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

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These peculiar damage modes often result in considering higher safety factors during a design process compared to similar metallic structures, which makes a detailed study of failure modes of sandwich structures essential if maximum structural efficiency is to be reached. Face/core debonding and its propagation are among the most critical damages a sandwich structures may experience, as structural integrity is closely linked to the adequacy of the bonding in the face/core interface in these structures. Debonds may emerge due to production defects, in-service overloading and local loads like impact, see Figure 1.1. A debond may be initiated directly in the face/core interface, in the core just below the resin-rich cells or in the face sheet (for composite face sheets). If a debond emerges in any of these locations, depending on the loading at the crack tip and toughness of other neighbouring layers, it may continue propagating in the original debond position or kink into the core, interface or face sheet, see Figure 1.2. Studies have shown that face/core debonding considerably reduces the load carrying capacity of sandwich structures (Nøkkentved et al., 2005, and Berggreen et al., 2005). A question that arises for debond damaged sandwich structures is that of damage tolerance: how is the structural performance influenced by the presence of debonding? The question of damage tolerance does not only apply to the design and optimisation of sandwich strcutures, but is also relevant to the residual strength and lifetime of already in service structures with minor or major damages. In recent years, a number of analytical and numerical studies have been conducted to predict the initiation and propagation of debonds in sandwich structures exposed to static loading, e.g. Kardomateas and Huang (2003), Sankar and Narayan (2001), Chen and Bai (2002) and Avilés and Carlsson (2007). Furthermore, experiments have been performed to determine the residual strength and identify the failure mechanisms of debonded sandwich structures, e.g. Avery and Sankar (2000), Vadakke and Carlsson (2004) and Xie and Vizzini (2005). Linear Elastic Fracture Mechanics (LEFM) has been extensively used to model debond initiation and propagation where the energy dissipation zone (fracture process zone) is relatively small compared to specimen dimensions, (Hutchinson and Suo, 1992). Furthermore, several studies have dealt with the determination of the fracture toughness of face/core interface in sandwich structures, e.g. Cantwell and Davies (1996), Li and Carlsson (1999) and Østergaard et al. (2007). In sandwich structures with composite face sheets the fracture process zone becomes large due to kinking of the crack into the composite face sheet and consequent fibre bridging which violates LEFM assumptions, see Figure 1.2. As an alternative to LEFM, cohesive zone modelling has been used in the literature, e.g. Lundsgaard-Larsen et al. (2008, 2010) and Østergaard et al. (2008) to model face/core debonding in the presence of fibre bridging. In few studies experiments have been conducted to some extent in order to examine the accuracy of the developed analysis methods in debonded sandwich structures e.g. see Berggreen et al. (2005), Jolma et al. (2007) and Aviles et al. (2006). However, despite all the proposed numerical and analytical methods, a comprehensive study of debond damaged sandwich structures, addressing systematically issues like debond propagation, characterisation of the fracture 2
toughness of the interface at different mode-mixities and finally validation of these methods against experiments is still missing. Regarding the analysis of sandwich composites exposed to cyclic loading only a limited number of studies are found in the literature. Fatigue analyses of undamaged sandwich beams have been conducted by beam bending tests by Shenoi et al. (1995), Burman and Zenkert (1997), Kenny et al. (2002, 2005), Kulkarni et al. (2003) and Zenkert et al. (2011). The objective of these studies was to analyse the fatigue response of foam cores subjected to shear loading. In the case of debond damaged sandwich structures subjected to cyclic loading, fatigue experiments have been conducted by Shipsha et al. (1999, 2000, 2003) on debond damaged sandwich beams to determine stress-life S-N diagrams, crack growth rates and indentify fatigue crack growth mechanisms. Burman et al. (1997, 2000) also conducted four-point bending tests on debond damaged sandwich beams. However, all these studies have considered loading cases with pure mode I or II dominated loading at the crack tip and not a general mixed-mode condition. Figure 1.1: Debond in the structure of a ship after removal of the face sheet, from Berggreen (2005). Figure 1.2: Three different scenarios for face/core debond propagation. 3
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 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 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
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arising due to the junction between
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(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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