The effects of mismatch fracture properties in encapsulation-based self-healing concrete using cohesive-zone model

Abstract

Finite element analysis is developed to simulate the breakage of capsule in capsule-based self-healing concrete. A 2D circular capsule with different core-shell thickness ratios embedded in the mortar matrix is analyzed numerically along with their interfacial transition zone. Zero-thickness cohesive elements are pre-inserted into solid elements to represent potential cracks. This study focuses on the effects of mismatch fracture properties, namely fracture strength and energy, between capsule and mortar matrix into the breakage likelihood of the capsule. The extensive simulations of 2D specimens under uniaxial tension were carried out to investigate the key features on the fracture patterns of the capsule and produce the fracture maps as the results. The developed fracture maps of capsules present a simple but valuable tool to assist the experimentalists in designing appropriate capsule materials for self-healing concrete.

Keywords

self-healing concrete / interfacial zone / capsule materials / cohesive elements / fracture maps

References

[1] Li J, Zong B, Wang Y, Zhuang W. Experiment and modeling of mechanical properties on iron matrix composites reinforced by different types of ceramic particles. Materials Science and Engineering A, 2010, 527(29–30): 7545–7551

[2] Srivatsan T. Microstructure, tensile properties and fracture behaviour of Al₂O₃ particulate-reinforced aluminium alloy metal matrix composites. Journal of Materials Science, 1996, 31(5): 1375–1388

[3] Sigl L S, Mataga P, Dalgleish B, McMeeking R, Evans A. On the toughness of brittle materials reinforced with a ductile phase. Acta Metallurgica, 1988, 36(4): 945–953

[4] Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

[5] Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122

[6] Areias P, Rabczuk T, Camanho P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63

[7] Oucif C, Mauludin L M. Numerical modeling of high velocity impact applied to reinforced concrete panel. Underground Space, 2019, 4(1): 1–9

[8] Oucif C, Ouzaa K, Mauludin L M. Cyclic and monotonic behavior of strengthened and unstrengthened square reinforced concrete columns. Journal of Applied and Computational Mechanics, 2019, 5: 517–525

[9] Chen L, Rabczuk T, Bordas S P A, Liu G, Zeng K, Kerfriden P. Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering, 2012, 209–212: 250–265

[10] Nguyen-Vinh H, Bakar I, Msekh M, Song J H, Muthu J, Zi G, Le P, Bordas S, Simpson R, Natarajan S, Lahmer T, Rabczuk T. Extended finite element method for dynamic fracture of piezo-electric materials. Engineering Fracture Mechanics, 2012, 92: 19–31

[11] Zhang C, Wang C, Lahmer T, He P, Rabczuk T. A dynamic XFEM formulation for crack identification. International Journal of Mechanics and Materials in Design, 2016, 12(4): 427–448

[12] Vu-Bac N, Nguyen-Xuan H, Chen L, Bordas S, Kerfriden P, Simpson R, Liu G, Rabczuk T. A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. Computer Modeling in Engineering & Sciences, 2011, 73(4): 331–356

[13] Zhang Y, Zhuang X. Cracking elements method for dynamic brittle fracture. Theoretical and Applied Fracture Mechanics, 2019, 102: 1–9

[14] Zhang Y, Lackner R, Zeiml M, Mang H A. Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations. Computer Methods in Applied Mechanics and Engineering, 2015, 287: 335–366

[15] Zhang Y, Zhuang X. Cracking elements: A self-propagating strong discontinuity embedded approach for quasi-brittle fracture. Finite Elements in Analysis and Design, 2018, 144: 84–100

[16] Zhang Y, Zhuang X. A softening-healing law for self-healing quasi-brittle materials: Analyzing with strong discontinuity embedded approach. Engineering Fracture Mechanics, 2018, 192: 290–306

[17] Zhuang X, Wang Q, Zhu H. Multiscale modelling of hydro-mechanical couplings in quasi-brittle materials. International Journal of Fracture, 2017, 204(1): 1–27

[18] Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

[19] Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

[20] Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760

[21] Zhuang X, Augarde C, Bordas S. Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling. International Journal for Numerical Methods in Engineering, 2011, 86(2): 249–268

[22] Zhuang X, Augarde C, Mathisen K. Fracture modeling using meshless methods and level sets in 3D: Framework and modeling. International Journal for Numerical Methods in Engineering, 2012, 92(11): 969–998

[23] Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350

[24] Amiri F, Millán D, Shen Y, Rabczuk T, Arroyo M. Phase-field modeling of fracture in linear thin shells. Theoretical and Applied Fracture Mechanics, 2014, 69: 102–109

[25] Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

[26] Zhou S, Rabczuk T, Zhuang X. Phase field modeling of quasi-static and dynamic crack propagation: Comsol implementation and case studies. Advances in Engineering Software, 2018, 122: 31–49

[27] Zhou S, Zhuang X, Rabczuk T. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203

[28] Zhou S, Zhuang X, Zhu H, Rabczuk T. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192

[29] Zhou S, Zhuang X, Rabczuk T. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198

[30] Areias P, Msekh M, Rabczuk T. Damage and fracture algorithm using the screened poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143

[31] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[32] Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

[33] Areias P, Rabczuk T. Quasi-static crack propagation in plane and plate structures using set-valued traction separation laws. International Journal for Numerical Methods in Engineering, 2008, 74(3): 475–505

[34] Nguyen V P, Lian H, Rabczuk T, Bordas S. Modelling hydraulic fractures in porous media using flow cohesive interface elements. Engineering Geology, 2017, 225: 68–82

[35] Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second order boundary value problems. Computers, Materials & Continua, 2019, 59(1): 345–359

[36] Rabczuk T, Ren H, Zhuang X. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem, Computers. Materials and Continua, 2019, 59(1): 31–55

[37] Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456

[38] Atkinson C. The interaction between a crack and an inclusion. International Journal of Engineering Science, 1972, 10(2): 127–136

[39] Erdogan F, Gupta G, Ratwani M. Interaction between a circular inclusion and an arbitrarily oriented crack. Journal of Applied Mechanics, 1974, 41(4): 1007–1013

[40] Patton E, Santare M. The effect of a rigid elliptical inclusion on a straight crack. International Journal of Fracture, 1990, 46(1): 71–79

[41] Li Z, Chen Q. Crack-inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method. International Journal of Fracture, 2002, 118(1): 29–40

[42] Ayyar A, Chawla N. Microstructure-based modeling of crack growth in particle reinforced composites. Composites Science and Technology, 2006, 66(13): 1980–1994

[43] Romanova V A, Balokhonov R R, Schmauder S. The influence of the reinforcing particle shape and interface strength on the fracture behavior of a metal matrix composite. Acta Materialia, 2009, 57(1): 97–107

[44] Knight M, Wrobel L, Henshall J, De Lacerda L. A study of the interaction between a propagating crack and an uncoated/coated elastic inclusion using the BE technique. International Journal of Fracture, 2002, 114(1): 47–61

[45] Bush M. The interaction between a crack and a particle cluster. International Journal of Fracture, 1997, 88(3): 215–232

[46] Leggoe J, Hu X, Bush M. Crack tip damage development and crack growth resistance in particulate reinforced metal matrix composites. Engineering Fracture Mechanics, 1996, 53(6): 873–895

[47] Hall J N, Wayne Jones J, Sachdev A K. Particle size, volume fraction and matrix strength effects on fatigue behavior and particle fracture in 2124 aluminum-SiCp composites. Materials Science and Engineering A, 1994, 183(1–2): 69–80

[48] Fu S Y, Feng X Q, Lauke B, Mai Y W. Effects of particle size, particle/matrix interface adhesion and particle loading on mechanical properties of particulate-polymer composites. Composites. Part B, Engineering, 2008, 39(6): 933–961

[49] Rao K V, Soboyejo W, Ritchie R. Ductile-phase toughening and fatigue-crack growth in Nb-reinforced molybdenum disilicide intermetallic composites. Metallurgical Transactions. A, Physical Metallurgy and Materials Science, 1992, 23(8): 2249–2257

[50] Sun X, Yeomans J. Optimization of a ductile-particle-toughened ceramic. Journal of the American Ceramic Society, 1996, 79(10): 2705–2717

[51] Yang J, Jeng S. Interface and mechanical behavior of MoSi 2-based composites. Journal of Materials Research, 1991, 6(3): 505–513

[52] Maes M, Van Tittelboom K, De Belie N. The efficiency of self-healing cementitious materials by means of encapsulated polyurethane in chloride containing environments. Construction & Building Materials, 2014, 71: 528–537

[53] Dong B, Wang Y, Fang G, Han N, Xing F, Lu Y. Smart releasing behavior of a chemical self-healing microcapsule in the stimulated concrete pore solution. Cement and Concrete Composites, 2015, 56: 46–50

[54] Gruyaert E, Van Tittelboom K, Sucaet J, Anrijs J, Van Vlierberghe S, Dubruel P, De Geest B, Remon J, De Belie N. Capsules with evolving brittleness to resist the preparation of self-healing concrete. Materiales de Construcciόn, 2016, 66(323): 092

[55] Yang Z, Hollar J, He X, Shi X. A self-healing cementitious composite using oil core/silica gel shell microcapsules. Cement and Concrete Composites, 2011, 33(4): 506–512

[56] Huang H, Ye G. Simulation of self-healing by further hydration in cementitious materials. Cement and Concrete Composites, 2012, 34(4): 460–467

[57] Van Tittelboom K, Adesanya K, Dubruel P, Van Puyvelde P, De Belie N. Methyl methacrylate as a healing agent for self-healing cementitious materials. Smart Materials and Structures, 2011, 20(12): 125016

[58] Van Tittelboom K, De Belie N. Self-healing in cementitious materials-a review. Materials (Basel), 2013, 6(6): 2182–2217

[59] White S, Maiti S, Jones A, Brown E, Sottos N, Geubelle P. Fatigue of self-healing polymers: Multiscale analysis and experiments. In: ICF11. Italy, 2013

[60] Mauludin L M, Oucif C. Modeling of self-healing concrete: A review. Journal of Applied and Computational Mechanics, 2019, 5: 526–539

[61] Oucif C, Mauludin L. Continuum damage-healing and super healing mechanics in brittle materials: A state-of-the-art review. Applied Sciences (Basel, Switzerland), 2018, 8(12): 2350

[62] Mauludin L M, Zhuang X, Rabczuk T. Computational modeling of fracture in encapsulation-based self-healing concrete using cohesive elements. Composite Structures, 2018, 196: 63–75

[63] Gilabert F, Garoz D, Van Paepegem W. Stress concentrations and bonding strength in encapsulation-based self-healing materials. Materials & Design, 2015, 67: 28–41

[64] Alexeev A, Verberg R, Balazs A C. Patterned surfaces segregate compliant microcapsules. Langmuir, 2007, 23(3): 983–987

[65] Kaltzakorta E, Erkizia I. Silica microcapsules encapsulating epoxy compounds for self-healing cementitious materials. In: Proceedings of the 3rd International Conference on Self-Healing Materials. Bath, 2011

[66] Parmigiani J, Thouless M. The roles of toughness and cohesive strength on crack deflection at interfaces. Journal of the Mechanics and Physics of Solids, 2006, 54(2): 266–287

[67] Wang W, Sadeghipour K, Baran G. Finite element analysis of the effect of an interphase on toughening of a particle-reinforced polymer composite. Composites. Part A, Applied Science and Manufacturing, 2008, 39(6): 956–964

[68] Cid Alfaro M V, Suiker A S J, Verhoosel C V, de Borst R. Numerical homogenization of cracking processes in thin fibre-epoxy layers. European Journal of Mechanics. A, Solids, 2010, 29(2): 119–131

[69] Ponnusami S A, Turteltaub S, van der Zwaag S. Cohesive-zone modelling of crack nucleation and propagation in particulate composites. Engineering Fracture Mechanics, 2015, 149: 170–190

[70] Mauludin L M, Oucif C. The effects of interfacial strength on fractured microcapsule. Frontiers of Structural and Civil Engineering, 2019, 13(2): 353–363

[71] Mauludin L M, Oucif C. Interaction between matrix crack and circular capsule under uniaxial tension in encapsulation-based self-healing concrete. Underground Space, 2018, 3(3): 181–189

[72] Hilloulin B, Van Tittelboom K, Gruyaert E, De Belie N, Loukili A. Design of polymeric capsules for self-healing concrete. Cement and Concrete Composites, 2015, 55: 298–307

[73] Keller M, Sottos N. Mechanical properties of microcapsules used in a self-healing polymer. Experimental Mechanics, 2006, 46(6): 725–733

Acknowledgements

This work was supported and financed by RISTEK-DIKTI (Directorate General of Resources for Science, Technology and Higher Education. Ministry of Research, Technology and Higher Education of Indonesia) under funding agreement No: 153.39/E4.4/2014, and the German Academic Exchange Program (DAAD). The supports are gratefully acknowledged.

RIGHTS & PERMISSIONS

2020 Higher Education Press