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

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4.4 Face/Core Fatigue Crack Growth in Sandwich Panels In this section the 2D fatigue crack growth finite element routine is further developed to account for 3D fatigue crack growth. Here, instead of having a crack tip and one point of crack propagation, a crack front propagates in different points in different directions. As schematically described in Figure 4.10, an iterative procedure is devised to couple the debond propagation routine and the cycle jump method, including a control criterion to ensure accuracy and computational efficiency of the simulation as described earlier in this chapter. Figure 4.10: Route diagram of the 3D fatigue debond growth and cycle jump routines. Initially, a set of station points defining the debond shape is chosen and the finite element model of the debonded panel is generated. The debond front is defined by passing a spline through the station points. To evaluate the direction of debond propagation, the normal and tangential directions of the debond front at each station point are determined and an orthogonal mesh at the debond front is imposed. The debond only propagates at the station points used to define the debond front. The finite element model is solved for the first three cycles. The strain energy 74
elease rate and mode-mixity phase angle at each station point along the debond front are evaluated, and by means of experimentally determined relationships between crack growth rate and strain energy release rate for a range of mode-mixity phase angles as inputs to the FE routine, the crack growth at each station point in the debond front is determined. After evaluating the debond growth at each station point, a new debond front is defined by passing a spline through the new location of the station points. By means of a control function introduced earlier (Equation (4.5)) ensuring the accuracy and efficiency of the simulation, the number of cycle jumps is evaluated and state variables and the new position of the station points defining the debond front are estimated after the cycle jump. With the new debond shape defined after the cycle jump, the debonded panel is reconstructed and new normal and tangential directions of the debond front are determined, and the procedure is repeated for the next iteration. The efficiency of the devised methodology is examined by the simulation of sandwich panels with an elliptical face/core debond at the centre of the panels, exposed to cyclic loading. To study the effect of debond geometry, panels with different elliptical debond shapes are analysed. The sandwich panels are fully constrained at all four edges and the centre of the debond is loaded by a cyclic load. Due to geometry and loading symmetry, only a quarter panel is modelled and symmetry boundary conditions are applied to the symmetry planes, see Figure 4.11. A schematic presentation of the boundary conditions imposed on the finite element model is given in Figure 4. 11. Finite element models with different element densities were generated and analysed to ensure the sufficiency of the mesh refinement. The mesh refinement convergence analysis showed that a minimum element edge length of 0.02 mm at the crack tip is needed for an accurate simulation. 75
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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
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
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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
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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 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
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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
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Page 122 and 123: Figure 5.14: Kinking of the crack i
Page 124 and 125: Crack length [mm] Crack length [mm]
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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 136 and 137: compared to the 65% efficiency obta
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
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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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