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

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Table 2.4: Instability loads determined from Southwell plots applied to experimental and finite element results using 0.2 mm initial imperfection. Experiment Finite element analysis Debond length (mm) Debond length (mm) 25.4 38.1 50.8 25.4 38.1 50.8 Core Instability load (kN) Instability load (kN) H45 12.9±1.5 10.1±1.1 6.1±0.9 14.1 8.5 5.6 H100 14.8±0.8 10.5±1.7 8.7±0.6 15.2 11.6 8.8 H200 -- 13±1.2 8.5±0.3 -- 13.8 9 Energy release rate and mode-mixity were determined across the width of the columns. Generally it is assumed that the edges of the columns are under plane stress and the interior is in plane strain. Thus, in the analysis of energy release rate and phase angle a plane stress formulation was adopted for nodes on the specimen edges and a plane strain formulation for the interior points. Figure 2.20 presents the distributions of energy release rate normalised with the interface fracture toughness, Gc, and phase angle across the width of a column with H45 core and 50.8 mm debond. Similar results were obtained for columns with other core materials and debond lengths. Figure 2.20 shows the classical thumb-nail distribution of the energy release rate, normalised with the fracture toughness of the interface, increasing from the edges towards the centre of the specimen. The phase angle also displays a maximum in the interior. The magnitude of the phase angle, however, is minimum in the interior, which means that the loading in the centre is more mode I dominated than the edges. Based on the results shown in Figure 2.20 the debond propagation is expected to initiate in the interior. Thus, in the debond propagation analysis, the plane strain formulation in the centre of the specimen was employed. G/Gc 1.1 1 0.9 0.8 0.7 0 0.2 0.4 0.6 0.8 1 x/b (a) Figure 2.20: Distribution of energy release rate (a) and phase angle (b) across the column width for a column with H45 core and 50.8 mm debond. 34 Phase angle (deg) -21 -22 -23 -24 -25 -26 x/b 0 0.2 0.4 0.6 0.8 1 (b)
Figure 2.21 shows energy release rate and mode-mixity in terms of phase angle vs. load for columns with a 50.8 mm debond and H45, H100 and H200 cores. Figure 2.21 (a) shows that G increases significantly in a certain load regime which can be associated with the opening of the debond. The fracture toughness values shown in Figure 2.21 (a) were determined by the TSD tests, described in Section 4. The reduction of phase angle as the load increases, Figure 2.21 (b), shows that the crack tip loading becomes more shear dominated at high loads. G (J/m 2 ) 1200 800 400 0 H45 H100 H200 (-24º) H45 (-29º) H100 Gc(-29), H100 G c(-24), H45 0 3 6 9 12 Load (kN) (a) Phase angle (deg.) Figure 2.21: (a) Energy release rate vs. load and (b) phase angle vs. load for columns with a 50.8 mm debond and H45, H100 and H200 cores. In order to investigate the influence of the initial imperfection on G and , columns with H100 core and 38.1 mm debond with three initial imperfection magnitudes (0.1, 0.2 and 0.5 mm) were analysed. Figure 2.22 shows G and vs. load for these columns. From Figure 2.22 (a) it is seen that G is not highly sensitive to the initial imperfection magnitude. The phase angle, Figure 2.22 (b), is sensitive to the initial imperfection at small loads, but appears to converge to a value about -30 ° at higher loads, which indicates that the mode-mixity is less influenced by the initial imperfection at higher loads. The crack propagation load was estimated using fracture toughness data from the TSD tests. Energy release rate and mode-mixity in terms of phase angle were determined in the interior (centre) of the columns. Numerically predicted and experimentally determined propagation loads, which means the maximum load in the load vs. axial displacement diagrams (Figure 2.3 (a)), for the debonded columns are listed in Table 2.5. 35 -18 -22 -26 -30 -34 -38 Load (kN) 0 3 6 9 12 (b) H45 H100 H200
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Residual Strength and Fatigue Lifet
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Published in Denmark by Technical U
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Page 8 and 9: method to accelerate the simulation
Page 10 and 11: Synopsis Sandwich kompositter er i
Page 14 and 15: Contents Preface Executive Summary
Page 16 and 17: 5 Face/core Interface Fatigue Crack
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 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 66 and 67: sheet and the core thickness, respe
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
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Debond radius (mm) 100 90 80 70 60
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using the cycle jump method, more t
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Chapter 5 Face/Core Interface Fatig
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of this chapter, sandwich panels wi
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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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