Localized necking under global compression in two-scale metallic hierarchical solids

Abstract

Hierarchically structured cellular solids have attracted increasing attention for their superior mass-specific mechanical properties. Using a remeshing-based continuum finite element (FE) framework, we reveal that two-scale metallic hierarchical solids exhibit a distinct, localized deformation mode that involves necking and fracture of microscale tension members even at small global compressive strains (3-5%). The tensile failure is always preceded by plastic buckling of a complementary compression member. This combined necking-buckling (NB) mode critically underlies the collapse of hexagon-triangle (HTH) hierarchical lattices over a wide range of relative densities and length-scale ratios and is also seen in diamond-triangle (DTH) lattices. In lattices with very slender microscale members, necking is prevented by a competing failure mode that involves coordinated buckling (CB) of multiple members. Our custom remeshing FE framework is critical to resolve the localized large plastic strains, ductile failure, and complex local modes of deformation (including cusp formation) that are characteristic of the NB mode. A theoretical buckling analysis supports the inevitability of the NB and CB modes in HTH lattices. The occurrence of the NB mode has consequences for energy absorption by two-scale hierarchical solids, and hence influences their design.

Figures (15)

• Figure 1: FE meshes (i)-before and (ii)-after remeshing for (a) inter-member contact emanating at the junction between two members, (b) necking of a tension member, (c) self-contact and cusp formation in a stocky microscale member undergoing large flexure. Remeshing is essential in all three cases.
• Figure 2: (a) A unit cell of a hexagon-triangle hierarchical (HTH) lattice (b) Schematic of a multi-cell HTH specimen of width $w$ subjected to uniaxial compression along the y-axis
• Figure 3: (a) Global force-strain response of an $r=7$, $\rho=0.1$ HTH lattice subjected to uniaxial compression (b) Deformed geometry of the HTH lattice at a global strain of $\varepsilon = 0.15$; the centrelines of plastically deformed macro-cell walls are highlighted in magenta.
• Figure 4: (a) Deformed configuration of a $\rho=0.1$, $r=7$ HTH lattice at a global strain of $\varepsilon=0.14$. The elastic (green) and plastic (red) members are shown, with the latter highlighted for visibility (b) Zoomed-in view (to scale) of the deformed unit cell inside the box in panel (a).
• Figure 5: The necking-buckling (NB) mode in an $r=7$, $\rho=0.1$ HTH lattice. Effective plastic strain field $\overline{\epsilon}$ is superimposed on the deformed geometry in all sub-panels. (a) Frames (a-i)--(a-iii) show the $\overline{\epsilon}$ evolution in the near-junction zone 'P' in Fig. \ref{['fig::mech1_elastic_plastic']}(b) as global strain $\varepsilon$ increases from 0.03 to 0.14. Note the necking of member '$t$' in (a-ii) and its fracture in (a-iii). (b) Frames (b-i)--(b-iii) similarly show the NB mechanism in zone 'Q' in Fig. \ref{['fig::mech1_elastic_plastic']}(b) as $\varepsilon$ increases from 0.05 to 0.14. (c) Frames (c-i)--(c-iii) show the initiation, growth, and fracture of the neck in the boxed zone 'R' in (a-ii) as $\varepsilon$ increases from 0.03 to 0.05. (d) Zoomed-in views of zones 'S' and 'T' in panels (a-iii) and (b-iii) respectively, showing self-contact and inter-member contact.