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

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Figure 1.3: Fracture modes, from Berggreen (2005). A stress singularity at the crack tip for a 2D problem, introduced by each mode of loading, can be defined in a polar coordinate system as where is Kronecker’s delta, T the non-singular stress parallel to the crack surface. r and are radius and angle in a polar coordinate system with origin at the crack tip. and are two functions defining the shape of the stress field, see Figure 1.4. KI and KII are the mode I and II stress intensity factors. If the definition of three crack tip loading modes is applied to the stress field, then the pure mode I stress field will be symmetric with respect to the crack line with and for =0, and the pure mode II is anti-symmetric with and for =0. Consequently, KI and KII can be defined as (1.4) Figure 1.4: Homogeneous near-crack tip definitions. The theory described above is known as homogeneous linear elastic fracture mechanics, which is applicable to the fracture of homogeneous solids where the plasticity at the crack tip is very small compared to the crack geometry. 6 r (1.3)
1.4 Linear Elastic Fracture Mechanics in Material Interfaces Linear elastic fracture mechanics (LEFM) addresses the fracture of solids in which the size of the zone dominated by non-linear inelastic deformations close to the crack tip is small compared to the crack length. When a crack propagates in homogeneous solids it mostly occurs in opening mode I loading. Even if there is an initial mixed-mode loading at the crack tip, the crack will eventually kink into a path with pure mode I loading. However, in an interface crack between two dissimilar materials this is not the case and the crack tip loading is a mixed-mode loading even if the global load is pure mode I. This is to due asymmetries of moduli and Poisson’s ratios along the interface, where both shear and normal stresses exist in the crack front (He and Hutchinson, 1989). A strong dependency of the fracture toughness and mode-mixity has been observed in different experimental investigations, e.g. Liechti and Chai (1992), making the mode-mixity phase angle an important parameter for the characterisation of interface cracks. Figure 1.5: Interface crack geometry. A general interface crack problem assumes that a crack is located between two orthotropic elastic materials denoted as #1 and #2, as shown in Figure 1.5. Two materials are joined along a straight interface and the crack tip is located at x=0. The displacement and stress fields close to the crack tip can be described according to Suo (1989): where y and x are the opening and sliding relative displacements of the crack flanks, and are normal and shear stresses. K is the complex stress intensity factor defined as (1.7) 7 (1.5) (1.6)
Page 1: 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 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 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
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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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This page is intentionally left bla
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composite laminates under thermal c
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S S y( t ) y( t ) ( t ) 2 1 12 2
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listed in Table 4.1. The length and
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The strain energy release rate, G,
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high growth rate of G (see Figure 4
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4.4 Face/Core Fatigue Crack Growth
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Debond 310 mm Symmetry B. C. a Figu
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B 2 1/ 2 ( S44 S55 S45) (4.17) wh
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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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