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A multi-modal data-merging framework that enables the reconstruction of slip bands in three dimensions over millimeter-scale fields of view is presented. The technique combines 3D electron back-scattered diffraction (EBSD) measurements with high-resolution digital image correlation (HR-DIC) information collected in the scanning electron microscope (SEM). A typical merging workflow involves the segmentation of features within the strain field (slip bands, deformation twins) and the microstructure (grains), alignment of datasets and the projection of slip bands into the 3D microstructure, using the knowledge of the local crystallographic orientation. This method is demonstrated in two materials: a face-centered cubic (FCC) nickel-base superalloy and hexagonal close-packed (HCP) titanium alloy.

The details of polycrystalline microstructure often influence the early stages of yielding and strain localization under monotonic and cyclic loading, particularly in elastically anisotropic materials. A new software package, MechMet (mechanical metrics) provides a convenient finite element tool for solving field equations for elasticity in polycrystals in conjunction with investigations of microstructure-induced heterogeneity. The simulated displacement field is used to compute several mechanical metrics, such as the strain and stress tensors, directional stiffness, relative Schmid factor, and the directional strength-to-stiffness ratio. The virtual polycrystal finite element meshes needed by MechMet can be created with the Neper package or any other method that produces a 10-node, tetrahedral, serendipity element. Formatted output files are automatically generated for visualization with Paraview or VisIt. This paper presents an overview of the MechMet package and its application to polycrystalline materials of both cubic and hexagonal structures.

Titanium alloys are processed to develop a wide range of microstructure configurations and therefore material properties. While these properties are typically measured experimentally, a framework for property prediction could greatly enhance alloy design and manufacturing. Here a microstructure-sensitive framework is presented for the prediction of strength and ductility as well as estimates of the bounds in variability for these properties. The framework explicitly considers distributions of microstructure via new approaches for instantiation of structure in synthetic samples. The parametric evaluation strategy, including the finite element simulation package FEpX, is used to create and test virtual polycrystalline samples to evaluate the variability bounds of mechanical properties in Ti-6Al-4V. Critical parameters for the property evaluation framework are provided by measurements of single crystal properties and advanced characterization of microstructure and slip system strengths in 2D and 3D. Property distributions for yield strength and ductility are presented, along with the validation and verification steps undertaken. Comparisons between strain localization and slip activity in virtual samples and in experimental grain-scale strain measurements are also discussed.

The microstructural origins of highly localized elastic strain concentrations in polycrystalline microstructures under monotonic loading are studied using grain-scale, in situ digital image correlation and crystal plasticity finite element method. It is shown that the locations of exceptionally high elastic strain concentrations in the microstructure depend on particular crystallographic and morphological orientations of grains and less so on crystalline details of their local neighborhood. Based on these results, we discuss how topological and crystallographic features of annealing twin boundaries can increase the likelihood of slip band initiation throughout the microstructure of polycrystalline Ni-base superalloys.

Pathways for ductility Alloys containing multiple elements can be very strong but often suffer from poor ductility. F. Wang et al. found that different mechanisms accommodated plasticity in a molybdenum-niobium-titanium multiprincipal element alloy (see the Perspective by Cairney). Instead of so-called “screw” dislocations, deformation is accommodated by multiple pathways that include “edge” dislocations and activation of crystallographic slip planes. These results offer a design paradigm for developing new high-strength alloys. Science , this issue p. 95 ; see also p. 37

Background: Advancements in the Digitial Image Correlation (DIC) technique over the past decade have greatly improved spatial resolution. However, many processes, such as plastic deformation, have a temporal component spanning from fractions of a second to minutes that has not yet been addressed in detail, particularly for DIC conducted in-situ in the scanning electron microscope (SEM). Objective: To develop a methodology for conducting time-resolved digital image correlation in the SEM for analysis of time-dependent mechanical deformation phenomena. Methods: Microscope and electron beam scanning parameters that influence the rate at which time-resolved DIC information is mapped are experimentally investigated, providing a guide for use over a range of timescales and resolutions. Results: Time-resolved DIC imaging is demonstrated on a Ti-7Al alloy, where slip band propagation is resolved with imaging dwell times of seconds. The limits of strain resolution and strain collection speeds are analyzed. Conclusions: The new developed methodology can be applied to a wide range of materials loaded in-situ to quantify time-dependent plastic deformation phenomena.

International audience; Fatigue crack nucleation in crystalline materials typically develops due to highly localized cyclic slip. During a fatigue cycle, reverse slip differs locally from slip in the forward direction particularly in precipitate-containing materials such as superalloys. In this paper we report the first direct measurements of irreversibility at the scale of individual slip bands by high-resolution digital image correlation (DIC) in a polycrystalline nickel-based superalloy. Quantitative measurements of the slip irreversibility are challenging for regions of material that have a size that captures the microstructure and its variability. High spatial resolution at the nanometer scale during experimental measurements is needed to observe slip localization during deformation. Moreover, large fields are also needed to obtain the material response over statistically representative populations of microstructural configurations. Recently, high resolution scanning electron microscope (SEM) digital image correlation (DIC) has been extended for quantitative analysis of discontinuities induced by slip events using the Heaviside-DIC method. This novel method provides quantitative measurements of slip localization at the specimen surface. In this paper, the Heaviside-DIC method is used to measure slip irreversibility and plastic strain accumulation in a nickel-based superalloy. The method detects bands with high levels of irreversibility early in cycling that ultimately form fatigue cracks upon further cycling. The local microstructural configurations that induce large amounts of plasticity and slip irreversibility are correlated to crack nucleation locations.

International audience; Non-metallic inclusions (NMIs) and slip bands parallel to and slightly offset from twin boundaries are observed to be preferential sites for fatigue crack nucleation in wrought superalloys. Potential interactions between NMI cracking and slip activity within neighboring grains or at twin boundaries were investigated under monotonic tensile loading (up to 1.3% total strain) at room temperature. High resolution- and Heaviside-digital image correlation measurements were performed during interrupted tensile loading to identify strain localization, associated slip systems, and damage initiation. Different mechanisms and scenarios were identified: (1) Microplasticity generally starts at twin boundaries even at stresses as low as 70% of the macroscopic yield strength, (2) transgranular slip activity intensively develops above the macroscopic yield stress, (3) intense slip activity develops near and parallel to 21% of the twin boundaries intercepting NMIs, (4) 7% of the twin boundaries intercepting NMIs lead to slip-assisted NMI cracking, (5) no transgranular slip activity participates in NMI cracking, (6) the fraction of cracked NMIs progressively increases with the load, and (7) within the NMIs that initiated cracks, 67% cracked below 90% of the macroscopic yield strength without the presence of slip activity in the neighboring grains. While slip-assisted NMI cracking was evidenced in the present study, most NMI cracking is due to strain incompatibility between NMIs and neighboring grains at the high end of the elastic regime without slip interaction.

A new class of $$\gamma ^{\prime }$$-containing Co-based superalloys that are promising for high temperature applications has been investigated under cyclic loading conditions. A series of single crystal variants of these Co-based superalloys have been cyclically loaded above their elastic limit at $$750\,^{\circ }\hbox {C}$$ in air to study their behavior in the low cycle regime. Interrupted testing was performed to observe the early stages of fatigue failure. Optical microscopy, scanning electron microscopy, and transmission electron microscopy were used to characterize post-mortem specimens. Fatigue failure occurred due to surface cracks that developed during the early stages of cycling in the aluminide-coated sample gauge sections. Growth of these surface cracks into the substrate was associated with extensive oxidation and intermetallic phase precipitation, which accelerated crack propagation as compared to Ni-based superalloys. These observations suggest that improvements in the oxidation resistance and high temperature strength of $$\gamma ^{\prime }$$-containing Co-based superalloys will enhance their fatigue behavior.

Micro-tensile specimens of nickel-based superalloy oligocrystals were tested in-situ in an scanning electron microscope in transmission mode (TSEM) enabling observation of dislocations. The dynamics of dislocation motion during tensile loading were captured and correlated with the measured intermittencies during plastic flow recorded by high load- and temporal-resolution sensors. This investigation in particular focused on the dislocation behavior near twin boundaries with different slip configurations. A multiplicity of deformation mechanisms at the dislocation scale were observed within individual slip bands, including precipitate shearing, dislocation decorrelation and antiphase boundary-coupled shearing. These processes affect strain localization near twin boundaries and provide new defect-level insights on plastic localization and fatigue crack initiation in these alloys.

This paper develops a Bayesian, probabilistic crack nucleation model in the Ni-based superalloy Ren\'e 88DT for fatigue loading. A data-driven, machine learning approach is developed to identify the underlying mechanics driving crack nucleation. An experimental set of fatigue-loaded microstructures is characterized near crack nucleation sites using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) images to correlate grain morphology and crystallography to the spatial location of crack nucleation sites. A concurrent multiscale model that embeds polycrystalline microstructures, created from the EBSD images, in a self-consistent homogenized material is developed for low cycle fatigue simulations needed to create a database of state variables. The polycrystalline domain is modeled by a crystal plasticity finite element model (CPFEM), while a homogenized anisotropic plasticity model is used for the exterior domain. A Bayesian classification method is introduced to optimally select the most informative state variable predictors of crack nucleation and constructs a near-Pareto frontier of models with varying complexity. From this principal set of state variables, a simplified scalar crack nucleation indicator is formulated which encompasses all of the relevant components derived from the main discriminators. This Bayesian approach allows the micromechanical state variables responsible for causing crack nucleation events to come out naturally from existing data. The final result is a model that predicts the probability of nucleating a crack at a microstructural location, given the mechanical state of the material.

The advancement of materials science at the mesoscale requires improvements in both sampling volumes/areas and spatial resolution in order to make statistically significant measurements of microstructures that influence higher-order material properties, such as fatigue and fracture. Therefore, SEM-based techniques have become desirable due to improvements in imaging resolution, large sample handling capability, and flexibility for in-situ instrumentation. By using fast sampling of SEM electron detector signals, intrinsic beam scanning defects have been identified that are related to the response time of the SEM electron beam deflectors and electron detectors. Mitigation of these beam scanning defects using detector sampling approaches and an adaptive model for settling time is shown to produce higher resolution SEM images, at faster image acquisition times, with a means to quantify the different response functions for various beam deflectors and detectors including those for electrons and ions.

Quantification of mesoscale microstructures of polycrystalline materials is important for a range of practical tasks of materials design and development. The current protocols of quantifying grain size and morphology often rely on microstructure metrics (e.g., mean grain diameter) that overlook important details of the mesostructure. In this work, we present a quantification framework based on directionally resolved chord length distribution and principal component analysis as a means of extracting additional information from 2-D microstructural maps. Towards this end, we first present in detail a method for calculating chord length distribution based on boundary segments available in modern digital datasets (e.g., from microscopy post-processing) and their low-rank representations by principal component analysis. The utility of the proposed framework for capturing grain size, morphology, and their anisotropy for efficient visualization, representation, and specification of polycrystalline microstructures is then demonstrated in case studies on datasets from synthetic generation, experiments (on Ni-base superalloys), and simulations (on steel during recrystallization).

This paper details the creation of experimental and computational frameworks to capture high-resolution, microscale deformation mechanisms and their relation to microstructure over large (mm-scale) fields of view. Scanning electron microscopy with custom automation and external beam control was used to capture 209 low-distortion micrographs of 360 μm × 360 μm each, that were individually correlated using digital image correlation to obtain displacement/strain fields with a spatial resolution of 0.44 μm. Displacement and strain fields, as well as secondary electron images, were subsequently stitched to create a 5.7 mm × 3.4 mm field of view containing 100 million (7678 × 13,004) data points. This approach was demonstrated on Mg WE43 under uniaxial compression, where effective strain was shown to be relatively constant with respect to distance from the grain boundary, and a noticeable increase in the effective strain was found with an increase in the basal Schmid factor. The ability to obtain high-resolution deformations over statistically relevant fields of view enables large data analytics to examine interactions between microstructure, microscale strain localizations, and macroscopic properties.

This paper has three major objectives related to the development of computational micromechanics models of Ni-based superalloys, containing a large number of annealing twins. The first is the development of a robust methodology for generating 3D statistically equivalent virtual polycrystalline microstructures (3D-SEVPM) of Ni-based superalloys. Starting from electron backscattered diffraction (EBSD) images of sections, the method develops distributions and correlation functions of various morphological and crystallographic parameters. To incorporate twins in the parent grain microstructure, the joint probability of the number of twins and parent grain size, and the conditional probability distributions of twin thickness and twin distance are determined. Subsequently, a method is devised for inserting twins following the distribution functions. The overall methodology is validated by successfully comparing various statistics of the virtual microstructures with 3D EBSD data. The second objective is to establish the microstructure-based statistically equivalent representative volume element or M-SERVE that corresponds to the minimum SERVE size at which the statistics of any morphological or crystallographic feature converge to that of the experimental data. The Kolmogorov–Smirnov (KS) test is conducted to assess the convergence of the M-SERVE size. The final objective is to estimate the property-based statistically equivalent RVE or P-SERVE, defined as the smallest SERVE, which should be analyzed to predict effective material properties. The crystal plasticity finite-element model is used to simulate SERVEs, from which the overall material response is computed. Convergence plots of material properties including the yield strength and hardening rate are used to assess the P-SERVE. A smaller P-SERVE compared to the M-SERVE indicates that the characteristic features of twins implemented in determining the M-SERVE are more stringent than those for determining material properties.

Cyclic fatigue experiments in the high and very high cycle fatigue regimes have been performed on a Rene 88DT polycrystalline nickel-based superalloy. The microstructural configurations that favor early strain localization and fatigue crack initiation at high temperature from 400 °C to 650 °C have been investigated. Competing failure modes are observed in the high to the very high cycle fatigue regime. Fatigue cracks initiate from non-metallic inclusions and from intrinsic internal microstructural features. Interestingly, as stresses are reduced into the very high cycle regime, there is a transition to initiation only at crystallographic facets. At higher stress in the high cycle fatigue regime, a significant fraction of specimens initiate cracks at non-metallic inclusions. This transition is analyzed with regard to microstructural features that favor strain localization and accumulate damage early during cycling.

First-principles DFT methods are combined with an experimental approach to characterize the creep behavior of quinary Co-based L1 $$_2$$ -containing superalloys at elevated temperature conditions. Temperature-dependent SISF energies have been modeled, combining 0 K formation energies with vibrational free energy calculations to assess deformation mechanisms at finite temperature. Two different Co-Al-W alloys, containing the maximum possible amount of DFT-identified d-block alloying additions, were identified and cast as single crystals via the Bridgman process. Creep tests have been performed at two primary testing conditions, one at 900 $$^\circ $$ C and the other at 982 $$^\circ $$ C. Transmission scanning electron microscopy (TSEM) was performed at 30 kV in a scanning electron microscope to rapidly characterize the defect substructures. We observe a coupled APB/SISF/APB defect structure in Co-based superalloys at the low-temperature condition, similar to the defect structure observed in CoNi, in spite of containing no Ni. At 982 $$^\circ $$ C, there is no evidence of faults and precipitates instead contain antiphase boundaries. The role of composition and temperature-dependent fault energies in the deformation process is addressed.

The microstructural configurations that favor early strain localization and fatigue crack initiation at intermediate and high temperature (400 °C–650 °C) have been investigated using novel experimental techniques, including high resolution digital image correlation and transmission scanning electron microscopy. Cyclic fatigue experiments in the high and low cycle fatigue regimes have been performed on a Rene 88DT polycrystalline nickel-base superalloy at temperatures up to 650 °C and compared to previous fatigue results obtained from tests in the very high cycle fatigue regime. Competing failure modes are observed along with an inversion in the temperature fatigue life dependence of fatigue strength from the low to high cycle fatigue regime. Oxidation-assisted processes are dominant at high applied stresses while cyclic plastic localization and accumulation govern fracture at low applied stresses. In addition, a second competing mode exists in the high and very high cycle fatigue regime from non-metallic inclusions as compared to internal intrinsic initiation sites. The grain-scale features that exhibit strain localization and crack initiation were investigated in detail. Transmission electron microscopy (TEM), transmission scanning electron microscopy (TSEM) and electron channeling contrast imaging have been conducted on samples removed from targeted regions with microstructural configurations that favor crack initiation to characterize the associated dislocation sub-structure and its evolution with temperature. Plasticity is observed to be less localized during cyclic loading at high temperature compared to room temperature. The microstructural features that drive initiation across the temperature range investigated are: twin-parent grains pairs that are at the upper end of the size distribution, are oriented for near maximum elastic modulus mismatch, and have high stresses along planes parallel to the twin boundaries.

In this work, we investigate the relationship between an intense slip band (ISB) and the zone of large lattice rotations that forms ahead of the tip of the ISB. We develop a crystal plasticity finite element model of a discrete ISB lying within an oligocrystalline assembly and calculate the local crystalline stress and lattice rotation fields generated by the ISB. The calculations demonstrate that, first, a region of severe lattice rotations, commonly referred to as a microvolume, does not form without the ISB, and second, large amounts of accumulated slip in the ISB are required to enlarge the microvolume to sizes and rotation magnitudes observed experimentally. Ahead of the ISB tip, the quintessential plastic zone always forms, but the atypical microvolume forms when non-concentrated and spatially diffuse slip is activated by the ISB-induced stress field. This result suggests that the detrimental ISB/microvolume pair will likely appear in pairs of crystals in which transmission of the slip from the ISB is severely blocked by the grain boundary, a hypothesis that we verify with a few target cases.

Fatigue crack nucleation at annealing twin boundaries (TBs) within polycrystal nickel-based superalloy Rene 88 D T is investigated with a microstructure-sensitive crystal plasticity (CP) model, digital image correlation strain measurements and experimental SEM crack nucleation observations. Strong slip localizations at TBs were experimentally observed and predicted by the CP model, which also showed high predicted geometrically necessary dislocation and corresponding stored energy densities, capturing experimental observations of crack nucleation. In a systematic study, elastic anisotropy was found to drive local elastic constraint and hence resolved shear stress, slip activation, GND density and stored energy density, demonstrating for this reason that TBs are preferential sites for crack nucleation in this alloy. The parent grain / twin pair crystallographic orientation with respect to remote loading was also demonstrated to be key to slip activation parallel to TBs and hence to stored energy density and fatigue crack nucleation, and the range of most damaging parent grain orientations has been identified.

The process of crack initiation has been investigated in three widely used titanium alloys with different microstructures and loading conditions. Using low-cycle fatigue tests, a unique crack nucleation mechanism involving strain localization at ( 0001 ) twist boundaries has been identified. In order to constitute a potential crack initiation site, the twist boundary must experience a high resolved shear stress and a high normal stress. Crack initiation at these boundaries is most frequently associated with twist angles spanning the 10° - 20° range. Deformation prior to crack initiation at these rare microstructural configurations has been characterized using transmission electron microscopy and high-resolution digital image correlation across large fields of view. The ( 0001 ) twist boundaries are preferential locations for early and intense strain localization. Prior to crack nucleation, deformation proceeds via shear along such boundaries where no β layer at the interface was evidenced. The presently discussed crack formation mechanism is believed to be of broad relevance as it is not significantly influenced by microstructural parameters such as the α grain size, the degree of microtexture, the β phase fraction or the surrounding microstructure as well as α and β compositions.

International audience; The slip localization behavior of the polycrystalline nickel base superalloy Inconel 718 during monotonic tensile loading at room temperature, is investigated for the first time in relation to the 3D microstructure. Multi-modal data merging tools are used to recombine high resolution digital image correlation (HR-DIC) data with 3D electron back-scatter diffraction tomography (3D EBSD), over a wide region of interest. This procedure enables reconstruction of the slip band planes in the 3D microstructure. Statistical analyses conducted over 500 individual slip bands reveal strong correlations between their location and specific microstructure configurations. In particular, over half of the slip bands emanate from triple junction lines (3D lines defined by the junction of three crystals). Moreover, the most intense and longest slip bands, which would become critical fatigue crack nucleation sites during cyclic loading, are located close and parallel to particular annealing twin boundaries and are simultaneously connected to triple junction lines. Crystal plasticity finite elements calculations are performed on the experimental microstructure to identify the slip activity that results in the formation of high intensity slip bands (localized plasticity) or zones of high lattice rotation (non-localized plasticity) in these particular microstructure regions.

In advanced engineering alloys where inclusions and pores are minimized during processing, the initiation of cracks due to cyclic loading shifts to intrinsic microstructural features. Criteria for the identification of crack initiation sites, defined using elastic-plastic loading parameters and twin boundary length, have been developed and applied to experimental datasets following cyclic loading. The criteria successfully quantify the incidence of experimentally observed cracks. Statistical microstructural volume elements are defined using a convergence approach for two nickel-base superalloys, IN100 and Rene 88DT. The material element that captures the fatigue crack-initiating features in Rene 88DT is smaller than IN100 due to a combination of smaller grain size and higher twin density.

A computational study of 3D virtual instantiations of microtextured Ti-6Al-4V with varying initial slip system strengths is presented. Electron backscatter diffraction (EBSD) scans of a rolled and heat-treated mill annealed plate were used in order to determine the approximate geometric morphology of both the grain structure and the microtextured regions. Data from the EBSD experiments were used to calculate representative orientation distribution functions (ODFs) and grain size distributions for the α (HCP) crystallographic phase. Laguerre tessellations were employed to create idealized geometric representations of the microstructure and microtextured regions, while orientations were sampled from the experimentally derived ODFs. A highly parallelized crystal plasticity finite element framework was used to model the deformation response of single phase polycrystals under uniaxial tension, with attention paid to the intragrain slip system activity. Simulations were conducted with changes in the orientations within microtextured regions, as well as with various sets of initial slip system strengths to reflect differences in reported values in literature. Results were compared to a strength-to-stiffness parameter designed to predict succession of yield as a function of orientation. Presented are slip activity trends as a function of microstructure and initial slip system strengths, as well as results concerning the development of long-range localization of plasticity as a function of the microstructure. Predictions are compared to slip system activity measured by scanning electron microscope based digital image correlation.

This paper applies the three-dimensional visualization techniques explored theoretically by Callahan, Echlin, Pollock, Singh & De Graef [J. Appl. Cryst.(2017),50, 430–440] to a series of experimentally acquired texture data sets, namely a sharp cube texture in a single-crystal Ni-based superalloy, a sharp Goss texture in single-crystal Nb, a random texture in a powder metallurgy polycrystalline René 88-DT alloy and a rolled plate texture in Ti-6Al-4V. Three-dimensional visualizations are shown (and made available as movies as supplementary material) using the Rodrigues, Euler and three-dimensional stereographic projection representations. In addition, it is shown that the true symmetry of Euler space, as derived from a mapping onto quaternion space, is described by the monoclinic color space groupPccin the Opechowski and Guccione nomenclature.

International audience; The recent development of the high resolution and discontinuity-tolerant digital image correlation technique enables the extraction of discontinuities within a displacement field. The technique provides quantitative analysis of discontinuities arising from slip, shear bands, cracks, and grain boundary sliding in a variety of material systems, including polycrystalline metallic materials. The discontinuity-tolerant digital image correlation method can be implemented to retrieve not only quantitative discontinuity analysis but also the local strain and rotation fields that operate near these discontinuities. The present implementation includes high-resolution digital image correlation (HR-DIC) measurements collected in a scanning electron microscope for analysis of both the plastic and elastic fields that develop during deformation of polycrystalline metallic materials. The combination of the discontinuity-tolerant DIC technique with the computation of internal gradients enables extraction of non-localized strain and rotation fields during plastic deformation of a nickel-based superalloy. Therefore the lattice rotation/expansion and plastic localization that occur during deformation can be determined in a single experiment. This method is validated using synthetic images with preset deformation, and experimental measurements using the electron back scatter diffraction (EBSD) technique.

The component design and fatigue life prediction of turbine disk alloys are critically dependent on the thermomechanical properties of the material. The TriBeam microscope provides a pathway to capture large, targeted 3D microstructural data volumes from turbine disk alloys in order to instantiate models that are used to simulate mechanical loading and assess material properties. The TriBeam experiments used to capture the microstructure, the analysis methods, data requirements, and future needs for 3D infrastructure will be discussed.

Thermomechanical processing routes are used to produce microstructures that minimize plastic strain localization at the sub-grain scale in a polycrystalline \(\gamma -\gamma \)’ nickel-based superalloy. This novel approach is made possible by the use of innovative experimental tools and statistical data analysis that capture slip events over large representative fields of view. Results are correlated to conventional observations of fatigue crack initiation and early stage of propagation. The effect of coherent twin boundaries and primary \(\gamma '\) precipitates on fatigue properties and plastic localization is detailed.

This chapter discusses fundamental aspects of the development of statistically equivalent virtual microstructures (SEVMs) and microstructure and property-based statistically equivalent representative volume elements (M-SERVE and P-SERVE) of the Ni-based superalloy at multiple scales. The two specific scales considered for this development are the subgrain scale of intragranular γ − γ′ microstructures and the polycrystalline scale of grain ensembles with annealing twins. A comprehensive suite of computational methods that can translate microstructural data in experimental methods to optimally defined representative volumes for effective micromechanical modeling is the objective of this study. The framework involves a sequence of tasks, viz., serial sectioning, image processing, feature extraction, and statistical characterization, followed by micromechanical analysis and convergence tests for statistical functions. A principal motivation behind this paper is to translate high-fidelity microstructural image data into statistics of parametric descriptors in constitutive laws governing material performance.

International audience; The mechanical properties of titanium alloys result from their complex multi-scale microstructural features, including micron scale precipitates and millimeter scale microtextured regions (MTRs). While previous investigations have revealed that the presence of mm-scale MTRs can degrade mechanical properties, particularly fatigue, the accompanying strain localization processes that operate at the microscale within the α grains in MTRs are not well understood. The present work is a mechanistic investigation of MTRs using crystal plasticity simulations of mm3-scale experimentally captured and synthetically generated 3D microstructure datasets. The explicit modeling of both the α grains and MTRs in Ti–6Al–4V enables assessment of the effect of microtexture and local structure variations within the MTR on overall deformation behavior and the onset of plastic slip in MTRs. The presence of MTRs with a dominant [0001] orientation results in both stress and plastic strain hotspots during the early stages of straining. Crystal plasticity predictions are compared to previous digital image correlation studies on early strain localization. The influence of MTRs on the local stress and strain fields is discussed with regard to the monotonic tension, fatigue and dwell-fatigue behavior of titanium alloys.

Fatigue cracks initiating from surface and sub-surface non-metallic inclusions (NMIs) have recently been demonstrated to be a necessary but not sufficient explanation for atypically short low-cycle fatigue life in Inconel 718 alloy at intermediate temperature. Therefore, the early stages of short crack propagation from surface NMIs were investigated in a crystallographic and two-dimensional versus three-dimensional morphological manner after room temperature low cycle fatigue (LCF) testing. In the present investigation, NMIs were purposely pre-cracked using different techniques to suppress the natural crack initiation period and thus the incubation period prior to the early stages of crack propagation. Under such fatigue testing conditions, different mechanisms of crack transmission from pre-cracked NMIs were identified: (i) no propagation, (ii) NMI/adjacent metallic grain interfacial debonding, (iii) transgranular crack propagation within the adjacent metallic grain. Focused-ion-beam cross-section observations of numerous fatigue tested NMIs aimed to define a morphological criterion for non-propagating NMIs. Large cracked NMIs at the surface (2c) with limited extension into the depth (a) did not propagate under such fatigue conditions for 2c/a ratio higher than 3. Furthermore, specific crystallographic relationships between NMIs and the adjacent metallic grain explained different crack propagation configurations from pre-cracked NMIs, i.e. interfacial debonding and transgranular crack propagation involving single or multiple-slip activity.

Fatigue crack initiation at high temperatures occurs at microscopic fatigue shear bands that form near twin boundaries in polycrystalline nickel-base superalloys that contain minimal metallurgical defects. The associated dislocation sub-structure is complex and dependent on thermal and mechanical conditions. Here we show the formation of fine-scale carbide precipitates along these fatigue shear bands in a nickel-base superalloy during fatigue above 650 °C. The formation of carbide precipitates is studied using calculations of bulk and pipe diffusion. The contribution of pipe diffusion is observed to be critical in the formation of fine-scale carbides and occurs coincident with the delocalization of slip during fatigue.

The equiaxed microstructure of Ti-6Al-4V contains nominally 10µm to 15µm α -phase grains. Depending on processing, these fine grains may aggregate into large, millimeter-scale regions of similar crystallographic orientation. These so-called microtextured regions are detrimental to quasi-static and fatigue properties. Their presence may facilitate the formation of long-range strain localization—bands of plastic strain that traverse grain boundaries and terminate at the boundaries of the microtextured region which compromises strength and ductility—and can cause early fatigue crack nucleation. Furthermore, the low angle boundaries within microtextured regions offer little resistance to crack growth, and corresponding increases in crack growth rates have been observed in these regions. Despite significant research into the effects of microtextured regions on macroscopic properties, there is still a lack of rigorous definition of what constitutes a microtextured region. To this end, we present a computational study in which deformation simulations are performed to study the effect of the intensity and character of microtexture on the localization of plastic strain. Mean orientation and intensity of microtexture are parameterized in a suite of simulations. Simulations indicate that strain localization is facilitated both by the presence of some amount of orientation spread within a microtextured region, and further by the intensity of microtexture in neighboring regions. Simulations are further discussed with respect to high resolution experimental measurements of intragrain strain in a microtextured Ti-6Al-4V specimen, which exhibit similar mechanical trends.

The local mechanical properties of a dissimilar friction stir welded AA-2024-T3/AA-2198-T3 joint were documented during a uniaxial tensile test. High-resolution digital image correlation was performed during monotonic tensile tests to capture the local in-plane strain fields of the heterogeneous macrostructure of the weld. In the shoulder-affected region, banded macrostructures with heterogeneous mechanical properties were found. They were related to pronounced textures regions, which can be associated to strain-rate gradient during one rotation of the tool. The banded macrostructures in the nugget region were observed to be responsible for early plasticity in the joint and ultimately to be the fracture location of the weld. The heterogeneous mechanical response of the joint was also investigated by microhardness measurements. Differences were found between hardness and local tensile properties, demonstrating microhardness measurements can be misleading and only direct high-resolution digital image correlation techniques can document the mechanical behavior of materials having complex and heterogeneous micro-/macrostructures. Keywords: Friction stir welding (FSW), Digital image correlation (DIC), Electron backscattered diffraction (EBSD), Texture, Aluminum alloys, Banded macrostructures, Microhardness, Dissimilar joint

High resolution scanning electron microscope digital image correlation (SEM DIC) was performed in situ during uniaxial loading on Ti-6Al-4V rolled titanium plate to determine the dependence of strain localization on microstructure and microtexture. Individual grains with preferred orientation for basal slip exhibited plastic localization along basal planes before macroscopic yielding. With additional strain, but still below macroscopic yielding, pyramidal and prismatic plastic activity was observed as slip bands transmitting across many grains and entire microtextured regions (MTRs). The localization of long range plastic strain occurred within MTRs that allowed for slip transmission across grains with low angle boundaries. The rolled titanium plate material having strong [ 0001 ] and [ 10 1 ¯ 0 ] texture components showed pyramidal and prismatic type slip extending across entire MTRs at strains well below macroscopic yielding. These strain localization processes occur much earlier in straining and over lengthscales much longer than observed with conventional slip offset imaging. The implications for properties are discussed.

The mechanical properties of titanium alloys result from their complex multi-scale microstructural features such as micron scale precipitates and millimeter scale microtextured regions (MTRs). Deformation processes that operate at the scale of the α grain are of critical importance to mechanical properties, especially to fatigue performance. However, previous investigations also highlighted that the mm-scale MTRs affect the mechanical properties of titanium alloys. Specifically, MTRs promote long-range strain localization due to the low intergranular misorientation within a MTR. Furthermore, the elastic anisotropy of the alpha phase and the non-random spatial distribution of crystallographic orientations within the MTRs produce complex mechanical effects. The present work is a mechanistic investigation of MTRs using crystal plasticity simulations of mm3-scale experimentally captured and synthetically generated 3D microstructure datasets. The explicit modeling of both the α grains and MTRs in a titanium alloy is used to determine the effect of the degree of microtexture on the deformation behavior and on the onset of plastic slip. The presence of MTRs with a dominant [0001] orientation results in both stress and plastic strain hotspots during the early stages of straining. The influence of MTRs on the local stress and strain fields are analyzed and discussed with regard to the monotonic tension, fatigue and dwell-fatigue behavior of titanium alloys.

Fatigue crack nucleation in crystalline materials typically develops due to highly localized cyclic slip. During a fatigue cycle, reverse slip differs locally from slip in the forward direction particularly in precipitate-containing materials such as superalloys. In this paper we report the first direct measurements of irreversibility at the scale of individual slip planes in a polycrystalline nickel base superalloy. Quantitative measurements of the slip irreversibility is challenging to be performed for regions of material that have a size that captures the microstructure and its variability. High spatial resolution at the nanometer scale during experimental measurements is needed to observe slip localization during deformation. Moreover, large fields are also needed to obtain the material response over statistically representative populations of microstructural configurations. Recently, high resolution scanning electron microscope (SEM) digital image correlation (DIC) has been extended for quantitative analysis of discontinuities induced by slip events using the Heaviside-DIC method. This novel method provides quantitative measurements of slip localization at the specimen surface. In this paper, the Heaviside-DIC method is used to measure slip irreversibility and plastic accumulation in a nickel base superalloy. The local microstructural configurations that induces large amounts of plasticity and slip irreversibility are captured and correlated to crack nucleation locations.

International audience; High-resolution digital image correlation (HR-DIC) techniques have become essential in material mechanics to assess strain measurements at the scale of the elementary mechanisms responsible of the deformation in polycrystalline materials. The purpose of this study is to demonstrate the use of laser scanning confocal microscopy (LSCM) coupled with DIC techniques to deepen knowledge on the deformation process of polycrystalline nickel-based superalloy at room temperature. The LSCM technique is capable of detecting both in-plane and out-of-plane strain localization within slip bands at the sub-grain level. The LSCM observations are consistent with previous in-situ scanning electron microscopy (SEM) studies: The onset of crystal plasticity occurs primarily near Σ3 twin boundaries with bulk locations in the elastic domain (macroscopic stress as low as 80% of the 0.2 % offset yield strength (Y.S.0.2%)). This intense irreversible strain localization occurs with either a high Schmid factor (μ > 0.43) or a significant elastic modulus difference between the pair of twins (ΔΕ > 100 GPa). In the plastic deformation domain, transgranular slip activity following slip systems with the highest Schmid factor is mostly responsible for the deformation at the grain level, thus leading to strain percolation. The simultaneous in-plane and out-of-plane deformation assessment via the HR-LSCM-DIC technique was found to be essential for the identification of active slip systems. Finally, the HR-LSCM-DIC technique enabled the quantification of the real glide amplitude involved in the three-dimensional shearing process at the grain level that solely in-plane measurements cannot provide.

International audience; High resolution scanning electron microscopy (HR-SEM) and laser scanning confocal microscopy (HR-LSCM) digital image correlation (DIC) techniques were investigated for assessing strain distribution within individual grains during deformation in the macroscopic elastic and plastic regime. The anisotropic response of a Ni-based polycrystalline superalloy was experimentally demonstrated at the grain scale. Local plastic strain localization within preferentially oriented grains was documented under loading as low as 80% of the macroscopic yield strength of the material. Intense strains along bands were observed in the macroscopic plastic regime, correlating with {111}[1-10] slip systems.

Damage initiation during cycling loading of polycrystalline metallic alloys involves localized damage at the scale of individual grains. To better understand damage processes and to build models for material behavior, there is a need for quantitative assessment of the microstructural configurations that favor fatigue crack initiation. In materials that form annealing twins during processing, these special interfaces are often locations of particular interest for their role in strain and damage accumulation. In the present study, fatigue experiments in the very high and low cycle fatigue regime on a Rene 88DT polycrystalline nickel-base superalloy were performed to statistically evaluate grain-scale features that favor crack initiation. Combined elastic and plastic criteria at the grain scale have been developed. A crack distribution function is defined to compare and assess the effect of the microstructural parameters for the two fatigue regimes.

Damage during cycling loading of polycrystalline metallic alloys involves localized plastic straining at the scale of individual grains. To better understand damage accumulation processes and to build models for material behavior there is a need for quantitative assessment of the heterogeneous strain fields at the grain and even more microscopic scales. In the present study, a digital image correlation (DIC) approach has been developed to measure the strains at the grain level and at finer scales where plastic strain localization is manifested as physical slip bands. Strain fields have been measured in situ and ex situ on a Rene 88DT polycrystalline nickel-based superalloy to assess the grain-scale deformation processes during monotonic straining in tension and compression. DIC analysis and transmission electron microscopy demonstrate that slip occurs in a highly localized manner. The highest localized strains developed in slip bands that formed on {1 1 1} planes parallel to, and slightly offset from, annealing twins. Enhanced local straining below yield was observed during compression loading. The degree of strain concentration caused by slip bands impinging on grain boundaries was also analyzed. The results are compared to predictions of plasticity models.

Damage during loading of polycrystalline metallic alloys is localized at or below the scale of individual grains. Quantitative assessment of the heterogeneous strain fields at the grain scale is necessary to understand the relationship between microstructure and elastic and plastic deformation. In the present study, digital image correlation (DIC) is used to measure the strains at the sub-grain level in a polycrystalline nickel-base superalloy where plasticity is localized into physical slip bands. Parameters to minimize noise given a set speckle pattern (introduced by chemical etching) when performing DIC in a scanning electron microscope (SEM) were adapted for measurements in both plastic and elastic regimes. A methodology for the optimization of the SEM and DIC parameters necessary for the minimization of the variability in strain measurements at high spatial resolutions is presented. The implications for detecting the early stages of damage development are discussed.

A liquid metal cooled (LMC) solidification technique was used to produce nickel-base GTD 444 and Rene N4 superalloy bicrystals with varying degrees of misorientation. Creep experiments with loading normal to the bicrystal boundaries were conducted at 1255 K (982 °C). Despite the similar overall compositions of these two alloys, the GTD 444 alloy with higher levels of carbon and boron displayed significantly higher tolerance to high-angle boundaries. Creep ductilities at rupture of greater than 5 pct were observed in GTD444 for boundaries misoriented by greater than 20 deg. Electron backscatter diffraction analysis showed significant lattice rotation adjacent to the bicrystal boundary in GTD444. In contrast, the Rene N4 bicrystal accumulated damage along the grain boundary early in creep, failing at less than 2 pct strain.