No / Autodesk Moldflow Simulation Insights has been used to predict the fibre orientation within notched specimen injection mouldings. Currently available fibre orientation models including the classis Folgar-Tucker (FT), the modified version of Folgar-Tucker (MFT) and the Reduced Strain Closure (RSC) [1] have been assessed, alongside the relative effects of their associated parameters, for their suitability for fibre orientation prediction. Compared to experimentally determined values the Reduced Strain Closure model was shown to most closely represent the fibre orientation within the moulded components.

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Composite materials are widely used in demanding applications in aerospace and other industries. In order to understand the complex behaviour of the composite materials and their components, standardised test methods are used. One example is the double cantilever beam (DCB) test in which the test specimen is loaded in an opening, i.e., tensile mode. Failures in composite materials loaded compression are different from those in tension, for example, kink band or buckling-like failures can occur. In this project, several DCBs are designed and a new fixture which allows for compression testing of a DCB is developed for an existing Instron testing machine. The fixture overcomes a known problem of tensile peak causing the failure of the adhesive at the inner surfaces of the DBC by applying additional compressive loads along the outer surfaces of the DBC. The compressive forces can induce the desired kink band formation so that researchers can better study the failure mode. The conceptual development of the new DCBs and the new fixture are presented. Several prototypes of the specimens and the fixture are modelled using the three-dimensional (3D) computer-aided design software Creo Parametric 2.0.  One of the fixtures is selected to further study. The different DCB specimens are studied in order to obtain information about the kink band using 3D finite element analysis with the software programme Abaqus CAE. The selected fixture is analysed to determine if there are any areas of concern. Finally, the behaviour of the compression stress along the DCB using two pairs of forces is studied. Unfortunately, it is determined that the tensile peak experienced by the adhesive cannot be eliminated by the application of two pairs of compressive loads, one at the free end and the other in the vicinity of the tensile peak. Several suggestions are made for future work which might serve to reduce the tensile peak; e.g., the movable force couple is applied as a surface load instead of a point load. For this, the fixture will have to be modified with a new geometry, although the DCB could be the same. This will allow further work to focus on the combined behaviour of the tensile peak and the fixture.

This work investigates the effects of long range hydrodynamic fibre-fibre interactions on the orientation state of a semi-dilute, rigid fibre suspension flowing through a linear contracting channel under laminar flow conditions. The effects of fibre-fibre interactions are modeled mathematically, the governing equations solved numerically and the predicted results compared with experimental observations. The theoretical model is based on the assumption that the orientation state of the suspension can be completely described by a probability distribution function and that fibre-fibre interactions are random in nature, thus giving rise to a diffusion-type process. The orientation distribution evolves spatially according to a Fokker-Plank type equation using closure equations for the rotary diffusion coefficient advanced by either (i) Folgar and Tucker (J. Reinforced Plast. Comp. 3 98–119 1984) or (ii) Koch (Phys. Fluids 7(8) 2086–2088 1995). Each of these two closure models for the rotary diffusion coefficient contains an unknown empirical constant that must be determined from experiments. These were fit to experimental data along the central streamline of the contraction as a function of fibre concentration. The diffusion coefficient was found to first increase with increasing suspension concentration up to a maximum, and then decrease with concentration above this point. This non-monotonic behavior was attributed to fibre flocculation, a mechanism not considered in the relationships for the rotary diffusion coefficient. The theoretical model is then extended to predict fibre orientation over the entire plane of the contraction and the two-way momentum coupling between the fluid and fibre phases were investigated numerically. The results show that the structure of the flow field within the contraction is significantly altered when the fibre phase is considered, demonstrating the non-negligible effect of the momentum exchange between the two phases. Comparison is made between the predicted orientation state of the suspension with experimental observations over the contraction plane. Good agreement was found between the model predictions and the experimental observations except in a small region near the solid boundaries. These near wall discrepancies were attributed to an inability to correctly handle the wall boundary conditions in the fibre orientation model.

In 2013 the European journal of wood and wood products published an article regarding a new method to predict strength in structural timber (Olsson et al 2013). By determining the fibres orientation on all four surfaces of each board in sample of timber using a high resolution scanner the authors were able to achieve a coefficient of determination, R2, as high as 0.71 between bending strength and a new indicating property (IP). For the same sample of timber Olsson et al (2013) determined the R2 by axial dynamic excitation as 0.59. However, all boards used in their investigation were planed before scanning. This study examines if a high resolution scanner could be used to determine the fibre orientation on the surfaces of sawn timber boards of Norway spruce. Both band sawn surfaces and circular sawn surfaces were examined. The procedure in this investigation is described as follows. Firstly, both the band sawn and the circular sawn boards were scanned by a WoodEye® scanner and together with dimensions, weight and the first longitudinal resonance frequency, a modulus of elasticity (MOE) profile was calculated for each board. The MOE profiles were calculated according to Olsson et al (2013) i.e. by a transformation matrix based upon the fibres orientation and a compliance matrix based on material parameters for Norway spruce. Secondly, the corresponding MOE profiles were then determined after the boards had been planed. As a result two MOE profiles were determined for each board. An indicating property (IP) was defined as the lowest value along each MOE profile. To compare the results a regression analysis was performed in which the IPs defined before planing worked as predictor variable and IPs defined after planing worked as response variable. The band sawn band boards yielded an R2 = 0.94 and the circular sawn boards an R2 = 0.93. Further the standard error of estimate was SEE = 829.1 MPa and SEE = 640.9 MPa respectively. As a last step in this investigation the SEE values achieved in this study where implemented on to the sample Olsson et al (2013) used in their investigation.

This work investigates the effects of long range hydrodynamic fibre-fibre interactions on the orientation state of a semi-dilute, rigid fibre suspension flowing through a linear contracting channel under laminar flow conditions. The effects of fibre-fibre interactions are modeled mathematically, the governing equations solved numerically and the predicted results compared with experimental observations. The theoretical model is based on the assumption that the orientation state of the suspension can be completely described by a probability distribution function and that fibre-fibre interactions are random in nature, thus giving rise to a diffusion-type process. The orientation distribution evolves spatially according to a Fokker-Plank type equation using closure equations for the rotary diffusion coefficient advanced by either (i) Folgar and Tucker (J. Reinforced Plast. Comp. 3 98–119 1984) or (ii) Koch (Phys. Fluids 7(8) 2086–2088 1995). Each of these two closure models for the rotary diffusion coefficient contains an unknown empirical constant that must be determined from experiments. These were fit to experimental data along the central streamline of the contraction as a function of fibre concentration. The diffusion coefficient was found to first increase with increasing suspension concentration up to a maximum, and then decrease with concentration above this point. This non-monotonic behavior was attributed to fibre flocculation, a mechanism not considered in the relationships for the rotary diffusion coefficient. The theoretical model is then extended to predict fibre orientation over the entire plane of the contraction and the two-way momentum coupling between the fluid and fibre phases were investigated numerically. The results show that the structure of the flow field within the contraction is significantly altered when the fibre phase is considered, demonstrating the non-negligible effect of the momentum exchange between the two phases. Comparison is made between the predicted orientation state of the suspension with experimental observations over the contraction plane. Good agreement was found between the model predictions and the experimental observations except in a small region near the solid boundaries. These near wall discrepancies were attributed to an inability to correctly handle the wall boundary conditions in the fibre orientation model.

This work investigates the effects of long range hydrodynamic fibre-fibre interactions on the orientation state of a semi-dilute, rigid fibre suspension flowing through a linear contracting channel under laminar flow conditions. The effects of fibre-fibre interactions are modeled mathematically, the governing equations solved numerically and the predicted results compared with experimental observations. The theoretical model is based on the assumption that the orientation state of the suspension can be completely described by a probability distribution function and that fibre-fibre interactions are random in nature, thus giving rise to a diffusion-type process. The orientation distribution evolves spatially according to a Fokker-Plank type equation using closure equations for the rotary diffusion coefficient advanced by either (i) Folgar and Tucker (J. Reinforced Plast. Comp. 3 98–119 1984) or (ii) Koch (Phys. Fluids 7(8) 2086–2088 1995). Each of these two closure models for the rotary diffusion coefficient contains an unknown empirical constant that must be determined from experiments. These were fit to experimental data along the central streamline of the contraction as a function of fibre concentration. The diffusion coefficient was found to first increase with increasing suspension concentration up to a maximum, and then decrease with concentration above this point. This non-monotonic behavior was attributed to fibre flocculation, a mechanism not considered in the relationships for the rotary diffusion coefficient. The theoretical model is then extended to predict fibre orientation over the entire plane of the contraction and the two-way momentum coupling between the fluid and fibre phases were investigated numerically. The results show that the structure of the flow field within the contraction is significantly altered when the fibre phase is considered, demonstrating the non-negligible effect of the momentum exchange between the two phases. Comparison is made between the predicted orientation state of the suspension with experimental observations over the contraction plane. Good agreement was found between the model predictions and the experimental observations except in a small region near the solid boundaries. These near wall discrepancies were attributed to an inability to correctly handle the wall boundary conditions in the fibre orientation model. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

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This thesis deals with fibre orientation in wall-bounded shear flows. The primary application in mind is papermaking. The study is mainly experimental,but is complemented with theoretical considerations.The main part of the thesis concerns the orientation of slowly settlingfibres in a wall-bounded viscous shear flow. This is a flow case not dealt withpreviously even at small Reynolds numbers. Experiments were conducted usingdilute suspensions with fibres having aspect ratios of rp ≈ 7 and 30. It is foundthat the wall effect on the orientation is small for distances from the wall wherethe fibre centre is located farther than half a fibre length from the wall. Farfrom the wall most fibres were oriented close to the flow direction. Closer tothe wall than half a fibre length the orientation distribution first shifted to bemore isotropic and in the very proximity of the wall the fibres were orientedclose to perpendicular to the flow direction, nearly aligned with the vorticityaxis. This was most evident for the shorter fibres with rp ≈ 7.Due to the density difference between the fibres and the fluid there is anincreased concentration near the wall. Still, a physical mechanism is requiredin order for a fibre initially oriented close to the flow direction at about half afibre length from the wall to change its orientation to aligned with the vorticityaxis once it has settled down to the wall. A slender body approach is usedin order to estimate the effect of wall reflection and repeated wall contacts onthe fibre rotation. It is found that the both a wall reflection, due to settlingtowards the wall, and contact between the fibre end and the wall are expectedto rotate the fibre closer to the vorticity axis. A qualitative agreement withthe experimental results is found in a numerical study based on the theoreticalestimation.In addition an experimental study on fibre orientation in the boundarylayers of a headbox is reported. The orientation distribution in planes parallelto the wall is studied. The distribution is found to be more anisotropic closerto the wall, i.e. the fibres tend to be oriented closer to the flow direction nearthe wall. This trend is observed sufficiently far upstream in the headbox.Farther downstream no significant change in the orientation distribution couldbe detected for different distances from the wall. / QC 20100706