Contact Mechanics · Wear

Hardness and wear resistance: is harder always better?

Start with hardened steel in quartz sand below, then swap the sand for feldspar and watch the wear fall. Then see why cold work does not help, and why the hardest ceramic can chip first.

1 Grit against surface 2 Cold work or heat treatment 3 Hardness or toughness Takeaways Questions References

Why does hardened steel still wear in sand?

What counts is the surface hardness Hs compared with the grit hardness Ha, not Hs on its own.

Left: the grit sliding over the surface (side view). Right: wear rate against Hs/Ha, a schematic. Dashed lines: the 1.2 rule (Tabor 1954) read both ways. The size of the fall is not to scale. Bottom: hardness ladder (log scale); the grey band is Ha/1.2 to 1.2Ha.
Worn surface
Abrasive grit
Grit hardness Ha
Hs/Ha
Grit is harder by
Wear rate (schematic)

Try it: hardened steel (697 HV) with quartz sand gives Hs/Ha = 0.59: the sand is 1.7 times harder and cuts. Pick feldspar: the ratio jumps to 0.98, inside the steep fall.

Does work hardening improve wear resistance?

Heat treatment raises abrasion resistance; cold work raises the hardness but hardly the abrasion resistance.

Left: relative wear resistance against bulk hardness, a schematic after Khruschov (1974), whose plot Hutchings and Shipway (2017) reproduce. Right: hardness under the worn surface, a schematic after Richardson (1967). Steel at 392 and 697 HV: ASTM E140 values for 40 and 60 HRC. Copper at 50 HV is a typical value. Illustrative only: cold-worked copper (110 HV), annealed and cold-worked steel (180 and 280 HV), the worn-surface hardness and the wear-resistance scale.
Metal
Treatment
Bulk hardness
Worn-surface hardness (illustrative)
Relative wear resistance (schematic)
Change from annealed

Try it: in this illustrative model, pick copper, then Cold worked: the hardness goes from 50 to 110 HV but the wear resistance stays at 0.50. Carbon steel, As quenched: 697 HV gives 3.35, below the 7.0 of the pure-metal line.

Which matters more for wear: hardness or toughness?

Under a smooth ball, H3/E2 sets the load to first yield. Under a sharp grit, low toughness Kc lets chips break out.

Left: rank by hardness H against rank by the load Py at which a rigid ball first yields the surface. Right: chipping under one sharp grit (lateral cracks, after Evans and Marshall 1981); each line starts at its crack threshold P*. Volumes are relative because the model's constants are not well known.
Py of A (H = 3Y)
Py of B (H = 3Y)
Crack threshold P*, A/B
Chipped volume, A/B

Try it: SiC against alumina at a grit load of 0.30: SiC is twice as hard, yet it chips and alumina does not, because SiC's threshold is 1/16 of alumina's. With a 1 mm ball, the H = 3Y estimate of Py is 18 N for glass and 14 N for alumina.

What to take away

Harder than the grit is what countsWear falls steeply once the surface is about as hard as the grit. Quartz (1103 to 1260 HV) is about 1.7 times harder than 60 HRC steel, so the steel still wears in sand.
Cold work does not buy abrasion resistanceThe worn surface work-hardens itself anyway. Pure metals follow hardness and heat-treated steels gain less per HV (Khruschov 1974). Cold-worked nickel wore at about the same rate as annealed nickel (Sin, Saka and Suh 1979).
Toughness and stiffness matter tooGlass is three times softer than alumina, yet its H3/E2 is higher: under a 1 mm ball its estimated Py is 18 N against 14 N. SiC is twice as hard as alumina but starts chipping at 1/16 of the load.
More detail: the equations, the numbers and the limits

The 1.2 rule. A grit needs to be about 1.2 times harder than a surface to scratch it (Tabor 1954; Pintaude 2010). So it cuts freely when Ha ≥ 1.2Hs, that is Hs/Ha ≤ 0.83. Grit softer than the surface causes much less wear (Gee, Gant and Hutchings 2002); Richardson (1968) studied this range. The page reads the factor the other way round too: when Hs ≥ 1.2Ha, the surface dents the grit. That second edge is a reading of the rule, not a measured value. Hs is the hardness of the worn, work-hardened surface, so for a soft metal it is well above the annealed value. The curve shows the shape only.

The worn surface sets the result. Richardson (1967) linked abrasion resistance to the highest hardness a surface reaches by straining. Abrasion takes an annealed or a cold-worked surface to that value anyway. Heat treatment raises the value itself, but steels that start hard harden less (Chintha 2019, from Richardson's data). Widget 2 draws this with Hsat = 2.5[Hann + 0.3(H − Hann)]; the 2.5 and 0.3 are drawing choices, not data.

Hardness values. Quartz 1103 to 1260 HV and corundum 2085 HV at 50 g (Taylor 1949). Sintered alumina 15 GPa and sintered SiC 32 GPa ±15% at 1 kg, TiB2 25 GPa at 5 N (NIST). SiC grit is also quoted near 2800 HV (Gee, Gant and Hutchings 2002). Steel at 60 HRC is 697 HV (ASTM E140); mild steel at 131 HV is a typical value. Hardness depends on the test load.

Load to first yield. For a ball of radius R on a flat (Hertz), the peak pressure is p0 = (6PE*2/π3R2)1/3. Yield starts below the surface at p0 = 1.6Y (Johnson 1985). With H = 3Y, Py = 0.78R2H3/E*2 (Tsui et al. 1995); with H = 2.8Y the constant is 0.96. The ball is rigid, so E* = E/(1 − ν2) of the flat. H/E tracks the elastic strain a surface takes before it fails; Leyland and Matthews (2000) argued it predicts wear better than H alone.

Chipping. Under a sharp grit, cracks start above a load P* ∝ Kc4/H3 (Lawn and Evans 1977). Above it, lateral cracks remove a volume per unit distance V ∝ P9/8(E/H)4/5/(Kc1/2H5/8) (Evans and Marshall 1981).

Limits. H = 3Y holds for metals. When Y/E is high, as in glass and hard ceramics, H is a smaller multiple of Y (Johnson 1985, chapter 6; Vandeperre, Giuliani and Clegg 2004). So their Py here is a low estimate, useful only to compare. Under a ball, glass and other brittle solids can also form cone cracks instead of yielding (Lawn 1998). Hardmetals wear mainly by small fractures, so their wear does not drop sharply at the 1.2 ratio (Gee, Gant and Hutchings 2002). A thin coating also feels its substrate. The chipping model has no known constants, so it compares materials only. Grit shape, size and rolling also matter.

Questions people ask

Does a harder material always wear less?

No. In abrasion it wears much less only once it is about as hard as the grit. Cold work adds hardness with little gain. Hard, brittle solids can chip: SiC is twice as hard as alumina but starts chipping at 1/16 of the load.

Why do hardened steels still wear in sand?

Quartz sand is 1103 to 1260 HV (Taylor 1949). A 60 HRC steel is 697 HV, so the sand is about 1.7 times harder. That is above the 1.2 factor a grit needs to cut, so the steel stays in the high-wear regime.

What is the hardness of quartz sand?

Taylor (1949) measured 1103 HV on a face normal to the optic axis and 1260 HV on a face parallel to it (50 g load). That is about 11 to 12 GPa. Corundum (natural alumina) gave 2085 HV.

Does work hardening improve abrasive wear resistance?

Very little. Abrasion strains the surface to its highest hardness anyway (Richardson 1967). In tests on nickel, annealed (870 MPa) and fully cold-worked (2370 MPa) samples wore at 8.1 and 8.7 × 10−10 m3/m. Both worn surfaces ended near 2350 MPa (Sin, Saka and Suh 1979).

What is the H/E ratio and why does it matter for wear?

H/E is about the elastic strain a surface can take before it yields. A high value lets a contact spring back instead of denting. For a 60 HRC steel H/E is 0.033; for silica glass 0.071.

What is H3/E2 in coatings?

It sets the load at which a ball first yields a surface: Py = 0.78R2H3/E*2, taking H = 3Y (Tsui et al. 1995). A slightly softer but less stiff coating can carry more load before it starts to yield. With a 1 mm rigid ball, the estimate is 4.8 N for 60 HRC steel and 14 N for alumina.

Why do hard coatings crack and flake?

Very hard coatings are often stiff and not very tough. Under a sharp contact they crack above a load that scales as Kc4/H3, so more hardness alone lowers it. A soft substrate also bends under the coating and loads the interface.

Which is more important for wear, hardness or toughness?

It depends on the contact. With blunt contacts, or grit softer than the surface, hardness and H3/E2 matter most. Against sharp grit at high load, toughness decides when chips start: doubling Kc raises the crack threshold 16 times.

Related: Wear mechanisms and wear depth (Archard models) · Wear rate calculator · Sliding-induced microstructure (the hard worn layer) · Scratch hardness and H/E · Hardness scales and conversions · Fracture toughness · Subsurface contact stresses · Scratch test critical loads (coatings flaking)

References

Show the 16 references
  1. I. Hutchings and P. Shipway, Tribology: Friction and Wear of Engineering Materials, 2nd ed., Butterworth-Heinemann (2017): chapter 6, Wear by hard particles, pp. 165 to 236.
  2. M. G. Gee, A. Gant and I. M. Hutchings, Rotating Wheel Abrasive Wear Testing, Measurement Good Practice Guide No. 55, National Physical Laboratory, Teddington (2002): section 6.2.
  3. A. R. Chintha, Metallurgical aspects of steels designed to resist abrasion, and impact-abrasion wear, Materials Science and Technology 35, 1133 to 1148 (2019), doi:10.1080/02670836.2019.1615669; its Table 1 gives the nickel data of H.-C. Sin, N. Saka and N. P. Suh, Abrasive wear mechanisms and the grit size effect, Wear 55, 163 to 190 (1979), doi:10.1016/0043-1648(79)90188-1.
  4. R. C. D. Richardson, The wear of metals by relatively soft abrasives, Wear 11, 245 to 275 (1968). doi:10.1016/0043-1648(68)90175-0
  5. R. C. D. Richardson, The maximum hardness of strained surfaces and the abrasive wear of metals and alloys, Wear 10, 353 to 382 (1967). doi:10.1016/0043-1648(67)90276-1
  6. M. M. Khruschov, Principles of abrasive wear, Wear 28, 69 to 88 (1974). doi:10.1016/0043-1648(74)90102-1
  7. D. Tabor, Mohs's hardness scale: a physical interpretation, Proceedings of the Physical Society B 67, 249 to 257 (1954). doi:10.1088/0370-1301/67/3/310
  8. G. Pintaude, An overview of the hardness differential required for abrasion, Journal of Tribology 132, 034502 (2010). doi:10.1115/1.4001896
  9. E. W. Taylor, Correlation of the Mohs's scale of hardness with the Vickers's hardness numbers, Mineralogical Magazine 28, 718 to 721 (1949). doi:10.1180/minmag.1949.28.206.08
  10. K. L. Johnson, Contact Mechanics, Cambridge University Press (1985): chapters 4 and 6 (Hertz contact, first yield at p0 = 1.6Y, indentation hardness and yield stress). L. J. Vandeperre, F. Giuliani and W. J. Clegg, An analytical approach for relating hardness and yield strength for materials with high ratio of yield strength to Young modulus, MRS Proceedings 841, R11.10 (2004). doi:10.1557/PROC-841-R11.10
  11. T. Y. Tsui, G. M. Pharr, W. C. Oliver, C. S. Bhatia, R. L. White, S. Anders, A. Anders and I. G. Brown, Nanoindentation and nanoscratching of hard carbon coatings for magnetic disks, MRS Proceedings 383, 447 (1995). doi:10.1557/PROC-383-447
  12. B. R. Lawn, Indentation of ceramics with spheres: a century after Hertz, Journal of the American Ceramic Society 81, 1977 to 1994 (1998). doi:10.1111/j.1151-2916.1998.tb02580.x
  13. A. Leyland and A. Matthews, On the significance of the H/E ratio in wear control: a nanocomposite coating approach to optimised tribological behaviour, Wear 246, 1 to 11 (2000). doi:10.1016/S0043-1648(00)00488-9
  14. B. R. Lawn and A. G. Evans, A model for crack initiation in elastic/plastic indentation fields, Journal of Materials Science 12, 2195 to 2199 (1977). doi:10.1007/BF00552240; and D. B. Marshall, B. R. Lawn and A. G. Evans, Elastic/plastic indentation damage in ceramics: the lateral crack system, Journal of the American Ceramic Society 65, 561 to 566 (1982). doi:10.1111/j.1151-2916.1982.tb10782.x
  15. A. G. Evans and D. B. Marshall, Wear mechanisms in ceramics, in D. A. Rigney (ed.), Fundamentals of Friction and Wear of Materials, American Society for Metals, Metals Park, Ohio (1981); the chipping volume as written in B. R. Lawn, O. Borrero-López, H. Huang and Y. Zhang, Micromechanics of machining and wear in hard and brittle materials, Journal of the American Ceramic Society 104, 5 to 22 (2021), eq. 5. doi:10.1111/jace.17502
  16. NIST Structural Ceramics Database, SRD 30 (doi:10.18434/T42G62), after R. G. Munro: alumina, J. Am. Ceram. Soc. 80, 1919 (1997); SiC, J. Phys. Chem. Ref. Data 26, 1195 (1997); TiB2, J. Res. NIST 105, 709 (2000). Silica glass E = 70 GPa, H = 5 GPa, Kc = 0.7 MPa√m from S. G. Roberts, Depths of cracks produced by abrasion of brittle materials, Scripta Materialia 40, 101 to 108 (1998), doi:10.1016/S1359-6462(98)00403-5 (ν = 0.2 is a typical value, assumed). ASTM E140 Table 1 (60 HRC = 697 HV); steel E = 207 GPa from Callister and Rethwisch, Materials Science and Engineering, Wiley, Table B.2.
Cite this page: Tripathy, Manisha. “Hardness and Wear Resistance Lab.” untethered atom, 2026, https://untetheredatom.com/tribology/hardness-and-wear-resistance.
BibTeX 
@misc{tripathy2026hardnesswear,
  author = {Tripathy, Manisha},
  title  = {Hardness and Wear Resistance Lab},
  year   = {2026},
  howpublished = {\url{https://untetheredatom.com/tribology/hardness-and-wear-resistance}},
  note   = {Interactive web tool}
}
Last updated 3 November 2026.