20 Composites forming technologies Conference on Composite Materials (ICCM-11),Gold Coast,Australia,July 1997, 238-248. 5.Prodromou A G and Chen J,'On the relationship between shear angle and wrinkling of textile composite preforms',Composites Part A,1997 28A 491-503. 6.Mohammad U,Lekakou C,Dong L and Bader M G,'Shear deformation and micromechanics of woven fabrics',Composites Part A,2000 31 299-308. 7.Milani A S,Nemes J A,Pham X T and Lebrun G,'The effect of fibre misalignment on parameter determination using picture frame test',Proc.14th International Conference on Composite Materials (ICCM-14),San Diego,USA,July,2003. 8.Lebrun G.Bureau M N and Denault J,'Evaluation of bias-extension and picture- frame test methods for the measurement of intraply shear properties of PP/glass commingled fabrics',Composite Structures,2003 61 341-352. 9. Harrison P,Clifford M J and Long A C,'Shear characterisation of woven textile composites:a comparison between picture frame and bias extension experiments' Composites Science and Technology,2004 64(10-11)1453-1465. 10.Potter K D.'The influence of accurate stretch data for reinforcements on the production of complex structural mouldings',Composites,July 1979 161-167. 11.Murtagh A M and Mallon P J.'Shear characterisation of unidirectional and fabric reinforced thermoplastic composites for pressforming applications',Proc.10th International Conference on Composite Materials (ICCM-10).Whistler,Canada, August1995,373-380. 12.Wang J,Page R and Paton R,'Experimental investigation of the draping properties of reinforcement fabrics',Composites Science and Technology,1998 58 229-237. 13.Souter B J,Effects of fibre architecture on formability of textile preforms,PhD Thesis,University of Nottingham,2001. 14.Harrison P,Clifford M J,Long A C and Rudd C D,'A constituent based predictive approach to modelling the rheology of viscous textile composites',Composites Part A200537(7-8)915-931. 15.Boisse P,Borr M,Buet K and Cherouat A,'Finite element simulations of textile composite forming including the biaxial fabric behaviour',Composites Part B,1997 28(4),453-464. 16.Boisse P,Gasser A and Hivet G,'Analyses of fabric tensile behaviour:Deter- mination of the biaxial tension-strain surfaces and their use in forming simulations', Composites Part A,2001 32(10)1395-1414. 17.Long A C (editor),Design and manufacture of textile composites,Woodhead Publishing Ltd,Cambridge,2005.Chapter 2. 18. Scherer R and Friedrich K,'Inter-and intraply-slip flow processes during thermoforming of CF/PP-laminates',Composites Manufacturing,1999 2(2)92-96. 19. Murtagh A M,Characterisation of shearing and frictional behaviour in sheetforming of thermoplastic composites,PhD Thesis,University of Limerick, 1995. 20.Wilks C E,Processing technologies for woven glass/polypropylene composites,PhD Thesis,University of Nottingham,2000. 21. Hearle J W S,Backer S,Grosberg P,Structural mechanics of fibers,yarns and fabrics.Wiley.New York.1969. 22.BS 3356:1990,'Determination of bending length and flexural rigidity of fabrics', British Standards Institution,June 1991. 23.Young M,Cartwright B,Paton R,Yu X,Zhang L and Mai Y-W,'Material
Conference on Composite Materials (ICCM-11), Gold Coast, Australia, July 1997, 238±248. 5. Prodromou A G and Chen J, `On the relationship between shear angle and wrinkling of textile composite preforms', Composites Part A, 1997 28A 491±503. 6. Mohammad U, Lekakou C, Dong L and Bader M G, `Shear deformation and micromechanics of woven fabrics', Composites Part A, 2000 31 299±308. 7. Milani A S, Nemes J A, Pham X T and Lebrun G, `The effect of fibre misalignment on parameter determination using picture frame test', Proc. 14th International Conference on Composite Materials (ICCM-14), San Diego, USA, July, 2003. 8. Lebrun G, Bureau M N and Denault J, `Evaluation of bias-extension and pictureframe test methods for the measurement of intraply shear properties of PP/glass commingled fabrics', Composite Structures, 2003 61 341±352. 9. Harrison P, Clifford M J and Long A C, `Shear characterisation of woven textile composites: a comparison between picture frame and bias extension experiments' Composites Science and Technology, 2004 64(10±11) 1453±1465. 10. Potter K D, `The influence of accurate stretch data for reinforcements on the production of complex structural mouldings', Composites, July 1979 161±167. 11. Murtagh A M and Mallon P J, `Shear characterisation of unidirectional and fabric reinforced thermoplastic composites for pressforming applications', Proc. 10th International Conference on Composite Materials (ICCM-10), Whistler, Canada, August 1995, 373±380. 12. Wang J, Page R and Paton R, `Experimental investigation of the draping properties of reinforcement fabrics', Composites Science and Technology, 1998 58 229±237. 13. Souter B J, Effects of fibre architecture on formability of textile preforms, PhD Thesis, University of Nottingham, 2001. 14. Harrison P, Clifford M J, Long A C and Rudd C D, `A constituent based predictive approach to modelling the rheology of viscous textile composites', Composites Part A 2005 37(7±8) 915±931. 15. Boisse P, Borr M, Buet K and Cherouat A, `Finite element simulations of textile composite forming including the biaxial fabric behaviour', Composites Part B, 1997 28(4), 453±464. 16. Boisse P, Gasser A and Hivet G, `Analyses of fabric tensile behaviour: Determination of the biaxial tension-strain surfaces and their use in forming simulations', Composites Part A, 2001 32(10) 1395±1414. 17. Long A C (editor), Design and manufacture of textile composites, Woodhead Publishing Ltd, Cambridge, 2005. Chapter 2. 18. Scherer R and Friedrich K, `Inter- and intraply-slip flow processes during thermoforming of CF/PP-laminates', Composites Manufacturing, 1999 2(2) 92±96. 19. Murtagh A M, Characterisation of shearing and frictional behaviour in sheetforming of thermoplastic composites, PhD Thesis, University of Limerick, 1995. 20. Wilks C E, Processing technologies for woven glass/polypropylene composites, PhD Thesis, University of Nottingham, 2000. 21. Hearle J W S, Backer S, Grosberg P, Structural mechanics of fibers, yarns and fabrics, Wiley, New York, 1969. 22. BS 3356:1990, `Determination of bending length and flexural rigidity of fabrics', British Standards Institution, June 1991. 23. Young M, Cartwright B, Paton R, Yu X, Zhang L and Mai Y-W, `Material 20 Composites forming technologies Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 6:57:44 PM IP Address: 158.132.122.4
Composite forming mechanisms and materials characterisation 21 characterisation tests for finite element simulation of the diaphragm forming process',Proc.4th Int.ESAFORM Conference on Material Forming,University of Liege,April 2001. 24.Martin T A,Bhattacharyya D and Collins I F,'Bending of fibre-reinforced thermoplastic sheets',Composites Manufacturing,1995 6(3-4)177-187. 25.Lindberg J,Behre B and Dahlberg B,'Shearing and buckling of various commercial fabrics',Textile Research Journal,Feb 1961 99-122. 26.Wang J,Lin H,Long A C,Clifford M J and Harrison P,'Predictive modelling and experimental measurement of the bending behaviour of viscous textile composites', Proc.9th Int.ESAFORM Conference,Glasgow,April 2006. 27.Robitaille F and Gauvin R,'Compaction of textile reinforcements for composites manufacturing.I:Review of experimental results',Polymer Composites,1198 19(2) 198-216. 28. Garcia Gil R,Forming and consolidation of textile composites,PhD Thesis, University of Nottingham,2003. 29. Correia N,Analysis of the vacuum infusion moulding process,PhD Thesis, University of Nottingham,2004. 30.Cai Z and Gutowski T G,The 3D deformation behaviour of a lubricated fibre bundle',Journal of Composite Materials,1992 26(8)1207-1237. 31.Hubert P and Poursartip A,'A method for the direct measurement of the fibre bed compaction curve of composite prepregs',Composites Part A,2001 32 179-187. 32. Van West B P,Pipes R B and Advani S G,'The consolidation of commingled thermoplastic fabrics',Polymer Composites,1991 12(6)417-427. 33. Bernet N,Michaud V,Bourban P-E and Manson J-A E,'Commingled yarn 1:59 composites for rapid processing of complex shapes',Composites Part A,2001 32(11)1613-1626
characterisation tests for finite element simulation of the diaphragm forming process', Proc. 4th Int. ESAFORM Conference on Material Forming, University of Liege, April 2001. 24. Martin T A, Bhattacharyya D and Collins I F, `Bending of fibre-reinforced thermoplastic sheets', Composites Manufacturing, 1995 6(3±4) 177±187. 25. Lindberg J, Behre B and Dahlberg B, `Shearing and buckling of various commercial fabrics', Textile Research Journal, Feb 1961 99±122. 26. Wang J, Lin H, Long A C, Clifford M J and Harrison P, `Predictive modelling and experimental measurement of the bending behaviour of viscous textile composites', Proc. 9th Int. ESAFORM Conference, Glasgow, April 2006. 27. Robitaille F and Gauvin R, `Compaction of textile reinforcements for composites manufacturing. I: Review of experimental results', Polymer Composites, 1198 19(2) 198±216. 28. Garcia Gil R, Forming and consolidation of textile composites, PhD Thesis, University of Nottingham, 2003. 29. Correia N, Analysis of the vacuum infusion moulding process, PhD Thesis, University of Nottingham, 2004. 30. Cai Z and Gutowski T G, `The 3D deformation behaviour of a lubricated fibre bundle', Journal of Composite Materials, 1992 26(8) 1207±1237. 31. Hubert P and Poursartip A, `A method for the direct measurement of the fibre bed compaction curve of composite prepregs', Composites Part A, 2001 32 179±187. 32. Van West B P, Pipes R B and Advani S G, `The consolidation of commingled thermoplastic fabrics', Polymer Composites, 1991 12(6) 417±427. 33. Bernet N, Michaud V, Bourban P-E and Manson J-A E, `Commingled yarn composites for rapid processing of complex shapes', Composites Part A, 2001 32(11) 1613±1626. Composite forming mechanisms and materials characterisation 21 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 6:57:44 PM IP Address: 158.132.122.4
2 Constitutive modelling for composite forming R AKKER MAN and E A D LA MERS,University of Twente, The Netherlands 2.1 Introduction Sunysijqnd 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,corres- ponding 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 sub- sequent 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 00 induced fibre orientations and stresses,which can speed up the product develop- ment 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
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 2 Constitutive modelling for composite forming R A K K E R M A N and E A D L A M E R S , University of Twente, The Netherlands Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 6:57:44 PM IP Address: 158.132.122.4
Constitutive modelling for composite forming 23 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. tical model,also referred to as the kinematics or fishnet Several methods are used to predict the fibre reorientation of the fabric.The 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
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 Constitutive modelling for composite forming 23 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 6:57:44 PM IP Address: 158.132.122.4
24 Composites forming technologies 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 Ween (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 inter- ference 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 台四 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
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 WeeÈn (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 24 Composites forming technologies Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 6:57:44 PM IP Address: 158.132.122.4