Nanoindentation

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The nanoindentation (also instrumented indentation) is a method of testing of materials for determining the hardness of materials on small length scales ( nanometers, nm ). The main area of ​​application is the determination of hardness on thin layers .

Scheme nanoindentation

history

The investigation of the material properties of metals has been of interest since the Middle Ages. In the course of industrialization at the latest, it has become essential to be able to manufacture high-quality metallic materials for a wide variety of tasks. In order to be able to meet the ever increasing demands on the materials, a good understanding of the material parameters, such as hardness, brittleness and roughness , is imperative. All these material properties were examined early on with the help of so-called indentation tests, in which initially only the plastic impression was measured after hitting a hammer. Conceptually, today's measuring methods for determining hardness still correspond to Friedrich Mohs' approach: A material to be tested is plastically deformed using standard materials of different hardness. Based on the resulting plastic deformation, the hardness is then determined in relation to the standard materials. On the Mohs scale from 1 (talc) to 10 (diamond), the materials copper and aluminum used in the present work have a hardness of 3 and 2.3 ... 2.9 respectively. Then as now, the question arises as to how certain macroscopic material properties can be influenced. Often desirable properties are mutually exclusive: For example, it is a particular challenge to find a material that is both hard and ductile at the same time. Today we can search for the causes of the macroscopic material properties at the atomic level, and more and more possibilities are available to process materials on the smallest length scales. Ever since Feynman's seminal speech, the miniaturization of everyday objects (especially electrical ones) has begun. Of course, this places completely new demands on the mechanical properties of the materials. At the same time, the resolution of the measuring equipment has increased significantly. In 1968 it was pioneering to carry out stress tests on the μm scale, today measurements on the Å scale are feasible.

method

Force-penetration-depth curve

The nanoindentation is derived from the classic hardness test, but takes place on a much smaller scale. A diamond tip with a known geometry is pressed into the surface to be tested. Due to the miniaturization of the structure, it is only possible with great effort to measure the area of ​​the hardness indentation remaining in the test piece, as is done with conventional methods of hardness measurement. Therefore, during the test, the applied penetration force and the penetration path of the tip are measured simultaneously during the nanoindentation. The contact surface and subsequently the hardness can be calculated using the known geometry of the test tip and the measurement data for penetration force and penetration path.

The measuring head for nanoindentation (Hysitron Triboscope) consists of a three-plate capacitor and is attached to an atomic force microscope . If an electrical voltage is applied to the capacitor, a force is created on the middle capacitor plate, which presses a pin with a diamond tip into the surface to be tested. The displacement of the middle capacitor plate causes a change in capacitance of the capacitor and the necessary force and penetration depth data are obtained to determine the hardness. According to DIN EN ISO 14577, 0.2 µm is defined as the limit between the micro and nano measuring range. Most devices for instrumented penetrant testing, however, also measure in the micro range up to the limit of the macro testing range of 2 N.

Why nanoindentation?

First of all, of course, a general goal is to measure material properties with ever higher resolution - and thus to minimize the relative error of the measurements. In addition, the smaller the samples examined, the more precisely they can be prepared and therefore the smaller the fluctuations due to impurities. The influence of the individual parameters of a material can therefore be better separated. While the indentation on the μm scale is now quite well understood, there are still many unanswered questions regarding nanoindentation (on the nm scale). This means in particular that the atomistic processes and their repercussions on the macroscopic material properties are not yet understood in detail. Nanoindentation in metals is a complex process that can be used to study both elastic and plastic properties. When the indenter is pressed into the material, it initially deforms elastically. With further indentation up to the critical penetration depth d yield , the resulting plasticity initially leads to a load drop in the force. As soon as the first dislocations have been generated, they spread, react with one another and material transport takes place. Most of these atomistic processes have direct consequences for the force acting on the indenter; the indenter no longer penetrates an ideal material, but rather a material hardened by the indentation process (workhardening). While an ideal crystal is characterized by a pure, ideal crystal lattice, a real crystal is interspersed with various types of lattice defects. If the crystal lattice induces a length scale for the substrate, another length scale is given by the size and interaction range of the lattice defects. This length scale is inherently larger than that of the lattice constant. But because the macroscopic material properties continue to vary significantly with the microscopic lattice structures, real crystals are dominated by a coupling of different length scales. An understanding of the atomistic processes is therefore necessary for an understanding of the macroscopic material properties. The method of nanoindentation is particularly well suited to investigate the relationship between microscopic material parameters and macroscopic material properties. While a classic endurance test draws conclusions from macroscopic observations about microscopic properties, we are now following a reciprocal approach in which the microscopic properties are examined directly. An investigation of the atomistic structure of materials makes it possible to develop new continuum theoretical models. For example, the model of the geometrically necessary dislocations due to nanoindentation was developed. The reaction of a material to the loading by the indenter can be very different. The easiest to understand is the linear elastic range - even if it is complicated to describe in detail due to the multi-axis bracing. Because it is not only reversible, the crystal structure is also retained in it. With regard to its lattice structure, an ideal crystal remains homogeneous in the elastic range. It becomes more complicated when the crystal structure - i.e. the bonds between the atoms - changes under the load, i.e. the substrate becomes inhomogeneous. Thus, phenomena were discovered by means of nanoindentation that were not previously described by continuum theory: for example, phase transformations of the lattice structure can occur that lead to (reversible) load drops in the force . However, these load drops do not result from the onset of defect formation and are therefore not included in conventional models based on continuum theory. Furthermore, completely different phenomena can occur for other classes of materials. For example, shear bands are observed in amorphous silicon. In general, bond changes can lead to drastic effects: Recently, a crystal structure was found that is harder than diamond at a lower density. Although the method of indentation actually acts directly on the free surface, what happens inside the substrate still has a considerable influence on the reaction of the material to the load from the indenter. The obvious conclusion that the measured properties are dominated by the free surface is deceptive, because the indenter acts like a magnifying glass and focuses the maximum shear stress in the material. Due to the long range in the interactions of the stresses in the substrate, conclusions can also be drawn about the bulk properties by means of indentation. This makes the method of indentation interesting for the investigation of single crystals. While a real monodisperse crystal is largely determined in its properties by dislocations and grain boundaries, we only consider ideal single-crystalline materials here.

Indenter shape

Defects on the metal surface

The shape of the indenter tip (indenter shape) is usually either pyramidal, rectangular or spherical. It greatly influences the results obtained. For example, a pointed indenter leaves a different plastic impression than a spherical indenter. Since the tension under the indenter is very different depending on the indenter shape, different sliding systems are activated in each case. With the method of indentation there is therefore a strong influence on the determined characteristic values ​​by the measurement method. It is therefore always necessary to specify the method used for a measured value.

Indentation as an endurance test

The method of hardness measurement by means of indentation is in principle quite simple. The indenter is pressed into a material with a certain force and the acting force is measured. The plastic impression can then be measured and the contact area can be approximated from this. The hardness is then calculated using the relationship .

Material properties on the nanoscale

Defects below the metal surface

Material properties can change drastically through atomistic movements. This motivates the production and investigation of so-called nano-materials. Such materials can be harder than diamond or their plastic deformations can heal. On the other hand, the causes of their material properties are not yet fully understood for classic materials. These include in particular the mechanisms of plastic deformation of metals, which are the subject of current scientific debates.

application

AFM image with a Berkovich indenter.

The classic and still most common area of ​​application for nanoindentation is the determination of hardness and modulus of elasticity on layered materials. The low forces and penetration depths limit the interaction with the identified sample to very small volumes. This makes it possible, for. B. to examine very thin layers of less than 1 micron thickness without significant influences of the underlying substrate material. Further possible uses are the investigation of individual grains or material phases as well as the recording of hardness gradients in surface layers. Since nanoindentation requires electronic and thus continuous displacement measurement, not only the maximum force and penetration area, but a complete force-displacement curve are available as measurement data. In addition to various hardness parameters, this additional information also includes parameters for elastic relief behavior and creep behavior. Advanced devices can be B. Determine depth profiles of hardness and modulus of elasticity as well as characteristic values ​​for plastic flow behavior in one measurement by cyclical loading and unloading. An overview of the currently common areas of application is given below.

Hardness test

In the macroscopic hardness test , a defined force is applied for a defined period of time and the remaining plastic impression is then optically measured. In contrast, with nanoindentation, the force and the depth of penetration are measured continuously. By varying the loading and unloading speed, the maximum force, the holding time of the maximum force and the type of loading (e.g. linear or quadratic force increase), a large number of different hardness parameters and other mechanical parameters can be determined. Since deviations of the indenter from the ideal geometric shape (e.g. due to tip rounding or material accumulation) must not be neglected with the small penetration depths of the nanoindentation, the geometric shape of the indenter must be determined at regular intervals using suitable test methods. Using this shape function of the indenter, the nanoindenter can then calculate the correct contact area for each penetration depth. Other special features of nanoindentation are the consideration of the thermal drift, which can have a considerable influence on the measured penetration depth due to temperature changes due to the thermal expansion of the sample and indenter. The thermal drift is usually measured before the start of the load and shortly before the load is completely removed. The determined value is then calculated from the measurement curve. Material-specific features in nano-penetrant testing, such as sink-in or pile-up, are taken into account using suitable mathematical processes. With newer devices, it is possible, by superimposing the continuously increasing force signal during the load with a cyclically oscillating force signal of small amplitude (continuouse stiffness measurement - csm), to determine the hardness and modulus of elasticity for each cycle and thus determine a hardness curve over the penetration depth to determine.

E-module determination

A quantity related to the modulus of elasticity can be calculated from the relief part of the penetration curve, which is often equated with it in scientific literature. The method for calculating this penetration modulus was developed by Oliver & Pharr. For the calculation, that part of the relief curve is used in which a purely elastic reaction of the counter body to the decreasing penetration force of the indenter can be assumed. Like the hardness measurement, the modulus of elasticity can be determined in depth by csm measurement. In this case, the modulus of elasticity is obtained from the relief curve of the cyclical measurement signal, which should always be elastic. When determining the modulus of elasticity, it should be noted that there is always a certain influence of the substrate material, since the stress fields spreading from the penetrating indenter in the material generally spread infinitely (with increasingly lower intensity) and therefore everywhere also cause an elastic reaction, which ultimately is included in the measurement. With depth-resolved measurements, the true modulus of elasticity of a homogeneous layer can be estimated well by taking the modulus of elasticity vs. Penetration depth curve extrapolated against the penetration depth 0.

Plastic flow behavior

The hardness value of a material in the hardness test results from the elastic and plastic deformation behavior of the material. While the elastic component can be calculated quite easily as a singular value from the relief curve, the plastic deformation parameters are much more complex to determine. This is particularly due to the non-linear character of the flow curve , which means that a separate stress value must be determined for each value of the strain. An important and comparatively easy to determine characteristic value for the plastic flow is the yield point, which can be determined analytically depending on the indenter geometry. To determine the further flow curve, special measurements are required in which a usually spherical indenter is pressed into the material in a predetermined manner. The flow curve is then determined from the measurement data, for example via FEM simulation (Imprintec I3dTest) or neural networks (ASMEC nanoindenter). In combination with adapted measurement methods, the FEM simulation also enables the strain rate dependency and temperature dependency to be determined.

Scratch test

Most nanoindenters allow the sample table to move laterally while the indenter is being pressed into the sample, so that the indenter tip “plows” through the sample. Depending on the device, it is possible to vary test parameters such as penetration force and travel speed as well as to measure penetration depth and lateral force. Many devices also make it possible to travel the scratched section before and after scratching with very little indenter force and thus determine the maximum (elastic & plastic) and the remaining (only plastic) depth of the scratch trench for the entire distance. The scratch method is now used for a variety of investigations. For example, the use of a ramp scratch (a scratch with increasing penetration force during scratching) is common in adhesive characterization. By observing the point in time or the distance from which delamination of the layer occurs, the associated force value can be determined and layers can thus be compared with regard to their adhesive strength. By combining nanoscratches and FEM simulation, it is possible to examine the load conditions under which failure (delamination, cracking) occurs in a material. This enables, for example, the development of failure criteria for materials. It is also possible to determine the coefficient of friction using scratch tests.

swell

literature

  • Karsten Durst: Microstructural and micromechanical characterization of precipitation-hardened materials with the nanoindenting atomic force microscope. 1st edition. Der Andere Verlag, Osnabrück 2003, ISBN 3-89959-129-1 .
  • G. Ziegenhain: Atomistic Simulation of Nanoindentation. 2009, DNB 1002491576 .

Individual evidence

  1. ↑ a b c d G. Ziegenhain: Atomistic simulation of nanoindentation. 2009, DNB 1002491576 .
  2. ^ G. Agricola: De Re Metallica. Basel 1556.
  3. ^ D. Tabor: The Hardness of Metals. Clarendon Press, Oxford 1951.
  4. ^ R. Feynman: Plenty of Room at the Bottom. In The annual meeting of the American Physical Society at the California Institute of Technology (Caltech, December 29th 1959). In: Caltech's Engineering and Science. 1960.
  5. ↑ N. Gane, F. Bowden: Microdeformation of Solids. In: Journal of Applied Physics. 39 (3), 1968, pp. 1432-1436.
  6. ↑ M. Göken, M. Kempf: Pop-ins in Nanoindentations - the Initial Yield Point. In: Zeitschrift fuer Metallkunde. 92 (9), 2001, pp. 1061-1067.
  7. ↑ Vickers hardness test
  8. ↑ a b A. C. Fischer-Cripps: Nanoindentation. 2nd Edition. Springer, New York 2004.
  9. ↑ A. Gouldstone, N. Chollacoop, M. Dao, J. Li, A. Minor, Y. Shen: indentation across size scales and disciplines: Recent developments in experimentation and modeling. In: Acta Materialia. 55 (12), 2007, pp. 4015-4039.
  10. ↑ U. Landman, W. Luedtke, N. Burnham, R. Colton: Atomistic Mechanisms and Dynamics of Adhesion, Nanoindentation, and Fracture. In: Science. 248 (4954), 1990, pp. 454-461.
  11. ↑ WD Nix, H. Gao: Indentation size effects in crystalline materials: A law for strain gradient plasticity. In: Journal of the Mechanics and Physics of Solids. 46 (3), 1998, pp. 411-426.
  12. ^ Pan et al., 2007.
  13. ↑ Chrobak et al., 2007.
  14. ↑ I. Szlufarska, R. Kalia, A. Nakano, P. Vashishta: A molecular dynamics study of nanoindentation of amorphous silicon carbide. In: Journal of Applied Physics. 102, 2007, p. 023509.
  15. ↑ P. Walsh, R. Kalia, A. Nakano, P. Vashishta, S. Saini: Amorphization and anisotropic fracture dynamics during nanoindentation of silicon nitride: A multimillion atom molecular dynamics study. In: Applied Physics Letters. 77 (26), 2000, p. 4332.
  16. ^ Z. Pan, H. Sun, C. Chen: Colossal Shear-Strength Enhancement of Low-Density Cubic BC 2 N by Nanoindentation. In: Physical Review Letters. 98 (13), 2007, p. 135505.
  17. ^ A b J. Li: The mechanics and physics of defect nucleation. In: MRS bulletin. 32 (2), 2007, pp. 151-159.
  18. ↑ Y. Shi, ML Falk: Structural transformation and localization during simulated nanoindentation of a noncrystalline metal film. In: Applied Physics Letters. 86 (1), 2005, p. 011914.
  19. ^ WC Oliver, GM Pharr In: J. Mater. Res. 7, 1992, p. 1564.
  20. ^ X. Li, B. Bhushan: Materials Characterization. 48, 2002, pp. 11-36.
  21. ^ WC Oliver, GM Pharr, J. Mater In: Res. 7, 1992, p. 1564.
  22. ↑ TF Juliano, VMR vanLandingham, T. Weerasooriya, P. Moy: Extracting Stress-Strain and Compressive Yield Stress Information From Spherical Indentation. In: Army Research Laboratory Report ARL-TR-4229. 2007, p. 1.
  23. ↑ S. Basu, A. Moseson, MW Barsoum In: J. Mater. Res. 21, 2006, pp. 2628-2637.
  24. ↑ J. Perne: Plastic flow behavior of (Cr, A1) N hard coatings in dependence of strain rate and nanostructure. In: Thin Solid Films. 556, 2014, pp. 390-394.
  25. ↑ K.-D. Bouzakis, M. Pappa, S. Gerardis, G. Skordaris, E. Bouzakis: PVD Coatings' Strength Properties at Various Temperatures by Nanoindentations and FEM Calculations Determined. In: Tribology in Industry. Vol. 34, No 1, 2012, pp. 29-35.
  26. ↑ J. Perne: Experimental and simulative strain field investigation of nano- and microscratches on nanolaminated (Cr, Al) N coating. In: Thin Solid Films. 573, 2014, pp. 33-40.