Proceedings at ESIS TC4 Conference 14th September 2014 A CONTROLLED MIXED-MODE BENDING (CMMB) TEST TO INVESTIGATE THE FRACTURE OF STRUCTURAL ADHESIVE JOINTS S. Marzi 1), T. Walander 2), O. Hesebeck 1), M. Brede 1) 1) Fraunhofer IFAM, Germany 2) University of Skövde Contact e-mail: [email protected] WWW.HIS.SE/WALT Page 1 OUTLINE SHORT AGENDA Background Research idea Experimental set-up / results Evaluation Comparison Summary Future work Questions WWW.HIS.SE/WALT [email protected] Page 2 BACKGROUND FRACTURE OF ADHESIVE LAYERS • Ability to predict, and simulate, fracture of adhesive layers • Substantial work regarding Mode I and Mode II loading, e.g. thickness, temperature, loading rate, curing time…. • Bonded structures often fail in Mixed mode loading • Fracture energy essential parameter for strength WWW.HIS.SE/WALT [email protected] Page 3 BACKGROUND PREVIOUS MIXED MODE STUDIES LEFM APPROACH • Unsymmetrical double cantilever beam (UDCB) • • D. Alvarez, et al. Annual Meeting of the Adhesion Society, 2013. V. Mollon, et al. Structures, vol. 32, (2010) • Mixed mode bending (MMB) • R. JR. and C. JH. AIAA J, vol. 59, pp. 609 • End loaded split (ELS) • S. Gowrishankar, et al. Annual-Meeting of the Adhesion Society, 2013. • Mixed mode flexure (MMF) • H. Parvatarredy and D. Dillard. Int. J. Fract., vol. 96, 1999. • Fixed ratio mixed mode (FRMM) • M. Conroy, et al. Annual Meeting of the Adhesion Society, 2013. • Anti-symmetric FRMM (AFRMM) • D. Alvarez, et al. Annual Meeting of the Adhesion Society, 2013. NOTE: LEFM neglects flexibility of adhesive layer - not optimal for adhesives giving rise to a large process zone WWW.HIS.SE/WALT [email protected] (Figures taken from Alvarez, et al. 2013) Page 4 BACKGROUND PREVIOUS MIXED MODE STUDIES J-INTEGRAL APPROACH • Consider flexibility, suggested by e.g. • Z. Sou et al. J. of the Mechanics and Physics of Solids, vol. 40 1993 • DCB with uneven bending moments (DCB-UBM) • • B. Sorensen and T. Jacobsen Composite Sc. Tech, vol. 69, 2009. C. Lundsgaard-Larsen, et al. Eng. Frac. Mech., vol. 75, 2008. • Mixed mode cantilever beam (MCB) • J. Hogberg et al. Int. J.Solids Structures, vol. 44 2007. • Mixed mode bending (MMB) • F. Ducept, et al. Compos Sci Technol, vol. 59, 1999. WWW.HIS.SE/WALT [email protected] Page 5 BACKGROUND PREVIOUS MIXED MODE STUDIES MODE MIX DEFINITIONS • Energy based mode mix definition, e.g. arctan J. Hutchinson and Z. Sou, Adv. Appl. Mech., vol. 29, 1992. • Separation based mode mix definition, e.g. J. Hogberg et al. Int. J.Solids Structures, vol. 44 2007. • (Stress based mode mix definition) , WWW.HIS.SE/WALT [email protected] Page 6 BACKGROUND PREVIOUS MIXED MODE STUDIES FRACTURE ENVELOPES Energy based peel F. Ducept et al. I. J. Adhesion & Adhesives 20 2000 Separation based shear shear peel J. Hogberg et al. Int. J.Solids Structures, vol. 44 2007. Fracture energy strongly mode mix dependent WWW.HIS.SE/WALT [email protected] Page 7 BACKGROUND DEFINE ACTUAL MODE MIX? • and , i.e. mode mix, changes when damage initiates in the adhesive layer. Fracture indicated by circles J. Hogberg et al. Int. J.Solids Structures, vol. 44 2007. WHAT IS THE ACTUAL MODE MIX? • Mode mix defined in the elastic region, before damage? • Mode mix defined at fracture? WWW.HIS.SE/WALT [email protected] Page 8 RESEARCH IDEA CONTROLLED MIXED MODE BENDING SPECIMEN (CMMB) • Separation based mode mix definition arctan • J-integral approach for evaluation WWW.HIS.SE/WALT [email protected] Page 9 EXPERIMENTAL SET-UP Custom test machine designed and built by the authors Located at Fraunhofer IFAM, Bremen • PID regulation • DASY Lab software Technical data: • Two regulated 20 kN actuators • Four 20 kN load cells • Four incremental shaft encoders • Two clip gauges • Linear guide lines WWW.HIS.SE/WALT [email protected] Test for positive Page 10 EXPERIMENTAL SET-UP COD - MEASUREMENTS Regulation for constant : , arctan , WWW.HIS.SE/WALT [email protected] tan Proportional control of the velocity of the controlled actuator Page 11 EXPERIMENTAL RESULTS , THREE EXPERIMENTS 3000 Sum A B C D 2000 s F [N] U [mm] 1000 0 -1000 0.2 4000 0.15 3000 0.1 J [N/m 2] EX. 0.05 1000 Experiment Target 0 2000 0 -2000 0 100 200 Time [s] 300 -0.05 0 0.2 0.4 U [mm] n 0.6 0.8 0 0.2 U 0.4 [mm] 0.6 res SikaPower 498 adhesive WWW.HIS.SE/WALT [email protected] Page 12 0.8 EXPERIMENTAL RESULTS EX. , THREE EXPERIMENTS 8000 12000 0.8 6000 10000 0 J [N/m 2] 0.4 s F [N] 2000 8000 U [mm] Sum A B C D 4000 0.6 6000 4000 0.2 Experiment Target -2000 2000 0 -4000 0 200 400 Time [s] 600 0 0.1 0.2 U [mm] n 0.3 0.4 0 0 0.2 0.4 U res 0.6 [mm] 0.8 SikaPower 498 adhesive WWW.HIS.SE/WALT [email protected] Page 13 EVALUATION FRACTURE ENERGY " " 7 12000 4.5 x 10 4 10000 B 3.5 A 3 6000 C 4000 A "" [Pa] J [N/m2] 8000 2.5 C 2 1.5 1 2000 0.5 0 0 0.2 0.4 0.6 Ures [mm] WWW.HIS.SE/WALT [email protected] 0.8 0 0 0.2 0.4 0.6 Ures [mm] 0.8 Page 14 EVALUATION FRACTURE ENVELOPE 16000 CMMB CMMB CMMB TENF TENF TENF TDCB TDCB Constrained 2nd order regression TDCB Constrained order regression regression Constrained 2nd 4th order 14000 12000 J [N/m 2] 10000 8000 6000 4000 2000 0 -100 -50 WWW.HIS.SE/WALT [email protected] 0 [ ] 50 100 Page 15 COMPARISON COHESIVE MODELS • Separation based models of initial interest Two models evaluated: • Högberg (2006), J.L. Högberg. (2006). Unbalanced DCB-specimen. CDCM 2006 - Conference on Damage in Composite Materials 18th-19th of September 2006 in Stuttgart, Germany. Online-Proceedings. Parameter based cohesive law • Salomonsson and Andersson (2010). K. Salomonsson and T. Andersson (2010). Weighted potential methodology for mixed mode cohesive laws. Proceedings of the MECOM DEL BICENTENARIO, IX 2010, Buenos Aires Potential based cohesive law WWW.HIS.SE/WALT [email protected] Page 16 COMPARISON COHESIVE MODELS 15000 10000 Experimenet Experimenet 2 Högberg, Högberg, R R22=0 =0 Högberg, R =0 Salomonsson & Andersson exp22, R22=0.6 Salomonsson & Andersson exp4, R2=0.6 Salomonsson & Andersson exp , RR2=0.66 Constrained 2th order regression, =0.72 Constrained 2th order regression, R22=0.72 Constrained 2th order regression, R =0.72 2 2=0.74 Constrained 4th order regression, R Constrained Constrained 4th 4th order order regression, regression, R R2=0.74 =0.74 Högberg (2010) cos sin Salomonsson & Andersson (2010) 1 5000 J 1 1 0 -100 -50 0 50 100 1 WWW.HIS.SE/WALT [email protected] Page 17 COMPARISON CUSTOM, FITTED, 1.2 need to be a continuous function due to differentiation 1 0.8 0.6 f [-] ) 0.4 0.2 Hard to model the “drop” at 0 -0.2 0 0.5 1 [rad] WWW.HIS.SE/WALT [email protected] 1.5 An optimal would be continuous and would pass all means values Page 18 1 COMPARISON CUSTOM, FITTED, 14000 Experimenet Salomonsson & Andersson exp2, R2=0.6 Salomonsson & Andersson exp4, R2=0.66 12000 2 Salomonsson & Andersson Custom f, R =0.9 Very good agreement in fracture energy 10000 8000 6000 Only calibrates not the entire evolution of 4000 2000 -80 -60 -40 WWW.HIS.SE/WALT [email protected] -20 0 20 40 60 80 , 100 Page 19 COMPARISON COMPARE ENTIRE J-CURVES WWW.HIS.SE/WALT [email protected] Page 20 COMPARISON SALOMONSSON AND ANDERSSON Custom f( ) WWW.HIS.SE/WALT [email protected] Page 21 COMPARISON SALOMONSSON AND ANDERSSON 4000 3500 Black lines: Experiments 3000 J [N/m2] 2500 Red lines: From potential 2000 1500 1000 Mode I and Mode II are inputs 500 =-0 0 0 0.02 0.04 0.06 0.08 Ures [mm] 0.1 0.12 0.14 0.16 Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 22 COMPARISON SALOMONSSON AND ANDERSSON 4000 3500 Black lines: Experiments 3000 J [N/m2] 2500 Red lines: From potential 2000 1500 1000 Outsider? 500 Mode I and Mode II are inputs = - 15 = + 15 0 0 0.05 0.1 0.15 0.2 0.25 Ures [mm] Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 23 COMPARISON SALOMONSSON AND ANDERSSON 4000 3500 Black lines: Experiments 3000 J [N/m2] 2500 Red lines: From potential 2000 1500 1000 500 Mode I and Mode II are inputs = - 30 = + 30 0 0 0.05 0.1 0.15 0.2 Ures [mm] 0.25 0.3 0.35 Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 24 COMPARISON SALOMONSSON AND ANDERSSON 6000 5000 Black lines: Experiments J [N/m2] 4000 Red lines: From potential 3000 2000 Mode I and Mode II are inputs 1000 = - 45 = + 45 0 0 0.05 0.1 0.15 0.2 0.25 Ures [mm] 0.3 0.35 0.4 0.45 Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 25 COMPARISON SALOMONSSON AND ANDERSSON 10000 9000 Black lines: Experiments 8000 7000 J [N/m2] 6000 Red lines: From potential 5000 4000 3000 Mode I and Mode II are inputs 2000 = - 60 1000 = + 60 0 0 0.1 0.2 0.3 0.4 Ures [mm] 0.5 0.6 0.7 Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 26 COMPARISON SALOMONSSON AND ANDERSSON 12000 10000 Black lines: Experiments J [N/m2] 8000 Red lines: From potential 6000 4000 Mode I and Mode II are inputs 2000 = - 75 = + 75 0 0 0.1 0.2 0.3 0.4 Ures [mm] 0.5 0.6 0.7 Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 27 COMPARISON SALOMONSSON AND ANDERSSON 14000 12000 Black lines: Experiments J [N/m2] 10000 8000 Red lines: From potential 6000 4000 Mode I and Mode II are inputs 2000 = 90 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Ures [mm] 0.35 0.4 0.45 0.5 Model gives significantly lower stresses than experiments in mixed mode WWW.HIS.SE/WALT [email protected] Page 28 EVALUATION POTENTIAL FROM REGRESSION , , , , Constrained, 3D regression analysis, this case 3rd order WWW.HIS.SE/WALT [email protected] Page 29 COMPARISON POTENTIAL FROM REGRESSION 4000 3500 Black thin lines: Experiments 3000 J [N/m2] 2500 Black thick line: Potential from regression 2000 1500 1000 Red lines: From potential 500 =-0 0 0 0.05 0.1 0.15 0.2 Ures [mm] 0.25 0.3 0.35 New potential gives non-realistic stresses WWW.HIS.SE/WALT [email protected] Page 30 COMPARISON POTENTIAL FROM REGRESSION 4000 3500 Black thin lines: Experiments 3000 J [N/m2] 2500 Black thick line: Potential from regression 2000 1500 1000 500 Red lines: From potential = - 15 = + 15 0 0 0.05 0.1 0.15 0.2 Ures [mm] 0.25 0.3 0.35 New potential gives non-realistic stresses WWW.HIS.SE/WALT [email protected] Page 31 COMPARISON POTENTIAL FROM REGRESSION 4000 3500 Black thin lines: Experiments 3000 J [N/m2] 2500 Black thick line: Potential from regression 2000 1500 1000 500 Red lines: From potential = - 30 = + 30 0 0 0.05 0.1 0.15 0.2 Ures [mm] 0.25 0.3 0.35 New potential gives non-realistic stresses WWW.HIS.SE/WALT [email protected] Page 32 COMPARISON POTENTIAL FROM REGRESSION 6000 5000 Black thin lines: Experiments J [N/m2] 4000 Black thick line: Potential from regression 3000 2000 Red lines: From potential 1000 = - 45 = + 45 0 0 0.05 0.1 0.15 0.2 0.25 Ures [mm] 0.3 0.35 0.4 0.45 New potential gives non-realistic stresses WWW.HIS.SE/WALT [email protected] Page 33 COMPARISON POTENTIAL FROM REGRESSION 10000 9000 Black thin lines: Experiments 8000 7000 J [N/m2] 6000 Black thick line: Potential from regression 5000 4000 3000 2000 = - 60 1000 Red lines: From potential = + 60 0 0 0.1 0.2 0.3 0.4 Ures [mm] 0.5 0.6 0.7 New potential gives non-realistic stresses WWW.HIS.SE/WALT [email protected] Page 34 COMPARISON POTENTIAL FROM REGRESSION 14000 12000 Black thin lines: Experiments J [N/m2] 10000 8000 Black thick line: Potential from regression 6000 4000 Red lines: From potential 2000 = 90 0 0 0.05 0.1 0.15 0.2 0.25 0.3 Ures [mm] 0.35 0.4 0.45 0.5 New potential gives non-realistic stresses WWW.HIS.SE/WALT [email protected] Page 35 SUMMARY POTENTIAL FROM REGRESSION Fracture envelope: • Prediction by Högberg gives poor fit to the experimental data Adapted potential function by Salomonsson and Andersson : • Good agreement in fracture energy for all mode mixes, • Gives significantly lower stresses • Significantly exaggerated critical deformation Potential from regression analysis, • Mostly a good agreement to the experimental J-curves • Non-realistic stresses derived form the potential surface • Critical deformation not defined. WWW.HIS.SE/WALT [email protected] Page 36 FUTURE WORK IDEAS TO FUTURE WORK • Chebyshev polynomials? [Sørensen and Kirkegaard, Eng. Frac. Mech. 73 (2006)] • FE-simulations to determine the best model • Other adhesives are to be investigated at Fraunhofer IFAM WWW.HIS.SE/WALT [email protected] Page 37 Proceedings at ESIS TC4 Conference 14th September 2014 THANK YOU S. Marzi 1), T. Walander 2), O. Hesebeck 1), M. Brede 1) 1) Fraunhofer IFAM, Germany 2) University of Skövde Contact e-mail: [email protected] WWW.HIS.SE/WALT Page 38
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