An Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetry

An approximate solution for a contact problem of profiles which are not axially symmetrical but deviate only slightly from the axial symmetry is found in a closed explicit analytical form. The solution is based on Betti’s reciprocity theorem, first applied to contact problems by R.T. Shield in 1967, in connection with the extremal principle for the contact force found by J.R. Barber in 1974 and Fabrikant’s approximation (1986) for the pressure distribution under a flat punch with arbitrary cross-section. The general solution is validated by comparison with the Hertzian solution for the contact of ellipsoids with small eccentricity and with numerical solutions for conical shapes with polygonal cross-sections. The solution provides the dependencies of the force on the indentation, the size and the shape of the contact area as well as the pressure distribution in the contact area. The approach is illustrated by linear (conical) and quadratic profiles with arbitrary cross-sections as well as for “separable” shapes, which can be represented as a product of a power-law function of the radius with an arbitrary exponent and an arbitrary function of the polar angle. A generalization of the Method of Dimensionality Reduction to non-axisymmetric profiles is formulated

Characterizing the mechanical behavior of single and polycrystalline silicon carbide using nanoindentation.

This research aims at enhancing the fundamental understanding of mechanisms controlling the deformation and fracture of silicon carbide based ceramics (single- and poly-crystal). The role of microstructure and material properties on the energy absorption capability of SiC is studied. This research helps to improve the ability to quantitatively predict the initiation and propagation of fracture and the interaction between fracture and plasticity, which provides a step towards a mechanistic understanding of deformation and failure properties of ceramic single crystals and polycrystals. The validity of the indentation-cracking method for toughness measurement is examined using nanoindentation tests with different indenters (spherical, pyramidal). Pyramidal indenters with various centerline to face angles are used to produce a wide range of effective strains in the single and polycrystalline SiC. Crystal plasticity constitutive laws can be calibrated using below threshold indentation loads. Above threshold loads are used to construct a parametric map that delineates the dependence of the ratio of crack size and contact radius on indenter geometry, applied load, toughness, and hardness, thus providing important guidelines for the toughness measurement method. By examining the behavior of several SiC materials during nanoindentation experiments using spherical and pyramidal indenters, it is possible to make predictions about methods to improve the ductility and fracture toughness of SiC to optimize its energy absorption. The applicability of the area under the irreversible part of the indentation load displacement curve (energy dissipated during loading) to predict the performance of SiC under contact loading is examined

Axisymmetry in Mechanical Engineering

The reprint is devoted to the phenomena associated with exact or approximate axial symmetry in different areas of technical physics and mechanical engineering science. How can the symmetry of the problem be used most efficiently for its analysis? Why is the symmetry broken or why is it still approximately retained? These and other questions are discussed based on systems from different fields of engineering

Small-scale polymer structures enabled by thiol-ene copolymer systems

The research described herein is aimed at exploring the thermo-mechanical properties of thiol-ene polymers in bulk form, investigating the ability of thiol-ene polymers to behave desirably as photolithographic media, and providing the first characterization of the mechanical properties of two-photon stereolithography-produced polymer structures. The thiol-ene polymerization reaction itself is well-characterized and described in the literature, but the thermomechanical properties of thiol-ene and thiol-ene/acrylate polymers still require more rigorous study. Understanding the behavior of thiol-ene networks is a crucial step towards their expanded use in bulk form, and particularly in specialized applications such as shape memory devices. Additionally, the thiol-ene polymerization reaction mechanism exhibits unique properties which make these polymers well suited to photolithography, overcoming the typical dichotomy of current materials which either exhibit excellent photolithographic behavior or have controllable properties. Finally, before two-photon stereolithography can create mechanisms and devices which can serve any mechanically functional role, the mechanical properties of the polymers they produce must be quantitatively characterized, which is complicated by the extremely small scale at which these structures are produced. As such, mechanical characterization to date has been strictly qualitative. Fourier transfer infrared spectroscopy revealed functional group conversion information and sol-fraction testing revealed the presence of unconverted monomer and impurities, while dynamic mechanical analysis and tensile testing revealed the thermomechanical responses of the systems. Nanoindentation was employed to characterize the mechanical properties of polymers produced by two-photon stereolithography. Optical and electron microscopy were exploited to provide quantitative and qualitative evaluations of thiol-ene/acrylate performance in small-scale polymerization regimes. The broad objective of the research was to explore thiol-ene polymer behavior both in bulk and at the small scale in an effort to supplement the material library currently used in these fields and to expand the design envelope available to researchers. The significance of the research is the advancement of a more complete and fundamental understanding of thiol-ene polymerization from kinetics to final properties, the quantitative establishment of the mechanical properties of materials created with two-photon stereolithography, and the comprehensive characterization of a supplementary class of photopatternable polymers with greater property tunability than is possible with currently used materials.Ph.D.Committee Chair: Gall, Ken; Committee Member: Graham, Samuel; Committee Member: Jacob, Karl; Committee Member: Perry, Joe; Committee Member: Pierron, Olivie

Micromechanics of magnesium and its alloys studied by nanoindentation

Mención Internacional en el título de doctorLa fabricación de vehículos ligeros constituye una estrategia prometedora en cuanto a la reducción del consumo de combustibles fósiles y las emisiones de gases de efecto invernadero. El magnesio es un material muy conveniente para tal fin debido a su excelente resistencia específica. Sin embargo, ciertos aspectos, tales como su baja ductilidad y alta anisotropía mecánica a temperatura ambiente, obstaculizan su uso general a nivel industrial. La aleación de magnesio con otros elementos químicos es una estrategia prometedora dado que este material reacciona fácilmente con otros compuestos formando precipitados y/o fases intermetálicas que afectan de una manera severa a la competición entre los diferentes mecanismos de deformación y microestructura, y por lo tanto, a sus propiedades mecánicas. Las estrategias tradicionales enfocadas al desarrollo de nuevas aleaciones de magnesio con propiedades mecánicas avanzadas se han basado en extensas, largas y costosas campañas experimentales para evaluar las propiedades de las nuevas aleaciones. Esta limitación podría ser resuelta aplicando Métodos Combinatorios en este proceso. Dicha metodología, aplicada inicialmente en la industria química y farmacéutica, permite producir y caracterizar un gran número de nuevos materiales en muy poco tiempo. Sin embargo, su implementación efectiva en procesos metalúrgicos requiere el desarrollo de diversas nuevas tecnologías. En concreto, se pueden destacar dos aspectos tecnológicos sin resolver: en primer lugar, un nuevo método que permita la caracterización de los diferentes mecanismos de deformación del magnesio y sus aleaciones de una forma rápida requiriendo poco material; y segundo, nuevos modelos matemáticos que sean capaces de reproducir el comportamiento mecánico real de estos materiales a nivel tanto micro- como macroscópico. En cuanto al primero, nanoindentación es una técnica muy prometedora ya que, además de ser fácil de usar y rápida, requiere cantidades de material muy reducidas. Respecto al segundo aspecto, los modelos de plasticidad cristalina cumplen con los requisitos dado que son capaces de capturar la deformación plástica por deslizamiento cristalográfico y maclado. La presente tesis doctoral constituye un elemento fundamental en cuanto a la superación de estas dos limitaciones. El principal objetivo de esta tesis doctoral ha sido el estudio de la competición de los diferentes mecanismos de deformación del magnesio y sus aleaciones bajo diferentes condiciones, combinando técnicas avanzadas de caracterización, como nanoindentación de monocristales, microscopía de fuerza atómica o microscopía de electrones retrodispersados, junto con avanzadas técnicas de simulación basadas en novedosos modelos de plasticidad cristalina. Se ha constatado que la dureza y la deformación residual y la microtextura alrededor de la indentación dependen de una manera notoria de un efecto combinado de la orientación del cristal indentado así como de la temperatura de ensayo. Dichas dependencias han sido explicadas satisfactoriamente desde un punto de vista tanto analítico como numérico debido a la activación de diferentes modos de deslizamiento y maclado en las áreas cercanas a la zona de ensayo. Se ha demostrado que, mientras que los principales mecanismos de deformación a temperatura ambiente son el deslizamiento basal y el maclado de extensión, la deformación plástica a alta temperatura es dominada por deslizamiento basal y prismático. Se mostrado que el incremento de actividad prismática con la temperatura es compensada con una reducción muy importante de la actividad de maclado de extensión. Además, se ha desarrollado un novedoso modelo de plasticidad cristalina que considera la micromecánica real del maclado de extensión. Además, se ha constatado que es fundamental tener en cuenta que la nucleación de una macla es un proceso que requiere estados tensionales mucho más severos que su propagación a la hora de reproducir la evolución de la actividad de dicho mecanismo de deformación con la temperatura. Además, se ha demostrado que el maclado de extensión es un mecanismo de deformación afectado severamente por efectos tamaño. Nuestros resultados experimentales evidencian que la activación de una macla requiere la concentración de altas tensiones en un determinado volumen. Finalmente, se ha desarrollado una nueva y práctica metodología para estimar la tensión crítica resuelta de aleaciones de magnesio de interés industrial. Esta metodología, que se basa en la variación de la dureza con la orientación cristalográfica del grano indentado, ha sido diseñada teniendo en cuenta estándares industriales de manera que pueda ser utilizada fácilmente por la comunidad industrial. La metodología propuesta, validada inicialmente para magnesio puro, ha sido utilizada para estudiar los mecanismos de deformación de una aleación de magnesio de tierras raras aleada con un 1% de manganeso y 1% de neodimio. Se ha demostrado que la adicción de tierras raras conlleva una importante reducción de la resistencia relativa de los sistemas de deslizamiento basales y no basales, lo que justifica la mayor isotropía mecánica mostrada por este material en comparación con aleaciones de magnesio convencionales.Weight reduction is a cost-effective approach to decrease the fossil fuel consumption and greenhouse gas emissions of the transport industry. Magnesium, the lightest structural metal, constitutes a significant alternative as weight-saving material. However, some issues hinder its widespread use in the industry, like its low ductility and high mechanical anisotropy at room temperature. Due to its high chemical activity, alloying is a promising strategy to overcome these limitations, as magnesium easily reacts with other compounds to form precipitates and/or intermetallic phases which heavily affect the competition between the different deformation modes and microstructure, and therefore, its physical properties. Traditional approaches to develop novel magnesium alloys with enhanced mechanical properties rely on vast and time-consuming experimental campaigns in order to assess the mechanical properties of the new alloys. This limitation could be solved with the application of Combinatorial Methods in this process. This new methodology, initially applied in the chemist and pharmaceutical industries, allows to produce and characterise a great number of new materials in a very sort time. However, the effective implementation of such approach requires the development of several new technologies. Among others, two main unresolved technological issues can be mentioned: first, a new approach to characterise the different deformation modes of magnesium and its alloys in an easy and fast way; and second, new material models that are able to reproduce the real mechanical behaviour of magnesium and its alloys at the macro- and micro-mechanical scale. Regarding the first one, nanoindentation seems to be a perfect candidate as, in addition to being easy and fast, requires small amount of material. Regarding the second one, crystal plasticity models meet perfectly the requirements as they are able to capture plastic deformation by crystallographic glide and mechanical twinning. The present Ph.D. thesis constitutes a milestone in order to overcome these two last limitations. The main objective of this research has been to study the competition between the different deformation modes in magnesium and its alloys under different testing conditions, combining advanced characterisation techniques, like single crystal nanoindentation, atomic force microscopy and electron backscatter diffraction, with novel crystal plasticity modelling approaches. It has been shown that the hardness and the residual deformation and microtexture around an indent highly depend on the combined effect of the orientation of the indented plane and testing temperature. Such dependencies have been successfully explained from an analytical and numerical point of view due to the activation of different slip and twin modes in different areas in the surroundings of the indent. It is demonstrated that, while the main deformation modes at room temperature are basal slip and tensile twinning, the plastic deformation at high temperature is dominated by basal and prismatic slip. It is shown that the increase of prismatic activity with temperature is compensated by a dramatic decrease of tensile twin activity as temperature increases. In addition, a novel crystal plasticity model which takes into account the micromechanics of tensile twinning has been developed. In is shown that, in order to properly reproduce the evolution of tensile twin activity with temperature, it is fundamental to take into account the fact that twin activation is a process which requires a much bigger stress than twin propagation. It has been also demonstrated that mechanical twinning is a process highly affected by size effects. Our results provides experimental evidences that twin activation requires the concentration of high stresses in a certain activation volume. Finally, a novel and practical methodology has been developed in order to estimate the critical resolved shear stresses of industrial magnesium alloys. This methodology, which is based on the variation of the hardness with the crystallographic orientation of the indented grain, is designed taking into account industrial standards so it can be easily applied by the alloy development community. First validated in pure magnesium, the proposed methodology is applied to study the deformation modes of a rare-earth magnesium alloy containing 1% of Manganese and 1% of Neodymium. It is shown that the addition of rare-earth elements lead to an important reduction between the relative strength of the basal and non-basal slip systems, which justifies the much more isotropic mechanical behaviour of this material in comparison with conventional magnesium alloys.Programa Oficial de Doctorado en Ciencia e Ingeniería de MaterialesPresidente: Elisa María Ruiz Navas.- Secretario: David Mercier.- Vocal: Erica Lilleodde

Nanoindentation testing of soft polymers : computation, experiments and parameters identification

Since nanoindentation technique is able to measure the mechanical properties of extremely thin layers and small volumes with high resolution, it also became one of the important testing techniques for thin polymer layers and coatings. This dissertation is focusing on the characterization of polymers using nanoindentation, which is dealt with numerical computation, experiments and parameters identification. An analysis procedure is developed with the FEM based inverse method to evaluate the hyperelasticity and time-dependent properties. This procedure is firstly verified with a parameters re-identification concept. An important issue in this dissertation is to take the error contributions in real nanoindentation experiments into account. Therefore, the effects of surface roughness, adhesion force, friction and the real shape of the tip are involved in the numerical model to minimize the systematic error between the experimental responses and the numerical predictions. The effects are quantified as functions or models with corresponding parameters to be identified. Finally, data from uniaxial or biaxial tensile tests and macroindentation tests are taken into account. The comparison of these different loading situations provides a validation of the proposed material model and a deep insight into nanoindentation of polymers.Da Nanoindentation die Messung der mechanischen Eigenschaften von dünnen Schichten und kleinen Volumen mit hoher Auflösung ermöglicht, hat sich diese Messmethode zu einer der wichtigsten Testmethoden für dünne Polymerschichten und -beschichtungen entwickelt. Diese Dissertation konzentriert sich auf die Charakterisierung von Polymeren mittels Nanoindentation, die in Form von numerischen Berechnungen, Experimenten und Parameteridentifikationen behandelt wird. Es wurde ein Auswertungsverfahren mit einer FEM basierten inversen Methode zur Berechnung der Hyperelastizität und der zeitabhängigen Eigenschaften entwickelt. Dieses Verfahren wird zunächst mit einem Konzept der Parameter Re-Identifikation verifiziert. Fehlerquellen wie Oberflächenrauheit, Adhäsionskräfte, Reibung und die tatsächlichen Form der Indenterspitze werden in das numerische Modell eingebunden, um die Abweichungen der numerischen Vorhersagen von den experimentellen Ergebnissen zu minimieren. Diese Einflüsse werden als Funktionen oder Modelle mit dazugehörigen, zu identifizierenden Parametern, quantifiziert. Abschließend werden Messwerte aus uni- oder biaxialen Zugversuchen und Makroindentationsversuchen betrachtet. Der Vergleich dieser verschiedenen Belastungszustände liefert eine Bestätigung des vorgeschlagenen Materialmodells und verschafft einen tieferen Einblick in die bei der Nanoindentation von Polymeren ablaufenden Mechanismen

Molecular dynamics modelling of nanoindentation

This thesis presents an atomic-scale study of nanoindentation, with carbon materials and both bcc and fcc metals as test specimens. Classical molecular dynamics (MD) simulations using Newtonian mechanics and many-body potentials, are employed to investigate the elastic-plastic deformation behaviour of the work materials during nanometresized indentations. In a preliminary model, the indenter is represented solely by a non-deformable interface with pyramidal and axisymmetric geometries. An atomistic description of a blunted 90° pyramidal indenter is also used to study deformation of the tip, adhesive tip-substrate interactions and atom transfer, together with damage after adhesive rupture and mechanisms of tip-induced structural transformations and surface nanotopograpghy. To alleviate finite-size effects and to facilitate the simulation of over one million atoms, a parallel MD code using the MPI paradigm has also been developed to run on multiple processor machines. The work materials show a diverse range of deformation behaviour, ranging from purely elastic deformation with graphite, to appreciable plastic deformation with metals. Some qualitative comparisons are made to experiment, but available computer power constrains feasible indentation depths to an order of magnitude smaller than experiment, and over indentation times several orders of magnitude smaller. The simulations give a good description of nanoindentation and support many of the experimental features

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost

Mechanical behavior of ultrastructural biocomposites

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (leaves 154-163).For numerous centuries nature has successfully developed biocomposite materials with detailed multiscale architectures to provide a material stiffness, strength and toughness. One such example is nacre, which is found in the shells of many mollusks, and consists of an inorganic phase of aragonite tablets 5-8jim in planar dimension and 0.5-1gm in thickness direction and an organic phase of biomacromolecules. High resolution microscopy imaging was employed to investigate the microscale features of seashell nacre to reveal the nucleation points within tablets, the sector boundaries and an overlap between tablets of neighboring layers of [approx.] 20 %. Aragonite, the mineral constituting the inorganic phase of nacre, is a calcium carbonate mineral that is ubiquitous in many natural systems, including both living organisms and geological structures. Resistance to yield is an important factor in the ability of aragonite to provide both strength and toughness to numerous biological materials. Conversely, plastic deformation of aragonite is a governing factor in the formation and flow of large scale geological structures. The technique of nanoindentation combined with in-situ tapping mode atomic force microscopy imaging was used to show the anisotropic nanoscale plastic behavior of single crystal aragonite for indentations into three mutually orthogonal planes.(cont.) Force vs. indentation depth curves for nanoindentation coaxial to the orthorhombic crystal c-axis exhibited distinct load plateaus, ranging between 275-375gN for the Berkovich indenter and 400-500 [mu]N for the cono-spherical indenter, indicative of dislocation nucleation events. Atomic force microscopy imaging of residual impressions made by a cono-spherical indenter showed four pileup lobes; residual impressions made by the Berkovich indenter showed protruding slip bands in pileups occurring adjacent to only one or two of the Berkovich indenter planes. Anisotropic elastic simulations were used to capture the low load response of single crystal aragonite, with the elastic simulations for the (001) plane matching the experimental data up until the onset of plasticity. Numerical simulations based on a crystal plasticity model were used to interrogate and identify the kinematic mechanisms of plastic slip leading to the experimentally observed plastic anisotropy. In particular, in addition to the previously reported slip systems of the {100} family, the family of {110} slip systems is found to play a key role in the plastic response of aragonite.by Cathal Kearney.S.M

Assessment of thermally activated dislocation mechanisms via novel indentation approaches

The efficiency of gas turbines and jet engines used for energy generation and transportation can be increased by raising their combustion temperature. However, this is often limited by the materials used. For the development of new high-temperature materials, knowledge of the local mechanical properties of, for instance, individual phases in Ni-based superalloys is therefore of great importance. These properties are largely unknown, as they are not accessible with conventional macroscopic test methods. In the present work, the depth-sensing indentation testing technique was applied to assess the thermally activated deformation mechanisms on a local scale. For this purpose, a new in-situ indentation device was developed, which for the first time allows dynamic indentation experiments to be carried out on a small scale at temperatures of up to 1100 °C. Furthermore, a new indentation creep loading protocol was developed using a constant contact pressure approach similar to conventional uniaxial creep experiments. For indentation testing at high temperatures, a new step load method has been presented that allows a significant reduction of the contact time, thus minimizing the wear of the indenter tips. The method is suitable for the investigation of transients in material behavior at high to medium strain rates. In addition, a new approach for determining the brittle-ductile-transition temperature of body centered cubic metals was presented. In this approach, the change in the temperature-dependent activation volume was used to determine an intersection temperature that agrees well with the brittle-to-ductile-transition temperature from conventional Charpy pendulum impact tests