A 2-D lattice model for simulating the failure of paper

A new two-dimensional network model is proposed as a micromechanics model to simulate paper’s failure process due to sequentially breakages of fibers and/or bonds. Paper is approximated as a network composed of fibers any two of which link to each other by their intersecting point, namely so-called bond. Fibers distribute along three particular directions, leading to network’s macro-level isotropy. In the framework of finite element method, nodes correspond to fiber-to-fiber bonds, while elements are fiber segments between every two neighboring nodes and described by Timoshenko beam theory. Element breaks when its equivalent internal tensile stress reaches the tensile strength of fiber. Strength of nodes, i.e. fiber-to-fiber bonds is assumed to be dependant on shearing interaction between fibers, considering the dominant interaction is shearing in a plane problem. Numerical examples show the model’s capacity of reflecting basic failure characteristic in paper. Influences of fiber length and the ratio of fiber strength to bond strength are analyzed in detail.     

On the transverse compression response of Kevlar KM2 using fiber-level finite element model

Flexible textile composites like woven Kevlar fabrics are widely used in high velocity impact (HVI) applications. Upon HVI they are subjected to both longitudinal tensile and transverse compressive loads. To understand the role of transverse properties, the single fiber and tow transverse compression response (SFTCR and TTCR) of Kevlar KM2 fibers are numerically analyzed using plane strain finite element (FE) models. A finite strain formulation with a minimum number of 84 finite elements is determined to be required for the fiber cross section to capture the finite strain SFTCR through a mesh convergence study. Comparison of converged numerical solution to the experimental results indicates the dominant role of geometric stiffening at finite strains due to growth in contact width. The TTCR is studied using a fiber length scale FE model of a single tow comprised of 400 fibers transversely loaded between rigid platens. This study along with micrographs of yarn after mechanical compaction illustrates fiber spreading and fiber–fiber contact friction interactions are important deformation mechanisms at finite strains. The TTCR is also studied using homogenized yarn level models with properties from the literature. Comparison of TTCR between fiber length scale and homogenized yarn length scale models indicate the need for a nonlinear material model for homogenized approaches to accurately predict the transverse compression response of the fabrics.     

Determination of mechanical properties of fiber–matrix interface from pushout test

For ceramic matrix composites, the pushout test is the most widely used test for finding the two mechanical properties of the fiber–matrix interface – (1) the coefficient of friction and (2) the residual radial stress. Experimental measurements from the pushout test do not directly give the values of these two mechanical properties of the fiber–matrix interface, but need to be regressed to theoretical models. Currently, approximate theoretical models based on shear–lag analysis are used for regression. In this paper, the adequacy of the shear–lag analysis model in accurately finding the mechanical properties of the fiber–matrix interface is discussed. An elasticity solution of the pushout test based on boundary element method is developed. Regressing one set of available experimental data from a pushout test to both shear–lag analysis and boundary element method models gives values differing by 15% for the coefficient of friction but similar values for the residual radial stress. Parametric studies were also conducted to show the difference between the shear–lag analysis and boundary element method results for factors such as fiber to matrix elastic moduli ratios, coefficient of friction and fiber volume fractions.     

On the coupling between macroscopic material degradation and interfiber bond fracture in an idealized fiber network

The numerical analysis performed here, using a finite element network model, provides a number of important results regarding the evolution of micro fractures in planar random fiber networks where the only active microscopic fracture mechanism is bond fracture. The fibers are randomly distributed in the network meaning that the network is considered having in-plane isotropic properties on the macroscopic scale. The network is loaded so that, in an average sense, homogenous macroscopic stress and strain fields are present.Several conclusions are drawn. It is found that the development of macroscopic material degradation follows an exponential two-parameter law, consisting of an onset parameter and a fracture rate parameter, justifying a previous theory derived by the authors. The fracture rate parameter is linearly related to the inverse of the bond density above a certain density limit (percolation) and increases with increasing slenderness ratio of the fibers when keeping the bond density at a constant level. The strain energies stored in interfiber bonds are exponentially distributed over the whole network. The numerical analysis reveals that there is a linear relation between the ratio of fractured and initial number of loaded bonds, and the network’s macroscopic material stiffness normalized with its pristine stiffness, confirming earlier findings based on experimental observations. At localization the analyzed theory looses its validity because the fracture process is no longer randomly distributed over the whole network. Localization coincides with location of peak load in force–displacement tensile tests.     

Effects of polymer–fiber interactions on rheology and flow behavior of suspensions of semi-flexible fibers in polymeric liquids

Rheological properties of suspensions of fibers in polymeric fluids are influenced by fiber–polymer interactions. In this paper, we investigate this influence from both experimental and modeling standpoints. In the experimental part of this investigation, we have changed the fiber–polymer interactions by treating the surface of the fibers. The resulting effects are observed using scanning electron microscopy and dynamic mechanical analysis techniques and quantified from the measurements of the viscosity in the start-up of shear flows and dynamic tests in the linear viscoelastic range region. The results are interpreted with the help of a mesoscopic rheological model developed for suspensions of fibers in viscoelastic fluids.     

Experimental and numerical study of the response of flexible laminates to impact loading

Fabrics and flexible laminates comprising highly oriented polymers possess high impact resistance and are often used in flexible armour applications. This study presents an idealized computational model for flexible [0°/90°] polyethylene fiber-reinforced laminates and show how the model can simulate actual impact tests conducted on the laminates. As these materials are viscoelastic, accurate modeling of their impact and perforation responses requires the formulation of constitutive equations representing such behavior. The material is idealized as networks of one-dimensional pin-jointed fiber elements defined by viscoelastic constitutive relations. Three-element viscoelastic Zener models are used as they are simple yet sufficient to account for the effects of intermolecular and intramolecular bonds, as well as viscous slippage between molecular chains, on the mechanical properties of oriented polymeric fibers. The effects of delamination in laminates are also taken into consideration by modeling flexible laminates as two fiber network layers bonded to each other at corresponding element cross-over points in the adjacent layers. Inter-ply bonding is represented by infinitesimal rigid links which break when the inter-ply bond strength is exceeded resulting in delamination between the plies. Predictions of residual velocity, development of deformation and delamination correlate well with experimental results.     

Load-dependent constitutive response of fiber composites with compliant interphases

I , the influence of applied load on the overall transverse mechanical properties of fiberreinforced composites with compliant interphases is examined from a micromechanical perspective. The composite is modeled by a regular hexagonal array of circular fibers in an infinite matrix. It is assumed that a thin reaction zone (intermolecular bonding at the fiber/matrix interface) establishes the bond between the fiber and matrix phases. The model of the present paper allows us to derive expressions for the overall elastic constants in the transverse plane as a function of applied load. The finite element method is used to evaluate these expressions, and the results are discussed.     

Determination of Bond Strengths in Non-woven Fabrics: a Combined Experimental and Computational Approach

Interfiber bonds are important structural components in non-woven fabrics. Bond fracture greatly affects the strength and damage progression in a fiber network structure. Here, we present a novel combined experimental and computational approach to extract bond strengths in non-wovens. In this method, a small specimen is imaged and the obtained 3D geometry of the network is directly modeled in a finite element framework. Bond properties are determined by matching finite element simulation predicted mechanical response to the experimental data. This method is demonstrated by applying it to six specimens of a commercial polypropylene non-woven. A four parameter bi-linear interface law is used with normal stiffness k, shear stiffness βk, separation at the start of damage d ₁, and separation at total loss of bond stiffness d ₂. The determined normal strength (kd ₁)and shear strength (βkd ₁) are (1.3 ± 0.3) × 10² MPa and (1.0 ± 0.2) × 10² MPa, respectively. To show that the obtained bond parameters can be applied to a new specimen, a cross validation is conducted whereby parameters are fit from five specimens and then evaluated on the sixth. Additional validation of the obtained bond strength parameters was conducted with larger size artificial network simulations and peel tests. The proposed method in this work carries the dual advantages of characterizing actual bonds in a non-woven and characterizing hundreds of bonds simultaneously. The method can be applied to a variety of non-woven fabrics that are bonded at fiber-fiber intersections.     

An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics

The Folgar–Tucker model, which is widely-used to predict fiber orientation in injection-molded composites, accounts for fiber–fiber interactions using isotropic rotary diffusion. However, this model does not match all aspects of experimental fiber orientation data, especially for composites with long discontinuous fibers. This paper develops a fiber orientation model that incorporates anisotropic rotary diffusion. From kinetic theory we derive the evolution equation for the second-order orientation tensor, correcting some errors in earlier treatments. The diffusivity is assumed to depend on a second-order space tensor, which is taken to be a function of the orientation state and the rate of deformation. Model parameters are selected by matching the experimental steady-state orientation in simple shear flow, and by requiring stable steady states and physically realizable solutions. Also, concentrated fiber suspensions align more slowly with respect to strain than models based on Jeffery's equation, and we incorporate this behavior in an objective way. The final model is suitable for use in mold filling and other flow simulations, and it gives improved predictions of fiber orientation for injection molded long-fiber composites.     

Determination of the first ply failure load for a cross ply laminate subjected to uniaxial tension through computational micromechanics

A method for determining the in situ strength of fiber-reinforced laminas for three types of transverse loading including compression, tension and shear is presented. In the framework of this method, an analysis of local stresses that are responsible for the coalescence of matrix cracks is carried out by using a multi-fiber unit cell model and finite element method. The random distribution of fibers, fiber–matrix decohesion and matrix plastic deformations are taken into account in the micromechanical simulations. The present study also shows that the nonlinear hardening behavior of matrix reflects more realistically the influence of plastic deformations on the in situ transverse strength of lamina than the perfectly plastic behavior of matrix. The prediction of the in situ transverse strength is verified against the experimental data for a cross ply laminate subjected to uniaxial tension.     

空心光纤网络埋入复合材料中性能影响的研究

空心光纤网络可用来进行复合材料力学性能的监测,同时又可对材料的损伤进行自修复。空心光纤网络与复合材料性能的影响主要有三方面：1）复合材料对空心光纤的影响;2）空心光纤对复合材料的影响;3）空心光纤与复合材料力学性能的匹配。本文测试了三种规格的空心光纤埋入复合材料中受到的影响,依据国家有关的复合材料测试标准,对树脂基复合材料埋与不埋大直径空心光纤进行了对比实验,并论证了光纤与材料力学性能匹配点存在的必然性。从而为空心光纤网络用于复合材料的自诊断与自修复提供了研究的依据。     

Numerical simulation of flow kinematics for suspensions containing continuously dispersed aspect ratio fibers

Fiber suspension flow and fiber orientation through a parallel-plate channel were numerically simulated for fiber suspensions including continuously dispersed aspect ratios from 10 to 50. In the simulations, both the fiber–fiber and fiber–wall interactions were not taken into account. A statistical scheme that proceeds by evaluating the orientation evolution of a large number of fibers from the solution of the Jeffery equation along the streamlines was confirmed to be a very useful and feasible method to accurately analyze the orientation distribution of fibers with continuously dispersed aspect ratios. For monodisperse suspensions with small-aspect-ratio fibers, flip-over or oscillation phenomenon of the orientation ellipsoid caused the wavy patterns of the velocity profile and the streamlines as well as the abrupt and complex variation of the shear stress and the normal stress difference near the channel wall as proven in one of our former works. On the other hand, continuous dispersions containing from small- to large-aspect-ratio fibers were able to induce smoother evolutions of the fiber orientation and the flow kinematics. In the processing of fiber composites, the length of suspended fibers is always continuously distributed because of fiber breakage during processing; thus, the smooth evolutions of the flow kinematics and the stress distribution can be attained.This paper was presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

Modeling of fiber-reinforced cement composites: Discrete representation of fiber pullout

The discrete modeling of individual fibers in cement-based materials provides several advantages, including the ability to simulate the effects of fiber dispersion on pre- and post-cracking composite performance. Recent efforts in this direction have sought a balance between accurate representation of fiber behavior and computational expense. This paper describes a computationally efficient approach to representing individual fibers, and their composite behavior, within lattice models of cement-based materials. Distinguishing features of this semi-discrete approach include: (1) fibers can be positioned freely in the computational domain, irrespective of the background lattice representing the matrix phase; (2) the pre- and post-cracking actions of the fibers are simulated with little computational expense, since the number of system degrees of freedom is independent of fiber count. Simulated pullouts of single fibers are compared with theory and test results for the cases of perfectly-plastic and slip-hardening behavior of the fiber–matrix interface. To achieve objective results with respect to discretization of the matrix, pullout forces are distributed along the embedded lengths of fibers that bridge a developing crack. This is in contrast to models that lump the pullout force at the crack surfaces, which can lead to spurious break-off of matrix particles as the discretization of the matrix is refined. With respect to fracture in multi-fiber composites, the proposed model matches theoretical predictions of post-cracking strength and pullout displacement corresponding to the load-free condition. The work presented herein is a significant step toward the modeling of strain-hardening composites that exhibit multiple cracking.     

Fiber suspension flow in a tapered channel: The effect of flow/fiber coupling

A numerical model for predicting the flow and orientation state of semi-dilute, rigid fiber suspensions in a tapered channel is presented. The effect of the two-way flow/fiber coupling is investigated for low Reynolds number flow using the constitutive model of Shaqfeh and Fredrickson. An orientation distribution function is used to describe the local orientation state of the suspension and evolves according to a Fokker–Plank type equation. The planar orientation distribution function is determined along streamlines of the flow and is coupled with the fluid momentum equations through a fourth-order orientation tensor. The coupling term accounts for the two-way interaction and momentum exchange between the fluid and fiber phases. The fibers are free to interact through long range hydrodynamic fiber–fiber interactions which are modeled using a rotary diffusion coefficient, an approach outlined by Folgar and Tucker. Numerical predictions are made for two different orientation states at the inlet to the contraction, namely a fully random and a partially aligned fiber orientation state. Results from these numerical predictions show that the streamlines of the flow are altered and that velocity profiles change from Jeffery–Hamel, to something resembling a plug flow when the fiber phase is considered in the fluid momentum equations. This phenomenon was found when the suspension enters the channel in either a pre-aligned, or in a fully random orientation state. When the suspension enters the channel in an aligned orientation state, fiber orientation is shown to be only marginally changed when the two-way coupling is included. However, significant differences between coupled and uncoupled predictions of fiber orientation were found when the suspension enters the channel in a random orientation state. In this case, the suspension was shown to align much more quickly when the mutual coupling was accounted for and profiles of the orientation anisotropy were considerably different both qualitatively and quantitatively.     

Numerical simulation of flow kinematics and fiber orientation for multi-disperse suspension

The development of flow kinematics and fiber orientation distribution from the parabolic velocity profile and isotropic orientation at the channel inlet was computed in multi-disperse suspension flow through a parallel plate channel and their predictions were compared with those of mono- and bi-disperse suspensions. A statistical scheme (orientations of a large number of fibers are evaluated from the solution of the Jeffery equation along the streamlines) was confirmed to be very useful and feasible method to analyze accurately the orientation distribution of fibers in multi-disperse fiber suspension flow as well as mono- and bi-dispersions, instead of direct solutions of the orientation distribution function of fibers or the evolution equation of the orientation tensor which involves a closure equation. It was found that the flow kinematics and the fiber orientation depend completely on both the fiber aspect-ratio and the fiber parameter for multi-disperse suspension when the fiber–fiber and fiber-wall interactions are neglected. Furthermore, the addition of large aspect-ratio fibers as well as an increase in the fiber parameter related to the large aspect-ratio fibers could suppress the complex velocity field and stress distributions which are observed in suspensions containing small aspect-ratio fibers. From a practical point of view, therefore, the mechanical and physical properties of fiber composites should be improved with an increase in the volume fraction of large aspect-ratio fibers.     

Analysis of a high intensity shear zone between overlapping fiber ends in a polymer matrix composite

The formation of high intensity shear zones in a glass fiber reinforced thermoplast is studied numerically. The thermoplast is characterized by a finite strain elastic-viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program where plane strain conditions are assumed to prevail in the direction of the thickness. Different ratios of the elongation strain and the transverse strain are studied to consider the effect of different levels of stress triaxiality and the effect of these states on the shear zone development and emerging strain and stress concentrations. Comparing a case of embedded infinitely stiff fibers to a case with glass fiber reinforcement shows little difference thus illustrating that the glass fibers act approximately as infinitely stiff. Fiber spacing and fiber width are shown to influence the shear zones and the stress fields that develop as the highly deformed region approaches the limit resulting from network stiffening in the polymer. A simple analysis assuming periodicity is included in order to study the mechanical behaviour of the polymer matrix between fiber ends with long overlap.     

End-shaped copper fibers in an epoxy matrix—predicted versus actual fracture toughening

End-shaped copper fibers are placed in a brittle thermoset epoxy matrix at 10 vol% and tested in four-point bending to determine the fracture toughness of the composite. Results from four-point bend tests agree well with the theoretical predictions of the fracture toughness increment ‘ΔG’ of a metal fiber/brittle thermoset matrix composite based on single fiber pullout (SFP) tests. This close agreement demonstrates that SFP testing, along with the theoretical model, can be used as an effective end-shape screening tool for ductile fibers before full scale composite testing. The model predicts that the composite’s fracture toughness will be 46% higher with flat end-impacted fibers and 4% lower with rippled fibers compared to straight fibers at a 0° orientation. Four-point bend results show the actual composite’s fracture toughness is 49% higher with flat end-impacted fibers and 5% lower with rippled fibers compared to straight fibers. Further, four-point bend results show that end-shaped copper fibers improve both the flexural strength and modulus of the composite, demonstrating that end-shaped ductile fibers provide a good stress transfer to the fibers by anchoring the fibers into the matrix. Lastly, experimental validation of the model also indicates that at low fiber volume fractions, fiber–fiber interaction has only a minor influence on the fracture toughness for the tested ductile fiber/brittle matrix composite.     

Damage simulation of repaired composite laminate with rectangular cut-out

Repaired composite laminate with rectangular cut-out is studied by tensile experiments and FEM simulation in this paper. A user damage subroutine is implemented to ABAQUS to simulate the damage of laminate. Good agreements between experimental data and numerical results are reached. From the experiment and FEM simulation results, the integrality of composite structure is destroyed due to the existence of cut-out. However, the asymmetry of repair gets this effect farther. From damage simulation, the initiation and development of three types of damages are predicted. The matrix cracking occurs at first, fiber–matrix shear and fiber break are subsequent. The effect of matrix cracking to the carrying capacity of structure is very small, but when fiber–matrix shear and fiber break occur, dangerous to structure, the carrying capacity of structure loses rapidly.     

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.     

Bonds between metals and nanocomposites created by explosion welding

This paper describes the study of the influence of a microstructure characterized by directed or chaotic distribution of nanoinclusions and strain rate on the deformability of nanocomposites. It is revealed that, under identical loading conditions, cracks are formed in nanocomposites whose structural elements are mostly directed in the same way at lower strain rates than in nanocomposites with chaotic distribution of the reinforcer. It is shown that, as the strain rate increases, the influence of the structural order on the limiting deformation reduces due to transition from shear strain to rotational strain. No cracks are formed in the creation of bonds between metals and nanocomposites by explosion welding. The experimental results obtained in the study of transverse bending of two-layer welded beams and the structure in the vicinity of the weld reveal that the obtained metal–nanocomposite bond has a uniform structure retained in deformation, with fracture occurring in the nanocomposite.