Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

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462 R. C. ØSTERGAARD ET AL. process zone is increasing to a length several times the skin height whereby a large scale fracture process zone is present. As mentioned, the simple LEFM is not valid for this kind of problem [18] and the results must be interpreted with caution. Fortunately, the right-hand side of (8) was derived using the J-integral which is also valid for large-scale bridging problems [18]. Consequently, the circular data points in Figure 8 can be interpreted as the total amount of energy dissipated per unit area in the failure process zone. However, the mode mixity loses its validity as the fracture process zone becomes longer than the zone where the singular stress field dominates. Furthermore, the fibers bridging exert forces on the crack faces and change the mode mixity. Based on the observations here, it is clear that advanced modeling of crack growth in sandwich structures calls for more advanced modeling approaches that do not have the limitations of the LEFM e.g., cohesive zone modeling [22–24] or modeling using bridging laws and retaining a crack tip singularity [25]. The results in Figure 8(a) and 8(b) exhibit a significant spread. For initiation values the spread was in the order 200 J/m 2 . For the data points where fiber bridging was present the spread was much larger. These fracture property variations could be explained by spatial material property variation. The literature contains many results where interfacial fracture toughness has been measured for different structures. However, the fracture toughness appears to be very sensitive to the exact choice of materials. Ratcliffe and Cantwell [3] measured the fracture toughness of a number of different configurations and found values ranging from 170 to 2750 J/m 2 . For a sandwich specimen with a H80 core, various test methods gave an average fracture toughness of approximately 270 J/m 2 . In the present study the fracture toughness values for loading under dominated normal crack opening were approximately 300 J/m 2 . The discrepancies between our results and those of Ratcliffe and Cantwell [3] are reasonably small and can be attributed to the dissimilarity in manufacture process and differences in the skin lay-up. CONCLUSION The test carried out in this work on sandwich double cantilever beam specimens loaded with uneven bending moments showed that the fracture toughness of sandwich structures are strongly dependent on the mode mixity. For < 35 extensive fiber bridging results in rising fracture toughness. For the sandwich specimens tested here fiber bridges formed but a large spread in maximum toughness was seen.
Interface Fracture Toughness of Sandwich Structures 463 For future work it is suggested that the mechanism of fiber bridging is investigated so the ability to fail by fiber bridging formation is designed into the sandwich structures since this will result in a more fracture-resistant structure. ACKNOWLEDGEMENTS Part of this work was part of the SaNDI (THALES JP3.23) project with participants from Norway, Denmark, Sweden, Finland, and the United Kingdom. The support of the five participating nations is gratefully acknowledged. BFS was supported by the Danish Energy Authority under the Ministry of Economics and Business Affairs through a EFP2005-fund (journal no. 33031-0078). APPENDIX A Relation between Compliance Matrix and Engineering Constants Relation between engineering constants and the compliance matrices for a orthotropic and a isotropic material, respectively [26]: sij ¼ 2 sij ¼ 1 6 E 6 4 2 6 4 1 21 31 0 0 0 E22 E33 1 32 0 0 0 E22 E33 23 1 0 0 0 E22 E33 1 0 0 0 0 0 G23 1 0 0 0 0 0 G31 1 0 0 0 0 0 E11 12 E11 13 E11 G12 3 7 5 1 0 0 0 3 0 0 1 0 0 1 0 0 0 0 2ð1þÞ 0 0 0 0 2ð1þÞ 0 0 0 0 7 5 0 0 0 0 0 2ð1þÞ ðA1Þ ðA2Þ
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Technical University of Denmark Dep
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£ ¥ § © ¥ § £ § ¥
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£ ¥ § © ¥ § £ § ¥
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¢ ¢ ¥ § ©
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Sandwich columns Composite Structur
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γ
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μi, Ei νi (i =1, 2)
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K K = σCL iɛ+1
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sij = ⎡ ⎢ ⎣ ν21 ν31 − −
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ρ ρ
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σn
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utip,∗
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σn ˆσ ˙λ
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σ I n = un u∗ σ(λmax) n λmax
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˙δi
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• •
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M ∗ = Phχ+ M χ
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z1 z2 M = 0 M =0. ψ
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ω
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σ12H/P =0.1, 0.05, 0.01
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B, G = (s′ 11 )#2 2B2 2 2 P M +
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P ΔPFB Initiation ψ = −45 ◦
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Jc [J/m 2 ] Jc [J/m 2 ] 1000 800 60
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2
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Outward buckling of initially debon
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Pcr P gl 1 0.8 0.6 0.4 0.2 0.01 0.0
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0.6 0.5 0.4 0.3 0.2 0.1 initial cra
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P P gl P P gl 1 0.8 0.6 0.4 0.2 1 5
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ˆσ
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JR σn σt U ∗ n JR
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E
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σn(Un/H)ℓ EfH = Pn EfH σt(Ut
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(Ut ≡ 0)
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Γ/HEf.
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α
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ϕ = −30 ◦ ◦ −60 , ϕ = −
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Page 90 and 91: Int J Fract (2007) 143:301-316 DOI
Page 92 and 93: Interface crack in sandwich specime
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Page 130 and 131: Abstract Buckling driven debonding
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Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

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