Behavior Of Individual Grains Research Articles

Mechanical properties for irradiated face-centred cubic nanocrystalline metals.

In this paper, a self-consistent plasticity theory is proposed to model the mechanical behaviours of irradiated face-centred cubic nanocrystalline metals. At the grain level, a tensorial crystal model with both irradiation and grain size effects is applied for the grain interior (GI), whereas both grain boundary (GB) sliding with irradiation effect and GB diffusion are considered in modelling the behaviours of GBs. The elastic-viscoplastic self-consistent method with considering grain size distribution is developed to transit the microscopic behaviour of individual grains to the macroscopic properties of nanocrystals (NCs). The proposed theory is applied to model the mechanical properties of irradiated NC copper, and the feasibility and efficiency have been validated by comparing with experimental data. Numerical results show that: (i) irradiation-induced defects can lead to irradiation hardening in the GIs, but the hardening effect decreases with the grain size due to the increasing absorption of defects by GBs. Meanwhile, the absorbed defects would make the GBs softer than the unirradiated case. (ii) There exists a critical grain size for irradiated NC metals, which separates the grain size into the irradiation hardening dominant region (above the critical size) and irradiation softening dominant region (below the critical size). (iii) The distribution of grain size has a significant influence on the mechanical behaviours of both irradiated and unirradiated NCs. The proposed model can offer a valid theoretical foundation to study the irradiation effect on NC materials.

A mesoscale solidification simulation of fusion welding in aluminum–magnesium–silicon alloys

A 3-D granular model has been developed to simulate solidification during fusion welding of Al alloys. The model simulates the gradual development of the weld mushy zone composed of both continuous liquid films and solidifying grains by coupling thermal fields based on the Rosenthal equation, a modified Voronoi tessellation to provide grain structure at the mesoscale, and the evolution of solid fraction within a grain based on the Scheil equation. The shape and geometry of the columnar and equiaxed grains within the weld pool has been characterized from experiments, and therefore the model can be used to link the solidification behaviour of individual grains to the macroscopic properties of the weld. The gradual formation of microscale liquid channels lying along the grain boundaries within the mushy zone is investigated and the role of welding parameters, including amperage and welding speed, on transitions in the semisolid microstructure is explored. The study reveals that the ability of the microscale liquid channels to feed molten metal into the solidifying areas is not uniform through the weld, and is strongly affected by grain size since smaller grains hinder the feeding ability of the mushy zone.

Contribution of the Nanoindentation to the Study of HCP Metals

This study combines nanoindentation experiments, electron backscatter diffraction (EBSD) and atomic force microscopy (AFM) topographic measurements to investigate the material anisotropy contribution to the indentation behaviour of individual grains of various hexagonal-close packed (HCP) polycrystals with different axial ratio (zinc, magnesium and titanium). The grain size was much larger than the indents size to ensure quasi-single-crystal indentation and when, combined with an EBSD mapping, a wide variety of crystal orientations can be probed, which provides mechanical characterization of materials at the micro/nanoscale. Experimental curves can be used to determine the mechanical properties of the indented material. Furthermore, by using data issued from AFM topographic measurements, one can analyze the dislocations arrangements below and around the indentation print, and thus characterize the most probably activated deformation systems.

Measurement of X-ray diffraction-line broadening induced by elastic mechanical grain interaction

Various grain-interaction models have been proposed in the literature to describe the stress and strain behavior of individual grains within a massive aggregate. Diffraction lines exhibit a response to the occurrence of a strain distribution in the diffracting crystallites, selected by the direction of the diffraction vector with respect to the specimen frame of reference, by correspondingly induced diffraction-line broadening. This work provides a report of synchrotron diffraction investigations dedicated to the measurement of the experimentally observable diffraction-line broadening induced by external elastic loading of various polycrystalline specimens. The experimentally obtained broadening data have been compared with those calculated adopting various grain-interaction models. Although such grain-interaction models have been proven to accurately predict the average (X-ray) diffraction measured lattice strain, as derived from the diffraction-peak position, the present results have demonstrated that the extent of the diffraction-line broadening due to grain interactions, as calculated by employing these grain-interaction models, is much smaller than the experimentally determined broadening. The obtained results have vast implications for diffraction-line broadening analysis and the understanding of the elastic behavior of massive polycrystals.

High-energy transmission Laue micro-beam X-ray diffraction: a probe for intra-granular lattice orientation and elastic strain in thicker samples

An understanding of the mechanical response of modern engineering alloys to complex loading conditions is essential for the design of load-bearing components in high-performance safety-critical aerospace applications. A detailed knowledge of how material behaviour is modified by fatigue and the ability to predict failure reliably are vital for enhanced component performance. Unlike macroscopic bulk properties (e.g. stiffness, yield stress, etc.) that depend on the average behaviour of many grains, material failure is governed by `weakest link'-type mechanisms. It is strongly dependent on the anisotropic single-crystal elastic-plastic behaviour, local morphology and microstructure, and grain-to-grain interactions. For the development and validation of models that capture these complex phenomena, the ability to probe deformation behaviour at the micro-scale is key. The diffraction of highly penetrating synchrotron X-rays is well suited to this purpose and micro-beam Laue diffraction is a particularly powerful tool that has emerged in recent years. Typically it uses photon energies of 5-25 keV, limiting penetration into the material, so that only thin samples or near-surface regions can be studied. In this paper the development of high-energy transmission Laue (HETL) micro-beam X-ray diffraction is described, extending the micro-beam Laue technique to significantly higher photon energies (50-150 keV). It allows the probing of thicker sample sections, with the potential for grain-level characterization of real engineering components. The new HETL technique is used to study the deformation behaviour of individual grains in a large-grained polycrystalline nickel sample during in situ tensile loading. Refinement of the Laue diffraction patterns yields lattice orientations and qualitative information about elastic strains. After deformation, bands of high lattice misorientation can be identified in the sample. Orientation spread within individual scattering volumes is studied using a pattern-matching approach. The results highlight the inability of a simple Schmid-factor model to capture the behaviour of individual grains and illustrate the need for complementary mechanical modelling.

In situ synchrotron analysis of lattice rotations in individual grains during stress-induced martensitic transformations in a polycrystalline CuAlBe shape memory alloy

Two synchrotron diffraction techniques, three-dimensional X-ray diffraction and Laue microdiffraction, are applied to studying the deformation behaviour of individual grains embedded in a Cu 74Al 23Be 3 superelastic shape memory alloy. The average lattice rotation and the intragranular heterogeneity of orientations are measured during in situ tensile tests at room temperature for four grains of mean size ∼1 mm. During mechanical loading, all four grains rotate and the mean rotation angle increases with austenite deformation. As the martensitic transformation occurs, the rotation becomes more pronounced, and the grain orientation splits into several sub-domains: the austenite orientation varies on both sides of the martensite variant. The mean disorientation is ∼1°. Upon unloading, the sub-domains collapse and reverse rotation is observed.

A microstructure approach to the sensitivity and compressibility of some Eastern Canada sensitive clays

Investigation of micro–macro relationships in soils most often concerns granular soils in which both the elemental unit (the grain) and the physical laws governing inter-grain interactions appear to be better known. The situation is different for clays because the elementary unit and the inter-unit interactions at the micro-scale are more difficult to characterise. In fine-grained soils, it has been shown that an intermediate level, corresponding to the way clay and fine-grained particles are arranged together, had to be considered so as to link microscopic features to macroscopic behaviour. An investigation of the change in microstructure during compression carried out some time ago on a sensitive clay from Canada demonstrated that studying the changes in pore size distribution provides a satisfactory description of microstructure changes during compression. The analysis is applied here to six other sensitive clays. First, a careful examination of the intact and remoulded microstructure is conducted in order to understand better the relationship between microstructure and sensitivity. Second, an interesting correlation between the compressibility coefficient and the slope of the cumulative pore size distribution curve is observed in Champlain clays. This confirms the analysis conducted that compression in loose, low-plasticity soils can be attributed to the progressive and ordered collapse of pores, starting from the largest existing ones and progressively affecting smaller and smaller pores. A conclusion drawn from this work is that a micro–macro analysis in terms of changes of a rigid fragile porous matrix appears to be more relevant than a standard analysis based on the behaviour of individual grains, where the grains are taken to be the relevant elemental microstructure unit (a unit difficult to identify in natural clay soils). Also, further insight is provided for the interpretation of microstructure effects through comparing the compression curves of intact soil samples to those of remoulded samples.

The effect of crystal orientation on the indentation response of commercially pure titanium: experiments and simulations

This study combines nanoindentation, electron backscatter diffraction (EBSD) and crystal plasticity finite element analysis to examine the anisotropy in the indentation behaviour of individual grains within an α-Ti polycrystal. Nanoindentation is utilized to mechanically probe small volumes of material within grains for which orientations are known from prior EBSD mapping. Both indentation modulus and hardness decrease significantly as the indentation axis is inclined further from the c -axis; the plastic response showing the more marked anisotropy. Recently developed high angular resolution EBSD has been utilized to examine selected indents, providing maps of elastic strain variations and lattice rotations. From such maps lower bound solutions for the density of geometrically necessary dislocations (GNDs) have been established. Crystal plasticity modelling showed promise in capturing correctly the orientation dependence of load–displacement response and in lattice rotations local to the indenter, particularly for indentation into a basal plane which generated threefold rotational symmetry about an axis parallel with the indentation direction which was also observed in experiments.

Electromechanical Imaging and Spectroscopy of Ferroelectric and Piezoelectric Materials: State of the Art and Prospects for the Future

Piezoresponse force microscopy (PFM) has emerged as a powerful and versatile tool for probing nanoscale phenomena in ferroelectric materials on the nanometer and micrometer scales. In this review, we summarize the fundamentals and recent advances in PFM, and describe the nanoscale electromechanical properties of several important ferroelectric ceramic materials widely used in memory and microelectromechanical systems applications. Probing static and dynamic polarization behavior of individual grains in PZT films and ceramics is discussed. Switching spectroscopy PFM is introduced as a useful tool for studying defects and interfaces in ceramic materials. The results on local switching and domain pinning behavior, as well as nanoscale fatigue and imprint mapping are presented. Probing domain structures and polarization dynamics in polycrystalline relaxors (PMN‐PT, PLZT, doped BaTiO3) are briefly outlined. Finally, applications of PFM to dimensionally confined ferroelectrics are demonstrated. The potential of PFM for studying local electromechanical phenomena in polycrystalline ferroelectrics where defects and other inhomogeneities are essential for the interpretation of their macroscopic properties is illustrated.

Large lattice strain in individual grains of deformed nanocrystalline Ni

We have used nanobeam electron diffraction to monitor the behavior of individual grains in nanocrystalline Ni during in situ tensile straining in the transmission electron microscope. The diffraction patterns reveal large variations in the magnitude of grain rotation and indicate that grain interiors can experience large lattice distortions (up to 5.5% linear strain). These large distortions may assist grain rearrangement during grain boundary facilitated deformation and are consistent with the behavior expected of nanocrystalline Ni near its predicted peak in strength.

Coupling Between Mesoplasticity and Damage in High-cycle Fatigue

The multiaxial fatigue loading in the high-cycle regime leads to localized mesoscopic plastic strain that occurs in some preferential directions of individual grains for most metallic materials. Crack initiation modeling is difficult in this fatigue regime because the scale where the mechanisms operate is not the engineering scale (macroscopic scale), and local plasticity and damage act simultaneously. This article describes a damage model based on the interaction between mesoplasticity and local damage for the infinite and the finite fatigue life regimes. Several salient effects are accounted for via a simple localization rule, which connects the macroscopic scale with the mesoscopic one, and by the model presented here, which describes the coupled effects of mesoplasticity and damage growth. Irreversible thermodynamics concepts with internal state variables are used to maintain a balance between extensive descriptions of plastic flow and damage events. Cyclic hardening behavior is described by a combined isotropic and kinematic hardening rule while the damage evolution is governed notably by the accumulated plastic mesoscopic strain. In this study, predictions are compared to fatigue tests performed on a mild steel (C36) under different loading modes. All the experiments are carried out under in-phase loading conditions: reversed tension, torsion, and combined tension—torsion. The mean stress effect is also studied through tests conducted under tension. The predicted Wöhler curves under any loading mode can be readily obtained with this model, but the main feature of this approach is to ensure a clear link between the mesoscopic parameters like the hardening behavior of individual grains and the subsequent local damage.

A simple and efficient model for mesoscale solidification simulation of globular grain structures

A simple model for the solidification of globular grains in metallic alloys is presented. Based on the Voronoi diagram of the nuclei centers, it accounts for the curvature of the grains near triple junctions. The predictions of this model are close to those of more refined approaches such as the phase field method, but with a computation cost decreased by several orders of magnitude. Therefore, this model is ideally suited for granular simulations linking the behavior of individual grains to macroscopic properties of the material.

Continuum multiscale modeling of finite deformation plasticity and anisotropic damage in polycrystals

A framework for describing the deformation and failure responses of multi-phase polycrystalline microstructures is developed from micromechanical considerations and volume averaging techniques. Contributions from damage (i.e., displacement discontinuities such as cracks, voids, and shear bands) are captured explicitly in the framework’s kinematics and balance relations through additive decompositions of the total deformation gradient and nominal stress, respectively. These additive decompositions—which notably enable description of arbitrarily anisotropic deformations and stresses induced by damage—are derived following the generalized theorem of Gauss, i.e., a version of the divergence theorem of vector calculus. A specific rendition of the general framework is applied to study the response of a dual-phase tungsten (W) alloy consisting of relatively stiff pure W grains embedded in a more ductile metallic binder material. In the present implementation, a Taylor scheme is invoked to average grain responses within each phase, with the local behavior of individual grains modeled with finite deformation crystal plasticity theory. The framework distinguishes between the effects of intergranular damage at grain and phase boundaries and transgranular damage (e.g., cleavage fracture of individual crystals). Strength reduction is induced by the evolving volume fraction of damage (i.e., porosity) and microcrack densities. Model predictions are compared with experimental data and observations for the W alloy subjected to various loading conditions.

A constitutive high cycle fatigue damage model – based on the interaction between microplasticity and local damage*

Abstract This paper presents a new model that accounts, on a local scale, for the coupling between plasticity due to gliding in shear bands and damage occurring when the accumulated plastic strain has reached a threshold value. The irreversible thermodynamics with internal state variables is employed to keep a middle way between extensive description of plastic and damage flow and application of accessibility requirements. Plasticity and damage are governed by their proper complementary rules (yield functions and potentials). At the same time, a coupling occurs between the damage variable and the hardening parameters. A large experimental database relative to the fatigue behavior of a mild steel C36 submitted to different loading modes (tension, torsion, combined proportional tension and torsion) proves the efficiency of such a model. The prediction of Wöhler curves for cyclic complex stress states can be readily done, but the main feature of this approach is to ensure a clear link between mesoscopic parameters like the hardening behavior of individual grains and the subsequent local damage.

A mesoscale cellular automaton model for curvature-driven grain growth

A two-dimensional mesoscale cellular automaton algorithm is developed to simulate curvature-driven grain growth during materials processing. In the present model, a deterministic switch rule for the grain growth is adopted, and thus the kinetics of the grain growth can be simulated quantitatively. In addition, the grain-boundary energy is dependent on the misorientation between neighboring grains. At mesoscale, the simulations show that each grain displays a unique growth behavior. The growth behavior of individual grains can be categorized into four types: (1) grains with monotonically increasing equivalent diameters, (2) grains that first grow and then begin to shrink, (3) grains with almost constant diameters, and (4) grains that decrease in size. Furthermore, an oscillation grain-growth behavior is observed in the present mesoscale cellular automaton simulations. This simulated individual grain-growth behavior has not been reported in the literature.

Local impedance imaging and spectroscopy of polycrystalline ZnO using contact atomic force microscopy

A current detection scanning probe technique is developed that quantifies frequency-dependent local transport properties. The approach, referred to as nanoimpedance microscopy/spectroscopy (NIM), is based on impedance spectroscopy with a conductive atomic force microscopy (AFM) tip. NIM is applied to study the quality of a tip/surface contact and transport behavior of individual grains and grain boundaries in polycrystalline ZnO. Impedance spectra were measured in the frequency range 40 Hz to 110 MHz, and the grain boundary properties are studied by nonlinear fitting of experimental data to an equivalent circuit. Two-terminal measurements are performed in the vicinity of a single ZnO grain boundary and the Cole–Cole plot indicates two major relaxation processes attributed to grain boundary relaxation and tip/surface contact.

Misorientation analysis and the formation and orientation of subgrain and grain boundaries

In contrast to the behaviour of individual grains, both inter- and intra-granular boundaries within rocks have received much less attention. However, many geological processes, particularly during deformation (e.g., yielding, dislocation creep, recrystallisation, superplasticity and various fracture mechanisms), and petrophysical properties depend to some extent on the nature of boundaries present in a rock. In this contribution, we consider the role of intergranular and intragranular crystal boundaries. A precise characterisation of such boundaries depends on defining the crystallographic and dimensional orientations of the boundary and the misorientation between the adjacent regions (i.e. grains, subgrains, etc.) separated by the boundary. Although several theoretical descriptions of boundary configuration are available, practical precision is lacking and approximations are necessary. We describe two specific approximations for boundary formation and orientation obtained using the SEM electron channelling technique. The first is a geometrical interpretation of electron channelling patterns (ECP) in terms of the likely formation and orientation of the intervening boundary. The second considers the misorientation between adjacent regions across a boundary. This involves a model which assumes a simple geometrical relationship between crystal slip systems responsible for the rotation and misorientation between adjacent regions, and the formation and orientation of the resulting boundary. These approximations are capable of: (a) identifying trends in the dispersion of crystallographic directions during deformation; (b) identifying active slip systems; (c) calculating the relative Schmid Factors for each crystal slip system (and therefore the most likely system to be activated); (d) modelling synthetic misorientations and predicting the crystal slip systems and boundary configurations to be expected; and (e) comparing real data with synthetic models. Our analyses are illustrated via natural examples of dynamic recrystallisation in quartzite and a theoretical simulation of the behaviour of an individual quartz grain during deformation.

Angular dependence of magnetization reversal critical fields in individual grains of REFeB magnets

The magnetization reversal behaviour of individual grains was studied by direct domain structure observations. On this basis the angular dependence of the saturation field Hs, critical field of reverse domain removal, Hk, and nucleation field Hn was found to obey the law 1/cos(ϕ − ϕm), where ϕm is the angle between the grain easy axis and the axis of magnet texture.

Characterization of thin Al films using grating coupling to surface plasma waves

A detailed characterization of the optical, microstructural, and electrical properties of thin (5–50 nm) Al films grown by thermal evaporation, magnetron sputtering, and ion-assisted sputtering (IAS), is reported. Dielectric-function measurements were carried out by using grating coupling to surface plasma waves (SPW) and, for comparison, ellipsometric measurements were also performed. Scanning electron microscope (SEM) studies of film microstructure as well as dc electrical resistivity measurements were carried out and correlated with the optical data. Using the Bruggeman effective media approximation, good agreement was obtained for thicker films (30–50 nm), but not for thinner films (<30 nm). SEM and resistivity measurements suggest that conditions of film growth influence the behavior of individual grains, resulting in increased electron reflectance at the grain boundaries with increasing energy delivered to the substrate during deposition. This resulted in lower electrical resistivities for evaporated films than for IAS films. Finally, the influence of 5–20 Å Al2O3 on thick Al films was investigated: Both SPW and resistivity measurements suggest that the oxide film was not confined to film surface, but had penetrated inside the film leading to much higher electrical resistivities than would be otherwise expected.

Characterisation of crystalline UO2 oxidised in 1 Torr of oxygen at 25, 225 and 300 °C. Part 1.—X-ray photoelectron spectroscopy

The oxidation behaviour of individual grains in bulk UO2 has been simulated using single-crystal surfaces. To this end the oxidation of (111), (110) and (100) planar slices of crystalline UO2 together with a polycrystalline sample have been oxidised in 1 Torr of oxygen at 25, 225 and 300 °C. The oxidation process was monitored using X-ray photoelectron spectroscopy. At 25 °C surface oxidation only occurred (to a depth of ca. 10 Å) to form the hyperstoichiometric oxide UO2+x, with x in the range (0.03–0.06)±0.02. The surface reactivity decreased in the order (110) > (111) > (polycrystalline) > (100), and was governed by the two-dimensional surface crystal structure. At 225 °C the rate and extent of reaction was much greater, resulting in the formation and growth of a sub-stoichiometric layer of U3O7 on all the samples. The order of surface reactivity changed to (111) > (110) > (100) > (polycrystalline). Further oxidation at 300 °C enhanced these differences in reactivity, resulting in the growth of a layer of U3O8 on the (111) surface.