The effect of moisture-induced swelling on the absorption capacity of transversely isotropic elastic polymer-matrix composites

The interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (nonlinear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law

Modeling and simulation of laser shock waves in elasto-plastic polycrystalline microstructures

We study the propagation of elasto-plastic shockwaves induced by high power laser impacts in 2D polycrystalline metallic alloys in order to investigate the influence of the material microstructure on the fields of plastic strain and subsequent residual stresses. Implementing a visco-plastic constitutive relation at the grain scale accounting for two dislocation slip systems into a finite volume numerical scheme, simulations on single crystal specimens with different lattice orientations show that plastic strain is concentrated in narrow bands originating at the edges of the laser impact and parallel to the slip planes. In the case of polycrystalline microstructures composed of randomly oriented grains, it is found that the microstructure morphology is the origin of a heterogeneous distribution of the residual plastic strain and stress fields, which thus departs from the residual stress fields usually modeled when the microstructure is not accounted for. To account for the random character of polycrystal microstructures, we perform a statistical analysis of the mechanical fields over a large number of microstructures to quantify the dispersion of the results. It is found that even though the residual stresses induced by a laser impact are in compression on average at the center of the laser impact, some realizations of the microstructures can lead to localized concentrations of less compressive, or even tensile, residual stresses at the surface, thus probably reducing the fatigue resistance of the shocked material

Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape

The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean- eld homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori-Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are stud- ied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites

Contraintes et saturation en eau dans un composite à matrice polymère

De l'eau (ou tout autre fluide) peut diffuser dans un polymère et y provoquer un gonflement qui interagit avec les contraintes appliquées à celui-ci. L'objectif de notre étude est d'analyser l'interaction entre ces contraintes et la quantité d'eau absorbée à l'équilibre. Nous avons déjà pu montrer que l'isotherme de sorption d'un polymère homogène est modifiée en présence de contraintes dans une relation faisant intervenir solubilité, coefficient de gonflement et pression hydrostatique appliquée. Dans la matrice polymère d'un composite, des contraintes internes résultant de son gonflement contrarié se développent et modifient la saturation en eau. On veut alors établir le lien entre la saturation d'un composite, sa microstructure et ses propriétés mécaniques. Nous montrons ici que le problème a une solution simple dans le cadre du modèle de Mori et Tanaka. Il en résulte en particulier que si l'isotherme de la matrice suit une loi de Henry, alors celui du composite suit une loi de Langmuir

Generalized Euclidean Distances for Elasticity Tensors

The aim of this short paper is to provide, for elasticity tensors, generalized Euclidean distances that preserve the property of invariance by inversion. First, the elasticity law is expressed under a non-dimensional form by means of a gauge, which leads to an expression of elasticity (stiffness or compliance) tensors without units. Based on the difference between functions of the dimensionless tensors, generalized Euclidean distances are then introduced. A subclass of functions is proposed, which permits the retrieval of the classical log-Euclidean distance and the derivation of new distances, namely the arctan-Euclidean and power-Euclidean distances. Finally, these distances are applied to the determination of the closest isotropic tensor to a given elasticity tenso

Periodic smoothing splines for FFT-based solvers

The aim of this paper is to develop a periodic smoother based on splines for FFT-based solvers. Spurious oscillations in FFT-based methods are shown to be due to pseudo-spectral differentiation of discontinuous fields. An automatic smoother based on polynomial splines is developed, which permits to add smoothness to initial material properties. The method, which is applied in various problems including conductivity, elasticity and field dislocation mechanics, improves significantly the local fields and reduces spurious oscillations

In-situ experimental and numerical studies of the damage evolution and fracture in a Fe-TiB2 composite

A joint experimental and modelling study of plastic strain and ensuing damage in a novel metal matrix composite (Fe-TiB2) is presented. Damage is observed and quantified using SEM images processing and Acoustic Emission (AE) analysis. The use of AE confirms that the surface damage observed is strongly correlated to damage in the bulk of the material. The primary mode of damage is particle fracture. Very little particle decohesion is observed, indicating an exceptionally good cohesion of the steel/particle interface. Damage is initiated soon after the composite yield point is reached and increases significantly with strain. Macroscopic failure of the tensile specimen occurs when about 25% of the particles are fractured. This corresponds to about 21% engineering strain. Using in-situ SEM tensile tests with quantitative digital image correlation (DIC), full-field strain measurements are obtained and particle fracture quantified. The results of fields measurements are compared to results of a FFT based homogenization method with boundary conditions retrieved from the experiment. A good agreement is found between the DIC-measured and FFT-predicted results. Estimated values of the particle fracture stress are obtained

Exact expressions of the uniaxial perfectly elasto-plastic stress wave and induced mechanical fields in the case of a finite impact: application to laser shock peening

This paper aims at providing exact expressions for the mechanical fields induced by Laser Shock Peening and comparing them to their numerical estimations. We use a uniaxial strain field hypothesis with an elastic perfectly plastic behavior to derive the stress wave equation. An exact solution to this equation is given using the method of characteristics for a step time profile for the pressure loading, and numerically using finite differences schemes adapted for this hyperbolic equation. An additional residual stress modeling is used, providing the residual stress distribution assuming a planar infinite plate with a finite thickness. Results are presented for three loading pressures, each one corresponding to a different structure in the exact solution. The exact and numerical results present a good match, allowing either the use of the exact solution for an initial estimation of the mechanical fields, or to test the accuracy of other numerical methods. © 2023 Elsevier Masson SAS. All rights reserve

Multiscale modeling of the effective viscoplastic behavior of Mg 2 SiO 4 wadsleyite: bridging atomic and polycrystal scales

The viscoplastic behavior of polycrystalline Mg2SiO4 wadsleyite aggregates, a major high pressure phase of the mantle transition zone of the Earth (depth range: 410–520 km), is obtained by properly bridging several scale transition models. At the very fine nanometric scale corresponding to the dislocation core structure, the behavior of thermally activated plastic slip is modeled for strain-rates relevant for laboratory experimental conditions, at high pressure and for a wide range of temperatures, based on the Peierls–Nabarro–Galerkin model. Corresponding single slip reference resolved shear stresses and associated constitutive equations are deduced from Orowan’s equation in order to describe the average viscoplastic behavior at the grain scale, for the easiest slip systems. These data have been implemented in two grain-polycrystal scale transition models, a mean-field one (the recent Fully-Optimized Second-Order Viscoplastic Self-Consistent scheme of [1]) allowing rapid evaluation of the effective viscosity of polycrystalline aggregates, and a full-field (FFT based [2, 3]) method allowing investigating stress and strain-rate localization in typical microstructures and heterogeneous activation of slip systems within grains. Calculations have been performed at pressure and temperatures relevant for in-situ conditions. Results are in very good agreement with available mechanical tests conducted at strain-rates typical for laboratory experiments.This work was supported by the European Research Council under the Seventh Framework Programme (FP 7), ERC (grant number 290424 RheoMan) and under the Horizon 2020 research and innovation programme (grant number 787198 TimeMan)