[no title]

Bouscaren, Anthony Trawick

doi:10.1017/s0003055400080564

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The superior fracture behavior of kagome lattices was attributed to a reduced stress level around the crack tip due to elastic crack tip blunting . Subsequently, Romijn and Fleck applied the same technique with orthotropic K-field boundary conditions to show that of both square and diamond lattices scale as ̅ 1 (Romijn and Fleck, 2007;Sih et al, 1965). Finally, Christodoulou et al used a similar technique to investigate the effect of cell regularity on the fracture toughness of 2D hexagonal lattices (Christodoulou and Tan, 2013); they found that mode I fracture toughness is more sensitive to topological variations than mode II in the vicinity of the crack tip.…”

Section: Introductionmentioning

confidence: 99%

A versatile numerical approach for calculating the fracture toughness and R-curves of cellular materials

Hsieh

Deshpande

Valdevit

2020

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

We develop a numerical methodology for the calculation of mode-I R-curves of brittle and elastoplastic lattice materials, and unveil the impact of lattice topology, relative density and constituent material behavior on the toughening response of 2D isotropic lattices. The approach is based on finite element calculations of the J-integral on a single-edge-notch-bend (SENB) specimen, with individual bars modeled as beams having a linear elastic or a power-law elastoplastic constitutive behavior and a maximum strain-based damage model. Results for three 2D isotropic lattice topologies (triangular, hexagonal and kagome) and two constituent materials (representative of a brittle ceramic (silicon carbide) and a strain hardening elasto-plastic metal (titanium alloy)) are presented. We extract initial fracture toughness and R-curves for all lattices and show that (i) elastic brittle triangular lattices exhibit toughening (rising R-curve), and (ii) elasto-plastic triangular lattices display significant toughening, while elasto-plastic hexagonal lattices fail in a brittle manner. We show that the difference in such failure behavior can be * Corresponding Author. E-mail: Valdevit@uci.edu explained by the size of the plastic zone that grows upon crack propagation, and conclude that the nature of crack propagation in lattices (brittle vs ductile) depends both on the constituent material and the lattice architecture. While results are presented for 2D truss-lattices, the proposed approach can be easily applied to 3D truss and shell-lattices, as long as the crack tip lies within the empty space of a unit cell.exceed the relative density of the material, ̅ = / (Voigt bound). In the case of isotropic cellular materials, much tighter bounds exist, namely the Hashin-Shtrikman bound (Hashin and Shtrikman, 1963) and the Suquet-Ponte-Castaneda nonlinear bound (Castaneda and Debotton, 1992;Suquet, 1993), respectively. A number of nearly-isotropic topologies that achieve or approach the bounds have been identified, e.g., the plate-based closed cell architected material with cube-octet unit cell (Berger et al., 2017) and stochastic shell-based architected materials with spinodal topology (Hsieh et al., 2019).Conversely, the fracture toughness of cellular materials is theoretically unbounded, and has been much less investigated. The first systematic investigation dates back to 1984, when Maiti, Gibson, and Ashby derived the analytical expressions of mode I fracture toughness,, for both open and closed-cell brittle isotropic foams, by using dimensional analysis that relates the global stress intensity factor, K, to the local microscopic stress in the cell wall (Maiti et al., 1984); fracture occurs (K= ) when the maximum stress in the cell wall around the crack tip reaches the tensile strength, , of the constituent material. of open and closed-cell isotropic foams is found to scale with ̅ 1.5 and ̅ 2 , respectively (Maiti et al., 1984). Later, Gibson and Ashby showed that the of 2D elastic brittle hexagonal lattices scales with ̅ 2 (Gibson ...

show abstract

Section: Introductionmentioning

confidence: 99%