Contact Mechanics · Wear testing
Running-in and wear scar growth in a ball-on-flat test
Press Play: the scar spreads, the pressure falls, and the wear rate you report depends on when you stop.
Why does a wear scar grow fast at first and then slow down?
The ball loses the same volume each metre (Archard's law), spread over an ever wider flat.
Try it: press Play. At 1000 m the scar is 2.11 mm and the pressure has fallen from 1.0 GPa to 2.9 MPa.
What is running-in and why does it change the wear rate?
New surfaces touch on their tallest peaks, which wear off fast. This picture is an illustrative model.
Try it: a 200 m test reads 3.5 times the steady rate; a 10 km test only 5% high.
How do you measure wear volume from a scar (ASTM G99)?
You measure the scar diameter d and convert it to a volume.
Try it: double d from 1 to 2 mm: the volume grows 16 times.
What to take away
Pressure falls as the scar grows
In the G99 steel test it drops from about 1 GPa to 3 MPa. Depth per metre falls with it.
Running-in inflates short tests
Fast early wear makes a short test's rate too high.
Report the slope
Measure volume at several distances. Use the slope after running-in.
More detail: the equations and the limits of these models
Archard's law and the ball
Archard (1953): volume lost per metre is dV/ds = K W / H, with K the dimensionless wear coefficient and H the hardness of the wearing body. Testers usually quote the specific wear rate k = K/H = V/(W s), in mm³/N m. Mind the units: with H in N/mm² (MPa), K/H comes out in mm³ per N per mm, so multiply by 1000 to get mm³/N m. Picture 1 holds k constant, so V = kWs. The worn part of the ball is a spherical cap of height h: V = πh²(3R − h)/3 and d = 2√(h(2R − h)). For small h this gives the G99 form V ≈ πd⁴/64R, so d grows as s1/4 and h as s1/2.
Because dV/dh = πd²/4, the depth lost per metre is dh/ds = k W/(πd²/4) = k p: it falls with the mean pressure p. This holds only when the flat does not wear; if both bodies wear, the scar shape and the split of volume change.
The starting contact
Before wear, Hertz theory (Johnson 1985) gives the contact radius a = (3WR/4E*)1/3 and the peak pressure p0 = 3W/2πa², with 1/E* = 2(1 − ν²)/E for two steel bodies, E = 210 GPa and ν = 0.3 (typical steel values). While the scar is narrower than 2a, the page uses the Hertz mean pressure W/πa². The default k = 1.98 × 10⁻⁵ mm³/N m is chosen so a 10 mm ball at 10 N reaches, after 1000 m, the 2.11 mm mean ball scar of the steel on steel interlaboratory test reported in ASTM G99-04. In that test the disc also wore, so this k is a fitted, ball-only value, not a measured property.
The running-in model
Picture 2 is an illustrative model, not a prediction for a real pair. A random surface of roughness Rq has its peaks cut down, over distance, to 0.5 Rq above the mean line. The extra volume is that removed layer times the track area (a 1 mm wide track at 10 mm radius). Both the extra wear and the extra friction settle as 1 − e−s/sr, a simple shape chosen for illustration; Blau (2005) shows that measured running-in curves take many shapes. Friction starts at μ = 0.5 + 0.2 Rq/µm and settles at 0.5. The steady rate is fixed at 2 × 10⁻⁶ mm³/N m under 10 N.
The whole-test rate is kwhole = V(L)/(W L) = kss + Vr(1 − e−L/sr)/(W L). It always lies above kss in this model and falls towards it as 1/L. Blau also notes that running-in changes more than roughness: oxide films, the microstructure under the surface and loose debris change too.
What G99 asks for
ASTM G99 reports wear as volume lost, for the pin (or ball) and the disc separately, with the load, speed, sliding distance and surroundings. It gives V ≈ πd⁴/64R for a ball scar and V ≈ πRtw³/6R for a disc track of width w at radius Rt, and notes that volume against distance is often not a straight line because of break-in and changes of mechanism.
On this site: Wear rate calculator · Wear depth · Surface roughness · Real contact area
Questions people ask
What is running-in in tribology?
Running-in (also called break-in or wear-in) is the first part of a sliding test or a machine's life, when friction and wear change before settling. Roughness peaks wear off, the surfaces fit each other better, and oxide or other films form. Its length depends on the pair and the conditions.
Why does my wear rate change with test length?
A rate from total volume over total distance includes the fast running-in wear. In a short test that early wear is a large share of the total, so the rate comes out high. Measure volume at several distances and take the slope of the straight part.
Why does the wear scar on a ball grow more slowly over time?
The volume of a flat on a sphere grows as the fourth power of its diameter. With a constant volume loss per metre, the diameter grows only as the fourth root of distance. The pressure on the scar falls at the same time.
How do you calculate ball wear volume from the scar diameter?
ASTM G99 uses V = πd⁴/64R, with d the scar diameter and R the ball radius, both in mm. It assumes the scar is flat and the disc does not wear much. For large scars use the exact cap V = πh²(3R − h)/3.
Does contact pressure stay constant in a ball-on-disc test?
No. It starts at the Hertz pressure, often around 1 GPa for steel, and falls as the scar widens. A flat-ended pin keeps its contact area, so its pressure stays about the same. This is one reason ball and pin results are hard to compare.
References
- J. F. Archard, Contact and rubbing of flat surfaces, Journal of Applied Physics 24, 981 to 988 (1953). doi:10.1063/1.1721448
- P. J. Blau, On the nature of running-in, Tribology International 38, 1007 to 1012 (2005). doi:10.1016/j.triboint.2005.07.020
- I. M. Hutchings and P. Shipway, Tribology: Friction and Wear of Engineering Materials, 2nd ed., Butterworth-Heinemann (2017): chapter 5, sliding wear and the Archard equation.
- ASTM G99-04, Standard Test Method for Wear Testing with a Pin-on-Disk Apparatus, ASTM International (2004): volume loss formulas and the interlaboratory results (10 mm 100Cr6 (AISI 52100) ball on a 100Cr6 disc, 10 N, 0.1 m/s, 1000 m, ball scar 2.11 ± 0.27 mm). The current edition is G99-23.
- K. L. Johnson, Contact Mechanics, Cambridge University Press (1985): chapter 4, Hertz contact of spheres.
BibTeX
@misc{tripathy2026runningin,
author = {Tripathy, Manisha},
title = {Running-in and Wear Scar Growth Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tribology/running-in-and-wear-scar-growth}},
note = {Interactive web tool}
}