3 Mechanical modelling of solid woven fabric composites PHILIPPE VANDEURZEN,JAN IVENS AND IGNAAS VERPOEST 3.1 Introduction Solid woven fabric composites represent a class of advanced composites which are reinforced by 2-D or 3-D woven preforms [1].These materials offer new and exciting opportunities for tailoring the microstructure to spe- cific thermomechanical applications in the fields of aerospace,marine, L:0 medicine and sports technology.The variables under control include fibre and matrix materials,yarn placement,yarn size and type.Together with this ahiuin emerging ability to engineer composite materials comes the need to develop computationally efficient micromechanics models that can predict, with sufficient accuracy,the effect of the microstructural details on the inter- nal and macroscopic behaviour of these new materials.Computational effi- ciency is indispensable because there are many parameters that must be mposites In the future.it is probably inevitable that the varied in the course of engineering a composite material.This chapter addresses the issue of developing micromechanical models for solid woven tion of the microstructure of a woven fabric composite will require the marriage of such micromechanical models and optimization algorithms. 3.2 Review on solid woven fabric composites 3.2.1 Introduction This section provides a survey of the literature.First,an overview of woven fabric composites is presented.Solid woven preforms vary considerably in terms of fibre orientation,entanglement and geometry.Second,in order to exploit the advantages of these composites fully,it is important to create a link between the microstructural geometry and the thermomechanical per- formance [2].In the past decade,a variety of micromechanical models have been employed to study the overall thermo-elastic behaviour of orthogo- nal 2-D woven fabric composites based on the properties of the constituents 67
3.1 Introduction Solid woven fabric composites represent a class of advanced composites which are reinforced by 2-D or 3-D woven preforms [1]. These materials offer new and exciting opportunities for tailoring the microstructure to specific thermomechanical applications in the fields of aerospace, marine, medicine and sports technology. The variables under control include fibre and matrix materials, yarn placement, yarn size and type. Together with this emerging ability to engineer composite materials comes the need to develop computationally efficient micromechanics models that can predict, with sufficient accuracy, the effect of the microstructural details on the internal and macroscopic behaviour of these new materials. Computational effi- ciency is indispensable because there are many parameters that must be varied in the course of engineering a composite material. This chapter addresses the issue of developing micromechanical models for solid woven fabric composites. In the future, it is probably inevitable that the optimization of the microstructure of a woven fabric composite will require the marriage of such micromechanical models and optimization algorithms. 3.2 Review on solid woven fabric composites 3.2.1 Introduction This section provides a survey of the literature. First, an overview of woven fabric composites is presented. Solid woven preforms vary considerably in terms of fibre orientation, entanglement and geometry. Second, in order to exploit the advantages of these composites fully, it is important to create a link between the microstructural geometry and the thermomechanical performance [2]. In the past decade, a variety of micromechanical models have been employed to study the overall thermo-elastic behaviour of orthogonal 2-D woven fabric composites based on the properties of the constituents 3 Mechanical modelling of solid woven fabric composites PHILIPPE VANDEURZEN, JAN IVENS AND IGNAAS VERPOEST 67 RIC3 7/10/99 7:37 PM Page 67 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9
68 3-D textile reinforcements in composite materials 2-D Orthogonal:Plain,Twill,Satin Weaves Triaxial Layer-to-Layer Angle Interlock 3-D Through-Thickness Warp knit Orthogonal Interlock Sandwich Weave Weft knit 2-D Bias Triaxial Braids Tubular 3-D 2-Step Cartesian 4-Step Multi-Step 3.1 Classification of textile preforms for composite structures [31. and the fabric architecture.Some of these models also provide the oppor- WV:OS tunity to address strength properties.A review will assist in defining possi- ble modelling strategies for 3-D woven fabric composites. 2102 3.2.2 Classification Fibre reinforcement constitutes the structural backbone of a composite.The classification by Cox and Flanagan 3 of various textile preforms is repro- duced in Fig.3.1.The left column classifies textile preforms according to the machines and processes used to produce them.The major textile-forming techniques for composite reinforcements are weaving,knitting and braid- ing.Further,it is possible to make a distinction between the dimensional- ity of the textile preform.Following the definition of Cox [3],the division into 2-D and 3-D textile structures is determined by whether the fibre preform can transport an important load (higher than the load carried by the matrix alone)in two or three linearly independent directions. In general,an orthogonal 2-D woven fabric is made by weaving yarns together.A yarn is a continuous strand of textile fibres.The fabric is pro- duced on a loom that interlaces yarns at right angles to one another [2-8]. The lengthwise yarns are called warps,while the yarns that are shuttled across the loom are called fillings or wefts.The individual yarns in the warp and filling directions are also called an end and a pick,respectively.The interlacing of the yarns causes yarn undulation or yarn crimp.The weave type is determined by the method of interlacing both sets of yarns.Figure 3.2 shows three basic constructions:plain,twill and satin weave.Even in rather simple woven fabrics,there are important geometric differences between the warp and the weft direction.Those differences are the result
and the fabric architecture. Some of these models also provide the opportunity to address strength properties. A review will assist in defining possible modelling strategies for 3-D woven fabric composites. 3.2.2 Classification Fibre reinforcement constitutes the structural backbone of a composite.The classification by Cox and Flanagan [3] of various textile preforms is reproduced in Fig. 3.1.The left column classifies textile preforms according to the machines and processes used to produce them. The major textile-forming techniques for composite reinforcements are weaving, knitting and braiding. Further, it is possible to make a distinction between the dimensionality of the textile preform. Following the definition of Cox [3], the division into 2-D and 3-D textile structures is determined by whether the fibre preform can transport an important load (higher than the load carried by the matrix alone) in two or three linearly independent directions. In general, an orthogonal 2-D woven fabric is made by weaving yarns together. A yarn is a continuous strand of textile fibres. The fabric is produced on a loom that interlaces yarns at right angles to one another [2–8]. The lengthwise yarns are called warps, while the yarns that are shuttled across the loom are called fillings or wefts. The individual yarns in the warp and filling directions are also called an end and a pick, respectively. The interlacing of the yarns causes yarn undulation or yarn crimp. The weave type is determined by the method of interlacing both sets of yarns. Figure 3.2 shows three basic constructions: plain, twill and satin weave. Even in rather simple woven fabrics, there are important geometric differences between the warp and the weft direction. Those differences are the result 68 3-D textile reinforcements in composite materials 3.1 Classification of textile preforms for composite structures [3]. RIC3 7/10/99 7:37 PM Page 68 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9
Mechanical modelling of solid woven fabric composites 69 (a) (b) (c) 3.2 Basic weave constructions:(a)plain,(b)twill and (c)5HS satin weave.The black box represents the fabric unit cell. of numerous constructional and process parameters such as weaving density,warp tension,weft tension and beating motion. The term 'hybrid'is used to describe fabrics containing more than one type of fibre material.Hybrid fabrics are attractive preforms for structural materials for two major reasons.First,these fabrics supply an even wider variety of material selection for designers.They offer the potential of improved composites'mechanical properties,weight saving or excellent impact resistance.Second,a more cost-effective use of expensive fibres can be obtained by replacing them partially with less expensive fibres.Hybrid fabrics are woven from fibrous materials such as glass,aramid,carbon, boron,ceramics and natural fibres. Advances in textile manufacturing technology are rapidly expanding the number and complexity of 3-D woven preforms.By changing the traditional weaving technique to produce 2-D fabrics,it is now possible to achieve a s much higher degree of integration in the thickness direction of the textile. The two major classes of solid 3-D weaving are through-thickness angle interlock weaving [10]and orthogonal interlock weaving [1-3].Angle inter- lock 3-D woven fabrics can be produced on a dobby loom or a jacquard loom.The warp yarns can now enter more than one layer of weft yarns. Other textile structures with laid-in straight yarns are also possible.By changing the number of layers,the pattern of repeat and the position of the laid-in yarns,an almost infinite number of geometric variations becomes possible.In an orthogonal interlock 3-D weave,the yarns are placed in three mutually orthogonal directions.These fabrics are produced principally by the multiple warp weaving method.Matrix-rich regions are created in com- posites reinforced with a 3-D woven orthogonal preform. In general,solid woven fabrics offer the advantages of handleability, dimensional stability,improved impact and damage resistance.However, these advantages are obtained at the cost of reduced stiffness and strength properties owing to the undulation of the yarns.There is thus a significant need to model the mechanical behaviour of these composites
of numerous constructional and process parameters such as weaving density, warp tension, weft tension and beating motion. The term ‘hybrid’ is used to describe fabrics containing more than one type of fibre material. Hybrid fabrics are attractive preforms for structural materials for two major reasons. First, these fabrics supply an even wider variety of material selection for designers. They offer the potential of improved composites’ mechanical properties, weight saving or excellent impact resistance. Second, a more cost-effective use of expensive fibres can be obtained by replacing them partially with less expensive fibres. Hybrid fabrics are woven from fibrous materials such as glass, aramid, carbon, boron, ceramics and natural fibres. Advances in textile manufacturing technology are rapidly expanding the number and complexity of 3-D woven preforms. By changing the traditional weaving technique to produce 2-D fabrics, it is now possible to achieve a much higher degree of integration in the thickness direction of the textile. The two major classes of solid 3-D weaving are through-thickness angle interlock weaving [10] and orthogonal interlock weaving [1–3].Angle interlock 3-D woven fabrics can be produced on a dobby loom or a jacquard loom. The warp yarns can now enter more than one layer of weft yarns. Other textile structures with laid-in straight yarns are also possible. By changing the number of layers, the pattern of repeat and the position of the laid-in yarns, an almost infinite number of geometric variations becomes possible. In an orthogonal interlock 3-D weave, the yarns are placed in three mutually orthogonal directions. These fabrics are produced principally by the multiple warp weaving method. Matrix-rich regions are created in composites reinforced with a 3-D woven orthogonal preform. In general, solid woven fabrics offer the advantages of handleability, dimensional stability, improved impact and damage resistance. However, these advantages are obtained at the cost of reduced stiffness and strength properties owing to the undulation of the yarns. There is thus a significant need to model the mechanical behaviour of these composites. Mechanical modelling of solid woven fabric composites 69 3.2 Basic weave constructions: (a) plain, (b) twill and (c) 5HS satin weave. The black box represents the fabric unit cell. RIC3 7/10/99 7:37 PM Page 69 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9
70 3-D textile reinforcements in composite materials 3.2.3 Micromechanical models Considering the actual importance of 2-D woven fabric composites in the family of structural composites,the mechanical analyses of these compo- sites are now extensively reviewed and presented.Most of the published data are related to stiffness properties of plain weave laminae.There are few publications on the internal stress distribution and on the damage and strength analysis problem of general woven fabric composites.The possible extension of the different micromechanical models to analyse 3-D woven fabric composites will be discussed.It should also be stressed here that in this rapidly evolving field of study any review will soon be incomplete.New results are always being presented or printed. Models of Ishikawa and Chou In the 1980s,an extensive amount of work on the thermo-mechanical mod- elling of 2-D woven fabric composites was done by Ishikawa and Chou. They developed and presented three analytical 1-D elastic models [11-13]. These models are known as the mosaic model,the fibre crimp model and the bridging model.The classical lamination theory forms the basic analyt- ical tool for these developments [14. The models of Ishikawa and Chou are labelled 1-D models because they only consider the undulation of the yarns in the loading direction.Notice the total absence of any geometric analysis.That is,the actual yarn cross- sectional shape or the presence of a gap between adjacent yarns is not con- sidered.Therefore,no predictions are made for the out-of-plane yarn orientation and the fibre volume fraction.Moreover,these models consider balanced closed weaves only,whereas in practice the fabric can be unbal- anced and open.Since the classical laminated plate theory is the basis of each model only the in-plane elastic properties are predicted.The elastic models were extended to analyse the thermal properties,hybrid fabrics and the knee behaviour under uniaxial tensile loading along the filling direction only.However,an extension to treat 3-D woven preforms is not useful because of the geometric simplifications and the limitation to predicting only in-plane properties. Models of N.Naik,Shembekar and Ganesh N.Naik and Shembekar have developed 2-D elastic models for a 2-D non- hybrid plain weave fabric composite [15].These models are essentially an extension of the 1-D models of Ishikawa and Chou.However,these 2-D models take into account the undulation of both warp and weft yarns,the presence of a possible gap between adjacent yarns,the real cross-section of
3.2.3 Micromechanical models Considering the actual importance of 2-D woven fabric composites in the family of structural composites, the mechanical analyses of these composites are now extensively reviewed and presented. Most of the published data are related to stiffness properties of plain weave laminae. There are few publications on the internal stress distribution and on the damage and strength analysis problem of general woven fabric composites. The possible extension of the different micromechanical models to analyse 3-D woven fabric composites will be discussed. It should also be stressed here that in this rapidly evolving field of study any review will soon be incomplete. New results are always being presented or printed. Models of Ishikawa and Chou In the 1980s, an extensive amount of work on the thermo-mechanical modelling of 2-D woven fabric composites was done by Ishikawa and Chou. They developed and presented three analytical 1-D elastic models [11–13]. These models are known as the mosaic model, the fibre crimp model and the bridging model. The classical lamination theory forms the basic analytical tool for these developments [14]. The models of Ishikawa and Chou are labelled 1-D models because they only consider the undulation of the yarns in the loading direction. Notice the total absence of any geometric analysis. That is, the actual yarn crosssectional shape or the presence of a gap between adjacent yarns is not considered. Therefore, no predictions are made for the out-of-plane yarn orientation and the fibre volume fraction. Moreover, these models consider balanced closed weaves only, whereas in practice the fabric can be unbalanced and open. Since the classical laminated plate theory is the basis of each model only the in-plane elastic properties are predicted. The elastic models were extended to analyse the thermal properties, hybrid fabrics and the knee behaviour under uniaxial tensile loading along the filling direction only. However, an extension to treat 3-D woven preforms is not useful because of the geometric simplifications and the limitation to predicting only in-plane properties. Models of N. Naik, Shembekar and Ganesh N. Naik and Shembekar have developed 2-D elastic models for a 2-D nonhybrid plain weave fabric composite [15]. These models are essentially an extension of the 1-D models of Ishikawa and Chou. However, these 2-D models take into account the undulation of both warp and weft yarns, the presence of a possible gap between adjacent yarns, the real cross-section of 70 3-D textile reinforcements in composite materials RIC3 7/10/99 7:37 PM Page 70 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9
Mechanical modelling of solid woven fabric composites 71 the yarn and the possible unbalanced nature of the plain fabric lamina.The representative unit cell is discretized into slices along or across the loading direction.These slices are further divided into different elements such as straight cross-ply or unidirectional regions,undulated cross-ply or uni- directional regions and pure matrix elements.In the analysis of Naik and Shembekar,two schemes for combining the in-plane stiffness matrices of the different elements are used:parallel-series and series-parallel.In the parallel-series (PS)model,the elements are first assembled in parallel across the loading direction with the isostrain assumption(adding the stiff- ness matrices,weighted by their volume fractions).Then,those multi- elements are assembled in series along the loading direction with the isostress assumption.In the second scheme,all the infinitesimal elements of a section along the loading direction are assembled with an iso- stress assumption (adding the compliance matrices,weighted by their volume fractions).Then,all the sections along the loading direction are assembled with an isostrain condition.Such a scheme is called a series- parallel(SP)model.Both schemes yield a full 2-D stiffness matrix for the plain woven fabric composite.A full mathematical treatment of the problem has been presented in reference [16].Based on experimental work, the PS model is recommended for the prediction of all in-plane elastic con- stants.Out-of-plane properties cannot be predicted.Hence,the extension of the model Recently,Naik and Ganesh have presented an extension of their thermo- elastic models to include the prediction of failure in plain weave compos- ites under on-axis static tensile loading [17,18.The load is assumed along the filling direction.Different stages of failure such as warp yarn transverse failure,filling yarn shear failure,filling yarn transverse failure,pure matrix 8 element failure and filling yarn longitudinal failure are considered.The newness of the model lies in the calculation procedure for the stresses in the matrix and yarn elements.However,this is exactly where the model is most confusing.A lot of effort has been spent on describing material non- linearities,geometric non-linearities and geometric effects of matrix element failures,while the available information on the stress prediction procedure is inadequate.The failure analysis is then carried out by com- paring the local element stresses or strains with the admissible values of stress or strain.The Tsai-Wu failure criterion [19]is used to predict the failure in the filling yarn elements.The maximum stress and strain criteria are used to predict the failure in the warp yarn and matrix elements.If an element fails,the stiffness of that element is reduced (degraded stiffness). The final failure of the unit cell laminate is assumed to have occurred if the fibres in the filling yarn are broken. In conclusion,some more practical drawbacks and disadvantages of the strength model of Naik are provided.First,the stress model lacks logic and
the yarn and the possible unbalanced nature of the plain fabric lamina. The representative unit cell is discretized into slices along or across the loading direction. These slices are further divided into different elements such as straight cross-ply or unidirectional regions, undulated cross-ply or unidirectional regions and pure matrix elements. In the analysis of Naik and Shembekar, two schemes for combining the in-plane stiffness matrices of the different elements are used: parallel–series and series–parallel. In the parallel–series (PS) model, the elements are first assembled in parallel across the loading direction with the isostrain assumption (adding the stiffness matrices, weighted by their volume fractions). Then, those multielements are assembled in series along the loading direction with the isostress assumption. In the second scheme, all the infinitesimal elements of a section along the loading direction are assembled with an isostress assumption (adding the compliance matrices, weighted by their volume fractions). Then, all the sections along the loading direction are assembled with an isostrain condition. Such a scheme is called a series– parallel (SP) model. Both schemes yield a full 2-D stiffness matrix for the plain woven fabric composite. A full mathematical treatment of the problem has been presented in reference [16]. Based on experimental work, the PS model is recommended for the prediction of all in-plane elastic constants. Out-of-plane properties cannot be predicted. Hence, the extension of the model to treat 3-D woven preforms is not useful. Recently, Naik and Ganesh have presented an extension of their thermoelastic models to include the prediction of failure in plain weave composites under on-axis static tensile loading [17,18]. The load is assumed along the filling direction. Different stages of failure such as warp yarn transverse failure, filling yarn shear failure, filling yarn transverse failure, pure matrix element failure and filling yarn longitudinal failure are considered. The newness of the model lies in the calculation procedure for the stresses in the matrix and yarn elements. However, this is exactly where the model is most confusing. A lot of effort has been spent on describing material nonlinearities, geometric non-linearities and geometric effects of matrix element failures, while the available information on the stress prediction procedure is inadequate. The failure analysis is then carried out by comparing the local element stresses or strains with the admissible values of stress or strain. The Tsai–Wu failure criterion [19] is used to predict the failure in the filling yarn elements. The maximum stress and strain criteria are used to predict the failure in the warp yarn and matrix elements. If an element fails, the stiffness of that element is reduced (degraded stiffness). The final failure of the unit cell laminate is assumed to have occurred if the fibres in the filling yarn are broken. In conclusion, some more practical drawbacks and disadvantages of the strength model of Naik are provided. First, the stress model lacks logic and Mechanical modelling of solid woven fabric composites 71 RIC3 7/10/99 7:37 PM Page 71 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9