Determination of fiber/matrix interface debond growth parameters from cyclic loading of single fiber composites

Transcription

1 Deterination o iber/atrix interace debond growth paraeters ro cyclic loading o single iber coposites Andrejs Pupurs 1,, Janis Varna 1, Povl Brøndsted 3, Stergios Goutianos 3 1 Luleå University o Technology, S Luleå, Sweden Swerea SICOMP, SE-9416 Piteå, Sweden 3 Technical University o Denark, Risø Capus, DK-4000 Roskilde, Denark 6 th International Conerence on Coposites Testing and Model Identiication (CopTest 013) -4 April 013, Aalborg, Denark.

2 c Fatigue daage in UD coposites c FL FL Failure o coposite siilar to static ailure. Rando iber breaks and ailure in ew load cycles. N=1 Rando iber breaks during irst cycle, N=1. Further daage developent in or o growing iber/atrix interace debond cracks. Ater certain aount o load cycles, aligned atrix cracks appear and propagate as debond cracks. Bridged cracks ollowed by new iber cracks Applied strain level is too low (below atigue liit). N=

3 3 Objective To ocus on iber/atrix interace debond growth in tensiontension atigue To use racture echanics (energy release rate) or the debond growth analysis To calculate the energy release rate and to deterine its dependence on debond length and to describe it by siple itting unction Using experiental data and the calculated energy release rate to evaluate whether a power law can describe the debond length growth rate in cyclic loading To deterine aterial constants in this power law, i it is applicable

4 Debond growth in tensiontension atigue l d (N) 4 ax Paris law: da dn B K l d in ax 0 in 0 da increase o the crack surace area dn increase o nuber o applied load cycles K stress intensity actor range B, aterial constants da dn B G II dldn dn B * G II where l dn l d /r B * B r G II G( ax ) G( in )

5 5 Deterination o power law paraeters dl dn dn B * Proper values o Paris law paraeters and B can only be ound i experiental data o l d =(N) are available. Experiental easureents o debond growth in atigue is coplicated or UD coposites. Single iber (SF) coposite with transparent atrix, is a convenient tool to easure debond crack growth in cyclic loading. Analytical and FEM calculations o G II or SF coposites are necessary to account or the stress state. G II

6 6 Concentric cylinder odel T F M L L l d iber break debonded iber region

7 7 Long and short debonds F M Stress state regions d) Plateau stress-state in bonded iber region. Long debonds Debond growth in selsiilar anner Analytical odel or G II calculation l d c) Debond tip region with stress singularity. b) Plateau stress-state in debonded iber region. a) Very coplex stress state at the iber break. Short debonds Strong interaction between stress states in regions a) and c) Nuerical ethods or G II calculation

8 8 Analytical solution. Energy release rate or long debonds J.A. Nairn, Y.C. Liu, On the use o energy ethods or interpretation o results o single-iber ragentation experients, Coposite Interaces, vol.4, pp , T k k r E G th ech II 1 d Q d E k r r r th d Q d E k 1 r r E E d d E d r 1 1 d E Q r E = 3 [GPa] E = 3.5 [GPa] E = 4 [GPa] = k k th

9 9 Nuerical calculation o energy release rate or short debonds u L syetry axis outer boundary T Energy release rate calculation using Virtual Crack Closure Technique (VCCT) Calculations perored using FEM sotware ANSYS G II (l d ) li dl d 0 1 dl d l d dl d l d u l d dl d l d r d r iber break Syetry b.c.

10 10 Magniication o energy release rate or short debonds.5 CF, k 1.8 FEM.0 CF, k th BEM k j * GF, k k * GF, k th l dn l dn BEM results taken ro: E. Graciani, V. Mantič, F. París, J. Varna, Nuerical analysis o debond propagation in the Single Fibre Fragentation Test, Coposites Science and Technology, vol.69, pp , 009.

11 11 General expression or energy release rate Long debonds: G k k T II E 4 r ech th Short debonds: k k * (l dn )k k th k th * (l dn )k th Fitting the whole range: k 0 k * * ( ldn) kth( ldn) k0 a1 1 a a3l ldn 1; dn ; ( l dn ) 1 l Energy release rate change in one load cycle: l dn dn G II (l dn ) r E k 0 (l dn ) 4 ( ech ax ) ( in ech ) ( )T( ax ech in ech )

12 Experiental easureents 1 1 st iber break Glass iber/epoxy E r [GPa] [-] [1/ C] E [GPa] [-] [1/ C] Fiber was pre-stressed with 7g o weight suspended at each end o iber First a static load was applied until irst break was initiated in iber ( 1st ) Tension-tension cyclic loading with requency =H, R=0.1 was applied under load control. Measureents o debond length l d were perored ater selected nuber o load cycles. Two dierent values o axial atigue strain level were studied: Saples A, B: ax = 1.76%; Saple C: ax = 1.3%. The strain levels approxiately correspond to 80% and 60% o the stress 1st respectively.

13 Experiental results. Debond growth in cyclic loading 13 N=1 N=1000 N= l d () 40 ld1 Saple A ld SapleA ld3 Saple A ld4 Saple A ld1 Saple B ld Saple B ld3 Saple B ld4 Saple B N= N

14 dldn dn B * G Deterination o the power law paraeters II r E k0 ( ldn) ax in ax in GII ( ldn) ( ech ) ( ech ) ( ) T ( ech ech ) 4 r 0 ( ) 0 E k ldn ax in ax in GII g ( ech) ( ech) ( ) T ( ech ech) 4 14 ln( l dn /N ) Saple A Saple B y = 8.799x y =.938x dl ln dn dn dldn dn ln B Saple B * * G 0 II g ln G 0 II ln g ln B * A B lng II 0

15 Validation o power law paraeters Saple A experiental Saple A odeling 8 Saple B experiantal Saple B odeling Saple C experiental 6 Saple C odeling l dn N

16 Conclusions 16 The strain energy release rate in Mode II or debond growth was analyed cobining analytical solution or long debonds and FEM solution or short debonds. Using the quantiied debond length versus nuber o cycles data it was shown that the power law with respect to the strain energy release rate change is applicable or debond growth characteriation in tension-tension atigue. Siulations showed that the obtained paraeters give acceptable predictions or cases, when the debond grows as well as when it does not grow. Being aterial properties the power law paraeters deterined in this study using single iber coposites can also be applied or the case o UD coposites ade o the sae aterial syste

17 17 Related papers A. Pupurs, S. Goutianos, P. Brøndsted, J. Varna, Interace debond crack growth in tension-tension cyclic loading o single iber polyer coposites, Coposites Part A, vol.44, pp , 013. A. Pupurs, J. Varna, FEM odeling o iber/atrix debond growth in tension-tension cyclic loading o unidirectional coposites, International Journal o Daage Mechanics, In Press, 013. (available online)

18 Thank you or your attention!