Long Composites Forming Technologies

1. Auflage 2014
ISBN: 978-1-84569-253-7
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 344 Seiten

Reihe: Woodhead Publishing Series in Textiles

Composites are versatile engineered materials composed of two or more constituent materials which, when combined, lead to improved properties over the individual components whilst remaining separate on a macroscopic level. Due to their versatility, composite materials are used in a variety of areas ranging from healthcare and civil engineering to spacecraft technology. Composites forming technologies reviews the wealth of research in forming high-quality composite materials.The book begins with a concise explanation of the forming mechanisms and characterisation for composites, as well as covering modelling and analysis of forming techniques. Further chapters discuss the testing and simulation of composite materials forming. The book also considers forming technologies for various composite material forms including thermoset and thermoplastic prepreg, moulding compounds and composite/metal laminates.With its distinguished editor and array of international contributors, Composites forming technologies is an essential reference for engineers, researchers and academics involved with the production and use of composite materials. - Reviews the wealth of research in forming high-quality composite materials - Includes a concise explanation of the forming mechanisms and charaterisation for composites - Considers forming technologies for various composite material forms

Autoren/Hrsg.

Long, A C

Leseproben

2 Constitutive modelling for composite forming
R. Akkerman; E.A.D. Lamers    University of Twente, The Netherlands 2.1 Introduction
Fibre reorientation occurs when forming a reinforced structure, such as a fabric onto a doubly curved surface. This leads to a change in the angle between warp and fill yarns. The composite properties change inhomogeneously, corresponding to the varying angle between warp and fill yarns. Many composite properties are determined by the angle between the warp and fill yarns, such as the mechanical properties, the coefficients of thermal expansion, the local fibre volume fractions, the local thickness and the permeability. The extent of the fibre reorientation is affected by the product shape and the forming process. The forming process may cause tensile stresses in the fabric yarns, causing subsequent product distortions. Also, wrinkling risks are present due to the incapability of the fabric to deform beyond a maximum shear deformation. The local change in composite properties must be taken into account in order to predict the properties of a product. Drape modelling can predict the process induced fibre orientations and stresses, which can speed up the product development process compared with trial-and-error development. The constitutive model for these biaxially reinforced composite materials is the primary element of these process simulations. 2.2 Review on constitutive modelling for composite forming
Both dry and pre-impregnated fabrics can be draped over a mould during the composite forming process. When forming a dry fabric over the mould, the result is a preform. This preform can be impregnated subsequently with a polymer, for instance in one of the Liquid Composite Moulding (LCM) processes. When draping pre-impregnated composites, the fabric is embedded in the matrix material. In the case of thermoplastics, several plies can be stacked into a pre-consolidated laminate preform. This preform is heated above the glass transition or melting temperature of the polymer matrix, formed on the tool and subsequently cooled or cured until the product is form stable. Various drape models for dry and pre-impregnated fabrics have been proposed in the past. Lim and Ramakrishna published a review in 2002 on the forming of composite sheet forming. Two approaches are distinguished in their review: the mapping approach and the mechanics approach. The use of mapping approaches is discussed in Chapter 12, whilst the mechanical modelling of forming is described in Chapter 3. Here, we will concentrate on the underlying constitutive models, using a different classification: the discrete approach and the continuum approach. This classification is based on the representation of the material by the models. Draping multi-layered composites gives rise to additional complexity which will be discussed subsequently. 2.2.1 Discrete models
Three schemes are distinguished in the discrete drape approach: the mapping schemes, the particle based schemes and the truss based schemes. Mapping based schemes Mapping schemes are most commonly employed in commercial packages for drape predictions. A layer of fabric is represented by a square mesh which is fitted onto the drape surface. The mapping scheme is based on the assumption that the fabric only deforms due to shear deformation, and fibre extension can be neglected. The resin, if present, is also neglected during the simulation. The fabric always remains in a fixed position on the draping surface after having been mapped. The shape of the product must be represented in algebraic expressions when modelling draping with a mapping scheme. Several methods are used to predict the fibre reorientation of the fabric. The geometrical model, also referred to as the kinematics or fishnet model, is a widely used model to predict the resulting fibre reorientation for doubly curved fabric reinforced products. This model was initially described by Mack and Taylor in 1956, based on a pinned-joint description of the weave. The model assumes inextensible fibres pinned together at their crossings, allowing free rotation at these joints. An analytic solution of the fibre redistribution was presented for a fabric oriented in the bias direction on the circumference of simple surfaces of revolution, such as cones, spheres and spheroids. The resulting fibre orientations were solved as a function of the constant height coordinate of the circumference. From the early 1980s up to the late 1990s many authors presented numerically based drape solutions, based on the same assumptions as Mack and Taylor (see, for example, Robertson et al., 1984; Smiley and Pipes, 1988; Heisey and Haller, 1988; Long and Rudd, 1994; Bergsma, 1995; and Trochu et al., 1996). Typically, these drape models start from an initial point and two initial fibre directions. Further points are then generated at a fixed equal distance from the previous points creating a mesh of quadrilateral cells. There is no unique solution for this geometrical drape method. This problem is generally solved by defining two fibre paths on the drape surface. Bergsma (1995) introduced ‘strategies’ in order to find solutions for the drape algorithm, without pre-defining fibre paths. Bergsma also included a mechanism to incorporate the locking phenomenon in his drape simulations. Alternatively to the fishnet model, Van der Weën (1991) presented a computationally efficient energy based mapping method in 1991. Rather than creating a new cell on a geometric basis, the cell in the mesh is mapped onto the drape surface by minimising the elastic energy in the drape cell, while only accounting for the deformation energy used to extend the fibres. Long et al. (2002) presented a similar approach based on minimisation of shear strain energy, demonstrating the capability to predict different fibre patterns depending on material type. The mapping scheme is quite simple in its application and implementation, and requires very limited computational efforts. The results of the mapping scheme agree well with reality if the product shape is convex. However, the mapping schemes do not predict unique solutions. User interference or ‘strategies’ are required to solve the drape problem. Inaccurate drape predictions are obtained for products where bridging occurs or when the preform slides over the mould during forming. The scheme is not suited to incorporate the processing conditions accurately during draping or to give an accurate representation of the composite properties. Especially in tight weaves, the error of assuming a zero in-plane fabric shear stiffness during draping leads to errors. From the late 1970s it was shown experimentally that the resin material also affects the deformation properties (Potter, 1979). In addition, the geometrical approach might find infeasible solutions when draping products with holes. Forming of multi-layered composites is simulated by repeatedly draping single layers of fabric, since the model only represents one layer of fabric. The through-thickness shear interaction between the individual layers is not accounted for. Particle based schemes From the first half of the 1990s particle based schemes were used to predict the fabric drape behaviour. The fabric, or cloth, is represented as a discontinuous sheet using micro-mechanical structural elements. These elements, also called particles, interact and must be chosen to be small enough to still represent the weave's behaviour. An interacting particle model was developed by Breen et al. in 1994. Energy functions define the interaction between the particles, placing the particles at the crossings of the yarns in the fabric. The energy contribution in the particles consists of thread repelling, thread stretching, thread bending, thread trellising and gravity. The total energy in the cloth is simply the sum of the energy of all particles. The modelling strategy for particle based solutions is generally time dependent. In the first time step, the model accounts for the gravity and the collision between the cloth and the drape surface. In the next step a stochastic energy-minimising technique is used to find the local energy minima for the cloth. Finally, permutations are introduced to produce a more asymmetric final configuration. Similarly to the energy based functions, force based functions were also developed for the interactions of the particles (Colombo et al., 2001). This representation method is applied in commercially available software, since it is computationally more attractive than the energy based particle interaction functions. Cordier and Magnenat-Thalmann (2002) simulated the cloth behaviour on dressed virtual humans in real time. They proposed a hybrid drape algorithm combining the advantages of physically (particle) based and geometric deformations, avoiding the computationally expensive collision calculations as much as possible. The cloth is segmented into three sections in their simulations. Cloths that remain at constant distance to the drape body are modelled in the first section. Typically, these are stretch cloths. In the second layer, the loose cloth follows predefined discs, representing the limbs. Finally, floating cloth such as skirts is represented in the third section. A force based particle method is used for modelling the floating cloth, incorporating the collision with the underlying body and the cloth itself. Real-time modelling of...