Abstract
To conveniently and feasibly characterize the interface debonding in particle-reinforced nonlinear viscoelastic polymer composites (PRNVPCs), a micromechanical model is proposed based on a normalization method that can convert the rate-dependent constitutive relationship of a nonlinear viscoelastic matrix into a rate-independent linear viscoelastic constitutive relationship. With this treatment, a linear homogenization scheme is used to achieve closed-form solutions for the critical particle stress and the critical time at the initiation of interface debonding in PRNVPCs. The change in the particle debonding stress versus the debonding angle is theoretically predicted with the new model, and the predicted change is qualitatively consistent with the experimental data. Furthermore, it is found that the particle debonding stress increases monotonically with decreasing particle size. The increase of the applied strain rate leads to an increase of the particle debonding stress but a decrease in the critical debonding time. This demonstrates that a smaller particle and a higher loading rate are both beneficial for improving the interfacial adhesion, while the latter will shorten the time needed to initiate interface debonding. The present research provides a convenient approach to theoretically characterize the interface debonding in PRNVPCs, which should be of guiding value for the design of advanced polymeric composites with a good load bearing capacity.
Similar content being viewed by others
References
Gibson RF (2011) Principles of composite material mechanics, 3rd edn. Taylor & Francis Group, USA
Fu SY, Feng XQ, Lauke B, May YW (2008) Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate–polymer composites. Compos Part B 39:933–961
Pukanszky B (2005) Interfaces and interphases in multicomponent materials: past, present, future. Euro Polymer J 41(4):645–662
Meng JC, Ru CQ (2019) Effective mass density of rigid sphere-reinforced elastic composites. Meccanica 56:1209–1221
Alves PD, Simone A, Duarte CA (2021) A generalized finite element method for three-dimensional fractures in fiber-reinforced composites. Meccanica 56:1441–1473
Alimardani M, Razzaghi-Kashani M, Ghoreishy MHR (2017) Prediction of mechanical and fracture properties of rubber composites by microstructural modeling of polymer-filler interfacial effects. Mater Des 115:348–354
Parrinello F, Borino G (2018) Integration of finite displacement interface element in reference and current configurations. Meccanica 53:1455–1468
Zhang LQ (2018) Rubber nanocomposites: basics and applications. Chemical Industry Press, Beijing
Meng QH, Wang TJ (2019) An improved crack-bridging model for rigid particle-polymer composites. Eng Fract Mech 211:291–302
Benveniste Y (1985) The effective mechanical behavior of composite materials with imperfect contact between the constituents. Mech Mater 4:197–208
Hashin Z (1990) Thermoelastic properties of particulate composites with imperfect interface. J Mech Phys Solids 39(6):745–762
Chen JK, Wang GT, Yu ZZ, May YW (2010) Critical particle size for interfacial debonding in polymer/nanoparticle composites. Compos Sci Technol 70:861–872
Lauke B (2008) On the effect of particle size on fracture toughness of polymer composites. Compos Sci Technol 68:3365–3372
Lauke B, Fu SY (2013) Aspects of fracture toughness modelling of particle filled polymer composites. Compos Part B 45:1569–1574
Tan H, Liu C, Huang Y, Geubelle PH (2005) The cohesive law for the particle/matrix interfaces in high explosives. J Mech Phys Solids 53:1892–1917
Tan H, Huang Y, Liu C, Ravichandran G, Inglis HM, Geubelle PH (2007) The uniaxial tension of particulate composite materials with nonlinear interface debonding. Int J Solids Struct 44:1809–1822
Ben SD, Zhao JH, Rabczuk T (2014) A theoretical analysis of interface debonding for coated sphere with functionally graded interphase. Compos Struct 117:288–297
Cui HR, Shen ZB, Li HY (2018) A novel time dependent cohesive zone model for the debonding interface between solid propellant and insulation. Meccanica 53:3527–3544
Toulemonde PA, Diani J, Gilormini P, Desgardin N (2016) On the account of a cohesive interface for modeling the behavior until break of highly filled elastomers. Mech Mater 93:124–133
Karimi D, Milani AS, Alavi F (2019) Recycled stone/ABS particulate composite: micromechanical finite element fracture analysis. Compos Part B 177:107315
Chen JK, Huang ZP, Chu H, Bai SL (2003) Nonlinear viscoelastic constitutive relations based on the rate sensitive relaxation time under the condition of uniaxial stress. Acta Polymer Sin 3:414–419
He DJ, Hu YH (2021) A nonlinear visco-poroelasticity model for transversely isotropic gels. Meccanica 56:1483–1504
Xu JS, Chen X, Wang HL, Zheng J, Zhou C (2014) Thermo-damage-viscoelastic constitutive model of HTPB composite propellant. Int J Solids Struct 51(18):3209–3217
Shaw MT, Macknight WJ (2018) Introduction to polymer viscoelasticity. Wiley, New York
Ward IM (1983) Mechanical properties of solids polymers, 2nd edn. Wiley-Interscience, UK
Cao K, Ma XZ, Zhang BS, Wang Y, Wang Y (2010) Tensile behavior of polycarbonate over a wide range of strain rates. Mater Sci Eng A 527:4056–4061
Cao K, Wang Y, Wang Y (2012) Effects of strain rate and temperature on the tension behavior of polycarbonate. Mater Des 38:53–58
Song H, Chen JK, Qian C, Lv YF, Cao YH (2018) Rate-dependent characteristic of relaxation time of concrete. Acta Mech Solida Sin 32(1):69–80
Thamburaja P, Sarah K, Srinivasa A, Reddy JN (2019) Fracture of viscoelastic materials: FEM implementation of a non-local & rate form-based finite-deformation constitutive theory. Comput Methods Appl Mech Eng 354:871–903
Sarah K, Thamburaja P, Srinivasa A, Reddy JN (2020) Numerical simulations of damage and fracture in viscoelastic solids using a nonlocal fracture criterion. Mech Adv Mater Struct 27(13):1085–1097
Shen RL, Waisman H, Guo LC (2019) Fracture of viscoelastic solids modeled with a modified phase field method. Comput Methods Appl Mech Eng 346:862–890
Yin B, Kaliske M (2020) Fracture simulation of viscoelastic polymers by the phase-field method. Comput Mech 65:293–309
Cui HR, Li HY, Shen ZB (2019) Cohesive zone model for mode-I fracture with viscoelasticsensitivity. Eng Fract Mech 221:106578
Ciavarella M, Papangelo A, McMeeking R (2021) Crack propagation at the interface between viscoelastic and elastic materials. Eng Fract Mech 257:108009
Barbero EJ, Luciano R (1995) Micromechanical formulas for the relaxation tensor of linear viscoelastic composites with transversely isotropic fibers. Int J Solids Struct 32(13):1859–1872
Tan H, Huang Y, Liu C (2008) The viscoelastic composite with interface debonding. Compos Sci Technol 68:3145–3149
Sanahuja J (2013) Effective behaviour of ageing linear viscoelastic composites: homogenization approach. Int J Solids Struct 50:2846–2856
Levesque M, Derrien K, Mishnaevski L Jr, Baptiste D, Gilchrist MD (2004) A micromechanical model for nonlinear viscoelastic particle reinforced polymeric composite materials-undamaged state. Compos Part A 35:905–913
Muliana AH, Kim JS (2007) A concurrent micromechanical model for predicting nonlinear viscoelastic responses of composites reinforced with solid spherical particles. Int J Solids Struct 44:6891–6913
Zhu HL, Muliana A, Rajagopal KR (2016) On the nonlinear viscoelastic deformations of composites with prestressed inclusions. Compos Struct 149:279–291
Chen JK, Huang ZP, Mai YW (2003) Constitutive relation of particulate-reinforced viscoelastic composite materials with debonded microvoids. Acta Mater 51:3375–3384
Chen JK, Huang ZP, Zhu J (2007) Size effect of particles on the damage dissipation in nanocomposites. Compos Sci Technol 67:2990–2996
Chen JH, Hu HJ, Li S, Zhang K (2016) Quantitative relation between the relaxation time and the strain rate for polymeric solids under quasi-static conditions. J Appl Polymer Sci 133(42):44114
Regrain C, Laiarinandrasana L, Toillon S, Saï K (2009) Multi-mechanism models for semi-crystalline polymer: constitutive relations and finite element implementation. Int J Plast 25:1253–1279
van Breemen LCA, Klompen ETJ, Govaert LE, Han EHM (2011) Extending the EGP constitutive model for polymer glasses to multiple relaxation times. J Mech Phys Solids 65:2191–2207
Ban HX, Yao Y, Chen SH, Fang D (2019) A new constitutive model of micro-particle reinforced metal matrix composites with damage effects. Int J Mech Sci 152:524–534
Zhao YH, Weng GJ (2002) The effect of debonding angle on the reduction of effective moduli of particle and fiber-reinforced composites. J Appl Mech 69:292–302
Yang BJ, Kim BR, Lee HK (2012) Micromechanics-based viscoelastic damage model for particle-reinforced polymeric composites. Acta Mech 223:1307–1321
Mura T (1987) Micromechanics of defects in solids. Kluwer Academic Publisher, Boston
Bai SL, Wang M, Zhao XF (2003) Interfacial debonding behavior of a rigid particle-filled polymer composite. Compos Interface 10(2–3):243–253
Zhang MH, Chen JK (2012) Analysis of interfacial fracture strength of an inclusion in a polymeric composite considering cohesive force. Comput Mater Sci 61:6–11
Feng X, Meitl MA, Bowen AM, Huang Y, Nuzzo RG, Rogers JA (2007) Competing fracture in kinetically controlled transfer printing. Langmuir 23:12555–12560
Chen H, Li M, Wu J, Carlson A (2013) A viscoelastic model for the rate effect in transfer printing. ASME J Appl Mech 80:041019
Acknowledgements
The work reported here is supported by NSFC through Grants (Nos. 11772333, 21902007). We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Chen, J., Yao, Y. & Zhang, B. The interface debonding in particle-reinforced nonlinear viscoelastic polymer composites. Meccanica 57, 1353–1367 (2022). https://doi.org/10.1007/s11012-022-01484-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-022-01484-x