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  • 1. Alkhagen, M.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    A triaxial rheometer for soft compressible solids2002In: Journal of Rheology, ISSN 01486055 (ISSN), Vol. 46, no 1, p. 31-47Article in journal (Refereed)
    Abstract [en]

    The compression and the shear of soft compressible solids were studied using the triaxial rheometer. The sample was fixed between two parallel plates and the deformation was controlled by an x, y, z displacement on one plate while the stress was measured on the other. The triaxial stress transducer eliminates the edge effects by only measuring the stress on an interior region of the plate. The edge effects and the associated measurement errors were analyzed by the simple isotropic elastic theory and were compared to the measurements done on the chloroprene rubber foam.

  • 2. Alkhagen, M.
    et al.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Micromechanics of a compressed fiber mass2007In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 74, no 4, p. 723-731Article in journal (Refereed)
    Abstract [en]

    A theory is presented for the rate modeling of flexible granular solids based on affine average motion of interparticle contacts. We allow contacts to form and break continually but assume the existence of a finite friction coefficient rendering contacts force free as they form or break. The resulting constitutive equations are of the hypoelastic type. A specific model for the deformation of a fiber mass is then developed. The model improves on previous theories for fiber masses in at least two respects: First, it is more general in that it is not restricted to uniaxial compression, although it is restricted to predominantly compressive deformations histories, due to neglect of frictional dissipation. Second, by allowing torsion as well as bending of fibers, this theory covers a larger deformation range. Compression experiments are performed on carded slivers of PA6 fibers under various conditions. The measured response is found to be in close agreement with that predicted by the model.

  • 3. Alkhagen, M.
    et al.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    The effect of fiber diameter distribution on the elasticity of a fiber mass2009In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 76, no 4, article id 041014Article in journal (Refereed)
    Abstract [en]

    A random mass of loose fibers interacting by fiber-fiber contact is considered. As proposed in a previous paper, the elastic response is modeled based on the statistical mechanics of bending and torsion of fiber segments between fiber-fiber contact points. Presently we show how the statistical approach can be used to account for a distribution of fiber diameters rather than just a single diameter. The resulting expression has the same form and the same set of parameters as its single-diameter counterpart, except for two dimensionless reduction factors, which depend on the fiber diameter distribution only and reduce to unity for monodisperse fibers. Uniaxial compressibility experiments are performed on several materials with different bimodal fiber diameter distributions and are compared to model predictions. Even though no additional parameters were introduced to model the effect of mixed fiber diameters, the behavior is accurately predicted. Notably, the effect of the nonuniform fiber diameter is strong: A mixture of two fiber diameters differing by a factor of 2 can reduce the response by an order of magnitude, compared to the case of uniform diameter.

  • 4. Allaoui, Aissa
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Evesque, Pierre
    Bai, JinBo
    On the compressive response of carbon nanotube tangles2009In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 373, no 35, p. 3169-3173Article in journal (Refereed)
    Abstract [en]

    The nonlinear bulk compressibility of entangled multiwalled carbon nanotubes is studied. The analogy with textile fibre assemblies is explored by means of the well established van Wyk model. In view of the small diameter of the nanotubes. the possible effect of adhesive van der Waals interactions at tube-tube contacts is analysed. It is found, however, that the contribution of adhesive contacts to the bulk stress should be negligible. Compression experiments are performed on multi-walled carbon nanotubes and show that van Wyk's model is able to describe the response, although the values of the dimensionless parameter k of van Wyk's model were lower than expected. There is indeed no indication that van der Waals interactions play any significant role.

  • 5. Al-Zubaidy, M. N.
    et al.
    Chan, J. F. L.
    Gibson, A. G.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Properties of orthotropic glass-polypropylene composites manufactured by weaving of prepreg tapes and other routes2000In: Plastics, Rubber and Composites Processing and Applications, ISSN 09598111 (ISSN), Vol. 29, no 10, p. 520-526Article in journal (Refereed)
    Abstract [en]

    This paper reports a study of the melt impregnation and weaving of glass-polypropylene prepreg tapes into sheet for use as a precursor for pressed thermoplastic composite products and a comparison of the properties attainable with those achievable by other comparable routes. Melt impregnation has been used successfully to manufacture well impregnated tapes, with and without internal coupling agent. It appears that weaving could be an economically viable process for converting unidirectional tape into a conformable, press formable prepreg. The properties of glass-polypropylene laminates manufactured by pressing the tape woven product were compared with those of other glass-polypropylene composites, including crossply laminate made from Plytron and samples prepared by film stacking. Quasi-static mechanical properties were found to be comparable with those of Plytron and superior to those of the other materials. In the coupled samples, coupling was somewhat less effective than in Plytron. The impact behaviour of the pressed, tape woven products was impressive and superior to any of the other materials tested. © 2000 IoM Communications Ltd.

  • 6. Connor, M.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Manson, J. -AE.
    Gibson, A. G.
    Model for the consolidation of aligned thermoplastic powder impregnated composites1995In: Journal of Thermoplastic Composite Materials, ISSN 08927057 (ISSN), Vol. 8, no 2, p. 138-162Article in journal (Refereed)
    Abstract [en]

    This paper describes the role of surface energy effects, externally applied pressure, resin flow and fiber bed elasticity on the consolidation of thermoplastic-matrix composites manufactured by the powder impregnation route. Surface energy effects in the spreading of polymer droplets on fiber surfaces are discussed; then a model for the consolidation process is developed, relating the variables mentioned above. Consolidation experiments on powder-impregnated composites of the FIT type (Fibres Impregnees de Thermoplastique) were carried out using a mold attached to a servo-hydraulic testing machine. The model accurately predicts variations in void content during consolidation of carbon fiber/PEEK (CF/PEEK) and carbon fiber/PEI (CF/PEI) laminates. It was found that, at the pressures needed to achieve rapid consolidation, surface energy has a negligible influence on impregnation rate, but its effects on the void topology can be considerable. It was also shown that, when laminates of low void content are required, a minimum pressure is needed to overcome the effect of fiber bed elasticity.

  • 7. Connor, M.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    MÃ¥nson, J. -AE.
    On surface energy effects in composite impregnation and consolidation1995In: Composites Manufacturing, ISSN 09567143 (ISSN), Vol. 6, no 3-4, p. 289-295Article in journal (Refereed)
    Abstract [en]

    Macroscopic capillary pressure and microscopic interparticle forces due to surface tension are examined. A general equation for the capillary pressure during impregnation is derived and subsequently specialized to particular processes. For fibre composites, the capillary pressure can be of the order of ±104 Pa, the sign depending on the contact angle between solid and liquid. Next, the attractive and repulsive forces between particles connected by liquid droplets are analysed by two different model geometries. At contact angles between π/2 and π, an equilibrium particle separation distance is obtained in the absence of applied force. At lower contact angles, spontaneous impregnation can be achieved. The effect of capillary action on impregnation rate may be significant if applied pressures are small (e.g. filament winding) but negligible at applied pressures greater than ∌100 kPa (e.g. compression moulding). The topology and concentration of voids may, however, be greatly influenced by surface energies. © 1995.

  • 8. Djalili-Moghaddam, M.
    et al.
    Ebrahimzadeh, R.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Study of geometry effects in torsional rheometry of fibre suspensionsIs The “Creative Class” Necessarily Urban?2004In: Rheologica Acta, ISSN 0035-4511, E-ISSN 1435-1528, Vol. 44, no 1, p. 29-37Article in journal (Refereed)
    Abstract [en]

    This work concerns the problem of measuring the viscosity of a suspension of fibres that are not short compared to the dimensions of the measurement device. We have examined various geometry effects in shear using parallel-plate and cone-and-plate configurations. Steady state viscosity, transient viscosity and first normal stress difference have been studied. Silicone oil with milled glass fibres at 8 vol.% was used as a model fibre suspension. The conventional parallel-plate geometry exhibits a significant gap dependence of the apparent viscous response. Too small gaps constrain the fibre rotations, thus lowering the initial stress peak and delaying the development of steady state. Too large gaps lead to a loss of liquid at the sample perimeter, which reduces the apparent steady state viscosity. The steady state response, however, seems to be correct for gaps in the range 1-2 mm when the maximum fibre length is 1.5 mm. The cone-and-plate geometry is less sensitive to large gaps. Too small a gap at the (truncated) cone apex leads to anomalous response due to bridging of the gap by fibres. The use of unusually large plates (100 mm diameter) and different cone angles and truncations was explored. It was shown that cone-and-plate configurations of large diameter and large truncation can effectively decrease the geometry disturbances both due to fibre bridging at the cone apex and loss of liquid at the edge.

  • 9. Djalili-Moghaddam, M.
    et al.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    A model for short-range interactions in fibre suspensions2005In: Journal of Non-Newtonian Fluid Mechanics, ISSN 0377-0257, E-ISSN 1873-2631, Vol. 132, no 1-3, p. 73-83Article in journal (Refereed)
    Abstract [en]

    This paper introduces a model for short-range fibre-fibre interaction and combines it with the Shaqfeh-Fredrickson result for long-range hydrodynamic interactions. The short-range interactions are assumed to be localised, such that the interaction forces may be taken to act at points on the fibre axes. Only interactions of viscous Newtonian character are explored in this work; the approach, however, may be used to treat more general nonlinear interactions, such as non-Newtonian vicous forces or friction. To simulate the orientation evolution, a convective discretisation technique combined with a modification of the Folgar-Tucker rotary diffusion model is proposed. The rotational parallel-plate geometry is analysed, and transient as well as steady state responses are computed. Experiments are performed on suspensions of polyamide fibres in silicon oil, using a rotational parallel-plate rheometer. It is demonstrated that the effect of fibre volume fraction and aspect ratio are well captured by this theory. Normal force as well as torque is adequately predicted. Other effects, however, such as shear thinning and effect of absolute particle size, are not predicted by the linear theory.

  • 10. Djalili-Moghaddam, M.
    et al.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Fibre suspension rheology: Effect of concentration, aspect ratio and fibre size2006In: Rheologica Acta, ISSN 0035-4511, E-ISSN 1435-1528, Vol. 45, no 3, p. 315-320Article in journal (Refereed)
    Abstract [en]

    Viscosity data for fibre suspensions are produced using cone-and-plate geometry of enhanced dimensions for the reduced influence of fibre-wall interactions. Semi-concentrated suspensions of monodisperse polyamide fibres in silicone oil, with a variety of fibre concentrations (2, 5 and 8%), lengths and diameters, were studied. The suspension viscosity was measured in a range of shear stress in order to study the stress dependence. The study here focuses on the nature of the forces and interactions that contribute to the suspension viscosity. The results show that at sufficiently high stress levels, the suspension viscosity tends to reach a steady-state. At very low stress levels the suspension viscosity increases over time, most likely due to structures formed by adhesive forces. At higher concentrations, the viscosity depends on the absolute size of the fibres, again indicating the presence of non-hydrodynamic interactions.

  • 11. Ericsson, K. A.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Manson, J. -AE.
    The two-way interaction between anisotropic flow and fiber orientation in squeeze flow1997In: Journal of Rheology, ISSN 01486055 (ISSN), Vol. 41, no 3, p. 491-511Article in journal (Refereed)
    Abstract [en]

    The rheology of a discontinuous fiber filled polypropylene in squeeze flow between parallel plates is studied. The material has an initial anisotropic fiber orientation distribution and therefore displays a strongly anisotropic in-plane flow behavior with predominant flow transverse to the axis of principal orientation. The kinematic field is computed using a linear, orthotropic constitutive model, where the fibers are assumed to move affinely with the surrounding fluid. The fiber orientation distribution is updated in each timestep thus coupling orientation and flow. Two different orientation descriptions are evaluated: orientation tensors with closure approximations, and a technique based on direct solution of the orientation of a set of test fibers. The two methods are first compared to exact solutions of the orientation distribution function in simple shear and pure extension; the direct solution is exact within numerical error, wheras the methods based on orientation tensors and quadratic and hybrid closure fail to correctly describe any transient fiber orientation evolution. Finally, the orientation representations are implemented in the kinematic model and compared to the experimental data; the direct solution method is found to give a very accurate prediction of the observed flow kinematics, whereas the other techniques result in substantial errors. © 1997 The Society of Rheology.

  • 12. Ericsson, K. A.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Månson, J. -AE.
    Sliding plate rheometry of planar oriented concentrated fiber suspension1997In: Rheologica Acta, ISSN 0035-4511, E-ISSN 1435-1528, Vol. 36, no 4, p. 397-405Article in journal (Refereed)
    Abstract [en]

    The rheology of concentrated planar fiber suspensions is investigated. A new experimental technique for fiber suspensions based on a sliding plate rheometer incorporating a shear stress transducer is developed. It is shown that this instrument works well for the tested material systems. The Theological behavior in steady shear is subsequently investigated. The results can be largely explained by a combination of frictional and hydrodynamic interaction. Despite this evidence of friction no yield stress could be detected for the investigated shear rates. It was also found that the fiber aspect ratio did not influence the steady shear viscosity.

  • 13. Gibson, A. G.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Mechanics of the squeeze flow of planar fibre suspensions1999In: Journal of Non-Newtonian Fluid Mechanics, ISSN 03770257 (ISSN), Vol. 82, no 1, p. 1-24Article in journal (Refereed)
    Abstract [en]

    This paper discusses the axisymmetric squeeze flow of concentrated transversely isotropic fibre suspensions in a power-law matrix and relates to the processing of composite materials such as sheet moulding compounds (SMCs) and glass mat thermoplastics (GMTs). A solution to the squeeze flow problem for a transversely isotropic power-law fluid is presented first, followed by a more detailed micromechanical analysis. In the first part of the paper a variational approach is applied to the interpretation of squeeze flow behaviour. This gives a simple expression for the total pressure, which enables the contributions due to extension and shear to be separated. Applying the procedure to GMT data suggests that the dissipation is predominantly extensional, except at very low plate separations. In the second part, a non-local constitutive equation is derived based on a simple drag law for hydrodynamic interactions. This is then used to model the pressure distribution when the effective length of the fibres is comparable to or determined by the dimensions of the squeeze flow plates. The model is shown to describe the observed squeeze flow stresses in both long and short fibre systems and to relate behaviour to the underlying resin flow properties. © 1999 Elsevier Science B.V. All rights reserved.

  • 14. Grauers, L.
    et al.
    Szpieg, M.
    Wysocki, M.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    Deformation processes in composites preforms2012In: ECCM 2012 - Composites at Venice, Proceedings of the 15th European Conference on Composite Materials, European Conference on Composite Materials, ECCM , 2012Conference paper (Refereed)
    Abstract [en]

    The work concerns the inelastic response of composite preforms when subjected to large deformations. The Kawabata equipment has been used to measure the shear and bending properties of the textile reinforcements. In addition, the newly developed triaxial rheometer for out-of-plane shear and compression testing is presented and used. The triaxial rheometer is capable of simultaneous compression and two independent shear deformation modes, allowing for triaxial deformation states. Compared to previous techniques the main benefits are triaxiality, elimination of edge effects and suitability for anisotropic materials. Also, a constitutive theory for the modelling of a wide range of fibrous performs based on hypoplasticity is also presented. The experimental results indicates that even dry preforms behaves viscoelastoplastic as well as showing unsymmetrical behaviour in bending.

  • 15. Håkanson, J. M.
    et al.
    Toll, Staffan
    University College of Borås, Sweden.
    Lundström, T. S.
    Liquid permeability of an anisotropic fiber web2005In: Textile research journal, ISSN 0040-5175, E-ISSN 1746-7748, Vol. 75, no 4, p. 304-311Article in journal (Refereed)
    Abstract [en]

    The Darcian permeability of a dense network of fibers with general orientation is examined experimentally and analytically. The permeability of a carded PA6 fiber web is measured in the three principal directions using a saturated parallel flow technique. A model is introduced that generalizes existing theories for unidirectional fiber arrays to fiber networks of general orientation distribution. The average drag on a given fiber is assumed to be independent of the overall fiber orientation distribution. A second-order orientation tensor describes the orientation dependence. Our generalization applied to the models of Gebart predicts reasonably well the in-plane permeability, but overestimates the out-of-plane permeability by a factor of four.

  • 16.
    Hård af Segerstad, P.
    et al.
    Department of Applied Mechanics, Chalmers University of Technology.
    Larsson, R.
    Department of Applied Mechanics, Chalmers University of Technology.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy2008In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, ISSN 0749-6419, Vol. 24, no 5, p. 896-914Article in journal (Refereed)
    Abstract [en]

    A thermodynamically consistent approach is developed for modelling the response of an open-cell cellular solid at finite compressive strains. The cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is assumed to be 1-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz it is possible to include multiple nonlinear mechanisms, such as hyperelasto-viscoplasticity and damage. The macrostress is obtained by averaging over a statistical ensemble of struts. The model has been implemented in the context of finite strains and damage coupled to viscoplastic Perzyna type behaviour. All model parameters may be determined by performing tests in simple compression. The model is well capable of reproducing data from compression experiments on various open-cell aluminium foams.

  • 17.
    Hård af Segerstad, P.
    et al.
    Department of Applied Mechanics, Chalmers University of Technology.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Open-cell cellular solids: A constitutive equation for hyperelasticity with deformation induced anisotropy2008In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 45, no 7-8, p. 1978-1992Article in journal (Refereed)
    Abstract [en]

    A constitutive theory is developed for an open-cell flexible cellular solid consisting of a network of struts each connecting two vertex points. A hypothesis is proposed that vertex points move affinely in the large-deformation regime, when the struts buckle, and that the force carried by a strut is a function of the longitudinal and rotational change of its vertex-to-vertex vector. The forces consist of one longitudinal force, parallel with the vertex-to-vertex vector of the strut and one transverse force. The overall stress response is initially dominated by the longitudinal force whilst the addition of the transverse force becomes significant at large deformations. The model contains three parameters: longitudinal stiffness, bending stiffness and critical stretch of a strut. These three parameters are calibrated against a simple compression test. The model is then validated against independent experiments in a simple tension, simple shear and a combined shear-compression test on an isotropic flexible polyether urethane foam. Excellent agreement is obtained between the experiments and the model.

  • 18. Hård af Segerstad, P.
    et al.
    Toll, Staffan
    Chalmers University of Technology.
    Larsson, R.
    Computational modelling of dissipative open-cell cellular solids at finite deformations2009In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, ISSN 0749-6419, Vol. 25, no 5, p. 802-821Article in journal (Refereed)
    Abstract [en]

    This study concerns the constitutive modelling of dissipative open-cell structural cellular solids under primarily finite compressive deformations and the corresponding non-linear finite element implementation. A thermodynamically consistent, mechanistic approach presented in Hard of Segerstad et al. [Hard of Segerstad, P., Larsson, R., Toll, S., 2008. A constitutive equation for open-cell cellular solids, including viscoplasticity, damage and deformation induced anisotropy. International Journal of Plasticity. 24, 896-914.] is adopted for modelling the initial linear-elastic response and the subsequent plateau behaviour. In these regions the cellular solid is considered as a network of struts, where each strut connects two vertex points. A hypothesis is proposed that the vertex points move affinely in the finite strain regime, where the struts buckle plastically. The strut deformation is further assumed to be one-dimensional and depend directly on the macroscopic deformation; thus the description of the strut response requires only a scalar valued response function. Owing to this simple ansatz, the introduction of multiple non-linear mechanisms, such as hyperelasto-viscoplasticity and damage becomes feasible for large scale computations. An additional hyperelastic volumetric response, activated near the point-of-compaction, is introduced for two reasons, (i) to capture the stiffness recovery at high compressive volumetric deformations, where the struts come into contact, and (ii) to prevent numerical instability. The model is implemented as a user defined constitutive driver in the implicit version of the finite element code ABAQUS and tested experimentally for an open-cell aluminium alloy foam (Duocel 6101-0,40 ppi). All material parameters are determined by a simple compression test, and subsequently used to simulate the indentation of a rigid sphere into a foam cylinder. The model accurately captures the experimental load-displacement relation and the deformed geometry.

  • 19. Kim, P.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Stress spectra and the effective elastic and viscoelastic properties of unidirectional composites under transverse loading2000In: Journal of composite materials, ISSN 0021-9983, E-ISSN 1530-793X, Vol. 34, no 17, p. 1418-1436Article in journal (Refereed)
    Abstract [en]

    The relationship between the statistical characteristics of the microstructure, the stress state in the matrix and the effective properties of unidirectional composites have been studied. A representation of the stress state in the form of stress spectra is introduced. The skewness of spectra derived for the four basic regular periodic fiber arrays reflects the degree of order in the microstructure. A hybrid array combining features of these arrays was developed to approximate a random array. All stress components in the matrix of such a pseudo-random composite under transverse load exhibit an approximately Gaussian distribution. The stress state in the matrix determines the effective elastic modulus and the viscoelastic relaxation strength. This has led to a stress-based mechanical analysis using the moments of the stress spectrum for a representative, pseudo-random fiber arrangement.

  • 20. Lange, J.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    MÃ¥nson, J. -AE.
    Hult, A.
    Residual stress build-up in thermoset films cured below their ultimate glass transition temperature1997In: Polymer, ISSN 00323861 (ISSN), Vol. 38, no 4, p. 809-815Article in journal (Refereed)
    Abstract [en]

    The stress build-up during isothermal cure below the ultimate glass transition temperature of epoxy and acrylate films is investigated in detail. Four systems are studied; two acrylates and two epoxies, with different crosslink densities. Relaxation modulus and film shrinkage are measured simultaneously during cure. The stress build-up is measured independently using a bi-layer beam bending technique. A model for the build-up of cure stresses is proposed, in which stresses are generated by the cure shrinkage and decay by viscoelastic relaxation. The relaxation is described by a simple, modified Maxwell model. Owing to the absence of memory in the Maxwell model, the resulting equation is simple and numerical stress computation straight-forward. The stress build-up over time is thus simulated for the four model systems based on the relaxation and shrinkage data, and the simulations compared with the experimentally observed stress build-up. The model successfully predicts the cure stresses where more standard elastic methods fail. It is found that the amount of stress build-up during cure varies greatly between the different systems. In general, a higher crosslink density results in higher stress build-up. The stress on cure ranged from less than 1% of the total stress on cure and cool-down in a lightly crosslinked epoxy to more than 30% of the total stress in densely crosslinked epoxies and acrylates. Finally simple approximations for estimating the stress levels after cure and cool-down from basic material properties, e.g. modulus and cure shrinkage, are proposed. © 1997 Elsevier Science Ltd. All rights reserved.

  • 21. Lange, J.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Månson, J. -AE.
    Hult, Anders
    KTH, Superseded Departments, Polymer Technology.
    Residual stress build-up in thermoset films cured above their ultimate glass transition temperature1995In: Polymer, ISSN 0032-3861, E-ISSN 1873-2291, Vol. 36, no 16, p. 3135-3141Article in journal (Refereed)
    Abstract [en]

    The build-up of in-plane stress over time during curing and on cooling of thermoset films is investigated. The stress in a thin contracting film on a rigid substrate is analysed, and obtained as an integral of essentially the shear modulus and thickness of the curing film. Films are cured and cooled between parallel plates in a dynamic torsional rheometer, which allows dynamic shear modulus and film thickness to be monitored simultaneously. Stress predictions are compared with independent stress observations, obtained using a bilayer beam bending technique. A conventional epoxy system and a low molar mass difunctional acrylate are studied and compared. The epoxy, in agreement with the literature, exhibits no detectable stress during the curing reaction, nor during cooling to the glass transition temperature (Tg), but develops stress on cooling below Tg. The acrylate, by contrast, generates considerable stress throughout the reaction and cooling, with the major part of the stress originating above Tg. The observed stress build-up agrees well with the theoretical calculations based on the time-evolution of shear modulus and film thickness. Finally, approximate formulae for the estimation of residual stress are given. It is shown how the overall residual stress, as well as the contributions from the different parts of the cure process in a wide variety of systems, can be estimated from the mechanical and thermal properties of the polymer and the substrate.

  • 22. Larsson, R.
    et al.
    Wysocki, M.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Process-modeling of composites using two-phase porous media theory2004In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 23, no 1, p. 15-36Article in journal (Refereed)
    Abstract [en]

    A biphasic continuum model is proposed for the modeling of a family of forming processes for fiber composites. The processes considered involve deformation of a fiber bundle network, wetting by penetration of resin into fiber bundles, and resin flow through the fiber bundle network. The continuum model represents three (or more) actual micro constituents as two continuous phases: a solid phase being the fiber network plus any extra void within the fiber bundles and a fluid phase being the liquid matrix. The model framework thus comprises the continuum formulation of a nonlinear compressible porous solid saturated with an incompressible fluid phase. Guided by the entropy inequality, we specify constitutive relations concerning three different mechanisms pertinent to the forming process: effective stress response of the fiber bundle network, compaction of the solid phase, and Darcian interaction between the two phases. We are particularly concerned with the compaction of the fiber-bundles of the solid phase, consisting of elastic packing combined with a viscous wetting process driven by the fluid pressure. The paper is concluded with a couple of numerical examples, where the volumetric deformation-pressure response of a fluid saturated fiber bundle network at undrained conditions is considered. Both volumetric relaxation and volumetric creep tests are analyzed. In particular, the response for different loading rates is assessed. As a final example, a finite element analysis of a relaxation test for the macroscopically undrained compression of a fluid-filled fibernetwork specimen is carried out.

  • 23. Lundström, T. S.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Modelling of residual stresses and warpage in sandwich injection moulding2003In: International polymer processing, ISSN 0930-777X, E-ISSN 2195-8602, Vol. 18, no 1, p. 95-106Article in journal (Refereed)
    Abstract [en]

    Sandwich injection moulding offers the possibility of combining materials with different properties and, for instance, hide a recycled constituent within a virgin ditto. This attractive potential puts great demands on the manufacturing and therefore also on the process modelling. In particular the effect on the final stress state and the deformation of the part due to the heterogeneity of the material must be clarified. This topic is addressed in this study. To start with it is confirmed that expressions for the temperature field can be much simplified without major loss of accuracy in the solution. This enables us to take an analytical approach to the modelling and the resulting equations can be solved on a spread-sheet or with a simple code. It is also shown that the derived models compare well to experiments made with a two-layered structure, indicating that the models presented can be used to estimate changes of processing conditions or material properties for sandwich structures.

  • 24. Lundström, T. S.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Håkanson, J. M.
    Measurement of the permeability tensor of compressed fibre beds2002In: Transport in Porous Media, ISSN 01693913 (ISSN), Vol. 47, no 3, p. 363-380Article in journal (Refereed)
    Abstract [en]

    A new method to measure the permeability tensor of highly compressed fibre beds is developed. The method is based on saturated parallel flow and is evaluated through experiments with various textile materials: press fabrics used in papermaking and fibre reinforcements designed for composites. Since the materials are in the form of sheets, two measuring cells are used, one for the principal in-plane permeabilities and the other for the out-of-plane permeability. A unique feature is that the edge and the bulk flow are measured separately, so that any influence from enhanced or suppressed edge flow may be eliminated. The technique is evaluated with good results in terms of scatter in the measured permeability and the influence of test geometry, pressure, and liquid properties.

  • 25. Segerstad, P. H. A.
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Larsson, R.
    A micropolar theory for the finite elasticity of open-cell cellular solids2009In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 465, no 2103, p. 843-865Article in journal (Refereed)
    Abstract [en]

    A mechanistic model is presented for an open-cell cellular solid consisting of a threedimensional network of elastic struts. By considering the bending and torsion as well as stretching and buckling of the struts, we allow for length-scale effects in the macroscopic response. Constitutive equations are developed for the force and couple stress tensors, accounting for finite deformations and anisotropy. The consistent tangent stiffness operators are derived and the equations are fully implemented in a nonlinear twodimensional finite-element solution scheme for the coupled displacement/rotation problem. A boundary-value problem of a shear gap with prescribed boundary rotations is analysed, and the model is shown to predict the well-known gap size effect. The mechanistic model allows some detailed interpretation of the micropolar behaviour, such as the effects of strut slenderness, strut length and anisotropy.

  • 26. Servais, C.
    et al.
    MÃ¥nson, J. -AE.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Fiber-fiber interaction in concentrated suspensions: Disperse fibers1999In: Journal of Rheology, ISSN 01486055 (ISSN), Vol. 43, no 4, p. 991-1004Article in journal (Refereed)
    Abstract [en]

    A hypothesis for fiber-fiber interaction in planar randomly oriented concentrated fiber suspensions is proposed and tested. The idea is that at sufficiently high fiber concentrations, friction and lubrication at fiber-fiber contact points are the dominant interaction mechanisms. A fiber pull-out technique is introduced to measure the force per unit fiber length on a single longitudinally moving fiber embedded in a volume of bulk suspension. By varying both the fiber velocity and the fiber volume fraction, the lubrication and frictional components of the force are identified. Furthermore, the corresponding bulk shear viscosity resulting from the same mechanisms is derived and compared with experimental data. The results support the hypothesis. © 1999 The Society of Rheology.

  • 27. Strååt, Martin
    et al.
    Toll, Staffan
    Swerea, Department of Textiles and Plastics, Box 104, Mölndal SE-431 22, Sweden.
    Boldizar, A.
    Rigdahl, M.
    Hagström, B.
    Melt spinning of conducting polymeric composites containing carbonaceous fillers2011In: Journal of Applied Polymer Science, ISSN 0021-8995, E-ISSN 1097-4628, Vol. 119, no 6, p. 3264-3272Article in journal (Refereed)
    Abstract [en]

    Fibers produced by melt spinning of conductive polymer composites are attractive for several applications; the main drawback is however reduced processability at high filler concentrations. Carbon nanotubes (CNTs) are considered suitable fillers for conductive polymer composites, replacing conductive grades of carbon black (CB). In this study, the fiber-forming properties of conductive polymer composites based on a conductive grade of CB and two masterbatches with CNT in a polyethylene matrix were investigated. The CB was also used in a polypropylene matrix for comparison. The rheological properties of the filler-containing melts in shear and their extensional behavior were evaluated. A piston-driven device was used to extrude the molten materials through a capillary; different capillary geometries were tested. Fibers were produced at various draw ratios, and their conductivity was determined. To assess the ultimate extensibility, a modified Rheotens method was used. The results showed that a conductive CB grade can have a lower percolation threshold and higher conductivity than a material with CNT. Conductivity decreased with increasing melt draw ratio for both types of fillers. The spinnability of the materials decreased with increasing concentration of filler material and correlations were found between spinnability and melt elasticity.

  • 28.
    Toll, S.
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Andersson, P. -O
    Microstructural characterization of injection moulded composites using image analysis1991In: Composites, ISSN 00104361 (ISSN), Vol. 22, no 4, p. 298-306Article in journal (Refereed)
    Abstract [en]

    A complete procedure for the assessment of the microstructure of discontinuous fibre composites is described. Image analysis routines are developed, which analyse scanned images of metallographically polished surfaces and evaluate spatial orientation distributions and volume fractions of the fibres. The paper deals with image analysis problems, limitations in the analysis, and the interpretation of the results. © 1991.

  • 29.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    A solution technique for longitudinal Stokes flow around multiple aligned cylinders2001In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 439, p. 199-216Article in journal (Refereed)
  • 30.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Interpolative aggregate model for short-fibre composites1992In: Journal of Composite Materials, ISSN 00219983 (ISSN), Vol. 26, no 12, p. 1767-1783Article in journal (Refereed)
    Abstract [en]

    A simplified aggregate model is proposed which predicts the elastic constants of short-fibre composites in any state of fibre orientation. The only material properties needed are two elastic constants for one known orientation state. In essence, this implies an interpolation of elastic properties between different orientation states of the same material. Engineering moduli and fibre orientation distributions of an injection moulded nylon/glass fibre composite are measured and predictions are made. Predicted and experimental moduli correlate excellently.

  • 31.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Note: On the tube model for fibre suspensions1993In: Journal of rheology (New York, N.Y.), ISSN 0148-6055, E-ISSN 1520-8516, Vol. 37, p. 123-125Article in journal (Refereed)
  • 32.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Packing mechanics of fiber reinforcements1998In: Polymer Engineering and Science, ISSN 0032-3888, E-ISSN 1548-2634, Vol. 38, no 8, p. 1337-1350Article in journal (Refereed)
    Abstract [en]

    Theories of fiber packing, of use in manufacturing composite materials, are developed. The maximum packing fraction of force free fibers is estimated based on a statistical analysis of the distribution of fiber-fiber contact points. The new expressions are more general than previous ones by allowing for a distribution in fiber length and orientation. The forced packing beyond this limit is governed by the bending of fiber segments between contact points. A micromechanical theory is developed for this, again based on the contact point statistics, and equations relating the force response per unit area of a fiber bed to the fiber volume fraction are derived for three basic types of assembly: a general 3D wad, a planar mat of dispersed fibers, and a bundle of almost parallel fibers. Other types of reinforcement structure, such as woven fabrics, and the effect of lubrication are also treated briefly.

  • 33.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. Swerea IVF, Sweden.
    Second order shear lag theory2012In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 72, no 12, p. 1313-1317Article in journal (Refereed)
    Abstract [en]

    The standard shear lag theory for elastic aligned short-fibre composites is extended to allow for a gradient of overall strain. The result is a one-dimensional strain gradient theory of the Toupin-Mindlin type. All parameters are the same as in the standard theory, and in the limits of weak strain gradients, large fibre aspect ratios or low elastic modulus ratios, the standard theory is recovered. The gradient effect is illustrated by a simple one-dimensional boundary value problem: a vertical composite rod fixed at both ends and loaded by gravity. The fibre length significantly affects the solution when the fibres are rigid and their length is near the rod length; but otherwise the effect is weak.

  • 34.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    The dissipation inequality in hypoplasticity2011In: Acta Mechanica, ISSN 0001-5970, E-ISSN 1619-6937, Vol. 221, no 1-2, p. 39-47Article in journal (Refereed)
    Abstract [en]

    Standard hypoplasticity is examined with respect to the thermodynamic requirement of non-negative energy dissipation. We introduce a stress energy function and derive a dissipation inequality in terms of the stress-dependent operators of the hypoplastic law. A general form for the non-linear operator is also found, which makes it straightforward to construct thermodynamically consistent hypoplasticity laws. We further examine the subclass of hypoplasticity where the linear term is non-dissipative and construct some examples of hypoplastic laws based on a quadratic stress energy function.

  • 35.
    Toll, Staffan
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Andersson, P. -O
    Microstructure of long-and short-fiber reinforced injection molded polyamide1993In: Polymer Composites, ISSN 02728397 (ISSN), Vol. 14, no 2, p. 116-125Article in journal (Refereed)
    Abstract [en]

    The variation of fiber orientation and content within injection molded rectangular plates is investigated. Fiber orientation and volume fraction are measured using metallographic polishing and a newly develop image-analysis system: fiber weight-fractions are measured using an ashing method.

  • 36.
    Toll, Staffan
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Aronsson, C. -G
    Notched strength of long- and short-fibre reinforced polyamide1992In: Composites Science and Technology, ISSN 02663538 (ISSN), Vol. 45, no 1, p. 43-54Article in journal (Refereed)
    Abstract [en]

    A test programme has been conducted to evaluate the tensile strength of injection moulded plates with machined and moulded-in notches. The long-fibre compound, Verton, is consistently less notch sensitive than the short-fibre compound, Maranyl. Moulded-in holes appear to have several advantages over machined holes: they yield up to 25% higher strength and less sensitivity to plate thickness and injection speed. Five existing laminate fracture models are applied to the machine-notched plates; the average stress criterion and the damage zone model give the most accurate predictions. © 1992.

  • 37.
    Toll, Staffan
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Manson, J. -AE.
    Elastic compression of a fiber network1995In: Journal of Applied Mechanics, Transactions ASME, ISSN 00218936 (ISSN), Vol. 62, no 1, p. 223-226Article in journal (Refereed)
    Abstract [en]

    A constitutive equation for a planar fiber network under transverse compression is derived allowing for an in-plane fiber orientation distribution. The fibers are assumed to be well dispersed in space and to have a large aspect ratio and uniform diameter. A compression experiment, performed on a glass-fiber network obtained by ashing a commercial composite preform, is accurately described by the theory.

  • 38.
    Toll, Staffan
    et al.
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Manson, Jan-Anders E.
    Dynamics of a planar concentrated fiber suspension with non-hydrodynamic interaction1994In: Journal of Rheology, ISSN 01486055 (ISSN), Vol. 38, no 4, p. 985-997Article in journal (Refereed)
    Abstract [en]

    Equations for particle motions and bulk stresses are derived based on a balance of frictional contact forces on a test particle. Very high particle concentrations are considered, so that contact forces dominate and hydrodynamic interaction is negligible. The analysis is restricted to homogeneous flows of statistically homogeneous suspensions in which the particles are planarly oriented and straight. An explicit solution is given for the case where the friction force between contacting particles is proportional to their relative velocity. Particle motion is then essentially affine, and stresses are quadratic in both particle concentration and particle aspect ratio.

  • 39. Wysocki, M.
    et al.
    Asp, L.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Larsson, R.
    Two phase continuum modelling of composites consolidation2009In: Plastics, rubber and composites, ISSN 1465-8011, E-ISSN 1743-2898, Vol. 38, no 2-4, p. 93-97Article in journal (Refereed)
    Abstract [en]

    A finite element model is developed to solve consolidation problems for composites manufacturing. The model is developed from a generic two-phase continuum theory allowing for coupling between the solid and fluid responses. The code is applied to a case study consisting of consolidation of a hat stringer to evaluate nonlinear effects.

  • 40. Wysocki, M.
    et al.
    Larsson, R.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Hydrostatic consolidation of commingled fibre composites2005In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 65, no 10, p. 1507-1519Article in journal (Refereed)
    Abstract [en]

    A molten hybrid-yarn composite is modelled as a continuum. Constitutive equations governing hydrostatic consolidation are formulated, based on a two-phase continuum mechanical framework developed in a recent paper [Larsson R, Wysocki M, Toll S. Process-modelling of composites using two-phase porous media theory. European Journal of Mechanics-A 2004;23:15-36]. The fibre bundles are assumed to be completely surrounded by resin, thus subjected to hydrostatic pressure. To model the infiltration of resin into the fibre bundles, we introduce a compressible solid phase consisting of fibres plus intra-fibre void. The compression of the solid phase is caused by a combination of infiltration and elastic compression of the fibre bundles. The models are micromechanical, and all parameters have a clear physical meaning and are measurable in principle. Using parameter values out of the literature and estimated from micrographs, the number of adjustable parameters may be brought down to one: a spring constant for the fibre bundle elasticity. Consolidation experiments are performed, where a tool is closed to a prescribed compression and then held fixed, while the pressure is monitored over time. The predicted and measured pressure traces are in good agreement.

  • 41. Wysocki, M.
    et al.
    Toll, Staffan
    Chalmers University of Technology, Sweden.
    Larsson, R.
    Press forming of commingled yarn based composites: The preform contribution2007In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 67, no 3-4, p. 515-524Article in journal (Refereed)
    Abstract [en]

    The process of press forming commingled yarn composites is studied and modelled based on the theory of porous media. Two sub processes are considered: (1) the wetting and compaction of individual bundles and (2) the overall preform deformation. An experimental method is introduced, to study these two sub processes separately. The experiment suppresses the fluid pressure build-up, and thus the process of wetting and bundle compaction, by draining the resin into a porous wall. In consequence, the measured response consists only of the preform contribution. Finally, the total response is simulated and tested against independent consolidation experiments. It was demonstrated that the present approach gives better predictions compared to models based on the bundle response only.

  • 42. Wysocki, Maciej
    et al.
    Toll, Staffan
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
    Larsson, Ragnar
    Asp, Leif E.
    Anisotropic and tension-compression asymmetric model for composites consolidation2010In: Composites. Part A, Applied science and manufacturing, ISSN 1359-835X, E-ISSN 1878-5840, Vol. 41, no 2, p. 284-294Article in journal (Refereed)
    Abstract [en]

    A constitutive model for anisotropic and tension-compression asymmetric response of a fibrous preform is developed and solved using a FE software. Applicability of the method to complex geometries is demonstrated by analysis the consolidation of an axisymmetric filament wound pressure vessel made from commingled yarns. Three different winding patterns are considered. In conclusions, the consolidation of the whole vessel, except at the opening, is prevented by the loading mode, where the pressure is applied on the interior. To succeed in manufacturing of this type of pressure vessel, use of an oversized preform that allows extension in the fibre direction is suggested.

1 - 42 of 42
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