Representative volume elements for the simulation of isotropic composites highly lled with monosized spheres

A method is proposed for generating reliable representative volume elements (RVEs) that allows reducing the statistical analysis required for the simulation of the mechanical behavior of isotropic composites highly filled with monosized spheres. The method combines (i) an algorithm inspired from molecular dynamics and associated with an analytical equation of state, and (ii) a geometrical analysis using the two-point correlation function and a nearest-neighbor distribution function. A restrictive selection process is defined, which leads to microstructures reasonably close to randomness and isotropy. The pertinence of the proposed generation and selection of RVEs is confirmed by the simulation of their elastic behavior with the nite element method. In particular, it is shown how the selection procedure allows reducing the computational e ort required to reach reliable elastic moduli by operating on a limited number of suitable RVEs. The results are in good agreement with the generalized self-consistent model and with original experimental data obtained on a composite where an acrylate matrix was reinforced by sifted glass beads.ANR contrat ANR-10-EQPX-37, Délégation Générale de l'Armement (DGA) et ArianeGroup

Comparison of the finite strain macroscopic behavior and local damage of a soft matrix highly reinforced by spherical or polyhedral particles

Motivated by the different uniaxial responses of two actual materials filled with either sifted glass beads or sifted glass grits, the influence of the fillers shape on the finite strain behavior of highly filled composites (>50%) is examined through micromechanical finite element simulations accounting for matrix/filler debonding with a cohesive-zone model. Three-dimensional matrix cells filled with 64 monosized spherical particles are compared to cells filled with the same number of monosized polyhedra. For this purpose, an original generation process was developed to obtain periodic cells with random dispersions of non-regular polyhedra. Finite element simulations of uniaxial tensile tests on the periodic cells allow studying the influence of the fillers shape on the macroscopic behavior and on the local damage at the matrix/filler interfaces. Actually, the presence of sharp edges and apexes for polyhedral particles seems to have a second order impact compared to the cohesive-zone parameters. The damage fields demonstrate the same trends for both particles shapes. The different behaviors observed on actual composites are rather due to different adhesion properties between fillers and matrix than to the shape of particles

Relationship between local damage and macroscopic response of soft materials highly reinforced by monodispersed particles

A rubberlike matrix highly filled with spherical micrometric glass beads is submitted to uniaxial tension tests until break. X-ray tomography imaging performed on the material while submitted to uniaxial tension reveals early debonding at the matrix/filler interfaces at the poles of the particles followed by void coalescence creating damage localization. The latter causes a downturn of the macroscopic stress-strain response. These phenomena are analyzed further with three-dimensional finite element simulations, where 64 spherical beads are distributed randomly in a periodic cell. A simple version of the Tvergaard-Hutchinson cohesive-zone model allows to reproduce all the experimental trends well. The effects of the three parameters involved are analyzed, and three different types of macroscopic behaviors are observed corresponding to three different microstructure damages. The value of the initial stiffness of the interface, limited by numerical convergence, has little effect on how the local damage evolves but has a significant impact on the overall macroscopic stress values. The local damage is strongly dependent on the critical strength and the separation failure displacement, and the adhesion energy may be considered as a resulting parameter of the two previous ones. The interfacial critical strength appears to have a significant impact on the damage initiation, either spread across the structure for low values, or localized for high values. Increasing the interface separation failure displacement delays the possible loss of adhesion to a higher strain and preserves the integrity of the composite material

Use of a micromechanical approach to understand the mechanical behavior of solid propellants

The development of new generations of propellants with better energetic properties may be hampered by unsatisfactory mechanical behaviors in terms of strength and toughness. A micromechanical approach is adopted to provide a better understanding of the existing links between the constitutive phase behaviors and the local damage, and the macroscopic mechanical behavior of these materials. Three model materials have been made and tested in uniaxial tension. The stress-strain responses were recorded while monitoring their volume changes that quantify the macroscopic damage. A qualitative description of the local damage was obtained thanks to scanning electron microscopy images of samples under loading. The micromechanical approach consists in finite elements analyses on periodic microstructures of non-regular polyhedral particles embedded in a soft matrix. An original microstructure generation tool has been developed specifically in order to obtain highly filled isotropic microstructures. Debonding at the matrix/filler interface was taken into account with a cohesive-zone model (CZM). The impact of the CZM parameters is discussed, in an effort to make the link between the CZM parameters and how the local damage appears and develops, and between the cohesive behavior and the shape of the macroscopic stress-stretch responses of the heterogeneous materials.This work was supported by the ANR (France) under contract num-ber ANR-10-EQPX- 37, and the authors thank the Délégation Générale de l’Armement (DGA) and ArianeGroup, Vert-le-Petit (France), for their financial supports

Micromechanical study of the link between local damage and macroscopic behavior of solid propellants.

L'objectif de ce projet de recherche est le développement de simulations numériques de l'endommagement de propergols solides, qui sont dédiés à la propulsion anaérobique, afin d'identifier quelles propriétés affectent leur comportement. Pour étudier l'effet de la géométrie des différentes particules énergétiques, des microstructures 3D sont générées avec une dispersion aléatoire d'inclusions monomodales, sphériques ou polyédriques, à très forte fraction volumique (55%). Dans le cas des sphères, les propriétés élastiques des volumes élémentaires représentatifs (VER) sont confrontées à un modèle analytique et à des caractérisations expérimentales de composites modèles, démontrant une cohérence remarquable entre les trois approches. Par la suite, la réponse linéaire des VER contenant des polyèdres est comparée à celle des particules sphériques, démontrant un effet très limité de la géométrie des charges. L'endommagement de ces matériaux étant majoritairement dû aux décohésions matrice/particules, une loi de zone cohésive bilinéaire est implémentée avec une régularisation visqueuse et un affichage de l'état d'endommagement des interfaces. L'influence du premier ordre des paramètres de zone cohésive, tant sur le comportement global que l'endommagement local, peut alors être démontrée. Si les difficultés de convergence numérique ne permettent pas d'envisager une confrontation quantitative avec les données expérimentales, les tendances spécifiques de ces dernières sont remarquablement reproduites, que ce soit à l'échelle des particules ou du matériau. Une étude paramétrique permet de mettre en évidence l'influence des paramètres de zone cohésive sur la réponse globale. L'analyse de l'impact de la géométrie des particules sur le comportement endommagé conduit au même effet du second ordre observé précédemment. Enfin, une étude des propriétés de quasi-propergols, représentatifs des propergols les plus communs, est proposée. En suivant un processus industriel de caractérisation, leurs propriétés d’interface sont identifiées qualitativement, en s'appuyant sur les tendances suggérées par les simulations. Afin de compléter cette analyse, des caractérisations non conventionnelles sont proposées, permettant de valider sa cohérence et de fournir de nouveaux éléments d'identification des propriétés d'adhésions.The goal of this present project is the development of numerical tools for simulating damage of solid propellants, which are used for anaerobic propulsion. It should allow identifying which properties disturb their behavior. To study the effect of energetic particles shapes, 3D microstructures are generated with a random dispersion of monosized spheres or polyhedra at high volume fraction (55%). In case of spheres, the elastic properties of the representative volume elements (RVE) are confronted with an analytical model and experimental characterizations of model composites, with a remarkable coherence of the three approaches. Then, the linear behavior of REV filled with polyhedra is compared to the one in case of spheres, highlighting only a limited effect of particles shapes. Damage of those materials being mostly due to matrix/filler debounding, a bilinear cohesive zone model with a viscous regularization and posting of interfaces damage state is implemented. The first order influence of the cohesive zone parameters either on the mechanical response or on the local damage is demonstrated. If convergence troubles prevent any quantitative confrontation with experimental data, their specific trends are well reproduced at either the particles or the global scales. A parameter study highlights also the impact of each cohesive zone parameter on the global behavior. Study of the damaged behavior, depending on particles shape, leads again to a second order impact. Finally, analyses of quasi-propellants, representative of common propellants, are proposed. Following the industrial characterization process, the interfaces properties are identified qualitatively based on the trends of the simulations. This analysis is completed by non-conventional characterization techniques to validate its coherence and to offer exhaustive information on the adhesives properties

Etude micromécanique du lien entre endommagement local et comportement macroscopique de propergols solides

The goal of this present project is the development of numerical tools for simulating damage of solid propellants, which are used for anaerobic propulsion. It should allow identifying which properties disturb their behavior. To study the effect of energetic particles shapes, 3D microstructures are generated with a random dispersion of monosized spheres or polyhedra at high volume fraction (55%). In case of spheres, the elastic properties of the representative volume elements (RVE) are confronted with an analytical model and experimental characterizations of model composites, with a remarkable coherence of the three approaches. Then, the linear behavior of REV filled with polyhedra is compared to the one in case of spheres, highlighting only a limited effect of particles shapes. Damage of those materials being mostly due to matrix/filler debounding, a bilinear cohesive zone model with a viscous regularization and posting of interfaces damage state is implemented. The first order influence of the cohesive zone parameters either on the mechanical response or on the local damage is demonstrated. If convergence troubles prevent any quantitative confrontation with experimental data, their specific trends are well reproduced at either the particles or the global scales. A parameter study highlights also the impact of each cohesive zone parameter on the global behavior. Study of the damaged behavior, depending on particles shape, leads again to a second order impact. Finally, analyses of quasi-propellants, representative of common propellants, are proposed. Following the industrial characterization process, the interfaces properties are identified qualitatively based on the trends of the simulations. This analysis is completed by non-conventional characterization techniques to validate its coherence and to offer exhaustive information on the adhesives properties.L'objectif de ce projet de recherche est le développement de simulations numériques de l'endommagement de propergols solides, qui sont dédiés à la propulsion anaérobique, afin d'identifier quelles propriétés affectent leur comportement. Pour étudier l'effet de la géométrie des différentes particules énergétiques, des microstructures 3D sont générées avec une dispersion aléatoire d'inclusions monomodales, sphériques ou polyédriques, à très forte fraction volumique (55%). Dans le cas des sphères, les propriétés élastiques des volumes élémentaires représentatifs (VER) sont confrontées à un modèle analytique et à des caractérisations expérimentales de composites modèles, démontrant une cohérence remarquable entre les trois approches. Par la suite, la réponse linéaire des VER contenant des polyèdres est comparée à celle des particules sphériques, démontrant un effet très limité de la géométrie des charges. L'endommagement de ces matériaux étant majoritairement dû aux décohésions matrice/particules, une loi de zone cohésive bilinéaire est implémentée avec une régularisation visqueuse et un affichage de l'état d'endommagement des interfaces. L'influence du premier ordre des paramètres de zone cohésive, tant sur le comportement global que l'endommagement local, peut alors être démontrée. Si les difficultés de convergence numérique ne permettent pas d'envisager une confrontation quantitative avec les données expérimentales, les tendances spécifiques de ces dernières sont remarquablement reproduites, que ce soit à l'échelle des particules ou du matériau. Une étude paramétrique permet de mettre en évidence l'influence des paramètres de zone cohésive sur la réponse globale. L'analyse de l'impact de la géométrie des particules sur le comportement endommagé conduit au même effet du second ordre observé précédemment. Enfin, une étude des propriétés de quasi-propergols, représentatifs des propergols les plus communs, est proposée. En suivant un processus industriel de caractérisation, leurs propriétés d’interface sont identifiées qualitativement, en s'appuyant sur les tendances suggérées par les simulations. Afin de compléter cette analyse, des caractérisations non conventionnelles sont proposées, permettant de valider sa cohérence et de fournir de nouveaux éléments d'identification des propriétés d'adhésions