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

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The compact tension specimen (CT) is typically used to measure the fatigue crack growth rate in metals in the Paris regime (regime II) according to the test procedure specifications ASTM E647-93. The stress intensity factor of the CT specimen can be determined by (1.21) where Bct is thickness of the specimens and is a finite width correction factor, given by 12 (1.22) Burman et al. (1998) used the CT specimen with some dimensional modifications to extract both the mode I fracture toughness and the mode I crack growth rate of H100 PVC foam, see Figure 1.9. Figure 1.9: Modified CT specimen, after Burman et al. (1998). The resulting crack growth rate data for H100 PVC foam was more scattered compared to typical fatigue crack growth rate diagrams, which can be attributed to the brittleness of the PVC foam material. Zenkert et al. (2008, 2010) also studied the fatigue response of various closed-cell foam materials under tension, compression and shear loading. In the case of an interface crack, the crack growth rate is a function of both the stress intensity factor and mode-mixity. There is no standard testing procedure for the measurement of face/core interface fatigue crack growth rate in sandwich structures. However, in recent years several precracked test specimens including the Cracked Sandwich Beam (CSB) (Carlsson et al., 1991), the
sandwich Double Cantilever Beam (DCB) (Prasad and Carlsson, 1994), the modified Tilted Sandwich Debond specimen (TSD) (Berggreen and Carlsson, 2010), the Single Cantilever Beam (SCB) (Cantwell and Davies, 1994, 1996), the Three-Point Sandwich Beam (TPSB) (Cantwell and co-authors, 1999, 2001), the sandwich DCB subjected to Uneven Bending Moment named DCB-UBM (Lundsgaard et al., 2008) and the sandwich Mixed Mode Bending (Quispitupa et al., 2009) have been proposed for interface fracture toughness characterisation of sandwich structures. Many of these specimens can be applied to fatigue crack propagation testing as well, see Figure 1.10. Among these test specimens, Shipsha et al. (1999) used DCB and CSB specimens to measure face/core interface fatigue crack growth rates in foam cored sandwich beams under pure mode I and II loading. The disadvantage of utilising the CSB, DCB, TPSB and SCB specimens is the impossibility of mode-mixity variation for a fixed specimen geometry and material configuration. Utilising the CSB specimen, only mode II dominated crack growth rates and fracture toughness can be measured while with the DCB and TPSB only mode I dominant loading of the crack tip is possible. The TSD specimen may be used to measure the fracture toughness in a wide range of mode-mixities. However, since the mode-mixity is a function of crack length in this specimen, it is not directly suitable for standard interface fatigue characterisation at a specific mode-mixity. As to the DCB-UBM and MMB specimens, apart from being able to load the crack at different mode-mixities, the mode-mixity also remains constant as the crack grows, which makes these specimens ideal candidates for the measurement of interface fatigue crack growth rates. The DCB-UBM specimen has not been used for fatigue tests yet. However, Quispitupa et al. (2008) used the sandwich Mixed Mode Bending (MMB) specimen to measure face/core interface crack growth rates for a range of mode-mixities. The MMB test rig allows for adjustment of the mixed-mode ratio simply by changing the location of the support at point A, see Figure 1.10. The MMB test rig is used in this thesis to measure fracture toughness in Chapter 3 and crack growth rates in Chapter 5. In Chapter 2 as an alternative method, the TSD specimen is used to measure the face/core fracture toughness of the sandwich configurations. 13
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 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 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
Page 78 and 79: Figure 3.19 shows the determined en
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Page 82 and 83: 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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