Shearing flow of highly anisotropic laminated composites

A model is presented to describe the flow in a laminated composite when it is subjected to shearing traction. The model is formulated for an arbitrary number of plies which may be arranged in an arbitrary stacking sequence. The plies are assumed to be separated by thin, resin-rich layers. These layers are found to appear automatically during the forming process when the individual plies of the laminate are consolidated. Each resin layer is modelled as a Newtonian viscous fluid and each ply as a fibre-reinforced, inextensible viscous fluid. The velocity field in each layer is assumed to consist of simple plane extensional and shear flows. It is shown that the plies in successive layers cannot rotate relative to each other so that the angular separation of the fibre directions in successive plies is preserved throughout the motion. For a five layer configuration the velocity profiles are obtained explicitly and these are illustrated graphically for several different stacking sequences.     

A rate-dependent non-orthogonal constitutive model for describing shear behaviour of woven reinforced thermoplastic composites

A rate dependent constitutive model for woven reinforced thermoplastic matrix composites at forming temperatures is proposed in this work. The model is formulated using a stress objective derivative based on the fibre rotation. Nonlinear shear behaviour is modelled as a polynomial function and the rate dependence is described using a Cowper–Symonds overstress law formulated in terms of shear angle rate. The model parameters are determined by means of bias extension tests. The applicability of the material model is validated through a forming experiment.     

FE-investigation of shear localization in granular bodies under high shear rate

Shear localization in granular materials under high shear rate is analysed with the finite element method and a micro-polar hypoplastic constitutive model enhanced by viscous terms. We consider plane strain shearing of an infinitely long and narrow granular strip of initially dense sand between two very rough walls under conditions of free dilatancy. The constitutive model can reproduce the essential features of granular materials during shear localization. The calculations are performed under quasi-static and dynamic conditions with different shear rates. In dynamic regime, the viscosity terms are formulated based on a modified Newtonian fluid and according to the formula by Stadler and Buggisch (Proceedings of the conference on Reliable flow of particulate solids, EFCE Pub. Series, vol 49. Chr. Michelsen Institute, Bergen, 1985). Emphasis is given to the influence of inertial and viscous forces on the shear zone thickness and mobilized wall friction angle.     

On the non-linear behaviour of fluid jets

In this paper we consider a one-dimensional theory for the flow of fluid jets, formulated with the help of one-dimensional postulates. The theory is applied to a circular cylindrical jet of incompressible viscous fluid with constant pressure and constant surface tension over its surface. A phase plane analysis is used to obtain some (non-linear) solutions of the governing equations when viscosity is neglected. For steady state problems, including viscosity, earlier work of Matovich and Pearson[2] is obtained as a limiting case of the theory.     

Manufacturing characteristics of the continuous tow shearing method for manufacturing of variable angle tow composites

Automated fibre placement (AFP) is well-known as a cutting-edge technology for manufacturing variable angle tow (VAT) composites with tailored fibre paths. However, its process-induced defects prevent the wide application of VAT composite structures. As an alternative manufacturing method, the continuous tow shearing (CTS) technique, utilising the ability to shear dry tows, has been developed. It was shown that CTS could significantly reduce process-induced defects such as fibre wrinkling, resin rich areas and fibre discontinuities. In this paper, its manufacturing characteristics such as material characteristics, layup accuracy, and thickness variation are investigated experimentally.     

Forming induced wrinkling of composite laminates with mixed ply material properties; an experimental study

One disadvantage of multi-layer forming of unidirectional (UD) prepreg tape is the risk of out-of-plane wrinkling. This study aims to show how mixed ply material properties affect global wrinkling behaviour.An experimental study was performed using pre-stacked UD prepreg on a forming tool with varying cross sections. Parameters studied include local interply friction, effects of co-stacking and fibre stresses in critical fibre directions. Experimental evaluation was performed on out-of-plane defect height, type and location. The study shows that fibre stresses in some fibre directions were crucial for the shearing required to avoid wrinkling. The same fibre stresses may cause wrinkling if the lamina is stacked in a non-beneficial order. Changing the friction locally, or reducing the number of difficult combinations of fibre angles, improves the forming outcome slightly. However, in order to make a significant improvement, co-stacking or different fibre stacking is required.     

Analysis of knitted fabric reinforced composites: Part I. Fibre orientation distribution

The fibre orientation distributions in different types of warp knitted fabric are studied. The fibre orientations are represented by orientation tensors. This allows for the production of second- and fourth-order approximations of the orientation distribution function, which contain the relevant part of the orientation distribution for second- and fourth-order tensorial properties, respectively. Also, the symmetry that is present in the knitted fabrics can be analysed with the help of orientation tensors. It is shown that all the knitted fabrics are ‘almost' monoclinic. Determination of the ‘nearly' on-axis coordinate system is of interest for the data reduction of tensile test data.     

Normalisation of biaxial bias extension test results considering shear tension coupling

A theoretical background is proposed for the normalisation of biaxial bias extension results for rate-independent fabrics, whose shear compliance depends on both the shear angle and the fibre tension within the fabric. The theory is used to predict the form of biaxial bias extension results from known shear force–shear angle–fibre tension behaviours. Hypothetical data sets are used to perform a parametric study of the likely influence of the nature of the shear–tension coupling on the form of the biaxial bias extension test results. The theory is then used in implementing an iterative numerical code designed to retrieve the underlying material response from biaxial bias extension test results and examples predictions are given. A discussion of the information required in order to perform the normalisation, and the methods by which this information can be obtained, is presented. Finally, assumptions behind the theory are outlined and critically assessed.     

Second-gradient plane deformations of ideal fibre-reinforced materials II: forming flows of fibre–resin systems when fibres resist bending

The continuum theory of ideal fibre-reinforced fluids, namely incompressible viscous fluids exhibiting some direction of inextensibility is extended to account for the fibre bending stiffness; namely a property that prevents discontinuity of the fibre slope under normal loading conditions. The principal kinematics of this new theoretical development is consistent with three-dimensional forming flows of fibre–resin systems though, for simplicity, formulation of relevant constitutive equations is confined within the framework of relevant plane flows. The theory adopts the macroscopic view that the resin matrix behaves as a viscous fluid but the resin and fibres form a homogeneous composite material. Consideration of the fibre bending resistance requires the inclusion of couple-stress and, hence, non-symmetric stress. The outlined theoretical developments are therefore relevant to polar-media behaviour; in this context, the anisotropic viscous fluids of interest become part of the material class of the so-called polar fluids. For plane flows of this type of fluids, a manner is also outlined in which the non-symmetric stress distributions sought can be determined by solving two simultaneous, first-order linear differential equations. Moreover, a relevant stress-resultants technique is adopted and extended appropriately to make possible complete determination of the kinematics dictating the creeping forming plane flow of the composite fluids of interest. Details of the mechanisms that capture fibre bending resistance are revealed and illustrated through a relatively simple example application. This considers and resolves the forming flow process of an ideal fibre-reinforced composite, moulded into a sharp corner under the action of an external line force.     

Finite element modelling of thermally bonded bicomponent fibre nonwovens: Tensile behaviour

Nonwovens are polymer-based engineered textiles with a random microstructure and hence require a numerical model to predict their mechanical performance. This paper focuses on finite element (FE) modelling the elastic–plastic mechanical response of polymer-based core/sheath type thermally bonded bicomponent fibre nonwoven materials. The nonwoven fabric is treated as an assembly of two regions having distinct mechanical properties: fibre matrix and bond points. The fibre matrix is composed of randomly oriented core/sheath type fibres acting as load-transfer link between bond points. Random orientation of individual fibres is introduced into the model in terms of the orientation distribution function (ODF) in order to determine the material’s anisotropy. The ODF is obtained by analysing the data acquired with scanning electron microscopy (SEM) and X-ray micro computed tomography (CT). On the other hand, bond points are treated as a deformable bicomponent composite material composed of the sheath material as matrix and the core material as fibres having random orientations. An algorithm is developed to calculate the anisotropic material properties of these regions based on properties of fibres and manufacturing parameters such as the planar density, core/sheath ratio and fibre diameter. Having distinct anisotropic mechanical properties for two regions, the fabric is modelled with shell elements with thicknesses identical to those of the bond points and fibre matrix. Finally, nonwoven specimens are subjected to tensile tests along different loading directions with respect to the machine direction of the fabric. The force–displacement curves obtained in these tests are compared with the results of FE simulations.     

Analysis of the mechanical behavior of woven fibrous material using virtual tests at the unit cell level

The determination of the mechanical properties of fabrics in biaxial tension and in-plane shearing is made from 3D finite element analyses of the unit woven cell. Compared to experimental tests these virtual tests have several advantages. They can easily be carried out for sets of varied parameters, they provide local information inside the woven material and above all they can be performed on woven materials that have not yet been manufactured. The 3D computations are not classical analyses because the yarns are made up of several thousands of fibres and their mechanical behaviour is very special. Several specific aspects of the analysis are detailed, especially the use of a hypoelastic law based on an objective derivative using the rotation of the fibre which allows a strict evolution of the directions of orthotropy according to the fibre direction. Examples of analyses are presented in biaxial tension and in-plane shear for woven reinforcements and in the case of the biaxial tension of a knitted fabric. The results obtained are in good agreement with experimental results.     

防X射线纤维材料流变性能及形态结构的研究

主要论述屏蔽剂的含量对新型防Ｘ射线纤维材料流变性能的影响，分析了其初生纤维的形态结构和声速模量的变化。结果发现，随剪切速率的增加，其剪切应力提高，而表观粘度下降。随屏蔽剂含量的增加，混合料表面出更高的剪切应力，其表观粘度也相应增加。初生纤维截面形态结构，由紧密形态变成疏松结构。     

Evaluation of the mechanical and damage behaviour of tufted non crimped fabric composites using full field measurements

This paper investigates the effect of tufting on the mechanical properties of non crimped fabric (NCF) composites. In-plane behaviour is examined under tension and compression in the axial [0/90] and shear [±45] directions. Cyclic experiments in the bias and axial directions combined with a digital image correlation method (DICM) allow the investigation of damage distribution through the reduction of apparent stiffness and operations on the strain field. The out of plane mechanical response is studied via delamination tests in mode I and mode II. After studying each loading case individually, small structures of both composites are subjected to multi-loadings. Experimental results show that tufting reduces both the in plane stiffness and the strength in the axial direction (by approximately 10%), while it greatly enhances delamination resistance in the normal and shear directions. On the other hand tufts influence on in plane properties is moderate in the bias direction. But large differences were monitored between compression and tension response in the bias direction for standard and tufted composites. Discs punched tests inducing multi-loading (in and out of plane loading) show greater energy absorption but lower failure load for tufted specimens than for untufted. It was found that cyclic loading experiments monitored with DICM yields damage maps that offer a useful insight into damage development. Large damage differences are recorded between different load cases and lay ups. The results also show that the tufts influence the damage progression in the NCF.     

Influence of fabric on liquefaction and densification potential of cohesionless sand

For simple shearing under constant pressure, the effects of fabric on liquefaction and densification potentials of saturated cohensionless granular materials are examined theoretically and experimentally. The fabric is identified with the distribution of the dilatancy angles (the angle between the sliding and the macroscopic shearing directions), and the influence of prestraining on this distribution and hence on the macroscopic sample behavior is studied. It is shown that prestraining with zero residual stress can reduce resistance to liquefaction by one or even two orders of magnitude, although the sample density and other conditions are kept the same. The micromechanical features responsible for this and related behaviors are examined in some detail. Finally, some tentative results on the effect of the inherent anisotropy that is produced during sample preparation are reported, showing that a method which yields samples more resistive in triaxial cyclic tests may provide samples less resistive in cyclic shearing.     

Fatigue crack growth in thin notched woven glass composites under tensile loading. Part II: Modelling

Fatigue propagation of a through-the-thickness crack in thin woven glass laminates is difficult to model when using homogeneous material assumption. Crack growth depends on both the fatigue behaviour of the fibres and of the matrix, these two phenomena occurring at different time and space scales. The developed finite element model is based on the architecture of the fabric and on the fatigue behaviours of the matrix and the fibre, even if the pure resin and fibre behaviours are not used. That thus limits the physical meaning of this model. Basically, the objective of this simulation is to illustrate and to confirm proposed crack growth mechanism. The fatigue damage matrix is introduced with user spring elements that link the two fibre directions of the fabric. Fibre fatigue behaviour is based on the S-N curves. Numerical results are compared to experimental crack growth rates and observed damage in the crack tip. Relatively good agreement between predictions and experiments was found.     

Dependence of the acoustoelastic properties and texture of an orthorhombic polycrystalline aggregate on stress

Summary The propagation of ultrasonic plane waves in a solid bulk sample is considered for the case when the sample material is of the form of a polycrystalline aggregate (e.g., steel) made of crystallites of the highest cubic symmetry. The crystallite orientation disitribution is assumed to be such that it implies the orthorhombic symmetry of the macroscopic (effective) acoustoelastic properties of the polycrystalline aggregate. Moreover, the sample is assumed to be subjected to an increasing stress, the principal directions of the stress being coincident with the axes of the orthorhombic symmetry of the bulk sample. It is assumed that the ultrasonic waves also propagate and are linearly polarized in the directions coincident with the axes of the orthorhombic symmetry. The Voigt's averaging procedure and Jaynes' principle of maximum Shannon entropy are accepted as a reliable basis for the evaluation of the influence of the changes in stress on both the effective acoustoelastic properties of the polycrystalline aggregate and the probability density function of the crystallite orientation in the sample. In this way, an algorithm is prepared which enables us to evaluate numerically these effects under the assumption that the single-crystallite elastic moduli are constant. Some results obtained by using this algorithm are presented for the case of a plane increasing stress. An erratum to this article can be found at     

Fabric,force and strength anisotropies in granular materials: a micromechanical insight

In micromechanics, the stress–force–fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.     

Internal reflections in bleached reflection holograms

Bleached reflection holograms produced by two plane waves in Agfa 8E56 photographic emulsion and recorded in an index-matching liquid tank at 514 nm are studied. Replay at 514 nm is both in the tank and in air, boundary reflections giving rise to multiple-output beams in the latter case. The intensities in the various output beams are measured as a function of the angle of incidence of the input beam. A simple theory based on two-wave grating diffraction and the Fresnel boundary coefficients is formulated and shown to agree with good approximation with the observed intensities of all significant output beams.     

Attenuation and quality factor surfaces in anisotropic-viscoelastic media

We obtain expressions of the attenuation vector and quality factor of the three possible wave modes propagating in a linear anisotropic medium. The theory assumes, in principle, a general stiffness matrix. Probing the medium with a time-harmonic homogeneous plane wave gives the attenuations and quality factors as simple forms of the propagation direction, complex stiffnesses and mass density. As an application, we introduce a new constitutive relation, based on four complex moduli, for which the values of the quality factor along three preferred directions can be matched with experimentally pre-determined values. The rheology is causal and allows an arbitrary frequency-dependence of the stiffnesses based on the generalized standard linear solid model. Two examples are explicitly worked out. The first is clay shale, a material of hexagonal symmetry. Since, by Neumann's principle, the attenuation symmetries are determined by the crystal class, the medium presents isotropic attenuation in a plane normal to the symmetry axis. For instance, in materials with c₁₁ > c₃₃, it is found that the quasi-compressional wave attenuates more along the symmetry axis direction than in the plane of isotropy. The second medium is tellurium dioxide, a strongly anisotropic material of tetragonal symmetry. In this case, the diagrams show that strong attenuation is associated with high slowness values, as at around 45° in the horizontal plane. Both case studies show that the features of the attenuation surfaces strongly depend on the values of the elasticities.     

Rate dependent modelling of the forming behaviour of viscous textile composites

A predictive approach to modelling the forming of viscous textile composites has been implemented in two finite element codes; Abaqus Standard™ and Abaqus Explicit™. A multi-scale energy model is used to predict the shear force–shear angle–shear rate behaviour of viscous textile composites, at specified temperatures, using parameters supplied readily by material manufacturers, such as fibre volume fraction, weave architecture and matrix rheology. The predictions of the energy model are fed into finite element simulations to provide the in-plane shear properties of two different macro-scale constitutive models implemented in the finite element codes. The manner of coupling predictions of the multi-scale energy model with the macro-scale models is shown to affect the rate-dependent material response in the simulations. These coupling methods are evaluated using picture frame test simulations.