SAMPE Journal - May/June 2024 - 47

Figure 7. A deformation-mechanism map is developed for uniform glass foams. Each foam possesses relative densities of 0.08 through 0.19. In the
map, a heavy green line delineates the field boundary, while dotted line indicates empirical boundaries.
it first deforms in a linear-elastic way. The boundary of the linearelastic
field (green line) is obtained from
[1]
sy is the yield strength of cell-wall material and ES
is the
Young's modulus of cell-wall material. The equation was
obtained from the equations related to linear elasticity and
plastic collapse[50]
that sy
. When building this map, it was assumed
/ES =0.01. Adjacent to the linear-elastic field lies the
field of plastic collapse. With brittle glass foams, progressive
crushing can again lead to a plateau, ending when the
material is completely crushed. Densification begins when
the cell walls come in contact and is complete when the
relative density reaches 1. The field boundary (green line)
defining the onset of densification is determined by the
arguments leading to the following equation[50]
.
[2]
Overlaying the fields are stress-strain curves representing
foams with initial relative densities ranging from 0.08 to 0.19.
The diagram delineates the domains of behavior for three
defor- mations across the range of densities. These curves
exhibit a linear elastic phase followed by a plateau indicative of
plastic collapse and lastly, densification regime.
As illustrated
in the diagram, the field boundary diverges from the onset of
densification, with the empirical line (depicted as a dotted line)
offering a more realistic depiction compared to the calculated
boundary. This empirical line was established at approximately
twice the compressive stress level. The discrepancy arises due
to the utilization of Equation (2), which is intended for rigid
plastic foam materials with significantly lower Young's modulus,
despite the glass material having a Young's modulus of around
60 GPa. Consequently, this leads to lower normalized stress
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values, providing an explanation for the deviation observed in
the densification field boundary.
4. TAILORABLE ENERGY ABSORPTION
Applications focused on crashworthiness, such as safety
systems for occupants in vehicles or aircraft, stand to gain
significant advantages from materials capable of adjustable
energy absorption. This capability allows for a gradual increase
in stroking load, thereby diminishing acceleration and peak
stress levels encountered during impact. For example, lighter
passengers in seats designed for heavier passengers may face
stress beyond safety limits, while heavier occupants in seats
designed for lighter individuals may experience excessive stress
due to inadequate energy absorption. Such impacts often cause
bodily harm, including damage to the intervertebral disc, leading
to prolonged reductions in quality of life[51,52]
. Passenger seats,
with an energy absorber tailored for a specific occupant weight,
can handle various weights efficiently.
Functionally graded foam utilizes a density gradient to
enhance energy absorption at various stress levels. Research
has shown that adjusting the density gradient can tailor the
profiles and amplitudes of stress waves, thus improving energy
absorption and reducing damage[41,53,54,55,56]
. The mechanical
response of a functionally graded foam sample can be tailored
by changing the local density or selecting different cell materials.
Typically, layers of varying densities are adhered together with
glue to create a structure with graded density.
4.1 Layered Foam Structures
The DPP system, coupled with an optimized glass foam
fabrication process, facilitates the creation of multilayered foam
structures to fine-tune their stress vs. strain profile and energy
absorption capability. The potential tailorability of glass foam by
sequential compression of a bilayer structure is shown in figure
8. This data demonstrates that it is feasible to tailor compressive
stress-strain curves within certain levels. This tailoring of the
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SAMPE Journal - May/June 2024

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