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Identification of crystallographic slip in metals and alloys is crucial to understand and improve their mechanical behavior. Recently, a novel slip system identification framework, termed SSLIP (for Slip System-based Local Identification of Plasticity), was introduced to leap from conventional trace-based identification to automated, point-by-point identification that exploits the full deformation kinematics. Using microstructure-correlated deformation data, SSLIP matches the measured in-plane displacement gradient tensor to the kinematics of the optimal combination of multiple slip system activities, at each DIC datapoint. SSLIP was applied and demonstrated to be successful on virtual and experimental case studies of FCC and BCC metals. However, for more advanced and anisotropic HCP crystal structures the complete identification of all slip systems was found to be more challenging, posing limitations on automation and flexibility. Here, we propose a significant extension to the SSLIP framework with the aim of automated slip system identification of HCP. The main extensions of the SSLIP method, hereinafter referred to as the +SSLIP method, include (i) a pre-selection of slip systems using a Radon transform, (ii) robustness to measured rigid body rotation by simultaneous identification of the local elastic rotation field, (iii) identification of the two best matching slip systems for each data point, and (iv) a procedure to deal with slip systems with in-plane displacement gradient tensors that cannot be discriminated, yielding the full slip system activity maps with all slip systems for each grain. The resulting objective identification method does not rely on, e.g., the Schmid factor to select which slip system is active at each point. We show how slip systems from multiple slip families are successfully identified on virtual and real experiments on a Zn polycrystalline coating.

A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric mechanical metamaterials, in which patterning emerges from local buckling of the underlying microstructure. Because pattern transformations significantly influence the resulting effective behaviour, it is vital to distinguish them from the overall deformation. To this end, the following kinematic decomposition into three parts was introduced in the micromorphic scheme: (i) a smooth mean displacement field, corresponding to the slowly varying deformation at the macro-scale, (ii) a long-range correlated fluctuation field, related to the buckling pattern at the meso-scale, and (iii) the remaining uncorrelated local microfluctuation field at the micro-scale. The micromorphic framework has proven to be capable of predicting relevant mechanical behaviour, including size effects and spatial as well as temporal mixing of patterns in elastomeric metamaterials, making it a powerful tool to design metamaterials for engineering applications. The long-range correlated fluctuation fields need to be, however, provided a priori as input parameters. The main goal of this study is experimental identification of the decomposed kinematics in cellular metamaterials based on the three-part ansatz. To this end, a full-field micromorphic Integrated Digital Image Correlation (IDIC) technique has been developed. The methodology is formulated for finite-size cellular elastomeric metamaterial specimens deformed in (i) virtually generated images and (ii) experimental images attained during in-situ compression of specimens with millimetre sized microstructure using optical microscopy., Comment: 27 pages, 8 figures, abstract shortened to fulfil 1920 character limit

The role of heterogeneity in the plastic flow of thin ferrite specimens is investigated in this study. This is done through a recently introduced quasi-2D experimental-numerical framework that allows for a quantitative comparison of the deformation fields of metal microstructures between experiments and simulations at a high level of detail and complexity. The method exploits samples that are locally ultra-thin ("2D") and hence have a practically uniform microstructure through their thickness. This allows testing more complex loading conditions compared to uniaxial micromechanical experiments while avoiding the complexity of an unknown subsurface microstructure, which limits comparisons between experiments and simulations in traditional integrated approaches at the level of the polycrystalline microstructure. The present approach enables to study the effect of microstructural features such as grain boundaries. To study the role of stochastic fluctuations, a constitutive model is employed which introduces random heterogeneity into a crystal plasticity model. A detailed analysis of the simulations is performed at the level of individual slip systems. Since both experimental and numerical results are susceptible to stochastic fluctuations, the outcomes of many simulations are compared to the experimentally obtained result. This comparison allows us to determine how a single experiment relates to an ensemble of simulations. Additionally, results obtained with a conventional crystal plasticity model are considered. The analysis reveals that the heterogeneity in the plasticity model is essential for accurately capturing the deformation mechanisms., Comment: 25 pages, 13 figures, submitted for publication

The slip system activity in microtensile tests of ferrite single crystals is compared with predictions made by the discrete slip plane model proposed by Wijnen et al. (International Journal of Solids and Structures 228, 111094, 2021). This is an extension of conventional crystal plasticity in which the stochastics and physics of dislocation sources are taken into account in a discrete slip band. This results in discrete slip traces and non-deterministic mechanical behavior, similar to what is observed in experiments. A detailed analysis of which slip systems are presumed to be active in experiments is performed. In small-scale mechanical tests on BCC metals and alloys, non-Schmid effects are often needed to explain the observed response. Therefore, these effects are incorporated into the model by extending a non-Schmid framework commonly used to model {110} slip to {112} planes. The slip activity in the simulations is compared to the slip activity in single crystal ferrite microtensile tests. This is done for the discrete slip plane model with and without non-Schmid effects, as well as for a conventional crystal plasticity model. The conventional crystal plasticity model fails to predict the diversity in active slip systems that is observed experimentally. The slip activity obtained with the discrete slip plane model is in convincingly better agreement with the experiments. Including non-Schmid effects only entails minor differences. This suggests that stochastic effects dominate the behavior of ferrite crystals with dimensions in the order of a few micrometers and that non-Schmid effects may not play a large role., Comment: 26 pages, 10 figures, submitted for publication

The state-of-the-art in paper mechanics calls for novel experimental data covering the full-field hygro-expansion of inter-fiber bonds in paper, i.e., the 3D morphological changes and inter-fiber interactions. Therefore, a recently developed full-field single fiber hygro-expansion measurement methodology based on global digital height correlation is extended to orthogonally bonded inter-fiber bonds, to investigate their full-field quasi-3D hygroscopic behavior. A sample holder has been developed which enables the quasi-3D characterization of the initial geometry of individual inter-fiber bonds, including the fiber thickness and width along the length of the fibers as well as the degree of wrap around and contact area of the bond, which are vital for understanding the inter-fiber bond hygro-mechanics. Full-field hygroscopic testing revealed novel insights on the inter-fiber interactions: (i) the transverse hygro-expansion of each fiber strongly reduces when approaching the bonded area, due to the significantly lower longitudinal hygro-expansion of the other bonded fiber. (ii) The relatively large transverse strain of one fiber stretches the other crossing fiber in its longitudinal direction, thereby significantly contributing to the sheet scale hygro-expansion. (iii) Out-of-plane bending is observed in the bonded region which is driven by the significant difference in transverse and longitudinal hygro-expansion of, respectively, the top and bottom fiber constituting the bond. A bi-layer laminate model is derived to rationalize the bending deformation and an adequate match is found with the experimental data. Under the assumption of zero bending, which represents constrained inter-fiber bonds inside a paper sheet, the model is able to predict the contribution of the transverse strain in the bonded regions to the sheet-scale hygro-expansion., Comment: 30 pages, 8 figures, 4 tables

Earlier works in literature on the hygro-expansion of paper state that the larger hygro-expansivity of freely compared to restrained dried handsheets is due to structural differences between the fibers inside the handsheet. To unravel this hypothesis, first, the hygro-expansion of freely and restrained dried, hardwood and softwood handsheets has been characterized. Subsequently, the transient full-field hygro-expansion (longitudinal, transverse, and shear strain) of fibers extracted from these handsheets was measured using global digital height correlation, from which the micro-fibril angle was deduced. The hygro-expansivity of each individual fiber was tested before and after a wetting period, during which the fiber's moisture content is maximized, to analyze if a restrained dried fiber can "transform" into a freely dried fiber. It was found that the longitudinal hygro-expansion of the freely dried fibers is significantly larger than the restrained dried fibers, consistent with the sheet-scale differences. The difference in micro-fibril angle between the freely and restrained dried fibers is a possible explanation for this difference, but merely for the hardwood fibers, which are able to "transform" to freely dried fibers after being soaked in water. In contrast, this "transformation" does not happen in softwood fibers, even after full immersion in water for a day. Various mechanisms have been studied to explain the observations on freely and restrained dried hardwood and softwood, fiber and handsheets including analysis of the fibers' lumen and cross-sectional shape. The presented results and discussion deepens the understanding of the differences between freely and restrained dried handsheets., Comment: 43 pages, 15 figures, 2 tables

The transient dimensional changes during \textit{hygro}-expansion and \textit{hydro}-expansion of freely and restrained dried, softwood and hardwood sheets and fibers is monitored, to unravel the governing micro-mechanisms occurring during gradual water saturation. The response of individual fibers is measured using a full-field global digital height correlation method, which has been extended to monitor the transient \textit{hydro}-expansion of fibers from dry to fully saturated. The \textit{hygro}- and \textit{hydro}-expansion is larger for freely versus restrained dried and softwood versus hardwood handsheets. The transient sheet-scale \textit{hydro}-expansion reveals a sudden strain and moisture content step. It is postulated that the driving mechanism is the moisture-induced softening of the so-called "dislocated regions" in the fiber's cellulose micro-fibrils, unlocking further fiber swelling. The strain step is negligible for restrained dried handsheets, which is attributed to the "dislocated cellulose regions" being locked in their stretched configuration during restrained drying, which is supported by the single fiber \textit{hydro}-expansion measurements. Finally, an inter-fiber bond model is exploited and adapted to predict the sheet-scale \textit{hygro}-expansion from the fiber level characteristics. The model correctly predicts the qualitative differences between freely versus restrained dried and softwood versus hardwood handsheets, yet, its simplified geometry does not allow for more quantitative predictions of the sheet-scale \textit{hydro}-expansion., Comment: 37 pages; 12 figures; 5 tables

Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of the microstructure is observable only at small scales, requiring SEM or other microscopy techniques; (ii) external loadings are applied at a (larger) engineering or device scale; and (iii) material parameters typically depend on the applied manufacturing process, necessitating measurements on material produced with the same process. In this paper, micromechanical parameter identification in heterogeneous solids is addressed through multiscale experiments combined with Integrated Digital Image Correlation (IDIC) in conjunction with various possible computational homogenization schemes. To this end, some basic concepts underlying multiscale approaches available in the literature are first reviewed, discussing their respective advantages and disadvantages from the computational as well as experimental point of view. A link is made with recently introduced uncoupled methods, which allow for identification of material parameter ratios at the microscale, still lacking a proper normalization. Two multiscale methods are analysed, allowing to bridge the gap between microstructural kinematics and macroscopically measured forces, providing the required normalization. It is shown that an integrated experimental--computational scheme provides relaxed requirements on scale separation. The accuracy and performance of the discussed techniques are analysed by means of virtual experimentation under plane strain and large strain assumptions for unidirectional fibre-reinforced composites. The robustness against image noise is also assessed., Comment: 44 pages, 16 figures, 4 tables, 7 procedures, abstract shortened to fulfil 1920 character limit

In particular types of layer- or lamellar-like microstructures such as pearlite and lath martensite, plastic slip occurs favorably in directions parallel to inter-lamellar boundaries. This may be due to the interplay between morphology and crystallographic orientation or, more generally, due to constraints imposed on the plastic slip due to the lamellar microstructural geometry. This paper proposes a micromechanics based, computationally efficient, scale independent model for particular type of lamellar microstructures containing softer lamellae, which are sufficiently thin to be considered as discrete slip planes embedded in a matrix representing the harder lamellae. Accordingly, the model is constructed as an isotropic visco-plastic model which is enriched with an additional orientation-dependent planar plastic deformation mechanism. This additional mode is activated when the applied load, projected on the direction of the soft films, induces a significant amount of shear stress. Otherwise, the plastic deformation is governed solely by the isotropic part of the model. The response of the proposed model is assessed via a comparison to direct numerical simulations (DNS) of an infinite periodic two-phase laminate. It is shown that the yielding behavior of the model follows the same behavior as the reference model. It is observed that the proposed model is highly anisotropic, and the degree of anisotropy depends on the contrast between the slip resistance (or yield stress) of the planar mode versus that of the isotropic part. The formulation is then applied to model the substructure of lath martensite with inter-layer thin austenite films. It is exploited in a mesoscale simulation of a dual-phase (DP) steel microstructure.The results are compared with those of a standard isotropic model and a full crystal plasticity model.

Experimental findings in the literature reveal that DP steels with identical strength and composition, but different microstructures, exhibit inconsistent trends under either necking-controlled or damage-controlled ductility tests. A special case of this phenomenon is referred to in the forming community as the cut-edge failure or edge cracking issue of DP steels. It is observed that globally ductile microstructures are prone to premature damage at cut edges while a comparatively less ductile DP steel performs better under the locally applied deformation at such edges. In this paper, a systematical statistical study is conducted to analyse this paradox from a micromechanical point of view. The obtained results qualitatively confirm the experimental observations and allowed us to explain/rationalize them, as follows. To reach a higher necking-controlled ductility, i.e. global ductility, the mechanical contrast between ferrite and martensite must be increased. Since martensite reveals a very high initial hardening and fast saturation, activation of martensite plasticity will lead to early necking in the microstructure and should therefore be avoided; a high mechanical phase contrast has this effect. However, at the same time a higher mechanical phase contrast is detrimental for the local ductility. More heterogeneity in the microstructure causes the generation of higher local plastic strains and triaxial stresses which leads to early damages. Therefore, in DP steel, increasing the global ductility may come at the expense of decreasing local ductility, and vice versa. The martensite hardening behavior is the main factor governing this phenomenon, and therefore also constitutes the key to processing improved steels that combine the best of both.

The onset of plasticity in quenched martensitic microstructures is characterized by a low initial yield stress followed by an extremely strong initial hardening response, and then a sudden hardening saturation. Literature attributes this behavior to residual stresses and dislocations inherited from the martensitic transformation, or to microstructural heterogeneities causing strength differences among the grains. Here, we argue that orientation-dependent yielding of lath martensite due to inter-lath sliding, which induces a substructure boundary sliding mechanism, may also contribute significantly to the observed behavior. To demonstrate this, we systematically study its quantitative contribution to the elasto-plastic transition behavior in a numerical microstructural model. In the simulations, we employ an effective laminate model for the martensite packets which takes into account the yielding anisotropy due to sliding along the packet's habit plane orientation. To account for the effect of carbon content, martensitic microstructures with different levels of lath strength are considered. It is shown that the martensite packets with a favorable habit plane orientation start to yield earlier compared to those with an unfavorable orientation, which initially remain elastic. As a consequence, the macro-scale response of the microstructures exhibits a low yield stress, followed by a significant degree of initial hardening which continues until the saturation stress level is approached. The apparent work hardening rate depends on the contrast between the in-habit plane and out-of-habit plane yield strength used in the model.

This work presents a detailed experimental-numerical analysis of a low-carbon dual-phase steel microstructure, revealing evidence of significant anisotropic plastic deformation in lath martensite. A careful determination of the habit plane orientations in the present martensitic variants demonstrates that the observed traces of plastic slip coincide with the directions of the corresponding habit planes. To study the local lath martensite plastic activity, a dedicated substructure-enriched crystal plasticity based model is exploited. Compared with conventional bcc crystal plasticity, the model incorporates an extra crystallographic slip plane containing 3 softer slip systems parallel to the habit planes to capture the role of habit-plane plasticity. Simulations reveal consistent strain localization patterns as those observed in the experiments, with most plasticity localized in the martensite packets with their habit plane oriented favorably with respect to the applied load. Based on these insights, recommendations for future martensite modelling strategies and potential improvements of steels are discussed.

Martensite damage in Dual-Phase (DP) steel has been studied extensively, yet, the exact deformation mechanisms that trigger or inhibit damage initiation remain mostly unexplored. Whereas generally assumed to be hard and brittle, lath martensite in fact deforms in a highly anisotropic manner, showing large strains under favorable habit plane orientations, which is attributed both to the lath morphology and to so-called 'substructure boundary sliding'. Yet, the correlation (or interplay) between plasticity and damage in lath martensite has not received much attention. Therefore, we raise the question whether these soft martensite plasticity mechanisms can delay or even inhibit damage initiation. We analyze several 'damage-sensitive' martensite notches, {i.e. thin contractions of two martensite islands,} by combining several state-of-the-art experimental and analysis methods. Deformations are tracked in-situ at the nanoscale, aligned to detailed microstructure maps, and categorised, for each martensite variant, into habit plane or out-of-habit-plane slip. In these experiments, strong plasticity (>70%) is observed in martensite notches, enabled by slip along a favorably oriented habit plane, whereas damaged notches have unfavorably oriented habit planes, showing limited pre-damage strains (<10%), carried by out-of-habit-plane slip. Additionally, one-to-one experimentally based Crystal Plasticity (CP) simulations are performed in parallel, employing a recently introduced Enriched CP approach which models a soft plasticity mechanism on the variants' habit plane. The Enriched CP simulations show considerably lower hydrostatic stresses in non-damaged and plastically deforming notches, thereby revealing that the soft habit plane mechanism is key for introducing the high plastic anisotropy that can lead to the inhibition of martensite damage in highly strained martensite notches., Comment: accepted for publication in Acta Mater. (33 pages, 12 figures)

Cellular elastomeric metamaterials are interesting for various applications, e.g. soft robotics, as they may exhibit multiple microstructural pattern transformations, each with its characteristic mechanical behavior. Numerical literature studies revealed that pattern formation is restricted in (thick) boundary layers causing significant mechanical size effects. This paper aims to experimentally validate these findings on miniaturized specimens, relevant for real applications, and to investigate the effect of increased geometrical and material imperfections resulting from specimen miniaturization. To this end, miniaturized cellular metamaterial specimens are manufactured with different scale ratios, subjected to in-situ micro-compression tests combined with digital image correlation yielding full-field kinematics, and compared to complementary numerical simulations. The specimens' global behavior agrees well with the numerical predictions, in terms of pre-buckling stiffness, buckling strain and post-buckling stress. Their local behavior, i.e. pattern transformation and boundary layer formation, is also consistent between experiments and simulations. Comparison of these results with idealized numerical studies from literature reveals the influence of the boundary conditions in real cellular metamaterial applications, e.g. lateral confinement, on the mechanical response in terms of size effects and boundary layer formation., Comment: 20 pages, 6 figures, Materials & Design, 11 May 2020

Integrated Digital Image Correlation (IDIC) is nowadays a well established full-field experimental procedure for reliable and accurate identification of material parameters. It is based on the correlation of a series of images captured during a mechanical experiment, that are matched by displacement fields derived from an underlying mechanical model. In recent studies, it has been shown that when the applied boundary conditions lie outside the employed field of view, IDIC suffers from inaccuracies. A typical example is a micromechanical parameter identification inside a Microstructural Volume Element (MVE), whereby images are usually obtained by electron microscopy or other microscopy techniques but the loads are applied at a much larger scale. For any IDIC model, MVE boundary conditions still need to be specified, and any deviation or fluctuation in these boundary conditions may significantly influence the quality of identification. Prescribing proper boundary conditions is generally a challenging task, because the MVE has no free boundary, and the boundary displacements are typically highly heterogeneous due to the underlying microstructure. The aim of this paper is therefore first to quantify the effects of errors in the prescribed boundary conditions on the accuracy of the identification in a systematic way. To this end, three kinds of mechanical tests, each for various levels of material contrast ratios and levels of image noise, are carried out by means of virtual experiments. For simplicity, an elastic compressible Neo-Hookean constitutive model under plane strain assumption is adopted. It is shown that a high level of detail is required in the applied boundary conditions. This motivates an improved boundary condition application approach, which considers constitutive material parameters as well as kinematic variables at the boundary of the entire MVE as degrees of freedom in..., Comment: 37 pages, 25 figures, 2 tables, 2 algorithms

An original experimental approach is presented to automatically determine the average phase distribution around damage sites in multi-phase materials. An objective measure is found to be the average intensity around damage sites, calculated using many images. This method has the following benefits: no phase identification or manual interventions are required, and statistical fluctuations and measurement noise are effectively averaged. The method is demonstrated for dual-phase steel, revealing subtle unexpected differences in the morphology surrounding damage in strongly and weakly banded microstructures.