Tribology, indentation & scratch FAQ

Real surfaces are rough at the asperity scale, so only the tips of the highest asperities actually touch, and Greenwood–Williamson-style rough-surface models show the true contact area can be orders of magnitude smaller than the nominal footprint. This page's four contact models (Hertz, elastic-plastic, Greenwood–Williamson, JKR/DMT adhesion) let you see how small it actually gets. See it worked out on Asperities & the Real Area of Contact →

It comes down to a mechanism-competition comparison: each law (Archard adhesive, two/three-body abrasive, rolling-contact fatigue, tribo-oxidative, erosive, fretting) predicts a different wear rate from the same contact conditions, and whichever predicts the fastest removal usually wins in practice. This page's mechanism-competition map runs that comparison live. See it worked out on Wear Mechanisms & Wear Depth →

Two honest routes: convert a wear coefficient into a volume-loss rate and divide by contact area, or measure a real wear scar directly and back out depth (ASTM G99-style). This page walks through both. See it worked out on Wear Mechanisms & Wear Depth →

Three steps, and each one throws away a condition you then have to report separately. Divide the mass loss by the density to get a volume, which is exact because a density in g/cm³ is the same number as one in mg/mm³. Multiply the hours by the sliding speed to get the distance in metres. Then divide by the load and by that distance. A rate quoted per hour hides the speed inside it and a rate quoted per metre hides the load, which is why two numbers in different units almost never compare directly. If your answer looks a thousand times off, check whether the distance was in metres or millimetres before you conclude anything about the material. See it worked out on the Wear Rate Calculator →

The specific wear rate k = V/(F·s) has units of mm³/N·m and divides out the load and the distance. The Archard coefficient K = kH is dimensionless and divides out the hardness as well, which is what makes it a statement about the mechanism rather than about the material: it is read as the fraction of asperity contacts that shed a particle. With k in mm³/N·m and H in GPa the conversion is just K = kH, because the thousand that turns metres into millimetres and the thousand that turns GPa into N/mm² cancel. The practical consequence is that the same volume loss is mild wear in a soft material and severe wear in a hard one. Neither number is a material property; both belong to the system that produced them. See it worked out on the Wear Rate Calculator →

Because G99 fixes the geometry and the reporting, not the test. It specifies a pin loaded perpendicular against a rotating disc, that wear is reported as a volume loss for each body, how to get those volumes from a scar diameter, a track profile or a mass loss, and what has to be reported for the result to mean anything. It deliberately leaves the load, the speed, the track radius, the sliding distance, the materials, the surface finish, the atmosphere and the number of repeats to you. Those are exactly the variables a wear rate is most sensitive to, so an order of magnitude between two compliant laboratories is ordinary rather than surprising. Compliance makes a result reportable, not comparable. See it worked out on the Wear Rate Calculator →

The Oliver–Pharr method fits the initial unloading slope to get stiffness S and contact depth h_c, which combine with the known indenter area function to give both hardness and reduced modulus. This page's workbench lets you drag the fit window yourself against a curve whose true hardness is already known. See it worked out on How a Hardness Number Gets Made →

At shallow depths especially, tip rounding versus the assumed ideal geometry can shift the contact-area estimate substantially, this page's live error budget and Berkovich-to-sphere indenter comparator quantify it directly rather than leaving it as a vague caveat. See it worked out on How a Hardness Number Gets Made →

Oliver-Pharr assumes elastic unloading from a homogeneous, isotropic half-space with negligible pile-up, so it fails when any of those break: significant pile-up or sink-in (uncorrected contact area), a compliant substrate within the plastic zone (the 10% rule), a blunt or damaged tip (area function wrong), drift or creep during the hold (apparent stiffness shift), surface roughness comparable to the indent depth, and viscoelastic nose-in unloading (the slope goes the wrong way). Each failure mode leaves a signature in the load-displacement curve. See it worked out on How a Hardness Number Gets Made →

Both produce the same qualitative trend, higher apparent hardness at small depth, but the Nix–Gao strain-gradient size effect and a blunt-tip artifact have different depth-dependence. This page's sandbox lets you tell them apart against a case where the true answer is already known. See it worked out on When Your Hardness Number Lies →

Both change the true contact area at a given depth without changing the load-displacement curve's obvious shape, so a "clean-looking" fit can still report the wrong hardness. This page shows the area error directly against ground truth. See it worked out on When Your Hardness Number Lies →

A depth-dependent modulus is almost always an artifact: tip rounding inflates the area function at shallow depths, substrate compliance pulls it toward the film-substrate composite at greater depths, surface roughness corrupts the initial contact, and drift or compliance errors add a systematic slope. The Nix-Gao workbench on this page separates the real size effect from the blunt-tip artifact; the substrate widget shows the composite modulus. See it worked out on When Your Hardness Number Lies →

The plastic zone under a Berkovich tip extends roughly 3 to 5 times the contact radius into the material, so any interface, edge, or free surface within that distance contaminates the measured hardness and modulus. The safe spacing depends on load, material yield strength, and the elastic mismatch across the interface. This page's plastic-zone model shows the zone radius as a function of depth. See it worked out on When Your Hardness Number Lies →

Spherical indentation stress-strain analysis uses the Hertzian contact relations plus an effective zero-point correction to convert load-displacement data into an indentation stress-strain curve. This page works through the effective zero point, the part most people get wrong. See it worked out on What Indentation Tells You Beyond Hardness →

The common indentation fracture-toughness equations were fit under different assumptions (crack geometry, elastic/plastic ratio), so they don't agree even given identical crack-length measurements, and the disagreement itself is informative. This page runs three equations on the same crack side by side. See it worked out on What Indentation Tells You Beyond Hardness →

On its own, only that the material yielded suddenly rather than gradually, at a load you measured. At least six things produce a displacement burst: homogeneous dislocation nucleation, a pre-existing source running, a surface film breaking, a phase transformation, cracking, and the instrument itself. The evidence for homogeneous nucleation is a shear stress near the theoretical strength (roughly G/10 to G/30), a distribution measured over many indents rather than one load, and the right scaling: the pop-in load goes as the square of the tip radius while the stress does not, so changing the tip separates it from everything else. What it never proves is anything about the bulk: the stressed volume is a cubic micrometre or less and was chosen because it was small enough to be defect free, so a pop-in stress is not a yield strength. The mechanism line-up on the page gives the separating check for each row. See it worked out on What Indentation Tells You Beyond Hardness →

Indent fused silica. It does not pop in, so a burst there is the machine: actuator stick-slip, a step in the feedback loop, or a contact that was not seated. That costs one indent and settles the question before any physics is argued. Two more cheap separations follow. A machine artifact lands at the same load or the same displacement whatever is under the tip, while a nucleation event moves with the tip radius as R². And a native oxide breaking gives a burst that tracks the film thickness rather than the substrate, which is why aluminium and silicon need the oxide excluded first. If the burst survives all three, the distribution over many indents is the measurement, not the single load. See it worked out on What Indentation Tells You Beyond Hardness →

It depends what you're measuring: a simple ramp is fine for a single hardness/modulus number, CSM (continuous stiffness) gives properties as a function of depth in one indent, and fatigue or nano-impact modes target damage accumulation specifically. This page's decision chooser walks through all eight schedules with what failure looks like in each. See it worked out on How to Decide a Loading Mode →

They mark successive failure transitions as load ramps up, typically first cracking (Lc1), then coating spallation or delamination (Lc2), and full exposure of the substrate (Lc3), identified from the ASTM C1624 failure-mode gallery alongside the friction and acoustic-emission traces. This page's simulator produces all three from a progressive-load scratch. See it worked out on What a Scratch Test's Critical Loads Mean →

ASTM G171 scratch hardness is calculated from groove width, and there are four defensible width-measurement conventions that don't agree, a 10% error in width measurement becomes roughly a 21% error in the resulting hardness number. This page compares all four conventions on the same groove. See it worked out on Scratch vs. Indentation Hardness →

Hardness alone doesn't predict wear resistance well; the ratio H³/E² (hardness cubed over modulus squared) correlates much better with resistance to plastic deformation under repeated contact, so a very hard but low-toughness coating can still wear faster than a softer, tougher one. This page covers why H³/E² outranks hardness as a screening index for coatings. See it worked out on Scratch vs. Indentation Hardness →