Staffan Toll

Residual stress build-up in thermoset films cured above their ultimate glass transition temperature

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 straightforward. 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.

Elastic compression of a fiber network

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 sp ...

Dynamics of a planar concentrated fiber suspension with non‐hydrodynamic interaction

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.

Fiber–fiber interaction in concentrated suspensions: Disperse fibers

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.

Mechanics of the squeeze flow of planar fibre suspensions

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.

Measurement of the Permeability Tensor of Compressed Fibre Beds

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.

A model for the consolidation of aligned thermoplastic powder impregnated composites

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.

A micropolar theory for the finite elasticity of open-cell cellular solids

A mechanistic model is presented for an open-cell cellular solid consisting of a three-dimensional 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 two-dimensional 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.

The two-way interaction between anisotropic flow and fiber orientation in squeeze flow

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 d ...

Notched strength of long- and short-fibre reinforced polyamide

Abstract 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.