Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I – Constitutive modelling

Micromechanical analyses of unidirectional continuous-fibre reinforced composite materials were performed to study the mechanisms of deformation and fracture of the constituents, and their influence on the mechanical properties of the composite. Special focus was given to the matrix material behaviour as well as to the interface between constituents. The matrix was modelled using a pressure dependent, elasto-plastic thermodynamically consistent damage model. Cohesive elements were used to model the interface between matrix and fibres. Part I of this paper details the continuum model developed for a typical epoxy matrix. Part II will focus on micromechanical analyses of composite materials and the estimation of its elastic and strength properties.     

Helical Fiber Pull-out in Biological Materials

Many biological materials, such as wood and bone, possess helicoid microstructures at microscale, which can serve as reinforcing elements to transfer stress between crack surfaces and improve the fracture toughness of their composites. Failure processes, such as fiber/matrix interface debonding and sliding associated with pull-out of helical fibers, are responsible mainly for the high energy dissipation needed for the fracture toughness enhancement. Here we present systemic analyses of the pull-out behavior of a helical fiber from an elastic matrix via the finite element method(FEM) simulation, with implications regarding the underlying toughening mechanism of helicoid microstructures. We find that, through their uniform curvature and torsion, helical fibers can provide high pull-out force and large interface areas, resulting in high energy dissipation that accounts, to a large extent, for the high toughness of biological materials. The helicity of fiber shape in terms of the helical angle has significant effects on the force-displacement relationships as well as the corresponding energy dissipation during fiber pull-out.     

Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses

This paper presents the application of a new constitutive damage model for an epoxy matrix on micromechanical analyses of polymer composite materials. Different representative volume elements (RVEs) are developed with a random distribution of fibres. Upon application of periodic boundary conditions (PBCs) on the RVEs, different loading scenarios are applied and the mechanical response of the composite studied. Focus is given to the influence of the interface between fibre and matrix, as well as to the influence of the epoxy matrix, on the strength properties of the composite, damage initiation and propagation under different loading conditions.     

高聚物细观损伤演化的研究进展

聚合物的银纹化损伤与断裂是一个复杂和重要的研究课题。简述了银纹引发的(热)力学条件和银纹成核的微观机理。结合最新的研究进展,对银纹向前扩展的弯月面不稳定机理、银纹增厚的蠕变机理和界面转入机理作了较详细的分析与综合。考虑银纹细观结构中横系的作用,对银纹结构模型、银纹微纤断裂判据、微纤断裂行为的分子量和缠结密度相关性以及银纹与裂纹相互作用等问题进行了较详细的综述。指出银纹生长和断裂的深入研究可望建立材料宏观断裂韧性和材料细观结构以及微观参数之间的关联,为进行材料韧性的微观设计提供一条可行的途径。并对今后这一领域的研究方向和重点进行了展望。      

Crack initiation direction from interface of bonded dissimilar media

Debonded region of an interface between two dissimilar materials are modeled as a line crack that tends to enhance the initiation of failure by fracture. Depending on the load that interacts with dissimilar materials, no a priori knowledge of how failure would initiate from an existing interface crack is assumed. By application of the strain energy density criterion, potential crack initiation sites are obtained for different biaxial loading states and materials with dissimilar properties.Numerical results are obtained for an epoxy/aluminum medium. In each case, a finite line segment of debonding is assumed. Uniform stresses are applied normal and parallel to the interface so that a biaxial load factor k determines the relative magnitude of biaxiality. Positive and negative k correspond, respectively, to applied tension and compression parallel to the interface. For a fixed ratio of the elastic moduli, crack initiation angles measured from the interface would increase with positive k and decrease with an increase of negative k. These findings are presented for different values of k. The direction of maximum yield initiation could also be determined from the stationary values of the strain density function. These locations are identified with elements that undergo excessive distortion while the possible fracture sites are assumed to coincide with regions where dilatational effects would dominate.     

缝合复合材料层间开裂的试验和数值研究

缝合复合材料层合板中贯穿厚度方向的缝线,能有效增强层合板的抗分层能力。本文对一种碳纤/环氧缝合复合材料层板进行了短梁三点弯试验,测得了压头的载荷-位移曲线,并观察了层间裂纹的扩展,证实了缝线对层间裂纹的阻滞作用。建立了三维有限元模型模拟了上述试验,模型中相邻的铺层之间布置了一层初始无厚度的界面单元,界面单元的失效自然模拟层间开裂,而缝线简化为面积等效的梁单元,数值结果与试验观测吻合。     

Thermomechanics of Swelling Biopolymeric Systems

A two-scale theory for the swelling biopolymeric media is developed. At the microscale, the solid polymeric matrix interacts with the solvent through surface contact. The relaxation processes within the polymeric matrix are incorporated by modeling the solid phase as viscoelastic and the solvent phase as viscous at the mesoscale. We obtain novel equations for the total stress tensor, chemical potential of the solid phase, heat flux and the generalized Darcy's law all at the mesoscale. The constitutive relations are more general than those previously developed for the swelling colloids. The generalized Darcy's law could be used for modeling non-Fickian fluid transport over a wide range of liquid contents. The form of the generalized Fick's law is similar to that obtained in earlier works involving colloids. Using two-variable expansions, thermal gradients are coupled with the strain rate tensor for the solid phase and the deformation rate tensor for the liquid phase. This makes the experimental determination of the material coefficients easier and less ambiguous.     

Overview on mesomechanics of plastic deformation and fracture of solids

Mesomechanics involves analyzing the deformation and/or fracture of solids at the micro-, meso- and macro-scale level. Base elements for each scale level are chosen such that the behavior of the solid would be described by a combination of these elements. Special attention is given to the fragmentation of solid which is the main character of plastic flow at the mesoscale level. The final stage of fragmentation corresponds to fracture as the changes from the meso- to the macro-scale level.     

A percolation-type fracture criterion for composites with randomly oriented fibres

A fracture model is built up for a solid composed of brittle fibres randomly oriented in the matrix volume. The fracture process includes a stable growth of microcracks caused by fibre breaking under the load and formation of an infinite cluster of the microcracks. Both upper and lower bounds for ultimate stress in a fibre system are found as functions of the fibre volume fraction. The calculation of the ultimate stresses are performed by using the percolation theory and the theory of branching processes. At the present stage of the theory under consideration, only two types of the microcracks are appraised, namely that of a delamination type which corresponds to a weak fibre/matrix interface, and that of a penny shape which corresponds to a strong fibre/matrix interface. A particular solid contains only one type of the microcracks. In both cases, non-linear dependencies of the ultimate composite strength on fibre volume fraction are obtained.     

Length-scale effects on damage development in tensile loading of glass-sphere filled epoxy

Particle-reinforced polymers are widely used in load-carrying applications. The effect of particle size on damage development in the polymer is still relatively unexplored. In this study, the effect of glass-sphere size on the damage development in tensile loaded epoxy has been investigated. The diameter of the glass spheres ranged from approximately 0.5–50 μm. The first type of damage observed was debonding at the sphere poles, which subsequently grew along the interface between the glass spheres and epoxy matrix. These cracks were observed to kink out into the matrix in the radial direction perpendicular to the applied load. The debonding stresses increased with decreasing sphere diameter, whereas the length to diameter ratio of the resulting matrix cracks increased with increasing sphere diameter. These effects could not be explained by elastic stress analysis and linear-elastic fracture mechanics. Possible explanations are that a thin interphase shell may form in the epoxy close to the glass spheres, and that there is a length-scale effect in the yield process which depends on the strain gradients. Cohesive fracture processes can contribute to the influence of sphere size on matrix-crack length. Better knowledge on these underlying size-dependent mechanisms that control damage development in polymers and polymer composites is useful in development of stronger materials. From a methodology point of view, the glass-sphere composite test can be used as an alternative technique (although still in a qualitative way) to hardness vs. indentation depth to quantify length-scale effects in inelastic deformation of polymers.     

A piezoelectric biaxial loading device for interfacial fracture experiments

In this paper we describe the development of a new biaxial loading device for investigating mixed-mode fracture at bimaterial interfaces. The new device makes use of piezoelectric actuators and specially arranged flexures to provide independent displacements normal and tangential to the interface. Capacitive probes and special washer load cells were used for measuring the displacements and reactive loads, respectively. A closed-loop circuit was formed with a personal computer to control the applied displacements to within 10 nm. Preliminary experiments with quartz/epoxy/aluminum sandwich specimens with cracks growing between the quartz and the epoxy found that the intrinsic toughness of this interface was 30% lower than the value for a glass/epoxy interface. Crack opening interferometry measurements having a resolution of 30 nm revealed the presence of a cohesive zone whose size was about 0.5 μm.     

EXPERIMENTAL INVESTIGATIONS OF STRENGTH,TOUGHNESS AND FAILURE MECHANISM OF THE METAL/EPOXY/METAL ADHESIVE SYSTEM

本文系统地开展了金属/环氧/金属胶结体系的强韧机理及失效行为实验研究,针对铝合金圆棒与铝合金圆棒通过环氧树脂胶层的各种斜截面方向粘结,实验观测了该体系的拉伸变形和失效行为,测量了界面失效载荷对胶层厚度和粘结界面倾斜角的依赖关系;通过引入胶结界面平均正应力、平均剪应力、平均正应变、平均剪应变等概念,可对界面失效强度进行测量,获得界面强度与界面粘结角度以及胶层厚度的关系,进而获得了铝合金/环氧胶层/铝合金体系的强度失效面以及胶结界面的断裂能和胶结体系的能量释放率.上述研究结果为深入认识金属胶结体系的强韧性能和失效机制提供了科学依据,对金属胶结体系的优化设计和性能评判具有重要指导意义.研究结果表明,铝合金/环氧胶层/铝合金体系的拉伸失效总体呈弹脆性破坏特征,失效表现为胶层粘结界面的断裂,失效强度和界面断裂能在胶层厚度为百微米量级时表现出强烈的尺度效应：界面粘结强度随着胶层厚度的减小而显著增大,临界状态的平均正应力和平均剪应力在强度破坏面上近似位于同一圆上,界面断裂能随着胶层厚度的减小而显著减小;与此同时,界面失效强度和界面断裂能也密切依赖于界面粘结角度.     

A Multiscale Theory of Swelling Porous Media: II. Dual Porosity Models for Consolidation of Clays Incorporating Physicochemical Effects

A three-scale theory of swelling clay soils is developed which incorporates physico-chemical effects and delayed adsorbed water flow during secondary consolidation. Following earlier work, at the microscale the clay platelets and adsorbed water (water between the platelets) are considered as distinct nonoverlaying continua. At the intermediate (meso) scale the clay platelets and the adsorbed water are homogenized in the spirit of hybrid mixture theory, so that, at the mesoscale they may be thought of as two overlaying continua, each having a well defined mass density. Within this framework the swelling pressure is defined thermodynamically and it is shown to govern the effect of physico-chemical forces in a modified Terzaghi's effective stress principle. A homogenization procedure is used to upscale the mesoscale mixture of clay particles and bulk water (water next to the swelling mesoscale particles) to the macroscale. The resultant model is of dual porosity type where the clay particles act as sources/sinks of water to the macroscale bulk phase flow. The dual porosity model can be reduced to a single porosity model with long term memory by using Green's functions. The resultant theory provides a rational basis for some viscoelastic models of secondary consolidation.     

Vertical stability of bubble chain: Multiscale approach

Linear stability is investigated of a uniform chain of equal spherical gas bubbles rising vertically in unbounded stagnant liquid at Reynolds number Re = 50–200 and bubble spacing s > 2.6 bubble radii. The equilibrium bubble positions are questioned for their stability with respect to small displacements in the vertical direction, parallel to the chain motion. The transverse displacements are not considered, and the chain is assumed to be laterally stable. The bubbles are subjected to three kinds of forces: buoyant, viscous, inviscid. The viscous and inviscid forces have both pairwise (local) and distant (nonlocal) components. The pairwise forces are expressed by the leading-order formulas known from the literature. The distant forces are expressed as a linear superposition of the pairwise forces taken over several farther neighbours. The stability problem is addressed on three different length scales corresponding to: discrete chain (microscale), continuous chain (mesoscale), bubbly chain flow (macroscale). The relevant governing equations are derived for each scale. The microscale equations are a set of ODE’s, the Newton force laws for the individual discrete bubbles. The mesoscale equation is a PDE for bubbles continuously distributed along a line, obtained by taking the continuum limit of the microscale equations. The macroscale equations are two PDEs, the mass and momentum conservation equations, for an ensemble of noninteracting mesoscale chains rising in parallel. This transparent two-step process (micro → meso → macro) is an alternative to the usual one-step averaging, in obtaining the macroscale equations from microscale information. Here, the scale-up methodology is demonstrated for 1D motion of bubbles, but it can be used for behaviour of 2D and 3D lattices of bubbles, drops, and solids.It is found that the uniform equilibrium spacing results from a balance between the attractive and repulsive forces. On all three length scales, the equilibrium is stabilized by the viscous drag force, and destabilized by the viscous shielding force (shielding instability). The inviscid forces are stability neutral and generate conservative oscillations and concentration waves. The stability region in the parameter plane s − Re is determined for each length scale. The stable region is relatively small on the microscale, larger on the mesoscale, and shrinks to zero on the macroscale where the bubbly chain flow is inherently unstable.The shielding instability is expected to occur typically in intermediate Re flows where the vertical bubble interactions dominate over the horizontal interactions. This new kind of instability is studied here in a great detail, likely for the first time. Its relation to the elasticity properties of bubbly suspension on different length scales is discussed too. The shielding force takes the form of a negative bulk modulus of elasticity of the bubbly mixture.     

Atomistic-based continuum representation of the effective properties of nano-reinforced epoxies

In this paper, an atomistic-based representative volume element (RVE) is developed to characterize the behavior of carbon nanotube (CNT) reinforced amorphous epoxies. The RVE consists of the carbon nanotube, the surrounding epoxy matrix, and the CNT/epoxy interface. An atomistic-based continuum representation is adopted throughout all the components of the RVE. By equating the associated strain energies under identical loading conditions, we were able to homogenize the RVE into a representative fiber. The homogenized RVE was then employed in a micromechanical analysis to predict the effective properties of the newly developed CNT-reinforced amorphous epoxy. Numerical examples show that the effect of volume fraction, orientation, and aspect ratio of the continuous fibres on the properties of the CNT-reinforced epoxy adhesives can be significant. These results have a direct bearing on the design and development of nano-tailored adhesives for use in structural adhesive bonds.     

Macro-to-microchannel transition in two-phase flow: Part 1 - Two-phase flow patterns and film thickness measurements

The classification of macroscale, mesoscale and microscale channels with respect to two-phase processes is still an open question. The main objective of this study focuses on investigating the macro-to-microscale transition during flow boiling in small scale channels of three different sizes with three different refrigerants over a range of saturation conditions to investigate the effects of channel confinement on two-phase flow patterns and liquid film stratification in a single circular horizontal channel (Part 2 covers the flow boiling heat transfer and critical heat flux). This paper presents the experimental two-phase flow pattern transition data together with a top/bottom liquid film thickness comparison for refrigerants R134a, R236fa and R245fa during flow boiling in small channels of 1.03, 2.20 and 3.04 mm diameter. Based on this work, an improved flow pattern map has been proposed by determining the flow patterns transitions existing under different conditions including the transition to macroscale slug/plug flow at a confinement number of Co ≈ 0.3-0.4. From the top/bottom liquid film thickness comparison results, it was observed that the gravity forces are fully suppressed and overcome by the surface tension and shear forces when the confinement number approaches 1, Co ≈ 1. Thus, as a new approximate rule, the lower threshold of macroscale flow is Co = 0.3-0.4 while the upper threshold of symmetric microscale flow is Co ≈ 1 with a transition (or mesoscale) region in-between.     

压电材料反平面界面裂纹的杂交元分析

基于奇异性电弹场数值特征解开发了一种新型反平面界面裂纹尖端单元。将新型单元与四节点压电P-S单元组装,求解从绝缘到导通的任意电边界条件下,压电结构反平面界面裂纹尖端电弹场的数值解。考察了层厚、载荷类型和裂纹面间电边界条件等对反平面界面裂纹尖端断裂参数的影响。算例证明新型单元能使P-S单元数显著降低,计算结果更为精确。     

Variational bound finite element methods for three-dimensional creeping porous media and sedimentation flows

We present an analytico-computational methodology for the prediction of the effective properties of two types of three-dimensional particulate Stokes flows: porous media and sedimentation flows. In particular, we determine the permeability and average settling rate of media that consist of non-colloidal monodisperse solid spherical particles immersed in a highly viscous Newtonian fluid. Our methodology recasts the original problem into three scale-decoupled subproblems: the macro-, meso- and microscale subproblems. In the macroscale analysis the appropriate effective property is used to calculate the bulk quantity of interest. The mesoscale problem provides this effective property through the finite element solution of the transport equations in a periodic cell containing many particles distributed according to a prescribed joint probability density function. Finally, the microscale analysis allows us to accommodate mesoscale realizations in which two or more inclusions are in very close proximity; this geometrical stiffness is alleviated by introducing simple domain modifications that relax the mesh generation requirements while simultaneously yielding rigorous bounds for the effective property. Our methodology can treat random particle distributions as well as regular arrays; in the current paper we analyse only the latter. © 1998 John Wiley & Sons, Ltd.