Joost J. Vlassak

Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments

The phenomena of pile-up and sink-in associated with nanoindentation have been found to have large effects on the measurements of the indentation modulus and hardness of copper. Pile-up (or sink-in) leads to contact areas that are greater than (or less than) the cross-sectional area of the indenter at a given depth. These effects lead to errors in the absolute measurement of mechanical properties by nanoindentation. To account for these effects, a new method of indenter tip shape calibration has been developed; it is based on measurements of contact compliance as well as direct SEM observations and measurements of the areas of large indentations. Application of this calibration technique to strain-hardened (pile-up) and annealed (sink-in) copper leads to a unique tip shape calibration for the diamond indenter itself, as well as to a material parameter, a, which characterizes the extent of pile-up or sink-in. Thus the shape of the indenter tip and nature of the material response are separated in this calibration method. Using this approach, it is possible to make accurate absolute measurements of hardness and indentation modulus by nanoindentation.

A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films

A new analysis of the deflection of square and rectangular membranes of varying aspect ratio under the influence of a uniform pressure is presented. The influence of residual stresses on the deflection of membranes is examined. Expressions have been developed that allow one to measure residual stresses and Youngs moduli. By testing both square and rectangular membranes of the same film, it is possible to determine Poissons ratio of the film. Using standard micromachining techniques, free-standing films of LPCVD silicon nitride were fabricated and tested as a model system. The deflection of the silicon nitride films as a function of film aspect ratio is very well predicted by the new analysis. Youngs modulus of the silicon nitride films is 222 ± 3 GPa and Poissons ratio is 0.28 ± 0.05. The residual stress varies between 120 and 150 MPa. Youngs modulus and hardness of the films were also measured by means of nanoindentation, yielding values of 216 ± 10 GPa and 21.0 ± 0.9 GPa, respectively.

Measuring the elastic properties of anisotropic materials by means of indentation experiments

Abstract The unloading process in an indentation experiment is usually modeled by considering the contact of a rigid punch with an elastically isotropic half space. Here we extend the analysis to elastically anisotropic solids. We review some of the basic formulae for describing the indentation of elastically anisotropic solids with axisymmetric indenters. We show how the indentation modulus can be calculated for arbitrary anisotropic solids and give results for solids with cubic crystal symmetry. We have calculated the contact stiffness for a flat triangular punch on a half space for various anisotropic materials. The indentation modulus for a triangular indenter is typically 5–6% higher than that for an axisymmetric indenter and varies only slightly with the orientation of the indenter in the plane of the indentation. We have conducted microindentation experiments to measure the indentation moduli of differently oriented surfaces of both cubic and hexagonal single crystals. For copper and β-brass, the (111) indentation moduli are approximately 10 and 25% larger than the {100} modulus. The (110) moduli are typically slightly smaller than the (111) moduli. The indentation modulus of zinc varies by as much as a factor of two, depending on the sample orientation. The hardnesses of the single crystals do not vary much with the orientation of the plane of indentation. For /gb-brass, the hardness of a {110} surface is only about 13% lower than the hardness of a {100} or {111} surface; for copper, the {110} hardness is 6% higher than for the other orientations. For zinc the maximum change in hardness with orientation is 20%.

Indentation modulus of elastically anisotropic half spaces

The unloading process in an indentation experiment is often modelled as a contact problem of a rigid punch on an elastically isotropic half space. This allows one to derive simple formulae to determine the indentation modulus from experimental data. We have studied the contact problem of a flat circular punch and a paraboloid on an elastically anisotropic half space and have shown that the formulae used for isotropic materials can be used for anisotropic materials as long as the half space has three or fourfold rotational symmetry. In the case of lower symmetry, the indentation modulus depends on the shape of the indenter. We have calculated the indentation modulus of {100}, {111} and {110} surfaces of cubic crystals for a wide range of elastic constants. The {110} indentation modulus was calculated for the case of a flat circular punch. The single-crystal indentation moduli differ substantially from the isotropic polycrystalline indentation moduli and the differences increase with increasing anisotropy f...

Indentation plastic displacement field: Part I. The case of soft films on hard substrates

The plastic deformation behavior of Knoop indentations made in a soft, porous titanium/aluminum multilayered thin film on a hard silicon substrate is studied through use of the focused-ion-beam milling and imaging technique. Pileup is observed for indentations with depths larger than 30% of the total film thickness. Analysis of the indentation cross sections shows that plastic deformation around the indentation is partly accommodated by the closing of the pores within the multilayers. This densification process reduces the amount of pileup formed below that predicted by finite element simulations. Experimental results show that the pileup is formed by an increase of the titanium layer thickness near the edges of the indentation. The thickness increase is largest near the film/substrate interface and decreases toward the surface of the multilayered film. The amount of normal compression near the center of the indenter is characterized, and it is demonstrated that the deformation becomes more nonuniform with increasing indentation depth.

Indentation plastic displacement field: Part II. The case of hard films on soft substrates

The plastic displacements around Knoop indentations made in hard titanium/aluminum multilayered films on soft aluminum alloy substrates have been studied. Indentations were cross-sectioned and imaged using the focused-ion-beam (FIB) milling and high-resolution scanning electron microscopy (SEM), respectively. The FIB milling method has the advantage of removing material in a localized region without producing mechanical damage to the specimen. The micrographs of the cross-sectioned indentations indicate that most of the plastic deformation around the indentation is dominated by the soft aluminum substrate. There is a very small change in the multilayered film thickness around the indentation{emdash}less than 10{percent}. The plastic deformation of the thin film resembles a membrane being deflected by a localized pressure gradient across the membrane. Stress-induced voids are also observed in the multilayered film, especially in the area around the indentation apex. The density and the size of the voids increase with indentation depth. Indentation sink-in effects are observed in all of the indentations inspected. Based on the experimental results, the amount of sink-in of the hard film{endash}soft substrate composite is larger than the bulk substrate and film alone. This is confirmed by the finite element analyses conducted in this work. {copyright} {ital 1999 Materials Research Society.}

A SIMPLE TECHNIQUE FOR MEASURING THE ADHESION OF BRITTLE FILMS TO DUCTILE SUBSTRATES WITH APPLICATION TO DIAMOND-COATED TITANIUM

We have developed a new technique for measuring the adhesion of brittle films to ductile substrates. In this technique, a wedge indenter is driven through the brittle coating and into the underlying substrate. Plastic deformation of the substrate causes the coating to delaminate from the substrate. The width of the delaminated area can be directly related to the interface toughness. We present a simple analysis of this technique and apply it to diamond-coated titanium. The toughness of the diamond-titanium interface as measured with this wedge delamination technique is approximately 51 ± 11 J/m 2 . XPS measurements reveal that a reaction layer of titanium carbide forms between the diamond coating and the titanium substrate. Delamination of the coating occurs by crack propagation in this reaction layer and in the diamond film itself. These observations agree well with nanoindentation measurements performed in the delaminated area of the substrate.

Measuring the Mechanical Properties of Thin Metal Films by Means of Bulge Testing of Micromachined Windows

Free-standing films of gold and aluminum have been fabricated using standard micro-machining techniques. LPCVD silicon nitride films are deposited onto (100) silicon wafers. Square and rectangular silicon nitride membranes are made by anisotropic etching of the silicon substrates. Then, metal films are deposited onto the silicon nitride membranes by means of evaporation. Finally, the sacrificial silicon nitride film is etched away by means of reactive plasma etching, resulting in well-defined, square and rectangular metal membranes. Bulge testing of square windows allows one to determine the biaxial modulus of the film as well as the residual stress in it. Testing rectangular windows yields the plane-strain elastic modulus and the residual stress. Since deformation in rectangular membranes approaches plane-strain deformation, this geometry is ideal for studying the plastic properties of the metal films. Stress-strain curves can be readily determined from the load-deflection curves of rectangular membranes. The gold films have a biaxial modulus of 161±3 GPa and a plane-strain modulus of 105±5 GPa, slightly lower than the literature values for a (111) textured film. The yield stress of these films is approximately 231±17 MPa at 10 −4 % plastic strain. The elastic moduli of the aluminum films are 105±3 GPa and 76.4±0.7 GPa, respectively; the yield stress of these films is 187±30MPa.

Measuring Interfacial Fracture Toughness With The Blister Test

The adhesion of thin films to substrates can be quantified using the blister test , which measures the crack extension force ( G ) required to propagate a crack along the film/substrate interface. We summarize the derivation of crack extension force for the blister test, and discuss how blister tests can be conducted by measuring only the pressure and volume of liquid injected into the test system. We describe a way to calculate the velocity of the interface crack front. Data from blister tests of acrylate films (14 μm thick) on nitride substrates are analyzed. The critical crack extension forces ( G C ) measured were 25 − 34 J/m 2 for samples which had a commercial adhesion promoter at the interface, and 0.5 − 2.0 J/m 2 without the adhesion promoter. G C was observed to increase with the velocity of the interface crack, and the dependence appears to obey a power-law.

Measuring the Adhesion of Diamond Thin Films to Substrates Using the Blister Test

It is shown that the blister testing technique can be used to measure the adhesion of thin films to their substrates. A brief discussion of blister test mechanics is presented here, leading to a simple equation relating adhesion to the height of the blister and the pressure causing it to grow. Blister test data for plasma-enhanced CVD diamond films on Si substrates have been analyzed using this relation. The tests show adhesion energies of 1.8– 2.6 J/m 2 .