NanoTest Sample Oscillation Technique

In conventional small-scale indentation testing, the mechanical properties of a material at a particular depth below the surface are determined through analysis of a Depth vs. Load hysteresis curve. In a similar way, a mechanical property depth profile may be achieved by producing a sequence of such curves at a single point, in which the load and depth are increased to progressively higher values.

In order to derive the diamond-material contact areas in a depth profile sequence of indentations, which are necessary for hardness and modulus determination, the elastic compliance of each contact must first be obtained.

An alternative approach, in which it is unnecessary to produce unloading curves, is based on the established technique of Dynamic Mechanical Analysis. In the NanoTest implementation, the specimen is oscillated with a very small amplitude, and the phase difference between the applied stress and the response of the diamond is monitored by means of a piezoelectric detector as shown. A dynamic model of the system shows that the phase angle F is given by

tanF = Dw /(C^-1 - mw ²)

where D is the damping coefficient of the system, w is the frequency, C is the contact compliance, and m is the equivalent mass of the pendulum.

Thus the instantaneous contact compliance can be measured as the load is increased without the necessity of analysing unloading data. However, it should be noted that in order to eliminate time-dependent effects, it is still necessary to hold the load periodically.

Hooke's law of elasticity implies an instantaneous and unique response of a material to an imposed stress. However, Hooke's law may be generalised to include anelastic and viscoelastic behaviour, that is, to include time-dependent effects such as gradual material relaxation or flow.

A particularly important example of anelasticity is the dynamical case where stress and strain are both periodic, with the strain lagging behind the stress by a phase angle F . Since elastic and viscous stresses occur simultaneously, a complex modulus is defined for the material as G* = G' + G'', where G' is the elastic (energy storing) and G'' is the loss (energy dissipating) modulus. The phase angle F by which the strain lags the stress is given by tanF = G''/G' and is a measure of the energy dissipated per cycle.

Using sample oscillation both G' and G'' can be determined with the NanoTest over a wide frequency range.

Illustrative Results Using the Sample Oscillation Technique...

Indentation data for a tungsten sample oscillated with a frequency of 30 Hz. The phase difference F was 57.16° , giving a Young's modulus of 394.6 GPa. Note the creep at maximum load, necessitating a dwell period to achieve mechanical equilibrium. A Berkovitch diamond was used.

Variation in phase angle with frequency for polyethylene. A 1 mm diameter indenter was used with a load of 25 mN. At a sample oscillation frequency of 10 Hz, for instance, the storage modulus was found to be 4.525 GPa and the loss modulus (using linear viscoelastic theory) was determined to be 1.063 GPa.