Doctor of Philosophy / Department of Industrial & Manufacturing Systems Engineering / Zhijian Pei / Poor machinability of hard-to-machine materials (such as advanced ceramics and titanium) limits their applications in industries. Ultrasonic-vibration-assisted grinding (UVAG), a hybrid machining process combining material-removal mechanisms of diamond grinding and ultrasonic machining, is one cost-effective machining method for these materials. Compared to ultrasonic machining, UVAG has much higher material removal rate while maintaining lower cutting pressure and torque, reduced edge chipping and surface damage, improved accuracy, and lower tool wear rate. However, physics-based models to predict cutting force in UVAG have not been reported to date. Furthermore, edge chipping is one of the technical challenges in UVAG of brittle materials. There is no report related to effects of cutting tool design on edge chipping in UVAG of brittle materials. The goal of this research is to provide new knowledge of machining these hard-to-machine materials with UVAG for further improvements in machining cost and surface quality. First, a thorough literature review is given to show what has been done in this field. Then, a physics-based predictive cutting force model and a mechanistic cutting force model are developed for UVAG of ductile and brittle materials, respectively. Effects of input variables (diamond grain number, diamond grain diameter, vibration amplitude, vibration frequency, spindle speed, and federate) on cutting force are studied based on the developed models. Interaction effects of input variables on cutting force are also studied. In addition, an FEA model is developed to study effects of cutting tool design and input variables on edge chipping. Furthermore, some trends predicted from the developed models are verified through experiments. The results in this dissertation could provide guidance for choosing reasonable process variables and designing diamond tools for UVAG.

Contact fatigue damages resulting either from static or dynamic contact are of interest for understanding the failure modes and mechanisms leading to improvement of the components’ performances in tribological applications. The objective of this research was to ascertain how and to what extent the counterface materials, loading conditions, contact configuration, lubrication, and the environment affect the failure behaviours of material under static and dynamic contact fatigue loading. An experimental ball-on-flat test configuration was employed for both static and dynamic contact fatigue testing. In house designed test rig was used to study static cyclic loading contact fatigue behaviours of brittle polymethylmethacrylate (PMMA) in contact with balls made of different materials, i.e. Si3N4, steel, aluminium, bronze and PMMA in dry and oil-lubricated conditions. A modified four ball test machine was used to study dynamic rolling contact fatigue behaviours of thermally sprayed molybdenum and titanium coatings in contact with steel balls in dry and seawater conditions. The static contact fatigue and the dynamic contact fatigue test results revealed that counterface material, loading magnitude, lubricant and the environment play a vital role in controlling failure modes and the extent of damage. In static contact fatigue, adhesive strength of the interface was the key factor controlling damage of the PMMA plate in both dry and oil-lubricated conditions. In dry conditions, three failure modes, i.e. adhesive wear, ring cracks, and radial cracks controlled the damage of PMMA to a different degree for each combination of materials. Whereas, the damage of each combination in oil-lubricated conditions was affected by the extent of three failure modes, i.e. adhesive wear, radial cracks and abrasive wear. In dynamic contact fatigue tests, adhesive wear and inter-lamellar cracking were the major failure modes controlling damage of molybdenum coating and titanium coating in dry contact conditions while abrasive wear, corrosion and lubrication controlled damage processes in seawater conditions.

Titanium alloys are highly resistant to all types of corrosion due to their excellent ability to form an oxide film on the surface. However, under certain circumstances, these alloys may experience an environmental degradation which could potentially, under the application of mechanical stress, lead to a complete failure of the material. One of these cracking processes is stress-corrosion cracking (SCC). SCC has an embrittling effect on otherwise ductile materials under tensile stress. Since titanium alloys are frequently used in the aerospace industry and it is therefore of interest to test these alloys in different environment in order to prevent any future accidents. SCC testing is frequently tested at GKN Aerospace and a new testing method is of interest. The main objective with this work was to gain knowledge of the testing method. Bent-beam testing method has been used to investigate stress-corrosion cracking (SCC) of titanium alloys in a laboratory based experiment. The bent-beam testing method was of type 2-point bent beam test, where a saline solution was applied at the apex of the specimen. The specimens were loaded to a range of stresses from 40%, to 95% of the materials yield strength and the salt concentration in the saline solution was 1wt% and 3wt%. By doing so, a relative susceptibility of the different alloys could be established. Three different titanium alloys were tested: Ti-6Al-4V, Ti-8Al-1Mo-1V, and Ti-6Al-2Sn-4Zr-2Mo. The testing method was able to cause cracking on all titanium alloys, where Ti-6Al-4V was found to be the least susceptible to SCC. Ti-8Al-1Mo-1V, and Ti-6Al-2Sn-4Zr-2Mo showed an overall high susceptibility to SCC as cracking occurred in all testing configurations. Cracking was observed on both the surface of the specimen as well as in the cross sections, where the cracks grew perpendicular to the surface. SEM was also used to evaluate the crack propagation in Ti-8Al-1Mo-1V, and Ti-6Al-2Sn-4Zr-2Mo, and it was found that the cracks grew mostly along the grain boundaries.

Este trabalho apresenta o estudo da Retificação de Ultraprecisão de ligas de carbeto de tungstênio-cobalto (WC-Co) com diferentes microestruturas. A motivação para este estudo foi o grande potencial desta liga para a fabricação de componentes que requerem materiais de alta dureza e resistência à fratura. Devido à combinação dessas características, esses materiais vêm sendo usados na fabricação de moldes para injeção de lentes ópticas de dispositivos eletrônicos e ópticos. Assim, amostras de carbeto de tungstênio-cobalto foram submetidas a vários testes para determinação da correlação entre os parâmetros de corte e parâmetros estruturais (tamanho de grão e teor de cobalto) com o regime de remoção de material. As amostras foram polidas e posteriormente microendentadas com cargas variadas para pré-avaliar a ocorrência de formação de microtrincas. Testes de usinagem foram conduzidos em uma retificadora de ultraprecisão, usando rebolos de diamante e posteriormente a rugosidade e os danos da superfície (microtrincas e crateras) foram avaliados. Para melhor entendimento da influência dos parâmetros estruturais e dos parâmetros de corte sobre os resultados de rugosidade foi realizado um teste ANOVA. As forças de usinagem foram medidas durante os ensaios usando um microdinamômetro piezelétrico com objetivo de estimar a temperatura na zona de retificação. Os resultados obtidos indicam que tanto os parâmetros estruturais como os parâmetros de corte influenciam na rugosidade, microdureza e temperatura na zona de retificação das ligas de carbeto de tungstênio-cobalto. Amostras com maior tamanho de grãos apresentam as menores rugosidades e altas temperaturas na zona de retificação. A velocidade de avanço (Vf) mostrou-se mais influente que a profundidade de corte (ap). Menores velocidades de avanço aumentam a temperatura na zona de retificação e a microdureza na camada superficial. Entretanto, verificou-se que as maiores temperaturas obtidas nos ensaios não foram suficientes para promover alteração metalúrgica no material. Algumas condições de corte combinadas com parâmetros estruturais levam a remoção de material em regime dúctil, resultando em superfícies com qualidade óptica. A porcentagem de cobalto e a velocidade de avanço (Vf) têm forte influência na alteração da microdureza da camada superficial das amostras retificadas. A diminuição da velocidade de avanço tende a aumentar a microdureza na camada. Há aumento de microdureza de até 200 kgf/mm2, sugerindo a ocorrência de encruamento por tensões compressivas. Com base nestes resultados, acredita-se que a retificação de ultraprecisão apresenta-se como uma opção viável para a manufatura de componentes de carbeto de tungstênio com acabamento submicrométrico, possibilitando a eliminação dos processos tradicionais de manufatura óptica, tais como a lapidação e o polimento. / The ultraprecision grinding of different tungsten carbide-cobalt microstructures (WC-Co) were investigated. The motivation for this study is the materials high hardness and potential application for micromolds. These materials have been used as optical inserts in glass injection molding processes for optical and electric devices, due to their excellent combination of high hardness, ductility and fracture toughness. Tungsten carbide samples were subjected to tests to determine the correlation between cutting parameters and microstructures to achieve the ductile regime of material removal. Polished surfaces of carbide samples were indented using varying loads to evaluate the microcracks formation. The machining tests were conducted using an ultraprecision grinding and A V-shaped metal-bond was used. Surface roughness was investigated as functions of the grinding conditions by means Analysis of Variance (ANOVA). The tangential force was measured using a piezoelectric dynamometer to estimate the grinding zone temperature. The results indicate that structural parameters (grain size and cobalt content) and cutting parameters have a significant influence on surface roughness, micro-hardness and grinding zone temperature for tungsten carbide-cobalt alloys.Tungsten carbide-cobalt samples with the larger grain size presented lower surface finish results and high grinding temperatures. The feed rate (Vf) showed greater influence that the in-feed (ap). The grinding zone temperature and the hardness are increased when speed rate is reduced. However, it was found that the highest temperature achieved did not reach a critical temperature for phase transformation. Some cutting parameters combined with structural parameters lead to ductile mode grinding mechanism, and as consequence, high optical quality surfaces are obtained. The micro-hardness of layer is extremely influenced by cobalt content and speed rate. Lower feed rate tends to increase the micro-hardness up to 200 kgf/mm2, suggesting that the compressive stress occurs. Considering the results presented it is believed that the Ultraprecision grinding showed to be a viable option for the fabrication of components made of tungsten carbide-cobalt with nanometer surface finish possibly eliminating traditional optical manufacturing processes such as lapping and polishing.

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.

Este trabalho apresenta o estudo da Retificação de Ultraprecisão de ligas de carbeto de tungstênio-cobalto (WC-Co) com diferentes microestruturas. A motivação para este estudo foi o grande potencial desta liga para a fabricação de componentes que requerem materiais de alta dureza e resistência à fratura. Devido à combinação dessas características, esses materiais vêm sendo usados na fabricação de moldes para injeção de lentes ópticas de dispositivos eletrônicos e ópticos. Assim, amostras de carbeto de tungstênio-cobalto foram submetidas a vários testes para determinação da correlação entre os parâmetros de corte e parâmetros estruturais (tamanho de grão e teor de cobalto) com o regime de remoção de material. As amostras foram polidas e posteriormente microendentadas com cargas variadas para pré-avaliar a ocorrência de formação de microtrincas. Testes de usinagem foram conduzidos em uma retificadora de ultraprecisão, usando rebolos de diamante e posteriormente a rugosidade e os danos da superfície (microtrincas e crateras) foram avaliados. Para melhor entendimento da influência dos parâmetros estruturais e dos parâmetros de corte sobre os resultados de rugosidade foi realizado um teste ANOVA. As forças de usinagem foram medidas durante os ensaios usando um microdinamômetro piezelétrico com objetivo de estimar a temperatura na zona de retificação. Os resultados obtidos indicam que tanto os parâmetros estruturais como os parâmetros de corte influenciam na rugosidade, microdureza e temperatura na zona de retificação das ligas de carbeto de tungstênio-cobalto. Amostras com maior tamanho de grãos apresentam as menores rugosidades e altas temperaturas na zona de retificação. A velocidade de avanço (Vf) mostrou-se mais influente que a profundidade de corte (ap). Menores velocidades de avanço aumentam a temperatura na zona de retificação e a microdureza na camada superficial. Entretanto, verificou-se que as maiores temperaturas obtidas nos ensaios não foram suficientes para promover alteração metalúrgica no material. Algumas condições de corte combinadas com parâmetros estruturais levam a remoção de material em regime dúctil, resultando em superfícies com qualidade óptica. A porcentagem de cobalto e a velocidade de avanço (Vf) têm forte influência na alteração da microdureza da camada superficial das amostras retificadas. A diminuição da velocidade de avanço tende a aumentar a microdureza na camada. Há aumento de microdureza de até 200 kgf/mm2, sugerindo a ocorrência de encruamento por tensões compressivas. Com base nestes resultados, acredita-se que a retificação de ultraprecisão apresenta-se como uma opção viável para a manufatura de componentes de carbeto de tungstênio com acabamento submicrométrico, possibilitando a eliminação dos processos tradicionais de manufatura óptica, tais como a lapidação e o polimento. / The ultraprecision grinding of different tungsten carbide-cobalt microstructures (WC-Co) were investigated. The motivation for this study is the materials high hardness and potential application for micromolds. These materials have been used as optical inserts in glass injection molding processes for optical and electric devices, due to their excellent combination of high hardness, ductility and fracture toughness. Tungsten carbide samples were subjected to tests to determine the correlation between cutting parameters and microstructures to achieve the ductile regime of material removal. Polished surfaces of carbide samples were indented using varying loads to evaluate the microcracks formation. The machining tests were conducted using an ultraprecision grinding and A V-shaped metal-bond was used. Surface roughness was investigated as functions of the grinding conditions by means Analysis of Variance (ANOVA). The tangential force was measured using a piezoelectric dynamometer to estimate the grinding zone temperature. The results indicate that structural parameters (grain size and cobalt content) and cutting parameters have a significant influence on surface roughness, micro-hardness and grinding zone temperature for tungsten carbide-cobalt alloys.Tungsten carbide-cobalt samples with the larger grain size presented lower surface finish results and high grinding temperatures. The feed rate (Vf) showed greater influence that the in-feed (ap). The grinding zone temperature and the hardness are increased when speed rate is reduced. However, it was found that the highest temperature achieved did not reach a critical temperature for phase transformation. Some cutting parameters combined with structural parameters lead to ductile mode grinding mechanism, and as consequence, high optical quality surfaces are obtained. The micro-hardness of layer is extremely influenced by cobalt content and speed rate. Lower feed rate tends to increase the micro-hardness up to 200 kgf/mm2, suggesting that the compressive stress occurs. Considering the results presented it is believed that the Ultraprecision grinding showed to be a viable option for the fabrication of components made of tungsten carbide-cobalt with nanometer surface finish possibly eliminating traditional optical manufacturing processes such as lapping and polishing.

No trabalho estuda-se o crescimento de trincas em carga monotônica e cíclica nos casos de materiais quase-frágeis, introduzindo uma lei de dano cíclico. Revisam-se conceitos sobre modelos coesivos, leis de carga-descarga, leis de evolução de dano e efeito de escala. É seguido o modelo coesivo irreversível proposto por Wang e Siegmund (2006). Em particular se dá ênfase aos efeitos de escala não estatísticos. O modelo de zona coesiva irreversível apresenta uma formulação de dano e considera carregamento em fadiga. Quando o tamanho estrutural é reduzido (ou as trinca se extendem), a fratura por fadiga não mais ocorre por propagação de trinca, mas sim por uma decoesão uniforme. O objetivo desde trabalho é implementar este modelo e verificar sua potencialidade na captura de efeitos de escala, comparando com experimentos e dados disponíveis na literatura. / At present work is intended to study crack growth in cyclic and monotonic loading in the case of quasi-brittle materials, introducing a damage mechanism, is reviewed concepts of cohesive models, loading-unloading laws, damage evolution laws and effect of scale. The irreversible cohesive zone model proposed by Wang e Siegmund (2006) is followed. In particular emphasizes in the not statistical size effects. The irreversible cohesive zone model, presents a damage formulation and considers fatigue loading. It is demonstrated in this study that, when the structure size is reduced (or extend cracks), the fatigue fracture no longer occurs by crack propagation, then occurs by uniform decohesion . The objetive of this work is implementing this model and verify its capability to capture the scale effect compared with experiments and data available in literature.

Este trabalho tem como objetivo discutir a evolução tectônica meso-cenozóica do Domo de Lages, SC, envolvendo análise das estruturas rúpteis que afetam as rochas da região, análise morfométrica e da rede de drenagem e aspectos geomorfológicos relevantes. O Domo de Lages, localizado na borda leste da Bacia do Paraná, na porção sul do estado de Santa Catarina, é caracterizado pela ocorrência de uma grande variedade de rochas alcalinas de idade neo-cretácea. Estas rochas afloram na forma de sills e diques e são intrusivas no pacote sedimentar da Bacia do Paraná, causando-lhe um soerguimento da ordem de centenas a milhares de metros. As rochas alcalinas foram afetadas por estruturas rúpteis, particularmente falhas transcorrentes e normais, denotando a presença de uma tectônica ativa durante o cenozóico. Para o entendimento do quadro evolutivo do domo, além da análise estrutural, foram elaborados diversos mapas morfométricos (hipsométrico, declividades, orientação de vertentes, superfícies de base, rugosidade, gradiente hidráulico e densidade de lineamentos e drenagens) derivados diretamente do Modelo Digital de Elevação, que por sua vez foi obtido pelo tratamento de dados SRTM (Shuttle Radar Topographic Mission) da Agência Espacial Americana (NASA). O trabalho foi complementado com a análise da rede de drenagem e de lineamentos extraídos de imagens, juntamente com a elaboração de perfis topográficos. Os resultados mostram tratar-se de uma estrutura dômica alongada com eixo maior orientado na direção NW-SE, marcada pelo alinhamento de intrusões alcalinas e basculamento dos acamamentos das rochas sedimentares que apresentam mergulho radial para fora da estrutura. A análise do relevo revelou a existência de uma superfície de aplainamento, hoje preservada na cota de 1200 m, que teria sido afetada por falhas normais de direções NW-SE e NE-SW. O modelo tectônico evolutivo elaborado para a região contempla a seguinte seqüência de eventos: atuação de esforços compressivos NE-SW no final do cretáceo, gerando falhas normais NE-SW, que afetam as rochas básicas da Formação Serra Geral e condicionam a colocação de diques alcalinos e a estruturação do domo; geração de falhas transcorrentes destrais que afetam todas as rochas da região, incluindo as rochas alcalinas, com binário orientado na direção NNE-SSW; configuração de uma superfície de aplainamento preservada na cota de 1200m, que perdurou, provavelmente, até o mioceno; distensão NE-SW e geração de falhas normais NW-SE que abatem e basculam a superfície aplainada e reorganizam a rede de drenagens; instalação de um provável evento distensivo NW-SE, responsável pela formação de falhas normais NE-SW, marcadas principalmente nos mapas morfométricos. / This study was focused on the meso-cenozoic tectonic evolution of the Domo de Lages region (south Santa Catarina State, Southern Brazil), through the analysis of brittle structures affecting sedimentary and igneous rocks, morphometric parameters, drainage network and main geomorphological features. Located in the border of the Paraná sedimentary basin, the Domo de Lages is characterized by a great variety of Late Cretacic alkaline rocks, which crops out as sills and dikes cutting the Paleozoic sedimentary rocks, and are associated with an uplift of hundreds to thousands of meters. These alkaline rocks are affected by brittle structures, mainly transcurrent and normal faults, indicative of Cenozoic active tectonics. In addition to the structural analysis, several morphometric maps were developed, as an aid to enlighten the evolutionary history of the region. Maps of hypsometry, slope, aspect, isobase surfaces, surface roughness, hydraulic gradient, lineament density and drainage density were derived from SRTM (Shuttle Radar Topographic Mission) Digital Elevation Models provided by NASA, and were complemented by topographic profiles, analysis of drainage network and lineament orientation. Results show that the dome has a elongated shape with major axis oriented NW-SE, defined by alignment of intrusive bodies and tilting of sedimentary rocks bedding planes, dipping radially outwards the center of the structure. Topographic analysis revealed the existence of a planation surface, preserved at 1200m a.s.l., wich would have been affected by NW-SE and NE-SW normal faults. A tectonic evolutionary model for the region was elaborated, according the following sequence of events: in the end of Cretaceous, a compressive NE stress generates NE-SW normal faults, which affect the basic rocks of Serra Geral Formation and controls the emplacement of alkaline dikes and the uplift of the domic structure; formation of transcurrent dextral faults affecting all rocks of the area, including the alkalines, with NNE-SSW oriented binary; development of a planation surface preserved at 1200m a.s.l. which remained probably until the Miocene; NE-SW extension, creating NW-SE normal faults that lowered and tilted the levelled surface and affected the drainage network; a last extensive NW-SE event probably happened, responsible for NE-SW normal faults seen mainly in the morphometric maps.

Lithium ion batteries (LIBs) have gained increasing popularity due to their high potential, low self-discharge, zero priming and minimal memory effect. However, the emergence of electrical vehicles and hybrid electrical vehicles in the automobile industry, where LIBs are predominantly in use, instilled a need to improve LIB batteries by experimenting with new materials. Graphite, the commonly used anode material for LIBs suffers from low theoretical capacity (372 mA h g-1) and torpid rate performance. Germanium (Ge) seems to be a promising substitute of carbon due to its high theoretical capacity, high Li+ diffusivity and electrical conductivity. However, Ge undergoes large volumetric change (±370%). This causes deboning of the thin film Ge electrode from the substrate current collector, causing a rapid decrease in the electrolytic performance. The process of ion beam mixing claims to have overcome this problem. In our current study, the adhesion strength of Ge thin film over Nickel (Ni) substrate (with and without ion beam mixing) is being measured using nanoindentation and the superlayer indentation test. Nanoindentation is one of the popular techniques to measure the mechanical properties and adhesion of thin film coatings. In this technique, a very small indenter of a desired geometry indents the film/substrate pair and the work of adhesion is calculated by knowing the plastic depth of indentation and the radius of indentation. Superlayer indentation is analogous to normal indentation but with a highly stressed superlayer on top to restrict the out-of-plane displacements, it reduces the plastic pile up around the indenter tip. The results from our study strongly suggest the possibility of dramatically increasing the adhesion strength by ion bombardment, which can be achieved by atomic level intermixing of the film/substrate pair. These, in turn, suggest that Ge could be an effective successor to graphite in the near future.

The classical theory of linear elastic fracture mechanics for a quasi-static crack in an infinite linear elastic body has two significant mathematical inconsistencies: it predicts unbounded crack-tip stresses and an elliptical crack opening profile. A new theory of fracture developed by Sendova and Walton, based on extending continuum mechanics to the nanoscale, corrects these erroneous effects. The fundamental attribute of this theory is the use of a dividing surface to describe the material interface. The dividing surface is endowed with an excess property, namely surface tension, which accounts for atomistic effects in the interfacial region. When the surface tension is taken to be a constant, Sendova and Walton show that the theory reduces the crack-tip stress from a square root to a logarithmic singularity and yields a finite angle opening profile. In addition, they show that if the surface tension depends on curvature, the theory completely removes the stress singularity at the crack-tip, for all but countably many values of the two surface tension parameters, and yields a cusp-like opening profile. In this work, we develop a numerical model using the finite element method for the Sendova-Walton fracture theory applied to the classical Griffith crack problem in the case of constant surface tension. We show that the numerical model behaves as predicted by the theory, yielding a reduced crack-tip singularity and a finite opening angle for all nonzero values of the constant surface tension. We also lay the groundwork for the numerical implementation of the curvature-dependent model by constructing an algorithm to determine the appropriate threshold values for the surface tension parameters that guarantee bounded crack-tip stresses. These values can then be directly applied to the forthcoming numerical model.