TY - JOUR
T1 - Fracture toughness of self-similar hierarchical material
AU - Kumar, Puneet
AU - Kucherov, Leonid
AU - Ryvkin, Michael
N1 - Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/10/15
Y1 - 2020/10/15
N2 - Two-dimensional materials with self-similar second-order hierarchy are considered. The microstructure with fourfold cubic symmetry is generated by a periodic system of voids in brittle parent material, in one case, macrovoids are filled by a microvoided phase, and in the second one, this phase surrounds hollow macrovoids. A crack is embedded in a rectangular periodic domain subjected to the K-field boundary conditions, and the fracture toughness is determined by the analysis of stresses in the crack-tip vicinity. A novel approach based on the discrete Fourier transform reduces the computational cost of the problem. The analysis of the domain, consisting of several hundreds repeating patterns, is reduced to the multiple analysis of a single representative cell in the Fourier transform space. A parametric study is carried out and, in particular, the influence of parent material redistribution between the hierarchical levels is examined. It is found that for the material with filled macrovoids increasing the relative stiffness at the second hierarchical level diminishes the fracture toughness, while for the second layout the effect is opposite. A comparison with non-hierarchical voided materials of the same relative density emphasizes the role of the length scale parameter of a layout.
AB - Two-dimensional materials with self-similar second-order hierarchy are considered. The microstructure with fourfold cubic symmetry is generated by a periodic system of voids in brittle parent material, in one case, macrovoids are filled by a microvoided phase, and in the second one, this phase surrounds hollow macrovoids. A crack is embedded in a rectangular periodic domain subjected to the K-field boundary conditions, and the fracture toughness is determined by the analysis of stresses in the crack-tip vicinity. A novel approach based on the discrete Fourier transform reduces the computational cost of the problem. The analysis of the domain, consisting of several hundreds repeating patterns, is reduced to the multiple analysis of a single representative cell in the Fourier transform space. A parametric study is carried out and, in particular, the influence of parent material redistribution between the hierarchical levels is examined. It is found that for the material with filled macrovoids increasing the relative stiffness at the second hierarchical level diminishes the fracture toughness, while for the second layout the effect is opposite. A comparison with non-hierarchical voided materials of the same relative density emphasizes the role of the length scale parameter of a layout.
KW - Discrete Fourier transform
KW - Fracture toughness
KW - Hierarchy
KW - Voided material
UR - http://www.scopus.com/inward/record.url?scp=85089803809&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2020.07.011
DO - 10.1016/j.ijsolstr.2020.07.011
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AN - SCOPUS:85089803809
SN - 0020-7683
VL - 203
SP - 210
EP - 223
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
ER -