Experimental assessment of mixed-mode partition theories for fracture toughness in laminated composite beams

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1 Loughborough University Institutional Repository Experimental assessment of mixed-mode partition theories for fracture toughness in laminated composite beams This item was submitted to Loughborough University's Institutional Repository by the/an author. Citation: HARVEY, C.M., EPLETT, M.R. and WANG, S., 05. Experimental assessment of mixed-mode partition theories for fracture toughness in laminated composite beams. Presented at the 8th International Conference on Composite Structures (ICCS8), Lisbon, Portugal, 5-8th June. Additional Information: This is a powerpoint presentation presented at 8th International Conference on Composite Structures (ICCS8), Lisbon, Portugal, 5-8th June. Metadata Record: Version: Accepted for publication Publisher: c The Authors Rights: This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC Y-NC-ND 4.0) licence. Full details of this licence are available at: Please cite the published version.

2 Experimental assessment of mixedmode partition theories for generally laminated composite beams Christopher Harvey, Matthew Eplett, Simon Wang Department of Aeronautical & Automotive Engineering Loughborough University, LE 3TU UK 8 th International Conference of Composite Structures (ICCS8)

3 Fracture toughness depends on the fracture mode partition. Predicting fracture toughness requires knowledge of the partition of a mixedmode fracture. It is therefore essential to have a correct analytical partition theory in order to predict the fracture toughness. Introduction

4 Introduction Previous work by the authors shows that Loughborough University s Euler beam (E) partition theory performs very well when predicting the modedependent fracture toughness. Davidson et al. s (Syracuse, NY) non-singular field (NSF) partition theory is developed based on experimental fracture toughness measurements. It also works very well. Therefore, it is reasonable to speculate that Davidson et al. s NSF partition theory approaches to Loughborough s E partition theory. Harvey, Wang (0), Compos Struct 94. Davidson et al. (000), Int J Fract 05. 3

5 To assess the E and NSF theories thoroughly using Davidson s et al. s experimental fracture toughness data. To explore the connections between the two theories,. Aims Harvey, Wang (0), Compos Struct 94. Davidson et al. (000), Int J Fract 05. 4

6 Partition theories Loughborough University s E partition theory (completely analytical): Davidson et al. s NSF partition theory: The mode mix parameter Ω is determined with the aid of experimental data. 5 = 3 3 β β β β β β IE IE N N M M N N M M c G = 3 3 θ θ θ θ θ θ IIE IIE N N M M N N M M c G Γ + + Ω + Γ Ω + = sin )] sin( cos [ c c c c c c II M N c c M c N c c M c N G G ( ) ( ) ( ) log log log if > < < < Ω = h h h h h h η η

7 Davidson et al. s fracture testing methods Double cantilever beam (DC) test Gives the pure mode I fracture toughness GG IIII Load (kn) Displacement (mm) 6

8 Davidson et al. s fracture testing methods End-notched flexure (ENF) test Gives the pure mode II fracture toughness GG IIIIcc Single leg bending (SL) test Mixed mode 7

9 Davidson et al. s fracture testing methods Mixed mode bending (MM) test 8

10 Methodology Objective was to compare the fracture toughness obtained at each partition GG IIII GG against the failure locus. However, the failure locus is not readily available: In early work, a linear failure locus was assumed. In Davidson et al. s work, unidirectional (UD) midplane delamination testing work was used to obtain the failure locus. This is possible because all existing partition theories agree for UD midplane delamination. Therefore, in Davidson et al. s work and in our work, the UD midplane failure locus is used to assess the accuracy of a partition theory for offset delaminations and general layups. 9

11 Test specimens Davidson et al. (000), Int J Fract 05. CK/R6376 graphite/epoxy (relatively low toughness) Davidson et al. (006), Compos Sci Tech 66. T800H/3900- graphite/epoxy (relatively high toughness) 3 specimen types and DC, ENF, MM, SSL, UENF tests. UD 0 / 0 interface. Constrained UD 0 / 0 interface ( d = delamination location) [0/0/-5/0 0 /-5/0/0/d] s Layup A [(0/±5/0) 3 /d/(0/±5/0)/(0/ 5/0) 4 ) Layup [(0/±5/0) 4 /(0/ 5/0)/d/(0 5/0) 3 ) Layup C 3. Multi-Directional (MD) interfaces 5A [(0 45/90) s /d/(45/90/0/-45 /0/90/45) s /(0 45/90) s ] Layup D A [(±45 /0 / 45/±45 /0 / 45) s /d/(0±45/ 45/0) s ] Layup E 9A [( 45 /0 8 /±45 ) s /d/( 45 /0 8 /±45 )] Layup F 0

12 UD 0/0 Interface Data from Davidson et al. (000) CK/R6376 graphite/epoxy (relatively low toughness)

13 Difference between E and NSF partitions

14 Constrained UD 0 / 0 interface Data from Davidson et al. (000) CK/R6376 graphite/epoxy (relatively low toughness) 3

15 Multi-Directional (MD) interfaces First set Data from Davidson et al. (000) CK/R6376 graphite/epoxy (relatively low toughness) 4

16 Multi-Directional (MD) interfaces First set Data from Davidson et al. (000) CK/R6376 graphite/epoxy (relatively low toughness) 5

17 Multi-Directional (MD) interfaces First set Data from Davidson et al. (006) T800H/3900- graphite/epoxy (relatively high toughness) : (Layups D F together) 6

18 Conclusions SF does not have great agreement with the fracture toughness data Care must be taken when using the D finite element method. ERR partitions will be based on the SF and this gives poor predictions offracture toughness. NSF theory based on experimental data works very well in predicting mixed-mode fracture toughness. E theory completely analytical works very well in predicting mixed-mode fracture toughness. 7

19 Thank you for listening

20 Appendix Table : Unidirectional material properties Data from Davidson et al. (000) for CK/R6376 graphite/epoxy Data from Davidson et al. (006) for T800H/3900- graphite/epoxy 9

21 Appendix Table : Fracture toughness of midplane and offset delaminations in unidirectional laminates made from CK/R Data from Davidson et al. (000)

22 Appendix Table 3: Fracture toughness of midplane and offset delaminations in constrained unidirectional laminates made from CK/R6376. Data from Davidson et al. (000)

23 Appendix Table 4: Fracture toughness of midplane and offset delaminations in multidirectional laminates made from CK/R6376 Data from Davidson et al. (000)

24 Appendix Table 5: Fracture toughness of offset delaminations under the loading case Data from Davidson et al. (000) 3

25 Appendix Table 6: Fracture toughness of midplane and offset delaminations in multidirectional laminates T800H/ Data from Davidson et al. (006)