Cohesive zone model for mode-I fracture with viscoelastic-sensitivity

Abstract A viscoelastic cohesive zone model (CZM) is formulated herein to model the time- and temperature-dependent fracture process of the interface between the solid propellant and insulation. The model is suitable for the simulation of a wide range of problems especially for the relaxation response of the fracture process. Independent control parameters of the Park-Paulino-Roesler (PPR) models are deduced first. By introducing the relaxed critical displacement, cohesive strength and initial slope parameter into the static PPR model, a viscoelastic CZM is established. Numerical time integration about obtaining the reduced time is described considering the change of the temperature. The properties of the proposed model are discussed in detail through the stretch and relaxation test of the double cantilever beam (DCB). Stretch test of the double cantilever sandwich beam (DCSB) under different loading rates and loading temperatures are designed to inverse the time-dependent and temperature-dependent model parameters respectively. To check the effectiveness of the proposed model and the accuracy of the inversed model parameters, three different tests including stretch test, multiple stretch-relaxation test, and creep test are conducted. The agreement is achieved between the numerical and experimental results.

[1]  Xiaohong Yang,et al.  Cohesive zone modeling of creep–fatigue crack propagation with dwell time , 2017 .

[2]  Andrew E. W. Jones,et al.  An adaptive simulated annealing algorithm for global optimization over continuous variables , 1995, J. Glob. Optim..

[3]  Alberto Corigliano,et al.  Rate-dependent interface models: formulation and numerical applications , 2001 .

[4]  G. Ruiz,et al.  A loading-rate dependent cohesive model to simulate concrete fracture , 2013 .

[5]  G. Ruiz,et al.  A loading rate dependent cohesive model for concrete fracture , 2012 .

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

[7]  Michael Kaliske,et al.  Time-dependent cohesive zone modelling for discrete fracture simulation , 2010 .

[8]  K. Liechti,et al.  Mixed-mode, time-dependent rubber/metal debonding , 2001 .

[9]  Karthik Ramani,et al.  Rate-dependent crack growth in adhesives II. Experiments and analysis , 2003 .

[10]  Bing Lam Luk,et al.  Adaptive simulated annealing for optimization in signal processing applications , 1999, Signal Process..

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

[12]  R. Landel,et al.  The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids , 1955 .

[13]  David H. Allen,et al.  A micromechanical model for a viscoelastic cohesive zone , 2001 .

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

[15]  G. Tang,et al.  Study on the Viscoelastic Poisson‘s Ratio of Solid Propellants Using Digital Image Correlation Method , 2016 .

[16]  Glaucio H. Paulino,et al.  An Efficient Mixed-Mode Rate-Dependent Cohesive Fracture Model Using Sigmoidal Functions , 2017 .

[17]  K. Dilger,et al.  Modeling of adhesive layers with temperature-dependent cohesive zone elements for predicting adhesive failure during the drying process of cathodic dip painting , 2018, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications.

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

[19]  Glaucio H. Paulino,et al.  A unified potential-based cohesive model of mixed-mode fracture , 2009 .

[20]  Jian-ye Zheng,et al.  Modeling the temperature-dependent mode I fracture behavior of adhesively bonded joints , 2017 .

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

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

[23]  Haiyang Li,et al.  A novel time dependent cohesive zone model for the debonding interface between solid propellant and insulation , 2018, Meccanica.

[24]  Marco Musto,et al.  A fractional rate‐dependent cohesive‐zone model , 2015 .

[25]  G. Paulino,et al.  Fractional calculus derivation of a rate-dependent PPR-based cohesive fracture model: theory, implementation, and numerical results , 2019, International Journal of Fracture.

[26]  Zdeněk P. Bažant,et al.  Cohesive Crack with Rate-Dependent Opening and Viscoelasticity: I. Mathematical Model and Scaling , 1997 .

[27]  G. Alfano,et al.  Thermodynamic Derivation and Damage Evolution for a Fractional Cohesive Zone Model , 2017 .

[28]  Marco Musto,et al.  A novel rate-dependent cohesive-zone model combining damage and visco-elasticity , 2013 .

[29]  Xi-Qiao Feng,et al.  Multiscale fracture mechanics model for the dorsal closure in Drosophila embryogenesis , 2019, Journal of the Mechanics and Physics of Solids.

[30]  A. Yee,et al.  Effects of rate on crack growth in a rubber-modified epoxy , 2000 .

[31]  M. Kaliske,et al.  A thermomechanically coupled viscoelastic cohesive zone model at large deformation , 2013 .

[32]  Karthik Ramani,et al.  Rate-dependent crack growth in adhesives: I. Modeling approach , 2003 .

[33]  Glaucio H. Paulino,et al.  Computational implementation of the PPR potential-based cohesive model in ABAQUS: Educational perspective , 2012 .

[34]  M. A. Crisfield,et al.  Progressive Delamination Using Interface Elements , 1998 .

[35]  Michael Kaliske,et al.  Peel process simulation of sealed polymeric film computational modelling of experimental results , 2007 .

[36]  Zdeněk P. Bažant,et al.  Cohesive Crack Model with Rate-Dependent Opening and Viscoelasticity: II. Numerical Algorithm, Behavior and Size Effect , 1997 .

[37]  V. Prakash,et al.  Dynamic brittle fracture of high strength structuralsteels underconditions of plane strain , 1999 .

[38]  Glaucio H. Paulino,et al.  A study on the thermodynamic consistency of the Park–Paulino–Roesler (PPR) cohesive fracture model , 2016 .

[39]  Shiyong Sun,et al.  The interfacial fracture behavior of foam core composite sandwich structures by a viscoelastic cohesive model , 2011 .