Knitted fabric composites 185 the constituent fiber and matrix materials [22-26].Typical tensile stress-strain curves of three different kinds of knitted fabric composites are shown in Fig.6.5.These curves are obtained from tensile testing in the wale direction of the composite.The tensile stress-strain curve of composite made from knitted glass fiber fabric and epoxy matrix is grossly linear with 70 (edW) 60 Glass Fabric/Epoxy 50 40 30 20 10 woo'ssaudmau'peoupoow//:dny Aq paanad WV LS:06:ZI I10Z'ZZ ' %)】 0 0.1 0.2 0.3 0.4 0.5.0.60.70.80.9 1111.21.31.4 Unidirectional Strain in Wale Direction (a) o Glass Fabric/Polypropylene 60 50 40 30 20 (%) 2 4 6 7 Unidirectional Strain in Wale Direction (b) 6.5 Typical tensile stress-strain curves of(a)knitted glass fiber fabric reinforced epoxy composite,(b)knitted glass fiber fabric reinforced polypropylene composite,and(c)knitted polyester fiber fabric reinforced polyurethane composite
the constituent fiber and matrix materials [22–26]. Typical tensile stress–strain curves of three different kinds of knitted fabric composites are shown in Fig. 6.5. These curves are obtained from tensile testing in the wale direction of the composite. The tensile stress–strain curve of composite made from knitted glass fiber fabric and epoxy matrix is grossly linear with Knitted fabric composites 185 6.5 Typical tensile stress–strain curves of (a) knitted glass fiber fabric reinforced epoxy composite, (b) knitted glass fiber fabric reinforced polypropylene composite, and (c) knitted polyester fiber fabric reinforced polyurethane composite. RIC6 7/10/99 8:11 PM Page 185 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:57 AM IP Address: 158.132.122.9
186 3-D textile reinforcements in composite materials 40 -Polyester Fabric/Polyurethane 30 20 10 5 (%)】 10 20 30 40 多 Unidirectional Strain in Wale Direction (c) 6.5(cont.) wo'ssaudmau'peaypoow/:dny a small ultimate failure strain,1.3%.In the case of knitted glass fiber fabric reinforced polypropylene composite material,the stress-strain curve e changes from an initial linearly elastic relationship to a significantly non- linear relationship with an intermediate ultimate failure strain of 8.5%.The matrix polymer used in these composite materials mainly causes this dif- 豆 ference.At the other end of the spectrum,a highly flexible stress-strain behavior could be achieved by reinforcing elastomeric material with a knitted fabric.A typical stress-strain curve of a knitted polyester fiber fabric reinforced polyurethane elastomer is shown in Fig.6.5.The stress-strain behavior is characterized by a small initial linear elastic relationship,fol- lowed by nonlinear behavior with large ultimate failure strain of 60%.In other words,by selecting the type of matrix and reinforcement materials, the mechanical characteristics of a knitted fabric composite can be tailored from rigid to flexible. This chapter mainly concerns the mechanical behavior of the knitted glass fiber fabric reinforced epoxy composites,in which the stresses and strains are connected by fixed linear relationships.Hence,let us consider the tensile behavior of knitted glass fiber fabric reinforced epoxy compo- site in detail.The stress-strain curve is linear up to the knee point,which occurred at approximately 0.45%strain.Above the knee point,the mater- ial deformation and microfracture processes in the specimen cause the non- linearity.A schematic representation of a typical fracture process in a knitted fabric composite is given in Fig.6.6.At strain levels immediately
a small ultimate failure strain, 1.3%. In the case of knitted glass fiber fabric reinforced polypropylene composite material, the stress–strain curve changes from an initial linearly elastic relationship to a significantly nonlinear relationship with an intermediate ultimate failure strain of 8.5%. The matrix polymer used in these composite materials mainly causes this difference. At the other end of the spectrum, a highly flexible stress–strain behavior could be achieved by reinforcing elastomeric material with a knitted fabric.A typical stress–strain curve of a knitted polyester fiber fabric reinforced polyurethane elastomer is shown in Fig. 6.5. The stress–strain behavior is characterized by a small initial linear elastic relationship, followed by nonlinear behavior with large ultimate failure strain of 60%. In other words, by selecting the type of matrix and reinforcement materials, the mechanical characteristics of a knitted fabric composite can be tailored from rigid to flexible. This chapter mainly concerns the mechanical behavior of the knitted glass fiber fabric reinforced epoxy composites, in which the stresses and strains are connected by fixed linear relationships. Hence, let us consider the tensile behavior of knitted glass fiber fabric reinforced epoxy composite in detail. The stress–strain curve is linear up to the knee point, which occurred at approximately 0.45% strain. Above the knee point, the material deformation and microfracture processes in the specimen cause the nonlinearity. A schematic representation of a typical fracture process in a knitted fabric composite is given in Fig. 6.6. At strain levels immediately 186 3-D textile reinforcements in composite materials 6.5 (cont.) RIC6 7/10/99 8:12 PM Page 186 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:57 AM IP Address: 158.132.122.9
Knitted fabric composites 187 Debonding Wale Course WV LS:OE:ZI I IOZ 'ZZ AInur Aupines Fracture Plane Wale Course 6.6 Schematic representation of a typical fracture process in tensile tested knitted fabric composite
Knitted fabric composites 187 6.6 Schematic representation of a typical fracture process in tensile tested knitted fabric composite. RIC6 7/10/99 8:12 PM Page 187 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:57 AM IP Address: 158.132.122.9
188 3-D textile reinforcements in composite materials above the knee point,debonding of yarns oriented normal to the testing direction occurs.The cracks nucleated from the debonded sites propagate into resin-rich regions and coalesce into large transverse cracks.Unfrac- tured yarns bridge the fracture plane.The ultimate fracture of the tensile specimen occurs upon the fracture of bridging yarns.In other words,the tensile strength of composite material is determined mainly by the fracture strength of yarns bridging the fracture plane. 6.4 Analysis of 3-D elastic properties 6.4.1 Methodology of analysis The plain weft knitted fabric reinforced composite material investigated in this study is assumed to have only reinforcement fiber yarns and polymer matrix.For analysis purposes,a unit cell representing the complete knitted fabric composite is identified.A geometric model is proposed to determine the orientation of yarn in the composite (Section 6.4.2).Section 6.4.3 out- lines the procedure for estimating the fiber volume fraction of the com- posite.The unit cell is divided into four representative volumes,also called a 'crossover model'.The crossover model is further divided into sub- volumes,which are considered as transversely isotropic unidirectional fiber reinforced composites.A new micromechanical model is used to predict all the five independent elastic constants of the unidirectional fiber reinforced composites (Section 6.4.4).By considering the contributions of both the fibers and net matrix material,the compliance/stiffness matrix of each sub- volume in the material co-ordinate system is calculated using the new for- mulae.This compliance/stiffness matrix of each sub-volume is then transformed to the global co-ordinate system (see Section 6.4.5).A volume- averaging scheme has been applied to obtain the overall compliance/stiff- ness matrix of the knitted fabric composite (Section 6.4.6).The effects of fiber content and other parameters of knitted fabric on the elastic proper- ties of the composite material are identified (Section 6.4.7). 6.4.2 Geometric model A schematic diagram of an idealized unit cell of the plain weft knitted fabric is given in Fig.6.7.The basic assumption is that the projection of the central axis of the yarn loop on the fabric plane is composed of circular arcs.This assumption is reasonable as the knit loops are formed during knitting by bending the yarns round a series of equally spaced knitting needles and sinkers.The physical meanings of various symbols used below are also shown in the figure.The geometry of the unit cell can be described using
above the knee point, debonding of yarns oriented normal to the testing direction occurs. The cracks nucleated from the debonded sites propagate into resin-rich regions and coalesce into large transverse cracks. Unfractured yarns bridge the fracture plane. The ultimate fracture of the tensile specimen occurs upon the fracture of bridging yarns. In other words, the tensile strength of composite material is determined mainly by the fracture strength of yarns bridging the fracture plane. 6.4 Analysis of 3-D elastic properties 6.4.1 Methodology of analysis The plain weft knitted fabric reinforced composite material investigated in this study is assumed to have only reinforcement fiber yarns and polymer matrix. For analysis purposes, a unit cell representing the complete knitted fabric composite is identified. A geometric model is proposed to determine the orientation of yarn in the composite (Section 6.4.2). Section 6.4.3 outlines the procedure for estimating the fiber volume fraction of the composite. The unit cell is divided into four representative volumes, also called a ‘crossover model’. The crossover model is further divided into subvolumes, which are considered as transversely isotropic unidirectional fiber reinforced composites. A new micromechanical model is used to predict all the five independent elastic constants of the unidirectional fiber reinforced composites (Section 6.4.4). By considering the contributions of both the fibers and net matrix material, the compliance/stiffness matrix of each subvolume in the material co-ordinate system is calculated using the new formulae. This compliance/stiffness matrix of each sub-volume is then transformed to the global co-ordinate system (see Section 6.4.5).A volumeaveraging scheme has been applied to obtain the overall compliance/stiffness matrix of the knitted fabric composite (Section 6.4.6). The effects of fiber content and other parameters of knitted fabric on the elastic properties of the composite material are identified (Section 6.4.7). 6.4.2 Geometric model A schematic diagram of an idealized unit cell of the plain weft knitted fabric is given in Fig. 6.7. The basic assumption is that the projection of the central axis of the yarn loop on the fabric plane is composed of circular arcs. This assumption is reasonable as the knit loops are formed during knitting by bending the yarns round a series of equally spaced knitting needles and sinkers. The physical meanings of various symbols used below are also shown in the figure. The geometry of the unit cell can be described using 188 3-D textile reinforcements in composite materials RIC6 7/10/99 8:12 PM Page 188 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:57 AM IP Address: 158.132.122.9
Knitted fabric composites 189 A y N 0 WV LS:0E:ZI I10Z 'ZZ Krenunr 'Kupes : 6'ZZI'ZEI'8SI :ssauppy dl E R 1 6.7 Schematic diagram of an idealized unit cell of the plain weft knitted fabric
Knitted fabric composites 189 6.7 Schematic diagram of an idealized unit cell of the plain weft knitted fabric. RIC6 7/10/99 8:12 PM Page 189 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:57 AM IP Address: 158.132.122.9