| dc.description.abstract | Metallic honeycombs and foams are widely used in the automotive and aerospace industries due to their desirable mechanical properties such as light-weight, high and tailorable specific stiffness, high specific strength, and high specific energy absorption. The uniaxial crushing response of honeycombs has been studied extensively using both experiments and simulations. These crushing studies have covered numerous honeycomb geometries and a wide range of strain rates; this is on account of crushing as a key test to assess the energy absorption capacity of cellular solids.
In contrast to crushing, the indentation of honeycombs – which also represents a broadly compressive boundary condition – has received limited attention. Unlike crushing, indentation induces deformation in a confined region, not affecting regions distant from the indenter. Moreover, indenting a sufficiently large specimen (representative of a halfspace) allows one to avoid finite-size effects, and obtain a response that is more representative of the cellular architecture itself. Indentation is also more representative of impact by a projectile, or hardness-testing of honeycombs.
The present thesis uses high-fidelity, continuum finite element analysis (FEA) to simulate the flat punch indentation of metallic honeycombs with several different unit-cell geometries (armchair hexagons, zigzag hexagons, square- and square-variant honeycombs) under plane strain conditions. These simulations allow one to accurately resolve phenomena like large plastic deformation near junctions and inter-cell–wall contacts. AA2024-T351, a work-hardened aerospace aluminum alloy, is used as a representative base material and the indentation is carried out to a depth of 3.5-5.0 unit cells.
The FE simulations for armchair hexagon indentation reveal a distinct mode of deformation: near-junction-yield–dominated localization. Here, the deformation is confined to two inclined bands of unit cells starting from below either corner of the punch and radiating toward the symmetry line, with an unstrained region immediately below the punch. The force-indentation response is characterized by alternating, well-separated force maxima and minima. Interestingly, the observed periodic recovery of global indentation stiffness at force minima in the plateau region in armchair honeycombs is not due to the formation of new inter-wall contacts, but occurs prior to the formation of such contacts. The plastic strain field at the unit-cell level reveals that yielding occurs almost exclusively near junctions ( 0.2 l, 20% of length of cell wall) over a range of member slenderness values (15-25), reaching a maximum plastic strain of 0.70. In localization, the armchair unit cells finally collapse and fold into an easy chair configuration. Zigzag hexagonal honeycombs show a more spatially diffuse deformation pattern, but their deformation at the unit-cell level is also driven by near-junction yield as in armchair honeycombs.
On the other hand, square honeycombs under punch indentation show a plastic-buckling-dominated, `pancaking’ mode of deformation. Unlike armchair honeycombs, the region immediately below the indenter is severely deformed on indenting to a sufficient depth. The indentation force response of square honeycombs also shows a high initial peak force, with numerous subsequent local maxima and minima in the force plateau region. The unit-cell plastic strain fields reveal that square honeycombs show extensive mid-span (~0.25 l, 25 % of length of cell wall) plasticity in vertical members (max plastic strain of 0.87) in addition to near-junction yielding, over a range of slenderness values. The unit cells in the deformation zone collapse almost completely as the indentation progresses. The opposite vertical walls of square unit-cells assume a characteristic C-shape and inverse-C-shape, which increase in curvature as collapse progresses. The presence of mid-span plasticity in addition to near-junction yield greatly increases the energy absorption capacity of square honeycombs in comparison to hexagonal honeycombs of the same relative density.
Four normalized energy absorption parameters are proposed to characterize the global indentation response of honeycombs : peak indentation force (PIF), mean indentation force (MIF), specific energy absorption in indentation (SEAI), and specific plastic dissipation in indentation (SPDI); these are defined in a manner analogous to PCF, MCF, SEA and SPD in uniaxial crushing. SEAI and SPDI are more useful as relative measures to gauge the energy absorption across different indentation simulations. Perfect square honeycombs show a PIF to MIF ratio in the range 2.04-2.71. The former corresponds to a slenderness ratio of 15, while the latter a slenderness of 25. In absolute terms, both the PIF and MIF decrease with increase in slenderness. Hexagonal honeycombs have much lower SPDI and PIF than square honeycombs.
Pre-buckling of the vertical cell walls of square honeycombs is shown to be a way to reduce the high PIF in square honeycomb indentation without an appreciable loss of SPDI or SEAI. A parametric study varying the normalized pre-buckled amplitude e* (ratio of amplitude to wall thickness) reveals that with e*=1.0, the PIF to MIF ratio reduces from 2.04 to 1.21, while the SPDI decreases from 1.23 to 0.88. An e*=0.5 is optimal, with PIF/MIF of 1.19 and SPDI of 1.03. Pre-buckling thus seems to provide a way to suitably tailor the force-indentation response of square honeycombs. Notably, unlike perfect square honeycombs, the unit cells in the deformation zone do not collapse completely; this is likely due to the reduced resistance to buckling in other unit cells.
A series of uniaxial crushing simulations are also conducted for hexagonal and square honeycombs. Interestingly, in crushing, square honeycombs show a mode of deformation in which neighboring rows of unit cells shear / slip almost rigidly past each other. Unlike indentation, there is no mid-span plasticity, and yielding only occurs near junctions. This explains why square honeycombs are very inefficient in absorbing energy in crushing. This also reinforces the fact that otherwise identical honeycombs can behave quite differently under crushing and indentation, although both are compressive boundary conditions.
The thesis also explores the indentation response of honeycombs with perturbed joints. It is seen that misplaced-joint square honeycombs are very effective in reducing the PIF with only a slight loss in the SPDI; the PIF is reduced by almost 50\% is several instances. Misplaced joints thus provide an alternative to pre-buckling to reduce the PIF. However, there is a wide-spectrum of indentation responses depending on the spatial distribution of the perturbations in the honeycomb. Importantly, pre-buckling and joint misplacement can be so effective in altering the force-depth response that the initial peak force (IPF) is sometimes lower than the PIF in these simulations. An armchair honeycomb with misplaced joints shows a similar mode of localization as a perfect armchair honeycomb. This shows that the localization mode is a highly preferred mode of deformation in armchair honeycombs, and robust to moderate perturbations in geometry.
A study comparing indentation responses using continuum elements and shell-elements is carried out for both hexagonal and square honeycombs. It is found that while shell elements are adequate to model slender armchair hexagonal honeycombs with a localization-dominated response, they are inferior to continuum elements in modeling square honeycombs -- even those with an apparently high wall-slenderness of 20-- as well as less-slender honeycombs of any geometry. In particular, accurate resolution of the complex patterns of plasticity , self-contact, and inter-wall contact in square honeycombs, and accurate treatment of junctions in general, demands high-fidelity continuum FE simulations.
Comparisons of the FE results with prior experimental work (indentation and uniaxial crushing) are presented whenever possible, and are generally quite encouraging. This thesis highlights the crucial role of both near-junction plasticity and mid-span plasticity in determining the indentation response of square honeycombs, as well as the overall importance of using continuum-element FE as a reference or standard against which other simulations are compared. Further, design modifications like pre-buckling and joint perturbation can be used to tailor indentation force-depth curves and indentation energy. High-fidelity FE simulations can thus aid in the design and optimization of honeycomb geometries in large strain plastic deformation. | en_US |
