Javier Segurado

A numerical approximation to the elastic properties of sphere-reinforced composites

Abstract Three-dimensional cubic unit cells containing 30 non-overlapping identical spheres randomly distributed were generated using a new, modified random sequential adsortion algorithm suitable for particle volume fractions of up to 50%. The elastic constants of the ensemble of spheres embedded in a continuous and isotropic elastic matrix were computed through the finite element analysis of the three-dimensional periodic unit cells, whose size was chosen as a compromise between the minimum size required to obtain accurate results in the statistical sense and the maximum one imposed by the computational cost. Three types of materials were studied: rigid spheres and spherical voids in an elastic matrix and a typical composite made up of glass spheres in an epoxy resin. The moduli obtained for different unit cells showed very little scatter, and the average values obtained from the analysis of four unit cells could be considered very close to the “exact” solution to the problem, in agreement with the results of Drugan and Willis (J. Mech. Phys. Solids 44 (1996) 497) referring to the size of the representative volume element for elastic composites. They were used to assess the accuracy of three classical analytical models: the Mori–Tanaka mean-field analysis, the generalized self-consistent method, and Torquatos third-order approximation.

A numerical investigation of the effect of particle clustering on the mechanical properties of composites

The effect of the reinforcement spatial distribution on the mechanical behavior was investigated in model metalmatrix composites. Homogeneous microstructures were made up of a random dispersion of spheres. The inhomogeneous ones were idealized as an isotropic random dispersion of spherical regions—which represent the clusters—with the spherical reinforcements concentrated around the cluster center. The uniaxial tensile stress-strain curve was obtained by finite element analysis of three-dimensional multiparticle cubic unit cells, which stood as representative volume elements of each material, with periodic boundary conditions. The numerical simulations showed that the influence of reinforcement clustering on the macroscopic composite behavior was weak, but the average maximum principal stress in the spheres—and its standard deviation—were appreciably higher in the inhomogeneous materials than in the homogeneous ones (up to 12 and 60%, respectively). The fraction of broken spheres as a function of the applied strain were computed from experimental values of the Weibull parameters for the strength of the spheres, and the local stress computed in the simulations. It was found that the presence of clustering greatly increased (by a factor between 3 and

Multiscale modeling of composite materials: a roadmap towards virtual testing.

A bottom-up, multiscale modeling approach is presented to carry out high-fidelity virtual mechanical tests of composite materials and structures. The strategy begins with the in situ measurement of the matrix and interface mechanical properties at the nanometer-micrometer range to build up a ladder of the numerical simulations, which take into account the relevant deformation and failure mechanisms at different length scales relevant to individual plies, laminates and components. The main features of each simulation step and the information transferred between length scales are described in detail as well as the current limitations and the areas for further development. Finally, the roadmap for the extension of the current strategy to include functional properties and processing into the simulation scheme is delineated.

On the accuracy of mean-field approaches to simulate the plastic deformation of composites

The accuracy of classical and modified secant mean-field methods to simulate the elasto-plastic response of spherereinforced composites was assessed by means of the finite element analysis of various three-dimensional multiparticle periodic unit cells. 2002 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.

Finite deformation of porous elastomers: a computational micromechanics approach

The finite deformation of porous elastomers was studied by means of the numerical simulation of a representative volume element of the microstructure. The size and the discretization of the volume element were selected to obtain an exact response (to a few percent) of the plane-strain deformation of a material made up of a random and isotropic dispersion of circular cylindrical voids embedded in an incompressible neo-Hookean matrix. Three different loading modes (in-plane isotropic deformation, uniaxial elongation, and uniaxial traction) were simulated, and the corresponding stress—strain curves as well as the evolution of the microstructure with deformation were presented for materials with an initial porosity of 5, 10 and 20%. The numerical results were compared with the available homogenization models for the finite deformation of porous elastomers. It was found that the second-order estimate with field fluctuations of López-Pamiés and Ponte Castañeda led to very good approximations to the numerical results in most cases, and significant differences were only found under conditions of highly constrained deformation. The sources of these differences were discussed in the light of the changes in the microstructure provided by the numerical simulations.

Latent hardening size effect in small-scale plasticity

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

Molecular dynamics modeling and simulation of void growth in two dimensions

The mechanisms of growth of a circular void by plastic deformation were studied by means of molecular dynamics in two dimensions (2D). While previous molecular dynamics (MD) simulations in three dimensions (3D) have been limited to small voids (up to ≈10 nm in radius), this strategy allows us to study the behavior of voids of up to 100 nm in radius. MD simulations showed that plastic deformation was triggered by the nucleation of dislocations at the atomic steps of the void surface in the whole range of void sizes studied. The yield stress, defined as stress necessary to nucleate stable dislocations, decreased with temperature, but the void growth rate was not very sensitive to this parameter. Simulations under uniaxial tension, uniaxial deformation and biaxial deformation showed that the void growth rate increased very rapidly with multiaxiality but it did not depend on the initial void radius. These results were compared with previous 3D MD and 2D dislocation dynamics simulations to establish a map of mechanisms and size effects for plastic void growth in crystalline solids.

Computational issues in the simulation of two-dimensional discrete dislocation mechanics

The effect of the integration time step and the introduction of a cut-off velocity for the dislocation motion was analysed in discrete dislocation dynamics (DD) simulations of a single crystal microbeam. Two loading modes, bending and uniaxial tension, were examined. It was found that a longer integration time step led to a progressive increment of the oscillations in the numerical solution, which would eventually diverge. This problem could be corrected in the simulations carried out in bending by introducing a cut-off velocity for the dislocation motion. This strategy (long integration times and a cut-off velocity for the dislocation motion) did not recover, however, the solution computed with very short time steps in uniaxial tension: the dislocation density was overestimated and the dislocation patterns modified. The different response to the same numerical algorithm was explained in terms of the nature of the dislocations generated in each case: geometrically necessary in bending and statistically stored in tension. The evolution of the dislocation density in the former was controlled by the plastic curvature of the beam and was independent of the details of the simulations. On the contrary, the steady-state dislocation density in tension was determined by the balance between nucleation of dislocations and those which are annihilated or which exit the beam. Changes in the DD imposed by the cut-off velocity altered this equilibrium and the solution. These results point to the need for detailed analyses of the accuracy and stability of the dislocation dynamic simulations to ensure that the results obtained are not fundamentally affected by the numerical strategies used to solve this complex problem.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Microstructure-based fatigue life model of metallic alloys with bilinear Coffin-Manson behavior

Abstract A microstructure-based model is presented to predict the fatigue life of polycrystalline metallic alloys which present a bilinear Coffin-Manson relationship. The model is based in the determination of the maximum value of a fatigue indicator parameter obtained from the plastic energy dissipated by cycle in the microstructure. The fatigue indicator parameter was obtained by means of the computational homogenization of a representative volume element of the microstructure using a crystal-plasticity finite element model. The microstructure-based model was applied to predict the low cyclic fatigue behavior of IN718 alloy at 400 °C which exhibits a bilinear Coffin-Manson relationship under the assumption that this behavior is triggered by a transition from highly localized plasticity at low cyclic strain ranges to more homogeneous deformation at high cyclic strain ranges. The model predictions were in very good agreement with the experimental results for a wide range of cyclic strain ranges and two strain ratios ( R e = 0 and −1) and corroborated the initial hypothesis. Moreover, they provided a micromechanical explanation for the influence of the strain ratio on the fatigue life at low cyclic strain ranges.