Irreversible mixed mode interface delamination using a combined damage-plasticity cohesive zone enabling unloading

Delamination is often identified as an important failure mechanism in structures with a high interface density, such as modern microelectronic systems and advanced composite materials. Delamination tests performed on different interface structures reveal complex failure mechanisms (crack bridging, fibre pull out, micro-void coalescence, fibrilation, crack meandering, etc.) in the fracture process zone that lead to an irreversible unloading response of the interface, ranging from full damage to full plasticity. Modeling the unloading response of an interface is important for predicting phenomena such as crack branching and crack propagation at multiple interfaces. This paper presents a 2D irreversible combined plasticity-damage unloading model, which can be used to extend the cohesive zone (loading) models with a proper unloading description that is suitable for modeling the entire loading-unloading response in the process zone. The presented model is able to capture changes in unloading behavior as a function of mode mixity, whereas it introduced only two additional model parameters that can be determined from dedicated delamination experiments. As a demonstration, the improved Xu–Needleman cohesive zone law has been extended with the proposed combined damage-plasticity unloading formulation. Numerical simulations with this extended model are performed for a glue interface system, recovering the typical observed behavior in delamination experiments. Finally, a complete procedure to extract all CZ model parameters is presented and illustrated for the glue interface system.

[1]  Marc G. D. Geers,et al.  Cohesive zone modeling for structural integrity analysis of IC interconnects , 2007, Microelectron. Reliab..

[2]  De Xie,et al.  Discrete cohesive zone model for mixed-mode fracture using finite element analysis , 2006 .

[3]  P. Camanho,et al.  A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites , 2009 .

[4]  James R. Rice,et al.  Embrittlement of interfaces by solute segregation , 1989 .

[5]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[6]  S. R. Olsen,et al.  An in situ rapid heat–quench cell for small-angle neutron scattering , 2008 .

[7]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[8]  Bert Sluys,et al.  Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces , 2000 .

[9]  Stephan Marzi,et al.  A Rate-Dependent , Elasto-Plastic Cohesive Zone Mixed-Mode Model for Crash Analysis of Adhesively Bonded Joints , 2009 .

[10]  Arne Hillerborg,et al.  Application of the fictitious crack model to different types of materials , 1991, International Journal of Fracture.

[11]  A. Biel,et al.  Damage and plasticity in adhesive layer: an experimental study , 2010 .

[12]  van den Mj Marco Bosch,et al.  An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion , 2006 .

[13]  K. Liechti,et al.  Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear , 1992 .

[14]  Mgd Marc Geers,et al.  A cohesive zone model with a large displacement formulation accounting for interfacial fibrilation , 2007 .

[15]  M Mohammad Samimi,et al.  An enriched cohesive zone model for delamination in brittle interfaces , 2009 .

[16]  M. D. Thouless,et al.  Use of a cohesive-zone model to analyze the fracture of a fiber-reinforced polymer-matrix composite , 2005 .

[17]  J. V. Dommelen,et al.  An improved miniature mixed-mode delamination setup for in situ microscopic interface failure analyses , 2011 .

[18]  Bent F. Sørensen,et al.  Cohesive law and notch sensitivity of adhesive joints , 2002 .

[19]  Akira Todoroki,et al.  Measurement of orthotropic electric conductance of CFRP laminates and analysis of the effect on delamination monitoring with an electric resistance change method , 2002 .

[20]  M. Kortschot,et al.  The role of the resin fillet in the delamination of honeycomb sandwich structures , 2002 .

[21]  J. Hutchinson,et al.  The relation between crack growth resistance and fracture process parameters in elastic-plastic solids , 1992 .

[22]  Bent F. Sørensen,et al.  Determination of cohesive laws by the J integral approach , 2003 .

[23]  H. Nakamura,et al.  結晶粒界拡散過程により作製したNd―Fe―B焼結磁石における保磁力分布 , 2011 .

[24]  Z. Suo,et al.  Mixed mode cracking in layered materials , 1991 .

[25]  Glaucio H. Paulino,et al.  Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials , 2005 .

[26]  J. P. M. Hoefnagels,et al.  In-situ characterization of interface delamination by a new miniature mixed mode bending setup , 2009 .

[27]  Xiaopeng Xu,et al.  Void nucleation by inclusion debonding in a crystal matrix , 1993 .

[28]  Z. Suo,et al.  Interface crack between two elastic layers , 1990 .

[29]  Akira Todoroki,et al.  Electrical resistance change method for monitoring delaminations of CFRP laminates: effect of spacing between electrodes , 2005 .

[30]  Leslie Banks-Sills,et al.  A new cohesive zone model for mixed mode interface fracture in bimaterials , 2008 .

[31]  R. Fedele,et al.  Characterization of a cohesive-zone model describing damage and de-cohesion at bonded interfaces. Sensitivity analysis and mode-I parameter identification , 2010 .

[32]  J. V. Dommelen,et al.  A practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment , 2013, International Journal of Fracture.

[33]  Mgd Marc Geers,et al.  Fatigue damage modeling in solder interconnects using a cohesive zone approach , 2005 .

[34]  C. Sato,et al.  Comparison of the Mechanical Behaviour Between Stiff and Flexible Adhesive Joints for the Automotive Industry , 2010 .

[35]  V. Tvergaard.  Effect of fibre debonding in a whisker-reinforced metal , 1990 .

[36]  van Jaw Hans Dommelen,et al.  A self-adaptive finite element approach for simulation of mixed-mode delamination using cohesive zone models , 2011 .

[37]  G. I. Barenblatt.  THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[38]  Willem D. van Driel,et al.  Efficient damage sensitivity analysis of advanced Cu/low-k bond pad structures by means of the area release energy criterion , 2007, Microelectron. Reliab..

[39]  G. I. Barenblatt.  The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks , 1959 .

[40]  G.A.O. Davies,et al.  Predicting delamination and debonding in modern aerospace composite structures , 2006 .

[41]  P. Geubelle,et al.  Impact-induced delamination of composites: A 2D simulation , 1998 .

[42]  Ulf Stigh,et al.  Shear behaviour of adhesive layers , 2007 .

[43]  Jung-Ryul Lee,et al.  Structural health monitoring for a wind turbine system: a review of damage detection methods , 2008 .

[44]  A. Needleman.  A Continuum Model for Void Nucleation by Inclusion Debonding , 1987 .

[45]  Ulf Stigh,et al.  The stress–elongation relation for an adhesive layer loaded in peel using equilibrium of energetic forces , 2004 .

[46]  A. Needleman.  An analysis of decohesion along an imperfect interface , 1990 .

[47]  M. Elices,et al.  The cohesive zone model: advantages, limitations and challenges , 2002 .

[48]  Willem D. van Driel,et al.  Prediction of Delamination Related IC & Packaging Reliability Problems , 2005, Microelectron. Reliab..

[49]  Viggo Tvergaard,et al.  Effect of strain-dependent cohesive zone model on predictions of crack growth resistance , 1996 .

[50]  M. Ortiz,et al.  FINITE-DEFORMATION IRREVERSIBLE COHESIVE ELEMENTS FOR THREE-DIMENSIONAL CRACK-PROPAGATION ANALYSIS , 1999 .