It is well known that dislocation slip plays a major role in plastic deformation of polycrystals. Depending on the crystal’s symmetry, only a limited number of Slip Systems (SSs) are possible, and their activities depend on the crystal orientation with respect to the applied stress. High Resolution Digital Image Correlation (HR-DIC) can be used to get the full-field measurements of displacement fields on the surface of the strained material during an in situ tensile test, whereas the EBSD technique provides local crystallographic orientations. Therefore, coupling them can lead to full description of the local slip activities. Recently, an algorithm (named SSLIP) was proposed in the literature to automatically estimate the plastic activity from HR-DIC and EBSD data. The aim of the present paper is first to improve this algorithm so that it works for incremental straining, and to propose a way to take account for the anisotropic behaviour through a well-known set of Crystal Plasticity (CP) constitutive laws. It is shown that slip identification, together with those CP laws, can be used to estimate the tensile stress at grain scale. The influence of the DIC resolution is investigated and “correction rules” for small grains are proposed. Finally, the experimental results are compared against those found using the CP Finite Element Method (CPFEM), showing good consistency, specially in terms of active SSs and local stress.

As the computational capability of modern computers increases, the Crystal Plasticity Finite Element Method (CPFEM) becomes more and more popular in materials science to model the mechanical behaviour of polycrystals. Indeed, such analysis provides extensive information about local mechanical fields (such as plastic strain and stress), which can be useful for understanding the behaviour of bulk materials. However, estimating the parameters of the CP constitutive laws is still challenging because they are not directly related to the macroscopic behaviour of the polycrystalline aggregates. Thus, one way to identify such parameters is by inverse analysis from CPFEM simulations. However, such approach is usually extremely time consuming. This paper proposes a two-step optimization scheme to determine these coefficients. The first step is based on a simple model, similar to that proposed by Sachs back in 1928. The second step is based on CPFEM simulations, to be compared with experimental data acquired by an in situ tensile test and full-field measurements made by High-Resolution Digital Image Correlation (HRDIC). The uniqueness of the solution found by inverse analysis is studied and ways to solve the local minima issues are provided. Finally, the ability of CPFEM to replicate an in situ tensile test is assessed.

Modelling the physical behaviour of fibrous materials still remains a great challenge because it requires to evaluate the inner structure of the different phases at the phase scale (fibre or matrix) and the at constituent scale (fibre). X-ray computed tomography (CT) imaging can help to characterize and to model these structures, since it allows separating the phases, based on the grey level of CT scans. However, once the fibrous phase has been isolated, automatically separating the fibres from each other is still very challenging. This work aims at proposing a method which allows separating the fibres and localizing the fibre-fibre contacts for various fibres geometries, that is: straight or woven fibres, with circular or non-circular cross sections, in a way that is independent of the fibres orientations. This method uses the local orientation of the structure formed by the fibrous phase and then introduces the misorientation angle. The threshold of this angle is the only parameter required to separate the fibres. This paper investigates the efficiency of the proposed algorithm in various conditions, for instance by changing the image resolution or the fibre tortuosity on synthetic images. Finally, the proposed algorithm is applied to real images or samples made up of synthetic solid fibres.

Understanding the mechanisms at the microstructure scale is of great importance for modeling the behavior of materials at different scales. To this end, digital image correlation (DIC) is an effective measurement method for evaluating the strains generated by various loading conditions. The objective of this paper is to describe the experimental setup and the use of high resolution digital image correlation (HRDIC) during in situ Scanning Electron Microscope (SEM) tests in order to provide a coupling between polycrystalline modeling and experiment in the near future. The HRDIC technique is used to evaluate the tensile behavior of a pure copper polycrystal at room temperature. Several magnitudes are investigated in order to discuss the representativeness of the results with respect to the macroscopic scale. The selected image correlation parameters are discussed regarding the ability of the technique to define inter-and intra-granular strain heterogeneities. Finally, based on EBSD ana-lyzes, the impact of grain orientation on the mechanical behavior is discussed. The Schmid factor, calculated from a macroscopic stress, appears to be the determining factor concerning the orientation of the location bands. On the other hand, it is not sufficient to define the mean strains in the grains.

In materials science, the microstructures of materials are generally characterized by 2D observation (e.g. electron microscopy). For polycrystalline materials, such as crystalline rocks or ceramics, those observations can be used to measure the grain size distribution. However, the fact that grain sizes are measured in planar cuts introduces a statistical bias, since the real (3D) grain sizes cannot be directly measured. For almost spherical grains, this bias can be computed thanks to the so-called Wicksell's equation. This paper proposes a method, based on Maximum Likelihood Estimation (MLE) for unfolding the apparent 2D distribution. The efficiency of this method is extensively investigated in the special case of lognormal distribution. In this case, 10% uncertainty on the distribution parameters can be reached with only 580 empirical values.

In material sciences applied to crystalline materials, such as metals or ceramics, the grain morphology (size and shape) and the crystallographic texture are of great importance for understanding the macroscopic behaviour of the materials.Micromechanics of polycrystalline aggregates consists in evaluating the thermo-mechanical behaviour of the aggregates at their grain scale.If the investigated material is subjected to macroscopic deformation, the local strain can be obtained either experimentally, thanks to full-field measurement methods such as microgrid technique (Allais, Bornert, Bretheau, & Caldemaison, 1994) or Digital Image Correlation (DIC) (Hild, Raka, Baudequin, Roux, & Cantelaube, 2002), or thanks to numerical simulation of the microstructure.The latter needs to take into account the mechanical heterogeneities (due to the different constituents) and the anisotropy of each phase, depending on its crystalline orientation.

For the sake of understanding the behaviour of a polycrystal at its grain scale, Finite Element (FE) numerical simulations can be performed, taking into account the physical properties of each grain. Those simulations must take into account the phase heterogeneities, the local anisotropies and the crystalline orientations as well. In addition, the actual grain morphologies must be well described in order to model localization phenomena. An algorithm, named MTEX2Gmsh, is proposed to automatically generate an EF mesh from EBSD data. The resulting mesh gives smooth and accurate descriptions of the grain boundaries together with reduced Degrees of Freedom (DoF), hence limited computational times. Using this algorithm, the fragile-elastic behaviour of a ceramic and micro-plasticity phenomena in a nitrided steel are studied as application cases. The latter is based on a crystal-plasticity model for the ferrite phase.

The estimation of the grain size in granular materials is usually performed by 2D observations. Unfolding the grain size distribution from apparent 2D sizes is commonly referred as the corpuscle problem. For spherical particles, the distribution of the apparent size can be related to that of the actual size thanks to the Wicksell's equation. The Saltikov method, which is based on Wicksell's equation, is the most widely used method for resolving corpuscle problems. This method is recursive and works on the finite histogram of the grain size. In this paper, we propose an algorithm based on a minimizing procedure to numerically solve the Wicksell's equation, assuming a parametric model for the distribution (e.g. lognormal distribution). This algorithm is applied on real material and the results are compared to those found using Saltikov or Saltikov-based stereology techniques. A criterion is proposed for choosing the number of bins in the Saltikov method. The accuracy of the proposed algorithm, depending on the sample size, is studied.

This paper investigates the relevance of the representation of polycrystalline aggregates using Radical Voronoï (RV) tessellation, computed from Random Close Packs (RCP) of spheres with radius distribution following a lognormal distribution. A continuous relationship between the distribution of sphere radii with that of RV cell volumes is proposed. The stereology problem (deriving the 3D grain size distributions from 2D sections) is also investigated: two statistical methods are proposed, giving analytical continuous relationships between the apparent grain size distribution and the sphere radius distribution. In order to assess the proposed methods, a 3D aggregate has been generated based on a EBSD map of a real polycrystalline microstructure.

Cold flowforming is a chipless forming process that deforms tubular parts by reducing theirouter diameter and thickness while increasing their length. It consists of a rotating mandrel and oneor more rollers that are translated along the tube axis, thus plastically deforming it. Flowforming ofTi-6Al-4V (also known as Ti64) is of great interest for improving the mechanical properties of thematerial, such as yield stress and fatigue strength. However this alloy is known to have poor ductilityat room temperature. Therefore, flowforming of Ti64 without failure or crack is a great challenge. Inthis present paper, the authors have attempted to predict the different failure modes occurring duringflowforming. An experimental machine has been built at the Center forMaterial Forming (CEMEF) inorder to monitor the force on the single roller, the torque on the mandrel and the actual rotation speedof the roller as well. Numerous flowforming tests have been performed using different processingparameters, such as working depth, roller feed and initial geometry, in order to investigate the criticalvalues which lead to the failure of the flowformed tube. In addition, numerical simulations of theprocess have been performed using the FORGE FEM solver. The results of the simulations have beenused to evaluate the relevance of usual failure criteria (Crockford-Latham, Rice-Tracey and Oyane).

Shape Memory Alloys (SMAs) undergo an austenite–martensite solid–solid phase transformation which confers its pseudo-elastic and shape memory behaviours. Phase transformation can be induced either by stress or temperature changes. That indicates a strong thermo-mechanical coupling. Tensile test is one of the most popular mechanical test, allowing an easy observation of this coupling: transformation bands appear and enlarge giving rise to a large amount of heat and strain localisation. We demonstrate that the number of transformation bands is strongly associated with the strain rate. Recent progress in full field measurement techniques have provided accurate observations and consequently a better understanding of strain and heat generation and diffusion in SMAs. These experiments bring us to suggest the creation of a new one-dimensional thermomechanical modelling of the pseudo-elastic behaviour. It is used to simulate the heat rise, strain localisation and thermal evolution of the NiTi SMA sample submitted to tensile loading.

Le fluotournage est un procede de fabrication de tubes sans soudures par deformation plastique a froid. Il consiste a reduire l'epaisseur d'une preforme tubulaire montee sur un mandrin en utilisant plusieurs molettes en translation parallelement au tube. Grâce a la conicite des molettes, l'epaisseur du tube diminue, donc celui-ci s'allonge dans la direction de fluotournage. Le TA6V est un alliage de titane de type α-β. Ses tres bonnes proprietes mecaniques et sa faible densite en font l'alliage de titane le plus utilise dans l'industrie aeronautique. Toutefois, le fluotournage d'un tel alliage represente un vrai defi, car il est connu pour avoir une faible ductilite a temperature ambiante. Afin d'optimiser les conditions operatoires, permettant ainsi de tres grandes deformations du TA6V, le materiau fluotourne a d'abord ete analyse, tant du point de vue microscopique (MEB, EBSD) que macroscopique (proprietes mecaniques). De plus, un fluotour experimental instrumente a ete concu afin d'analyser les mecanismes de deformation lors de la mise en forme. Celui-ci a permis d'identifier les phenomenes microstructuraux a l'origine de la deformation et de determiner une loi de comportement valide pour la simulation numerique. Cette derniere a enfin servi a l'optimisation des conditions operatoires.

Flowforming is a means to produce seamless tubes by plastic deformation at room temperature. It consists in reducing the thickness of a tubular part mounted on a mandrel by deforming it using several rollers translating along the tube axis, while the tube is rotating along its axis. Thanks to the high compressive stresses, and to the incremental nature of the deformation process, flowforming can lead to a high thickness reduction and thus to high elongation of the deformed tubes. Ti-6Al-4V (Extra Low Interstitial grade) tubes have been deformed by cold flowforming, with a thickness reduction ratio higher than 60%, and their microstructures have been investigated using light optical microscopy (LOM), scanning electron microscopy (SEM) and electron backscattered diffraction (EBSD). Based on EBSD data, a post-processing analysis has been performed in order to study the texture of the flowformed parts. Optical Microscopy showed that the material could be deformed without displaying flow instability such as adiabatic shear banding, despite the fact that it has been processes out of the stable processing maps (high strain rate and low temperature). It also evidenced a major deformation along the tube axis accompanied with a slight twist due to torsion stress. EBSD analysis indicated the occurrence of continuous dynamic recrystallization, which is rarely reported in the α-β domain of such alloys. The recovery/ recrystallization effects resulted in a submicrocrystalline equiaxed structure, which is consistent with that previously reported for Ti-6Al-4V subjected to severe plastic deformation (SPD). The texture of the hexagonal α-phase appeared to be similar to that obtained on extruded Ti-6Al-4V, with a basal component perpendicular to the tube axis.

SMA’s peculiar properties are due to a reversible solid to solid phase transformation which can be induced either by stress or temperature. For Ni49,75at%-Ti SMA this isochoric transformation forms a monoclinic phase (martensite) from a cubic parent phase (austenite), with 24 possible orientations (variants). From the local geometries and the Gibbs energy of each variant, we propose a polycristalline multiaxial model which reflects the strong thermomechanical coupling of the phase transformation. Quasi-static tests are performed for validation. Mots clefs : couplage thermo-mecanque ; modele micro-macro ; Alliage a Memoire de Forme

The pseudo-elasticity of Shape Memory Alloys is due to a change in volumetric fraction between the high temperature phase (Austenite) and the low temperature phase (Martensite) under a mechanical loading. When a tensile loading is considered, transformation bands occur leading to strong localization of the deformation and a strong local heating. The modeling of this strongly coupled phenomenon is discussed for a polycrystalline specimen in a multiaxial mechanical framework. Three different scales are considered: the variant scale (or phase scale), the single-crystal scale and the polycrystalline scale. The free energy of each variant is first computed from the loading and the geometrical lattice transformations associated to each variant. The volumetric fraction of each phase is then defined at the grain scale as function of their free energy. A simple averaging operation allows to estimate the deformation at the grain scale. The polycrystalline scale is not considered at present.