and the initial pre-stretch distribution, which is not taken into account in analytical estimates. DN simulations further show that the assumption of one-to-one mapping between chain stretch and chain orientation on which microsphere models rely is not satisfied.

A mesoscale numerical model based on shear transformation zone (STZ) theory is implemented in a commercial finite element software. The model is designed to predict the (visco)plastic deformation response of amorphous solids at the nano- and micro-scale. The theoretical framework relies on earlier models developed by Bulatov and Argon (1994a) and of Homer and Schuh (2009). We justify the potential of the computational model by conducting reference calculations for model metallic and polymeric glasses in plane strain compression. Emphasis is placed on the effect of time and space discretisation on the predicted macroscopic response. The dependence of the predicted yield strength upon the values of the fundamental model parameters is analysed via a mean-field approximation. The mean-field approximation is validated based on a series of simulations in model parameter space. We provide guidelines for a straightforward but consistent parameter identification method via the mean-field approximation while starting from experimental data.

Polymeric glasses exhibit complex behaviour when subjected to deformation below the glass transition temperature. Uniaxial stress-strain curves typically include post-yield strain softening, strain hardening, and non-linear unloading. In addition, the deformation and failure responses are sensitive to the rate of deformation, pressure, and temperature. Sophisticated (visco-)elastic-(visco-)plastic continuum constitutive models have been developed to simulate the large strain deformation of (glassy) polymers; they generally give excellent fits to uniaxial stress-strain curves. However, they require the calibration of a large number of mostly phenomenological parameters, give limited insights into failure, and struggle to accurately predict the response for more complicated loading states and histories. At the opposite scale, molecular dynamics (MD) simulations have been used to elucidate the discrete molecular deformation mechanisms leading to the heterogeneous inelastic behaviour of polymeric glasses. The results of MD calculations suggest that plastic deformation of polymeric glasses is caused by thermally activated molecular rearrangements and conformational changes of a collection of polymer chains parts. The use of a mesoscale numerical model based on the activation of shear transformation zones (STZs) offers a convenient approach to bridge continuum and molecular dynamics simulations, which are typically limited to small length and time scales. We have used the implementation by Homer and Schuh [1] of Argon’s STZ theory [2] to develop a mesoscale finite element model for polymeric glasses. It is assumed that the elementary deformation mechanism giving rise to macroscopic plastic deformation in a polymeric glass is a pure shear deformation of an STZ; this corresponds to a change in molecular conformational state. Plastic deformation is governed by these changes and their interaction with the surrounding (visco-)elastic matrix. The mesoscale STZ framework require

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.

Martensite volume fraction, composition and grain size are the known primary factors controlling the mechanical behavior of ferrite-martensite dual-phase steels. Recently, excellent performances of dual-phase steels with a fibrous microstructure have been reported. However, the precise role of martensite morphology and orientation has not been thoroughly elucidated yet. This study develops a two-scale micromechanical modeling strategy in order to investigate the effect of particle morphology and orientation on the elastoplastic behavior of dual-phase steels. Finite element simulations are carried out on 3D periodic unit cells, each having a given orientation and volume fraction of spheroidal particles. The overall response is obtained by averaging the response of grains with different orientations, thus bypassing the need for costly full-field simulations on representative volume elements of realistic microstructures. A detailed parameter study systematically investigates the effect of particle morphology and orientation at grain level and at grain assembly level. While particle morphology and orientation effects lead to significant differences at grain level in terms of strain hardening behavior and back-stress development, the impact of the phase morphology at the homogenized multigrain level is almost negligible up to the onset of necking. However, the mechanical fields at the micro-scale are considerably influenced by both particle morphology and orientation, and are expected to largely impact the damage behavior through, among others, generating large grain-to-grain heterogeneities.

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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 deformation behavior of polymer materials below their glass transition temperature involves a complex intermingling of elasticity, of viscoplastic yielding with softening and large strain hardening, and of significant rate, temperature and pressure dependency. During unloading, the response exhibits large non-linearity as well, combining forward and backward creep. Even though the nature of the atomistic underlying mechanisms is relatively well understood, a full picture of the interactions between the elementary distortions mechanisms and their collective organization capturing the complexity of the macroscopic behavior is still lacking. Here, we propose a mesoscale approach based on the heterogeneous activation of molecular level shear transformation zones and we show that it is rich enough to unravel the physical origin of most aspects of the macroscopic viscoplastic response. The study is based on a wide micro- and macro-mechanical test campaign on a thermoset material. In addition to providing a full characterization of all macroscopic properties, evidence of a complex rate reversal mechanism upon unloading is given. Other experiments provide insights about the characteristic length scales at play. Compared to existing continuum models involving typically more than 25 parameters, the present formalism is based on only 7 physical parameters while allowing quantitative predictions of all the experimental data. The present approach opens new avenues for the prediction of the mechanical response of a variety of polymer applications in confined state such as in composites or in adhesive joints. It also offers a new line of thought to address the mechanics of polymers at small and intermediate length scales.

Dual-phase steels have long been used in the automotive industry for their excellent mechanical properties in terms of strength and ductility balance combined to a low processing cost. The good compromise between strength and ductility results from the very different properties of the constituent phases, namely ductile ferrite and hard martensite. In contrast with the plastic flow properties, the fracture toughness of dual-phase steels (quantified by K Ic or J Ic ) has been far less investigated. Common values of the fracture toughness are -2 around 100 kJ.m or lower. However, a minimum level of fracture toughness is required to prevent the propagation during forming operations of small edge damage or cracked zones induced by cutting. Therefore, unravelling the relationship between fracture toughness, microstructure and damage mechanisms is essential to develop advanced steels with superior forming ability. Furthermore, reaching superior fracture toughness could open to other potential applications. Dual-phase steels are usually processed following an intercritical annealing which generally leads to equiaxed martensite particles. An alternative heat treatment, consisting of a double annealing as first proposed N.J. Kim and G. Thomas [1], brings about martensite particles in the form of platelets. A recent study on bulk samples of such steels shows that this microstructure can potentially lead to a very high fracture toughness, while retaining good properties in terms of strength and ductility [2]. In this work, rather oriented towards thin sheets, the Essential Work of Fracture (EWF) method [3] is used to quantify the work per unit area spent in the fracture process zone by separating it from the total work expended for material failure. EWF -2 values in excess of 300 kJ.m have been found on platelet-like microstructure steels confirming their interesting resistance to the propagation of a crack. Equiaxed microstructures are investigated as well and the impact of ma

Highly-crosslinked epoxies are widely used as matrix material in highperformance fibre-reinforced composites, governing several aspects of their behaviour. Yet, attempts to model their viscoplastic response have been limited, as compared to thermoplastic polymers. However, the viscoplastic response of highly cross-linked thermosets, in particular under compression, is very similar to glassy thermoplastics below their glass-transition temperature, exhibiting complex features such as strain- and temperature-sensitivity, post-yield softening followed by rehardening, and severe non-linearity upon unloading. These phenomena can in principle be captured by advanced constitutive models for glassy polymers mixing phenomenological and micromechanical elements. However, this often comes at the price of a very large number of parameters (sometimes more than 30), while the physical basis of such models remains limited. In this work, we develop a micromechanical model to describe and predict the viscoplastic behaviour of the RTM6 epoxy resin. The model relies on the concept of STZ’s (Shear Transformation Zones) as the elementary carriers of plasticity, whose activation is sensitive to the local stress, temperature and microstructural state. STZ’s interact through the (possibly polarized) elastic stress field, resulting in overall viscoplastic flow. This model involves only 5 parameters to identify, all with a physical meaning. It is rich enough to quantitatively capture all the experimental trends, even the complex rate-reversal phenomenon observed during creep tests performed after plastic deformation at intermediate stress levels. While such a model cannot replace closed-form constitutive models for the treatment of large-scale components, it provides physical insights into the small-scale mechanics and is also useful to identify the parameters in macroscopic models.

Advanced constitutive models for polymers have been essentially developed for thermoplastics with relatively limited applications/extensions to thermosets. Thermosets differ from thermoplastics by the cross-linking. Recent extensions of these constitutive models provide accurate predictions over a wide range of loading configurations, strain rates and temperature, encompassing below and above transition temperature regimes, although at the prize of a very large number of parameters, often larger than 30. Still, these models, mixing phenomenological and micromechanics ingredients, are often not rich enough to capture complex behaviors such as for instance severe non-linearity upon unloading, while missing also micromechanical connection to the failure process. Based on an extensive experimental test program on the highly cross-linked RTM6 epoxy, the viscoplastic response is found very similar to thermoplastics, with hardening-softening-re-hardening, large back stress upon unloading and existence of shear band patterns at very small scale. A molecular physics-based model of the deformation process occurring through the activation of nanometer scale shear transformation zones (STZ) has been developed, borrowed from the metallic glass field. The viscoplastic deformation is the result of the cooperative activation of STZ’s, sensitive to rate, temperature, stress state and stress level. This model involves only 5 parameters to identify, all with physical meaning. The model quantitatively captures all the experimental trends, even some complicated responses during creep tests performed after plastic deformation at intermediate stress levels showing backward followed by forward creep. Such as model will never replace closed form constitutive models for the treatment of large scale components but can be used to understand small scale mechanics as well as for identifying macroscopic models. In this research, a new micromechanics-based fracture model based on the attainment of

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.

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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.

Dual-Phase steels have long been used in the automotive industry for their excellent mechanical properties in terms of strength and ductility balance combined to a low processing cost. The good compromise between strength and ductility results from the very different properties of the constituent phases, namely ductile ferrite and hard martensite. In contrast with the plastic flow properties, the fracture toughness of Dual-Phase steels (quantified by KIc or JIc) has been far less investigated. Common values of the fracture toughness are around 100 kJ.m-2 or lower. However, a minimum level of fracture toughness is required to prevent the propagation during forming operations of small edge damage or cracked zones induced by cutting. Therefore, unravelling the relationship between fracture toughness, microstructure and damage mechanisms is essential to develop advanced steels with superior forming ability. Furthermore, reaching superior fracture toughness could open to other potential applications. Dual-Phase steels are usually processed following an intercritical annealing which generally leads to equiaxed martensite inclusions. An alternative heat treatment, consisting of a double annealing as first proposed N.J. Kim and G. Thomas [1], brings about martensite inclusions in the form of platelets. A recent study on such steels shows that this microstructure can potentially lead to a very high fracture toughness, while retaining good properties in terms of strength and ductility [2]. The general objective of this research is to investigate the fundamental damage mechanisms governing the fracture toughness of Dual-Phase steels. Our approach is based on the processing of microstructures in which parameters are varied one by one. In particular, both equiaxed and platelet-like microstructures are investigated in the form of thin sheets. Experimentally, the Essential Work of Fracture (EWF) method [3] is used to quantify the work per unit area spent in the fracture process zo

Model dual-phase microstructures were developed to decouple the effect of martensite volume fraction and martensite hardness on the plastic behavior of dual-phase steels. The martensite volume fraction ranges from 11% to 37%, involving two levels of martensite hardness. The yield strength and tensile strength increase with increasing martensite volume fraction, while the uniform elongation decreases. The martensite hardness has a weak impact on the initial yield strength, but it significantly affects the flow behavior for sufficiently large martensite volume fraction. Increasing the hardness of the martensite leads to higher tensile strength combined with only a limited impact on uniform elongation, resulting in an improved strength/ductility balance. The experimental results are successfully captured using finite element based micromechanical analysis. Among others, periodic cell calculations show very good predictive capabilities of the overall plastic response when the stage-IV hardening of the ferrite is taken into account. Our numerical analysis reveals that an accurate description of the elasto-plastic behavior of the martensite is a key element to rationalize the mechanical behavior of DP steels. This modeling approach provides a framework for designing dual-phase steels with optimized plastic flow properties.

Dual-Phase steels have long been used in the automotive industry for their excellent mechanical properties in terms of strength and ductility balance combined to a low processing cost. The good compromise between strength and ductility results from the very different properties of the constituent phases, namely ductile ferrite and hard martensite. In contrast with the plastic flow properties, the fracture toughness of Dual-Phase steels (quantified by KIc or JIc) has been far less investigated. Common values of the fracture toughness are around 100[kJ.m-2] or lower; but seldom exceed the 200[kJ.m-2]. However, a minimum level of fracture toughness is required to prevent the propagation during forming operations of small edge damage or cracked zones induced by cutting. Therefore, unravelling the relationship between fracture toughness, microstructure and damage mechanisms is essential to develop advanced steels with superior forming ability. Dual-Phase steels are usually processed following an intercritical annealing which generally leads to equiaxed martensite inclusions. An alternative heat treatment, consisting of a double annealing as first proposed N.J. Kim and G. Thomas [1], brings about fibrous martensite inclusions. A very recent study on such steels shows that this fibrous microstructure can potentially lead to a very high fracture toughness, while retaining good properties in terms of strength and ductility [2]. The general objective of this research is to investigate the fundamental damage mechanisms that govern the fracture toughness of Dual-Phase steels. Our approach is based on the processing of microstructures in which parameters are varied one by one. In particular, both equiaxed and fibrous microstructures are investigated in the form of thin sheets. Experimental works as well as numerical calculations are used to study the behaviour of such steels. Experimentally, the characterization using a serial sectioning reveals that what seemed to be fibrous ma

This paper presents a new micromechanical damage model, called ‘‘First Pseudo-Grain Damage’’ (FPGD) model, to predict the overall elasto-plastic behavior and damage evolution in short fiber reinforced thermoplastic materials typically produced by injection molding. The model combines mean-field homogenization theory with a continuum damage model, leading to a semi-analytical estimate of the composite incremental response that is convenient for the large scale simulation of composite structures. Each representative volume element (RVE) of the composite is decomposed into a set of pseudo-grains (PGs), which are two-phase composites with aligned fibers of the same aspect ratio. The PGs are homoge- nized individually according to a nonlinear Mori–Tanaka scheme. Then, a self-consistent scheme is applied to the aggregate of homogenized PGs. An anisotropic damage model is used at the PG level which enables accommodating arbitrary multiaxial and non-monotonic loading histories. Damage evolution inside PGs progressively affects the overall stiffness and strength of the RVE up to total failure. An evaluation of the proposed model against experimental data is conducted for short glass–fiber reinforced polyamide 6,6 (PA6,6). It is shown that the model yields satisfactory predictions of the response under uniaxial tension on samples with different fiber contents and under various loading directions relative to the main injection flow direction

The influence of the martensite volume fraction (Vm)on the damage and fracture behavior of dual-phase steels was studied by combining experiments and micromechanical modeling. A transition in the dominating damage mechanism is observed when varying Vm. Martensite fracture dominates the void nucleation process at high Vm, while interface decohesion prevails at low Vm. Damage accumulation accelerates when Vm increases, resulting in a decrease of the fracture strain. Brittle fracture areas are observed in uniaxial tensile specimens for a sufficiently high Vm. The damage mechanisms and evolution are rationalized using a micromechanical analysis based on periodic finite element cell calculations. The results show that Vm is a key factor for controlling the ballance between strength and fracture resistance.

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Dual-Phase steels have long been used in the automotive industry due to their excellent mechanical properties in terms of strength and ductility, as well as their low processing cost. The good compromise between strength and ductility results from the very different properties of the constituent phases comprising ductile ferrite and hard martensite. In contrast with their plastic flow properties, the fracture toughness of Dual-Phase steels (quantified by KIc or JIc) has been far less investigated. Common values of the fracture toughness are around 100[kJ.m-2] or even lower; but seldom exceed the 200[kJ.m-2]. However, a minimum level of fracture toughness is required to prevent the propagation of small edge damage or cracked zones induced by cutting. Therefore, unravelling the relationship between fracture toughness, microstructure and damage mechanisms is essential to develop advanced steels with superior forming ability. Dual-Phase steels are usually processed following an intercritical annealing which generally leads to equiaxed martensite inclusions. An alternative heat treatment, consisting of a double annealing first proposed N.J. Kim and G. Thomas [1] brings about fibrous martensite inclusions. A very recent study on such steels shows that this fibrous microstructure can potentially lead to a very high fracture toughness, while retaining good properties in terms of strength and ductility [2]. The general objective of this research is to investigate the fundamental damage mechanisms that govern the fracture toughness of Dual-Phase steels. Our approach is based on the processing of microstructures in which parameters are varied one by one. In particular, both equiaxed and fibrous microstructures were investigated in the form of thin sheets. The Essential Work of Fracture (EWF) method [3] was used to quantify the work per unit area needed at the crack tip for material failure separating it from the total work expended for material failure. An extension of the EWF

Addressing the stability challenges in silicon-­‐based anode materials is necessary for achieving high capacity lithium-­ion batteries. Recent studies have shown that surface coatings favorably influence the cycling performance of such materials. These surface coatings enhance the current collection efficiency and promote the formation of a stable solid electrolyte interface, and act as a mechanical constraining layer. Despite the potential benefits, little knowledge is available on the impact of such coatings on the lithiation behavior and the reverse. This work details on the effect of conformal metallic Ni coatings on the lithiation behavior of crystalline Si nanopillars. The fabricated composite structures have different morphological parameters: Ni shell thicknesses of 40 nm, 80 nm and 120 nm with a Si core diameter of 170 nm, 330 nm and 480 nm. Pristine nanopillars display anisotropic swelling along <110> directions and fracture sites along <100> directions consistent with previous literature reports. The Ni coated structures exhibit a different swelling behavior with two distinct fracture regimes. For Ni thickness lower than 80 nm, the anisotropic behavior is preserved but fracture sites are present along <110> directions. With thicker coatings, an anisotropy reduction is observed together with a single randomly oriented fracture. A combined thermodynamic-­mechanical model corroborated these observations. The proposed theoretical framework can be extended to other types of coatings or nanostructures and provide guidelines for tailoring electrode materials to overcome the drawbacks around Si-based anodes.

Surface passivation of silicon anodes is an appealing design strategy for the development of reliable, high-capacity lithium-ion batteries. However, the structural stability of the coating layer and its influence on the lithiation process remain largely unclear. Herein, we show that surface coating mediates the swelling dynamics and the fracture pattern during initial lithiation of crystalline silicon nanopillars. We choose conformally nickel coated silicon architectures as a model system. Experimental findings are interpreted based on a chemomechanical model. Markedly different swelling and fracture regimes have been identified, depending on the coating thickness and silicon nanopillar diameter. Nanopillars with relatively thin coating display anisotropic swelling similar to pristine nanopillars, but with different preferred fracture sites. As the coating thickness increases, the mechanisms become isotropic, with one randomly oriented longitudinal crack that unzips the coreshell structure. The morphology of cracked pillars resembles that of a thin-film electrode on a substrate, which is more amenable to cyclic lithiation without fracture. The knowledge provided here helps clarify the cycling results of coated nanosilicon electrodes and further suggests design rules for better performance electrodes through proper control of the lithiation and fracture.

This paper presents a systematic experimental study of the relative contributions of the martensite volume fraction, morphology and carbon content to the overall strength and ductility of dual-phase steels. To this end, model dual-phase steels combining three volume fractions of martensite, three martensitic carbon contents, and three arrangements of the phases were generated by suitable control of the heat treatments. The microstructures include long and short elongated, as well as equiaxed martensitic islands. The yield and tensile strengths increase with both the amount of martensite and its carbon content. The ductility in general increases with the volume fraction of martensite at constant martensitic carbon content, and conversely increases with the martensitic carbon content for a fixed volume fraction of martensite. Departure from the general trend is observed for combinations of a large volume fraction of martensite with a large martensitic carbon content, and is attributed to damage-induced softening or fracture. Specimens with long elongated martensite demonstrate an improved ductility compared to other microstructures. The plastic flow properties were further investigated by relying on a non-linear homogenization model which explicitly accounts for the microscopic parameters. The micromechanical model captures reasonably well the tensile behaviour for the complete range of martensite carbon contents and volume fractions.

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Presentation of an original homogenization scheme for the simulation of the off-axis loading of biaxial woven carbon-epoxy composites.

In the search for high-energy density materials for Li-ion batteries, silicon has emerged as a promising candidate anode material due to its ability to absorb a large number of Li atoms. How- ever, the lithiation of silicon is accompanied by huge volumetric expansion (up to 300%) and severe structural changes. Lithiation-induced stresses may cause mechanical degradation of the electrode, resulting in capacity fading after several cycles of lithiation and delithiation. Stresses also affect the kinetics of reaction and diffusion of lithium into the Si host. Understanding the com- plex relationship between mechanics and chemistry in electrode materials is crucial for designing batteries with improved cycle life and reliability. It is now well-recognized that the lithiation strain in silicon can be accomodated by plastic de- formation in electrodes of small feature size. Lithiation of silicon leads to dramatic changes in its mechanical properties, from a brittle material in its pure form to an amorphous material that can sustain large inelastic deformation in the lithiated form. In particular, silicon demonstrates remark- able softening when subject to a combined chemo-mechanical loading, as compared to mechanical loading alone. However, the micro-mechanisms inducing the macroscopically observed plastic deformations in amorphous silicon are not well understood. In this work we propose a continuum model that couples diffusion, chemical reaction and large, inelastic deformations within a consistent thermodynamic framework. The model introduces a coupling between mechanical and chemical driving forces which reproduces the observed chemo- mechanical softening. The model formulation and parameter identification is supported by ab-initio calculations, as well as experimental measurements on thin film electrodes. The model was implemented into a FE software, allowing us to predict the stress and electric potential in silicon electrodes subjected to cycles of lithiation and del

In the development of the next generation of batteries with high capacity, improving our understanding of the complex interplay between mechanics and chemistry in electrode materials appears as a crucial issue. The lithiation reactions in batteries lead to a variety of mechanical phenomena, such as large deformations, plasticity and fracture. Conversely, mechanics can influence the chemistry of lithiation in a significant manner. Stress affects the kinetics of surface and bulk reactions and the diffusion of lithium within the host. In this work we develop a continuum theory to investigate the strong coupling between mechanics and chemistry in electrode materials. The theory couples mass transport to large, inelastic deformations and is written within a consistent thermodynamic framework. In particular, the model introduces a coupling between the kinetics of plastic flow and that of insertion reaction. The model formulation and parameter identification is supported by ab-initio calculations, as well as experimental measurements on thin film electrodes.

Rechargeable Li-ion batteries operate by cyclically inserting lithium into, and extracting lithium from, solid electrodes. The diffusion of lithium into a solid host induces significant volume change, which in turn generates stresses when the expansion is constrained. Diffusion-induced stresses often lead to mechanical degradation of the electrode, and also have a major impact on the diffusion process and the electrochemistry of the battery. Predicting the stress generated during lithiation and delithiation is crucial for designing batteries with enhanced cycle life and electrochemical performance. We focus on silicon, a promising anode material with high specific capacity: each silicon atom can host up to 4.4 lithium atoms. Lithiation of silicon is accompanied by huge swelling (up to 300%), which can be accommodated by plastic deformations. However, the micro-mechanisms inducing the macroscopically observed plastic deformations in amorphous silicon are not well understood, raising fundamental questions regarding the coupling between inelastic deformation, diffusion and bulk chemical reactions. We propose a continuum model that couples mass transport to large, inelastic deformations within the framework of the thermodynamics of irreversible processes. In particular, the model introduces a coupling between the kinetics of plastic flow and that of insertion reaction. The model formulation and parameter identification is supported by ab-initio calculations, as well as experimental measurements on thin film electrodes. The model was implemented into a FE software, allowing us to predict the stress and electric potential in silicon electrodes subjected to cycles of lithiation and delithiation. The influence of several parameters (electrode dimensions, charging rate, yield strength) are discussed. The numerical tool is useful for optimizing electrode geometry and loading conditions.

Silicon is a promising anode material in lithium batteries due to its high specific capacity and low operation voltage. The major concern in using Si-based anodes is the huge volume expansion and continuous solid-electrolyte interphase formation during the lithiation that leads to a fast degradation of the electrode material and a reduced life cycle of the battery with limited use in real life Li-ion applications. In this talk we report an approach to roll out Li-ion battery components from silicon chips by a continuous and repeatable etch-infiltrate-peel cycle. Vertically aligned silicon nanowires etched from silicon chips are captured in a polymer matrix that operates as Li-ion gel-electrolyte and electrode separator and peeled off to make multiple battery devices out of a single chip. Porous, electrically interconnected copper nanoshells are conformally deposited around the silicon nanowires to stabilize the electrodes over extended cycles and provide efficient current collection. Using this process we demonstrate an operational full cell 3.4 V lithium-polymer silicon nanowire battery which is mechanically flexible and scalable to large dimensions [1]. The influence of the metal shell morphology and thickness on swelling and fracture modes of the crystalline silicon nanowire core are also investigated. Above a critical metal shell thickness, anisotropic swelling and fracturing during lithiation of crystalline silicon are suppressed. In order to get better insight into the observed deformation patterns, we implemented a continuum model that couples lithium transport and large, inelastic deformations. Simulated morphological changes of the silicon nanowires are in good agreement with experimental observations [2]. Optimized core-shell structures show enhanced rate performance and capacity retention (less than 5% capacity loss after 150 cycles). [1] A. Vlad et al., Proc. Natl. Acad. Sci. USA 109, 15168 (2012). [2] A. Vlad et al., in preparation.

When guest atoms diffuse into a host solid and react, the host may flow inelastically. Often a reaction can stimulate flow in a host too brittle to flow under a mechanical load alone. We formulate a theory of reactive flow in solids by regarding both flow and reaction as nonequilibrium processes, and placing the driving forces for flow and reaction on equal footing. We construct chemomechanical rate-dependent kinetic models without yield strength. In a host under constant stress and chemical potential, flow will persist indefinitely, but reaction will arrest. We also construct chemomechanical yield surface and flow rule by extending the von Mises theory of plasticity. We show that the host under a constant deviatoric stress will flow gradually in response to ramp chemical potential, and will ratchet in response to cyclic chemical potential.

Of all materials, silicon has the highest capacity to store lithium, and is being developed as an electrode for lithium-ion batteries. Upon absorbing a large amount of lithium, the electrode swells greatly, with a volumetric change up to 300%. The swelling is inevitably constrained in practice, often leading to stress and fracture. Evidence has accumulated that the swelling-induced stress can be partially relieved by plastic flow, and that electrodes of small feature sizes can survive many cycles of lithiation and delithiation without fracture. Here we simulate a particle of an electrode subject to cyclic lithiation and delithiation. A recently developed theory of concurrent large swelling and finite-strain plasticity is used to co-evolve fields of stress, deformation, concentration of lithium, and chemical potential of lithium. We identify three types of behavior. When the yield strength is high and the charging rate is low, the entire particle deforms elastically in all cycles. When the yield strength is low and the charging rate is high, the particle (or part of it) undergoes cyclic plasticity. Under intermediate conditions, the particle exhibits the shakedown behavior: part of the particle flows plastically in a certain number of initial cycles, and then the entire particle remains elastic in subsequent cycles. We discuss the effect of the three types of behavior on the capacity and the electrochemical efficiency.

This paper deals with J2 elasto-visco-plasticity and analyzes in details a variational formulation of associated constitutive updates. The variational formulation is briefly presented and compared with the traditional radial return algorithm. Differences are highlighted in the case of combined hardening and rate-dependency models. In that case, the variational formulation introduces an algorithmic parameter, which effect is analyzed on precision and convergence behavior. A practical rule is proposed for choosing an optimal value for this parameter

Predicting the mechanical response of composite materials requires careful modeling strategies. Among them, multiscale methods are particularly attractive, because they have the potential to link microscale processes to the macroscopically observed behavior. This thesis focuses on mean-field (MF) approaches in which the effective response of the composite is computed based on statistical moments (mean and variance) of the mechanical fields throughout each constitutive phase. The general objective of the research is to provide a reliable constitutive model for elasto-(visco)plastic composites. The micro-macro scheme must be suited for general loading histories and constructed on sound theoretical foundations. A fundamental assumption sustaining our approach is that reliable estimates for linear elastic composites are available. Therefore, our task is to transform the homogenization problem of the nonlinear composite into that of a Linear Comparison Composite (LCC), which can in turn be tackled using linear schemes. Two radically different types of models are developed. We first consider incremental approaches in which the phase constitutive relations are linearized over each time step. Original strategies are proposed in order to account for intra-phase field heterogeneities. Then, we develop a variational formulation of the homogenization problem according to which the macroscopic stress-strain relation derives from an effective incremental potential. An original linearization procedure allows expressing the effective potential in terms of the potential of a LCC. The procedure crucially exploits the algorithmic structure of elasto-(visco)plasticity equations. Predictions of the different models are verified against finite element results obtained on representative volume elements of the microstructure for several two-phase systems., (FSA 3) -- UCL, 2011

This work addresses the micro–macro modeling of composites having elasto-plastic constituents. A new model is proposed to compute the effective stress–strain relation along arbitrary loading paths. The proposed model is based on an incremental variational principle (Ortiz, M., Stainier, L., 1999. The variational formulation of viscoplastic constitutive updates. Comput. Methods Appl. Mech. Eng. 171, 419–444) according to which the local stress–strain relation derives from a single incremental potential at each time step. The effective incremental potential of the composite is then estimated based on a linear comparison composite (LCC) with an effective behavior computed using available schemes in linear elasticity. Algorithmic elegance of the time-integration of J2 elasto-plasticity is exploited in order to define the LCC. In particular, the elastic predictor strain is used explicitly. The method yields a homogenized yield criterion and radial return equation for each phase, as well as a homogenized plastic flow rule. The predictive capabilities of the proposed method are assessed against reference full-field finite element results for several particle-reinforced composites.

This paper deals with the micromechanical modeling of particle reinforced elasto-plastic composites under general non-monotonic loading histories. Incremental mean-field (MF) homogenization models offer an excellent cost-effective solution, however there are cases where their predictions are inaccurate. Here, we assess the applicability of the equivalent inclusion representation, which sustains many homogenization schemes. To this end, MF models are fully coupled with a finite element (FE) solution of the equivalent inclusion problem (EIP). Consequently, Eshelby's tensor is not used and most (but not all) approximations involved in the generalization of MF models from linear elasticity to the nonlinear regime are avoided. The proposal is implemented for Mori-Tanaka (M-T) and dilute inclusion models and applied to several composite systems with elasto-plastic matrix and spherical or ellipsoidal particles, subjected to various loadings (tension, plane strain, cyclic tension/compression). The predictions are verified against reference full-field FE simulations of multiparticle cells. Results show that the M-T model coupled with the nonlinear FE solution of the EIP is very accurate at the macro level up to 25% volume fraction of reinforcement, while the phase averages remain accurate as long as the volume fraction does not exceed 15%. The strain concentration tensor computed almost exactly from single inclusion FE analysis is compared against approximate expressions assumed by classical MF models. Implications for the development of advanced MF homogenization models are discussed. (C) 2009 Elsevier Ltd. All rights reserved.

In the present study, the strength and failure of elastomeric composites are predicted by extending the Mori and Tanaka [T. Mori, K. Tanaka, Acta Metallurgica 21 (1973) 571-574] model from the case of perfectly adherent, linear elastic constituents to the case of nonlinear (hyperelastic) constituents Subjected to particle debonding. A finite strain formalism is adopted, and an exponential cohesive zone model is used at the particle-matrix interface. instead of relying on Eshelby's solution, the isolated inclusion problem is solved numerically using a finite element discretization. The proposed homogenization scheme is applied to a solid propellant in which the particles are much stiffer than the matrix. The analysis is performed in plane strain under axisymmetric tensile loading conditions, and the predictions are compared to reference full-field Solutions obtained by finite element simulations on unit cells with periodic boundary conditions. It is demonstrated that the new method yields acceptable predictions until the onset of damage, while dramatically reducing the computational time. (C) 2008 Elsevier B.V. All rights reserved.

This work presents a new mean-field approach for the modeling of two-phase elasto-plastic composites. Themultisitemodelwas initially designed for texture prediction in polycrystalline aggregates [L. Delannay et al., Comput. Mater. Sci. (2008), doi:10.1016/j.commatsci.2008.06.013]. Here, it is used to simulate short range interactions between the matrix and the inclusions. Stacks of two subregions lying on either sides of a planar interface are treated as pseudograins. A self-consistent scheme governs the strain partitioning among the pseudo-grains and the remaining matrix. Predictions of the model are compared to finite element results.