Rasmus ÿstergaard forside 100%.indd - Solid Mechanics

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460 R. C. ØSTERGAARD ET AL. (a) (b) G c (J/m 2 ) G c (J/m 2 ) 1000 800 600 400 200 2000 1500 1000 500 0 −60 0 −60 Fiber bridging Subinterface crack growth −50 −50 −40 −30 Mode mixity, (°) −40 −30 Mode mixity, (°) GFRP/H80 with H130, an increasing trend was apparent as applying a larger negative mode mixity. The increasing initiation toughness for H130 is a tendency also seen for other material combinations. Experimental investigations by Liechti and Chai [5] showed that for a glass/epoxy interface the toughness could increase by a factor of 10. The phenomenon has been extensively studied and Tvergaard and Hutchinson [19] showed that in an interface between elastic plastic solids the energy uptake in the plastic zone increased significantly for tangential crack deformation. Other sources for the increasing toughness is friction by asperity contact and locking near the crack tip [5,20]. The formation of the crack branches might also −20 Fiber bridging Subinterface crack growth GFRP/H130 Figure 8. The measured fracture toughness as function of mode mixity. (a) Shows the fracture toughness as function of mode mixity for the sandwich configuration with GFRP skin H80 core and (b) GFRP/H80. −20 −10 −10
Interface Fracture Toughness of Sandwich Structures 461 (a) (b) Skin material Core material Skin material Core material = −30° 1mm = −45° Bridging fibers 1mm Figure 9. (a) When the specimen has been loaded with normal crack opening, the crack grows just below the interface in the core material and (b) when the tangential crack deformation is the loading, extensive fiber bridging develops in the interface. explain an increased toughness. However, a detailed study to reveal which mechanisms account for the increase in toughness is beyond the scope of this work. The observation that the crack is growing towards the skin layer for loadings giving tangential crack deformation (Figure 6(a)) can be understood from an analysis of the stresses in front of the crack tip. Under dominated normal crack opening the largest principal stress is approximately perpendicular to the interface and the crack prefers to grow just below the interface. It is well known [21] that in a homogenous material, a crack selects a mode I path, i.e., it propagates in the direction perpendicular to the largest principal stress. As the mode mixity becomes more negative, higher shear stresses arise at the crack tip. At some point the shear stresses reaches a level where crack growth in the interface becomes preferable. With a further decrease in , the crack turns away from the interface and propagates into the skin laminate. The growth in the outer layer of the skin laminate leads to extensive fiber bridging and results in an increasing toughness. From Figure 9 it is clear that the length of the fracture
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Technical University of Denmark Dep
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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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Page 90 and 91: Int J Fract (2007) 143:301-316 DOI
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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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