Delamination and debonding failure of laminated composite T-joints

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Summary

Composites are increasingly being used in aerospace, automotive and other industries. The T-joint (also named stringer stiffened skin) is a typical connection, broadly used in thin-walled structures, such as the wing and fuselage of aircraft. This thesis presents the analysis of the delamination and debonding failure of laminated composite T-joints, in support of the design and manufacture of integrated composite structures. Major attention has been paid to expand current knowledge on the failure response of the subcomponents of the T-joints: the through thickness reinforcements and adhesive layers were investigated both numerically and experimentally. Novel experimental methods and computational models have been developed to facilitate the characterization of these subcomponents and the in-depth understanding of the failure mechanisms of these subcomponents. The cohesive zone model has been used widely for modeling various fracture problems of the investigated materials. Novel cohesive laws were developed to represent the complex constitutive responses of these materials, and different mesh distribution strategies were employed as well. Pull-off and bending tests of T-joints were carried out where the failure process and loading capacity were evaluated. On the basis of the knowledge and analysis methods accumulated from the subcomponent studies, the delamination and debonding failure of T-joints has been numerically modeled; comparisons with experimental results have validated the accuracy and reliability of these numerical models. It is believed that this thesis has contributed to better understanding of the delamination and debonding failure of composite T-joints; the knowledge, methods and philosophy outlined here may also be applied to other composite/adhesively bonded structures as well.

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Samenvatting

Composieten worden in toenemende mate gebruikt in the luchtvaart-, ruimtevaart-, automobiel- en andere industrieën. De zogenaamde T-joint (eigenlijk de verbinding tussen huid en verstijver bij bijvoorbeeld vliegtuigvleugels) is een klassieke samenstelling van constructieve elementen, veelvuldig gebruikt in dunwandige constructies. In deze dissertatie presenteren wij de delaminatie en separatie analyse (schade evolutie) van gelamineerde T-verbindingen met als voornaamste doel het faciliteren van het ontwerp en de productie van geïntegreerde composieten constructies. Er is veel aandacht besteed aan het aanvullen van de hedendaagse kennis over bezwijkmechanismen en structurele responsie van de sub componenten van T-joints: de door-de-dikte versterkingen en lijmlagen zijn onderworpen aan uitgebreide experimentele programma’s en numerieke analyse procedures. Nieuwe experimentele en computer-gebaseerde methoden zijn hierbij ontwikkeld om de karakterisering en fundamentele begrip van de bezwijkmechanismen te faciliteren. Het CZM (Cohesive Zone Model) is hierbij veelvuldig gebruikt om het bezwijken in detail te kunnen beschrijven. Nieuwe tractie-separatie curves zijn hierbij ontwikkeld om de complexe materiaal responsies te representeren, en verscheidene discretisatie strategieën zijn hierbij gebruikt. De zogenaamde “Pul-off” en buig experimenten zijn veelvuldig uitgevoerd waarbij het bezwijk proces en schade evolutie van de proefstukken werd geëvalueerd. Gebaseerd op de gegenereerde kennis over deze basiscomponenten, de delaminatie en separatie faalgedrag van de volledige T-joints is hierna gesimuleerd. Door middel van vergelijkingen met experimentele data is de bruikbaarheid, betrouwbaarheid en nauwkeurigheid van de gebruikte numerieke modellen gevalideerd. Op basis van deze vergelijkingen kan er geconcludeerd dat deze dissertatie bijdraagt aan betere begripsvorming over delaminatie en schade propagatie van composiet T-verbindingen. De gepresenteerde kennis, methoden en filosofie kunnen ook op andere, gerelateerde constructie vormen worden toegepast.

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Nomenclature

a crack length

a0 initial crack length

ae equivalent crack length

b specimen width

C specimen compliance

d displacement of loading head

E Young’s modulus

E11 longitudinal Young’s modulus

E22 transverse Young’s modulus

G shear modulus

G13 transverse shear modulus

h adherend beam thickness

JI, GIC mode I fracture energy/critical strain energy release rate

JII, GIIC mode II fracture energy/critical strain energy release rate

JM, GMC mixed mode fracture energy/ critical strain energy release rate

k shear stiffness of adhesive layer

2L beam span length

P concentrated force/load

r nominal mode mix ratio

t adhesive layer thickness

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w opening deformation of adhesive layer

σ tensile stress

σc tensile strength

σ11 longitudinal normal stress

τ shear stress

τc shear strength

σ13 transverse shear stress

φa shear strain of adhesive layer

φ shear strain of laminates at the adherent interface

ϕ phase angle (true mode mix ratio)

ALT adhesive layer theory

BBA building block approach

CBT classical beam theory

CTE crack tip element

CST classical sandwich theory

CZM cohesive zone model

DCB double cantilever beam

DIC Digital image correlation

ECM Equivalent crack method

ENF end notched flexure

FEM finite element model

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XI HLT higher order laminate theory

LEFM linear elastic fracture mechanics

MMB mixed mode bending

OM optical microscopy

SBS short beam shear

SLJ single lap joint

SEM scanning electron microscopy

TTR through thickness reinforcement

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1

Introduction

Chapter 1

1.1 Brief introduction to composites and fracture mechanics

Composites, a combination of materials designed to achieve better overall properties than each of the constituents, is not a new thing emerged in recent years. The philosophy of composite material is even not a unique gift owned by humankind, some resourceful animals are also good at making composites, and they have benefited from it for tens of thousands of years. The nest of the Chinese swallow shown in Figure 1-1ashares some of the same mechanical characteristics as advanced carbon fiber reinforced composites (Figure 1-1b): the matrices (clay or resin) ensure the composites to be integral and protect the reinforcements (straw or carbon fiber) from being affected by the environment; the reinforcements dominate the strength and toughness properties of the composites.

Figure 1-1 (a) “Composite” nest of the Chinese swallow; (b) carbon fiber reinforced epoxy composites

Humankind has been making use of fracture phenomena for more than 2 million years. Brittle solids, such as flint stones, usually crack in terms of cleavage when they are tapped, and sharp edges are formed on the stones as shown in Figure 2-1, which can be used as tools for cutting food or hunting. In fact, the emergence of chipped stone tools, which meant successful application of fracture phenomena, declared the initiation of human civilization: the Paleolithic age. Fracture mechanics (Figure 1-3) was initiated as a

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new discipline by the English aeronautical engineer Griffith in 1921 [1] to explain the failure of brittle solids. In the 1960s, plasticity was incorporated into the field of fracture mechanics [2, 3].

Figure 1-2 Chipped stone tool in Paleolithic age[4]

Figure 1-3 Failure modes defined in fracture mechanics

Although composite materials and the fracture phenomena have been employed by humankind a long time ago, most knowledge about the fracture process of composite materials was accumulated in the last dozens of years attributed to the production and application of advanced composites. Due to the complexity of fracture physics and the strongly nonlinear nature of the fracture response, our knowledge about the failure of composites under various loading conditions remains insufficient. The failure mechanism of composites, which include the detailed formulation of its mechanical response at different sizes ranging from the macro-scale to the nano-scale, is vital for improving the efficiency of composite applications and for developing advanced composite materials.

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1.2 Origin of this thesis project

Figure 1-4 Application of composite materials in commercial airliners

Figure 1-5 Building block approach in composite aircraft structure development

The structural weight of aircraft is a critical issue for the operating cost of commercial airliners. In order to reduce the weight and improve the fuel efficiency of aircraft, the application of composite materials on aircraft structures has increased significantly, see Figure 1-4. During composite structure design and certification processes, the building block approach (BBA) is usually applied [5]. As shown in Figure

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1-5, the BBA comprises analyses and associated tests at various levels of structural complexity, beginning with small coupons and progressing through structural elements, sub-components, components, to finally the complete full-scale structure. Tests at the lower levels of the pyramid are conducted to generate the material properties to feed appropriate analysis methods. By combining testing and analysis, theoretical predictions are validated by tests, test plans are guided by analysis, and the cost of the overall effort is reduced, while the degree of confidence and safety is increased [6]. The benefits from the interaction between experiments and analysis strongly rely on the predictive ability and accuracy of analytical methods.

Figure 1-6 T-joints reinforced in the through thickness direction with (a) Z-pinning and (b) stitching[7]

The T-joint is a typical connection in composite airframes and marine structures [8, 9]. It transfers load between two orthogonally placed members meeting at a joint [10]. The longitudinal strength of carbon fiber reinforced composites is superior to that of aluminum alloys widely used in aircraft structures. However, their strength in the transverse direction is generally weak due to the lack of reinforcement. Accordingly, the efficiency of a T-joint to transfer out of plane load is restricted by the through the thickness performance of composite laminates. Some methods to improve the strength and toughness of composites in through-the–thickness (TT) direction have been developed (Figure 1-6), such as Z-pinning [11], stitching [12] and 3D braiding [13]. Furthermore, the stringer stiffened panel can also be made by bonding the skin and stringer together with an adhesive [14], as shown in Figure 1-7. In the future, thermoplastic components of simple geometric complexity can be thermoformed, which can then be adhesively bonded by robots; the production rate of complex structures is expected to be dramatically improved.

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5 and debonding at the adhesive layer, which is the same phenomenon taking place for many other composite structures and even the adhesive bonding of metal parts. This thesis work focuses on the specific T-joint configuration. The goal of this thesis is to improve the method to analyse the delamination and debonding failure, which is also applicable to other laminated composite structures and adhesively bonded parts.

Figure 1-7 Application of adhesive bonding in composites: (a) laminates for helicopter fuselage, and (b) sandwiches for windmill

Figure 1-8 (a) VCCT methods for modeling delamination [15]; (b) cohesive zone model

1.3 Academic background and research subject

Delamination in laminated composites is often constrained to grow along the preferred interlaminar direction due to anisotropy and non-homogeneity [16]. Some failure analysis methods based only on critical fracture toughness (GIC, GIIC), have been

developed to analysis the growth of delamination, such as the virtual crack closure technology (VCCT) shown in Figure 1-8a and crack tip element (CTE) method. An initial

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crack is required for both VCCT [15] and CTE methods, which hindered its application to the prediction of the initiation of delamination. Cohesive zone models (CZM) shown in Figure 1-8b, originated from the work of Dugdale and Barbenlatt [17], are increasingly used in modeling the damage and fracture of materials [18]. The delamination response of composite laminates is formulated with a traction-separation law in the CZM [19-21], which is described with the following factors: stiffness, strength, fracture energy and its shape [22]. Among these factors, the fracture energy was traditionally considered as most critical for obtaining reliable prediction. Accordingly, the CZM is quite similar to VCCT and CTE from the viewpoint of energy balance, while CZM offers the advantages of predicting crack initiation and the ability to model multiple crack paths [23, 24]. Besides, cohesive elements need to be inserted at the potential crack path to predict the crack growth, which is very convenient for laminated composites as the delamination is constrained at a certain interface. CZM has been used in the prediction of mode I/II and mixed mode delamination of composite structures [9, 22, 25-30]; good correlation between experiments and simulation confirms the applicability of CZM in the delamination analysis.

Figure 1-9 Dependence of dominating cohesive parameters on the size of failure process zone (FPZ)

Failure of adhesive bonding shares the common feature with delamination in laminates: the crack is confined between two substrates and the potential crack path is predictable. CZM has been employed to predict the failure of adhesively bonded structures, and its performance is promising [28, 31-34]. Modern adhesive materials are usually made of toughened polymers, which ensure the ductility and toughness of the adhesive bonding. Hence, there is yet a major difference between adhesive failure and delamination: the size of failure process zone (FPZ). The size of FPZ of adhesive layer is comparable with or even larger than the crack length; each cohesive parameter of the traction-separation law may have significant influence on the accuracy of analysis.

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7 In recent years, some researchers have reported the dependence of CZM simulation on cohesive parameters including the strength and stiffness [35, 36]. This dependence is more significant when the FPZ gets bigger. As summarized in Figure 1-9, the FPZ size of delamination is generally small provided that the bridging effect [37] is not taken into account. Accordingly, the interlaminar failure of laminates can be analyzed within the framework of linear elastic fracture mechanics (LEFM), and the fracture toughness is the single dominating parameter. On the contrary, the damage evolution within the FPZ of adhesive layers may have noticeable influence on the overall structural response, and accurate traction-separation law representing the adhesive response may be vital for reliable analysis of ductile adhesively bonded structures.

Some through-the-thickness reinforcements such as Z-pinning experience large crack open/slip displacements before their complete failure, which is comparable to the thickness of reinforced laminates [38, 39]. The FPZ of Z-pinned laminates are expected to be much bigger than unreinforced laminates, which means the necessity of accurately representing the Z-pin response to achieve correct analysis of Z-pinned composites.

The fracture toughness of composite laminates can be measured with some standard methods such as the double cantilever beam (DCB), end-notch flexural (ENF) and mixed mode bending (MMB) setups on the base of LEFM [40]. The fracture toughness of adhesive bonding is also currently measured with DCB, ENF and MMB tests, despite the challenges in tests such as the monitoring of macro crack tip[41] and the compliance of adhesive layer [42]. However, the single fracture parameter, fracture toughness, may be enough for the analysis of the delamination but is not sufficient for adhesive analysis. Some pioneering studies have been carried out on measuring the local constitutive response of adhesive layers. On the base of the path independence of the J-integral method [43, 44], the differentiation of the energy release rate J with respect to the deformation at initial crack tip δ gives the local constitutive law [45]. The theory was recently used to experimentally measure the mode I, mode II and mixed mode traction-separation law with standard fracture test configurations[42, 44-50].

In this thesis, the following two subjects were paid major attention: (1) Numerical scheme to account for various material combinations and various unpredictable crack paths, as well as the formulation and application of novel traction-separation laws on the base of results from theoretical analysis and experiments. (2) Finite element models and experimental methods to investigate the failure mechanisms and traction-separation laws of through thickness reinforcements and ductile adhesive bonding.

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1.4 Outline of the thesis work

The T-joints investigated in this thesis were manufactured with the following two methods: 1) through thickness reinforcement methods for preform, and co-curing process of CF/epoxy prepregs; 2) adhesive bonding of composite laminates produced with vacuum injection methods. These different configurations were studied here to highlight the most critical considerations during the test and analysis of composite T-joints. The structure of the thesis is presented in Figure 1-10.

The thesis starts with the pull-off test of co-cured T-joints without TT reinforcement in Chapter 2. The loading capacity of T-joints is evaluated, and the failure modes are analyzed with focus on the failure near the fillet. The traditional bilinear traction-separation law is employed to analyze the delamination failure of T-joints. A new element distribution method is developed to predict the random crack path within the fillet.

In Chapter 3, Co-cured T-joints with TT reinforcements are tested under bending loads to evaluate the efficiency of Z-pinning and stitching methods. A theoretical model is developed to predict the improvement of delamination toughness caused by Z-pinning and stitching.

A numerical model for analyzing the bridging mechanisms of Z-pining in composite laminates is presented in Chapter 4. The main failure modes of the Z-pin including debonding between the Z-pin and matrix, where split and rupture of the Z-pin material have been taken into account. The CZM is utilized to simulate splitting and rupturing within the Z-pin. The interfacial contact between the Z-pin and matrix is assumed to be initially bonded, followed by debonding and frictional sliding.

An uncoupled cohesive zone model is developed for modeling the Z-pin response in composite laminates in Chapter 5. The mode I/II bridging response components of the Z-pins are represented by two unrelated traction-separation laws, which allow the mode I/II damage evolution law to be different from each other. The standard mode I, II and mixed mode delamination toughness tests of Z-pinned composite laminates are simulated. The modeling methodology is then used to predict the failure process of Z-pinned composite T-joints.

The second part of the thesis focuses on the adhesively bonded T-joints. Most of the attention is paid to characterize the mechanical response of adhesive layers at various loading conditions.

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9 new beam theory using the short beam shear (SBS) test configuration. A novel higher-order sandwich beam theory is developed to analyze the adhesively bonded beam that consists of two adhered laminates and a single layer of adhesive in between. The closed form analytical solution for the SBS test model of the adhesively bonded beam is obtained in terms of deflection and stress distribution. The present theory is used for calculating the adhesive layer’s shear modulus from the structural compliance.

The end notched flexure (ENF) tests of flexible and ductile adhesively bonded specimen are carried out in Chapter 7. Two different methods for calculating the fracture energy JII are employed: the equivalent crack method (ECM) and the adhesive layer

theory (ALT). The local traction-separation (T-S) laws of the tested adhesive layer are obtained from the measured JII values. The applicability of T-S laws obtained from ECM

and ALT is verified through reproducing the experimental results with FEM.

The mode I traction-separation law of the adhesive layer is measured with DCB test in Chapter 8. Data process methods based on LEFM and the J-integral method are used to evaluate the mode I fracture toughness and the constitutive response. The traction-separation obtained is then used for the simulation of the DCB test.

A new analysis theory is presented in Chapter 9 to measure the mixed mode constitutive law of adhesive bonding. The theory is on the base of J-integral theory and load decomposition, and the mixed mode bending test is employed. The fracture energy and mode I/II constitutive law components are obtained at different mode mix ratios. A comprehensive discussion is carried out with focus on the plastic yielding and initiation of localized damage, and in situ scanning electron microscopy (SEM) is used to analyze the tension/shear deformation mechanisms.

The adhesively bonded T-joints as well as some other composite structures are made and tested under pull-off loading in Chapter 10. On the base of traction-separation laws obtained from Chapter 7-9, a novel cohesive zone model is developed to predict the mixed mode failure of ductile adhesive layers. The present numerical method is validated by reproducing the MMB tests, and further used to simulate the failure process of T-joints.

Conclusions with regard to the thesis work are drawn in Chapter 10. The analysis procedure for composite joints is summarized within the framework of BBA. The limitations of the proposed methodology are discussed, and some recommendations about improving the accuracy of predictive models are given. Besides, the accuracy of cohesive zone is discussed, and some comments about the future development of cohesive zone

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model are given.

Figure 1-10 Outline of the thesis

As concluded in Figure 1-10, the fracture toughness is considered as the only dominating parameters of delamination failure in Chapter 2 and 3, which is within the framework of LEFM. The analytical solution for the adhesively bonded beam is obtained with linear elasticity (LE) in Chapter 5. The nonlinear response of material with large deformation before complete failure is investigated in Chapter 4 and 7-9. Improved cohesive zone models are then developed, and used to predict the failure of T-joints with large FPZ, as presented in Chapter 5 and 10.

1.5 References

[1] A.A. Griffith, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 221 (1921) 163-198. [2] Z.H. Stachurski, Deformation mechanisms and yield strength in amorphous polymers,

Progress in Polymer Science, 22 (1997) 68.

[3] J.R. Rice, A Path independent integral and the approximate analysis of strain concentration by notched and cracks, Journal of Applied Mechanics, 35 (1968) 8.

[4] http://bbs.sssc.cn/viewthread.php?tid=1883838, in, 2012, pp. Chipped stone tools for collections.

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11 [6] P. Feraboli, F. Deleo, B. Wade, M. Rassaian, M. Higgins, A. Byar, M. Reggiani, A. Bonfatti,

L. DeOto, A. Masini, Predictive modeling of an energy-absorbing sandwich structural concept using the building block approach, Composites Part A: Applied Science and Manufacturing, 41 (2010) 774-786.

[7] D.D.R. Cartié, G. Dell’Anno, E. Poulin, I.K. Partridge, 3D reinforcement of stiffener-to-skin T-joints by Z-pinning and tufting, Engineering Fracture Mechanics, 73 (2006) 2532-2540. [8] T.M. Koh, S. Feih, A.P. Mouritz, Experimental determination of the structural properties and

strengthening mechanisms of z-pinned composite T-joints, Composite Structures, 93 (2011) 2222-2230.

[9] J. Chen, E. Ravey, S. Hallett, M. Wisnom, M. Grassi, Prediction of delamination in braided composite T-piece specimens, Composites Science and Technology, 69 (2009) 2363-2367. [10] H. Cui, Y.L. Li, Failure of Composite T-Joints in Bending with Through-the-Thickness

Reinforcement: Stitching Vs Z-Pinning, Key Engineering Materials, 525-526 (2012) 233-236. [11] A.P. Mouritz, Review of z-pinned composite laminates, Composites Part A: Applied Science

and Manufacturing, 38 (2007) 2383-2397.

[12] P.B. Stickler, M. Ramulu, Transverse stitched T-Joints in bending with PR520 resin: initial results, Journal of Reinforced Plastics and Composites, 20 (2001) 65-75.

[13] L.G.H. Stringer, M.J, Through-thickness reinforcement of composites z-pinning, stitching and 3-D Weaving, N/A, (N/A).

[14] S. Feih, H.R. Shercliff, Adhesive and composite failure prediction of single-L joint structures under tensile loading, International Journal of Adhesion and Adhesives, 25 (2005) 47-59. [15] H.X. Li, C.P. Buckley, Evolution of strain localization in glassy polymers: A numerical

study, International Journal of Solids and Structures, 46 (2009) 1607-1623.

[16] F. Greco, P. Lonetti, R. Zinno, An analytical delamination model for laminated plates including bridging effects, International Journal of Solids and Structures, 39 (2002) 29. [17] G.I. Barbenlatt, Concerning equilibrium cracks forming during brittle fracture. The stability

of isolated cracks. Relationships with energetic theories, PMM, 33 (1959) 8.

[18] B.N. Cox, H. Gao, D. Gross, D. Rittel, Modern topics and challenges in dynamic fracture, Journal of the Mechanics and Physics of Solids, 53 (2005) 565-596.

[19] R.R. Settgast, M.M. Rashid, Continuum coupled cohesive zone elements for analysis of fracture in solid bodies, Engineering Fracture Mechanics, 76 (2009) 1614-1635.

[20] N.L. Borg R, Simonsson K., Simulating DCB, ENF and MMB experiments using shell elements and a cohesive zone model, Composites Science and Technology, 64 (2004) 10. [21] L.S.T.M.D.W.A.M.S.J.A.Z. P.D., Mixed-mode cohesive zone models for fracture of an

adhesively bonded polymer-matrix composite, Engineering Fracture Mechanics, 73 (2006). [22] G. Alfano, On the influence of the shape of the interface law on the application of

cohesive-zone models, Composites Science and Technology, 66 (2006) 723-730.

[23] P.W. Harper, S.R. Hallett, Cohesive zone length in numerical simulations of composite delamination, Engineering Fracture Mechanics, 75 (2008) 4774-4792.

[24] F.P. van der Meer, L.J. Sluys, S.R. Hallett, M.R. Wisnom, Computational modeling of complex failure mechanisms in laminates, J Compos Mater, 46 (2011) 603-623.

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progressive delamination, in: 42nd AIAA SDM Conference, Seattle, WA, 2001.

[26] L.R. Jansson. N.E, A damage model for simulation of mixed-mode delamination growth, Composite structures, 53 (2001) 19.

[27] P.P. Camanho, C.G. Dávila, Mixed-mode decohesion finite elements for the simulation of delamination in composite materials, NSSA STI, (2002).

[28] B.B.K. Blackman, H. Hadavinia, A.J. Kinloch, J.G. Williams, The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints, International Journal of Fracture, 119 (2003).

[29] A. Biel, U. Stigh, Effects of constitutive parameters on the accuracy of measured fracture energy using the DCB-specimen, Engineering Fracture Mechanics, 75 (2008) 2968-2983. [30] J. Chen, D. Fox, Numerical investigation into multi-delamination failure of composite

T-piece specimens under mixed mode loading using a modified cohesive model, Composite Structures, 94 (2012) 2010-2016.

[31] K.S. Madhusudhana, R. Narasimhan, Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint, Engineering Fracture Mechanics, 69 (2002).

[32] W.A.M. Gustafson. P. A, The influence of adhesive constitutive parameters in cohesive zone finite element models of adhesively bonded joints, International Journal of Solids and Structures, 46 (2009).

[33] M. Ridha, V.B.C. Tan, T.E. Tay, Traction–separation laws for progressive failure of bonded scarf repair of composite panel, Composite Structures, 93 (2011) 1239-1245.

[34] C.D.M. Liljedahl, A.D. Crocombe, M.A. Wahab, I.A. Ashcroft, Damage modelling of adhesively bonded joints, International Journal of Fracture, 141 (2006) 147-161.

[35] P.W. Harper, L. Sun, S.R. Hallett, A study on the influence of cohesive zone interface element strength parameters on mixed mode behaviour, Composites Part A: Applied Science and Manufacturing, 43 (2012) 722-734.

[36] R.B. Sills, M.D. Thouless, The effect of cohesive-law parameters on mixed-mode fracture, Engineering Fracture Mechanics, (2012).

[37] Z. Suo, G. Bao, B. Fan, Delamination R-curve phenomena due to damage, Journal of Mechanics and Physics of Solids, 40 (1992) 16.

[38] S.-C. Dai, W. Yan, H.-Y. Liu, Y.-W. Mai, Experimental study on z-pin bridging law by pullout test, Composites Science and Technology, 64 (2004) 2451-2457.

[39] M. Meo, F. Achard, M. Grassi, Finite element modelling of bridging micro-mechanics in through-thickness reinforced composite laminates, Composite Structures, 71 (2005) 383-387. [40] A.B. Pereira, A.B. de Morais, Mixed mode I+II interlaminar fracture of carbon/epoxy

laminates, Composites Part A: Applied Science and Manufacturing, 39 (2008) 322-333. [41] M.F.S.F. de Moura, R.D.S.G. Campilho, J.P.M. Gonçalves, Pure mode II fracture

characterization of composite bonded joints, International Journal of Solids and Structures, 46 (2009) 1589-1595.

[42] K.S. Alfredsson, On the instantaneous energy release rate of the end-notch flexure adhesive joint specimen, International Journal of Solids and Structures, 41 (2004) 4787-4807.

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13 Mechanics and Physics of Solids, 40 (1992) 16.

[44] K. Leffler, K.S. Alfredsson, U. Stigh, Shear behaviour of adhesive layers, International Journal of Solids and Structures, 44 (2007) 530-545.

[45] B.F. Sørensen, Cohesive law and notch sensitivity of adhesive joints, Acta Mater, 50 (2002) 9.

[46] J.L. Högberg, U. Stigh, Specimen proposals for mixed mode testing of adhesive layer, Engineering Fracture Mechanics, 73 (2006) 2541-2556.

[47] J.L. Högberg, B.F. Sørensen, U. Stigh, Constitutive behaviour of mixed mode loaded adhesive layer, International Journal of Solids and Structures, 44 (2007) 8335-8354.

[48] Y. Zhu, K.M. Liechti, K. Ravi-Chandar, Direct extraction of rate-dependent traction– separation laws for polyurea/steel interfaces, International Journal of Solids and Structures, 46 (2009) 31-51.

[49] G. Ji, Z. Ouyang, G. Li, Effects of bondline thickness on Mode-II interfacial laws of bonded laminated composite plate, International Journal of Fracture, 168 (2010) 197-207.

[50] G. Ji, Z. Ouyang, G. Li, S. Ibekwe, S.-S. Pang, Effects of adhesive thickness on global and local Mode-I interfacial fracture of bonded joints, International Journal of Solids and Structures, 47 (2010) 2445-2458.

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Part I Co-Cured T-joints

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Pull-off Failure of Co-Cured Composite

T-Chapter 2

Joints

Pull-off tests and a detailed numerical model are presented in this chapter to predict the failure process and the strength of composite T-joints. The cohesive zone model (CZM) is employed to simulate the delamination and crack forming in the structure, including the stochastic crack paths in the filler. A series of simulations were carried out to evaluate the influence of matrix, adhesive, filler (placed in the T-joints) and the radius on the strength of the T-joint. The numerical results show that the nominal stiffness of the whole structure can be affected by the filler. The strength of the matrix, adhesive and filler have great impact on the loading capability, and the failure modes of the structure may change with varying the matrix, adhesive and filler material properties. Increasing the filler radius will raise the pull-off strength of T-joints. The numerical results agree reasonably well with experimental results.

2.1 Introduction

The classical T-joint is composed of composite laminates curved at the root as shown in Figure 2-1, and the radius part is inserted by a filler to form a smooth transition from the T-panel to the base panel. There is growing evidence that damage in the root of the T-joints is a potential source of catastrophic failure and expensive repairs [1].Various T-joints have been designed and investigated experimentally with focus on the failure modes, strength and damage tolerance [1-9]. Touché [9] and Shenoi [8] have tested sandwich T-joints for marine structures. Rao [7] studied T-joints subjected to pull-off load and evaluated their behavior up to ultimate failure in hydrothermal environments. Philips [1] outlined the load transfer mechanisms in single skin T-joints under representative boundary conditions, as well as the failure inception and damage progression under static loading. The T-joint region which is most susceptible to damage under both pull-off loads and three point bending loads is the radius region. Similar results have also been reported by Rispler et al [4]. Vijayaraju [2] found that in the case of failure initiating from the adhesive layer in the radius region, the failure progresses

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towards the skin/stiffener interface eventually leading to separation of the stiffener from the skin.

Besides experimental studies on composite T-joints, theoretical and numerical methods have been developed to analyze the load transfer mechanisms, ultimate strength levels and failure modes, in order to save experimental costs. Anil [3] employed Finite element analysis (FEA) to get the strain distribution in sandwich T-joints, Kesavan [10] and Phillips [1] conducted FEA by placing delamination of different sizes at various locations in the T-joint. Dharmawan [11], Li [12], Allegri [13] and Wang [14] have modeled composite T-joints using virtual crack closure technology (VCCT). The Mode I and II components of the strain energy release rate (SERR) were obtained by using the nodal forces and displacements. The failure loads and debonding propagation behavior was accordingly obtained. Dharmawan [15-16] describes some numerical methods for studying debonding in composite T-Joints using both the VCCT and CTE (Crack Tip Element) method, and proposes a modified CTE model for the T-joints. Cohesive zone models (CZM) have attracted a growing interest in the scientific community to describe failure processes and delamination in particular [17-21]. Compared to VCCT which requires topological information at the crack tip, CZM is able to predict both the crack initiation and propagation. Balzani [22] simulated the delamination between stringer and skin in T-joints under pull-off loads using the cohesive zone model, and demonstrated the applicability of the model to predict delamination in laminated composites as well as skin–stringer separation in stiffened curved composite panels.

Parametric design and analysis methods have been used in a variety of composite applications. The finite element method has been employed to evaluate the strength and damage tolerance of composites T-joints. The effect of geometry of the T-joint on the strain distribution was investigated by Dharmawan [12]. Hawkins [27] also investigated geometry effects, including filler radius and over-laminate thickness for T-joints under pull-off loading, and found that increasing the radius of the filler makes very little difference to the stiffness but significantly raises the ultimate load. Cui et al [24] performed experimental research on T-joints and compared their experimental data with theoretical results, leading to a conclusion similar to that of Hawkins. Rispler [4] carried out experimental and numerical investigations of different filler placed in the root of T-joints subject to pull-off loading, and found that in some cases the T-T-joints with filler are weaker than the ones without filler.

Parametric studies on the failure and strength of T-joints are highly desirable. Numerical simulations are potentially the most attractive tool to evaluate the performance

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19 of such structures as they substitute costly experiments. But existing numerical models cannot characterize the real structure completely since the failure within the filler at the root has not been successfully simulated yet, although it has been shown that the filler has great influence on the strength and failure modes of T-joints [4].

A detailed evaluation of the failure modes of T-joints subject to pull-off loading are carried out in this chapter. The failure process and loading capacity of T-joints were obtained with pull-off tests. A numerical model incorporating failure analysis of the filler was developed. Cohesive elements are employed to simulate the delamination and crack forming. The failure mode and load-displacement curves of the T-joint are predicted with the numerical model and compared with experiments. Based on the validated numerical model, a series of T-joints with different radius, material strength, and filler are analyzed. The effect of these parameters on the failure load and failure modes is then evaluated.

Figure 2-1 Geometry of co-cured T-joint

2.2 Experiments

The composite T-joint investigated here was made up of three T700/QY8911 laminates as shown in Figure 2-1; laminate-1, laminate-2, laminate-3 were connected by co-curing process. Thin epoxy adhesive tapes were placed at the interface to improve the adhesion between laminates. The triangle part at the root was filled with dense foam. The width of the specimen was 50 [mm], the length was 200 [mm] and the height was 120 [mm]. The mechanical properties of the T700/QY8911 laminates are presented in Table

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20

2-1. Laminates 1, 2 were made of 13 layers and the overall thickness was 1.5 [mm]. The layups of both laminates were (-45/0/45/90/-45/0/90/0/45/90/-45/0/45), Laminate 3 had 32 symmetrical layers and an overall thickness of 4 [mm]. The orientation of these layers were (45/0/-45/90/0/45/0/-45/90/0/45/0/-45/0/45/-45)s.

Table 2-1 Mechanical properties of T700/QY8911 laminar

E11 (GPa) E22 (GPa) G12 (GPa) G23 (GPa) v12

135 9.12 5.67 5.9 0.311

The test configuration of the T-joint under pull-off loading is shown in Figure 2-2. The bottom of the specimen was restricted to move in the Y direction and was not permitted to rotate in any direction. The T-joints were loaded at the head by means of prescribed displacements with a constant loading rate of 1 mm/min. The failure process was recorded with a digital camera.

Figure 2-2 Pull-off test configuration for T-joints

2.3 Numerical T-joint model

2.3.1 Geometry and mesh

A finite element model was built according to the pull-off tests of T-joints as shown in Figure 2-3. The composite laminates were meshed with continuum 8-node shell elements (SC8R in ABAQUS). Since experimental results showed that delamination usually occurs at the inboard side of the laminate, layers of cohesive elements with a thickness of 0.005 [mm] were embedded between these composite layers (see in Figure

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21 2-3). Delamination between these layers was then allowed. Cohesive elements were employed to model the crack at the interface between laminates and between the laminates and filler. The Abaqus standard solver was used for the simulation of multiple crack, there was slight difficulty in convergence, and it was treated by assign a viscosity factor to the cohesive elements (v=0.0005)

Figure 2-3 Finite element model for pull-off test of the T-joint

A dense foam material was used to fill the root in the T-joints, which is an isotropic elastomer made of epoxy and particle reinforcements. There is no predictable crack path within the filler, as the crack could propagate in any location of the filler. In this study, the cohesive elements were distributed over the whole filler to predict stochastic crack paths in the filler [25] as shown in Figure 2-4. All bulk elements in the filler were surrounded by cohesive elements as sketched in Figure 2-5a. The filler was meshed with 8-node, three-dimensional elements (C3D8); 8-node, three-dimensional cohesive elements (COH3D8) were inserted between every neighboring bulk element. Nodes at interface between laminates and foam were connected with the “Tie” constraint in Abaqus, which ensured the continuous displacement and stress of neighboring nodes.

The cohesive elements topology and node distribution are sketched in Figure 2-5b. Node 1, 2, 3, 4 have the same coordinates. Node 1 and node 2 belong to two neighboring bulk elements, and these two elements are connected by a cohesive element with nodes 1, 2. One bulk element has different nodes with the other elements nearby, while these nodes have the same coordinates at the corresponding location. The stress is transmitted by the embedded cohesive element. Since the cohesive elements are able to be deleted once the failure criteria are satisfied, stochastic crack forming can indeed be captured.

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Figure 2-4 Mesh distribution in the filler; (a) bulk elements for foaming rubber, (b) cohesive elements for crack simulation

Figure 2-5 (a) Bulk element surrounded by cohesive elements; (b) Nodes distribution of cohesive and bulk elements

2.3.2 Cohesive zone model

Cohesive elements were inserted into the interface where crack or delamination may take place as presented in the previous section. The element is deleted once the stress is reduced to zero, leading to the formation of a new crack area [21]. The constitutive response of cohesive element includes damage initiation and evolution. Various cohesive laws of different shapes have been introduced, such as bilinear, linear-parabolic, exponential and trapezoidal [18]. A bilinear cohesive law is used in this chapter, as shown in Figure 2-6.

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Figure 2-6 Bilinear cohesive law

The cohesive law is defined in terms of traction versus separation (displacement of cohesive element) curve. The bilinear cohesive law assumes initially linear elastic behavior followed by damage initiation and stiffness degradation. Initially, the stress increases linearly with the relative displacement. The degradation begins when the stresses satisfy certain damage initiation criteria. In this chapter, a quadratic nominal stress criterion is used [17-19]:

2 2 1 c c









              (2.1)

Here, σc and τc are the mode I and II interlaminar strengths. Means a (a a) 2, hence the normal compression stress has no effect on damage. Once the element satisfies the damage initiation criteria, progressive degradation of stiffness will occur. A parameter D is introduced to represent the overall damage in the material. D evolves monotonically from 0 to 1 upon further loading after the initiation of damage. The stress components of the element are affected by the damage according to:

(1 D) _c

    (2.2) A mixed mode failure criterion is introduced to estimate complete failure of the element after stiffness degradation:

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24 I II IIC IIC 1 G G G G                 (2.3) GiC is the critical strain energy release rate per unit length of material under mode I

loading, α is the power coefficient, normally in the range from 1 to 2, here it is chosen as 1, parametric analysis found that the α has slight influence on the simulation results. The element is deleted when it fulfills the damage criteria, and new crack forming or delamination takes place.

The critical strain energy release rate (GiC) of the cohesive element was determined

by delamination tests of carbon fiber reinforced QY8911 laminates [26]. The interfacial strength has rarely been determined by experiments due to the lack of reliable test methods. Empirical strength values were often used for simulation in former research [21]. It has been shown that the interfacial strength value has negligible influence on the obtained results [18-20] provided that the failure process zone (FPZ) is small compared to the crack size. A lower strength value was generally beneficial for improving calculation convergence and reducing computer cost [20]. Here, a comparatively lower strength was used as presented in Table 2-2. The adhesive film at the interface of the laminates is made of epoxy resin. It was assumed that they have the same properties as the composite resin matrix.

The cohesive stiffness was usually chosen empirically. Very high values of the interface stiffness may cause numerical difficulties, such as oscillations of the tractions; while artificial elastic deformations may come into play when the interface stiffness is too law [20]. The dummy cohesive stiffness was chosen as given in Table 2-2, which ensured the convergence of computation without causing degradation of overall structural stiffness.

The foaming rubber for filling the triangle was mode of epoxy and reinforcements, however, its mechanical properties were unknown. It was considered to be the same as QY8911 epoxy, and the Young’s modulus was 3000 [MPa]. The cohesive parameters for in filler were assumed to be the same as the interlaminar CZM. The influence of filler performance on the overall behavior of the T-joints was evaluated in Section 2.5.

Table 2-2 Cohesive properties for delamination of T300/QY8911 KN KS σc [MPa] τc [MPa] GIC [N/mm] GIIC [N/mm]

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2.4 Results and discussion

The failure process of the T-joint is presented in Figure 2-7. The crack appears at the top of the radius firstly, and propagates along the adhesive layer at the interface. The crack transfers into the filler and then develops downwards until reaching the bottom. Horizontal cracking occurs at the interface between filler and laminate-3, which triggers the final failure of the structure. The simulation agrees with the experiments quite well.

Figure 2-7 Failure mode of composite T-joint under pull-off load

Both the experimental and numerical load-displacement curves are sketched in Figure 2-8. The experimental pull-off load increased monotonically with displacement, which dropped sharply once the maximum load was reached. Some “zig-zag” can be obtained on the experimental curves, due to the unstable crack propagation process. The numerical results agree quite well with the experimental curves before damage initiation. The ultimate strength is nearly the same in both simulation and experiments. The structural stiffness in the simulation degrades before reaching the ultimate load; this is caused by the considerable number of cohesive elements that have already induced stiffness degradation (see FEM-1 in Figure 2-8). Hence, the FPZ in FEM was bigger than

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26

the true FPZ in tests due to the low cohesive strength. The point where the structure stiffness reduces is postponed when the strength of the cohesive elements is increased by a factor of 1.5 and keeping the fracture toughness constant (see FEM-2 in Figure 2-8). However, the structural load carrying capacity has no distinct improvement, which implies that the critical strain energy release rate was the dominating parameter for the cohesive elements in numerical simulations. A reasonably good prediction can be reached for the investigated T-joints here with an empirically determined cohesive strength. The numerical curve differs from the experiments only after damage occurrence.

Figure 2-8 Load-displacement curve of composite T-joint

Figure 2-9 Fiber bridging at the interface of laminates

The experiments showed that the T-joint was able to carry a higher load than that at the moment of damage initiation. There is no such increase of loading capacity in the simulation results. The fracture surface of the specimen can be employed to explain this difference. Fracture propagates mainly in the form of delamination and cracks in the resin

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27 at the initial phase of the failure process, which results in small FPZ. Hence, the bilinear cohesive law with a single dominating parameter, the critical strain energy release rate, was capable of analyzing the damage initiation of T-joints here. But the failure process becomes very complex as the fracture propagates, and effects like fiber bridging (see Figure 2-9) and rupture during fracture came into play, which result in much bigger FPZ than the initial FPZ controlled by matrix properties. Hence, the fracture energy is not sufficient to take into account all these fracture mechanisms. An improved cohesive law may be necessary to predict the large scale growth of delamination during the failure of composite structures.

2.5 Parametric evaluations

Based on the present numerical model, the influence of various T-joint design parameters on the performance of T-joints were evaluated in this section.

Figure 2-10 Dependence of T-joint stiffness on filler modulus

2.5.1 Influence of filler on the stiffness of T-joints

Several kinds of material were used to fill the triangle of T-joints, such as the foaming epoxy in this chapter and unidirectional tapes. The stiffness and strength of the filler may have noticeable effect on the overall response of T-joints. The pull-off stiffness of T-joints, defined as the slope of the linear part of the load-displacement curve, was evaluated here as function of the Young’s Modulus of the filler. The geometry of the T-joint model was constant in all simulations here. The overall stiffness increased linearly with the filler stiffness when the filler modulus is less than 1 [GPa], as shown in Figure

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2-10, and the overall stiffness is almost the same when the Young’s modulus of the filler is above 3000 [MPa]. It can be concluded that the filler affects the stiffness of the entire T-joints to a certain extent. This influence becomes negligible when the Young’s modulus of the filler is higher than 3000 [MPa].

2.5.2 Influence of filler stiffness and radius on the strength

The influence of corner radius and filler stiffness on the strength of T-joints is investigated in this section. A series of T-joints with different radii and filler stiffness were simulated under pull-off load. The pull-off strength of T-joints is presented in Figure 2-11. The loading capacity of T-joints increases with the radius when the filler stiffness is above 300 [MPa], which was also concluded by Pei [29] and Hawkins [27]. However, the loading capacity is not significantly affected by the radius of corner when the stiffness of the filler is low. The capacity is nearly the same at different stiffness values when the radius is equal to 4 [mm]. Hence, different fillers should be used for T-joints with a different radius to get the best pull-off strength.

Figure 2-11 Loading capacity changes with the radius and stiffness of filler

2.5.3 Influence of cohesive parameters on the strength of T-joints.

As presented in Figure 2-7, the damage in the specimen tested initiates close to the triangle part of the T-joints. The filler strength, the interlaminar strength and the strength of the co-curing interface may have significant influence on the pull-off strength of T-joints. A series of simulations were carried out in which the strength and GC of cohesive elements between the layers of the laminates and at the co-curing interface (CZM-A) were gradually reduced, while keeping the filler properties constant. Another series of

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29 simulations were carried out with reducing the strength and GC of the filler (CZM-B), while keeping the cohesive parameters of the matrix and adhesive constant. The numerical results are presented in Figure 2-12. The mechanical properties of the co-curing interface and laminates have more impact on the loading capacity than the filler has, which is similar to the conclusion presented by Adrian R. Rispler [4].

Figure 2-12 Loading capacity--material properties curve

Figure 2-13 Failure modes of T-joints with different cohesive parameters

The dependence of the failure modes of T-joints on the material strength is shown in Figure 2-13. It can be observed that the locations of the failure initiation are similarly right above the filler area, which is similar to the experimental results obtained by Pointer [28]. The crack propagation changed for different properties of filler, matrix and adhesive. The crack develops at the interface in terms of debonding when the adhesive is much weaker than the filler (Figure 2-13a). On the other hand, multiple cracks occur in

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the filler when it is weaker than the adhesive film and resin matrix. The failure mode is nearly the same when the difference of strength and GC between resin, adhesive and filler is less than 20%.

2.6 Conclusions

Co-cured composite T-joints have been tested under pull-off load in this chapter; the loading capacity was evaluated, and the failure process was analyzed.

A detailed numerical model on the base of CZM has been developed to simulate the failure process of T-joints in pull off load. Delamination, debonding in the laminates and cracks in the filler are incorporated in the analysis. A reasonably good agreement between the numerical model and the experiments can be observed. The model has been demonstrated as applicable to predict a stochastic crack by forming cohesive element between every two neighboring solid elements. The parametric evaluation was carried out based on this numerical model.

The performance of the present method to predict stochastic crack was indeed limited by the mesh distribution method. An irregular mesh (cohesive elements of different angles and sizes) would be better for the prediction of stochastic crack paths. The mesh of the filler here was generated with a C program, and the algorithm was very simple, which results in a dense mesh in the centre. The mesh in the vertical centre of the filler was not necessary to be so dense, while the mesh near the edge should be finer. The mesh distribution could be further refined to improve the capability to predict stochastic crack paths

It can be concluded that the filler stiffness influences the nominal stiffness of the whole structure to a certain extent. The pull-off strength of T-joint increased as the radius is increasing in most cases; this may also be influenced significantly by the filler stiffness. A larger radius may be beneficial in terms of pull-off strength when the filler stiffness is higher than 300 [MPa]; however, a smaller radius can increase the pull-off strength when the filler stiffness is low.

A bilinear cohesive law was used in this study, in which the critical strain energy release rate was the only parameter that was obtained from existing DCB and ENF test results, and the critical strength was chosen empirically. The cohesive laws selected have been proven to be able to predict the initiation of damage and small scale crack propagation in T-joints. However, due to fiber bridging and rupturing at the delamination surface, the present model is not able to predict the failure response of T-joints with large

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31 scale crack growth. Although the measurement of the fiber bridging effect and implementation of it into FEM is out of the scope of the thesis, the failure of through thickness reinforced T-joints is investigated in the next three chapters, where corresponding analysis methods are developed as well.

2.7 References

1. H. J. Phillips, R. A. Shenoi. Damage tolerance of laminated tee joints in FRP structures. Composites Part A, Vol. 29; pp 465-478, 1998.

2. K. Vijayaraju, P. D. Mangalgiri and B. Dattaguru. Experimental study of failure and failure progression in T-stiffened skins. Composite Structures, Vol. 64, pp227-234, 2004.

3. E. A. Diler, C. Ozes, G. Neser. Effect of T-joint geometry on the performance of a GRP/PVC sandwich system subjected to tension. Journal of Reinforced Plastics and Composites, Vol. 28, pp 49-57, 2009.

4. A. R. Rispler, G.P. Steven and L. Tong, Failure analysis of composite T-joint including inserts. Journal of Reinforced Plastics and Composites, Vol. 16, pp 1642-1658, 1997.

5. M. D. Banea，L. F. M. da Silva. Adhesively bonded joints in composite materials: an overview, Proc. IMechE Part L: J. Vol. 223, Materials: Design and Applications, 2009. 6. Pei junhou, R.A.Shenoi. Detailed research review of the performance characteristic of out of

plane FRP marine structure. Ship science report 83, July, 1994. ISSN :0140-3818.

7. V. V. S. Rao, K. Krishna Veni, and P. K. Sinha. Behaviour of composite wing T-joints in hygrothermal environments. Aircraft Engineering and Aerospace Technology, Vol. 76, pp 404-413, 2004.

8. R. A. Shenoi, P. J .C. L. Read, and C. L. Jackson. Influence of joint geometry and load regimes on sandwich tee joint behavior. Journal of Reinforced Plastics and Composites, Vol. 17, pp 725-740, 1998.

9. L. Hamitouche, Mostapha Tarfaoui and Alain Vautrin. Design and Test of a Sandwich T-Joint for Naval Ships. Damage and Fracture Mechanics: Failure Analysis of Engineering. Materials and Structures, 131–141.

10. A. Kesavan, M. Deivasigamani, S. John and I. Herszberg. Damage detection in T-joint composite structures. Composite Structures, Vol. 75, pp 313-320, 2006.

11. H. C. H. Li, F. Dharmawan, I. Herszberg and S. John. Fracture behavior of composite maritime T-joints Composite Structures, Vol. 75, pp 339-350, 2006.

12. Ferry Dharmawa，Rodney S. Thomson , Henry Li，Israel Herszberg and Evan Gellert. Geometry and damage effects in a composite marine T-joint. Composite Structures, Vol 66, pp 181–187, 2004.

13. G. Allegri, X. Zhang. On the delamination suppression in structural T-fiber pinning. Composites Part A: Applied Science and Manufacturing, Vol. 38, pp 1107-1115, 2007.

14. M. Wang, Z. Li and R. Bai. Delamination growth characteristics for composite grid stiffened plates [J]. Journal of Jilin University(Engineering and Technology Edition) Vol. 01—0229— 051, pp 671—5497, 2007.