Characterization Of Heterogeneous Materials Research Articles

Multiscale formulation for materials composed by a saturated porous matrix and solid inclusions

Despite all the progress achieved in the characterization of heterogeneous materials by using multiscale paradigms based on the Representative Volume Element concept (RVE), there are still many aspects that demand ongoing development. We mention, for instance, in-homogeneous media with internal micro-structure comprising a mixture of components that require a dissimilar number/character of primary fields to describe their physical behavior. Micro-structures constituted by a saturated porous matrix (described through the pair displacement/pore pressure fields) endowed with impermeable non-porous solid inclusions (described only by the displacement field) are a typical example among many other practical applications. This new level of heterogeneity, between the set of primal descriptors for each micro-scale constituent, claims detailed revisions and novel adjustments in multiscale RVE-based theories.In this work, we present a first-order RVE-based formulation to address with the aforementioned phenomenology at a smaller length scale. At the macro-scale, the well-known poromechanics theory is preserved, where the constitutive response is provided by homogenization of the corresponding micro-scale problem. Two important attributes feature the model: (i) it is encompassed within the general framework posited by the “Method of Multiscale Virtual Power (MMVP)”, this leads to a variationally consistent methodology; (ii) our formulation preserves the objectivity with respect to the RVE-size (an indispensable but uncommon characteristic in RVE-based multiscale approaches for saturated porous media), due to it is based in a recent contribution of the authors (the so-called Selective Order Expansion technique “SOE”).The formulation is implemented following the squared Finite Element (FE2) numerical scheme. The potentialities of the model are demonstrated through a detailed series of numerical examples, including rigorous comparisons against the Direct Numerical Simulation (DNS) procedure.

A step towards 6D WAXD tensor tomography.

X-ray scattering/diffraction tensor tomography techniques are promising methods to acquire the 3D texture information of heterogeneous biological tissues at micrometre resolution. However, the methods suffer from a long overall acquisition time due to multi-dimensional scanning across real and reciprocal space. Here, a new approach is introduced to obtain 3D reciprocal information of each illuminated scanning volume using mathematic modeling, which is equivalent to a physical scanning procedure for collecting the full reciprocal information required for voxel reconstruction. The virtual reciprocal scanning scheme was validated by a simulated 6D wide-angle X-ray diffraction tomography experiment. The theoretical validation of the method represents an important technological advancement for 6D diffraction tensor tomography and a crucial step towards pervasive applications in the characterization of heterogeneous materials.

A design strategy for analyzing signal integrity in DDR3 bus of high speed embedded systems

A complex modern embedded system using a multi-core Central Processing Unit (CPU) toward a compact integrated design in a single Printed Circuit Board (PCB). One of the biggest challenges of the design is to meet the Signal Integrity for high speed Double Data Rate 3 Synchronous Dynamic Random-Access Memory (DDR3) bus. A typical strategy to solve the challenge is the simulation on the computer, but this is not always an effective solution as has a gap between simulation software and practical PCB. The gap is correlated to localized changes in copper density within the PCB and characterization of heterogeneous materials in PCB that could lead to differences in the real PCB. The purpose of the research presents an analysis methodology to design DDR) memory interfaces in high speed embedded systems, related to Signal Integrity and the impact of copper density on PCB trace impedances to overcome these challenges. Moreover, the presented design methodology is also applied to the next generation DDR as well as other styles of CPU.

Optimized Polynomial Virtual Fields Method for Constitutive Parameters Identification of Orthotropic Bimaterials

Heterogeneous materials are widely applied in many fields. Owing to the spatial variation of its constitutive parameters, the mechanical characterization of heterogeneous materials is very important. The virtual fields method has been used to identify the constitutive parameters of materials. However, there is a limitation: constitutive parameters of one material have to be a priori; then, constitutive parameters of the other one can be identified. Aiming at this limitation, this article presents a method to identify the constitutive parameters of heterogeneous orthotropic bimaterials under the condition that constitutive parameters of both materials are all unknown from a single test. A constitutive parameter identification method of orthotropic bimaterials based on optimized virtual field and digital image correlation is proposed. The feasibility of this method is verified by simulating the deformation fields of a two‐layer material under three‐point bending load. The results of numerical experiments with FEM simulations show that the weighted relative error of the constitutive parameter is less than 1%. The results suggest that the variation coefficient‐to‐noise ratio can perform a priori evaluation of a confidence interval on the identified stiffness components. The results of numerical experiments with DIC simulations show that the weighted relative error is 1.44%, which is due to the noise in the strain data calculated by DIC method.

Determination of Liberation Degree of Mechanically Processed Waste Printed Circuit Boards by Using the Digital Microscope and SEM-EDS Analysis

Characterization of heterogeneous materials, such as particles from mechanically processed waste printed circuit boards, is a challenging task. The majority of characterization methods either give average information or information that is very limited and in a tiny area of specific interest. That said, capturing such heterogeneity is significantly important for any kind of processes. Degree of liberation, indicating how much the target component is liberated from the non-valuable components, is a key property to determine the success of subsequent process for valuable material recovery. This work analyzed the degree of liberation of metals within the products of hammer milling process via the combination of image acquisition and analysis. The digital microscope and a scanning electron microscope (SEM) coupled with the energy dispersive spectroscopy (EDS) were used for image acquisition and elemental mapping, in order to evaluate the selective liberation under different milling conditions (i.e., feed mass, milling time) for different metals (mainly Cu and Al) and particle size fractions. The obtained liberation degree was also modelled and determined the liberation parameters that were compared. The results showed that the degree of liberation significantly depend on the milling conditions and metals we analyzed, and well correlated with the selective metal enrichment behavior. Results between the two methods showed some similarities and discrepancies. The advantages and disadvantages of the above two methods were identified and discussed in the paper, in addition to their methodological developments.

A large coaxial reflection cell for broadband dielectric characterization of coarse-grained materials

Knowledge of the frequency-dependent electromagnetic properties of coarse-grained materials is imperative for the successful application of high frequency electromagnetic measurement techniques for near and subsurface monitoring. This paper reports the design, calibration and application of a novel one-port large coaxial cell for broadband complex permittivity measurements of civil engineering materials. It was designed to allow the characterization of heterogeneous material with large aggregate dimensions (up to 28 mm) over a frequency range from 1 MHz–860 MHz. In the first step, the system parameters were calibrated using the measured scattering function in a perfectly known dielectric material in an optimization scheme. In the second step, the method was validated with measurements made on standard liquids. Then the performance of the cell was evaluated on a compacted coarse-grained soil. The dielectric spectra were obtained by means of fitting the measured scattering function using a transverse electromagnetic mode propagation model considering the frequency-dependent complex permittivity. Two scenarios were systematically analyzed and compared. The first scenario consisted of a broadband generalized dielectric relaxation model with two Cole–Cole type relaxation processes related to the interaction of the aqueous phase and the solid phase, a constant high frequency contribution as well as an apparent direct current conductivity term. The second scenario relied on a three-phase theoretical mixture equation which was used in a forward approach in order to calibrate the model. Both scenarios provide almost identical results for the broadband effective complex relative permittivity. The combination of both scenarios suggests the simultaneous estimation of water content, density, bulk and pore water conductivity for road base materials for in situ applications.

Thermal characterization of materials using Karhunen–Loève decomposition techniques – Part II. Heterogeneous materials

A new method for thermal characterization of heterogeneous materials has been proposed. As for homogeneous materials in the first part of the paper, the method is based on the use of Karhunen–Loève decomposition (KLD) techniques in association with infrared thermography experiments or any other experimental device providing dense data in the spatial coordinate. Orthogonal properties of KLD eigenfunctions and states are used for achieving simple estimates of thermal diffusivities. It has been proven that diffusivities can be estimated without explicit knowledge of variables and parameters related to heat exchanges at the interfaces (i.e. thermal conductivities, thermal contact resistances). Indeed, the diffusivities estimates only depend on some few KLD eigenelements. As a result, a significant amplification of the signal/noise ratios is reached. Moreover, it is shown that spatially uncorrelated noise has no effect on KLD eigenfunctions, the noise being entirely reported on states (time-dependent projection coefficients). This is particularly interesting because thermal diffusivities estimates involve spatial derivatives of the eigenfunctions. Consequently, the proposed method results in an attractive combination of parsimony and robustness to noise. The effectiveness of the method is illustrated through some simulated experimental applications.

Characterization of Heterogeneous Materials with the Confocal Raman AFM

Characterization of Heterogeneous Materials with the Confocal Raman AFM

Characterization of heterogeneous materials under shear loading at finite strain

This article presents a homogenization procedure to predict the effective shear response of heterogeneous materials at large deformation. Assuming local periodicity, heterogeneous microstructure is identified by a representative volume element that is subjected to an equivalent macroscopic deformation field. The energy balance and periodicity conditions are considered to relate macro and micro-stress fields. Based on the symmetrical planes of the microstructure and local periodicity, it is shown that the analysis of one-quarter of three-dimensional representative volume element is enough to evaluate the effective shear response at finite deformation. A computational method is subsequently developed to obtain the shear response of heterogeneous microstructures. The homogenization procedure is implemented to evaluate shear response of two specific heterogeneous materials, elastomeric composite and reinforced viscoelastic fluid. The performance is successfully verified by comparison of the deformation in the macroscopic level to the response of a homogenized cell.

Characterization of Heterogeneous Materials with the Confocal Raman AFM

Extract Extended abstract of a paper presented at Microscopy and Microanalysis 2007 in Ft. Lauderdale, Florida, USA, August 5 – August 9, 2007

Characterization of Thin Polymer Films on the Nanometer Scale with Confocal Raman AFM

AbstractThe combination of an atomic force microscope (AFM) with a Confocal Raman Microscope (CRM) has been used to study the composition of various thin films of polymer blends. The high spatial resolution of the AFM enables the morphological characterization of the polymer blends on the nanometer scale. Furthermore, when operating the AFM in Digital Pulsed Force Mode (DPFM), topographic information and local stiffness can be simultaneously recorded. This allows the material‐sensitive characterization of heterogeneous materials. Thin films where PMMA (at room temperature a glassy polymer) is blended with two different styrene‐butadiene rubbers are investigated. The presence of PMMA in both phase‐separated thin films allows the comparison of the mechanical properties of the two different rubber phases using DPFM‐AFM. When PMMA is blended with PET due to their similar mechanical properties (both are in the glassy state at room temperature) the assignment of the two phases to the corresponding polymers by AFM is rather difficult. Here, Raman spectroscopy provides additional information on the chemical composition of materials. In combination with a confocal microscope, the spatial distribution of the various phases can be determined with a resolution down to 200 nm. Therefore, the topographically different structures observed in AFM images can be associated to the chemical composition by using the Confocal Raman Microscope (CRM).

Rheological Characterization of Heterogeneous Materials with Evolving Properties

The paper deals with the rheological characterization of different heterogeneous civil engineering materials that have time- dependent properties. Studies on cellular concrete, mortar, hydraulic concrete, and cold bituminous mixes are presented. The properties are monitored throughout setting and hardening. Such materials are heterogeneous mixtures containing solid particles, binder, fluids, and gas bubbles. For all of these materials, different formulations were investigated, such as water content, binder proportioning, and compaction level. A nondestructive device allows the setting to be monitored and to be clearly characterized. This device makes it possible to simultaneously study the propagation of compressional and shear waves in the same sample of material. To prevent diffraction of waves from heterogeneities, a condition of a long wavelength compared to the heterogeneity size is required, so low frequencies are used ~20-1,000 Hz!. Velocity and damping coefficients versus time are deduced, then related to rheological viscoelastic properties by an inverse analysis. The linear behavior of these materials under small strains is proved, and the measurements are very repetitive and sensitive to the nature and the component proportioning of the materials. The rheological evolutions of the different materials are presented and compared. It is shown that the normalized evolution of hydraulic concretes follows a single master curve for all of the different formulations investigated. Similar results are established for cellular concretes and mortars.

Grüneisen Tensor of an Anisotropic Composite

A phenomenological model of an anisotropic composite, quartz phe nolic, is presented. The model assumes that the quartz phenolic macro scopically has the same symmetry properties as a hexagonal single crystal. The formalism relating the Gruneisen tensor to elastic constants, coefficients of thermal expansion, and specific heat was applied to the composite, and the Gruneisen parameters were evaluated from measured values of these quantities. Further, direct measurements of the Gruneisen parameters were accomplished by means of an electron beam induced stress wave technique, and the resulting values were compared with those computed from the elastic and thermal data. Electron beam data produced values Γx = 0.23 ± 0.03 and r = 0.28 ± 0.03, while the values of the Gruneisen parameters computed from the elastic and thermal data were somewhat higher than the electron beam results. The analysis demonstrated the utility of symmetry properties for the characterization of heterogeneous materials.