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

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the debond opening initially increases slowly with increasing load, but then increases rapidly as the maximum load is approached. At the maximum load, which corresponds to the onset of propagation, the load decreases due to the displacement controlled loading and debond propagation resulting in increased compliance, while the out-of-plane displacement of the debonded face rapidly increases. The load reduction is shown only for the experimental results, as only initiation of debond propagation is modelled numerically (no crack propagation algorithms are implemented in the finite element model). It is seen that the initial imperfection magnitude does not influence the out-of-plane deflection of the columns very much. A bifurcation instability of the debonded face sheet is not observed until the propagation point. Evidently, the presence of initial imperfection transforms the behaviour of the debonded face sheet into compression loading of a curved column. The failure load is found from fracture mechanics analysis, when the crack tip loading reaches the fracture toughness. Because of the imperfection present in the debonded face sheet, the critical instability load is extracted from both experimental and finite element results applying the Southwell method (Southwell, 1932). The Southwell method is a graphical method which estimates the instability load of imperfect structural columns. Southwell showed that the deflection, , at the centre of an imperfect column, loaded by a load P, is given by where Pcr is the instability load, and is proportional to the initial imperfection ( ). By plotting vs. /P, Pcr,, the instability load, can be determined by the slope of the line (the so-called Southwell plot method). Figure 2.18: Deformed shape of a column with H100 core containing a 50.8 mm face/core debond after local buckling of the debonded face sheet. 32 (2.8)
Out-of-plane displacement (mm) 4 3 2 1 0 Column1 FEA, IMP=0.1 mm FEA, IMP=0.2 mm FEA, IMP=0.4 mm Debond= 25.4 mm 0 4 8 12 16 Load (kN) Out-of-plane displacement (mm) 4 3 2 1 0 (a) Figure 2.19: Finite element and experimental results for out-of-plane vs. load diagram for columns with H100 core and (a) 25.4 mm debond (b) 38.1 mm debond (c) 50.8 mm debond. The average initial imperfection magnitude in the tested columns is 0.2 mm. Numerical and experimental results are compared in terms of instability load values listed in Table 2.4. For the finite element analysis results, a 0.2 mm initial imperfection was selected, which is consistent with experimental values. From the results listed in Table 2.4, it is seen that experimental and numerical instability loads are in good agreement. Further, it is seen that the instability load drops significantly as the debond length increases, which is well-known for any buckling problem. 33 Out-of-plane displacement (mm) Column1 Column2 Column3 FEA, IMP=0.1 FEA, IMP=0.2 FEA, IMP=0.4 Debond= 50.8 mm 4 3 2 1 0 Column1 Column2 Column3 FEA, IMP=0.1 FEA, IMP=0.2 FEA, IMP=0.4 Debond= 38.1 mm 0 2 4 6 8 10 Load (kN) 0 4 8 12 (c) Load (kN) (b)
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Residual Strength and Fatigue Lifet
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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 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 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
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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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Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

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