Numerical study on crack propagation in linear elastic multiphase composite materials using phase field method

Engineering Computations - Tập 36 Số 1 - Trang 307-333 - 2018
Xiang Li1, Dongyang Chu1, Yue Gao1, Zhanli Liu1
1Applied Mechanics laboratory, Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing , China

Tóm tắt

PurposeThe purpose of this paper is to develop an efficient numerical method to study the complex crack initiation and propagation in linear elastic multiphase composites.Design/methodology/approachA phase field method is developed to study the complex fracture behavior in multiphase composites. A damage threshold is introduced for referring crack initiation in the proposed method. The damage threshold is assigned as a material property so that different composite components possess different thresholds. In this manner, smooth transition from crack initiation to propagation is revealed.FindingsThe proposed method is used to investigate complex crack evolution in mesoscale cementitious composite, which consists of aggregates, matrix and void pores. From a mesoscale point of view, it is found that cracks prefer to evolve within the matrix phase. As a crack encounters an aggregate, it tends to bypass the aggregate and evolve along the interface. Cracks tend to avoid to penetrate through aggregates. Also, cracks tend to be attracted by void pores. From a mesoscale point of view, it is revealed that the elastic modulus and strength of concrete models are closely related to porosity.Originality/valueA criterion with a damage threshold is introduced to the proposed method. The criterions with and without a damage threshold are compared with each other in details. The proposed method is proven to be a useful tool to study mechanical behavior and crack evolution of brittle multiphase composites.

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Tài liệu tham khảo

2014, Estimating the modulus of elasticity of pervious concrete based on porosity, Advances in Civil Engineering Materials, 3, 256, 10.1520/ACEM20130081

2014, Phase-field modeling of fracture in linear thin shells, Theoretical and Applied Fracture Mechanics, 69, 102, 10.1016/j.tafmec.2013.12.002

2016, Phase-field analysis of finite-strain plates and shells including element subdivision, Computer Methods in Applied Mechanics and Engineering, 312, 322, 10.1016/j.cma.2016.01.020

2015, Couple stresses and the fracture of rock, Phil. Trans. R. Soc. A, 373, 20140120, 10.1098/rsta.2014.0120

2018, An h-adaptive thermo-mechanical phase field model for fracture, Finite Elements in Analysis and Design, 138, 31, 10.1016/j.finel.2017.09.003

1990, Random particle model for fracture of aggregate or fiber composites, Journal of Engineering Mechanics, 116, 1686, 10.1061/(ASCE)0733-9399(1990)116:8(1686)

2001, Nonlocal weibull theory and size effect in failures at fracture initiation, Fracture Mechanics of Concrete Structures, 659

2000, Probabilistic nonlocal theory for quasibrittle fracture initiation and size effect. II: Application, Journal of Engineering Mechanics, 126, 175, 10.1061/(ASCE)0733-9399(2000)126:2(175)

2007, Numerical implementation of the variational formulation for quasi-static brittle fracture, Interfaces and Free Boundaries, 9, 411, 10.4171/ifb/171

2012, A variational approach to the numerical simulation of hydraulic fracturing, SPE Annual Technical Conference and Exhibition

2008, The variational approach to fracture, Journal of Elasticity, 91, 5

2014, Morphogenesis and propagation of complex cracks induced by thermal shocks, Physical Review Letters, 112, 014301, 10.1103/PhysRevLett.112.014301

2016, Relationship between pore structure and compressive strength of concrete: Experiments and statistical modeling, Sādhanā, 41, 337, 10.1007/s12046-016-0468-9

2013, Influence of porosity on compressive and tensile strength of cement mortar, Construction and Building Materials, 40, 869, 10.1016/j.conbuildmat.2012.11.072

2017, Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling, International Journal of Fracture, 208, 115

2011, Lattice discrete particle model (LDPM) for failure behavior of concrete. I: Theory, Cement and Concrete Composites, 33, 881, 10.1016/j.cemconcomp.2011.02.011

2009, Discrete fracture modeling of asphalt concrete, International Journal of Solids and Structures, 46, 2593, 10.1016/j.ijsolstr.2009.02.006

2011, The relationship between porosity and strength for porous concrete, Construction and Building Materials, 25, 4294, 10.1016/j.conbuildmat.2011.05.005

2012, Discrete damage zone model for fracture initiation and propagation, Engineering Fracture Mechanics, 92, 1, 10.1016/j.engfracmech.2012.04.019

2008, Meso-structural study of concrete fracture using interface elements. I: numerical model and tensile behavior, Materials and Structures, 41, 583, 10.1617/s11527-007-9314-1

1971, The effect of porosity on the compressive strength and elastic modulus of polymer impregnated concrete, Cement and Concrete Research, 1, 631, 10.1016/0008-8846(71)90018-4

2015, Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids, Computer Methods in Applied Mechanics and Engineering, 294, 486, 10.1016/j.cma.2014.11.017

2010, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, 199, 2765

2016, Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media, Computer Methods in Applied Mechanics and Engineering, 304, 619, 10.1016/j.cma.2015.09.021

2015, A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium, Multiscale Modeling and Simulation, 13, 367, 10.1137/140967118

2017, Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model, Engineering Fracture Mechanics, 188, 287

2015, Modelling of concrete fracture at aggregate level using FEM and DEM based on X-ray μCT images of internal structure, Engineering Fracture Mechanics, 147, 13, 10.1016/j.engfracmech.2015.08.010

1992, Mixed-mode fracture of concrete: an experimental approach

1973, Porosity‐strength relation in cementitious materials with very high strengths, Journal of the American Ceramic Society, 56, 549, 10.1111/j.1151-2916.1973.tb12410.x

1992, Experimental and numerical analysis of micromechanisms of fracture of cement-based composites, Cement and Concrete Composites, 14, 105, 10.1016/0958-9465(92)90004-F

1992, Simple lattice model for numerical simulation of fracture of concrete materials and structures, Materials and Structures, 25, 534, 10.1007/BF02472449

1991, Numerical simulation of crack propagation from microcracking to fracture, Cement and Concrete Composites, 13, 87, 10.1016/0958-9465(91)90003-Z

2016, Experimental investigations of fracture process in concrete by means of X‐ray micro‐computed tomography, Strain, 52, 26, 10.1111/str.12168

2017, Discrete element method simulations of fracture in concrete under uniaxial compression based on its real internal structure, International Journal of Damage Mechanics, 27, 1056789517690915

2001, Simulation of fracture of cementitious composites with explicit modeling of microstructural features, Engineering Fracture Mechanics, 68, 1245, 10.1016/S0013-7944(01)00017-0

1991, Mode I fracture of concrete: discontinuous crack growth and crack interface grain bridging, Cement and Concrete Research, 21, 1, 10.1016/0008-8846(91)90025-D

1975, An analysis of the brazilian disk fracture test using the weibull probabilistic treatment of brittle strength, International Journal of Fracture, 11, 495, 10.1007/BF00033536

1999, Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh, Computers and Structures, 70, 533, 10.1016/S0045-7949(98)00177-1

2015, Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model, Computational Mechanics, 55, 1, 10.1007/s00466-014-1079-0

2015, Monte carlo simulations of mesoscale fracture modelling of concrete with random aggregates and pores, Construction and Building Materials, 75, 35, 10.1016/j.conbuildmat.2014.09.069

1939, A statistical theory of the strength of materials, Ingeniors Vetenskaps Akademien

2014, An augmented-Lagrangian method for the phase-field approach for pressurized fractures, Computer Methods in Applied Mechanics and Engineering, 271, 69, 10.1016/j.cma.2013.12.005

1985, Simulation and analysis of composite structures, Materials Science and Engineering, 68, 239, 10.1016/0025-5416(85)90413-6

2006, Microcrack statistics, weibull distribution and micromechanical modeling of compressive failure in rock, Mechanics of Materials, 38, 664, 10.1016/j.mechmat.2005.12.002

2017, Mesoscale fracture analysis of multiphase cementitious composites using peridynamics, Materials, 10, 162, 10.3390/ma10020162

1998, Crack pattern evolution and a fractal damage constitutive model for rock, International Journal of Rock Mechanics and Mining Sciences, 35, 349, 10.1016/S0148-9062(97)00340-9

2014, Influence of pore structure on compressive strength of cement mortar, The Scientific World Journal, 2014

2018, A phase-field modeling approach of fracture propagation in poroelastic media, Engineering Geology, 240, 189, 10.1016/j.enggeo.2018.04.008