In this paper, an automated numerical simulation of the propagation of multiple cracks in a finite elastic plane by the distributed dislocation method is developed. Firstly, a solution to the problem of a two-dimensional finite elastic plane containing multiple straight cracks and kinked cracks is presented. A serial of distributed dislocations in an infinite plane are used to model all the cracks and the boundary of the finite plane. The mixed-mode stress intensity factors of all the cracks can be calculated by solving a system of singular integral equations with the Gauss–Chebyshev quadrature method. Based on the solution, the propagation of multiple cracks is modeled according to the maximum circumferential stress criterion and Paris' law. Several numerical examples are presented to show the accuracy and efficiency of this method for the simulation of multiple cracks in a 2D finite plane.
Accepted:
Published online:
Jiong Zhang 1; Zhan Qu 2; Weidong Liu 3; Liankun Wang 1
@article{CRMECA_2019__347_3_191_0,
author = {Jiong Zhang and Zhan Qu and Weidong Liu and Liankun Wang},
title = {Automated numerical simulation of the propagation of multiple cracks in a finite plane using the distributed dislocation method},
journal = {Comptes Rendus. M\'ecanique},
pages = {191--206},
publisher = {Elsevier},
volume = {347},
number = {3},
year = {2019},
doi = {10.1016/j.crme.2019.01.004},
language = {en},
}
TY - JOUR AU - Jiong Zhang AU - Zhan Qu AU - Weidong Liu AU - Liankun Wang TI - Automated numerical simulation of the propagation of multiple cracks in a finite plane using the distributed dislocation method JO - Comptes Rendus. Mécanique PY - 2019 SP - 191 EP - 206 VL - 347 IS - 3 PB - Elsevier DO - 10.1016/j.crme.2019.01.004 LA - en ID - CRMECA_2019__347_3_191_0 ER -
%0 Journal Article %A Jiong Zhang %A Zhan Qu %A Weidong Liu %A Liankun Wang %T Automated numerical simulation of the propagation of multiple cracks in a finite plane using the distributed dislocation method %J Comptes Rendus. Mécanique %D 2019 %P 191-206 %V 347 %N 3 %I Elsevier %R 10.1016/j.crme.2019.01.004 %G en %F CRMECA_2019__347_3_191_0
Jiong Zhang; Zhan Qu; Weidong Liu; Liankun Wang. Automated numerical simulation of the propagation of multiple cracks in a finite plane using the distributed dislocation method. Comptes Rendus. Mécanique, Volume 347 (2019) no. 3, pp. 191-206. doi : 10.1016/j.crme.2019.01.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.01.004/
[1] Numerical modeling of crack propagation: automatic remeshing and comparison of different criteria, Comput. Methods Appl. Mech. Eng., Volume 192 (2003), pp. 3887-3908
[2] Polygonal finite elements for finite elasticity, Int. J. Numer. Methods Eng., Volume 101 (2015), pp. 305-328
[3] A polygonal finite element method for modeling crack propagation with minimum remeshing, Int. J. Fract., Volume 194 (2015), pp. 123-148
[4] Numerical simulation of crack growth in brittle matrix of particle reinforced composites using the XFEM technique, Acta Mech. Solida Sin., Volume 25 (2012), pp. 9-21
[5] Numerical analysis of the inclusion–crack interaction by the extended finite element method, Int. J. Comput. Methods Eng. Sci. Mech., Volume 15 (2014), pp. 26-32
[6] Interaction between a circular inclusion and an arbitrarily oriented crack, J. Appl. Mech., Volume 41 (1974), pp. 1007-1013
[7] Effects of partial closure and friction on a radial crack emanating from a circular hole, Int. J. Fract., Volume 28 (1985), pp. 29-36
[8] A normally loaded half plane with an edge crack, Int. J. Solids Struct., Volume 21 (1985), pp. 399-410
[9] Open cracks at or near free of positive radial stresses along the crack line in the edges, J. Strain Anal. Eng. Des., Volume 22 (1987), pp. 177-185
[10] Solution of Crack Problems – the Distributed Dislocation, Kluwer Academic Publishers, Dordrecht, 1996
[11] Dislocation Based Fracture Mechanics, World Scientific, Singapore, 1996
[12] Solution of an inclined crack in a finite plane and a new criterion to predict fatigue crack propagation, Int. J. Mech. Sci., Volume 119 (2016), pp. 217-223
[13] Influence of a micro-crack on the finite macro-crack, Eng. Fract. Mech., Volume 177 (2017), pp. 95-103
[14] Solution of multiple edge cracks in an elastic plane, Int. J. Fract., Volume 137 (2006), pp. 121-137
[15] Analysis of Some Two-Dimensional Problems Containing Cracks and Holes, Northwestern University, Evanston, USA, 2006
[16] Development of a distributed dislocation dipole technique for the analysis of multiple straight, kinked and branched cracks in an elastic half-plane, Int. J. Solids Struct., Volume 51 (2014), pp. 2878-2892
[17] Modeling cracks in finite bodies by distributed dislocation dipoles, Fatigue Fract. Eng. Mater. Struct., Volume 25 (2002), pp. 27-39
[18] Modelling cracks in arbitrarily shaped finite bodies by distribution of dislocation, Int. J. Solids Struct., Volume 41 (2004), pp. 399-411
[19] Solution of multiple cracks in a finite plate of an elastic isotropic material with the distributed dislocation method, Acta Mech. Solida Sin., Volume 27 (2014), pp. 276-283
[20] Numerical distributed dislocation modeling of multiple cracks in piezoelectric media considering different crack-face boundary conditions and finite size effects, Strength Fract. Complex., Volume 10 (2017), pp. 49-72
[21] Numerical studies of an array of equidistant semi-permeable inclined cracks in 2-D piezoelectric strip using distributed dislocation method, Int. J. Solids Struct., Volume 80 (2016), pp. 137-145
[22] Numerical solution of singular integral equations (G.C. Sih, ed.), Methods of Analysis and Solutions of Crack Problems, Noordhoff, Leyden, The Netherlands, 1973
[23] Solution of multiple crack problems in a finite plate using coupled integral equations, Int. J. Solids Struct., Volume 49 (2012), pp. 87-94
[24] Evaluation of the T-stress and stress intensity factor for a cracked plate in general case using eigenfunction expansion variational method, Fatigue Fract. Eng. Mater. Struct., Volume 31 (2008), pp. 476-487
[25] A meshless method with enriched weight functions for fatigue crack growth, Int. J. Numer. Methods, Volume 59 (2004), pp. 1945-1961
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