Nanoindentation & the Oliver-Pharr Method (2D)

Sample Material

Test Setup

Peak load P_max 10.0 mN

Loading / unloading rate 1.0x

Ready

Live Readout

Load P

0.0 mN

Depth h

0 nm

Oliver-Pharr Result

Hardness H—

Reduced modulus E_r—

Elastic modulus E_sample—

Reference E (true)—

How it works

A diamond Berkovich (three-sided pyramidal) tip is pressed into the sample under load control, then withdrawn, while a transducer continuously records load P and penetration depth h — the depth-sensing indentation technique used by every commercial nanoindenter. This 2D view shows the same tip as a cross-sectional wedge pressing straight down into the sample surface.

Hardness:       H = Pmax / Ac
Contact area:   Ac = 24.56 · hc²         (Berkovich area function)
Contact depth:  hc = hmax − ε·Pmax/S      (ε = 0.75 for a Berkovich tip)
Unload stiffness: S = dP/dh at h = hmax
Reduced modulus: 1/Er = (1−ν²)/E + (1−νi²)/Ei

Loading follows the empirical Kick's law P = C·h² for a sharp pyramidal tip. Unloading is elastic and follows the Oliver-Pharr power law P = A·(h−hf)^m (m ≈ 1.5 for a Berkovich indenter), where hf is the residual (plastic) depth left once the tip is fully withdrawn. The initial slope of that unloading curve, S, is the one measurement the whole method hangs on — it is purely elastic contact stiffness, unaffected by the plastic deformation that happened during loading.

Material — sets the true hardness H, Young's modulus E and Poisson's ratio ν the tip is pressed into; the diamond indenter itself is fixed at Ei = 1141 GPa, νi = 0.07.
Peak load Pmax — how hard the tip is driven in; higher load reaches greater depth and a larger contact area.
Rate — animation speed of the loading/hold/unloading cycle; the underlying P-h curve is unchanged.

The "Oliver-Pharr Result" panel re-derives H and E purely from the recorded P-h curve — exactly what a real instrument's software does — so you can check it against the material's true reference modulus shown alongside it.

Berkovich tip (cross-section) Indentation crater