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

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Debond 310 mm Symmetry B. C. a Figure 4.11: Quarter finite element model of the debonded panels with an elliptical debond. The smallest element size is 10 m. In the majority of recent studies (see e.g. Gaudenzi et al., 2001, Riccio et al., 2001, and Shen et al., 2001), due to difficulties associated with tracing the orientation of the new debond front after the crack growth, it was assumed that the normal and tangential directions of the debond front do not change during the crack growth. This assumption is correct for the initiation of the debond growth in the first cycles, but for the subsequent debond growth the normal and perpendicular directions of the debond front are not similar to the initial debond. To avoid adopting this assumption, a remeshing algorithm imposing an orthogonal mesh with edges parallel and perpendicular to the actual debond front is implemented as illustrated in Figure 4.12. 76 Clamp B. C. x 310 mm x y z y
Figure 4.12: Orthogonal mesh at the debond front. The mode I+II strain energy release rate, GI+II, and the associated mode-mixity phase angle, I+II, are determined from relative nodal pair displacements, obtained from the finite element analysis using the CSDE method, as outlined in the introduction. The mode I+II energy release rate and the related phase angle are given by 2 14 H11 2 G I II GI GII y x 8H11x H 22 2 77 (4.14) 1 tan H 22 x x 1 I II ln tan 2 (4.15) 11 H y h where y and x are the opening and sliding relative displacement of the crack flanks (see Figure 4.13), H11, H22 and the oscillatory index are bimaterial constants determined from the elastic stiffnesses of the face and core, see the introduction chapter. h is the characteristic length of the crack problem. h has no direct physical meaning. Thus, it is here arbitrarily chosen as the face sheet thickness. To investigate the effect of mode III loading at the debond front, the mode III strain energy release rate, GIII, is evaluated. The mode III energy release rate is given by (Suo, 1990): G III 2 z 8x( B1 B2 ) (4.16) where z is the out-of-plane (crack plane) relative displacement of the crack flanks as shown in Figure 4.13, and x is the distance of the nodal pairs from the crack tip as shown in Figure 4.13. Subscript 1 and 2 refer to two materials in a bimaterial interface, and B is the inverse of an equivalent shear modulus given by (Suo, 1990):
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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
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 96 and 97: 4.4 Face/Core Fatigue Crack Growth
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 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
Page 146 and 147: 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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