The 400°C limitation to the most common nanoindenter material, diamond, is not due to diamond changing to graphite in air, which can happen above 750°C, but to the reaction of the nanoindenter with the sample, causing a change in the geometry. The nanoindentation methodology is very sensitive to a change in nanoindenter geometry, thus the typical solution for measurements above 400°C is to use a cBN nanoindenter. However, the cBN indenter that is commercially used at temperatures above 400°C is too soft for measuring hard coatings such as machine tool coatings. There is limited published research on improving nanoindentation measurements in this way. Thus, the objective of this thesis is to address whether a coated diamond could be used for nanoindentation between 400-750°C. Due to the results of early experiments PVD titanium is the focus of this thesis as it will adhere to diamond by forming a carbide interlayer, TiC. A methodology to determine the best coating based on resistance to oxidation and robustness of the coating at temperature was used, allowing the exploration of several different titanium based alloys and coating thickness. The methodology used is as follows: 1. PVD coatings of titanium and titanium based alloys TiAl, TiN, and TiAlN were oxidized at 500, 575, and 650°C. Measurements by SEM and EDS were taken after the oxidation at each temperature. Of the coatings tested, the pure titanium coating was determined to be the best coating. 2. The coating thickness of 0.25, 0.50, and 1.0 um were evaluated with the same static oxidation test applied to the different alloys. It was determined that 0.50 um was the best thickness. A duplicate 0.50 um thick sample had a cross-section machined by FIB, and was examined by STEM, HAADF and EELS. The results confirmed that TiC was being formed at the expected rate. 3. To determine whether a coated nanoindenter could be used for measurements, a nanoindenter was first calibrated, coated by PVD with 0.50 um thick titanium, and calibrated again. The results confirmed that a coated nanoindenter could be used for performing nanoindentation measurements. 4. To determine whether the titanium PVD coating would adhere to the diamond at temperature, a coated nanoindenter was used to measure fused silicon at 450°C. After each measurement, the nanoindenter was examined by SEM and EDS. The results confirmed that the titanium coating adhered to the diamond. This thesis demonstrates that a titanium PVD coating can protect a diamond nanoindenter during measurements between 400-750°C. The primary contributions are that coated diamond nanoindenters can be used for nanoindentation measurements, and that titanium PVD coated nanoindenters can be used for nanoindentation measurements between 400-750°C. Additional contributions include the testing of adhesion of titanium PVD coating to diamond between 400-750°C, and a methodology of evaluating coatings. / Thesis / Doctor of Philosophy (PhD)

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Es wird untersucht, inwieweit das Konzept des effektiv geformten Indenters zur Bestimmung der Fließgrenze massiver Materialien unterschiedlicher Duktilität zuverlässig einsetzbar ist. Dazu werden neun verschiedene Stahlproben sowie BK7-Glas zunächst hinsichtlich ihrer Duktilität charakterisiert. Dies erfolgt anhand des dimensionslosen Parameters Elastizitätsmodul zu Fließgrenze (E/Y). Die Bestimmung des E-Moduls erfolgt mittels akustischer Oberflächenwellen. Die Fließgrenze wird durch makroskopische Druckversuche ermittelt. Anschließend wird das Konzept des effektiv geformten Indenters auf die verschiedenen Materialien angewandt und es wird verglichen, inwieweit die somit erhaltenen Werte für die Fließgrenze mit dem Referenzwert übereinstimmen.

Es wird untersucht, inwieweit das Konzept des effektiv geformten Indenters zur Bestimmung der Fließgrenze massiver Materialien unterschiedlicher Duktilität zuverlässig einsetzbar ist. Dazu werden neun verschiedene Stahlproben sowie BK7-Glas zunächst hinsichtlich ihrer Duktilität charakterisiert. Dies erfolgt anhand des dimensionslosen Parameters Elastizitätsmodul zu Fließgrenze (E/Y). Die Bestimmung des E-Moduls erfolgt mittels akustischer Oberflächenwellen. Die Fließgrenze wird durch makroskopische Druckversuche ermittelt. Anschließend wird das Konzept des effektiv geformten Indenters auf die verschiedenen Materialien angewandt und es wird verglichen, inwieweit die somit erhaltenen Werte für die Fließgrenze mit dem Referenzwert übereinstimmen.

L’indentation instrumentée est largement utilisée pour la détermination des propriétés mécaniques des matériaux, principalement la dureté et le module d’élasticité. Pour obtenir des données fiables, plusieurs corrections comme la prise en compte du défaut de pointe et la complaisance de l’instrument doivent être apportées dans la méthodologie d’analyse des données de l’essai. Malgré tout, ces corrections ne suffisent plus pour la caractérisation de matériaux fragiles et poreux, qu’ils soient sous une forme massive ou de revêtement. En effet, d’autres sources d’erreurs peuvent provenir de la fragilité de ces matériaux, mais aussi de la représentativité des mesures locales dans le cas des matériaux hétérogènes, ou de l'influence du substrat dans le cas des revêtements. Pour limiter ces effets, l’indenteur Knoop semble être un bon candidat car, à charge équivalente, sa surface de contact est plus grande et la profondeur d’indentation plus faible. Toutefois, par rapport aux indenteurs habituels, le retour élastique du matériau au voisinage de l'empreinte Knoop, qui doit être pris en compte dans les calculs des propriétés, n’est pas bien connu. Ceci constitue donc un frein à son utilisation. C’est pourquoi, nous proposons d’adapter la méthodologie conventionnelle proposée par Oliver et Pharr pour obtenir des résultats fiables par indentation Knoop. Pour atteindre cet objectif, nous analysons d’abord des résultats obtenus par indentation de différents matériaux céramiques denses en comparant les indentations Knoop et Vickers, ce dernier étant utilisé comme référence. Tout d’abord, nous analysons le retour élastique en indentation Knoop et nous montrons qu’il est possible de retrouver les mêmes valeurs qu’en indentation Vickers en intégrant un facteur correctif lié simplement à des grandeurs géométriques de l’empreinte. Cette approche est valable qu’il s’agisse de la détermination du module d’élasticité ou de la dureté. Toutefois, pour cette dernière propriété, il est nécessaire de bien préciser la définition utilisée pour son calcul. Nous en justifions le choix. Ensuite nous appliquons la méthodologie d’analyse ainsi établie pour l’étude de la réponse mécanique des matériaux poreux sous forme massive et de revêtement où non seulement le paramètre de porosité joue un rôle important sur la réponse du matériau, mais aussi son hétérogénéité, sa rugosité et son épaisseur. De manière générale, nous montrons que l’indenteur Knoop présente un intérêt certain par rapport aux indenteurs habituels, tout au moins dans le cas des céramiques. / Instrumented indentation is widely used for the assessment of mechanical properties, mainly hardness and elastic modulus. In order to obtain reliable results, analysis methodology has to refer several corrections, such as tip defect and frame compliance. However, these corrections are insufficient for the characterization of brittle and porous materials, whether bulk or coatings. Not only brittleness but also local surrounding in the case of heterogeneous materials and substrate influence in the case of coatings raise error concerns. To limit these unwanted effects, the Knoop indenter appears to be a favorable candidate because of the larger contact area and lower indentation depth at equivalent loads. However, compared to other commonly used indenters, radial elastic recovery near Knoop indent that has to be taken into account in the analysis methodology, is not well known. This constitutes therefore an obstacle for its use. Thereof, we propose to adapt the conventional methodology proposed by Oliver and Pharr to obtain reliable results with Knoop indentation. To achieve this purpose, we analyze the indentation data of different dense ceramic materials by comparing Knoop and Vickers indentations, this latter being used as a reference. First, we analyze the elastic recovery using Knoop indenter. We show that correlation to Vickers indentation results is possible using a geometric correction factor. This approach is valid for the determination of elastic modulus and hardness. However, for the latter property, it is necessary to specify the definition used for its calculation. The established analysis methodology was applied for studying the mechanical response of porous bulk materials and coatings, with respect to material porosity, roughness and thickness. It was confirmed that Knoop indenter may be favorable compared to the commonly used indenters, at least in the case of ceramics.

ABSTRACT The rapid development of structural materials and their successful applications in various sectors of industry have led to increasing demands for assessing their mechanical properties in small volumes. If the size dimensions are below micron, it is difficult to perform traditional tensile and compression tests at such small scales. Indentation testing as one of the advanced technologies to characterize the mechanical properties of material has already been widely employed since indentation technology has emerged as a cost-effective, convenient and non-destructive method to solve this problem at micro- and nanoscales. In spite of the advances in indentation testing, the theory and development on indentation testing are still not completely mature. Many factors affect the accuracy and reliability of identified material parameters. For instance, when the material properties are determined utilizing the inverse analysis relying on numerical modelling, the procedures often suffer from a strong material parameter correlation, which leads to a non-uniqueness of the solution or high errors in parameter identification. In order to overcome that problem, an approach is proposed to reduce the material parameter correlation by designing appropriate indenter tip shapes able to sense indentation piling-up or sinking-in occurring in non-linear materials. In the present thesis, the effect of indenter tip geometry on parameter correlation in material parameter identification is investigated. It may be helpful to design indenter tip shapes producing a minimal material parameter correlation, which may help to improve the reliability of material parameter identification procedures based on indentation testing combined with inverse methods. First, a method to assess the effect of indenter tip geometry on the identification of material parameters is proposed, which contains a gradient-based numerical optimization method with sensitivity analysis. The sensitivities of objective function computed by finite difference method and by direct differentiation method are compared. Subsequently, the direct differentiation method is selected to use because it is more reliable, accurate and versatile for computing the sensitivities of the objective function. Second, the residual imprint mappings produced by different indenters are investigated. In common indentation experiments, the imprint data are not available because the indenter tip itself shields that region from access by measurement devices during loading and unloading. However, they include information about sinking-in and piling-up, which may be valuable to reduce the correlation of material parameter. Therefore, the effect of the imprint data on identification of material parameters is investigated. Finally, some strategies for improvement of the identifiability of material parameter are proposed. Indenters with special tip shapes and different loading histories are investigated. The sensitivities of material parameters toward indenter tip geometries are evaluated on the materials with elasto-plastic and elasto-visoplastic constitutive laws. The results of this thesis have shown that first, the correlations of material parameters are related to the geometries of indenter tip shapes. The abilities of different indenters for determining material parameters are significantly different. Second, residual imprint mapping data are proved to be important for identification of material parameters, because they contain the additional information about plastic material behaviour. Third, different loading histories are helpful to evaluate the material parameters of time-dependent materials. Particularly, a holding cycle is necessary to determine the material properties of time-dependent materials. These results may be useful to enable a more reliable material parameter identification.

Soft biological tissues, being live and due to their physiological structures, display considerably complex mechanical behaviors. For a better understanding and use in various applications, first study to be carried out is the tests made particularly as in vivo. An indenter test device developed for this purpose in the METU, Department of Mechanical Engineering, Biomechanics Laboratory is operational. In this study, in order to carry out precise and dependable tests, initially, various tests and improvements were conducted on the device and the software controlling the device. At the end of this study, displacement and load measurement accuracies and precisions were improved. Better algorithms for filtering the noisy data were prepared. Some test protocols within the software were improved and new protocols were annexed. To be able to conduct more dependable tests a new connection system was attached to the device. In order to study the anisotropic behavior of soft tissues ellipsoid tips were designed and produced. In the second phase of the study, tests on medial forearm were carried out. In these tests, hysteresis, relaxation and creep behaviors displaying the viscoelastic v properties of the soft biological tissues were observed. In addition to viscoelastic behaviors, preconditioning (Mullin&amp / #8217 / s) effect and anisotropic response were examined. By using the results of the relaxation and creep tests, parameters of the Prony series capable of modelling these data were determined. With this study, some important conclusions regarding the soft biological tissues were drawn and thus the behaviors of the soft biological tissues were better understood. Besides, the difficulties inherent to in-vivo tests were recognized and actions to reduce these difficulties were explained. Finally, clean experimental data, to be used in the computer simulations, were obtained.

Mechanical simulation of viscoelastic materials and assigning a viscoelastic material to the modeled parts in the simulations are difficult task. For the simulations, material model should be well chosen and material coefficients of the chosen models should be known. In order to obtain accurate simulations, hyperelastic characteristics of the viscoelastic materials should be investigated and hyperelastic model should be incorporated in the solutions. Material models and material model&rsquo / s coefficients are chosen with the help of mechanical tests/experiments for these situations. The main goal of this thesis is to optimize material model&rsquo / s coefficients by using an indenter test setup results and inverse finite element modeling. To achieve this, firstly by using a haptic device and other required equipments an indenter setup was prepared to test the materials mechanically. Inverse finite element modeling method is used in order to model the materials according to their viscoelastic and hyperelastic characteristics. The model obtained from analysis was optimized by using the results obtained from indenter setup according to experimental test data. By doing this, the correctness of the model chosen by inverse finite element modeling was proved for the tested material and material model coefficients were calculated correctly.

Partial differential equations describe a number of processes in the physical-technical environment. The equations of the elasticity theory, which can be used to describe the deformations of a sample under application of an outer load, may serve as an example. Among other things, such deformations appear at so-called indentation tests, which are used to determine mechanical properties of thin layers. Since most partial differential equations can not, or only with great difficulty, be solved in an analytical way, numeric attempts to obtain an approximate solution are common. For the solution of elliptical partial differential equations with boundary conditions, the finite element method (FEM) is widely used. A problematic aspect is the growing numeric effort when increasing the accuracy of the approximation. This issue intensifies at higher dimensions. Since the scope of this work is the three-dimensional case, we will investigate possibilities of dimension reduction. Two Fourier approaches, which allow a dimension diminution from three to two, are being examined. If combined with a cylindrical parametrization of the three-dimensional space, the solution can be calculated without loss of information. The application of these approaches is illustrated exemplarily by the modeling of an indentation test with a rotationally symmetric structur and loads without rotational symmetry. / Partielle Differentialgleichungen beschreiben im physikalisch-technischen Umfeld eine Reihe von Prozessen. Ein Beispiel hierfür sind die Gleichungen der Elastizitätstheorie, die genutzt werden können, um die Verformungen einer Probe unter Aufbringung einer äußeren Last zu beschreiben. Solche Verformungen treten unter anderem bei sogenannten Indenterversuchen auf, die eingesetzt werden, um mechanische Größen dünner Schichten zu ermitteln. Da die meisten partiellen Differentialgleichungen auf analytischem Wege nicht, oder nur sehr schwer zu lösen sind, existieren numerischen Ansätze, um eine Lösung auf approximativem Wege zu erzielen. Für die Lösung elliptischer partieller Differentialgleichungen mit Randbedingungen existiert das Verfahren der Finiten-Elemente-Methode (FEM). Ein problematischer Aspekt besteht im wachsenden numerischen Aufwand mit genauer werdender Approximation der Lösung. Mit dem Ansteigen der Dimension der beschriebenen Prozesse verschärft sich dieses Problem. Der Fokus dieser Arbeit liegt auf dreidimensionalen Aufgabenstellungen. Daher ist es ihr Ziel, Möglichkeiten der Dimensionsreduktion zu untersuchen. Betrachtet werden zwei Fourieransätze, die bei einer Parametrisierung eines dreidimensionalen Gebietes mittels Zylinderkoordinaten eine Reduktion von drei auf zwei Freiheiten in der Berechnung der Lösung ermöglichen, ohne dass dabei Informationen verloren gehen. Die Anwendung dieser Ansätze soll beispielhaft durch die Modellierung eines Indenterversuches mit rotationssymmetrischer Anordnung und nichtrotationssymmetrischen Lasten veranschaulicht werden.

Indentation is used as a technique for mechanical characterization of materials for a long time. In the last few decades, new techniques of mechanical characterization at micro and nano level using indentation have been developed. Mechanical character-ization of thin films has become an important area of research because of their crucial role in modern technological applications. Theoretical and computational models of indentation are less time consuming,cost effective, and flexible. Many researchers have investigated mechanical properties of thin films using theoretical and computational models. In this study, an indentation model for a thin layer-substrate geometry with the possibility of nonhomogeneous or homogeneous interface of finite thickness between layer and substrate has been developed. The layer and substrate can be nonhomogeneous or homogeneous. Three types of indenters are modeled: 1) Uniform pressure indenter 2) Flat indenter 3) Smooth indenter. Contact depth, maximum interfacial normal stress and maximum interfacial shear stress play an important role in design and mechanical characterization of thin films using indentation and the effect of modeling the interface as homogeneous and nonhomogeneous on these parameters is studied. A sensitivity analysis is also conducted to find the effect of indentation area, substrate to layer Young's modulus ratio, layer to interface thickness ratio on contact depth and critical interfacial stresses.