18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS FAILURE ANALYSIS OF ADHESIVELY BONDED JOINTS CONSISTING OF BI-LAYER COMPOSITES M. S. Kim 1* , C. Y. Park 1 and S. M. Jun 1 1 Agency for Defense Development, Daejeon, Korea *castle@add.re.kr Keywords : Double Cantilever Beam, Conformal Load-bearing Antenna Structure, Bonded Joints, Adherend, Cohesive Zone 1. Introduction cantilever beams(DCB) and adhesive layers or adhesive-adherend interfaced layers can be found. The 5 th generation fighter aircraft has been Sridharan and Li studied two distinct cohesive layer known as its invincible super-cruise, invisible models of delamination growth in the DCB. external shape, and low observable radar cross Makhecha et al. analyzed a double cantilever beam section area. Lots of technologies for undetectable under dynamic loading using cohesive zone model. functions were gathered to make outstanding stealth Colavito and Madenci distinguished differences of functions. One of those technologies for stealth failure strength from two kinds of initial cracks aircraft is embedded antenna structure technology. using digital image correlation. Needleman studied Broadband or multiband antenna is embedded in the progressive failure and crack growth using cohesive skin of an aircraft structure that carries aerodynamic elements. Other adhesive joint researches were load. The embedded antenna structure has carried out recently. advantages of lower weight, reduced drag, efficient Among the mechanical phenomena of adhesively aircraft maneuver, greater flexibility in locating bonded joints, this study focuses on a progressively antennas, cost saving, and reduced number of failure and crack propagation analyzed by cohesive antennas, etc, in addition to the stealth function. The zone modeling, i.e. cohesive elements. Especially, antenna also deforms together with the skin this study consider adhesively bonded joints when deformations maintaining antenna performance. This the adherends are made of different materials. To multi-functional embedded antenna structure is obtain a more fundamental view of fracture in called Conformal Load-bearing Antenna Structure damaged structures, it is necessary to introduce a (CLAS). new concept for a fracture process zone, so called CLAS is made of multi-layered composites; each cohesive zone, found in the very weakening bonded layer has different material properties. The interfaces joints. In particular, the focus of this paper is the of these layers are connected using adhesively fracture propagation behavior of brittle typed bonded joints. The failure strength of the interfaces composites that can be characterized taking into is the main issue of design when the CLAS system is account the finite element commercial software; subjected to aerodynamic loads. Invisible small ABAQUS. cracks, delaminations, and interface debonding of To verify the present model of adhesively bonded CLAS should be carefully analyzed and predicted. joints, this study conducts several testing on Glass To find out the failure mechanism of multi layered Fiber Reinforced Polymer(GFRP) and uni- structure(CLAS), this study deals on the bonding directional Carbon Fiber Reinforced Polymer strength of bi-layer specimen. With an application of (CFRP) specimens. The strain and the crack growth bi-layer specimen we perform the DCB test and shape under quasi-static loading are monitored numerical calculation to verify the delamination, during the Mode I DCB tests. After obtaining the crack propagation, and failure. The progressive experimental data and numerical solutions, these failure analysis using cohesive zone modeling results are compared together and then provide a technique was applied for the simulation. detailed explanation of mechanical behavior of From reviewing the previous researches, several composite specimens. analytical and computational approaches for double
2. Cohesive Damage Model Crack propagation is defined based on the energy called the fracture energy that is dissipated as a The plastic zone around crack tip region has been result of the damage process. Damage propagation is analyzed using extended finite element method simulated using the linear fracture energy based on (XFEM), crack tip elements and stress intensity the quadratic criterion : factors, etc. This study introduces cohesive zone æ ö æ ö æ ö G G G model to analyze crack propagation, delamination, ç ÷ + ç ÷ + ç ÷ = I II III 1 (3) ç ÷ ç ÷ ç ÷ and failure of adhesively bonded structure. G G G è ø è ø è ø Ic IIc IIIc Needleman suggested a material separation law based on the components of tractions and These two criteria are expressed in terms of separations in the cohesive zone and introduced the relative displacements between homogeneous points concept of cohesive surfaces as shown in Fig. 1. The of the interface finite element. The fracture energy is symbol a is initial crack, d is displacement, green specified as a material property shown in Eq. (3). zone is cohesive zone that traction forces which is The dependence of fracture energy on the mode can function of infinitesimal displacement D move be specified by analytical forms in terms of energies. toward normal and tangential directions of x-axis in The critical strain energy release rates for each pure Fig.1 mode loading can be written as In this work, the traction separation law of Ref. 1 = s d , = (4) [3] is applied to analyze the interface behavior. The G i I , II , III ic u , i u , i 2 constitutive behavior of crack tip is represented by defining potential function, f D n D of the type ( , ) t d In Eq.(4), the variable means the D and D are normal and tangential jump. where u , i n t corresponding relative displacements at the failure The interface tractions ( T ) across the cohesive zone under each pure and mixed mode loading. The surface are given by the surface energy density , = G ic i I , II , III critical strain energy release rates, , function per unit un-deformed area. are obtained from experiments on the mechanical é ù D property test. After finding the respective fracture 2 2 f = s d - s d - D d + - D d ( / ) n ( / ) e e e 1 e n n ê ú t t max n max n d energy of mode I/II/III, the cohesive modeling is ë û n applied into the commercial finite element package, ¶ f = - T ABAQUS to depict the initiation and growth of (1) ¶ Δ delamination. s In Eq.(1), the variable is used to scale the max normal and the shear cohesive stresses, and the 3. Finite Element Implementation characteristic distance of the normal and the shear To analyze Mode I fracture strength, a cohesive d 0 = d = d stresses are assumed to be , respectively. n t zone modeling is applied. Cohesive elements of A cohesive damage model is used to simulate ABAQUS S/W is implemented to depict the crack propagation. The damage model considers a cohesive zone area. COH3D8 element with 8 nodes quadratic stress criterion to deal with damage and 4 integration points is appropriate for modeling initiation assuming that normal compressive stresses the bonding adhesive. The thickness of cohesive do not induce damage. element can be a finite value or zero. The degree of 2 2 2 æ ö æ ö æ ö freedom of nodes is normal translation and two e e e ç ÷ ç ÷ ç ÷ e ³ + + = I II III 1 , if 0 shear movement. The crack growth of the adhesive ç ÷ ç ÷ ç ÷ I e e e è ø è ø è ø can be simulated using failure loading of the u , I u , II u , III cohesive element. Bottom and top surfaces are 2 2 æ ö æ ö e e ç ÷ ç ÷ + = e £ defined using the 8 nodes, and these surfaces open II III 1 0 , if (2) ç ÷ ç ÷ And e e I when they reach failure load : two surfaces of è ø è ø u , II u , III cohesive elements separate with each other.
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