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

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compared to the 65% efficiency obtained for the simulation of fatigue crack growth in sandwich beams in Chapter 4, the computational efficiency is here more than 33% higher. This is due to a somewhat unrealistic and arbitrary choice of da/dN vs. G relations in the simulations in Chapter 4, where the da/dN vs. G relations were chosen so that the crack reaches the end of the specimens in hundreds of cycles to make the reference simulation of all individual cycles possible. The use of realistic da/dN vs. G relations here makes the crack growth significantly smaller in every cycle and provides room for more cycle jumps in the simulation. Table 5.3: Computational efficiency of the simulations with different control parameters. Control parameter qG=q Number of simulated cycles H45 specimen Saved cycles (%) H100 specimen Saved cycles (%) 0.05 1104 98.896 1096 98.904 0.10 548 99.452 557 99.443 0.15 411 99.589 381 99.619 0.20 312 99.688 323 99.677 0.25 243 99.757 188 99.812 5.3 Fatigue Crack Growth in the Face/Core Interface of Sandwich Panels In this section the 3D fatigue crack growth scheme developed in Chapter 4 is used to simulate fatigue crack growth in debonded sandwich panels with a circular debond at the centre. The simulation results will be compared with fatigue experiments at the end of this section. 5.3.1 Fatigue Experiments on Debonded Panels Five sandwich panels with a circular face/core debond at the centre were manufactured for fatigue experiments. The panel face sheets consist of three layers of Devold AMT DBLT 850 quadraxial glass fibre mats of a total thickness of 2 mm, each with a dry density of 850g/m 2 . The core materials are H45 Divinycell PVC foam with nominal densities of 45 kg/m 3 . The core thickness is 50 mm. The properties of the core materials, taken from the manufacturers’ data sheets (DIAB), and the face materials are given in Table 5.4. Figure 5.34 presents a drawing of the panels, including the dimensions, and an image showing one of the manufactured panels. 114
Figure 5.34: Drawing of debonded sandwich panels with an image of a manufactured panel. Table 5.4: Face and core material properties. Material E (MPa) G (MPa) Face sheet 19400 7400 0.31 Core: H45 50 15 0.33 All specimens were reinforced with wooden inserts at the edges to avoid crushing of the core. The debond was introduced before the resin infusion by inserting a piece of 0.025 mm thick Airtech release film on the core in the centre of the panels and sealing the edges with resin. The test rig consists of welded steel square profiles with a wall thickness of 3 mm. A 4 Mpix Digital Image Correlation (DIC) measurement system (ARAMIS 4M) was placed above the panels to monitor 2D surface strains and displacements in order to estimate the crack growth continuously during the experiments. The test rig was inserted in an MTS 810 servo-hydraulic testing machine with a maximum capacity of 100kN and an integrated T-slot table upon which the test rig was positioned and fixed. However, a smaller 25 kN load cell was used in the experiments to increase the accuracy of the load measurements, see Figure 5.35. To load the centre of the debond using the actuator of the testing machine a hole of a diameter of 6 mm was drilled at the centre through the entire thickness of the panels, and the centre of the debond was bolted to a long steel rod connected to the actuator piston, see Figure 5.37 and 5.38. The panels were fixed to the test rig by twelve steel clamps and four 6 mm thick steel plates as shown in Figure 5.37. To avoid harmful side forces on the testing machine actuator, which may be generated by an uneven debond growth during the fatigue loading, the setup in Figure 5.36 was used. The setup includes a lubricated bronze cylinder in which the actuator piston of the testing machine can move freely. The cylinder is connected to the four columns of the testing machine by adjustable steel arms. In 115 Wood inserts Debond
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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
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5 Face/core Interface Fatigue Crack
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H11 bimaterial constant H22 bimater
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These peculiar damage modes often r
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1.2 Overview of the Thesis In this
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Figure 1.3: Fracture modes, from Be
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In Equations (1.5) and (1.6) H11, H
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Figure 1.6: Schematic illustration
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The compact tension specimen (CT) i
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A Figure 1.10: CSB, DCB, TSD, DCB-U
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Chapter 2 Buckling Driven Face/Core
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(DIC) measurement system (ARAMIS 2M
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corresponds to the onset of debond
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Figure 2.7: Crack kinking into the
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(2.2) where and for plane str
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A modified version of the tilted sa
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previous observations of crack path
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of contact elements (CONTACT173 and
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the debond opening initially increa
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Table 2.4: Instability loads determ
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G (J/m2) 600 400 200 0 H100 IMP=0.1
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Hayman (2007) has described a damag
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Table 3.1: Panel test specimens. La
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sheet and the core thickness, respe
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Load (N) 250 200 150 100 50 0 H130
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Table 3.4: Parameters in the face/c
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was used to monitor 3D surface disp
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arising due to the junction between
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(a) Debonded face sheet Figure 3.16
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Figure 3.19 shows the determined en
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H130 MMB H130 Panel H250 MMB Interf
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3.6 Conclusion In this chapter the
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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
Page 116 and 117: Figure 5.5: Test setup. Initially,
Page 118 and 119: H100 Specimen Fibre bridging Figure
Page 120 and 121: propagation, the crack continues to
Page 122 and 123: Figure 5.14: Kinking of the crack i
Page 124 and 125: Crack length [mm] Crack length [mm]
Page 126 and 127: mode-mixity phase angle was chosen
Page 128 and 129: should be taken into account for a
Page 130 and 131: Figure 5.25: Kinking of the crack i
Page 132 and 133: log (da/dN) (mm/cycle) 10 log G (J/
Page 134 and 135: erroneous extrapolations in the tra
Page 138 and 139: the case of uneven debond growth, t
Page 140 and 141: Load (kN) 2 1.5 1 0.5 0 Panel 1 Pan
Page 142 and 143: Figure 5.42: Zero and ninety degree
Page 144 and 145: G(J/m 2 ) 180 150 210 120 150 100 5
Page 146 and 147: 110 q=qG=0.4 Test #1 100 Test #2 Te
Page 148 and 149: panels were determined for differen
Page 150 and 151: Chapter 6 Conclusion and Future Wor
Page 152 and 153: toughness using MMB fracture toughn
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Page 156 and 157: Development of testing methods for
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Page 160 and 161: Bezazi A., Mahi A. E., Berthelot J.
Page 162 and 163: Kanny K. and Mahfuz H. (2005), Flex
Page 164 and 165: Ratcliffe J. and Cantwell W. J. (20
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Page 168 and 169: Out-of-plane displacement (mm) 1 0.
Page 170 and 171: Out-of-plane displacement (mm) 3 2
Page 172 and 173: A.5 Out-of-plane deflection of Debo
Page 174 and 175: (a) Figure A.14: Out-of-plane defle
Page 176 and 177: (a) (b) Figure A.18: Out-of-plane d
Page 178 and 179: Load (kN) 250 200 150 100 50 250 30
Page 180 and 181: Displacement (mm) 4 3 2 1 0 8 9 (a)
Page 182 and 183: (a) (b) Figure B.11: Out-of-plane d
Page 184 and 185: (a) (b) Figure B.15: Out-of-plane d
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DTU Mechanical Engineering Section
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