Computers structures PERGAMON Computers and Structures 80(2002)1177-1199 On a general constitutive description for the inelastic and failure behavior of fibrous laminates Part ll Laminate theory and applications Zheng-Ming Huang Biomaterials Laboratory, Division of bioengineering, Department of Mechanical Engineering, National University of Singapore, Received 10 April 2001; accepted 6 March 2002 These two parts of papers report systematically a constitutive description for the inelastic and strength behavior of laminated composites reinforced with various fiber preforms. The constitutive relationship is established microme- chanically, through layer-by-layer analysis. Namely, only the properties of the constituent fiber and matrix materials of the composites are required as input data. In the previous part( Comput. Struct(submitted)), the lamina theory was presented. Three fundamental quantities of the laminae, i.e. the internal stresses generated in the constituent fiber and matrix materials and the instantaneous compliance matrix, with different fiber preform (including woven, braided, and knitted fabric) reinforcements were explicitly obtained by virtue of the bridging micromechanics model. In the present paper, the laminate stress analysis is shown. The purpose of this analysis is to determine the load shared by each lamina in the laminate, so that the lamina theory can be applied. Incorporation of the constitutive equations into an FEM tware package is illustrated. A number of application examples are given in the paper to demonstrate the efficiency of the constitutive theory established. The predictions thus made include: failure envelopes of multidirectional laminates subjected to biaxial in-plane loads, thermo-mechanical cycling stress-strain curves of a titanium metal matrix composite laminate, S-n curves of multilayer knitted fabric reinforced laminates under tensile fatigue, and bending load- deflection plots and ultimate bending strengths of laminated braided fabric reinforced beams subjected to lateral loads. All these predictions are based on the constituent properties which were measured or available independently, and are compared with experimental results. Reasonably good correlations have been found in all the cases. It is expected that the present constitutive relationship can benefit the critical design and strength analysis of a primarily loaded structure made of composite materials. o 2002 Published by Elsevier Science Ltd. words Laminated Textile com Metal matrix composite; Composite structure; Mechanical property; Co relationship: In-plane failure: Thermo-mechanical fatigue; Flexural failure; Load-deflection curve, Stiffness discount; Strength prediction; Bridging micromechanics model; FEM structural analysis cuon nized as attractive candidates in most modern industries the usages of them are still relatively limited compared Although fiber reinforced composites have been in with their counterparts, i.e. homogeneous and isotropic practice for nearly half a century, and have been recog- materials such as metals, ceramics, and polymers. A major limitation is in the lack of an efficient and versatile constitutive description for the composite materials [2] Specifically, the composite load carrying capacity has not mailaddresses:huangzm@mail.tongji.edu.cn,huangzm@beenwellunderstood[3,4].Assuch,asignificantad- om亿ZM. Huang) vancement in composite failure theory is necessary. 0045-7949/02/- see front matter o 2002 Published by Elsevier Science Ltd. PI:S0045-7949(02)00075-5On a general constitutive description for the inelastic and failure behavior of fibrous laminates––Part II: Laminate theory and applications Zheng-Ming Huang Biomaterials Laboratory, Division of bioengineering, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received 10 April 2001; accepted 6 March 2002 Abstract These two parts of papers report systematically a constitutive description for the inelastic and strength behavior of laminated composites reinforced with various fiber preforms. The constitutive relationship is established microme￾chanically, through layer-by-layer analysis. Namely, only the properties of the constituent fiber and matrix materials of the composites are required as input data. In the previous part (Comput. Struct. (submitted)), the lamina theory was presented. Three fundamental quantities of the laminae, i.e. the internal stresses generated in the constituent fiber and matrix materials and the instantaneous compliance matrix, with different fiber preform (including woven, braided, and knitted fabric) reinforcements were explicitly obtained by virtue of the bridging micromechanics model. In the present paper, the laminate stress analysis is shown. The purpose of this analysis is to determine the load shared by each lamina in the laminate, so that the lamina theory can be applied. Incorporation of the constitutive equations into an FEM software package is illustrated. A number of application examples are given in the paper to demonstrate the efficiency of the constitutive theory established. The predictions thus made include: failure envelopes of multidirectional laminates subjected to biaxial in-plane loads, thermo-mechanical cycling stress–strain curves of a titanium metal matrix composite laminate, S–N curves of multilayer knitted fabric reinforced laminates under tensile fatigue, and bending load– deflection plots and ultimate bending strengths of laminated braided fabric reinforced beams subjected to lateral loads. All these predictions are based on the constituent properties which were measured or available independently, and are compared with experimental results. Reasonably good correlations have been found in all the cases. It is expected that the present constitutive relationship can benefit the critical design and strength analysis of a primarily loaded structure made of composite materials.
2002 Published by Elsevier Science Ltd. Keywords: Laminated composite; Textile composite; Metal matrix composite; Composite structure; Mechanical property; Constitutive relationship; In-plane failure; Thermo-mechanical fatigue; Flexural failure; Load–deflection curve; Stiffness discount; Strength prediction; Bridging micromechanics model; FEM structural analysis 1. Introduction Although fiber reinforced composites have been in practice for nearly half a century, and have been recog￾nized as attractive candidates in most modern industries, the usages of them are still relatively limited compared with their counterparts, i.e. homogeneous and isotropic materials such as metals, ceramics, and polymers. A major limitation is in the lack of an efficient and versatile constitutive description for the composite materials [2]. Specifically, the composite load carrying capacity has not been well understood [3,4]. As such, a significant ad￾vancement in composite failure theory is necessary. Computers and Structures 80 (2002) 1177–1199 www.elsevier.com/locate/compstruc E-mail addresses: huangzm@mail.tongji.edu.cn, huangzm@ email.com (Z.-M. Huang). 0045-7949/02/$ - see front matter
2002 Published by Elsevier Science Ltd. PII: S 0 0 4 5 - 7 9 4 9 ( 0 2 ) 0 0 0 7 5 - 5