is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe modeling of heterogeneous materials with an elasto-viscoplastic behavior is generally complex because of the differential nature of the local constitutive law. Indeed, the resolution of the heterogeneous problem involves space-time couplings which are generally difficult to estimate. In the present paper, a new homogenization model based on an affine linearization of the viscoplastic flow rule is proposed. First, the heterogeneous problem is written in the form of an integral equation. The purely thermoelastic and purely viscoplastic heterogeneous problems are solved independently using the self-consistent approximation. Using translated field techniques, the solutions of the above problems are combined to obtain the final self-consistent formulation. Then, some applications concerning two-phase fibre-reinforced composites and polycrystalline materials are presented. When compared to the reference solutions obtained from a FFT spectral method, a good description of the overall response of heterogeneous materials is obtained with the proposed model even when the viscoplastic flow rule is highly non-linear. Thanks to this approach, which is entirely formulated in the real-time space, the present model can be used for studying the response of heterogeneous materials submitted to complex thermo-mechanical loading paths with a good numerical efficiency.

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A micromechanical model is proposed to describe the interactions between the microstructure and the dissipative deformation mechanisms in ferritic steels under cyclic loading. The model aims at optimizing the microstructure of steels since the dissipative mechanisms can be responsible for the initiation of microcracks. Therefore, a better understanding of the influence of the microstructure could lead to an improvement of fatigue properties. The dissipative mechanisms are assumed to be either anelastic (dislocation oscillations) or inelastic (plastic slip) and are described at the scale of the slip system using the framework of crystal plasticity. The macroscopic behavior is then deduced with a homogenization scheme. The model is validated by comparing the simulations with experimental results and is finally used to predict the impact of different microstructure parameters on the heat dissipation.

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractTo obtain robust estimations of the fatigue limit from energy-based fatigue criteria, constitutive laws must include a correct description of the energy balance when modeling the cyclic behavior. The present paper aims at providing a better understanding of the evolution of the energy balance at both microscopic and macroscopic scales in a medium carbon steel. First, an experimental procedure is used to estimate the amount of energy which is either stored in the material or dissipated into heat at a macroscopic scale. The energy balance is observed to be very dependent on the stress amplitude and the number of loading cycles. A model is then developed to investigate the energy balance at a microscopic scale. From the simulation results, both the stored energy and dissipated energy fields are found to be strongly scattered. The dispersion is mostly explained by the crystallographic orientation distribution and the two-phased microstructure.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe macroscopic behavior of polycrystalline materials is largely influenced by the shape, the arrangement and the orientation of crystallites. Different methods have thus been developed to determine the effective behavior of such materials as a function of their microstructural features. In this work, which focuses on polycrystalline materials with an elastic-viscoplastic behavior, the selfconsistent, finite element and spectral methods are compared. These common methods are used to determine the effective behavior of different 316L polycrystalline aggregates subjected to various loading conditions. Though no major difference is observed at the macroscopic scale, the hardening rate is found to be slightly overestimated with the finite element method. Indeed, spatial convergence cannot be guaranteed for finite element calculations, even when fine mesh resolutions, for which the computational cost is important, are used. Also, as the self-consistent method does not explicitly account for neighborhood effects, important discrepancies between the self-consistent method and the other methods exist regarding the mechanical response of a specific grain. The selfconsistent method nevertheless provides a reasonable description of the average response obtained for a group of grains with identical features (e.g. shape, orientation).

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In this work, a crystal plasticity constitutive model is proposed to describe the mechanical behavior of metallic materials for which twinning plays a significant role in the deformation process. Constitutive relations are obtained from a micromechanical approach that explicitly considers the interactions between twinned and untwinned domains. Then, based on a thermodynamical analysis of the problem, a new expression for the driving force for the expansion of twinned domains is proposed. Finally, to account for the polycrystalline nature of metallic materials, the constitutive model is implemented in a FFT spectral solver. In the second part of this paper, the model is used to study the mechanical behavior of a AZ31 magnesium alloy under compression, for which a significant amount of experimental data is available in the literature. The comparison between numerical and experimental data allows for discussion of the influence of the different deformation modes on the development of both crystallographic texture and lattice strains. The evolution of lattice strains is found to be largely influenced by the internal stress redistribution process associated with the expansion of twinned domains. Also, the polycrystalline plasticity model provides a correct description of how the morphological texture is strongly altered during the deformation process due to the important activity of twinning systems.