Showing papers on "Representative elementary volume published in 2018"

Mechanical Characterizations of 3D-printed PLLA/Steel Particle Composites.

Abstract: The objective of this study is to characterize the micromechanical properties of poly-l-lactic acid (PLLA) composites reinforced by grade 420 stainless steel (SS) particles with a specific focus on the interphase properties. The specimens were manufactured using 3D printing techniques due to its many benefits, including high accuracy, cost effectiveness and customized geometry. The adopted fused filament fabrication resulted in a thin interphase layer with an average thickness of 3 µm. The mechanical properties of each phase, as well as the interphase, were characterized by nanoindentation tests. The effect of matrix degradation, i.e., imperfect bonding, on the elastic modulus of the composite was further examined by a representative volume element (RVE) model. The results showed that the interphase layer provided a smooth transition of elastic modulus from steel particles to the polymeric matrix. A 10% volume fraction of steel particles could enhance the elastic modulus of PLLA polymer by 31%. In addition, steel particles took 37% to 59% of the applied load with respect to the particle volume fraction. We found that degradation of the interphase reduced the elastic modulus of the composite by 70% and 7% under tensile and compressive loads, respectively. The shear modulus of the composite with 10% particles decreased by 36%, i.e., lower than pure PLLA, when debonding occurred.

Melting process in porous media around two hot cylinders: Numerical study using the lattice Boltzmann method

Abstract: Instantaneous melting of ice is accelerated inside a horizontal rectangular cavity with two vertically arranged cylinders using metallic porous matrix made of Ni-Steel alloys. The enthalpy-based lattice Boltzmann method (LBM) with a double distribution function (DDF) is employed at the representative elementary volume (REV) scale. Single-phase model is used and there is a local thermal equilibrium between porous structure and ice. Inserting metallic porous material into the base PCM results in the enhancement of the heat conduction and weakening of the natural convection flow. Concentric pattern of the solid–liquid interface persists in porous samples comparing to the pure PCM melting. Reducing porosity causes decrease of the full melting time and thermal storage capacity of the system. Thermal conductivity ratio has to be enlarged in porous samples with higher porosity from energy saving viewpoint.

A micromechanical study of stress concentrations in composites

Abstract: Random and periodic representations of composite microstructures are inherently different both in terms of the resultant range of stresses that each phase carries as well as the total load over the entire volume comprising both matrix and fiber phases. In this study, an algorithm was developed to generate random representative volume elements (RVE) with varying volume fractions and minimum distances between fibers. The random microstructures were analyzed using finite element models (FEM) and the results compared to those for periodic microstructured RVEs in terms of the range of stress values, maximum stress, and homogenized stiffness values. Using a large number of random RVE analyses, a meaningful estimation for range and average maximum stress in the matrix phase was achieved. Results show that random microstructures exhibit a much larger range of stress values than periodic microstructures, resulting in an uneven distribution of load and distinct areas of high and low stress concentration in the matrix. It is shown that the maximum stress in the matrix phase, often responsible for failure initiation, is largely dependent on the random morphology, minimum distances between fibers, and volume fraction. Moreover, it is shown that the predicted overall load-carrying capacity of the matrix changes depending on the use of random or periodic microstructures.

Probabilistic micromechanical spatial variability quantification in laminated composites

Abstract: This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the correlated spatially varying properties. The physically relevant random field based uncertainty modelling approach with spatial correlation is adopted in this paper on the basis of Karhunen-Loeve expansion. An efficient coupled HDMR and DMORPH based stochastic algorithm is developed for composite laminates to quantify the probabilistic characteristics in global responses. Convergence of the algorithm for probabilistic dynamics and stability analysis of the structure is verified and validated with respect to direct Monte Carlo simulation (MCS) based on finite element method. The significance of considering higher buckling modes in a stochastic analysis is highlighted. Sensitivity analysis is performed to ascertain the relative importance of different macromechanical and micromechanical properties. The importance of incorporating source-uncertainty in spatially varying micromechanical material properties is demonstrated numerically. The results reveal that stochasticity (/system irregularity) in material and structural attributes influences the system performance significantly depending on the type of analysis and the adopted uncertainty modelling approach, affirming the necessity to consider different forms of source-uncertainties during the analysis to ensure adequate safety, sustainability and robustness of the structure.

Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects

Abstract: The main objective is to investigate an effect of anisotropic distribution of the reinforcing particles in a cubic representative volume element (RVE) of the carbon–polymer composite including stochastic interphases on its homogenized elastic characteristics. This is done using a probabilistic homogenization technique implemented using a triple approach based on the stochastic perturbation method, Monte Carlo simulation as well as on the semi-analytical approach. On the other hand, the finite element method solution to the uniform deformations of this RVE is carried out in the system ABAQUS. This composite model consists of two neighboring scales–the micro-contact scale relevant to the imperfect interface and the micro-scale—having 27 particles inside a cubic volume of the polymeric matrix. Stochastic interface defects in the form of semi-spheres with Gaussian radius are replaced with the interphase having probabilistically averaged elastic properties, and then such a three-component composite is subjected to computational homogenization on the microscale. The computational experiments described here include FEM error analysis, sensitivity assessment, deterministic results as well as the basic probabilistic moments and coefficients (expectations, deviations, skewness and kurtosis) of all the components of the effective elasticity tensor. They also include quantification of anisotropy of this stiffness tensor using the Zener, Chung–Buessem and the universal anisotropy indexes. A new tensor anisotropy index is proposed that quantifies anisotropy on the basis of all not null tensor coefficients and remains effective also for tensors other than cubic (orthotropic, triclinic and also monoclinic). Some comparison with previous analyses concerning the isotropic case is also included to demonstrate the anisotropy effect as well as the numerical effort to study randomness in composites with anisotropic distribution of reinforcements and inclusions.

Sensitivity to material contrast in homogenization of random particle composites as micropolar continua

Abstract: Several composite materials used in engineering – such as ceramic/metal matrix composites, concrete, masonry-like/geo–materials and innovative meta–materials – have internal micro-structures characterized by a random distribution of inclusions (particles) embedded in a matrix. Their structural response is highly influenced not only by the mechanical properties of components, but also by the shape, size and position of the inclusions. In this work, we adopt a statistically-based micropolar homogenization procedure, to obtain the overall elastic properties of homogeneous micropolar continua able to naturally account for scale and skew–symmetric shear effects. Attention is paid to the sensitivity to material contrast, defined as the mismatch between classical and micropolar constitutive properties of matrix and inclusions. A statistical specifically conceived convergence criterion is adopted which allow us to identify the REV (Representative Volume Element) for any value of material contrast.

Old and New Approaches Predicting the Diffusion in Porous Media

Abstract: An accurate quantitative description of the diffusion coefficient in a porous medium is essential for predictive transport modeling. Well-established relations, such as proposed by Buckingham, Penman, and Millington–Quirk, relate the scalar diffusion coefficient to the porous medium’s porosity. To capture the porous medium’s structure in more detail, further models include fitting parameters, geometric, or shape factors. Some models additionally account for the tortuosity, e.g., via Archie’s law. A validation of such models has been carried out mainly via experiments relating the proposed description to a specific class of porous media (by means of parameter fitting). Contrary to these approaches, upscaling methods directly enable calculating the full, potentially anisotropic, effective diffusion tensor without any fitting parameters. As input only the geometric information in terms of a representative elementary volume is needed. To compute the diffusion–porosity relations, supplementary cell problems must be solved numerically and their (flux) solutions must be integrated. We apply this approach to provide easy-to-use quantitative diffusion–porosity relations that are based on representative single grain, platy, blocky, prismatic soil structures, porous networks, or random porous media. As a discretization method, we use the discontinuous Galerkin method on structured grids. To make the relations explicit, interpolation of the obtained data is used. We furthermore compare the obtained diffusion–porosity relations with the well-established relations mentioned above and also with the well-known Voigt–Reiss or Hashin–Shtrikman bounds. We discuss the ranges of validity and further provide the explicit relations between the diffusion and surface area and comment on the role of a tortuosity–porosity relation.

Micromechanical Progressive Failure Analysis of Fiber-Reinforced Composite Using Refined Beam Models

Abstract: An efficient and novel micromechanical computational platform for progressive failure analysis of fiber-reinforced composites is presented. The numerical framework is based on a recently developed micromechanical platform built using a class of refined beam models called Carrera unified formulation (CUF), a generalized hierarchical formulation which yields a refined structural theory via variable kinematic description. The crack band theory is implemented in the framework to capture the damage propagation within the constituents of composite materials. The initiation and orientation of the crack band in the matrix are determined using the maximum principal stress state and the traction-separation law governing the crack band growth is related to the fracture toughness of the matrix. A representative volume element (RVE) containing randomly distributed fibers is modeled using the component-wise (CW) approach, an extension of CUF beam model based on Lagrange type polynomials. The efficiency of the proposed numerical framework is achieved through the ability of the CUF models to provide accurate three-dimensional (3D) displacement and stress fields at a reduced computational cost. The numerical results are compared against experimental data available in the literature and an analogous 3D finite element model with the same constitutive crack band model. The applicability of CUF beam models as a novel micromechanical platform for progressive failure analysis as well as the multifold efficiency of CUF models in terms of CPU time are highlighted.

Microstructure and Property-Based Statistically Equivalent Representative Volume Elements for Polycrystalline Ni-Based Superalloys Containing Annealing Twins

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

Computational Homogenization of Mechanical Properties for Laminate Composites Reinforced with Thin Film Made of Carbon Nanotubes

Abstract: Elastic properties of laminate composites based Carbone Nanotubes (CNTs), used in military applications, were estimated using homogenization techniques and compared to the experimental data. The composite consists of three phases: T300 6k carbon fibers fabric with 5HS (satin) weave, baseline pure Epoxy matrix and CNTs added with 0.5%, 1%, 2% and 4%. Two step homogenization methods based RVE model were employed. The objective of this paper is to determine the elastic properties of structure starting from the knowledge of those of constituents (CNTs, Epoxy and carbon fibers fabric). It is assumed that the composites have a geometric periodicity and the homogenization model can be represented by a representative volume element (RVE). For multi-scale analysis, finite element modeling of unit cell based two step homogenization method is used. The first step gives the properties of thin film made of epoxy and CNTs and the second is used for homogenization of laminate composite. The fabric unit cell is chosen using a set of microscopic observation and then identified by its ability to enclose the characteristic periodic repeat in the fabric weave. The unit cell model of 5-Harness satin weave fabric textile composite is identified for numerical approach and their dimensions are chosen based on some microstructural measurements. Finally, a good comparison was obtained between the predicted elastic properties using numerical homogenization approach and the obtained experimental data with experimental tests.

Rapid multiscale modeling of flow in porous media

Abstract: Increasing our understanding of single and multiphase flow properties requires an accurate description of the pore system. Recent imaging technology provides images at different resolutions by which the pore space can be characterized properly. An accurate prediction of flow properties cannot be achieved computationally if the simulation domain is small. For a large sample, however, one may upscale the fine-scale information through pore-network modeling to expedite the computations. Due to a small field of view of the available images, such modeling can be conducted with ease for simple and heterogeneous rock samples. For complex and multiscale systems, however, one single-resolution image may not be sufficient. Thus, one should integrate the valuable information that lies in both the fine- and coarse scale into the pore network. In this paper, multiscale pore networks are generated which can take the microporosity, either in the solid phase (i.e., grain filling) or pore space (pore filling), into account. The proposed method can use the available high-resolution images for different pores and/or grains and stochastically build several micronetworks, which avoids fewer simplifications as present in the current methods. Next, depending on the location of high-resolution images, the generated micronetworks are implanted in the designated spots. Furthermore, cementation is also quantified and simulated by eroding the pore space. Finally, all the above physics are integrated within several stochastic multiscale networks. The final models are then used to evaluate the flow properties by comparing the statistical characteristics and single or multiphase flow behavior (e.g., capillary pressure, absolute and relative permeability). The results indicate the importance of incorporating the micropores as they can effectively connect the large-scale and isolated macropores. Furthermore, the single- and multiscale pore networks manifested a significant difference between the capillary pressure and residual saturation. Finally, a representative elementary volume study based on the generated multiscale pore networks for different scenarios is performed and the results are compared.