Folding of fiber composites with a hyperelastic matrix

This paper presents an experimental and numerical study of the folding behavior of thin composite materials consisting of carbon fibers embedded in a silicone matrix. The soft matrix allows the fibers to microbuckle without breaking and this acts as a stress relief mechanism during folding, which allows the material to reach very high curvatures. The experiments show a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. A finite element model has been created to study the micromechanics of the problem. The fibers are modeled as linear-elastic solid elements distributed in a hyperelastic matrix according to a random arrangement based on experimental observations. The simulations obtained from this model capture the detailed micromechanics of the problem and the experimentally observed non-linear response. The proposed model is in good quantitative agreement with the experimental results for the case of lower fiber volume fractions but in the case of higher volume fractions the predicted response is overly stiff.     

A time dependent micro-mechanical fiber composite model for inelastic zone growth in viscoelastic matrices

In this work, a fiber composite model is developed to predict the time dependent stress transfer behavior due to fiber fractures, as driven by the viscoelastic behavior of the polymer matrix, and the initiation and propagation of inelastic zones. We validate this model using in situ, room temperature, micro-Raman spectroscopy fiber strain measurements. Multifiber composites were placed under constant load creep tests and the fiber strains were evaluated with time after one fiber break occurred. These composite specimens ranged in fiber volume fraction and strain level. Comparison between prediction and MRS measurements allows us to characterize key in situ material parameters, the critical matrix shear strain for inelastic zones and interfacial frictional slip shear stress. We find that the inelastic zone is predominately either shear yielding or interfacial slipping, and the type depends on the local fiber spacing.     

A model long-discontinuous-fiber filled thermoplastic melt in extensional flow

The shear cell model works for dilute fiber filled systems in extensional flow. This research investigates the suitability of the idea for highly aligned fibers in a concentrated suspension. A model fiber-filled polymer system made from nylon fibers in low-density polyethylene provided a means of controlling the material parameters. Two systems, with fiber aspect ratios of 20 and 100, containing 50% 0.5 mm fibers by volume are investigated. The thickness of the polymer layer, i.e. with fibers this size, allows bulk viscosity data to be compared with the data from the filled fluid. A weaving process created the discontinuous fiber/polyethylene preforms with high alignment of the fibers and with control of the fiber to fiber overlap. Testing the polyethylene in simple shear and extending the nylon/polyethylene provided the data needed to check the micro mechanics. A cone and plate rheometer and a capillary instrument produced the viscosity/strain rate data that characterized the specific polyethylene used in the composite. A furnace inset placed in an Instron hydraulic test machine allowed extension of the filled system at strain rates from 0.002 to 0.4 s⁻¹. The shear experiments show that the low-density polyethylene is a simple shear-thinning melt that provides a good model fluid. The extension of the filled systems shows an increase of the apparent extensional viscosity from that of neat polyethylene. Apparent viscosity rises two to three orders of magnitude for the systems investigated. The micromechanics allowed the conversion of the extensional data from the two filled systems to the shear viscosity of the polymer surrounding the fibers. The calculated polyethylene viscosity compares well with the data from the standard rheometers. The shear cell approach may be applied to highly aligned, high fiber-volume-fraction suspensions when the viscosity of the polymer is known at the scale of the film surrounding each fiber.     

Transient shear flow behavior of concentrated long glass fiber suspensions in a sliding plate rheometer

In order to eventually predict the behavior of long fiber suspensions in complex flows commonly found in processing operations, it is necessary to understand their rheology and its connection to the evolution of fiber orientation and configuration in well defined flows. In this paper we report the transient behavior at the startup of shear flow of a polymer melt containing long glass fibers with a length (L) >1 mm, using a sliding plate rheometer (SPR). The operation of the SPR was confirmed by comparing the transient shear viscosity (η⁺) for a polymer melt and a melt containing short glass fibers (L < 1 mm) with measurements obtained from a cone-and-plate device, using a modified sample geometry that was designed to avoid wall effects. For the long fiber systems, measurements could only be obtained in the SPR because these systems would not stay within the gap of the rotational rheometer. Transient stress growth behavior of the long fiber systems was obtained as a function of shear rate and fiber concentration for samples prepared with three different initial orientations. Results showed that, unlike short fiber systems (with a random planar initial orientation) that usually exhibit a single overshoot peak followed by a steady state, η⁺ of the long fiber suspensions often passed through multiple transient regions, depending on the fiber concentration and applied shear rate. Additionally, η⁺ of the long fiber suspensions was found to be highly dependent on the initial orientation of the sheared samples. Finally, the initial and final fiber orientations of the long glass fiber samples were measured and used to initiate an explanation of the viscosity behavior. The results obtained in this research will be useful for future assessment of a quantitative correlation between transient rheology and the evolution of fiber orientation.     

Shear flow rheological properties of vinylon- and glass-fiber reinforced polyethylene melts

Shear viscosity, shear stress and first normal-stress difference have been investigated for glass- and vinylon-fiber filled polyethylene melts over a wide range of shear rate by means of three kinds of instruments. The influence of fiber content and fiber properties on the rheological properties is discussed. The viscosity increases with increasing aspect ratio and fiber content, and the influence of these parameters on the flow properties is evident at low shear rates. The first normalstress difference increases more rapidly with increasing glass fiber content, especially at low shear stresses. The influence of vinylon fibers on the first normal stress-difference vs. shear-stress relationship is different from that of glass fibers.     

Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones, notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode II component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.     

Analysis of elastic crack bridging in ceramic matrix composites

A micromechanics analytical model based on the consistent shear lag theory is developed for predicting the failure modes in fiber reinforced unidirectional stiff matrix composites. The model accounts for a relatively large matrix stiffness and hence its load carrying capacity. The fiber and matrix stresses are established as functions of the applied stress, crack geometry, and the microstructural properties of the constituents. From the predicted stresses, the mode of failure is established based on a point stress failure criterion. The role of the microstructural parameters of the constituents on the failure modes such as self-similar continuous cracking, crack bridging and debonding parallel to the fibers is assessed.     

Coupled twoscale analysis of fiber reinforced composite structures with microscopic damage evolution

The simultaneous twoscale analysis of unidirectionally fiber reinforced composite structures with attention to damage evolution is the objective of the contribution. The heterogeneous microstructure of the composite represents the microscale, whereas the laminate or the structural component are addressed as the macroscale. The macroscale is conventionally discretized by the finite element method (FEM). The generalized method of cells (GMC) in its efficient stress based formulation serves as the discrete microscale model. The stiff and brittle fibers behave linearly elastic. The epoxy resin is described by the nonlinear-elastic model of Ramberg–Osgood. By introducing microcrack models, the damage of the epoxy matrix under combined tensile and shear loading is taken into account. The cell boundaries of the micromodel are used to locate microscopic cracks deterministically. Interface models for the representation of damage in the matrix phase as well as for the weakening of the fiber–matrix-bond are used. This approach circumvents the need for the regularization, as it would be necessary for continuum damage models with softening characteristics. Hence, the micromodel is numerically stable and convergent. The GMC allows to obtain the consistently linearized constitutive tensor in the case of nonlinear material behavior in a simple and straight forward manner which is easily implemented in comparison to micromodels based on the finite element technique. The damage evolution on the microscale manifests itself macroscopically in the degradation of the homogenized stiffnesses.     

A failure criterion for fiber reinforced polymer composites under combined compression–torsion loading

A fracture mechanics based failure criterion for unidirectional composites under combined loading has been developed. The predictions from this criterion have been compared with experimental data obtained from combined compression–torsion loading of glass and carbon fiber reinforced polymer composites of 50% fiber volume fraction. The specimens were loaded under rotation control and displacement control in a proportional manner. Comparison of the Budiansky–Fleck kinking model, specialized to a solid circular cylinder, and the new failure model against experimental data suggests that the Budiansky–Fleck model predictions do not capture the variation of compressive strength as a function of shear stress for glass fiber composites. This is because these composites fail predominantly by compressive splitting. The Budiansky–Fleck model predictions are appropriate for composites that fail by compressive kinking. The new model predictions capture the experimental results for glass composites where the compression strength is initially unaffected by shear stress but undergoes a drastic reduction when a critical value of shear stress is reached.     

Field fluctuations and macroscopic properties for nonlinear composites

A recently introduced nonlinear homogenization method [J. Mech. Phys. Solids 50 ( 2002) 737–757] is used to estimate the effective behavior and the associated strain and stress fluctuations in two-phase, power-law composites with aligned-fiber microstructures, subjected to anti-plane strain, or in-plane strain loading. Using the Hashin–Shtrikman estimates for the relevant “linear comparison composite,” results are generated for two-phase systems, including fiber-reinforced and fiber-weakened composites. These results, which are known to be exact to second-order in the heterogeneity contrast, are found to satisfy all known bounds. Explicit analytical expressions are obtained for the special case of rigid-ideally plastic composites, including results for arbitrary contrast and fiber concentration. The effective properties, as well as the phase averages and fluctuations predicted for these strongly nonlinear composites appear to be consistent with deformation mechanisms involving shear bands. More specifically, for the case where the fibers are stronger than the matrix, the predictions appear to be consistent with the shear bands tending to avoid the fibers, while the opposite would be true for the case where the fibers are weaker.     

Stress concentrations in composites with interface sliding,matrix stiffness and uneven fiber spacing using shear lag theory

The stress concentrations near a single fiber break in a unidirectionally reinforced fiber composite are investigated using a shear lag theory within the framework of finite elements. A model for uniformly spaced, well bonded fibers embedded in a matrix that cannot carry axial loads that was formulated previously is first introduced. The solution of this problem involves Fourier transforms and requires only a two-dimensional numerical integration. The work described in the current paper characterizes the stress concentrations around a single fiber break in the presence of fiber/matrix interface sliding, axial matrix stiffness and uneven fiber spacing. Due to the introduction of these complicating factors, the model no longer lends itself to the simple Fourier transformation solution method. For the case of interface sliding a new method is developed to handle sliding in any shear lag system. For the cases of axial matrix stiffness and uneven fiber spacing a finite element code specifically written for this problem is used to determine the fiber stresses. The results are discussed in the context of global versus local load sharing, and the effects on composite failure.     

Interfacial stress transfer behavior in a specially-shaped fiber/matrix pullout test

Specially designed fibers are widely used in engineering practice because the specially-designed shape can help to improve the bonding strength of the fiber and the interface. Studied in this paper is the interfacial shear stress transfer behavior on both sides of the specially designed fiber when it is being pulled out; in which automatic analysis of three-dimensional photoelasticity is employed and the finite element method is adopted. The results show that the stress transfer occurs mainly in the region near the fiber＇s embedded end where the stress reaches its critical point, leading to debonding of the interface. Before debonding, as the pullout loading increases, the peak value of shear stress transfers along the fiber from the embedded end to the interior of the matrix, and then stops at the hooked part of the fiber because of its impediment. When the interface begins to debond as the load increases, the shear stress can be transferred to the hooked part.     

Uncertainties of unidirectional composite strength under tensile loading and variation of environmental condition

A probabilistic strength model is developed for unidirectional composites with fibers in hexagonal arrays. The model assumes that, a central core of broken fibers surrounded by unbroken fibers which are subjected to unidirectional tensile loading. The proposed approach consists in using a modified shear lag model to calculate the ineffective lengths and stress concentrations around fiber breaks. The main feature in the model lies in incorporating the variation of composite properties due to temperature and moisture, in order to predict degradation of fibers and matrix characteristics. The strength degradation is often seen as a result of changes in ineffective lengths at fiber breaks, leading to stress concentrations in intact neighboring fibers. As fiber breaks are intrinsically random, the variability of input data allows us to describe the probabilistic model by using the Monte-Carlo method. The sensitivities of the mechanical response are evaluated regarding the uncertainties in design variables such as Young’s modulus of fibers and matrix, fiber reference strength, shear yield stress, fiber volume fraction and shear parameter defining the shear stress in the inelastic region.     

A cohesive law for carbon nanotube/polymer interfaces based on the van der Waals force

We have established the cohesive law for interfaces between a carbon nanotube (CNT) and polymer that are not well bonded and are characterized by the van der Waals force. The tensile cohesive strength and cohesive energy are given in terms of the area density of carbon nanotube and volume density of polymer, as well as the parameters in the van der Waals force. For a CNT in an infinite polymer, the shear cohesive stress vanishes, and the tensile cohesive stress depends only on the opening displacement. For a CNT in a finite polymer matrix, the tensile cohesive stress remains the same, but the shear cohesive stress depends on both opening and sliding displacements, i.e., the tension/shear coupling. The simple, analytical expressions of the cohesive law are useful to study the interaction between CNT and polymer, such as in CNT-reinforced composites. The effect of polymer surface roughness on the cohesive law is also studied.     

Cyclic viscoelastoplasticity and low-cycle fatigue of polymer composites

Observations are reported on a polymer composite (polyamide-6 reinforced with short glass fibers) in tensile relaxation tests with various strains, tensile creep tests with various stresses, and cyclic tests with a stress-controlled program (ratcheting with a fixed maximum stress and various minimum stresses). Constitutive equations are developed in cyclic viscoelastoplasticity of polymer composites. Adjustable parameters in the stress–strain relations are found by fitting observations in relaxation tests and cyclic tests (16 cycles of loading–unloading). It is demonstrated that the model correctly predicts experimental data in creep tests and dependencies of maximum and minimum strains per cycle on number of cycles up to fatigue fracture of specimens. The influence of strain rate and minimum stress on number of cycles to failure is studied numerically.     

An analysis of thickness effects in the Izod test

The Izod impact test is analyzed numerically using a polymer constitutive relation with material parameters qualitatively representative of a polycarbonate. The computations are full 3D transient analyses using explicit time integration and accounting for finite strains. The main purpose of the analyses is a comparison of the stress and strain fields that develop for the various specimen geometries that are used in practice, ranging from a specimen with a square cross-section to a specimen with a width about a quarter of that value. It is shown that the response varies from something close to a plane strain response to something close to a plane stress response. The results illustrate the effect of the stress–strain behavior of polymers, which involves attaining a stress peak, followed by softening and then by the gradual evolution of a very stiff response resulting from increasing network stiffness.     

Rheological behavior of fiber-filled polymers under large amplitude oscillatory shear flow

Small and large amplitude oscillatory shear measurements (SAOS and LAOS) were used to investigate the rheological behavior of short glass fibers suspended in polybutene and molten polypropylene. Raw torque and normal force signals obtained from a strain-controlled instrument (ARES rheometer) were digitized using an analog to digital converter (ADC) card to allow more precise data analysis. The fiber concentration did not affect the torque signal in the SAOS mode, except for its magnitude, whereas the normal force signal was too low to be measurable. With increasing strain amplitude, the magnitude of the torque became a function of time. Depending on the applied frequency and strain rate, the stress in the filled polybutene increased with time, whereas for reinforced polypropylene (viscoelastic matrix), the behavior was opposite, i.e. the stress decreased with time. These effects were more pronounced at high fiber content. In addition the primary normal stress differences were no longer negligible at large deformation amplitude and exhibited a non-sinusoidal periodic response. Fast Fourier transform (FFT) analysis was performed and the resulting spectra, along with Lissajous figures of the shear stress and the primary normal stress differences, are explained in terms of fiber orientation. The experimental results for the suspensions in polybutene are well predicted by the Folgar-Tucker-Lipscomb (FTL) model.     

Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.     

An experimental and numerical investigation of different shear test configurations for sheet metal characterization

Simple shear tests are widely used for material characterization especially for sheet metals to achieve large deformations without plastic instability. This work describes three different shear tests for sheet metals in order to enhance the knowledge of the material behavior under shear conditions. The test setups are different in terms of the specimen geometry and the fixtures. A shear test setup as proposed by Miyauchi, according to the ASTM standard sample, as well as an in-plane torsion test are compared in this study. A detailed analysis of the experimental strain distribution measured by digital image correlation is discussed for each test. Finite element simulations are carried out to evaluate the effect of specimen geometries on the stress distributions in the shear zones. The experimental macroscopic flow stress vs. strain behavior shows no significant influence of the specimen geometry when similar strain measurements and evaluation schemes are used. Minor differences in terms of the stress distribution in the shear zone can be detected in the numerical results. This work attempts to give a unique overview and a detailed study of the most commonly used shear tests for sheet metal characterization. It also provides information on the applicability of each test for the observation of the material behavior under shear stress with a view to material modeling for finite element simulations.     

On the effect of fiber creep-compliance in the high-temperature deformation of continuous fiber-reinforced ceramic matrix composites

Creep models for unidirectional ceramic matrix composites reinforced by long creeping fibers with weak interfaces are presented. These models extend the work of Du and McMeeking (1995) [Du, Z., McMeeking, R. 1995. Creep models for metal matrix composites with long brittle fibers. J. Mech. Phys. Solids 43, 701–726] to include the effect of fiber primary creep present in the required operational temperatures for ceramic matrix composites (CMCs). The effects of fiber breaks and the consequential stress relaxation around the breaks are incorporated in the models under the assumption of global load sharing and time-independent stochastics for fiber failure. From the set of problems analyzed, it is found that the high-temperature deformation of CMCs is sensitive to the creep-compliance of the fibers. High fiber creep-compliance drives the composite to creep faster, leading however to greater lifetimes and greater overall strains at rupture. This behavior is attributed to the fact that the greater the creep-compliance of the fibers, the higher the creep rate but the slower the matrix stress relaxation – since the matrix must deform with a rate compatible with the more creep-resistant fibers – and therefore the less the load carried by the main load-bearing phase, the fibers. As a result, fewer fibers fail and less damage is accumulated in the system. Moreover, the greater the creep-compliance of the fibers, the slower the matrix shear stress relaxation – and thus the lower the levels of applied stress for which this effect becomes important. The slower the shear stress relaxes, the slower the “slip” length increases. Due to the Weibull nature of the fibers, the fiber strengths at the smaller gauge length of the slip length are stronger; therefore fewer fibers undergo damage. Hence, high fiber creep-compliance is desirable (in the absence of any explicit creep-damage mechanism) in terms of composite lifetime but not in terms of overall strain. These results are considered of importance for composite design and optimization.