Computational Materials Science 43(2008)1193-1206 Contents lists available at ScienceDirect Computational Materials Science ELSEVIER journalhomepagewww.elsevier.com/locate/commatsci A micromechanical characterization of angular bidirectional fibrous composites Nabi abolfathi, Abhay Naik, Ghodrat Karami Chad Ulven Department of Mechanical Engineering and Applied Mechanics, North Dakota State University, Fargo, ND 58105-5285, USA ARTICLE INFO A BSTRACT Article history Received 24 December 2007 A micromechanical numerical algorithm to efficiently determine the homogenized elastic properties of bidirectional fibrous composites is presented. A repeating unit cell (RUC) based on a pre-determined bidi- Received in revised form 7 March 2008 rectional fiber packing is assumed to represent the microstructure of the composite For angular bidirec- Available online 24 April 2008 tional fiber distribution, the symmetry lines define a parallelepiped unit cell, representing the periodic crostructure of an angular bidirectional fiber composite. The lines of symmetry extrude a volume to capture a three dimensional unit cell. Finite element analysis of this unit cell under six possible indepen 6143.Bn dent loading conditions is carried out to study and quantify the homogenized mechanical property of the cell. A volume averaging scheme is implemented to determine the average response as a function of load- of stresses and strains. The individual elastic properties of the constituents'materials, as well as, the composite can be assumed to be completely isotropic to completely anisotropic. The output of the analysis can determine this degree. The logic behind the selection of the unit cell and the implementation of the periodic boundary conditions as well as the constraints are presented. To verify this micromechan- ics algorithm, the results for four composites are presented. The results in this paper are mainly focused n the impact of the fiber cross angles on the stiffness properties of the ites chosen. The accuracy of the results from this micromechanics modeling procedure has been compared with the stiffness/ com pliance solutions from lamination theory. The methodology is to be accurate and efficient to the extent that periodicity of the composite material is maintained. In addition, the results will show the impact of fiber volume fraction on the material properties of the composite. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis e 2008 Elsevier B V. All rights reserved 1. Introduction entation In another study, the change of angle in bidirectional composites was studied for variation in permeability through composites against complicated loadings are determined by insert- ferent temperature for bidirectional ceramic composite has been ing fibers inside the matrix in different directions Composites with studied for fracture behavior [ 4. Domnanovich et al. [10] studied bidirectional and multidirectional fibers produce stiffness against the elastic module of bidirectional carbon/carbon composite under complicated structural and thermal loading scenarios. Mechanical heat treatment process. They also examined the shear strength as properties of mono-directional fiber reinforced composite have well as elastic modulus using resonant beam method. een extensively studied [1-7]. however, a detailed modeling ef- n application, a composite composed of a matrix with rein- fort investigation of the mechanical properties of bidirectional forced multidirectional fibers is a basic structural material in most composites as a function of the reinforcing fiber cross angles and aircraft constructions. glass fabric made with multi bidirectional entation has not been fully undertaken Studies related to bidi- fibers are used as stiffening materials at many applications. the rectional composites are usually focused on [ 0/90 or [0/45 ply use of glass in aerostructures, particularly, sandwich composite orientations. Among the many experimental efforts and proce- structures is a recent development. Glass fabric as a new infra- dures conducted for characterization of multidirectional fibrous structure composite material is now available commercially in composites, multi layer bidirectional composites made by vetrotex hundreds of different weights, weaves, strengths and working has been used as a lap joint by Ferreira et al. 8. This lap joint com- properties. Multiple layers of glass fabric oriented in different posite was studied for fatigue loading for [0/45] and [o/90 ply ori- directions are laminated together to form the panels for various applications In biomechanics applications and biological systems 4 Corres g author.Tel:+17012315859ax:+17012318913 nd organs, different loading directions and scenarios need to pre mail address: G Karami@ndsu. edu (G Karami) vide a material with proper strength in multiple directions. a bidi- s- see front matter o 2008 Elsevier B v. All rights reserved. doi: 10.1016/j-commatsci200803.017A micromechanical characterization of angular bidirectional fibrous composites Nabi Abolfathi, Abhay Naik, Ghodrat Karami *, Chad Ulven Department of Mechanical Engineering and Applied Mechanics, North Dakota State University, Fargo, ND 58105-5285, USA article info Article history: Received 24 December 2007 Received in revised form 7 March 2008 Accepted 11 March 2008 Available online 24 April 2008 PACS: 61.43.Bn 62.20.D 62.20.-x 81.05.Ni 02.70.Dh Keywords: Bidirectional fibrous composites Micromechanics Finite element method Repeating unit cell Periodic boundary conditions abstract A micromechanical numerical algorithm to efficiently determine the homogenized elastic properties of bidirectional fibrous composites is presented. A repeating unit cell (RUC) based on a pre-determined bidi￾rectional fiber packing is assumed to represent the microstructure of the composite. For angular bidirec￾tional fiber distribution, the symmetry lines define a parallelepiped unit cell, representing the periodic microstructure of an angular bidirectional fiber composite. The lines of symmetry extrude a volume to capture a three dimensional unit cell. Finite element analysis of this unit cell under six possible indepen￾dent loading conditions is carried out to study and quantify the homogenized mechanical property of the cell. A volume averaging scheme is implemented to determine the average response as a function of load￾ing in terms of stresses and strains. The individual elastic properties of the constituents’ materials, as well as, the composite can be assumed to be completely isotropic to completely anisotropic. The output of the analysis can determine this degree. The logic behind the selection of the unit cell and the implementation of the periodic boundary conditions as well as the constraints are presented. To verify this micromechan￾ics algorithm, the results for four composites are presented. The results in this paper are mainly focused on the impact of the fiber cross angles on the stiffness properties of the composites chosen. The accuracy of the results from this micromechanics modeling procedure has been compared with the stiffness/com￾pliance solutions from lamination theory. The methodology is to be accurate and efficient to the extent that periodicity of the composite material is maintained. In addition, the results will show the impact of fiber volume fraction on the material properties of the composite. This micromechanics tool could make a powerful viable algorithm for determination of many linear as well as nonlinear properties in continuum mechanics material characterization and analysis. 2008 Elsevier B.V. All rights reserved. 1. Introduction Improvements in mechanical properties of fiber reinforced composites against complicated loadings are determined by insert￾ing fibers inside the matrix in different directions. Composites with bidirectional and multidirectional fibers produce stiffness against complicated structural and thermal loading scenarios. Mechanical properties of mono-directional fiber reinforced composite have been extensively studied [1–7], however, a detailed modeling ef￾fort investigation of the mechanical properties of bidirectional composites as a function of the reinforcing fiber cross angles and orientation has not been fully undertaken. Studies related to bidi￾rectional composites are usually focused on [0/90] or [0/45] ply orientations. Among the many experimental efforts and proce￾dures conducted for characterization of multidirectional fibrous composites, multi layer bidirectional composites made by Vetrotex has been used as a lap joint by Ferreira et al. [8]. This lap joint com￾posite was studied for fatigue loading for [0/45] and [0/90] ply ori￾entation. In another study, the change of angle in bidirectional composites was studied for variation in permeability through change of fiber angles [9]. Creep loading of composites under dif￾ferent temperature for bidirectional ceramic composite has been studied for fracture behavior [4]. Domnanovich et al. [10] studied the elastic module of bidirectional carbon/carbon composite under heat treatment process. They also examined the shear strength as well as elastic modulus using resonant beam method. In application, a composite composed of a matrix with rein￾forced multidirectional fibers is a basic structural material in most aircraft constructions. Glass fabric made with multi/bidirectional fibers are used as stiffening materials at many applications. The use of glass in aerostructures, particularly, sandwich composite structures is a recent development. Glass fabric as a new infra￾structure composite material is now available commercially in hundreds of different weights, weaves, strengths and working properties. Multiple layers of glass fabric oriented in different directions are laminated together to form the panels for various applications. In biomechanics applications and biological systems and organs, different loading directions and scenarios need to pro￾vide a material with proper strength in multiple directions. A bidi- 0927-0256/$ - see front matter 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.03.017 * Corresponding author. Tel.: +1 701 231 5859; fax: +1 701 231 8913. E-mail address: G.Karami@ndsu.edu (G. Karami). Computational Materials Science 43 (2008) 1193–1206 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci