The best replacement for kevlar is carbon fiber.

The best alternatives to kevlar are rated as following:
★★★★★  carbon fiber
★★★  spectra
★★★  dyneema
★★  ceramic brake pads
★★  nomex
★★  sintered brake pads
★  carbon
★  carbon fibre
★  carbon fiber clutch
★  sword
★  knife
★  carbon fiber stronger
★  wire bead
★  arrow
  twaron
  spider silk
  fiberglass kayak
  aramid
  royalex
  teflon
  cordura
  mylar
  fiberglass canoes
  bfg km2
  uhmwpe
  steel bead
  semi metallic
  dragon skin
  fiberglass canoe
  spectra shield

Your alternative for kevlar is not listed? Suggest!
Speaking about kevlar, one probably shouldn't forget about fiberglass.

Other search terms related to kevlar and their ratings are:
★★★★★ fiberglass
You have in mind a companion for kevlar and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of kevlar in all years. Click on graph for more.
kevlar
carbon fiber
spectra