Deformation mechanisms of idealised cermets under multi-axial loading

The response of idealised cermets comprising approximately 60% by volume steel spheres in a Sn/Pb solder matrix is investigated under a range of axisymmetric compressive stress states. Digital volume correlation (DVC) analysis of X-ray micro-computed tomography scans (μ-CT), and the measured macroscopic stress-strain curves of the specimens revealed two deformation mechanisms. At low triaxialities the deformation is granular in nature, with dilation occurring within shear bands. Under higher imposed hydrostatic pressures, the deformation mechanism transitions to a more homogeneous incompressible mode. However, DVC analyses revealed that under all triaxialities there are regions with local dilatory and compaction responses, with the magnitude of dilation and the number of zones wherein dilation occurs decreasing with increasing triaxiality. Two numerical models are presented in order to clarify these mechanisms: (i) a periodic unit cell model comprising nearly rigid spherical particles in a porous metal matrix and (ii) a discrete element model comprising a large random aggregate of spheres connected by non-linear normal and tangential “springs”. The periodic unit cell model captured the measured stress-strain response with reasonable accuracy but under-predicted the observed dilation at the lower triaxialities, because the kinematic constraints imposed by the skeleton of rigid particles were not accurately accounted for in this model. By contrast, the discrete element model captured the kinematics and predicted both the overall levels of dilation and the simultaneous presence of both local compaction and dilatory regions with the specimens. However, the levels of dilation in this model are dependent on the assumed contact law between the spheres. Moreover, since the matrix is not explicitly included in the analysis, this model cannot be used to predict the stress-strain responses. These analyses have revealed that the complete constitutive response of cermets depends both on the kinematic constraints imposed by the particle aggregate skeleton, and the constraints imposed by the metal matrix filling the interstitial spaces in that skeleton.The authors are grateful to the Office of Naval Research (ONR) for their financial support through grant number N00014121063

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An evolving switching surface model for ferromagnetic hysteresis

We propose a thermodynamically consistent rate-independent three-dimensional model of magnetic hysteresis in terms of energetic and dissipation potentials making use of a relatively small number of model parameters that is capable of being implemented in a general incremental numerical setting. The dissipation process occurring during magnetization/demagnetization is described by a power-law potential, which leads to rate-independence at a certain limit of the rate-dependent exponent. The incorporation of isotropic hardening in the model enables us to describe phenomenologically at the macroscopic scale both nucleation and pinning type constitutive responses. We further model the symmetric and asymmetric minor loops by employing the idea of a bounding surface, which was originally introduced in the context of mechanical plasticity. Our model shows a very good agreement with experiments for spark plasma sintered NdFeB magnets, where nucleation is found to be the primary mechanism of coercivity. We also use our model to probe experiments for melt-spun NdFeB ribbons and powders, where both nucleation and pinning mechanisms are experimentally found to be significant. Moreover, we correlate the proposed model parameters with the underlying mechanisms for coercivity. We investigate the predictive capability of the proposed model by first probing an experimental minor loop and then use it to successfully predict the remaining minor loops, obtained from that experiment. We also construct a first-order reversal curve diagram for the floppy disk material and compare it with the corresponding experimental data

Programmable higher-order Euler buckling modes in hierarchical beams

International audienceWe present a numerical-aided experimental study on the buckling of hierarchical beams comprising multiple self-similar modules. Each module consists of multiple elemental beams and is arranged in series to form the hierarchical beam. We show, through a combination of experiments and computations, that these beams exhibit stable and realizable higher-order buckling modes. By contrast to the canonical Euler buckling problem, such modes emerge naturally in the proposed self-similar beams since they correspond to almost identical critical loads. By harnessing the imperfection sensitivity of the hierarchical structures, we 3D-print weakly imperfect polymer samples with a small geometric imperfection corresponding to the desired eigenmode. We subsequently carry out uniaxial compression experiments and show in practice that higher-order patterns can be triggered selectively upon buckling. Moreover, these patterns are preserved in the post-bifurcation regime in many cases and are reversible upon load release. The ability to trigger higher-order buckling modes is found to depend on two main geometrical parameters which lead to scale coupling. Those are the slenderness of the macroscopic hierarchical beam and the slenderness of the lower-scale elemental beam. With increasing slenderness of the hierarchical beam, we observe a significant softening in the overall stress-strain response and patterns exhibiting curvature lo-calization in the post-bifurcation regime. The numerical finite-strain simulations carried out in the present study are found to be in very good agreement with the experiments and are used to quantify further the observed curvature localization in the hierarchical beams. The present study and the obtained results are geometric in nature and thus can be extended to different scales and hierarchies ad infinitum

An Evolving Switching Surface Model for Ferromagnetic Hysteresis

International audienceWe propose a thermodynamically consistent rate-independent three-dimensional model of magnetic hysteresis in terms of energetic and dissipation potentials making use of a relatively small number of model parameters that is capable of being implemented in a general incremental numerical setting. The dissipation process occurring during magnetization/demagnetization is described by a power-law potential, which leads to rate-independence at a certain limit of the rate-dependent exponent. The incorporation of isotropic hardening in the model enables us to describe phenomenologically at the macroscopic scale both nucleation and pinning type constitutive responses. We further model the symmetric and asymmetric minor loops by employing the idea of a bounding surface, which was originally introduced in the context of mechanical plasticity. Our model shows a very good agreement with experiments for spark plasma sintered NdFeB magnets, where nucleation is found to be the primary mechanism of coercivity. We also use our model to probe experiments for melt-spun NdFeB ribbons and powders, where both nucleation and pinning mechanisms are experimentally found to be significant. Moreover, we correlate the proposed model parameters with the underlying mechanisms for coercivity. Finally, we probe the predictive capability of the proposed model by first fitting an experimental minor loop, and then use it to successfully predict the remaining minor loops, obtained from that experiment. We also construct a FORC diagram for the floppy disc material and compare it with the corresponding experimental data

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd

Numerical modeling of elasto-plastic porous materials with void shape effects at finite deformations

A new constitutive model for elasto-plastic (rate-independent) porous materials subjected to general three-dimensional finite deformations is presented. The new model results from simple modifications of an earlier model of Kailasam and Ponte Castaneda (1997, 1998) [40,41] so that it reproduces the exact spherical and cylindrical shell solution (composite sphere and composite cylinder assemblage) under purely hydrostatic loadings, while predicting (by calibration) accurately the void shape evolution according to the recent "second-order" model of Danas and Ponte Castaneda [17]. Furthermore, the present model is based on a rigorous homogenization method which is capable of predicting both the constitutive behavior and the microstructure evolution of porous materials. The microstructure is described by voids of arbitrary ellipsoidal shapes and orientations and as a result the material exhibits deformation-induced (or morphological) anisotropy at finite deformations. This is in contrast with the well-known Gurson [32] model which assumes that the voids remain spherical during the deformation process and thus the material remains always isotropic. The present model is implemented numerically in a finite element program where a three-dimensional thin-sheet (butterfly) specimen is subjected to a combination of shear and traction loading conditions in order to examine the effect of stress triaxiality and shearing upon material failure. The ability of the present model to take into account the nontrivial evolution of the microstructure and especially void shape effects leads to the prediction of material failure even at low stress triaxialities and small porosities without the use of additional phenomenological damage criteria. At high stress triaxialities, the present model gives similar predictions as the Gurson model. (C) 2012 Elsevier Ltd. All rights reserved

An explicit dissipative model for isotropic hard magnetorheological elastomers

Hard magnetorheological elastomers (h-MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible h-MREs. Energy dissipates in such hard-magnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto–mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto–mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender h-MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized h-MREs in terms of their pre-magnetization and the associated self-fields

Random 3D-printed isotropic composites with high volume fraction of pore-like polydisperse inclusions and near-optimal elastic stiffness

International audienceHighly porous materials with random closed-cell architecture combine isotropy with high stiffness. Yet in practice, the complexity of their manufacturing limits the experimental exploration of these materials, for which studies of the elastic response remain to date mainly theoretical. In this study, we measure experimentally the elastic moduli of random closed-cell porous-like composites fabricated by 3D-printing. These materials contain a high volume fraction (up to 82 vol pct) of non-overlapping, polydisperse void-like spherical inclusions, which are randomly dispersed in a homogeneous polymer matrix. We first generate the virtual microstructures of these materials using a random sequential adsorption (RSA) algorithm, and then use numerical homogenization to compute the size of the material representative volume element (RVE). The latter is used to assemble the test samples, whereby the void-like inclusions are 3D-printed using a gel-like polymer with mechanical properties that are in high contrast with those of the base polymer thus behaving mechanically as pores. Experiments reveal that the proposed isotropic