A component in a high-impact environment must survive sudden shock loads without shattering, and it must do so with only limited deformation. The single property that captures the ability to absorb energy before fracture is toughness, so the most critical requirement is low brittleness with high toughness.

Toughness is measured by the area under the stress–strain curve and represents the total energy the material can soak up before it breaks. Achieving high toughness needs a balance of two qualities:

• Strength — the ability to carry high stress, so the part resists deformation under the impact load.
• Ductility — the ability to deform plastically, which lets the material dissipate the impact energy instead of storing it and snapping.

Low brittleness is exactly what allows this energy-absorbing plastic behaviour; a brittle material fails suddenly, with little warning and little energy absorbed.

Examining the other combinations shows why they fail under impact:

• High brittleness with low ductility and high brittleness with high elasticity both mean the material is brittle, so it fractures abruptly under shock — the worst case for impact.
• Low brittleness with low stiffness would deform excessively, violating the "minimal deformation" requirement, and low stiffness says nothing about fracture resistance.

Therefore the governing property is low brittleness with high toughness.