Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

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sheet and the core thickness, respectively, Gxz is the shear modulus of the core, Gf is the shear modulus of the face sheet and Ef and Ec are the face and core moduli. Figure 3.2: Mixed mode bending test rig for sandwich specimens. The A, B and D terms are the extensional, coupling and bending stiffnesses of any given laminated beam given by A E h E h f f c c Ec E f B hf hc 2 (3.4) 1 3 2 3 2 D Efhf3hfhcEchc3hfhc 12 (3.5) where K is the elastic foundation modulus Ec b K hc 2 C1, C2 and C3 are compliances of the subbeams defined as (3.8) Saddle P C L 44 L Hinge a (3.3) (3.6) (3.7) (3.9)
is the elastic foundation modulus parameter defined as 3 hf bE f 3K and Ddebpnded and Dintact are the bending stiffness of the debonded and intact parts of the MMB specimen (Quispitupa et al., 2009): 45 (3.10) 2 B D debonded 1 D A (3.11) 3 3 E f hf 2 E f hf Echc Dintact hchf 2 6 12 (3.12) The energy release rate can be expressed as (3.13) When the expressions for the compliance and the energy release rate are known, it is possible to determine the crack length at a given load and deflection and fracture toughness as the crack grows. However, to fully characterise the face/core interface the mode-mixity must be evaluated as well. Since there is no analytical expression for the interface mode-mixity, it is usually determined by use of the finite element method. For static characterisation, the fracture toughness of the interface can be determined by Equation (3.13) and the mode-mixity is evaluated using finite element modelling and the CSDE method as explained before. For fatigue characterisation of the interface, Equation (3.1) is used to determine the crack length from the compliance of the MMB specimens evaluated from the actual applied load and displacement of the test specimen. Fracture testing of the MMB specimens was performed at a cross-head rate of 1 mm/min. Figure 3.3. shows typical load vs. displacement curves for representative loading conditions and specimens. In Figure 3.3 the point where the crack starts to propagate is marked with an open circle (“”). The load vs. displacement curves are fairly linear up to the point of crack propagation. It is seen that the load drops due to a change in the specimen stiffness as the crack propagates. The critical failure load was marked according to the ASTM D6671/D 6671M- 06 recommendation (the load at which the compliance has increased by 5%) and complemented by visual inspection. These critical failure loads (Pc) were used in the determination of the face/core interface fracture toughness (Gc), according to the procedure outlined by Quispitupa et al., (2009).
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Residual Strength and Fatigue Lifet
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Published in Denmark by Technical U
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method to accelerate the simulation
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Synopsis Sandwich kompositter er i
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Contents Preface Executive Summary
Page 16 and 17: 5 Face/core Interface Fatigue Crack
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Page 20 and 21: H11 bimaterial constant H22 bimater
Page 24 and 25: These peculiar damage modes often r
Page 26 and 27: 1.2 Overview of the Thesis In this
Page 28 and 29: Figure 1.3: Fracture modes, from Be
Page 30 and 31: In Equations (1.5) and (1.6) H11, H
Page 32 and 33: Figure 1.6: Schematic illustration
Page 34 and 35: The compact tension specimen (CT) i
Page 36 and 37: A Figure 1.10: CSB, DCB, TSD, DCB-U
Page 38 and 39: Chapter 2 Buckling Driven Face/Core
Page 40 and 41: (DIC) measurement system (ARAMIS 2M
Page 42 and 43: corresponds to the onset of debond
Page 44 and 45: Figure 2.7: Crack kinking into the
Page 46 and 47: (2.2) where and for plane str
Page 48 and 49: A modified version of the tilted sa
Page 50 and 51: previous observations of crack path
Page 52 and 53: of contact elements (CONTACT173 and
Page 54 and 55: the debond opening initially increa
Page 56 and 57: Table 2.4: Instability loads determ
Page 58 and 59: G (J/m2) 600 400 200 0 H100 IMP=0.1
Page 62 and 63: Hayman (2007) has described a damag
Page 64 and 65: Table 3.1: Panel test specimens. La
Page 68 and 69: Load (N) 250 200 150 100 50 0 H130
Page 70 and 71: Table 3.4: Parameters in the face/c
Page 72 and 73: was used to monitor 3D surface disp
Page 74 and 75: arising due to the junction between
Page 76 and 77: (a) Debonded face sheet Figure 3.16
Page 78 and 79: Figure 3.19 shows the determined en
Page 80 and 81: H130 MMB H130 Panel H250 MMB Interf
Page 82 and 83: 3.6 Conclusion In this chapter the
Page 86 and 87: composite laminates under thermal c
Page 88 and 89: S S y( t ) y( t ) ( t ) 2 1 12 2
Page 90 and 91: listed in Table 4.1. The length and
Page 92 and 93: The strain energy release rate, G,
Page 94 and 95: high growth rate of G (see Figure 4
Page 96 and 97: 4.4 Face/Core Fatigue Crack Growth
Page 98 and 99: Debond 310 mm Symmetry B. C. a Figu
Page 100 and 101: B 2 1/ 2 ( S44 S55 S45) (4.17) wh
Page 102 and 103: 75), which illustrates possible ina
Page 104 and 105: Figure 4.18 (a) presents the deflec
Page 106 and 107: Debond radius (mm) 100 90 80 70 60
Page 108 and 109: using the cycle jump method, more t
Page 110 and 111: Chapter 5 Face/Core Interface Fatig
Page 112 and 113: of this chapter, sandwich panels wi
Page 114 and 115: H250 Specimen H100 Specimen H45 Spe
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Figure 5.5: Test setup. Initially,
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H100 Specimen Fibre bridging Figure
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propagation, the crack continues to
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Figure 5.14: Kinking of the crack i
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Crack length [mm] Crack length [mm]
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mode-mixity phase angle was chosen
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should be taken into account for a
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Figure 5.25: Kinking of the crack i
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log (da/dN) (mm/cycle) 10 log G (J/
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erroneous extrapolations in the tra
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compared to the 65% efficiency obta
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the case of uneven debond growth, t
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Load (kN) 2 1.5 1 0.5 0 Panel 1 Pan
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Figure 5.42: Zero and ninety degree
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G(J/m 2 ) 180 150 210 120 150 100 5
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110 q=qG=0.4 Test #1 100 Test #2 Te
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panels were determined for differen
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Chapter 6 Conclusion and Future Wor
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toughness using MMB fracture toughn
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For the specimens with H250 core th
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Development of testing methods for
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Bezazi A., Mahi A. E., Berthelot J.
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Kanny K. and Mahfuz H. (2005), Flex
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Ratcliffe J. and Cantwell W. J. (20
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Out-of-plane displacement (mm) 1 0.
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Out-of-plane displacement (mm) 3 2
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A.5 Out-of-plane deflection of Debo
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(a) Figure A.14: Out-of-plane defle
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(a) (b) Figure A.18: Out-of-plane d
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Load (kN) 250 200 150 100 50 250 30
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Displacement (mm) 4 3 2 1 0 8 9 (a)
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(a) (b) Figure B.11: Out-of-plane d
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(a) (b) Figure B.15: Out-of-plane d
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DTU Mechanical Engineering Section
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