Geers, M.G.D.

Schreurs, P.J.G.

Sluis, van der, O.

Vossen, B.G.

English

Pure OAI Repository

 Multi-scale modelling of fibrillation in copper-rubber interfacedelaminationCitation for published version (APA):Vossen, B. G., Schreurs, P. J. G., Sluis, van der, O., & Geers, M. G. D. (2012). Multi-scale modelling offibrillation in copper-rubber interface delamination. Poster session presented at Mate Poster Award 2012 : 17thAnnual Poster Contest.Document status and date:Published: 01/01/2012Document Version:Accepted manuscript including changes made at the peer-review stagePlease check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 17. Nov. 2023Mechanics of MaterialsMulti-scale modelling of fibrillation incopper-rubber interface delaminationBart Vossen, Piet Schreurs, Olaf van der Sluis, Marc Geers/ Department of Mechanical EngineeringIntroductionCopper-rubber interfaces play a major role in a variety of prod-ucts, such as stretchable electronics, figure 1.John Rogers, Hopkins University Stephanie Lacour, University of CambridgeFigure 1: Stretchable electronics examples. Left: heart ablationcatheter. Right: Electronic skin for wearable mobile phone.Interface delamination causes failure of the product. An impor-tant delamination mechanism is fibrillation, see figure 2. Duringpeeling, the dissipation mechanisms depend on the loading con-ditions, rendering the experimentally determined interface prop-erties intrinsically case-specific. This hinders the development ofgenerally applicable predictive models.RubberCopperFibrilsFigure 2: Fibrillation in peel test [1].Objective: Develop a multi-scale method to take into accountthe micro-scale dissipation mechanisms explicitly in the macro-scopic interface description.MethodsThe multi-scale approach is outlined in figure 3. Cohesive zones(CZs) are used to describe the interface behavior on the macro-scale. The CZ traction-opening relation is obtained from theunderlying micro-mechanical model. The current micro-modelconsists of a single fibril. The roughness of the substrate istaken into account in a simplified way.rubbercohesivezonecopperCZ opening ΔCZ traction TΔcopperrubberOpeningTractionMicro-scale adhesionTmax,microGmicro:intrinsicadhesionenergyFigure 3: Multi-scale procedure. Macro (top) and micro (bottom).ResultsMicro-model results are shown in figure 4. The graph shows thehomogenized traction-separation response obtained from the sin-gle fibril model. The insets show several stages of the fibrillationprocess. The last inset shows the fibril right before it suddenlydebonds from the copper. This causes the loss of the energystored in the fibril, leading to macroscopically observed dissi-pated energy Gmacro.rubbercopper0 2.5 5 7.5 100.20.40.60.8CZ opening [Δ μm]CZ traction T [MPa]GmacroMicro-scaleadhesion:Tmax,microGmicroInitial defect: no adhesionTrue shear strain-1.00.41.8Micro-scale adhesion parameters:maximum traction T = 2.5 MPa,intrinsic adhesion energy G = 0.2 J/mmax,micromicro2Figure 4: Left: Initial single fibril geometry with simplified roughnessprofile. Right: Homogenized traction-separation response.The influence of the micro-scale adhesion parameters (maximumtraction Tmax,micro and intrinsic adhesion energy Gmicro) on themacroscopic dissipation Gmacro is shown in figure 5. The insetsshow the final deformed shape; for low Tmax,micro no fibrillationoccurs and micro-scale delamination prevails, Gmacro = Gmicro.0 0.5 1 1.5 2 2.5100101102G0.2 J/mmicro =2G 0.1 J/mmicro =2G 0.5 J/mmicro =2T [MPa]max,microG/ Gmacromicro[-]G 0.1 J/mmicro =2G 0.2 J/mmicro =2G 0.5 J/mmicro =2Figure 5: Tmax,micro controls the fibrillation process.Conclusions• A micro-model describing fibrillation was developed.• Fibrillation was taken into account in the macroscopic in-terface description.• The micro-scale parameter Tmax,micro mainly controls thefibrillation process.• The macro-scale dissipated energy Gmacro can be orders ofmagnitude larger than the intrinsic adhesion energy Gmicro.References:[1] vd Sluis, O. et al.: J. Phys. D: Appl. Phys., 44:034008, 2011

Multi-scale modelling of fibrillation in copper-rubber interface delamination

Vossen, BG Bart

Schreurs, PJG Piet

Sluis, O Olaf  van der

Geers, MGD Marc

Repository TU/e

 Multi-scale modelling of fibrillation in copper-rubber interfacedelaminationCitation for published version (APA):Vossen, B. G., Schreurs, P. J. G., Sluis, van der, O., & Geers, M. G. D. (2012). Multi-scale modelling offibrillation in copper-rubber interface delamination. Poster session presented at Mate Poster Award 2012 : 17thAnnual Poster Contest.Document status and date:Published: 01/01/2012Document Version:Accepted manuscript including changes made at the peer-review stagePlease check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 08. Jul. 2024Mechanics of MaterialsMulti-scale modelling of fibrillation incopper-rubber interface delaminationBart Vossen, Piet Schreurs, Olaf van der Sluis, Marc Geers/ Department of Mechanical EngineeringIntroductionCopper-rubber interfaces play a major role in a variety of prod-ucts, such as stretchable electronics, figure 1.John Rogers, Hopkins University Stephanie Lacour, University of CambridgeFigure 1: Stretchable electronics examples. Left: heart ablationcatheter. Right: Electronic skin for wearable mobile phone.Interface delamination causes failure of the product. An impor-tant delamination mechanism is fibrillation, see figure 2. Duringpeeling, the dissipation mechanisms depend on the loading con-ditions, rendering the experimentally determined interface prop-erties intrinsically case-specific. This hinders the development ofgenerally applicable predictive models.RubberCopperFibrilsFigure 2: Fibrillation in peel test [1].Objective: Develop a multi-scale method to take into accountthe micro-scale dissipation mechanisms explicitly in the macro-scopic interface description.MethodsThe multi-scale approach is outlined in figure 3. Cohesive zones(CZs) are used to describe the interface behavior on the macro-scale. The CZ traction-opening relation is obtained from theunderlying micro-mechanical model. The current micro-modelconsists of a single fibril. The roughness of the substrate istaken into account in a simplified way.rubbercohesivezonecopperCZ opening ΔCZ traction TΔcopperrubberOpeningTractionMicro-scale adhesionTmax,microGmicro:intrinsicadhesionenergyFigure 3: Multi-scale procedure. Macro (top) and micro (bottom).ResultsMicro-model results are shown in figure 4. The graph shows thehomogenized traction-separation response obtained from the sin-gle fibril model. The insets show several stages of the fibrillationprocess. The last inset shows the fibril right before it suddenlydebonds from the copper. This causes the loss of the energystored in the fibril, leading to macroscopically observed dissi-pated energy Gmacro.rubbercopper0 2.5 5 7.5 100.20.40.60.8CZ opening [Δ μm]CZ traction T [MPa]GmacroMicro-scaleadhesion:Tmax,microGmicroInitial defect: no adhesionTrue shear strain-1.00.41.8Micro-scale adhesion parameters:maximum traction T = 2.5 MPa,intrinsic adhesion energy G = 0.2 J/mmax,micromicro2Figure 4: Left: Initial single fibril geometry with simplified roughnessprofile. Right: Homogenized traction-separation response.The influence of the micro-scale adhesion parameters (maximumtraction Tmax,micro and intrinsic adhesion energy Gmicro) on themacroscopic dissipation Gmacro is shown in figure 5. The insetsshow the final deformed shape; for low Tmax,micro no fibrillationoccurs and micro-scale delamination prevails, Gmacro = Gmicro.0 0.5 1 1.5 2 2.5100101102G0.2 J/mmicro =2G 0.1 J/mmicro =2G 0.5 J/mmicro =2T [MPa]max,microG/ Gmacromicro[-]G 0.1 J/mmicro =2G 0.2 J/mmicro =2G 0.5 J/mmicro =2Figure 5: Tmax,micro controls the fibrillation process.Conclusions• A micro-model describing fibrillation was developed.• Fibrillation was taken into account in the macroscopic in-terface description.• The micro-scale parameter Tmax,micro mainly controls thefibrillation process.• The macro-scale dissipated energy Gmacro can be orders ofmagnitude larger than the intrinsic adhesion energy Gmicro.References:[1] vd Sluis, O. et al.: J. Phys. D: Appl. Phys., 44:034008, 2011

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Multi-scale modelling of fibrillation in copper-rubber interface delamination

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