Vickers microhardness measurement
Nanohardness tester "NanoScan-4D" and Vickers hardness meter "NanoScan-HV" allow to measure microhardness by recovered imprint in accordance with GOST 9450-76. Four-sided Vickers-type pyramid (angle between opposing faces 136°) is used as an indenter. Measurements are made on the basis of optical microphotographs. The hardness HV is calculated as the ratio of the maximum load applied to the indenter to the surface area of the recovered indentation measured from its image:
d – the average length of the diagonals of the quadrangular print, mm, P — maximum load in kilogram-force.
where F and Δf are the force and the shift of the resonance frequency measured during scanning, f0 and k are the resonance frequency of oscillations of the free probe and its dynamic stiffness. The last two parameters are determined in the process of calibration of each probe and are considered to be constant during further work. Using this expression, the dependence, H/E2 (and, respectively, H or E if at least one of these values is known), can be plotted as a function of depth or surface coordinates. Below are examples of hardness vs. depth measurements, for measurements on fused quartz, as well as hardness maps for fiberglass in an epoxy matrix. In both cases, the values of the modulus of elasticity were known from other sources.
The standard nanoindentation method implemented on the basis of ISO 14577 is based on the determination of hardness and modulus of elasticity from the slope of the unloading curve, the maximum load and the indentation depth. A number of methods now exist which combine oscillating oscillating motion with indentation penetration into the specimen, allowing for depth dependent measurement of modulus and hardness. A similar approach can be used to obtain maps of the elastic properties of the material.
The NanoScan devices employ the method of multi-cycle loading with partial unloading, which also allows to obtain hardness and modulus of elasticity depending on the depth of indentation; however, it should be noted that all these methods use information on the indenter shape, and thus are strongly affected by roughness influence on the measured result. The proposed method of dynamic hardness measurement is significantly less affected by surface roughness, but requires a priori information about the value of the modulus of elasticity, as it actually allows to measure the H/E2 value. The final dependence, which allows us to produce this value from the experimental data, is as follows:
Dynamic hardness measurement
Measured values of elastic modulus E' and loss modulus E'' for fused quartz (a), bitumen (b) .
The NanoScan-4D devices implement the method of dynamic measurement of contact stiffness. This method is based on the measurement of quadrature components of displacement when a harmonic force is applied, in addition to monotonic deepening of the probe into the sample. On the basis of obtained data the values of real and imaginary stiffness components are calculated and then E' and E'' values corresponding to in-phase and displacement component shifted by 900 are calculated on their basis. The typical operating frequency range is up to 50 Hz, but in the case of preloaded measurements it is possible to operate at frequencies up to 300 Hz.
Dynamic stiffness measurement
In devices of NanoScan series the method of tomogram of hardness and modulus of elasticity of the near-surface layer of the sample is implemented. The method is based on a combination of two methods: the method of multi-cycle loading and the mapping method (plotting a series of indents in a square grid), which allows obtaining the distribution of mechanical properties of the material in the volume (tomogram). A tomogram can be plotted on a sample surface up to 10 cm in size and up to 10 µm in depth. The resolution of the instrument allows to start measuring mechanical properties at depths of several tens of nanometers. Lateral resolution is determined by the size of plastic imprints remaining after loading tests and is in the order of tens of microns.
Fig. 1 Timing diagram of indenter plunge depth and loading force during multicyclic indentation.
Fig. 2 Dependence of loading force on indentation depth for multi-cycle indentation.
The traditional indentation method (ISO 14577) determines the mechanical properties of the material in one area at one depth. The devices of NanoScan series implement the method of multi-cycle loading with partial unloading technique, which allows to measure the mechanical properties at different depths during one indentation into the surface of the sample. In this method, the unloading is carried out to a certain fraction of the value of the maximum load, and at each subsequent cycle the loading is repeated by a larger value Fig. 1, Fig. 2.
Tomography of mechanical properties
Dependence of hardness and modulus of elasticity of PMMA on temperature (a); Load-displacement dependence at 30 0C and 100 0C obtained on PMMA sample (b).
The sample stage with heating control is used to measure mechanical properties of materials at elevated temperature. The sample can be heated to a temperature of 400 0C and all types of mechanical tests implemented in the NanoScan-4D hardness tester can be carried out. The accuracy of maintaining the specified temperature is 0.1 0C. The tests are used to measure such material characteristics as hardness, modulus of elasticity, coefficient of elastic recovery, crack resistance, wear resistance and a number of others at a given temperature. Typical sample dimensions for temperature tests with NanoScan are 25 x 25 x 10 mm. As an example of experimental dependence of mechanical properties of the material on temperature in figure a,b graphs of dependences of hardness and elasticity modulus on temperature for polymethylmethacrylate (PMMA) when heated to 140 0C are presented.
Measurement of the temperature dependence of mechanical properties
NanoScan micro-hardness testers enable the automatic dimensioning of indentations using an intelligent machine vision system. If there are cracks in the corners of the Vickers indentation, it is possible to calculate the crack resistance of the sample at the indentation point. Vickers hardness is one of the most common and longest-used hardness determination methods in the world. Its use in combination with nanohardness methods allows direct comparison and referencing of hardness values at different scales.
Examples of Vickers imprints on different materials. a - tool steel, b - bronze, c - zinc oxide ceramic