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Over the last decade, the use of fibremetal laminates (FMLs), such as glass fibre reinforced aluminum laminate(GLARE), is increasing in the manufacturing of aerospace structures toreduce weight and as a result to reduce emissions. In particular, GLARE is aFML made of several very thin layers of metal (usually aluminum) and interspersedplies of glass reinforced composite materials, bonded together with a matrixsuch as epoxy. FMLs have slow crack propagation and a good damage-tolerance tofatigue in aerospace structures. Glare is used in fuselageof Airbus A380 and the leading edge surfaces of the vertical and horizontaltail planes in the Airbus A380. Due to the nature of the industry, severetesting of components is required. This is an expensive task, requiring a largenumber of tests to achieve certification, and is complicated further by thenature of anisotropic materials. In general, the CAD and Ansys software havemade analysis of FMLs cheaper and attractive for practising engineers incomparison with experimentation.

From a computational point of view, the modellingof delamination in FMLs involve special features which make the taskchallenging as many of the necessary numerical strategies are still indevelopment. For instance, modelling discontinuities, mixeddamage modes, nonlinear interfaces, initiation and propagation of cracks etc.These techniques cause often divergence of the numerical procedure.Thegoal of this research is to use finite element methods to develop computationalmodels which can accurately replicate behavior to complement physical testing,in order to reduce the cost and time involved in testing.

However, finiteelement analyses are very expensive in terms of computational cost if extensiveremeshing is necessary, as in the case of dynamic crack propagation. Therelatively new Extended Finite Element Method (XFEM) solves this problemhowever, as no remeshing is necessary.Thisresearch aims to investigate, by means of the Extended Finite Element Method(XFEM), the mechanisms of fracture and crack propagation in advanced compositestructures such as fibre metal laminates (FML) used in the aerospaceindustries.  1.     ProblemStatementExperimental testing of compositematerials is an expensive task and finite element analyses are also veryexpensive in terms of computational cost if extensive remeshing is necessary,as in the case of dynamic crack propagation.

Extended Finite Element Method(XFEM) solves this problem as no remeshing is necessary. 2.     ObjectivesThe objective of this research are:a)     To investigate the stress intensityfactors into a GLARE 3 laminated plate subjected to biaxial loading by means ofXFEM.b)     To simulate the initiation and evolutionof a three-dimensional crack.

Specific challenges such as the 3D crackinitiation, based on a principal stress criterion, and its front propagation,in perpendicular to the principal stress direction will be convenientlyaddressed. c)     To validate the computational outcomesby means of comparison with theoretical and experimental results. 3.     ScopeThescope of work include the study of complex crack propagation problems like crackinitiation, its evolution path, velocity and the value of applied stress whichproduces the failure of the specimen on GLARE 3 laminated plate specimen subjectedto a biaxial loading scenario by means of extended finite element method (XFEM).                3.1  FibreMetal Laminate (FML)FibreMetal Laminate (FML) is a family of hybrid composite structure formed from the        combination of metal layers sandwichinga fibre-reinforced plastic layer. The metal currently being used is eitheraluminum, magnesium or titanium, and the fibre-reinforced layer is eitherglass-reinforced, carbon-reinforced or kevlar-reinforced composite. 1 Typicalclassification of FMLs is shown in figure 1.

1.                                        Figure 1.1       Typical classification of FMLsIn1978, ARALL has been developed at the Faculty of Aerospace Engineering at theDelft University of Technology in Netherland. In 1982 the first commercialproduct under the trade name ARALL was launched by ALCOA.

  ARALLlaminates are made of high strength aramid fibres embedded in a structuralepoxy adhesive sandwiched between multiple layers of thin aluminium alloy sheets.A schematic presentation of ARALL is shown in fig. 1.2               Figure 1.2 Schematicpresentation of Fibre Metal Laminate (ARALL 2)ARALLlaminates offer many advantages such as high strength and excellent fatigueproperties. Moreover, they retain the advantages of aluminium alloys, namelylower cost, easy machining, forming, and mechanical fastening abilities, aswell as substantial ductility. Commercially available ARALL laminates are shownin table 1.1.

 Table 1.1 Commercially available ARALLlaminates   Metal type Cure resin Cure Temp. Stretching Characteristics ARALL 1 7075-T6 AF-163-2 120 oC 0.4% permanent stretch Superior fatigue resistance High strength ARALL2 2024-T3 AF-163-2 120 oC With or without 0.4% stretch Excellent fatigue resistance Increased formability Damage tolerant ARALL3 7475-T76 AF-163-2 120 oC 0.4% permanent stretch Superior fatigue resistance Controlled toughness ARALL4 2024-T8 AF-191 175 oC With or without 0.

4% stretch Excellent fatigue Resistance Increased elevated Temperature properties GLARElaminates belong to fibre metal laminates family, they consist of alternatinglayers of unidirectional glass fibre reinforced pregregs and high strengthaluminium alloy sheets. Schematic illustration of a cross-ply GLARE laminate isshown in figure 1.3 .               Figure 1.3 Schematic illustration of across-ply GLARE laminatesAtfirst, they were developed for aeronautical applications as an improvement ofARALL with advanced glass fibre and introduced at the Technical University ofDelft in Netherlands in 1990. Commercially available GLARE and ARALL laminatesare shown in table 1.

12 Table1.2 Commercially available GLARE laminates Both ARALL and GLARE laminates are now beingused as structural materials in aircrafts.FibreMetal Laminates have been successfully introduced into the Airbus A380. ARALLhas                   been developed forthe lower wing skin panels of the former Fokker 27 aircraft and the cargo        door of the Boeing C-17. ARALL 3material is currently in production and flight test on the C-17 cargo doors andGLARE is selected for the Boeing 777 impact resistant bulk cargo floor. 2           3.2  ExtendedFinite Element Method (XFEM)                                                The extended finite element method (XFEM) developedto alleviate shortcomings of the finite element method and has been used tomodel the propagation of various discontinuities: strong (cracks) and weak(material interfaces). The idea behind XFEM is to retain most advantages ofmeshfree methods while alleviating their negative sides.

Alimitation is observed when using FEM for simulating moving cracks throughout astructure. To accurate represent discontinuities with FEM, it becomes necessaryto conform the discretisation to the discontinuity. Then, in the case of crackpropagation, the mesh is re-generated at each crack-growth increment with aconsiderable computational cost. Over the last decades several approaches formodelling material discontinuities have been proposed based on the partition ofunity concept, as the Generalized Finite Element Method (GFEM) or the XFEM  developed by Belytschko and Black in 1999 andimproved by Moes et al. In particular, XFEM has been a robust numericaltechnique for modelling fracture. 3

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