The best replacement for hardness is tensile strength.

The best alternatives to hardness are rated as following:
★★★★★  tensile strength
★★★★★  toughness
★★★★  strength
★★★  alkalinity
★★  yield strength
★  hardenability
★  cold work
★  tds
★  tensile
★  rockwell
★  softness
★  conductivity
★  young's modulus
★  elasticity
★  brittleness
  modulus
  wear
  tempering temperature
  total hardness
  wear resistance
  total dissolved solids
  grain size
  randomness
  elastic modulus
  durometer
  temporary hardness
  carbon content
  ultimate tensile strength
  brinell
  tensile properties
  rockwell c
  calcium hardness
  annealing time
  compressive strength
  ductility
  stiffness

Your alternative for hardness is not listed? Suggest!
Speaking about hardness, one probably shouldn't forget about grain size.

Other search terms related to hardness and their ratings are:
★★★★★ grain size
★★ tensile strength
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Google Trends

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hardness
tensile strength
toughness