an bu post sha holes ha in medical field.Carey et al.published a study about the of hole diameter on bearing strength.Smaller diameters design of fiber reinforced composite catheters [55]They used more local disturbance on the orientation of fibers analyzed the require than larger resin rich regions anc of braided composites [55] rical analysis.The chdedhathberoicntaionsaroundthchoiesSienicamly Icomposite Composite materials,including braided composites. Ohki et al.[63.64]and Nakai et al.[65]evaluated the may be manufactured to near net shape toavoid any pos wev there are al cen s had highe Assembly may be accomplished through adhesive or poly tions. bonding as well as mechanical joints.Us e of adh s related to lamage of the strand path of this review.mechanical ioints were investigated since caused by the presence of the hole 163-651 8.Elastic constant predictive modek centrations around holes and cutouts.Tsiang et al Mechanical behavior of 2D braided com sites can be plastic behavior. such as t te strength and fa mnosite Important public cations about the remaining two categorie bear were me high than that are liste or bibliographical purpos not detaile men fa compo has sions to explain the observed phenomena were provided failure behavior.Braided structures are assumed to behave In anothe set or tensile exp ments, linearly in the elastic range.In the plastic egion,a non-lir through pin s th complexity of times greater loads than tho with machined holes.This was associated to the fiber discontinuity at the machined papers that holes[56,57列 e dealt propertie as well s strength anc ng th udy of Br tein et ang fail to date Authors outlined that,in the previous studies.the overal find its origins inarlier woven fabric composite and lam- ens ed composit It wa s to increased the local bearing strength.In Wang and his co can he seen as a specific form of woven fabric comnosites workers'studies.wall thickness was kept constant.Change or textile composites [75]. e models dis sed are base eng ey co the dise f thi machined holes as compared to braided holes.Other stud are familiar with the well documented CLPT analysis,such as by Jones 16 Halpin al. 77]devel ped a model pr Fuiita et al 1621 nublished studies short fiber composites from a laminate analogy.This lam-
along the shaft. This was obtained by varying the braid angle along the post shaft [54]. Braided tubular products can also be used as catheters in medical field. Carey et al. published a study about the design of fiber reinforced composite catheters [55]. They analyzed the required rigidities of conventional catheters and set design objectives to achieve these targets by use of braided composites [55]. 7. Typical challenges in applications: joining methods braided and machined holes in 2D braided composites Composite materials, including braided composites, may be manufactured to near net shape to avoid any post-manufacturing processes; however, there are also numerous applications that require multi-part assembly with other composite or non-composite components. Assembly may be accomplished through adhesive or polymeric bonding as well as mechanical joints. Use of adhesives involves studying adhesive shear strength, surface finish of substrates and coupling agents. For the purposes of this review, mechanical joints were investigated since they require holes or other shape openings in the structures and will have effects on the integrity of the parts. Composite materials are susceptible to develop stress concentrations around holes and cutouts. Tsiang et al. [56] and Brookstein [57] compared the effect of integrally formed braided holes and machined holes on strength of cylindrical braided composites. Specimens with braided and machined holes were tested under tensile loads. In average, specimens with braided holes were observed to bear loads that were 1.23 times higher than that of machined holes. Observations on specimen failure modes were presented; however, limited micromechanical discussions to explain the observed phenomena were provided. In another set of tensile experiments, load was applied through pins inserted into the braided and machined holes. On average, specimens with braided holes supported 1.8 times greater loads than those with machined holes. This was associated to the fiber discontinuity at the machined holes [56,57]. Following the study of Brookstein et al., Wang and his co-workers published contradictory findings [58–60]. Authors outlined that, in the previous studies, the overall wall thickness of the tube specimens were not controlled due to excess resin surrounding the holes. It was suggested that these thicker resin rich regions contributed to the increased the local bearing strength. In Wang and his coworkers’ studies, wall thickness was kept constant. Change in fiber angles in the surrounding regions of the holes resulted in decreased bearing strength. They concluded that similar or greater bearing strengths were found for machined holes as compared to braided holes. Other studies on 3D braided composites support their findings [58–61]. However, Fujita et al. [62] published studies on comparison of machined holes versus braided holes on flat braided bars, and they found results parallel to that of Brookstein et al. They stated that machined holes have lower bearing strengths; however, their work concentrated on the effect of hole diameter on bearing strength. Smaller diameters caused more local disturbance on the orientation of fibers than larger diameters leading to resin rich regions and lower bearing strengths than their larger counterparts. Results were validated using numerical analysis. They concluded that fiber orientations around the holes significantly affected the bearing strength and failure mode [62]. They did not comment on the issue (i.e. the resin-rich regions surrounding the holes) raised by Wang et al. Ohki et al. [63,64], and Nakai et al. [65] evaluated the effect of machined versus braided holes in end loaded flat-braided specimen with a centralized hole. Specimens with braided holes had higher strength properties during both static and fatigue testing. From microscopic observations, authors conclude that the damage mechanism of the machined holes is related to the fiber–resin interface, while the damage mechanism of the braided holes is related to the reorientation of the continuous fibrous strand path caused by the presence of the hole [63–65]. 8. Elastic constant predictive models Mechanical behavior of 2D braided composites can be discussed in terms of elastic behavior, plastic behavior, and failure behavior such as ultimate strength and failure mechanism [66]. This review, due to the broadness of the topic, focuses on elastic behaviors of braided composites. Important publications about the remaining two categories are listed for bibliographical purposes but not detailed. Elastic property prediction of 2D braided composites has been studied far more than their plastic behavior and failure behavior. Braided structures are assumed to behave linearly in the elastic range. In the plastic region, a non-linear behavior is observed which increases the complexity of the problem. Nevertheless, a number of studies have been published regarding plasticity behavior and failure characteristics of braided composites [67–74]. Other papers that have dealt with elastic properties, as well as strength and failure mechanisms, will be covered in detail. The majority of braid analysis developed to date can find its origins in earlier woven fabric composite and laminated composite analysis; hence, this review also outlines major studies published in these fields to create a basis for the overall discussion. In this view, braided composites can be seen as a specific form of woven fabric composites, or textile composites [75]. Some of the models discussed are based on the well known Classical Laminate Plate Theory (CLPT). During the discussions of this review, it is assumed that readers are familiar with the well documented CLPT analysis, such as by Jones [76]. In early 1970s, Halpin et al. [77] developed a model predicting elastic stiffness and thermal expansion properties of short fiber composites from a laminate analogy. This lam- 48 C. Ayranci, J. Carey / Composite Structures 85 (2008) 43–58
C.Ayranel.J.Careyl Composite Siructures 85(2008)43-58 49 inate analogy was extended to two-and three-dimensiona cylinders using a simple micromechanics theory dmP心Soven fa es wer of t ply and Whitney and Halpin 78 analyzed laminated aniso tropic tubes subjected to combined tension or compression principle of superposition to the two sub-layers.Results for nternal pressur torque.A se elast us and Poi ment with ex ental to was done using Donnel's approximations Yang et al []proposed a predictive model for triaxial a followed were L th and st the nd C dulatio els that formed the basis to many subsequent textile fabric 79assumes 60fiber deposition angle.The model utilize namely,the undula haracterization of the braid architecture tion and e mod dy the sma cell.Th ite is treated as an ass of the unit cellan ssumed to he ve of the over. ated with matrix are taker all composites. Mosaic model treats the system as an The mode of Mi regions are sub quently consid zed a ing bon so-strain and iso-stress assumptions to respectively obtair stacked together with fibers in the bias braid and longitudi upper and ower bound compo al angles, be und to n s a result of the analys nuity char acteristics of the fibers in woven fabric comp ced by the fiber de sition angles. The tes omitted in the mo was not verified experimentally [84] e In a la Yang e al.[85 ume fraction of the unit cel The undulating he elastic erties of three.dimensional textile assumed to follow a path described by a sinusoidal func and braided)composites.Here.the unit cell used for the were used to CLP analysis is assumed to be compose 0 of the unidir of the local undulation angle (called"local offaxis angle onal directions.All the yarns in one direction were a and Chou).The authors state that the undu of the con analysis n exten th strain occurs at the mid-point of the undulating fiber. The In the analysis contribution of pure matrix re s to the bridging model was developed for satin weave fabrics and stiffness matrices were neglected (interested reader may this view [79 eter to the riginal text for the of h rid u en fab c6i gated effects of these fabric parameters on elastic pro ertie interlocking points and stated that it is still a convenient by using the m emodel.In this m the analysis.Predictions and experimenta nature g mo ngs g000 nt [ the Fabri Gaps that may exist between were Geomeury Model (FGM.to predict the aclose mesh configuration was adapted.In this report,Ishik three-dimensionally braided structures.FGM is based on thermal exp sion coe modified CLP where the uni ed as epeating an the stiftne s matrix of the fiber undulation model agreement was found betweer lent unidirectional lamina and transforming it into the experimental and theoretical results [82] tructural coordinate The contrib tions of each
inate analogy was extended to two- and three-dimensional woven fabric composites. Authors reported that predicted and experimental results for woven fabric composites were compared and found to be ‘‘qualitatively correct”. Whitney and Halpin [78], analyzed laminated anisotropic tubes subjected to combined tension or compression, internal pressure, and torque. Authors listed the governing equations as equilibrium, compatibility, strain and curvature displacement, and constitutive relations. The analysis was done using Donnel’s approximations. Some of the most influential studies that followed were published by Ishikawa and Chou [79–81] who proposed and compared three stiffness and strength predictive models that formed the basis to many subsequent textile fabric composite models, namely, the ‘‘mosaic”, ‘‘fiber undulation”, and ‘‘bridging” models. The models study the smallest repeating unit of the fabric, the unit cell. The properties of the unit cell are assumed to be representative of the overall composites. Mosaic model treats the system as an assemblage of asymmetric cross-ply laminates. The model uses the Classical Laminate Plate (CLPT) theory as the basis of the analysis. The model was analyzed using both iso-strain and iso-stress assumptions to respectively obtain upper and lower bound composite stiffness properties. The fiber undulation model was developed to validate and improve the mosaic model. Undulation (crimp) and continuity characteristics of the fibers in woven fabric composites omitted in the mosaic model were considered. Due to physically occurring matrix only regions, this model also allowed the recognition of changes in the overall fiber volume fraction of the unit cell. The undulating fibers, assumed to follow a path described by a sinusoidal function, were used to calculate stiffness matrices of CLPT analysis. The local stiffness matrices used in the calculation of the CLPT A, B, D matrices were computed as a function of the local undulation angle (called ‘‘local off-axis angle” by Ishikawa and Chou). The authors stated that the undulation of the fibers reduced the effective stiffness of the composite in the longitudinal direction, and that the maximum strain occurs at the mid-point of the undulating fiber. The bridging model was developed for satin weave fabrics and is therefore out of the scope of this review [79–81]. Ishikawa and Chou also characterized geometric and material properties of hybrid woven fabrics[82], and investigated effects of these fabric parameters on elastic properties by using the mosaic model. In this model, due to the hybrid nature of the fabric, in-plane and bending moduli (Aij, andBij matrices) are no longer uniform in the repeating region. Gaps that may exist between the fibers were neglected and a close mesh configuration was adapted. In this report, Ishikawa and Chou also investigated the thermal expansion coef- ficients and thermal bending coefficients. Investigation was conducted using the mosaic model and one-dimensional fiber undulation model. Agreement was found between experimental and theoretical results [82]. Tsiang et al. [83] investigated the longitudinal and transverse mechanical properties of triaxial braided graphite/ epoxy cylinders using a simple micromechanics theory based model. The braid architecture was modeled as a structure composed of unidirectional-ply and bias-angle ply yarns. The brief description of the model provided stated that material properties were calculated by applying the principle of superposition to the two sub-layers. Results for the longitudinal and transverse elastic modulus and Poisson’s ratio were provided, and were stated to be in reasonable agreement with experimental results. Yang et al. [84] proposed a predictive model for triaxially braided composites elastic properties. Unlike woven fabric models (45 fiber deposition angle), this model, based on the Ishikawa and Chou’s fabric undulation model [79], assumes 60 fiber deposition angle. The model utilizes the geometrical characterization of the braid architecture where the triaxial fabric composite is treated as an assemblage of three laminae; bias and longitudinal yarn laminae. The corrugated yarns impregnated with matrix are taken into account in the initial calculation, and the contribution of the matrix only regions are subsequently considered using a Rule of Mixtures prediction. The upper bound is calculated from a laminate that consists of three laminae stacked together with fibers in the bias braid and longitudinal angles, and the lower bound is calculated from the proposed model. As a result of the analysis, the stiffness of the non-orthogonal woven fabrics was determined to be strongly influenced by the fiber deposition angles. The model was not verified experimentally [84]. In a later study, Yang et al. [85] proposed the ‘‘Fiber Inclination Model” based on a modified CLPT to predict the elastic properties of three-dimensional textile (woven and braided) composites. Here, the unit cell used for the analysis is assumed to be composed of an assemblage of inclined unidirectional laminae. The idealized unit cell was described as fiber bundles oriented in four body diagonal directions. All the yarns in one direction were assumed to form inclined laminae after matrix impregnation. The rest of the analysis was explained as an extension of the fiber undulation model developed by Ishikawa and Chou. In the analysis, contribution of pure matrix regions to the stiffness matrices were neglected (interested reader may refer to the original text for the modifications and necessary assumptions). Authors recognized and underlined that the CLPT ignores the interactions of fiber yarns at the interlocking points and stated that it is still a convenient technique for the analysis. Predictions and experimental findings were in good agreement [85]. Whyte [86] proposed an analytical model, the Fabric Geometry Model (FGM), to predict the properties of three-dimensionally braided structures. FGM is based on a modified CLPT where the unit cell is defined as repeating volumes. The stiffness matrix is developed for each yarn in the unit cell by calculating the stiffness matrix of the equivalent unidirectional lamina and transforming it into the structural coordinate system. The contributions of each yarn are superimposed with respect to their volumetric contribution. Authors also suggest calculating the strain C. Ayranci, J. Carey / Composite Structures 85 (2008) 43–58 49