Phase field method with strain orthogonal decompositions for modelling of damage in heterogeneous materials obtained by X-ray computed tomography images
Email:
thanhvb@utc.edu.vn
Từ khóa:
phase field method, X-ray computed tomography, strain decompositions, interfacial damage
Tóm tắt
The phase-field method has become a robust tool to describe the complex crack nucleation and propagation in heterogeneous materials. In these materials, an interaction between bulk brittle damage and interfacial damage through the splitting the strain tensor into a bulk strain part and a jump strain part at the interfaces. Moreover, the material response of the heterogeneous materials in tension and compression, the bulk strain part needs to be decomposed into a positive part and a negative part. However, most of the previous works, these decompositions do not verify the negative part be orthogonal the positive part, which lead to the inaccuracy in the material mechanical behavior. To solve the shortcomings, the strain orthogonal decompositions problem that is applied to decompose the bulk strain in our work. In the present work, author combined the phase-field modeling taking into account interfacial damage with the problem of the bulk strain orthogonal decompositions by two proposed solutions. The successful prediction of the crack propagation for the inclusion-matrix structures and the multi-phases materials of X-ray computed tomography (XR-CT) images by two proposed solutions will be demonstrated in several numerical examples.Tài liệu tham khảo
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Int. J. Numer. Methods Engg, 50 (2001) 2667-2682. https://doi.org/10.1002/nme.143
Royal Society London Series A, 221 (1921) 163-198. https://doi.org/10.1098/rsta.1921.0006
[2]. G.R. Irwin, Analysis of stress and strains near the end of a crack traversing a plate, J. Appl.
Mech, 24 (1957) 361-364.
[3]. G.A. Francfort, J.J. Marigo, Revisiting brittle fracture as an energy minimization problem, J.
Mech. Phys. Solids, 46 (1998), 1319-1342. https://doi.org/10.1016/S0022-5096(98)00034-9
[4]. B. Bourdin, J.J. Marigo, C. Maurini, P. Sicsic, Morphogenesis and propagation of complex
cracks induced by thermal shocks, Phys. Rev. Lett, 112 (2014) 014301. https://doi.org/10.1103/PhysRevLett.112.014301
[5]. K. Pham, J.J. Marigo, C. Maurini, The issues of the uniqueness and the stability of the
homogeneous response in uniaxial tests with gradient damage models, J. Mech. Phys. Solids,
59 (2011b) 1163-1190. https://doi.org/10.1016/j.jmps.2011.03.010
[6]. D. Mumford, J. Shah, Optimal approximations by piecewise smooth functions and associated
variational problems, Commun. Pure. Appl. Math, 42 (1989) 577-685. https://doi.org/ 10.1002/cpa.3160420503
[7]. C. Miehe, M. Hofacker, F. Welschinger, A phase field model for rate-independent crack
propagation: robust algorithmic implementation based on operator splits, Comput. Methods
Appl. Mech. Eng, 199 (2010) 2765-2778. https://doi.org/10.1016/j.cma.2010.04.011
[8]. G.I. Barenblatt, The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks, J. Appl. Math. Mech, 23 (1959) 622–636.
[8]. D.S. Dugdale, Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 8 (1960) 100–104. https://doi.org/10.1016/0022-5096(60)90013-2
[10]. C.V. Verhoosel, R. de Borst, A phase-field model for cohesive fracture, Internat. J. Numer. Methods Engrg, 96 (2013) 43–62. https://doi.org/10.1002/nme.4553
[11]. N. Sukumar, N. Moes, B. Moran, T. Belytschko, Extended finite element method for threedimensional crack modelling, Internat. J. Numer. Methods Engg, 48 (2000) 1549-1570. https://doi.org/10.1002/1097-0207(20000820)48:11<1549::AID-NME955>3.0.CO;2-A
[12]. J. Gu, T. Yu, V.L. Le, T.T. Nguyen, S. Tanaka, Q.T. Bui, Multi-inclusions modeling by adaptive XIGA based on LR B-splines and multiple level sets, Finite Elem. Anal. Des, 148 (2018) 48-66. https://doi.org/10.1016/j.finel.2018.05.003
[13]. W.D. Carlson,Three-dimensional imaging of earth and planetary materials, Earth Planet Sci.
Lett, 249 (2006) 133-147. https://doi.org/10.1016/j.epsl.2006.06.020
[14]. L. Babout, T.J. Marrow, D. Engelberg, P.J. Withers, X-ray microtomographic observation
of intergranular stress corrosion cracking in sensitised austenitic stainless steel, Mater. Sci.
Technol, 22 (2006) 1068-1075. https://doi.org/10.1179/174328406X114090
[15]. L. Qian, H. Toda, K. Uesugi, M. Kobayashi, T. Kobayashi, Three-dimensional visualization
of ductile fracture in an Al-Si alloy by high-resolution synchrotron X-ray microtomography,
Mater. Sci. Engg, (2008) 293-296. https://doi.org/10.1016/j.msea.2006.10.201
[16]. W. Ren, Z. Yang, R. Sharma, C.H. Zhang, P.J. Withers, Two-dimensional X-ray ct image
based mesoscale fracture modelling of concrete, Eng. Fract. Mech, 133 (2015) 24-39. https://doi.org/10.1016/j.engfracmech.2014.10.016
[17]. T.T. Nguyen, J. Yvonnet, Q.Z. Zhu, M. Bornert, C. Chateau, A phase-field method for
computational modeling of interfacial damage interacting with crack propagation
in realistic microstructures obtained by microtomography, Comput. Methods Appl.
Mech. Eng, 312 (2016) 567–95. https://doi.org/10.1016/j.cma.2015.10.007
[18]. B. T. Vu, A.T. Tran, D.H. Nguyen, Modeling of crack propagation in multi-phase structure by phase field method with interfacial damage, Transport and communications science Journal, 72 (2021) 911-925. https://doi.org/10.47869/tcsj.72.8.5
[19]. Q.C. He, Q. Shao, Closed-form coordinate-free decompositions of the two-dimensional strain and stress for modeling tension-compression dissymmetry, J. Appl. Mech, 86 (2019) 031007. https://doi.org/10.1115/1.4042217
[20]. G.N. Wells, L.J. Sluys, A new method for modelling cohesive cracks using finite elements,
Int. J. Numer. Methods Engg, 50 (2001) 2667-2682. https://doi.org/10.1002/nme.143
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02/08/2022
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07/11/2022
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Kiểu trích dẫn
Vu Ba, T. (1673715600). Phase field method with strain orthogonal decompositions for modelling of damage in heterogeneous materials obtained by X-ray computed tomography images. Tạp Chí Khoa Học Giao Thông Vận Tải, 74(1), 20-34. https://doi.org/10.47869/tcsj.74.1.3
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