Brief Experimental Procedure

Prepare and polish the specimen surface.

Begin by sectioning the specimen to a convenient size and mounting it securely. Grind the surface using progressively finer SiC papers followed by polishing with diamond or alumina suspensions until a mirror-like finish is achieved. A smooth surface is essential to minimize roughness-induced errors and to ensure that the measured contact response reflects intrinsic material behavior rather than asperity effects. Clean the specimen thoroughly with ethanol or acetone to remove debris and contaminants.

Mount sample and align indenter normally.

Place the polished specimen firmly on the nanoindenter stage and ensure it is rigidly clamped to avoid vibrations or drift during testing. Using the instrument’s optical or camera alignment system, position the indenter tip perpendicular to the surface. Proper normal alignment ensures symmetric contact and prevents lateral forces that could distort the load–displacement response or produce non-Hertzian contact conditions.

Calibrate tip radius and sensors.

Before testing, perform instrument calibration following standard procedures. Verify the indenter tip radius using a reference material or calibration sample, as Hertzian calculations are highly sensitive to the tip geometry. Check the load frame compliance and displacement sensor accuracy to ensure reliable measurements at nanometer and micronewton scales. Accurate calibration directly improves the precision of contact radius and pressure calculations.

Apply low load to ensure elastic contact.

Select a sufficiently small maximum load such that the indentation remains within the elastic regime of the material. Excessive loads can cause yielding or permanent plastic deformation, which violates Hertzian assumptions. Gradually increase the load under controlled conditions to avoid sudden penetration and ensure stable elastic contact between the spherical tip and the surface.

Record load–displacement curve.

During indentation, continuously record the applied load and corresponding penetration depth to obtain the complete P–h curve. Include loading and unloading segments, and optionally a short hold period to minimize creep effects. This curve provides the primary experimental data required to evaluate elastic stiffness, deformation behavior, and subsequent contact mechanics parameters.

Determine stiffness and reduced modulus.

From the initial slope of the unloading segment, calculate the contact stiffness S = dP/dh. Use this stiffness together with the contact mechanics relations to determine the reduced modulus E*, which accounts for elastic deformation of both the indenter and the specimen. The reduced modulus is a key parameter in Hertz theory and governs the extent of elastic contact deformation.

Calculate contact radius a, area A, and pressures using Hertz equations.

Substitute the measured load, tip radius, and reduced modulus into the Hertzian equations to compute the contact radius a. From this, determine the projected contact area A = πa². Using the calculated area, evaluate the mean contact pressure and maximum Hertzian pressure. These quantities describe the stress distribution at the contact and indicate the likelihood of yielding or damage initiation.

Repeat multiple indents and average results.

Perform several indentations at different, well-spaced locations on the specimen to avoid interaction between plastic zones or residual stresses. Repeat measurements under identical conditions to ensure reproducibility. Finally, calculate the average and standard deviation of the obtained values to improve statistical reliability and reduce the influence of experimental scatter.

Essential Experimental Setup

• Instrumented nanoindenter (µN–mN load control)
• Spherical/rounded diamond tip of known radius R
• Load actuator
• Depth sensor (nm resolution)
• Rigid sample stage
• Data acquisition system
• Polished flat specimen