Development of two intrinsic cohesive zone models for progressive interfacial cracking of laminated composites with matching and non-matching cohesive elements

Abstract In recent decades, intrinsic cohesive zone models (CZMs) have proved to be an effective approach to modeling progressive interfacial cracking of laminated composite structures. However, matching cohesive interface elements are usually required, which imposes constraints on finite element mesh discretization and reduces computational efficiency for interfacial cracking analysis in bi-material structures with a large modulus mismatch. To address this issue, we develop two intrinsic CZMs, i.e. node- and facet-based models, allowing interfacial cracking modeling with both matching and non-matching cohesive elements in a unified way. Prior to cracking simulations, node and facet cohesive pairs can be easily constructed by recourse to contact detection algorithms. During cracking, cohesive forces of such two models are evaluated in pointwise and integral ways, respectively. The developed models are then respectively coupled with tributary node-to-segment and mortar algorithms to account for a smooth transition from cohesive failure to unilateral contact. Several representative numerical examples are performed to validate the effectiveness of the proposed models, where the numerical performance is also compared and discussed.

[1]  Ludovic Noels,et al.  A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous Galerkin‐cohesive band model framework , 2018 .

[2]  Wenlong Zhang,et al.  Cohesive element approach for dynamic crack propagation: Artificial compliance and mesh dependency , 2017 .

[3]  Shinobu Yoshimura,et al.  A nodal-based extrinsic cohesive/contact model for interfacial debonding analyses in composite structures , 2019, Computers & Structures.

[4]  E. M. Wu,et al.  CRACK EXTENSION IN FIBERGLASS REINFORCED PLASTICS , 1965 .

[5]  G. Paulino,et al.  Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces , 2011 .

[6]  Francesco Aymerich,et al.  Finite element modelling of damage induced by low-velocity impact on composite laminates , 2014 .

[7]  T. Truster,et al.  A variational multiscale discontinuous Galerkin formulation for both implicit and explicit dynamic modeling of interfacial fracture , 2019, Computer Methods in Applied Mechanics and Engineering.

[8]  M. Zang,et al.  An intrinsic cohesive zone approach for impact failure of windshield laminated glass subjected to a pedestrian headform , 2019, International Journal of Impact Engineering.

[9]  P. Camanho,et al.  Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials , 2003 .

[10]  Jacob Fish,et al.  Are the cohesive zone models necessary for delamination analysis , 2016 .

[11]  Giorgio Zavarise,et al.  Isogeometric treatment of frictional contact and mixed mode debonding problems , 2017 .

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

[13]  Haim Waisman,et al.  Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model , 2015 .

[14]  Carlos G. Davila,et al.  A thermodynamically consistent discontinuous Galerkin formulation for interface separation , 2015 .

[15]  H. Espinosa,et al.  A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementation , 2003 .

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

[17]  W. Cui,et al.  A comparison of failure criteria to predict delamination of unidirectional glass/epoxy specimens waisted through the thickness , 1992 .

[18]  Jiye Chen,et al.  An extended cohesive damage model for simulating multicrack propagation in fibre composites , 2016 .

[19]  Tomonori Yamada,et al.  Numerical analysis of impact failure of automotive laminated glass: A review , 2017 .

[20]  De Xie,et al.  Discrete Cohesive Zone Model to Simulate Static Fracture in 2D Triaxially Braided Carbon Fiber Composites , 2006 .

[21]  Debasish Roy,et al.  Phase field based peridynamics damage model for delamination of composite structures , 2017 .

[22]  Peter Wriggers,et al.  Mortar based frictional contact formulation for higher order interpolations using the moving friction cone , 2006 .

[23]  Zumei Zheng,et al.  Finite element modelling of impact damage in polyvinyl butyral laminated glass , 2016 .

[24]  Ted Diehl,et al.  On using a penalty-based cohesive-zone finite element approach, Part I: Elastic solution benchmarks , 2008 .

[25]  Pedro P. Camanho,et al.  An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models , 2007 .

[26]  Mengyan Zang,et al.  A three-dimensional computational framework for impact fracture analysis of automotive laminated glass , 2015 .

[27]  Mengyan Zang,et al.  LC-Grid: a linear global contact search algorithm for finite element analysis , 2014 .

[28]  P. Wriggers,et al.  NURBS- and T-spline-based isogeometric cohesive zone modeling of interface debonding , 2014 .

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

[30]  M. Paggi,et al.  Node-to-segment and node-to-surface interface finite elements for fracture mechanics , 2016, 1604.05236.

[31]  Lorenzo Iannucci,et al.  Formulation and implementation of decohesion elements in an explicit finite element code , 2006 .

[32]  Vinh Phu Nguyen.  Discontinuous Galerkin/extrinsic cohesive zone modeling: Implementation caveats and applications in computational fracture mechanics , 2014 .

[33]  Tinh Quoc Bui,et al.  Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures , 2019, J. Comput. Phys..

[34]  J. C. Simo,et al.  A continuum-based finite element formulation for the implicit solution of multibody, large deformation-frictional contact problems , 1993 .

[35]  Ludovic Noels,et al.  A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, Cohesive Element Method , 2011 .

[36]  Stephen R Hallett,et al.  Cohesive zone length in numerical simulations of composite delamination , 2008 .

[37]  Brian Lau Verndal Bak,et al.  A user programmed cohesive zone finite element for ANSYS Mechanical , 2017 .

[38]  Erik Lund,et al.  Analysis of the integration of cohesive elements in regard to utilization of coarse mesh in laminated composite materials , 2014 .

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

[40]  Lorenzo Iannucci,et al.  Dynamic delamination modelling using interface elements , 2006 .

[41]  Debasish Roy,et al.  A Phase-Field Damage Model for Orthotropic Materials and Delamination in Composites , 2018 .

[42]  Peter Wriggers,et al.  Frictionless 2D Contact formulations for finite deformations based on the mortar method , 2005 .

[43]  G. Meschke,et al.  A finite element model for propagating delamination in laminated composite plates based on the Virtual Crack Closure method , 2016 .

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

[45]  P. Wriggers,et al.  Real contact mechanisms and finite element formulation—a coupled thermomechanical approach , 1992 .

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

[47]  Hiroshi Suemasu,et al.  X-FEM analyses of a thin-walled composite shell structure with a delamination , 2010 .

[48]  T. Belytschko,et al.  Efficient large scale non‐linear transient analysis by finite elements , 1976 .

[49]  Jianqiao Ye,et al.  Modeling progressive delamination of laminated composites by discrete element method , 2011 .

[50]  Aniello Riccio,et al.  Inter-laminar and intra-laminar damage evolution in composite panels with skin-stringer debonding under compression , 2016 .

[51]  S. Wang,et al.  The inside–outside contact search algorithm for finite element analysis , 1997 .

[52]  Amin Heidarpour,et al.  Modelling interfacial cracking with non-matching cohesive interface elements , 2016 .

[53]  Chao Zhang,et al.  Modelling fracture and delamination in composite laminates: Energy release rate and interface stress , 2018 .