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NGHieNCCfU-TRAODOl STUDY ON CONSISTENCE OF USING COHEZIVE ZONE MODELTO SIMULATE DELAMINATION PROPAGATION IN MIXED MODE UNDER FATIGUE LOADING IN LAMINATED COMPOSITE J MATERIAL BY USING SAMCEF® SOFTWARE NGHIEN Ciru BO TIN CAY CUA VIEC CTNG DUNG MO HINH VUNG LIEN KET DE MO PHONG Slj PHAT TRIEN TACH L O P THEO KIEU HON HQP DU-CSl TAC DUNG CUA TAI MOI TRONG VAT LIEU COMPOSITE XEP LOP BANG P H A N M E M SAMCEF® ThS Nguyen Hii Nam, TS Ph?m Chung Hpc vien Ky thugt Quan su ABSTRACT This paper presents a study on consistence of using eohezive zone model to simulate delamination propagation in mixed mode under fatigue loading in laminated composite material by using SAMCEF® software Virtual mixed mode bending tests of delamination are performed Compositefiniteelement and interfacefiniteelement are used to model the specimen of the lest Constitutive law of interface element is constructed and added to SAMCEF® material library Simulation and analytical results are compared Keywords: Delamination, laminated composite, eohezive-zone model, interface element mixed-mode bending test T M TAT Bdi bdo trinh bdy nghien cOu stt on dfnh eua vigc sie dung md hinh vimg lien kit de md phdng Slf phdt Irien Idch l&p Iheo kieu hdn hgp, du&i Ide dung cua tdi mdi vgt ligu compos xep l&p bdng phdn mim SAMCEF® Cde thii nghigm udn kiiu hon hgp dlegc thifc hign Cd phdn ta hieu hgn kieu composite vd kieu be mat dugc sir dung di md hinh hda vgt mdu thi nghigm Quy lugl cdu thdnh phdn tti bi mgt dupc xay dung vd dupe tich hpp vdo thu vign vdt lifii eua SAMCEF® Ket qud md phdng dupe so sdnh v&i ket qud ly thuyit Tir khoa: Tdch l&p, composite xep l&p, md hinh vimg lien kit, phan tie Iri mat, thie nghig udn kieu hdn hpp ISSN 0866-7056 TAP CHl CO KHl V1$T NAM, Sd nim 2016 www.cokhivietnam.vn NGHieNCCrU-TRAOeOl II of delamination of composite laminated specimens INTRODUCTION Delamination is one of the most common types of damage in laminated fibrereinforced composites due to theu relatively weak interlaminar strengths[l].There are pure modes of delamination growth in essentially unidirectional carbon-fiber composites: Mode I (opening mode), mode II (shearing mode) mode in (twisting mode) as shown in Fig Mode I Mode U Mode HI Fig Standard delamination modes Delamination growth under fatigue loads in real composite components generally develops in mixed-mode 1/n The mode III contribution in delamination growth is not considered because it is typically quite small for composite structures due to the constraints of adjacent plies It is therefore important to develop methods that can characterize subcritical, mixed-mode growth in fatigue delamination [2] One of the models widely used for numerical simulation of delamilation in composite material is cohesive zone model (CZM) This model assumes the existence of a zone at the tip of the delaminated area where stresses are not zero and relative displacements can occur[3].Aspecial type of finite element, the interface element, is used to implement this model into numerical simulation The aun of this work is to study the consistence of using CZM for numerical modeling of delamination propagation under fatigue behaviour by using SAMCEF® to perform virtual tests for mixed mode 1/ THEORETICAL BACKGROUND 2.1 Numerical representation of the CZM The basic hypothesis of the CZM is that all the inelastic effects that occur at the vicinity of a crack can be lumped into a siorface - the cohesive damage zone Cohesive damage zone models relate tractions T to displacement at an interface where a crack develops Cohesive finite elements capture the initiation and propagation of delamination using the concept of CZM [3] The constitutive law used here is a bilinear relation between the tractions and the displacements as shown m Fig Thefirstpart of this relation is linear elastic with the slope Kthat ensures a stiff connection between the surfaces of the material discontinuity before damage onset d 6 Fig TYaction-displacement law The interfacial strength T^ and the penalty stif&iess define an onset displacement, d^, related to the initiation of damage When the area under the traction-displacement relation is equal to the fracture toughness G^.thc traction is reduced to zero and new crack surfaces are formed The new crack surfaces are completely formed when the displacement is equal to, or greater than, thefinaldisplacement [3] 2.2 Interface element Finite elements are used to model the resin rich layers between lamina of the •• ISSN 0866 - 7056 TAP CHl CO KHl V I £ T NAM S6 nam 2016 www.cokhivietnam.vn NGHIEN CCrU-TRAO l composite These elementsmodel a distribution of non-linear springs connecting upperand lower lamina The springs exert a reaction force on the connected lamina, simulating the cohesive effects of the matrix material which the tesin layer is principally composed of This reaction force is proportional to the displacement of the interface element [4] _^fc7 Fig MMB apparatus Mode I and mode II components of energy release rate are linked by the following expression, [6] G, Fig Displacement of interface element As shown in Fig 3, when upper and lower lamina are displaced, their relative displacement result in normal (Mode I, 5^) and shear (Mode ll, 8^) deformation fiom the initial state of the interface elements, and become the normal 5^ and 5^ tangential spring displacements respectively, which are related to a proportional nomial and shear element stiffness; the element stiffness being defined by a spring displacement/traction behavioural law of bilinear form All finite element simulations were carried out in the FEA package SAMCEF® There is already an interface finite element model contained in the SAMCEF& library The bilinear behavioural law however, is not available as a standard material law Therefore, it is left to construct the behavioural law using a user defined material subroutine 23 Mixed mode bending test The mixed mode bending (MMB) test configiu^tion is schematically shown in Figure 3 Ga 4(3c-Lf 3{c + Lf Since the mode 111 energy release rate can be neglected,mode mixture can be written as: R=^G Gi+G„ 3c'+6ic+3f 39c -ISLc+Ti' It can be seen thatmode mixture depends on lever arm c That means that it is possible to set the value ofc to obtain desired mode mixture by using following expression: c= + 9R + Sj3Ril-R) 39fi-3 FATIGUE TEST USING INTERFACE ELEMENTS In real MMB test, a 3D specimen of width b is used In the present work, the model of specimen is of 2D shape But it can be considered as a 3D specimen with the widtk equal to unity Finite element (FE) model of MMB apparatus is shown in Fig ISSN 0866-7056 TAP CHl CO KHl VI$T NAM, Sd nim 2016 www.cokhivietnam.vn NGHIEN CLfU-TRAO D O I is kept constant and fatigue load is imposed by defining material properties of interface elements Speed of fatigue load is 1000 cycles/s S,mm i t,s Fig.6 Load-point displacement Fig FE model of MMB apparatus The model is meshed using rectangular elements of different sizes as shown in Fig Composite layers are modeled by using ^ i ^ ^ ^ P ^ element while resin layer where
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