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

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Load (N) 250 200 150 100 50 0 H130 Core =-28 0 1 2 3 4 5 Displacement (mm) Load (N) 250 200 150 100 50 H250 Core =-29 0 0 1 2 3 4 Displacement (mm) Figure 3.3: Typical experimental load vs. displacement curves (“” indicates the onset of crack growth) for specimens with (a) H130 core (b) H250 core and (c) PMI core. Since the face/core interface toughness is strongly dependent on the mode-mixity at the crack tip, the mode-mixity was determined from finite element analysis of the MMB specimens for all loading conditions and materials tested in this study. A finite element model of the MMB specimen was developed in the commercial finite element code, ANSYS, using 4-node isoparametric elements (SOLID42), see Figure 3.4. Geometrically non-linear analysis of the MMB specimen was performed with displacement controlled loading. The mode-mixity phase angle () was determined from relative nodal pair displacements along the crack flanks obtained from the finite element analysis, applying the crack surface displacement extrapolation (CSDE) method presented in the Introduction of this thesis. The characteristic length h is arbitrarily chosen as the face sheet thickness in this study. Figure 3.4: Finite element model of the MMB sandwich specimen. The smallest element size is 3.33 m. 46 Load (N) 150 100 50 0 PMI Core =-20 (a) (b) (c) 0 0.5 1 1.5 2 2.5 Displacement (mm)
Figure 3.5 shows the face/core debond fracture toughnesses vs. phase angle for specimens with H130, H250 and PMI 51 IG cores. The mechanical properties for these materials were listed in Tables 3.2 and 3.3. It should be noted that the DBL reinforcement in lay-up C was oriented with the 0º plies parallel to the load direction in the panel tests and transverse to the beams in the MMB fracture specimens, thus simulating the fibre orientation in the 3 and 9 o’clock positions along the circular debond in the panels. Figure 3.5 reveals that the face/core interface fracture toughness is strongly dependent on the mode-mixity at the crack tip for all sandwich composites examined herein, especially in mode II dominated loading, i.e. increased shear loading at the crack tip. However, this dependency is weak in mode I dominated loadings, i.e. low magnitudes of mode-mixity, where roughly constant fracture toughness is observed, see Figure 3.5. A phenomenological relationship between fracture toughness and mode-mixity proposed by Hutchinson and Suo (1992) is used to fit the experimental data by Equation (3.14). A fitted curve (by visual inspection) is represented by a continuous line in Figure 3.5, for the three sandwich composites being examined, i.e. specimens with H130, H250 and PMI cores. In addition, the upper and lower bounds are shown as dashed lines. A large scatter in the fracture toughness vs. phase angle results is observed, which is expected in sandwich composites due to different manufacturing defects and crack propagation paths at the face/core interface. 2 tan G 1 1k Gc IC (3.14) In Equation (3.14), GIC is the interface fracture toughness in pure mode I and k is a nondimensional curve fitting parameter. Here, since in mode I dominated loading, a roughly constant fracture toughness is observed, GIC is assumed to be the minimum fracture toughness value for the material being evaluated. Thus, when =0, Gc() = GIC. (a) (b) (c) Figure 3.5: Fracture toughness vs. phase angle results and curves for specimens with (a) H130 (b) H250 and (c) PMI cores. Based on the face/core debond fracture toughness vs. phase angle results shown in Figure 3.5, the parameters for Equation (3.14) are provided in Table 3.4 for each sandwich configuration. 47
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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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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 66 and 67: sheet and the core thickness, respe
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
Page 116 and 117: 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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