Properties Of Individual Grains Research Articles

A sensitivity analysis of twinning crystal plasticity finite element model using single crystal and poly crystal Zircaloy

The popularity of crystal plasticity finite element method (CPFEM) models is increasing due to their ability to predict the mechanical response of crystalline materials such as metals and metal alloys more accurately than traditional continuum mechanics models. This is since the crystal plasticity models consider the effect of atomic structure, microstructural morphology, and properties of individual grains. These CPFEM models use a large number of material parameters in order to capture the mesoscale physics which comes with the downside of the tedious calibration process. In this paper, a CPFEM code was developed to include the twinning induced grain reorientation and subsequent crystallographic slip for HPC material. The developed code is incorporated in a large-scale, parallelized nonlinear solver WARP3D. A sensitivity analysis with respect to 22 material parameters was then conducted using single crystal and polycrystal representative volume element (RVE) of Zircaloy material. Loading was applied along five different crystallographic orientations for single crystal RVE and along three directions namely, rolling (RD), transverse (TD), and normal (ND) direction for polycrystal RVE. Results obtained from the sensitivity analysis were used for the calibration of material parameters for Zircaloy. Finally, developed code along with calibrated material parameters was used to investigate the effect of the hydride phase formation in Zircaloy which is a typical case observed for nuclear applications. It was found that the volume fraction of the hydride phase has a significant impact on the mechanical properties of Zircaloy.

Study of Micro-Upsetting by Finite Element Simulation Based on Crystal Plasticity and Grain Boundary Strengthening Theories

The properties of individual grains affect the mechanical behaviors and response of materials in micro-scaled deformation, viz., microforming, and there are unknown phenomena and deformation behaviors existing and limiting the wide application of microforming due to size effect. In this paper, a composite model combining crystal plasticity and grain boundary strengthening theories was developed for numerical investigation into the effect of grain boundaries on the plastic deformation of copper micro-upsetting. By comparing the results with and without grain-boundary structure, it is revealed that grain boundaries, which act as the barriers of crystal slip, result in the enhanced flow stress and the discontinuous distribution of stress and strain. The grain size effect is also considered in this research, and the results show the coarse-grained material reduces the flow stress and enhances the inhomogeneous deformation.

Application of nanoindentation technology in rocks: a review

Nanoindentation has become an increasingly popular method to determine the mechanical properties of both homogeneous and heterogeneous materials. Rocks are inherently heterogeneous and understanding their mechanical properties is of vital importance for relevant engineering applications. Due to its high precision and resolution in both force and displacement, nanoindentation can be utilized to extract the localized mechanical properties of individual grains. This review paper presents an overview of applications of nanoindentation techniques in various rocks, such as shale, coal, limestone, marble, sandstone and claystone. Apart from the conventional mechanical parameters, i.e., Young’s modulus and hardness, other parameters, such as fracture toughness, time-dependent creep and tensile strength can also be obtained using nanoindentation methods. Basic equations and parameters employed to obtain the above mechanical parameters are clearly explained. In addition, merits and demerits of previous nanoindentation studies are summarised and roadmap for future trends of nanoindentation in geomaterials are suggested.

Heterogeneous photoresponse of individual grain in all-inorganic perovskite solar cells

Photoresponse is affected by the microscopic structure and orientation of the perovskite crystals, but it is difficult to quantify the individual grain size and always acts as homogeneous. Using scanning probe microscopy, the local electrical properties of individual grains in all-inorganic perovskites are mapped. Surface potential variations on lateral distance scales within or larger than one grain size are presented. Among perovskite grains, three discrete photoconductivity levels are identified, corresponding to the facet-dependent density of trap states, which was further demonstrated by the light intensity dependence of the local current–voltage curve of each grain.

New insights into cooked rice quality by measuring modulus, adhesion and cohesion at the level of an individual rice grain

Causal relationships between physical properties and structure/composition of cooked rice are difficult to quantify when mechanical measurements are performed on bulk samples using large deformations that alter the structure irreversibly. We demonstrate here methods involving small-deformation to characterise the elastic modulus (E), adhesion and cohesion at the individual grain level, and show distinct differences between freshly cooked rice and shelf-stable retorted rice. On average, retorted rice is harder and less adhesive and cohesive than freshly cooked rice, but their distributions in each of these mechanical properties overlap. E is independent of adhesion and weakly correlated with moisture content. In addition, a ring-shear tester is shown to distinguish the bulk cohesion and flowing ability between rice samples. Measuring the inherent physical properties of individual grains has the potential to enable a more sensitive evaluation of new processes and grain varieties, and development of quantitative structure-property-processing relationships for rational design of products to perform optimally at different stages, from manufacturing through to oral processing.

Micromechanical modeling of intrinsic and specimen size effects in microforming

Size effect is a crucial phenomenon in the microforming processes of metallic alloys involving only limited amount of grains. At this scale intrinsic size effect arises due to the size of the grains and the specimen/statistical size effect occurs due to the number of grains where the properties of individual grains become decisive on the mechanical behavior of the material. This paper deals with the micromechanical modeling of the size dependent plastic response of polycrystalline metallic materials at micron scale through a strain gradient crystal plasticity framework. The model is implemented into a Finite Element software as a coupled implicit user element subroutine where the plastic slip and displacement fields are taken as global variables. Uniaxial tensile tests are conducted for microstructures having different number of grains with random orientations in plane strain setting. The influence of the grain size and number on both local and macroscopic behavior of the material is investigated. The attention is focussed on the effect of the grain boundary conditions, deformation rate and the grain size on the mechanical behavior of micron sized specimens. The model is intrinsically capable of capturing both experimentally observed phenomena thanks to the incorporated internal length scale and the crystallographic orientation definition of each grain.

Uniaxial compressive behavior of partially saturated granular media under high strain rates

This paper targets gaps in current literature pertaining to the influence of strain rate and particle shape on the dynamic compressive response of partially saturated porous media as a function of saturation. The extent of particle breakage in response to variations in saturation is also explored. Two materials consisting of Stockton Beach sand and glass beads with saturations ranging from 0% to above 90% under strain rates between 800s−1 and 2100s−1 were investigated via the split Hopkinson pressure bar. All specimens exhibited an initial void ratio of 0.68 (porosity of 0.40) and were confined within a hardened steel tube effectively inhibiting lateral expansion. The stress–strain of dry specimens was found to be invariant with respect to loading rate, but experimental results for samples with saturations between 25% and 75% prior to water lock-up suggest an increase in overall compressibility under higher strain rates. The shape and mechanical properties of individual grains was also shown to influence the sample response. With the addition of water, the compressibility of glass beads relative to the dry response was demonstrated to be much higher than that of the beach sand. The extent of grain crushing witnessed for Stockton Beach sand as quantified via Hardin's relative breakage potential was also characterized for specimens retrieved post-impact. It was found that crushing decreased linearly with increasing saturation under a given rate of strain.

OSL dating of individual quartz ‘supergrains’ from the Ancient Middle Palaeolithic site of Cuesta de la Bajada, Spain

Dose saturation represents a fundamental limitation for obtaining finite optically stimulated luminescence (OSL) quartz ages over Middle Pleistocene timescales. Single-grain OSL studies typically reveal significant intra- and inter-sample variability in quartz dose saturation properties at the individual grain level. This enhanced variability may offer the potential to obtain extended-range chronologies exceeding the traditional upper age limits of multiple-grain OSL dating. However, there have been relatively few detailed assessments of single-grain OSL properties over high dose ranges. In this study we investigate extended-range single-grain OSL dating potential at Cuesta de la Bajada, one of the most important Ancient Middle Palaeolithic sites in the Iberian Peninsula. The quartz samples from this site exhibit exceptional dose saturation properties and contain significant populations of individual ‘supergrains’ with bright OSL signals, very high characteristic saturation dose (D0) limits of 200 to >600 Gy, and dose-response curves that closely conform to single saturating exponential functions. Assessments of OSL signal composition and the ability to successfully recover a known laboratory dose of 470 Gy support the potential for obtaining high equivalent dose (De) values with reasonable fitting uncertainties. A series of novel sensitivity tests are used to assess potential biases in supergrain De estimation over high dose ranges related to (i) thermally transferred signal contributions, (ii) choice of dose-response curve fitting function, and (iii) insufficient dose saturation properties of individual grains. The single-grain De values obtained using the standard quality assurance criteria and novel sensitivity tests are consistent at 2σ, and are in agreement with quartz Ti-centre ages obtained on two of three paired electron spin resonance (ESR) samples collected from Cuesta de la Bajada. These comparisons support the suitability of our single-grain OSL results and suggest there may be good potential for using quartz supergrains to establish extended-range chronologies at some Middle Pleistocene sites. Comparisons with other single-grain OSL studies across the Iberian central plains suggest that favourable dose saturation properties may be influenced by regional-scale geological controls. The importance of undertaking single-grain OSL dating at Cuesta de la Bajada is also demonstrated by the results of synthetic aliquot experiments, which reveal multiple-grain age offsets of 60–170 ka when unsuitable grain types are inadvertently included in the final age calculations. The single-grain OSL results indicate that the main archaeological horizon at Cuesta de la Bajada (unit CB3) accumulated between 264 ± 22 and 293 ± 24 ka. These ages are consistent with the chronologies of other key early Middle Palaeolithic sites in the region (Ambrona AS6 and Gran Dolina TD10) and indicate that the Ancient Middle Palaeolithic techno-complex likely spread across Iberia from at least Marine Isotope Stage 9 onwards.

Multi-scale modeling and rendering of granular materials

We address the problem of modeling and rendering granular materials---such as large structures made of sand, snow, or sugar---where an aggregate object is composed of many randomly oriented, but discernible grains. These materials pose a particular challenge as the complex scattering properties of individual grains, and their packing arrangement, can have a dramatic effect on the large-scale appearance of the aggregate object. We propose a multi-scale modeling and rendering framework that adapts to the structure of scattered light at different scales. We rely on path tracing the individual grains only at the finest scale, and---by decoupling individual grains from their arrangement---we develop a modular approach for simulating longer-scale light transport. We model light interactions within and across grains as separate processes and leverage this decomposition to derive parameters for classical radiative transport, including standard volumetric path tracing and a diffusion method that can quickly summarize the large scale transport due to many grain interactions. We require only a one-time precomputation per exemplar grain, which we can then reuse for arbitrary aggregate shapes and a continuum of different packing rates and scales of grains. We demonstrate our method on scenes containing mixtures of tens of millions of individual, complex, specular grains that would be otherwise infeasible to render with standard techniques.

Determination of hardness and elastic modulus inverse pole figures of a polycrystalline commercially pure titanium by coupling nanoindentation and EBSD techniques

Nanoindentation and electron backscattered diffraction (EBSD) techniques were used to study the correlation between crystallographic orientations and mechanical properties of individual grains in CP-Ti polycrystalline samples. Therefore, a novel experimental protocol and a data analyses procedure have been implemented in order to obtain elastic modulus and hardness inverse pole figures (EIPF and HIPF). It has been demonstrated that the hardness varies significantly with orientation, and that the elastic modulus appears less sensitive than hardness to grain orientation.

Numerical study of mesoscale surface roughening in aluminum polycrystals under tension

A 3D numerical analysis of mesoscale surface roughening in a polycrystalline aluminum alloy under uniaxial tension has been performed. Three-dimensional microstructural models with equiaxial and extended grains inherent in cold rolling have been developed and used in calculations. Crystallographic anisotropy is not described in an explicit form by means of, say, a well-known crystal plasticity model. Instead, the elastic-plastic properties of individual grains are varied within 10% and in so doing the mechanical anisotropy due to the grain shape is accounted for. A combined effect of microstructure and loading and boundary conditions is investigated. Pronounced surface roughness of equiaxial grain structure and of a textured material loaded at the right angle to the rolling direction is observed in comparison with extended grain structure loaded along the rolling direction where the surface relief is fairly smooth. Computational results suggest that grain structure is responsible for the formation of a free surface relief during uniaxial loading. Microscale normal and shear stresses associated with the direction perpendicular to the free surface develop in the bulk of the material and, acting from the inside, give rise to surface ridges and valleys.

Modeling and analysis of dry friction in micro-forming of metals

The Tabor friction model was modified by introducing the friction factor. Based on the multi-region model, the micro-uniaxial compression process was simulated to study the size effect considering dry friction. It was found that the grain-boundary has little effect on the dry friction behavior. The mechanical properties of individual grains either in the contact area or in the non-contact area have a significant influence on the friction behavior. With decrease of specimen's size, the average friction coefficient did not vary much but the value of friction coefficient of each random grain orientation distribution becomes more dispersive.

Investigation of Strain Gradients and Magnitudes During Microbending

Sheet metal forming of parts with microscale dimensions is gaining importance due to the current trend toward miniaturization, especially in the electronics industry. In microforming, although the process dimensions are scaled down, the polycrystalline material stays the same (e.g., the grain size remains constant). When the specimen feature size approaches the grain size, the properties of individual grains begin to affect the overall deformation behavior. This results in inhomogeneous deformation and increased data scatter of the process parameters. In this research, the influence of the specimen size and the grain size on the distribution of plastic deformation through the thickness during a three-point microbending process is investigated via digital image correlation (DIC). Results showed that with miniaturization, a decrease in the strain gradient existed which matched previous research with respect to microhardness measurement.

Computational elastic up‐scaling of sandstone on the basis of X‐ray micro‐tomographic images

ABSTRACTUp‐scaling the elastic properties of digitized rock volumes as obtained from X‐ray computer tomography (CT) imaging via computer simulations has the potential to assist and complement laboratory measurements. This computational up‐scaling approach remains a challenging task as the overall elastic properties are not only dependent on the elastic properties of individual grains but also on the hardly resolvable pore spaces between adjacent grains such as micro‐cracks. We develop a digitized rock image and elastic up‐scaling workflow based on general‐purpose and widely available software packages. Particular attention is paid to CT image processing including filtering, smoothing and segmentation. A strategy for optimal meshing for subsequent finite‐element modelling is also proposed. We apply this workflow to the micro‐tomographic image of a well‐consolidated, feldspatic sandstone sample and determine the up‐scaled bulk and shear moduli. These effective elastic moduli are compared to the moduli inferred from laboratory ultrasound measurements at variable effective stresses (0–70 MPa). We observe that the numerically up‐scaled elastic moduli correspond to the moduli at a certain effective stress level (50 MPa), beyond which the effective‐stress dependency follows a linear trend. This indicates that the computational up‐scaling approach yields moduli as if all compliant (soft) porosity was absent, i.e., microcracks are closed. To confirm this hypothesis, we estimate the amount of soft porosity on the basis of the double‐porosity theory (Shapiro, 2003) and find that at 50 MPa the soft porosity is indeed practically zero. We conclude that our computational elastic up‐scaling approach yields physically consistent effective moduli even if some geometrical features are below CT resolution. To account for these sub‐resolution features either theoretical or additional computational approaches can be used.

Characterization of individual grain boundaries and grains of CaCu3Ti4O12 ceramic

Microcontact measurement is employed to locally investigate the electric and dielectric properties of individual grains and grain boundaries in CaCu3Ti4O12 ceramic. The measurements give more detail of the impedance spectroscopy, capacitance, and I–V characteristics of the microstructure, and will help with further understanding of the mechanism of the electric and dielectric properties of CaCu3Ti4O12 ceramics.

Ba0.5Sr0.5Co0.8Fe0.2O3-δ for Oxygen Separation Membranes

The crystal structure and chemical composition of Ba0.5Sr0.5Co0.8Fe0.2O3-δ bulk samples and powders were studied after heat treatments between 700 ° C and 1000 ° C. X-ray diffractometry (XRD) and in addition transmission electron microscopy (TEM) combined with energy dispersive X-ray spectroscopy (EDXS) was applied to analyze the properties of individual grains. Besides the cubic perovskite phase a hexagonal phase and an additional, not yet clearly identified phase was found at temperatures below 900 ° C.

Crystal plasticity modeling of cyclic deformation for a polycrystalline nickel-based superalloy at high temperature

Cyclic deformation at elevated temperature has been modeled for a polycrystalline nickel-based superalloy using the crystal-plasticity constitutive formulations. Finite element analyses were carried out for a representative volume element (RVE), consisting of randomly oriented grains and subjected to periodic boundary constraints. Model parameters were determined by fitting the strain-controlled cyclic test data at 650 °C for three different loading rates. Simulated results are in good agreement with the experimental data for both stress–strain loops and cyclic hardening behavior. The model was utilized to predict the stress relaxation behavior during the hold periods at the maximum and minimum strain levels, and the prediction compares well with the experimental results. Localized stress and strain concentrations were observed due to the heterogeneous nature of grain microstructure and the mismatch of the mechanical properties of individual grains.

Transport properties of low-angle grain boundaries and granular coated conductors

Grain boundaries in oxide superconductors are of central importance both for engineeringapplications and for issues in fundamental science. Although they have been closely studiedfor more than a decade, there is still by no means a consensus on the properties ofindividual boundaries, or their collective behaviour when current percolates in a granularmaterial. A quantitative description of current and flux percolation is essential forthe practical specification of conductors and for charting routes to conductoroptimization. There are three components to the problem: (i) the properties of individualgrains and grain boundaries, (ii) microstructure, texture and grain morphology, and(iii) the macroscopic geometrical constraints such as conductor size and shape. Onthe basis of new results on the angular variation in an applied magnetic fieldof the grain boundary critical current, it will be argued that grain morphologyas well as texture is important for the critical current of a coated conductor.Progress in characterizing and modelling current and flux percolation will besurveyed and particular gaps in understanding and areas of neglect discussed.

Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to r(-rho), r being the distance traveled by a grain in a single toppling event. The exponent rho controls the average rolling distance. We have shown that the crossover from the power law to the stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for 1<rho<2, where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short-range regime for rho>2, where the average rolling distance is independent of the system size.

Stress Concentrations At Grain Boundaries DueTo Anisotropic Elastic Material Behavior

Scanning electron microscopy (SEM) examinations on samples of the (3-titanium alloy LCB (low cost beta by TIMET) after fatigue tests revealed a strong influence of the crystallographic misorientation of adjacent grains on crack initiation and short crack growth. From that point of view the knowledge of the anisotropic elastic properties of individual grains and their influence on the stress distribution within the microstructure is of great importance to understand crack initiation and propagation mechanisms. For this purpose the microstructure of polycrystals at sites where cracks initiated was simulated by means of three dimensional finite element (FE) calculations, considering the elastic anisotropy of the grains. However, to ensure a realistic simulation, experimental data like the grain geometry and crystallographic orientation were used, which had been measured by the electron back-scattered diffraction (EBSD) technique. Beside this, the values of the elastic constants of the single-crystalline material were required. In this study a method was developed and applied to determine the three elastic constants of the anisotropic bcc structure of single-crystalline p-Titanium (solution annealed LCB) from experimental data of polycrystals. The results of local strain measurements by ISDG (inter ferometric strain-displacement gauge) and EBSD evaluation of the microstructure as well as the Young's modulus and the Poisson's ratio of the polycrystal serve as input parameters for this method. The calculated anisotropic elastic constants allow the application of the above-mentioned FE-simulation to the microstructure of the polycrystalline alloy LCB. SEM examinations of the fatigued samples show that short cracks initiate exactly at the locations where the FE-simulation yielded the highest stresses. Damage & Fracture Mechanics VI, C.A. Brebbia, A.P.S. Selvadurai, (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-812-0