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Influence of Cell Topology on Mode I Fracture Toughness of Cellular Structures

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Abstract

A cellular structure is made up by an interconnected network of beams or plates which forms the edges and faces of cells. This paper proposes three different micromechanical models to determine the fracture toughness values of cellular materials such as rigid polyurethane foams using the finite element micromechanical analysis and Abaqus software. This study was carried out for mode I fracture and fracture toughness was predicted based on linear elastic fracture mechanics. Models of two-dimensional cellular solids with square, hexagonal and circular cells were generated for five different relative densities (0.077, 0.105, 0.133, 0.182 and 0.333). A study of the influence of geometrical parameters on fracture toughness was also conducted. Based on the finite-element simulations, three linear correlations are proposed which could be useful for estimation of fracture toughness values if relative densities are in the considered range of 0.077 (90 kg/m3 density) and 0.333 (390 kg/m3 density). Finally, the authors validate their proposed micromechanical models presenting a comparison of analytical, numerical and experimental results of fracture toughness of cellular materials. It was found that at low relative densities (between 0.077 and 0.333), the proposed micromechanical models predict the fracture toughness values similar to experimental and numerical ones, but they must be used according with the real cellular structure.

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Abbreviations

a :

crack length

E :

Young’s modulus

F max :

maximum load from the load-displacement recordings

F I(a/W):

mode I nondimensional stress intensity factor

H :

height of the micromechanical model

K Ic :

mode I fracture toughness

l :

cell length

t :

cell wall thickness

W :

width of the micromechanical model

ρ*:

density of rigid PUR foam

ρs :

density of the solid material of which the foam is made

ρ*/ρs :

relative density

σ:

applied load in order to produce a mode I loading

σfs :

fracture strength of the solid material

σy,max :

maximum stress in the first unbroken strut

ν:

Poisson’s ratio.

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Authors and Affiliations

  1. Department of Mechanics and Strength of Materials, Politehnica University of Timisoara, Timisoara, 300222, Romania

    E. Linul, D. A. Serban & L. Marsavina

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  1. E. Linul
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  2. D. A. Serban
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  3. L. Marsavina
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Correspondence to L. Marsavina.

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Original Text © E. Linul, D.A. Serban, L. Marsavina, 2018, published in Fizicheskaya Mezomekhanika, 2018, Vol. 21, No. 1, pp. 84–91.

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Linul, E., Serban, D.A. & Marsavina, L. Influence of Cell Topology on Mode I Fracture Toughness of Cellular Structures. Phys Mesomech 21, 178–186 (2018). https://doi.org/10.1134/S1029959918020121

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