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The question of frame-indifference of the thermomechanical models has to be addressed to deal correctly with the behavior of matter undergoing finite transformations. In this work, we propose to test a spacetime formalism to investigate the benefits of the covariance principle for application to covariant modeling and numerical simulations for finite transformations. Several models especially for heat conduction are proposed following this framework and next compared to existing models. This article also investigates numerical simulations using the heat equation with two different thermal dissipative models for heat conduction, without thermomechanical couplings. The numerical comparison between the spacetime thermal models derived in this work and the corresponding Newtonian thermal models, which adds the time as a discretized variable, is also performed through an example to investigate their advantages and drawbacks.

International audience; In the present article, we propose a fully coupled thermo-elasto-plastic-damage theory, which includes both kinematic and isotropic hardening, and also accounts for hydrogen diffusion in metals. This theory is based on the thermodynamics of irreversible processes under small deformation hypothesis and suppose that hydrogen diffuses in both normal interstitial lattice sites and trapping sites. This model is implemented into Abaqus/Standard by developing a UEL user subroutine and using an “assumed strain” method. A numerical application is performed to simulate hydrogen diffusion in a metallic welded joint submitted to a long-time severe environment at constant temperature.

International audience; In the present article, metallic nanoparticles (NPs) used as nanogauges and electron backscattered diffraction (EBSD) are combined to investigate deformation mechanisms of the UR45 N duplex steel. The kinematic fields bring precious details in the evolution of the local deformation of austenitic and ferritic phases. The crystallographic information at the initial stage and in the plastic domain is obtained by the EBSD technique. Strain evolutions in each phase are analyzed. The first strain marks appear in austenite just before the elastoplastic transition. Slip and twinning activities in austenite constitute an important part of the work hardening of the material. The slips in ferrite are visible in the plastic domain and present complex geometry. The role of phase boundaries, which act as strain barrier is highlighted. The incompatibilities of deformations between the two phases modify the deformation mechanism of austenite in comparison with a pure austenitic stainless steel as 316 L. Local interactions between phases during the deformation are analyzed. The strong strain heterogeneities in the plastic domain are analyzed in the kinematic fields. Local evolutions of the deformation are also confronted to the macroscopic behavior of the material.

International audience; In this study, a Surface Mechanical Attrition Treatment (SMAT) is applied to a 17-4PH single edge notched tension (SENT) sample made by Atomic Diffusion Additive Manufacturing (ADAM). Grating of gold nanoparticles allowing multiscale characterizations is deposited on the surface of specimen by electron beam lithography. In-situ tensile test is carried out and images of the surface are recorded. The crack propagation is followed and the local parameters influencing the propagation are analyzed. The evolutions at the microstructure scale are compared with the macroscopic behavior of the specimen.

The object of this article is to introduce a covariant description for a thermo-mechanical continuum. The conservation equations are written in this context and a constitutive model is derived for a reversible transformation. It is then possible to formulate a weak form of the problem to be solved for the finite transformations of a solid. A finite-element computation is next proposed using this approach for thermo-mechanical problems. The advantages of such a formulation are highlighted throughout the article.

The present work deals with the investigation of the micromechanical behaviour of a duplex steel, which consists of two phases (austenite and ferrite) exhibiting significantly different mechanical properties. The stresses in both phases were experimentally determined in the elastic and plastic ranges of deformation using synchrotron radiation diffraction experiments. The used methodology enabled to determine the values of initial stresses and to study the evolutions of the principal phase stresses and the second order stresses during the elastic, as well as the plastic range of deformation. With the help of a self-consistent model, the critical resolved shear stresses and the work hardening parameters for slip systems, active in each phase, were also estimated. Comparison of the measured phase stresses and lattice strains evolutions with the model results showed a good agreement between prediction and experiment when the initial stress state in the sample and shape of grains approximated by ellipsoidal inclusions were taken into account. The overall outcome of the work is the determination of stress partitioning between the two phases of a polycrystalline material for all deformation stages, determined directly from diffraction experiment. The results enabled analyses of von Mises, hydrostatic stresses as well as second order stresses evolutions in both phases during tensile deformation. Finally, the experimental data were successfully compared with predictions of the self-consistent deformation model.

The main purpose of this work is to develop neutron diffraction methodology in order to determine stresses localised in polycrystalline grains during elastoplastic deformation, directly from experiment. As a result, for the first time, the von Mises stress for chosen grain orientations and Critical Resolved Shear Stresses (CRSS) for active slip systems were unambiguously measured without the help of crystallographic models, which introduce different theoretical assumptions. The stresses measured for groups of grains and the determined CRSS values are important characteristics of a material, which allow to study plastic deformation in textured material at different scales: slip system and grain, which play a key role in mechanical properties and formability of the material. The new method was successfully tested and applied to textured AZ31 alloy subjected to tensile deformation and the components of stress tensor were for the first time determined from measured lattice strains corresponding to chosen orientations of crystallite lattice. The obtained results positively verified hypotheses that, during plastic deformation, a large difference in the hardness as well as in the localised stresses occurs for grains having different lattice orientations. It was found directly from experiment that, the activation of basal glide, having small CRSS, does not lead to significant plastic deformation, and the activation of other non-basal systems (with higher CRSS) induces the development of plasticity at the macroscopic scale. The early plastic deformation occurring due to slip on basal system is small but it can destructively affect fatigue life, limiting applicability of the material for structural components. Finally, the comparison of experimental results with a modified version of Elastic-Plastic Self-Consistent (EPSC) model showed its capability to simulate the mechanical behaviour of such materials.

International audience; It is now well-known that the over-treatment during surface mechanical treatments such as shot peening can generate damage in the near surface region. In the present article, the damage evolution during impact loading is numerically investigated. For this purpose, a dislocation density based viscoplastic constitutive model coupled with damage is proposed. The mechanical behavior of twinning induced plasticity (TWIP) steels is described by a dislocation density based viscoplastic model, also including the kinetic of twinning. It allows investigating the strain hardening behavior of TWIP steels. To predict the damage evolution in these ductile steels, the Gurson–Tvergaard–Needleman (GTN) yield criterion is combined with the dislocation density based model. A user-defined subroutine is developed to implement this model in ABAQUS. 3D numerical simulations of single impact are then performed to investigate the impacting process, as well as the damage evolution due to high strain rate impact.

International audience; In this work, a dislocation density-based model including the kinetics of twinning and martensitic transformations is developed to study the strain hardening behavior of twinning induced plasticity (TWIP) and transformation induced plasticity (TRIP) steels. Based on the proposed model, the volume fractions of twinning and martensitic transformations, the dislocation densities in austenitic and martensitic phases are calculated to analyze the effects of twinning and martensitic transformations on the mechanical behavior of TWIP/TRIP steels. Comparison between modeling results and experimental data shows that the proposed model can well predict the evolution of the volume fractions of twinning and martensitic transformations, as well as the macroscopic mechanical behavior. The model is implemented in a subroutine of ABAQUS Explicit to perform 3D simulations of a single impact to investigate the impact process during Surface Mechanical Attrition Treatment (SMAT).

International audience; The present article investigates the effect of Surface Mechanical Attrition Treatment (SMAT) on the high temperature oxidation of AISI 316L, during isothermal oxidation between 650 and 750 °C in air. The observations show a beneficial effect of the SMAT process on the oxidation resistance of 316L steel, for high temperatures. Indeed, the oxidation kinetics of the treated samples is shown to be related to a preferential growth of chromia starting at 700 °C up to 750 °C. This leads us to conclude that the SMAT used on the 316L reverses the main oxide phase, inhibiting the growth of the hematite and promoting the chromia. © 2018 Elsevier Ltd

This work takes place in the general context of a better understanding of materials degradation mechanisms in extreme environments. In particular, the aim of the present study was to correlate microstructural elements to growth stress magnitude evolution and stress release mechanisms for thermally grown chromia thin films on NiCr alloys. Strains in thermally grown oxides have been measured in-situ, as the oxides develop and evolve. Data have been acquired from oxides grown for different high temperatures evolutions on NiCr model alloys that form Cr2O3. Using synchrotron X-Ray at the ESRF (Beamline BM02) coupled with an induction furnace, Debye-Scherrer diffraction patterns from the oxidizing specimen were recorded in air at temperature between 700-1000°C and during cooling. The distortion of the diffraction rings was analyzed to yield the in-plane strain. Thermal stresses imposed on Cr2O3/NiCr by abruptly reducing the sample temperature for a period of time, exploiting the thermal expansion difference between oxide and substrate, showed noticeable subsequent stress relaxation by creep. Such a mechanism was monitored using time-dependent in situ measurements of strain relaxation in the oxide. The main results obtained from these experiments are the kinetic of the growth stress from the isothermal measurements (isothermal plateau), and the study of the stress release mechanism after the low-temperature jumps. In complement, the oxide microstructure development during the course of oxidation is also investigated from both the peaks intensity and width evolution. In all cases, the steady stage growth strain was relatively low and compressive. Different degrees of relaxation were also found on cooling depending on scale microstructure through the variation of the initial oxidation conditions. Results are compared with other reports of residual stresses evolution in Cr2O3 scales.

International audience; In the present paper, constitutive equations accounting for coupled damage-thermo-elasto-(visco)plastic and diffusion at small deformation are proposed in the standard thermodynamics of irreversible processes framework. One main objective is to include the diffusion phenomenon in the models with ductile damage. The model is developed in the framework of thermodynamics of irreversible processes with a set of internal state variables. For illustration, we consider hydrogen diffusion in both normal interstitial lattice sites and trapping sites. The damage modelling of microvoids or microcracks is introduced by the use of Continuum Damage Mechanics framework leading to the definition of effective state variables on fictive undamaged configuration based on the total energy equivalence assumption. Consequently, the full coupling concerns not only the elastic and inelastic behaviour with hardening (isotopic and kinematic), but also the thermal and diffusion phenomena. The concept of the total energy equivalence is thus extended to define effective temperature, entropy, and effective state variables associated with diffusion. It enables to obtain different couplings between thermal phenomena, diffusion phenomena, and the mechanical behaviour, especially isotropic ductile damage. Such a full coupled model is then applied to a representative volume element subject to some typical simple loading paths for illustration and test of such couplings.

NiCr alloys develop chromia layers in oxidizing high temperature environments. The stress in oxide layer was largely explored, whereas too few works were devoted to the stress distribution in the underlying metallic substrate. To determine the stress distribution in a duplex oxide-metallic substrate system, a variant of sin2ψ method in transmission mode using high-energy synchrotron X-rays has been developed. 103.4 keV synchrotron X-rays have been used to penetrate 6 × 6 × 0.4 mm and O6 × 0.9 mm samples with different oxidation conditions. In order to obtain the stress gradient from the top surface to the bottom surface, the patterns of diffraction were collected and then were analyzed by a complete data processing. The stress varies towards the surface in a non-linear manner, especially near the interface zone. In order to better understand the stress distribution of such a duplex oxide-metallic substrate system, the stress caused by chromium diffusion is investigated by proposing numerical values for coupling coefficient, which finally can partially explain the stress variation near the interface zone.

Residual stresses in thermal oxide layer may be significant and can influence the lifetime of systems in high temperature environments. It is thus relevant to determine locally stress and strain mechanisms and especially the mechanical relation between the oxide layer and the metallic substrate. To achieve such a goal, an innovative approach is proposed by use of micro/nano-gratings. Monitoring experimentally the gauges displacement during high temperature oxidation and considering a specific model, we are able to determine thermomechanical quantities both in oxide Cr 2 O 3 and in metallic alloy Ni38Cr, as well as their evolution during the oxidation time. Parameters values for calculations of the stress versus time evolution are also provided.

International audience; Chromium-based alloys have been developed to form chromia layers in oxidizing environments for high temperature applications, providing a good protection against further oxidation. The mechanical behavior and oxide layer growth of yttria-coated or zirconium-doped Ni28Cr alloy are presently studied under high temperature oxidation conditions. These kind of reactive elements can decrease oxidation kinetics and significantly increase the adhesion of chromia layer on the metallic substrate. However, during oxidation, a compressive stress generally occurs in thermally grown oxide (TGO) due to the oxide layer and its mechanical interaction with the metallic substrate. These growth stresses, combined with the thermal stresses that develop during temperature changes, may initiate and cause layer cracking or spallation, which limits the lifetime of alloys in such a challenging environment. For prediction of this lifetime, it is important to know with accuracy the thermomechanical behavior of such a system. Therefore, a thermomechanical modelling is proposed and applied to optimize numerically the unknown parameters, especially viscoplastic ones. For the raw material and modified materials by reactive elements, the creep parameter decreases with a lower temperature, which means that the viscoplastic strain decreases with a decreasing temperature. For the yttria-coated or zirconium-doped material, the main result is an increase of the activation energy of this creep parameter with the quantity of reactive element.

International audience; The understanding of the mechanical properties at the microstructure scale is a key factor for the material macroscopic behavior comprehension and its appropriate engineering at the scale of the structure. In this study, a new approach which is based on the combination of both nanogauges displacements monitoring and electron backscatter diffraction (EBSD) techniques performed under Scanning Electron Microscope (SEM) during in-situ tensile tests is proposed. Strain evolutions at the microstructure components and the behavior of the material can be compared to the crystallographic data. The approach was applied to austenitic stainless steel 316L specimen in order to bring a proof of concept and put into evidence its potential. Among the information of interest which can be obtained through this technique, one can cite the possibility to highlight the strain initiations in the vicinities of twins and their evolutions during the tensile test or to evidence the strain heterogeneities at the surface of the specimen and its influence over the elongations and rotations of the microstructure components, which tends to be reorganized in order to balance the mechanical stress. Besides, such heterogeneities can be expressed in terms of misorientations and quantified from the EBSD data. The twinning and slip activities can also be correlated to the hardening of the material thanks to this method of characterization. As for its interest for characterizing the plastic domain, the technique can show how some grains may activate more than one slip system. Finally, it has been here demonstrated how complementary and powerful the combination of these two techniques may be considered and how it may give access to a better understanding of the material microstructure properties.

In order to clarify the mechanical features of a metal under thermal cyclic loading for the system Ni30Cr- Cr 2 O 3 , a specific study has been carried out. In the present work, the residual stresses in both the metal and the oxide layer have been investigated. An adapted method is applied to process the experimental results that were obtained by using in-situ high temperature synchrotron diffraction at European Synchrotron Radiation Facility. The sin 2 ψ analysis provides information about the stress in metal and oxide. X-ray diffraction provides also the lattice parameter between crystallographic planes in the metal. To obtain correct stress values, a correction method is also proposed taking into account different discrepancies sources to ensure the equation of mechanical balance.

International audience; The viscoplastic behaviour of the model yttria-coated Ni28Cr alloy was studied under high temperature oxidation conditions for various small quantities of reactive element (RE). The main purpose was to determine the way the RE acts on the non-destructive stress relaxation mechanisms (creep) occurring in thermally grown chromia scales. After building of an initial chromia microstructure by 3 h oxidizing at 1273 K, temperature jumps were applied to generate thermal stress loading, the chromia scale microstructure being considered as stable. The generated stress was then released along 3 h isothermal periods and X-ray Synchrotron diffraction was used to follow in situ its evolution. The experimental curves were then simulated in order to calculate the creep coefficients, to evaluate the activation energy of the diffusion-creep mechanism and determine the diffusion coefficients and the elementary mechanisms associated to the viscoplastic behaviour of chromia scales in relation with the introduced RE quantity.

This work takes place in the general context of a better understanding of materials degradation mechanisms in severe environments. More particularly, its purpose is to correlate microstructural elements to growth stress magnitude evolution and stress release mechanisms for chromia thin films thermally grown on model NiCr alloys. X-ray elastic strains have then been measured in situ, as the chromium oxides develop and evolve, by using synchrotron X-ray diffraction, coupled with an induction furnace. 2D diffraction patterns were continuously recorded by applying different temperature variation procedures between 1000°C and 700 °C. Thermal stresses imposed on Cr2O3/NiCr system by abruptly reducing the sample temperature, i.e. by exploiting the thermal expansion difference between oxide and substrate, showed noticeable subsequent stress relaxation by creep. The main results obtained from these experiments were the kinetic of the growth stress from the isothermal measurements, and the study of the stress release mechanism after the temperature jumps to lower values. In complement, the oxide microstructure development during the course of oxidation was also investigated from both the peaks intensity and peaks width evolution. The creep coefficients could be estimated for the first time for chromia under the thin film form. It was proposed that the stress release by diffusion creep in the chromia films is very likely governed by a mechanism involving diffusion of oxygen ions at the chromia grain boundaries.

The grain scale of materials is an area still open for investigations within the field of materials science. The most helpful tools to perform this type of research are diffraction methods. Within the research project presented in this paper two experiments were carried out employing two different types of radiation: neutron (ISIS) and synchrotron (ESRF). The aim of the work was to describe the stress state in the necking zone during the occurrence of a damage phenomenon (Fig. 1.) in separate phase and to check the level of the homogeneity. The supplemental tools were the finite elements method and self-consistent modeling – it testified, confirmed and completed our experimental results and allowed us to formulate the justifiable conclusions.

International audience; Component parts made of a commercial two-phase α + β Ti-6Al-4V alloy can be assembled by Nd:YAG pulsed laser beam welding. Welding processes are known to result in strong heterogeneities, i.e. strength mismatch and residual stresses and are also accompanied by a great variety of flaws, which is why the failure behavior of welded joints is still difficult to predict. The present work aims at gaining insights into the mechanical behavior of Ti-6Al-4V welds and also investigates the effect of defects such as the welding joint/weld root misalignment and pore size distribution. Comprehensive metallurgical analyses in the weld region are first carried on on the basis of optical, X-ray diffraction and SEM analyses. Then, the overmatch is highlighted from hardness measurements of a weld cross section. Next, tensile testing of both the base metal and fusion zone are performed. The tensile specimens are taken along and parallel to a partial penetration weld and also in the base metal. Two different thicknesses are chosen for weld embedding specimens, respectively 1.5mm and 2.5mm. The latter one embeds the notch coming from the partial penetration. Tensile tests displayed a slight overmatch, which effect is underlined by digital image correlation on transversal 1.5mm tensile specimens. Nevertheless, high-speed camera data acquisition revealed that such a slight overmatch was not sufficient to prevent the occurrence of plasticity within the weld in the case of the 2.5mm tensile specimens. It also highlighted the influence of plasticity on the crack path, which tends to bifurcate from the hardest to the softest area. Further aspects of the weld structure and mechanical behavior heterogeneities are finally discussed.

The coupling between mechanical and chemical behaviors is investigated. The Generalized Eigenstrain Method is used and enables to take easily into account several couplings, such as damage and corrosion. Modeling is then performed and compared for different configurations. Chemical reactions and diffusion effects are thus described in order to improve accuracy of such a micromechanical time-dependent model. Application is then performed on a steel reinforced concrete material. Moreover, a particular and original coupling has been introduced, which is justified by thermodynamics arguments.

Constitutive models of viscoelastic fluids are written with rate-form equations when considering finite deformations. Trying to extend the approach used to model these effects from an infinitesimal deformation to a finite transformation framework, one has to ensure that the tensors and their rates are indifferent with respect to the change of observer and to the superposition with rigid body motions. Frame-indifference problems can be solved with the use of an objective stress transport, but the choice of such an operator is not obvious and the use of certain transports usually leads to physically inconsistent formulation of hypoelasticity. The aim of this paper is to present a consistent formulation of hypoelasticity and to combine it with a viscosity model to construct a consistent viscoelastic model. In particular, the hypoelastic model is reversible. A methodology is proposed in this paper to model hypoelasticity as an equivalent incremental formulation of hyperelasticity. This method is based on the use of Lie derivative to write an equivalent hypoelastic model and simultaneously to respect the general covariance principle. By associating these hypoelastic models with viscous behaviors, a physically realistic model is obtained and can be used to represent the behavior of viscoelastic solids or fluids that are submitted to finite transformations or large rates of deformation. The validity of this approach is illustrated with the construction of a model for a Maxwell-like viscoelastic fluid. The model is implemented in the Z-set® numerical package and solved.

International audience; In oxidizing environments, the protection of metals and alloys against further oxidation at high temperature is provided by the oxide film itself. This protection is efficient only if the formed film adheres well to the metal (substrate), i.e., without microcracks and spalls induced by thermomechanical stresses. In this study, the residual stresses at both macroscopic and microscopic scales in the oxide film adhering to the substrate and over the damaged areas have been rigorously determined on the same samples for both techniques. Ni-30Cr and Fe-47Cr alloys have been oxidized together at 900 and 1000 °C, respectively, to create films with a thickness of a few microns. A multi-scale approach was adopted: macroscopic stress was determined by conventional X-ray diffraction and Raman spectroscopy, while microscopic residual stress mappings were performed over different types of bucklings using Raman micro-spectroscopy and synchrotron micro-diffraction. A very good agreement is found at macro- and microscales between the residual stress values obtained with both techniques, giving confidence on the reliability of the measurements. In addition, relevant structural information at the interface between the metallic substrate and the oxide layer was collected by micro-diffraction, a non-destructive technique that allows mapping through the oxide layer, and both the grain size and the crystallographic orientation of the supporting polycrystalline metal located either under a buckling or not were measured.

International audience; In the present work, mechanical features in thermal oxide films growing on metals have been investigated during cyclic thermal loadings. An adapted model is considered to describe the stress evolution within oxide films, taking into account thermomechanical couplings. These numerical predictions are compared with experimental results obtained using synchrotron diffraction at ESRF. In order to obtain the features of the system, an innovative data treatment is thus proposed and performed. By dealing with the frequency analysis of the system, the method is able to identify some mechanisms. This mechanical spectroscopy allows thus to confirm the thermomechanical description of a chromia-former alloy.

International audience; The mechanical behaviour of each phase in two-phase titanium Ti-18 was studied at room temperature under a low strain rate tensile test until fracture. Due to its selectivity, the X-ray diffraction method was applied for in-situ tensile test to analyse the behaviour of each phase in the direction perpendicular to the loading force. In addition, the biaxial stress states of the initial sample, as well as those of the sample during the tensile test, were determined using multi-reflection grazing incidence X-ray diffraction (MGIXD). The experimental data were compared with the prediction of an elasto-plastic self-consistent model in order to study slips on crystallographic planes and mechanical effects occurring during plastic deformation.

International audience; In the present work, the mechanical behavior of phases in duplex steel during tensile test was studied. Special interest was taken in the analysis of damage process just before failure. In this aim two diffraction methods: in-situ time of flight neutron diffraction and X-ray synchrotron diffraction were applied. Using diffraction data, the slip mechanism on crystallographic planes during plastic deformation was investigated. In the case of aged UR45N steel, it was found that significant softening caused by damage process was initiated in the ferritic phase. The lattice strains measured in situ by two above mentioned diffraction methods were compared with prediction of the self-consistent model.

International audience; Diffraction methods for lattice strain measurement provide useful information concerning the nature of grains behaviour during elastoplastic deformation. The main advantage of the diffraction methods is the possibility of studying mechanical properties of polycrystalline materials separately in each phase and in groups of grains with a specific orientation. In this work we present application of the neutron and X-ray diffraction to study “in situ” deformation of two phase stainless steels during tensile loading. The experimental results are compared with self-consistent model.

International audience; In this work a new method for analysis of neutron diffraction results obtained during “in situ” tensile load is proposed and tested. The methodology is based on the measurements of lattice strains during “in situ” tensile test for several hkl reflections and for different orientations of the sample with respect to the scattering vector. As the result the full stress tensor for preferred texture orientations in function of applied stress can be determined with help of crystallite group method. The experimental data are presented and compared with self-consistent model calculations performed for groups of grains corresponding to the measured hkl reflections.

International audience; To say that a constitutive model has to verify “the principle of material objectivity” to ensure its frame-indifference has become a common wisdom. Objective transports are thus defined to serve as tensor rates. These operators are in particular applied to the Cauchy stress tensor. They are used as time derivatives to describe non-linear or dissipative phenomena observed during the finite transformations of a material continuum. Because an infinite number of such transports may be constructed and shown to be objective, the selection of the appropriate transport and its validity still constitutes an open and debatable question.Differential geometry, within its four-dimensional formalism, has proven its ability to describe physical fields and their variations in space and time while ensuring the covariance of any physical law. This description is here applied to the motion of a material continuum within the classical hypotheses of Newtonian physics. In this context, we show that the rate of a tensor as seen by a point of space–time is uniquely defined by the covariant rate; this quantity is not invariant with respect to superposed rigid body motions. The rate of a tensor as seen by a moving particle of matter is uniquely defined by the Lie derivative of the tensor. This operator is invariant with respect to superposed rigid body motions. Both, the covariant rate and the Lie derivative are independent of the observer and could thus be used in a constitutive model within a four-dimensional formalism. We show next that the projection of the Lie derivative of the Cauchy stress tensor within an inertial 3D Cartesian frame corresponds to Truesdell’s transport and that the other 3D objective stress transports, if they have the dimension of a rate, do not correspond to a time derivative of this tensor. The Truesdell transport is thus the only objective transport that represents a frame-indifferent time derivative of the Cauchy stress tensor.

International audience; In the present work, mechanical features of different thermal oxide films growing on metals have been investigated at different temperatures. An adapted model is performed to describe the stresses evolution within the oxide films. These predictions are compared with experimental results obtained by different experimental techniques. In order to obtain some accurate mechanical characteristic parameters of the system, both an asymptotic approach and an optimization procedure have been developed and presented through a general methodology. In respect to the chosen assumptions, the present model enables to give a precise mechanical description of each considered layer.© 2013 Elsevier B.V. All rights reserved.

The goal of this work was the determination of lattice strains distribution in two phases of duplex steel during plastic necking. Subsequently, the stress heterogeneity in the neck was studied in order to determine the reason for the damage initiation and to verify the hypothesis that the damage begins in the ferritic phase. To do this, X-ray synchrotron radiation was used to scan the ‘in situ’ variation of the interplanar spacings along the necking zone for samples subjected to tensile loading. A self-consistent model and FEM simulation were applied for the experimental data interpretation.It was found that for advanced necking the phase lattice strains, especially those measured at some distance from the neck centre, show a large inversion of the loads localised in both phases compared to the undamaged state (the lattice strains in the ferrite become smaller than in the austenite). This effect indicates stress relaxation in the ferrite which is connected with the damage phenomenon. Correlation of the experimental results with the modelling shows that the value of von Mises stress is responsible for the initiation of the ferritic phase softening. Keywords: Elastoplastic deformation, Necking, Damage, Polycrystalline material, Self-consistent model, Synchrotron diffraction

International audience; The comprehension of deformation mechanisms and polycrystalline alloy properties is of great importance in materials science. One major challenge remains the measurements of the mechanical field components at the nanoscale. For the past twenty years, the development of nanotechnologies had a great impact on various scientific domains. Here we propose to take advantage of nanotechnologies in order to perform major breakthroughs in material strain determination. Indeed, in this study we investigate the use of metallic nanoparticles gratings to map local strains at the surface of materials. Nanoparticles can play the role of nanogauges, giving access to surface strains at the nanoscale by tracking their displacements during tensile tests performed under Scanning Electron Microscope (SEM). This original method is particularly helpful to map surface strains but also to evidence local heterogeneities as well to provide a direct comparison between local and macroscopic mechanical fields evolution. Therefore, this approach should be considered as an alternative technique both for academic and industrial researchers.

International audience; In the present work, mechanical features are investigated in the case of ZrO2 thermal oxide films growing on a Zr alloy at the temperature of 550°C. The effects of a nanocrystallisation treatment on high temperature oxidation of a zirconium alloy are specifically studied. High temperature oxidation is performed in order to show benefits of such a nanocrystallisation on corrosion resistance and its influence on the mechanical fields. Experimental results obtained by Raman spectroscopy give the growth stress evolution in ZrO2 films. Using a modelling of the system, both asymptotic forms and an optimization procedure are developed to determine the mechanical characteristic parameters of the system. © 2012 Elsevier Ltd.

International audience; When constructing viscoelastic models, rate-form relations appear naturally to relate strain and stress tensors. One has to ensure that these tensors and their rates are indifferent with respect to the change of observers and to the superposition with rigid body motions. Objective transports are commonly accepted to ensure this invariance. However, the large number of transport operators developed makes the choice often difficult for the user and may lead to physically inconsistent formulation of hypoelasticity. In this paper, a methodology based on the use of the Lie derivative is proposed to model consistent hypoelasticity as an equivalent incremental formulation of hyperelasticity. Both models are shown to be reversible and completely equivalent. Extension to viscoelasticity is then proposed from this consistent model by associating consistent hypoelastic models with viscous behavior. As an illustration, Mooney–Rivlin nonlinear elasticity is coupled with Newton viscosity and a Maxwell-like material is investigated. Numerical solutions are then presented to illustrate a viscoelastic material subjected to finite deformations for a large range of strain rates.

International audience; When constructing incremental constitutive models of elastoplasticity for materials undergoing finite deformations, the tensors and their rates should respect the principle of frame-indifference. Instead of classical 3D approaches in which different objective transports may be arbitrarily used in the constitutive equations, we propose to model the constitutive equations using the four-dimensional formalism of the theory of Relativity. This formalism ensures that any 4D tensor is frame-indifferent thanks to the principle of covariance. It is further possible to define 4D rate operators that are all, by construction, frame-indifferent. Among these covariant rates, the 4D Lie derivative is chosen to construct incremental constitutive relations because it is invariant to the superposition of rigid body motion. A 4D rate type model of elastoplasticity with isotropic hardening is thus developed and compared with existing classical 3D constitutive models of elastoplasticity established in the context of finite deformations.

International audience; When metals or alloys are oxidized at high temperature, an oxide film generally develops. Stress induced by oxide growth may influence the structure and the protective properties of the oxide scales. Classical models (taking into account elasticity and/or viscoplasticity and/or thermal mismatches) are able to predict some stress evolution. Moreover, the origin of that stress for isothermal condition must be sought-after in a growth strain related to the formation of the oxide above the substrate. In the present work, details are given on the modelling of stress under thermal loadings. The study is performed considering different thermomechanical behaviours and upgraded taking into account the origin of the different thermal couplings (weak and strong ones). Therefore, comparison with experimental results performed at ESRF allows extracting thermomechanical parameters with numerical values for different configurations (isothermal or with thermal evolution). This allows also investigating different mechanisms occurring at high temperature in chromia.

International audience; Multivectorial algebra is of both academic and technological interest. Its application, however, is not always easy. A distinction must be made between polar and axial vectors and between scalars and pseudo-scalars. Eight element types are often considered even if they are not always identified as multivectors. In some cases, for simplicity’s sake, only vectorial algebra or quaternion algebra is explicitly used for physical and mechanical applications. It would, however, be more convenient to use more complex algebra directly in order to have a wider range of mechanical applications. The aim of this paper is to examine one particular type of Clifford algebra that could solve this problem. The present study focusses on showing how these quantities can be used to model mechanical and engineering problems. First, continuum mechanics in a Cauchy medium is investigated for elastic transformations. Second, a specific type of shot-peening application is studied. Applications are then used to illustrate the scope and efficiency of this type of modeling based on geometric algebra.

Ductile damage is a consequence of large strains more or less localized inside bands. Taking into account damage in constitutive behaviour of metallic materials is necessary to model various engineering problems involved in forming processes (stamping, punching, shearing…). Damage can be described at macroscopic level with continuum mechanics theories but introducing microstructural features can lead to more accurate predictions. In the present study, two polycrystalline plasticity models including damage effects in the framework of scale transition methods are investigated. These models are based on different approaches with direct application to duplex stainless steel. The first one is a variant of the Lipinski–Berveiller model in which ductile damage effects have been introduced. The second one is a generalized Cailletaud model taking into account ductile damage. Because of the microstructural complexity of the chosen materials, some particular developments of the micro-mechanical approaches are considered. Moreover, continuous damage mechanics is used at grains scale including its coupling with plastic or elastic–plastic flow. The modelling is justified from previous experimental results obtained by neutrons diffraction on duplex stainless steels. The developed models allow then deducing from the grains behaviour the macroscopic behaviour of the aggregate with damage effects.

Ductile damage is a consequence of large strains more or less localized. Taking into account damage in constitutive behaviour of metallic materials is necessary to model various engineering problems involved in forming processes (stamping, punching, shearing...). It would lead to accurate predictions introducing microstructural features of materials [1-2]. In the present study, two crystalline plasticity models including damage effects in the framework of scale transition methods are investigated. These models are developed and based on different approaches with direct application to duplex stainless steels. The first approach is a variant of the Berveiller-Zaoui model in which the effect of ductile damage has been introduced. The second one is a generalized Cailletaud model taking into account the ductile damage [3-6]. Because of the microstructural complexity of the chosen materials, some particular developments of the micromechanical approaches are considered. Moreover, continuous damage mechanics is used at grain scale including its effect (or coupling) on plastic or elastic-plastic flow with more or less complex hardenings. The modelling is justified on some previous experimental results in metallic duplex materials [7-8]. The developed models allow then deducing the macroscopic behaviour of the aggregate with damage effects from the grains behaviour.

Dans cette etude, on s’interesse aux mecanismes d’endommagement de films minces d’oxydes thermiques de chromine qui se forment lors de l’oxydation d’alliages Ni-Cr30. En particulier, l’influence de certains parametres physiques et microstructuraux sur l’evolution des niveaux de contrainte residuelle dans les films d’oxyde est evaluee. Une approche fondamentale du probleme de la durabilite de la protection apportee par le film de chromine a ete realisee en etudiant successivement la genese du film d’oxyde et des contraintes de croissance qui l’accompagne et la perte d’integrite par formation de cloques et d’ecailles. L’essentiel des analyses a ete conduite par spectrometrie Raman. Il a ete possible de determiner les contraintes de croissance prenant naissance dans la chromine en cours de formation entre 700 ° et 900 °C, ainsi que les contraintes residuelles correspondantes permettant d’acceder a la composante thermique des contraintes a tout instant du processus d’oxydation. En outre, l’evolution du niveau de contrainte de croissance a pu etre reliee a la cinetique de grossissement des grains de l’oxyde. La stabilisation ou la diminution ulterieure resulte de l’entree en action du processus de relaxation, consequence d’un fluage de type Coble explique par le niveau de contrainte atteint dans l’oxyde en relation avec la taille de grain correspondante. Les principales caracteristiques thermomecaniques decrivant ces evolutions ont pu etre determinees au moyen d’une modelisation du systeme en fonctionnement, soit a partir de formes analytiques asymptotiques, soit par un processus d’optimisation. Par ailleurs, l’endommagement localise a ete etudie experimentalement de maniere detaillee. Lors du refroidissement, l’oxyde peut se detacher du substrat metallique pour donner naissance a des cloques puis des ecailles, dont la morphologie a ete analysee. De meme, le taux d’endommagement defini comme la proportion de surface delaminee, a egalement ete determine en fonction de la temperature et de la duree d’oxydation. Son evolution a pu etre mise en relation directe avec le niveau de contrainte de croissance dans le film d’oxyde de chromine, avant que celui-ci ne soit refroidi. Il apparait au final qu’en fonction de certains parametres (duree d’oxydation, vitesse de refroidissement), le mecanisme d’endommagement par cloquage suivi d’ecaillage, doit etre considere comme un processus de relaxation local intervenant en complement des autres mecanismes principaux de relaxation par fluage.

International audience; The lattice strains in large tensile deformations, up to the fracture of the sample were measured using neutron TOF method. For the first time, the range of large deformation was studied measuring lattice strain in the deformation neck and using special correction for macrostress value. It was found that during large plastic deformation the lattice stresses arise almost linearly with the macrostress value. The relaxation of elastic strains in some groups of ferritic grains (corresponding to reflections 211 and 200) can be connected with initiation of damage process in the ferritic phase.

Mechanical features have been investigated in the case of α - Cr 2 O 3 thermal oxide films growing on NiCr 30 alloy in the temperature range 700–900 °C. From previous experimental results obtained by Raman spectroscopy and giving the growth stress evolution in α - Cr 2 O 3 films, and based on a modelling of the system, both asymptotic forms and an optimization procedure have been developed which give values for the mechanical characteristic parameters of the system and also its evolution with the oxidation temperature.

International audience; The covariance principle of the theory of relativity within a four-dimensional framework ensures the validity of any equations and physical relations through any changes of frame of reference, due to the definition of the 4D space–time and the use of 4D tensors, operations and operators. This 4D formalism enables also to clearly distinguish between the covariance principle (i.e., frame-indifference) and the material objectivity principle (i.e., indifference to any rigid body motion superposition). We propose and apply here a method to build a constitutive relation for elastic materials using such a 4D formalism. The present article is specifically devoted in the application of this methodology to construct hypo-elastic materials with the use of the 4D Lie derivative. It enables thus to obtain consistent non-dissipative models equivalent to (hyper)elastic ones.

International audience; Cosserat’smedium is of both academic and technological interest. Thismedium offers a wider range of possible applications allowing a better description of the mechanical effectswithin materials; it should thus be used preferentially. It should be noted that the advantages of this kind ofmedia are nevertheless counterbalanced by the simplicity of Cauchy’s medium.One objective of this article is to investigate the correspondence between different multi-dimensional representations of Cosserat’s medium and hence advocate the advantages of this representation. It is demonstrated that the equations representing Cosserat’s medium may be derived from different frameworks. The comparison between these different approaches shows that Cosserat’s medium can be seen as the natural medium to describe material behaviors accurately. As an illustration, constitutive models for isotropic linear elastic behaviors are then derived using different multi-dimensional mechanical theories.