Mechanics of light weight proppants: A discrete approach

The computational and experimental assessment of light-weight proppants are undertaken to identify their effectiveness and efficiency to replace sand enlisted in hydraulic fracturing treatments in oil or gas well operations. A mixture of ground-nut-shells, aluminum or ceramic particles are shown to reduce the viscosity of the fracturing fluid while increasing its resistance to compression. Herein explicit dynamic finite element method is implemented to study quasi-static compression of a proppant pack where each granule (particle) is modeled individually. Various mixtures of hard and soft particles are investigated as a function of shape, size and inter-particle friction. The particle interactions clearly illustrate changes in pore space as a function of pressure, mixture composition and friction. The pressure vs displacement response of a proppant pack reflects strong dependence on mixture composition and initial particle configuration and has been compared with the test data. Friction leads to higher porosity by limiting particle rearrangement. Models reveal that softer rock with a mixture of hard and soft particles inhibit flowback but may decrease the pack permeability.     

On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis

Mechanical behavior of granular soils is a classic research realm but still yet not completely understood as it can be influenced by a large number of factors, including confining pressure, soil density, loading conditions, and anisotropy of soil etc. Traditionally granular materials are macroscopically regarded as continua and their particulate and discrete nature has not been thoroughly considered although many researches indicate the macro mechanical behavior closely depends on the micro-scale characteristics of particles. This paper presents a DEM (discrete element method)-based micromechanical investigation of inter-particle friction effects on the behavior of granular materials. In this study, biaxial DEM simulations are carried out under both ‘drained’ and ‘undrained’ (constant volume) conditions. The numerical experiments employ samples having similar initial isotropic fabric and density, and the same confining pressure, but with different inter-particle friction coefficient. Test results show that the inter-particle friction has a substantial effect on the stress-strain curve, peak strength and dilatancy characteristics of the granular assembly. Clearly, it is noted that apart from the inter-particle friction, the shear resistance is also contributed to the dilation and the particle packing and arrangements. The corresponding microstructure evolutions and variations in contact properties in the particulate level are also elaborated, to interpret the origin of the different macro-scale response due to variations in the inter-particle friction.     

A methodology to measure the interface shear strength by means of the fiber push-in test

A methodology is presented to measure the fiber/matrix interface shear strength in composites. The strategy is based on performing a fiber push-in test at the central fiber of highly-packed fiber clusters with hexagonal symmetry which are often found in unidirectional composites with a high volume fraction of fibers. The mechanics of this test was analyzed in detail by means of three-dimensional finite element simulations. In particular, the influence of different parameters (interface shear strength, toughness and friction as well as fiber longitudinal elastic modulus and curing stresses) on the critical load at the onset of debonding was established. From the results of the numerical simulations, a simple relationship between the critical load and the interface shear strength is proposed. The methodology was validated in an unidirectional C/epoxy composite and the advantages and limitations of the proposed methodology are indicated.     

Finite element modeling of the filament winding process

A finite element model of the wet filament winding process was developed. In particular, a general purpose software for finite element analysis was used to calculate the fiber volume fraction under different process conditions. Several unique user defined subroutines were developed to modify the commercial code for this specific application, and the numerical result was compared with experimental data for validation. In order to predict the radial distribution of the fiber volume fraction within a wet wound cylinder, three unique user defined subroutines were incorporated into the commercial finite element code: a fiber consolidation/compaction model, a thermochemical model of the resin and a resin mixing model. The fiber consolidation model describes the influence of the external radial compaction pressure of a new layer as it is wound onto the surface of existing layers. The thermochemical model includes both the cure kinetics and viscosity of the resin. This model analyzes the composite properties and tracks the viscosity of the resin, which is a function of the degree of cure of the resin. The resin mixing model describes the mixing of “old” and “new” resin as plies are compacted. Validations were made by comparing image analysis data of fiber volume fraction in each ply for filament wound cylinders with the FEM results. The good agreement of these comparisons demonstrated that the FEM approach has can predict fiber volume fraction over a range of winding conditions. This approach, then, is an invaluable tool for predicting the effects of winding parameters on cylinder structural quality.     

A numerical approach for determining the effective elastic symmetries of particulate-polymer composites

In this paper we deal with the problem of determining on the one hand the effective elastic properties of particulate-polymer composite materials and on the other hand the actual degree of symmetry of the resulting homogenised material. This twofold purpose has been accomplished by building a 2D as well as a 3D finite element model of the heterogeneous material and by using the strain-energy based numerical homogenisation technique. Both finite element models are able to reproduce with a good level of accuracy the real microstructure of the composite material by considering a random distribution of both particles and air bubbles (that are generated by the fabrication process). To assess the effectiveness of the proposed models, we present a numerical study to determine the effective elastic properties of the composite along with a comparison with the existing analytical and experimental results taken from literature and a sensitivity analysis in terms of the spatial distribution of the particles of the unit cell. Numerical results show that both models are able to provide the equivalent elastic properties with a very good level of accuracy when compared to experimental results and that the particulate-reinforced polymer composite could show, depending on the particles volume fraction and arrangement, an isotropic or a cubic elastic symmetry.     

Transient analysis of FGM and laminated composite structures using a refined 8-node ANS shell element

In this paper, we investigate the vibration analysis of functionally graded material (FGM) and laminated composite structures, using a refined 8-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The properties of FGM vary continuously through the thickness direction according to the volume fraction of constituents defined by sigmoid function, but in this method, their Poisson’s ratios of the FGM plates and shells are assumed to be constant. The finite element, based on a first-order shear deformation theory, is further improved by the combined use of assumed natural strains and different sets of collocation points for interpolation the different strain components. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The natural frequencies of plates and shells are presented, and the forced vibration analysis of FGM and laminated composite plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To validate and compare the finite element numerical solutions, the reference solutions of plates based on the Navier’s method, the series solutions of sigmoid FGM (S-FGM) plates are obtained. Results of the present theory show good agreement with the reference solutions. In addition the effect of damping is investigated on the forced vibration analysis of FGM plates and shells.     

A Numerical Study of the Development of Tensile Principal Stresses During Die Compaction

Although the average macroscopic stresses are compressive during die compaction, tensile stresses develop locally, and lead to fragmentation in low ductility particles. In this article, this phenomenon is analyzed using finite element discretization of an assembly of particles. The simulations show that there are two stages in die compaction, an early stage in which increased levels of tensile stresses develop in a number of particles located along discrete load transmission paths, and a second stage where the increasing homogeneity of the stress field leads to a decrease of the number of particles developing tensile principal stresses. A comparison between two scenarios with interparticle friction of w =0 and w =0.5 is presented. It is shown that: (1) high friction results in a higher number of particles under tensile stresses especially at low relative density, and (2) the peak fraction of material under high tensile stresses is double for w =0.5 compared to the frictionless case, and occurs at ~85% versus 88% for w =0.     

Stress analysis in hydroxyapatite/poly-l-lactide composite biomaterials

A three-dimensional (3D) finite element (FE) analysis of the stress concentration factor (SCF) in biocomposite model cell has been performed. The model composite consisted of a hydroxyapatite hard particle (HAp) embedded in poly-l-lactide soft matrix (PLLA). Two cases were considered, namely the shape of the particle was held constant while the volume fraction of HAp was varied and the particle shape was changed whilst the volume fraction was constant. For block shaped embedded particles, it was found that the SCF decreases with an increase of the HAp particle volume fraction. It was also found that the shape of reinforcing particles had little effect on the mechanical behaviour of material.     

Aggregate composites: a contact based modeling

A 3D model for elastic aggregate composites such as bituminous materials is presented. In this model, rigid angular particles are embedded into an elastic matrix; inter-particle contacts are modeled by a linear interface constitutive equation; Dirichlet tessellation and its dual Delaunay network are used to generate the particles and to connect them. The predictions of the model are compared with finite element estimates on periodic unit cells consisting of polyhedral particles. Simulations on several realizations of random materials are used for the determination of the minimum representative volume element (RVE) size.     

Effects of thickness and fiber volume fraction variations on strain field inhomogeneity

In this study, variations in thickness and fiber volume fraction are investigated as causes of elastic strain inhomogeneity in composite laminates under an applied transverse load. Standard carbon/epoxy tensile specimens were fabricated from unidirectional pre-impregnated material using two different manufacturing techniques that produced two different levels of surface roughness. Fiber volume fraction variation was computed by analyzing optical micrographs of the samples. During loading and unloading of the samples two-dimensional surface strain fields were measured on the specimen using digital image correlation. It was shown that in both cases the strain in the specimen is not uniform, as is generally assumed. Using finite element simulations the effects of fiber volume fraction variation and thickness variation were modeled individually and in combination. The simulations agree well with the experimental results and suggest that thickness variations are the dominant mechanisms involved in this elastic strain inhomogeneity.     

Cu-Cr粉体致密化颗粒变形及粒子流动三维数值模拟

基于MSC.Marc有限元软件对Cu-Cr粉体颗粒的单、双向致密化过程进行了细观数值模拟分析。研究了不同压制方式及摩檫系数对Cu-Cr粉体颗粒致密度及形貌变化的影响。结果表明:随着摩擦系数的增大,单向压制Cu-Cr粉体颗粒的致密化程度越高,摩擦系数为0.5时,单向压制的Cu-Cr粉体颗粒最高致密度为96.4040%;随着摩擦系数的减小,双向压制Cu-Cr粉体颗粒的致密化程度越高,在无摩擦理想条件下,双向压制Cu-Cr粉体颗粒致密度最高为89.1630%。在相同条件（摩擦系数、压制力）下,单向比双向压制Cu-Cr粉体颗粒有较高的流动性和致密度,Cu颗粒的应变量差值为1.3385,但双向致密化Cu-Cr粉体颗粒比单向压制的粒度均匀性好。模拟结果与实验结果相符合,验证了模型的准确性。      

Analysis and modeling of 3D Interlock fabric compaction behavior

During the preforming stage in Liquid Composite Molding (LCM), fibrous reinforcements are compacted to obtain the specified fiber volume fraction. Numerous studies have been carried out to understand their compression behaviors. The first objective of this investigation is to study experimentally the influence of the weaving parameters on the compaction behavior of five different 3D Interlock fabrics. In parallel, composite parts were fabricated to perform a microscopic analysis of fabric deformation after compression. The second objective is to provide a model of the experimental results. Since there is no nesting in three-dimensional woven fabrics, the compaction behavior turns out to be easier to predict than for laminates. A model based on experimental observations was devised to connect the compaction behavior with the deformation modes of five fabrics investigated. The good correlation with experiments confirms the assumptions on the main factors governing the compaction and relaxation of 3D Interlock fabrics.     

Densification behavior of aluminum alloy powder mixed with zirconia powder inclusion under cold compaction

Densification behavior of composite powders was investigated under cold compaction. Experimental data were obtained for aluminum alloy powder mixed with zirconia powder inclusion under triaxial compression. The Cap model with constraint factors was implemented into a finite element program (ABAQUS) to simulate compaction responses of composite powders during cold compaction. Finite element results were compared with experimental data for densification behavior of composite powders under cold isostatic pressing and die compaction. The agreement between experimental data and finite element calculations from the Cap model with the constraint factors was good for composite powders with low volume fractions of inclusions.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

Prediction of stiffness and stresses in z-fibre reinforced composite laminates

The mechanical properties of z-pinned composite laminates were examined numerically. Finite element calculations have been performed to understand how the through-thickness reinforcement modifies the engineering elastic constants and local stress distributions. Solutions were found for four basic laminate stacking sequences, all having two percent volume fraction of z-fibres. For the stiffness analysis, a micro-mechanical finite element model was employed that was based on the actual geometric configuration of a z-pinned composite unit cell. The numerical results agreed very well with some published solutions. It showed that by adding 2% volume fraction of z-fibres, the through-thickness Young's modulus was increased by 22–35%. The reductions in the in-plane moduli were contained within 7–10%. The stress analysis showed that interlaminar stress distributions near a laminate free edge were significantly affected when z-fibres were placed within a characteristic distance of one z-fibre diameter from the free edge. Local z-fibres carried significant amount of interlaminar normal and shear stresses.     

Fabrication process and electrical behavior of novel pressure-sensitive composites

A novel route was developed to fabricate a new pressure-sensitive composite by dispersing homogeneously conductive carbon particles in an insulating silicone rubber matrix. The composites showed a gradual change in electrical resistivity with applied pressure within percolation threshold region at a constant temperature. This type of gradual fall of resistivity with applied pressure is very important to fabricate pressure sensors. Various amounts of carbon particles were dispersed in a rubber matrix to understand the effect of volume fraction of conductive filler with applying external pressure on resistivity. A quantitative general effective media (GEM) theory was used to understand the resistivity of carbon–rubber composites system over a large range of volume fraction of carbon with applied pressure. The use of two different sizes of silicon rubber particles showed a significant effect in gradual fall of resistivity with applied pressure in the narrow range of percolation threshold. However, a large variation in resistivity from 1st measuring to 10th measuring was observed. A significant improvement in successive measuring of resistivity variation from 1st measuring to 10th measuring was observed when composites were fabricated in hexane solvent media. Finally, nano-sized Al₂O₃ was dispersed to control the resistivity variation upon successive measurement and to improve the mechanical properties of the composites. The material was suggested to use as unique materials as pressure sensors in practical applications mainly for robots.     

Modelling the relative permittivity of anisotropic insulating composites

Three models have been developed for predicting the dielectric permittivity of insulating composites with inclusions of different lengths (from nm and larger) and different shapes. Firstly, for approximately periodic materials, a finite element model based on a smallest repeating box method was used in order to mimic frameworks with fibres, crystals, clay platelets, foams and lamellar layers. The introduction of parameters for relative aspect ratio, overlap, rotation and packing density made the model very flexible while maintaining its simplicity. Secondly, a finite element composite model with oriented, randomly positioned particles of different shapes was constructed. Thirdly, an analytical relationship to approximate the effective permittivity of two- or three-phase insulators with brick-shaped inclusions was derived. For a wide range of volume fractions, permittivity ratios and packing conditions, this model gave solutions very close to corresponding finite element simulation data for lamellae, much closer than all the other analytical relationships found in the literature. Results obtained by simulation were in agreement with experimental data from the literature for composites of micrometre-sized hollow glass spheres in epoxy and nanocomposites of mica platelets in polyimide, provided that a third (interfacial) component was introduced.     

Densification Rates of Ceramic Matrix Composites with Initial Matrix Inhomogeneity

A viscoelastic finite element method is developed to analyze the effect of non-homogeneous matrix compaction on densification of ceramic matrix composites. The heterogeneous matrix of the composite is represented by a system of two or more co-axial cylinders of different initial matrix density. The sintering potential can be expressed in terms of a free strain rate. The free strain rate is derived from the relationship of relative density versus sintering time, measured from the neat matrix sample. The knowledge of free strain rate is a prerequisite for conducting the finite element analysis. For the heterogeneous matrix, two different density-time relationships are assumed, based on the concepts of neck formation and neck growth between contacting particles, and pore coarsening. The results of the finite element analysis show that a nonuniform compaction of the composite generally has a detrimental effect on the densification process.     

颗粒接触摩擦系数空间变异性对颗粒流双轴数值试验的影响

提出了考虑颗粒摩擦系数空间变异性的砂土双轴剪切响应分析方法。采用随机场模型表征颗粒摩擦系数空间变异性,通过Karhunen-Loève展开方法离散接触摩擦系数随机场,编写了基于颗粒流程序PFC2D和MATLAB的随机模拟耦合分析程序。研究了摩擦系数空间变异性对密砂试样的双轴剪切响应影响规律。结果表明:1） 提出方法可有效地考虑颗粒间接触摩擦系数变异性对土体材料双轴压缩宏观力学行为影响;2） 密砂试样在剪切过程中的应力-应变关系曲线、体积-应变关系曲线的变化规律与颗粒间接触摩擦系数不确定性密切相关,在初始加载阶段随机模拟的偏应力曲线、体积应变曲线基本重合,继续加载后曲线开始发散;3） 垂直相关距离对峰值偏应力均值与标准差影响明显大于水平相关距离。颗粒接触摩擦系数的均值对峰值偏应力的影响大于摩擦系数空间分布的影响。摩擦系数的空间分布会影响剪切带的形成位置。     

Mechanical properties of 3D printed interpenetrating phase composites with novel architectured 3D solid-sheet reinforcements

Interpenetrating phase composites (IPCs) are novel types of multifunctional composite materials. This work focuses on investigating experimentally and computationally the mechanical behavior of novel types of three-dimensional (3D) architectured two-phase IPCs. The current IPCs are architectured using several morphologies of the fascinating and mathematically-known triply periodic minimal surfaces (TPMS) that promote several multifunctional attributes. Specifically, the second hard reinforcing phase takes the architecture of one of the 3D non-intersecting and continuous TPMS-based solid sheets. The mechanical response of the 3D printed polymer-based IPCs is measured under uniaxial compression where the effect of varying the second-phase architecture and volume fraction is explored. Anisotropy induced by the 3D printing is also investigated. 3D finite element analysis has been performed and validated for predicting elastic properties of the various types of TPMS-based IPCs. The most effective TPMS architecture in enhancing the mechanical properties and damage-tolerance has been identified.