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Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (e.g., due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. In this work, we developed a generalizable, physically-constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on Li$_X$FePO$_4$, a technologically-relevant battery positive electrode material. We uncovered the functional form of composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 $\leq$ X $\leq$ 1), including inside the thermodynamically-unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

The well-known mechanisms of interaction between precipitates and dislocations are shearing (for shearable precipitates) and bypassing mechanisms (for nonshearable precipitates). The transition from shearable to nonshearable precipitates in precipitation hardening alloys leads to changes of dislocation motion mode and dislocation multiplication behavior, which inevitably causes different PLC behaviors. In this study, we systematically investigate the influence of shearable and nonshearable Al3(Sc, Zr) precipitates on PLC behaviors by experimental characterization for precipitation hardening AlMgScZr alloys. We analyze the onset strain, critical strain-rate range, serration amplitude, and propagation behavior of PLC bands in detail for AlMgScZr alloys with shearable and nonshearable precipitates, respectively. We find that the transition from shearable to nonshearable precipitates changes the PLC band propagation behavior, decreases the magnitude of serration amplitude, expands the strain-rate range as well as decreases the critical strain rate between normal behavior (the critical strain increases with the increase of strain rate) and inverse behavior (the critical strain decreases with the increase of strain rate) regimes due to the different dislocation-precipitate interactions. Besides, the transition from shearable to nonshearable precipitates increases the onset strain at normal behavior while decreases the onset strain at inverse behavior depending on the different roles of precipitates in the solute-dislocation interaction. Finally, we reveal the nature of influence of different dislocation-precipitate interactions on PLC behavior considering different strengthening mechanisms based on quantitative characterization on precipitates and dislocation density.

cited By 0; International audience; Damage evolution during tensile straining of an AlSi12Ni alloy has been analyzed in situ at synchrotron source using microtomography and in the scanning electron microscope by surface imaging. It is shown that damage development in the analyzed alloy presenting an interconnected network of intermetallic phases is completely different from damage progression previously observed in materials with disperse distribution of particles. In the present material, which is typical for most eutectic structures, damage is dominated by the rupture of the brittle intermetallic phase while void growth is limited by a shielding effect of the intermetallic particles encasing the void. Primary voids exhibit a size close to the thickness of branches of the intermetallic phase. Final failure occurs by void coalescence, but without the formation of secondary voids. Damage analysis from tomographic scans was only possible by applying 3D image correlation to successive reconstructions, which thanks to its sub-voxel resolution, could satisfactorily detect the volume fraction of small-voids inaccessible by conventional thresholding. The presence of many small voids issued from the breakage of the intermetallic phase also was confirmed by scanning electron microscopy imaging performed at higher resolution. © 2019 Acta Materialia Inc.

International audience; Precipitation hardening is the most effective strategy to enhance the mechanical properties of metals. Dislocation mechanisms to control strengthening during precipitation have been demonstrated extensively. However, owing to the complexity of different precipitates in alloys, variations in ductility caused by precipitation are complex and have not been clarified so far. In this study, the effects of precipitation on ductility in precipitation hardening aluminium alloys are investigated based on a modified dislocation-based approach and experimental characterisation. The AlMgScZr alloy with spherical Al3(Sc, Zr) precipitates is used as a model alloy system to understand the effects of precipitation on ductility. Via heat treatment, shearable and nonshearable Al3(Sc, Zr) precipitates are introduced in the AlMg matrix. The results show that the ductility of AlMgScZr alloy decreases when shearable precipitates occur, while it increases with shearable precipitates being replaced by nonshearable precipitates. The variation in ductility of AlMgScZr alloy is mainly controlled by the dynamic recovery rate of the dislocations. Finally, by analysing the different precipitate-dislocation interactions and evaluating the dislocation density evolution during deformation, the dislocation mechanisms of 2 ductility during precipitation for AlMgScZr alloy are demonstrated. This study reveals the dislocation mechanism for controlling ductility during precipitation for AlMgScZr alloy which can provide a theoretical foundation for the design of high-performance structural materials.

The homogenous redistribution of nanosized TiB2 particles in a fine-grained in-situ AA6063/TiB2 composite has been achieved by friction stir processing (FSP). The effects of TiB2 particles on as-deformed structure in the nugget zone and its thermal stability after additional T6 heat treatment are quantitatively evaluated by using neutron diffraction, scanning electron microscopy associated with electron backscatter diffraction and synchrotron X-ray line profile analysis. The results are compared to those obtained from a FSPed AA6063 alloy and, show first that, average grain size of the FSPed AA6063/TiB2 composite is smaller than that of the FSPed AA6063 alloy, while grain size distribution is more uniform. Second, dislocation density estimated in the FSPed AA6063/TiB2 composite is higher than that in the FSPed AA6063 alloy. Third, a small number of grains are dynamically recrystallized in the FSPed AA6063/TiB2 composite compared to its alloy counterpart, which indicates that recrystallization and grain growth during FSP and T6 heat treatment are effectively inhibited by the presence of nanosized TiB2 particles. Keywords: Metal-matrix composites (MMCs), X-ray diffraction (XRD), Transmission electron microscopy (TEM), Neutron diffraction, Friction stir processing

International audience; Microstructural modifications and mechanical properties of samples manufactured from conventional and nanocomposite WC/Co12 powders by means of Selective laser melting (SLM) are compared after processing with the same parameter set. Studying their homogeneity reveals that in both samples coarse and fine carbides segregate in the molten pool. X-ray diffraction (XRD) analysis shows significant changes in the microstructure and crystalline phases present in the WC/Co mixture and after SLM. Thermal decomposition of WC leads to the formation of W2C dicarbides and the appearance of the complex Co-W-C ternary phase. No residual pure cobalt after SLM was detected in the samples. The Williamson-Hall method allows determining coherent WC domain sizes of conventional and nanostructured powders (56 +/- 6nm and 10 +/- 3nm, respectively) and microstrains (approximate to 0 for both) as well as their modifications after SLM processing (180 +/- 50nm and 210(-3)+/- 410(-4) for the nanophased sample, and 330 +/- 100nm and 210(-3)+/- 410(-4) for the conventional one, respectively). The microhardness of the part produced from the nanophased powder is slightly increased in both the coarse (approximate to 1496 HV0.3) and fine (approximate to 1542 HV0.3) carbide segregation regions compared to the sample obtained from the conventional powder (1384 HV0.3 and 1515 HV0.3 for coarse and fine regions, respectively).

The microstructural evolution of in-situ TiB2 nano-particle reinforced AlZnMgCu composites during hot extrusion was investigated from micro to macro scales by a combination of various techniques, including neutron and synchrotron X-ray diffraction, optical microscopy, scanning and transmission electron microscopy and electron backscatter diffraction (EBSD). The development of microstructure has shown a bimodal grain structure with distinctive spatial distributions of TiB2 particles: the elongated coarse grain structure with smaller dispersed particles and the fine grains mixed with clusters of relatively larger particles. The particle stimulated nucleation occurs at large particle clusters, resulting in recystallized (sub)micron sized fine grains. The dispersed smaller particles are observed to promote dislocation generation and to prohibit recovery. They are shown to reduce the misorientation of low angle grain boundaries due to the pinning effects on independent dislocations, which also lead to the suppression of dynamic recovery and increase of driving force for dynamic recrystallization. Quantitative texture analysis combined with neutron diffraction and EBSD has exhibited the development of a strong 〈111〉 and 〈001〉 dual fiber texture, and both texture volume fractions are changing with the particle content. In addition, the synchrotron diffraction experiments have shown that dislocation density increases with the particle content in both texture components. The microstructure evolution is the result from a complex process of particles/matrix interaction during the deformation and dynamic recrystallization. In comparison with its particle-free alloy counterpart, the thermomechanical response of the composites at high temperature is discussed in terms of aluminum deformation and recrystallization mechanisms combined with nanosized particle effects. Keywords: Nano-sized TiB2 particles, Metal matrix composites, Neutron diffraction, Plastic deformation, Dislocation, Recovery & Recrystallization

International audience; The three-dimensional granular and damage structure of two creep deformed copper specimens has been reconstructed using an improved serial sectioning method combining optical profilometry, scanning electron imaging and backscatter electron diffraction. The reconstructions permitted associating creep voids to grain boundaries and evaluating the damage probability of each grain boundary type. The results indicate that creep damage of oxygen free high conductivity copper is governed by topological factors. Quadruple/grain boundaries have the highest probability of damage followed by two-and three-grain boundaries with decreasing percentages. The damage probability of quadruple and three-grain boundaries increases with decreasing stress due to a larger contribution of grain boundary sliding to void nucleation. The relative frequency of damaged two-grain boundaries increases with stress, suggesting a significant role of creep plasticity and the associated grain boundary ledges. No correlation between void location and the crystallographic orientation of neighbour grains was found.

The grain structure of a slightly deformed Al–0.3 wt%Mn alloy was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). The direct comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other., The grain structure of an Al–0.3 wt%Mn alloy deformed to 1% strain was reconstructed using diffraction contrast tomography (DCT) and high-energy diffraction microscopy (HEDM). 14 equally spaced HEDM layers were acquired and their exact location within the DCT volume was determined using a generic algorithm minimizing a function of the local disorientations between the two data sets. The microstructures were then compared in terms of the mean crystal orientations and shapes of the grains. The comparison shows that DCT can detect subgrain boundaries with disorientations as low as 1° and that HEDM and DCT grain boundaries are on average 4 µm apart from each other. The results are important for studies targeting the determination of grain volume. For the case of a polycrystal with an average grain size of about 100 µm, a relative deviation of about ≤10% was found between the two techniques.

International audience; A new evaluation procedure is presented to characterize the orientation and position of single grains within the bulk of a polycrystalline sample. Considering the symmetry properties of Friedel-pairs the contributions to reflection spot positions arising from grain orientation and position could be clearly separated. The proposed method avoids simultaneous fitting of all grain parameters with the goal of a higher accuracy. Depending on the number of reflections considered the accuracy of grain orientation may be less than 0.1 degrees, and the position of the center of mass of the grains can be accurate within one-third of the pixel size.

Microstructure evolution during high-temperature creep of a CuZn40Pb2 brass alloy was characterized in situ by synchrotron microtomography. It is shown that tomographic data are sufficiently accurate for local material characterization. Imposing a constant temperature gradient along the gauge length of the sample allows the apparent activation energy of steady-state creep to be evaluated for a single specimen.

International audience; Synchrotron X-ray diffraction and transmission electron microscopy (TEM) were applied to quantitatively characterize the average particle size and size distribution of free-standing TiB2 particles and TiB2 particles in an in-situ grown Al-TiB2 composite. The detailed evaluations were carried out by X-ray line profile analysis using the restricted moment method and multiple whole profile fitting procedure (MWP). Both numerical methods indicate that the formed TiB2 particles are well crystallized and free of crystal defects. The average particle size determined from different Bragg reflections by the restricted moment method ranges between 25 and 55 nm, where the smallest particle size is determined using the 110 reflection suggesting the highest lateral-growth velocity of (110) facets. The MWP method has shown that the in-situ grown TiB2 particles have a very low dislocation density (similar to 10(11) m(-2)) and their size distribution can be described by a log-normal distribution. Good agreement was found between the results obtained from the restricted moment and MWP methods, which was further confirmed by TEM. (C) 2015 Elsevier Inc. All rights reserved.

The structure of a real particle reinforced metal-matrix composite, Al/Al 2 O 3 , was retrieved by high resolution X-ray tomography. The paper presents a study of the influence of local structure variability on the elastic properties of the composite. The results are in good agreement with theoretical two-point bounds.

Based on evaluations of 3-D X-ray microtomographic reconstructions simple mean-field and multi-scale models were developed for predicting the plastic response of particle reinforced metal-matrix composites. It is shown that increasing heterogeneity, by taking more details of the microstructure into account, leads to stress-strain curves, which differ only slightly from the curve of the mean-field model.

A mean-field and a multiscale model of a particle reinforced metal–matrix composite were developed based on the knowledge of its three-dimensional microstructure obtained by holotomography. Both the mean-field and the multiscale model accounting for the distribution of particles’ local volume fractions approximate well the experimental stress–strain curves.

X-ray line profile analysis is an efficient non-destructive technique to determine some key statistical properties of dislocation structures developing during plastic deformation. In the first part of the paper recent developments describing the asymptotic behavior of the line profiles are outlined. A new evaluation method is presented to determine the average dislocation density and its spatial variation. The method is demonstrated on measurements obtained on compressed Cu single crystals. After this, it is shown that the relative dislocation density fluctuation exhibits a sharp maximum at the stages II–III transition. A nanoindentation tests indicate that the fluctuations of other quantities behave similarly. The results give new insight into the dislocation phenomena taking place in the stage III deformation regime.

Local crystallographic orientation of tensile deformed copper single crystals was investigated by the electron backscattering technique. Statistical evaluation of the data reveals the presence of an increased crystallographic correlation at the transition point between stages II and III of work-hardening. The transition state has the lowest probability of finding geometrically necessary dislocations in circular regions of radius smaller than 8 μm. According to the present results and other data showing that the relative fluctuation of the dislocation density has a maximum at the transition point, we conclude that the transition from stages II to III of work-hardening is similar to a second-order phase transformation of the statistical dislocation system.

Intergranular strain and the associated stored energy were investigated by X-ray diffraction in two texture components of cold-rolled ultra high purity (UHP) iron. Laue peaks were measured on plastically deformed samples and the center of the lines was compared with reference peaks recorded from a well-annealed powder sample of the same material. The intergranular stored energy as evaluated from the residual strain tensor was found to be much higher for the [1 1 0](0 0 1) α fibre component than for the [1 2 1](1−1 1) γ fibre component. Experimental results show that the soft α grains of the polycrystal, containing fewer dislocations, are more strained by their surrounding than hard γ grains with more dislocations. Generally intergranular strains decrease with deformation.

The elastic–plastic response of a metal–matrix composite (MMC) consisting of a AA6061-T6 aluminium matrix reinforced with 20 vol.% Al 2 O 3 particles was modeled using the finite element method. As input for the model, a real three-dimensional (3D) microstructure obtained by holotomography was used. The macroscopic behavior of the composite was obtained by multi-scale modeling based on a window-averaging and extrapolation technique. Model compression stress–strain curves obtained for a cubical volume of edge length 9–10 times larger than the two-point correlation length of the matrix show satisfactory agreement with experimental data.

The method of holotomography was applied to investigate the microstructure of a metal–matrix composite (MMC) consisting of an AA6061 aluminium matrix reinforced with 20 vol.% Al 2 O 3 particles. Various statistical functions characterizing the Al 2 O 3 particles and the matrix were evaluated, which facilitate a better understanding of the correlation between microstructural features and the overall physical properties of the composite. The shape of the particles is approximated by an ellipsoid and their spatial distribution is described in terms of the pair-distribution function of particle centers and the two-point probability functions of the component phases. The investigated statistical functions emphasize the existence of a short-range correlation in the microstructure, which has a correlation length of about two times the average nearest-neighbor distance. To understand better the influence of the particle shape on different statistical descriptors a comparison between the real microstructure and a system of random hard-spheres is presented.

Anisotropic strain broadening of diffraction peaks can be parameterised by dislocation contrast factors. A comprehensive software has been developed and made available through the internet to determine the individual and averaged contrast factors which are also compiled for cubic and hexagonal crystals. Using the theoretical and the measured values of contrast factor the microstructure of the specimen can be characterised in terms of active slip systems, Burgers vector populations, dislocation densities and crystallite size- and size distribution.

The influence of the free surface on the load carried by elastic inclusions embedded in an elastic–plastic matrix was investigated by the finite element method. A 2D multi-particle model was developed based on the statistical evaluation of the microstructure of a commercial metal–matrix composite. The results of simulated tensile tests show that the average particle stresses are sensitive to the adopted boundary conditions. Inclusions near a free boundary carry in general smaller loads than the inclusions in the bulk. Damage predictions of the model are in good agreement with the experimental data obtained by X-ray microtomography.

International audience; It was documented by Derby in 1992 that the flow stress is in power-law relationship with the steady-state grain size obtained in dynamic recrystallization. This relation has been found valid in this paper also for ultrafine-grained metals that can be obtained by severe plastic deformation. For these materials, the exponent is -0.5, which is the Hall-Petch relation. In copper, a uniform dislocation density without geometrically necessary dislocations is valid for this state. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A multi-particle 2D finite element model of a 20% particulate reinforced metal-matrix composite was developed on a statistical basis taking into account the correlations between the position, size and orientation of the ceramic particles in the matrix. The stress–strain curves in tension and compression given by the clustered multi-particle model are compared with the curves obtained from one-particle unit cell simulations. It is shown that clustering of particles increases the plastic strain accumulated in the matrix leading to a higher strain hardening and thus to a higher flow stress. The size of the representative volume element (RVE) should be at least equal to the correlation length of the geometrically relevant correlation functions, which was ∼2.4 times larger than the average interparticle distance for the experimentally studied case. Reasonable agreement is obtained between computed residual strains and data available in the literature.

Single and polycrystalline samples of Cu were deformed at a constant shear stress of 1.43×10 −3 G ( G , shear modulus). At room temperature deformation ceases owing to work hardening after formation of a cell structure; at 527 K a steady state of deformation is reached with formation of a subgrain structure which is frozen in by cooling to room temperature at constant load. The dislocation density and the internal stresses were determined by analyzing the 200 Bragg peaks measured with high resolution. Measurements under load show broadening of the peaks by deformation owing to an increase of dislocation density and a build-up of long-range internal stresses. Subsequent removal of the load causes the dislocation density to decrease by 17–30%, and the internal forward stress in the hard regions of concentrated stress to decrease by one-third. It is concluded that the factor of average stress concentration in hard regions is about 2 in the work hardened state at room temperature as well as in the steady-state deformation at 527 K.

Ball-milled WC powder has been compacted and sintered. The particle size has been determined by transmission and scanning electron microscopy and high resolution X-ray diffraction. The X-ray diffraction profiles were evaluated for particle size and dislocation densities by the recently developed procedures of modified Williamson-Hall plot and modified Warren-Averbach method. Log-normal particle size distributions have been obtained by a newly developed numerical method from the size parameters provided by X-ray line profile analysis. The size distributions obtained by TEM and X-rays are compared and discussed. The dislocation density was found to be 1.9 × 1017 m−2 in the ball-milled powder which decreases to 2.0 × 1015 m−2 after annealing.

Polycrystalline samples of Fe-0.005%-C were deformed by torsion at 300 K far into stage IV of deformation and investigated by X-ray peak profile analysis (XPA) for the microstructural evolution. The long-range internal stresses Δτ w −δτ c (τ w , τ c are the shear stresses in the cell wall and cell interior regions) pass through a maximum at the onset of stage IV, but reincrease within stage IV at higher deformation. A similar maximum is observed in the formal dislocation density derived directly from XPA which, however, is not seen in residual electrical resistivity. These results can be consistently explained by the assumption that in stages II and III the cell walls are formed as polarized dipole walls (PDW) which in stage IV change into polarized tilt walls (PTW), similarly to recent findings in cold rolled Cu. The significant constancy of total volume fraction of cell walls as well as of specific internal stresses in stage IV confirm the importance of the PTW s for stage IV strengthening.

The microstructure of ball-milled iron powder has been investigated by high resolution X-ray line profile analysis. Analysis of line breadths suggested that the contrast factors related to dislocations have to be taken into account in the Williamson-Hall procedure. This concluded to a modified Williamson-Hall plot which provided, in a straightforward manner, the grain size refinement of nanocrystals ball-milled for different periods of time. At the same time it has been shown that strain broadening, even in these nanoscale small-grain particles, is caused by the presence of dislocations. The line profiles were also studied by the method of Fourier analysis, which gave the absolute values of dislocation densities.

International audience; Application of in-situ microtomography to characterization of power law creep and creep damage in structural materials is presented. It is shown first that the successively reconstructed volumes are adequately monitoring the macroscopic sample shape and that microtomography is an optimal tool to characterize inhomogeneous specimen deformation. Based on a two-step image correlation technique the evolution of single voids is revealed and the basis of a pioneering approach to creep damage studies is presented. The method allows the unequivocal separation of three concurrent damage mechanisms: nucleation, growth, and coalescence of voids. The results indicate that growth rate of voids with equivalent diameters in the range of 2-5 mm is of about one order of magnitude higher than the prediction of continuum solid mechanics. Analysis of void coalescence points out the presence of two stable growth regimes related to coalescence between primary and secondary voids, respectively.

International audience; Damage distribution in a notched hollow cylinder made of E911 steel and crept for 26,000 h at 575 °C under multi-axial stress state is assessed. Based on high-resolution tomographic reconstructions the size, shape and spatial distribution of voids along the notch radius have been characterized. The spatial distribution of void density shows strong correlation with stress triaxiality, maximum principal stress and the equivalent von Mises stress. The analysis of the size distribution of non-coalesced voids in terms of general power-law functions describing nucleation and growth indicates that void growth in E911 steel is dominated by the constrained diffusion mechanism.

International audience; A new method for the evaluation of the apparent activation energy of steady-state creep in metals is presented. It is based on in situ monitoring by microtomography the geometry of a specimen subjected to uniaxial load and inhomogeneous temperature distribution. It is shown that microtomography acting as a three dimensional extensometer enables the evaluation of local strain-rates of small material volumes and is an adequate tool for characterization of inhomogeneously deforming specimens. Activation energies obtained with the new method for stainless steel agree within an error of 5% with values obtained according to the classical procedure.

The deformation mechanisms during indentation of aluminum-based metal foams are examined by use of X-ray tomography and the finite element method. The deformation was found to be almost totally restricted to a spherical cap-shape compacted zone under the indenter. An analytical expression is given which describes the changes in the size of the compacted zone as a function of the diameter of the indenter, the indentation depth and the relative density of the foam. Results of finite element simulations and the calculated function were found to be in reasonably good agreement.

International audience