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Analytic methods of elastic wave scattering in fiber-reinforced composite materials are investigated in this study to calculate the effective static stiffness (axial shear modulus, m) and wave properties (axially shear wave speed, B and attenuation, Y) in composites. For simplicity only out-of-plane shear waves are modeled propagating in a plane transverse to the fiber axis. Statistical averaging of a spatially random distribution of fibers is performed and a simultaneous system of linear equations are obtained from which the effective global wave numbers are numerically calculated. The wave numbers, K=Re(K)+iIm(K), are complex numbers where the real parts are used to compute the effective axial shear static stiffness and wave speed; the imaginary parts are used to compute the effective axial shear wave attenuation in composites. Three major parts of this study are presented. The first part is the discussion of multiple scattering phenomena in a successive-events scattering approach. The successive-events scattering approach is proven to be mathematically exact by comparing the results obtained by the many-bodies-single-event approach. Scattering cross-section is computed and comparison of the first five scattering orders is made. Furthermore, the ubiquitous quasi-crystalline approximation theorem is given a justifiable foundation in the fiber-matrix composite context. The second part is to calculate m, B and Y for fiber-reinforced composites with interfacial layers between fibers and matrix. The material properties of the layers are assumed to be either linearly or exponentially distributed between the fibers and matrix. A concise formula is obtained where parameters can be computed using a computationally easy-to-program determinant of a square matrix. The numerical computations show, among other things, that the smoother (more divisional layers), or thinner, the interfacial region the less damped are the composite materials. Additionally composites with exponential order distribution of the interfacial region are more damped than the linear distribution ones. The third part is to calculate m, B and Y for fiber-reinforced composites with interfacial cracks. The procedures and computational techniques are similar to those in the second part except that the singularity near the crack tip needs the Chebychev function as a series expansion to be adopted in the computation. Both the interfacial layers and interfacial crack cases are analyzed in the low frequency range. The analytic results show that waves in both cases are attenuated and non-dispersive in the low frequency range. The composites with interfacial layers are transversely isotropic, while composites with interfacial cracks are generally transversely anisotropic. / Ph. D.

Design based on damage tolerance concepts has become mandatory in high technology structures. These concepts are also essential for evaluating life extension of aged structures which are in service beyond originally stipulated life. Fracture analysis of such structures in the presence of single or multiple three-dimensional flaws is essential for this approach. Surface cracks are the most commonly occurring flaws and development of accurate methods of analysis for such cracks is essential for structural integrity evaluation of newly designed or aged structures. The crack fronts of these surface flaws are usually approximated mathematically to be of either part-elliptical or part-circular in geometry. In this thesis, some of the issues related to fatigue crack growth of single and multiple surface cracks are studied in detail. Here emphasis is given to the development of simple and accurate post-processing techniques to estimate stress intensity factors for surface cracks, development and/or implementation of simple numerical methods to simulate three-dimensional single and multiple cracks in fatigue and their experimental verification. Modified virtual crack closure integral (MVCCI) technique for estimation of strain energy release rates has been improved (chapter II) to deal with curved crack front and unequal elements across the crack front. The accuracy of this method is evaluated and presented in this chapter for certain benchmark surface flaw problems. The improved MVCCI is used in the investigation of interaction between multiple surface cracks in three-dimensional solids. The interaction effects are studied for both interacting and coalescing phases as observed to occur in the growth of multiple surface cracks. Extensive numerical work is performed to study the effects of various parameters such as aspect ratio, thickness ratio, interspacing on the interaction factors. These solutions are used in formulating empirical equations to estimate interaction factors. This facilitated the development of a simple semi-analytical method to study fatigue crack growth of multiple cracks. The growth of surface cracks under fatigue loading in the finite width specimens of an aero-engine superalloy has been studied experimentally (presented in chapter III). Four configurations for single semi-elliptical cracks are considered. Fatigue crack growth is simulated by two models viz. two degrees of freedom and "multi degrees of freedom with ellipse fit'. These models are sometimes referred to as semi-analytical models as the crack growth is predicted by numerical integration combining Paris equation with an empirical form of stress intensity factor solution. In order to use two degrees of freedom model for fatigue crack growth prediction of semi-elliptical cracks, empirical solution for the Ml range of geometric parameters for stress intensity factor is required for the considered configurations. The available Newman-Raju solution is useful for this purpose within a limited range of surface crack length to width (c/W) of the specimen. Based on the present finite element results, the empirical equations are developed for extended values of c/W. It is well understood that the fatigue prediction for two-dimensional crack can be improved by inclusion of crack closure effects. Usually, in semi-analytical models for growth of surface cracks under fatigue loading, the crack closure is included as a ratio of crack closure factor at surface and depth locations of semi-elliptical crack. In the present work, this ratio for the considered material of specimens is obtained by an experimental study. The difference in characteristics of preferred propagation path between semi-elliptical crack in a finite width plate and a wide plate is clearly brought out. Current crack growth predictions for most of the structures are based on the presence of only a single crack. However, in structures several cracks may initiate simultaneously within a stress critical zone and may interact depending upon their geometry, spatial location, structure geometry and mode of loading. In this work various configurations of twin semi-elliptical cracks have been studied by experiments. The beachmarks created on the specimens during experiments are used in the investigation of crack shape progression during fatigue. A three degrees of freedom crack growth model for interacting and coalescing cracks has been proposed. The experimentally determined crack shape and lives have been compared with the corresponding values from numerical simulation. The correlation of experimental results with numerical predictions was carried out through improved MVCCI for eight-noded brick elements. This has worked well in the configurations analysed. However, it is known in literature that there are benefits of using 20-noded singular elements. There could be special situations where the regular elements could fail, and singular elements could be essential. For this purpose, further development of MVCCI were carried out using 20-noded quarter-point elements (presented in chapter IV). Also a novel technique of decomposed crack closure integral (DCCI) was developed (presented in chapter V) for both regular and singular elements to represent the variation of MVCCI more accurately along the crack front. It is well known that quarter-point elements at crack front produce the required singularity at the crack tip and give accurate stress distribution with fewer degrees of freedom than conventional elements. Thus to develop more efficient post-processing tools, the MVCCI expressions are formulated for 20-noded singular quarter-point element for various assumptions regarding stress and displacement distributions in the elements across the crack front. A comprehensive study is presented (chapter IV) on MVCCI for 20-noded singular brick element including various simplified expressions for three-dimensional part-through cracks in pure and mixed-mode state of deformation of fracture. The developed MVCCI expressions are also valid for 15-noded quarter-point Penta elements. The reduction in model size can further be obtained if 12-noded three-dimensional singular element is employed at the crack front and eight-noded elements are used away from the crack front. The MVCCI expressions are also developed for 12-noded singular element and their accuracy is evaluated by numerical solutions. Presently, MVCCI, estimates the average stress intensity factor at the center of each element along the crack front. In this thesis, a Decomposed Crack Closure Integral (DCCI) is formulated to represent an assumed variation of stress intensity factor along the crack front in each element. The DCCI is formulated for 8-noded brick, 20-noded conventional brick and 20-noded singular brick elements. The numerical examples presented here deal with three-dimensional problems of patch repair technology and part-through cracks. The technique showed a major advantage for the patch repair problems where SIF variations along the crack front are of significance and large mesh sizes are computationally expensive. This along with MVCCI for 12-noded and 20-noded singular elements formed a part of the work on development of accurate and effective post-processing tools. It is expected that the present work will be helpful in damage tolerance design and assessment of aerospace structures and the experimental work performed as a part of this thesis will enhance confidence in the damage tolerance analysis. The thesis is concluded in chapter VI presenting the contributions of this thesis and projecting future lines of work possible in this area.

[pt] O projeto mecânico de componentes estruturais para vidas longas à fadiga requer limites de fadiga confiáveis. Porém, a previsão do limite de fadiga ainda apresenta alguns desafios, especialmente por causa dos inevitáveis entalhes e pela presença de pequenos defeitos intrínsecos do material que podem ser considerados como microtrincas. Os entalhes atuam como concentradores de tensão e microtrincas podem ser geradas na ponta destes. Tais microtrincas (geradas ou intrínsecas) podem propagar até provocar a falha do componente ou parar de propagar depois de crescer uma pequena distância e se tornarem não-propagantes, dependendo do nível de carga e do gradiente de tensão à frente do entalhe. Modelos empíricos e teóricos têm sido propostos para fazer previsão do limite de fadiga de componentes entalhados. Entre os teóricos, o chamado modelo do Gradiente de Tensão (GT), que utiliza conceitos da mecânica da fratura linear elástica, apresenta-se como um modelo promissor. No entanto, a validação experimental das previsões deste modelo ainda não tem sido completamente realizada. Neste contexto, corpos de prova tipo C(T) do aço 1020 e com vários valores do raio da ponta do entalhe foram testados sob controle de amplitude de carga constante, frequência de 40 Hz e razão de tensão R igual a 0.1 para avaliar o limite de fadiga através de testes acelerados com cargas tipo step up durante blocos de 3.10 elevado a sexta potência ciclos. O limite de fadiga determinado experimentalmente foi comparado com as previsões do modelo GT e do Método do Ponto, um dos métodos da chamada Teoria da Distância Crítica (TDC). No modelo GT foram considerados três métodos: GTc-p, GTs-e e GTquebra, segundo o método usado para achar o fator geométrico para determinar o fator de intensidade de tensão. As previsões dos modelos GTc-p, GTquebra e TDC são similares no caso de entalhes com raios de ponta grandes, e bem próximas do limite de fadiga medido experimentalmente, enquanto que eles são não-conservativos no caso de entalhes afiados (raios de ponta pequenos). As previsões do modelo GTs-e foram conservativas para entalhes afiados e não afiados. Devido a que os dois modelos são baseados em conceitos lineares elásticos, foi demonstrado que uma análise elástica apresenta limitações para modelar o comportamento à fadiga em entalhes afiados, pois nesses casos a tensão local no ponto crítico pode exceder o limite de escoamento do material. Alem disso, o modelo GT também permite estimar o tamanho da maior trinca curta não-propagante (TCNP) associada ao limite de fadiga. Tais TCNP foram monitoradas nas faces do C(T) através de técnicas não-destrutivas tais como microscopia óptica, correlação digital de imagens e tomografia; enquanto que as TCNP internas foram detectadas usando a técnica destrutiva da metalografia. Os tamanhos das TCNP detectadas foram muito menores do que as estimadas pelo modelo GT, dificultando ainda mais o problema de detecção daquelas trincas. / [en] The mechanical design of structural components for high cycle fatigue applications needs reliable fatigue limits. However, mainly because of notches and the unavoidable presence of small defects, such a task still presents some challenges. Notches cause a stress concentration effect that can initiate short cracks at their tips, but such short cracks may propagate or become non-propagating, depending not only on the load level, but on the stress gradient ahead of the notch tip as well. Notch-like defects, such as scratches, pores, and inclusions, behave in the same way. There are empirical and theoretical models to predict the fatigue limit of notched components. The latter includes the so-called Stress Gradient (SG) model, based on linear elastic fracture mechanics concepts and using the El Haddad-Topper-Smith (ETS) characteristic size aR, as a promissory approach. However, there is a lack of experimental data verifying their fatigue limit predictions. In this context, C(T)-like notched specimens of SAE 1020 steel with several notch root radii were tested under constant load amplitude control at 40 Hz and a stress ratio R equal 0.1, to evaluate their fatigue limit through accelerated tests involving step loading procedures with blocks of 3.10 to sixth power cycles. The experimental fatigue limit was compared with values predicted by SG model, following three approaches: SGc-p, SGs-e, and SGquebra, according to the determination of the geometric factor of the stress concentration factor; and with an alternative prediction by the Point Method based on the theory of critical-distance (TCD). SGc-p, SGquebra and TCD model predictions are almost coincident for blunt notches and they present a good agreement with experimental results, but they are non-conservatives in the case of sharp notches; while SGc-p predictions are conservative for both blunt and sharp notches. Since both models are based on linear elastic concepts, it was demonstrated that an elastic analysis presents limitations to model the behavior of short cracks emanating from sharp notches, due to the local stress at the critical point can exceed the yield strength of the material. Furthermore, according to SG model, the fatigue limit is related to the presence of non-propagating short cracks (NPSC). Such surface NPSCs on the face of the specimens were monitored by non-destructive techniques including optical microscopy, digital image correlation (DIC) and micro-computed tomography; whereas subsurface NPSCs were detected through destructive metallographic technique. The sizes of the detected NPSCs were much smaller than those values predicted by SG model, which in turn makes the detection of these cracks a more complex problem.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Plastic shrinkage cracking (PSC) in concrete is a well-known problem and usually occurs within the first few hours after the concrete has been cast. It is caused by a rapid loss of water from the concrete, either from the surface through evaporation or through absorption by dry subgrade or formwork in contact with the concrete and results in an overall reduction in concrete volume. If this volume reduction or shrinkage is restrained, plastic shrinkage cracks can occur. Plastic shrinkage cracks create an unsightly appearance on the concrete surface which reduces the quality of the concrete structure. These cracks also develop weak points in the concrete which can be widened and deepened later on by drying shrinkage and thermal movement. As a result harmful substances may enter the cracks causing accelerated concrete deterioration. These cracks may also expose the steel reinforcement causing it to corrode more aggressively. Consequently, the aesthetic value, serviceability, durability and overall performance of the concrete will be reduced. Therefore it is important to consider methods of limiting PSC. One of these methods is the addition of low volumes of polymeric fibres to concrete to reduce PSC. However, the application of this low volume fibre reinforced concrete (LV-FRC) is not clearly understood since there is a lack of knowledge and guidance available for the use of LV-FRC. The objective of this study is to gain a full understanding of PSC behaviour in conventional concrete and LV-FRC by investigating the effects of evaporation and bleeding as well as the effect of various fibre properties on PSC. The following significant findings were attained: A basis for a crack prediction model in conventional concrete was developed using the average differences in cumulative evaporation and cumulative bleeding to create a crack prediction value (CPV). This preliminary model showed that there exists a certain CPV range (-0.2 to 0.4 kg/m2 for this study) where a slight decrease in the CPV results in a significant PSC reduction. It also showed that if the CPV falls outside this range, varying the bleeding or evaporation conditions will have very little effect on the PSC. A study on the fibre properties in LV-FRC showed that there exist certain limits to the fibre volume, length and diameter where a further increase or decrease in value will have no or little effect on reducing PSC. It also showed that the effect of the fibres depend on the level of severity of PSC. The knowledge gained from this investigation can serve as a basis for the design of a model that can predict the risk of PSC in conventional concrete and specify preventative measures needed to reduce this risk. It also provides information that can be used to develop guidelines for the effective use of LV-FRC. / AFRIKAANSE OPSOMMING: Plastiese krimp krake (PKK) in beton is `n bekende probleem en vorm gewoonlik binne die eerste paar uur nadat die beton gegiet is. Dit word veroorsaak deur die vinnige waterverlies vanuit die beton, óf deur verdamping vanaf die beton oppervalk óf deur absorpsie van `n droeë grondlaag of bekisting wat in kontak is met die beton. Dit veroorsaak `n algehele vermindering in beton volume. As hierdie krimping van die beton beperk word, kan plastiese krimp krake ontstaan. PKK skep 'n onooglike voorkoms van die beton oppervlakte en verlaag die kwaliteit van die beton struktuur. Hierdie krake tree ook op as swak plekke in die beton wat later kan verbreed of verdiep deur droogkrimping en termiese beweging. Gevolglik kan skadelike stowwe vanuit die omgewing die krake binnedring wat lei tot versnelde agteruitgang van die beton. Hierdie krake kan ook die staalbewapening ontbloot wat veroorsaak dat dit vinniger roes. Gevolglik verminder die estetiese waarde, diensbaarheid, duursaamheid en algehele prestasie van die beton. Daarom is dit belangrik om metodes te ondersoek vir die beperking van PKK. Een van hierdie metodes is die byvoeging van lae volumes polimeer vesels tot beton om PKK te verminder. Die toepassing van hierdie lae volume - vesel versterkte beton (LV-VVB) word egter nog nie volledig verstaan nie as gevolg van 'n algemene gebrek aan kennis en riglyne vir die gebruik van die LV-VVB. Die doel van hierdie studie is om 'n volledige begrip van PKK gedrag in normale beton asook LV-VVB te kry. Dit word behaal deur die effek van verdamping en bloei op PKK sowel as die effek van verskillende vesel eienskappe op PKK te ondersoek. Die volgende noemenswaardige bevindinge is bekry. • Die basis van 'n kraak voorspellingsmodel vir gewone beton is ontwikkel deur gebruik te maak van die gemiddelde verskil tussen die kumulatiewe verdamping en die kumulatiewe bloei om 'n kraak voorspellingswaarde (KVW) te vorm. Hierdie voorlopige model toon dat daar `n sekere KVW interval ontstaan (-0,2 tot 0,4 kg/m2 vir hierdie studie) waar slegs 'n effense vermindering in die KVW 'n geweldige vermindering in die PKK tot gevolg het. Dit dui ook aan dat, indien die KVW buite hierdie interval val, ʼn verandering in die bloei of verdamping toestande `n baie klein invloed op die PKK het. 'n Studie oor die vesel eienskappe in LV-VVB het gewys dat daar sekere grense is aan die vesel volume, lengte en deursnee waardes, waar 'n verdere toename of afname in waarde min of geen effek het op die vermindering van PKK nie. Dit wys ook dat die effek van die vesels grotendeels afhanklik is van die risiko vlak vir PKK. Die kennis wat uit hierdie ondersoek opgedoen is, kan dien as 'n basis vir die ontwerp van 'n model wat die risiko van PKK in gewone beton kan voorspel en daarvolgens besluit op 'n voorkomingsmaatsreël om hierdie risiko te verminder. Dit bied ook inligting wat gebruik kan word om riglyne te ontwikkel vir die effektiewe gebruik van LV-VVB.

When casting the slab in a slab-on-ground structure most of the drying will occur through the surface of the slab, which is in contact with the air. This will create a non-uniform internal moisture distribution. With the top of the slab drying faster it will also have a faster shrinkage due to drying, which in turn leads to stress in the surface layers of the slab as these wants to contract. With the slab wanting to assume a curled geometry, but being restricted by external loads and self-weight, cracks will usually appear in the surface (Lange, Lee & Liu, 2011).  A concrete slab-on-ground does not dehydrate the same way as, for example, floor bellows or wall elements which has the same climate on both sides. The ground beneath a heated building standing on a slab-on-ground structure is warm and moist with a relative moisture close to 100%. After carefully examining moisture damaged slab-on-ground structures it was concluded that the temperature and moisture behavior in this type of structure is more complicated than earlier presumed. In an attempt to broaden the basis of knowledge about humidity conditions under a concrete slab-on-ground structure, measurements were performed on an existing slab.  The Council for Construction Competence (Rådet för ByggKompetens, RBK) sets the industry standard regarding moisture measurement in Sweden. In 2017 the method recommended by RBK for moisture measurement in concrete includes drilling a hole in the slab, sealing it with a plastic pipe and mounting the sensor inside. This is the method that was used for measurements in this paper. Three different measurement locations in the slab along with two sensors mounted at every location was used to gather data.  The results from the measurements show that the relative humidity near the bottom of the slab is close to 100%. The results from the sensors range from 90% to 100% RH with the majority of the results very close to 100% RH. The results discovered in this paper supports the assumption that the ground beneath a slab-on-ground structure is close to 100% RH. / Vid gjutning av en betongplatta på mark sker uttorkning främst genom ovansidan av plattan. De övre skikten av betongen får en snabbare uttorkning än de undre skikten, detta tillsammans med den krympning som sker under uttorkningen skapar spänningar i betongplattan. Fenomenet gör att plattan vill böja upp sig i kanterna men på grund av egentyngd samt laster ovanifrån uttrycker sig spänningarna istället som sprickor på ovansidan (Lange, Lee & Liu, 2011). Uttorkning av en betongplatta på mark skiljer sig från uttorkning av t.ex. väggelement och mellanbjälklag som har samma klimat på bägge sidor. Marken under en uppvärmd byggnad med grundkonstruktionen platta på mark antas vara varm och fuktig med en relativ fukthalt nära 100 %. Efter noggrann undersökning av fuktskadade platta på mark konstruktioner har det visat sig att temperatur- och fuktbeteende i dessa konstruktioner är mer komplicerade än tidigare förmodat. För att bredda underlaget för de fuktförhållanden som råder i underkant av en betongplatta på mark utfördes mätningar i en befintlig betongplatta. Rådet för ByggKompetens, RBK är de som bestämmer branschstandarden inom fuktmätning i Sverige. Från 2017 är den enda metoden för fuktmätning i betong som RBK rekommenderar en metod där ett hål borras i betongplattan, tätas med ett foderrör och en RF-givare monteras inuti. Denna metod användes vid mätningarna i detta arbete. Tre olika mätpunkter med två RF-givare vid varje mätpunkt har använts vid mätningarna. Resultaten från mätningarna visar på att den relativa fuktigheten i betongplattans underkant är nära 100 %. Resultaten från givarna varierade mellan 90 % till 100 % RF där majoriteten av resultaten ligger väldigt nära 100 % RF. I och med dessa resultat styrker denna rapport antagandet om att marken under en platta på mark har en RF på 100 % eller väldigt nära.

The research work performed in this thesis has been carried out at the Production Tech-nology Centre where the Thermal Spray research group of University West has its work-shop and labs. This research work has been performed in collaboration with the International Advanced Research Centre for Powder Metallurgy and New Materials (ARCI), Hyderabad, India. First of all, I would like to express my sincere thanks and gratitude to my supervisors Dr. Nicolaie Markocsan and Dr. Nicholas Curry for their guidance, great support and valuable suggestions without which this work could not have been possible. I would also like to thanks Prof. Per Nylén for keeping faith in me and providing me an opportunity to work at PTC, which is a great place to perform research. It is my pleasure being their student and I wish I would keep learning from all of them, both on academic and personal grounds. I would also like to thank my colleagues at PTC Mr. Mohit Gupta and Mr. Stefan Björklund, for their help and support during this work. I would like to acknowledge the H.C. Starck Company for its financial support for the pro-ject; Dr. Filofteia-Laura TOMA at Fraunhofer IWS, Dresden to help us in spraying suspen-sion sprayed YSZ top coats, G Shivkumar from ARCI to help us in spraying solution pre-cursor sprayed top coats and Toni Bogdanoff, Jönköping University to help us in conduct-ing the LFA experiment

During vibration of engineering structures, fatigue cracks may exhibit repetitive crack open-close breathing like phenomenon. In this thesis, the concept of entropy is employed to quantify this bi-linearity/irregularity of the vibration response so as to evaluate crack severity. To increase the sensitivity of the entropy calculation to detect the damage severity, entropy is merged with wavelet transformation (WT). A cantilever beam with a breathing crack is studied to asses proposed crack identification method under two vibration conditions: sinusoidal and random excitations. Through numerical simulations and experimental testing, the breathing crack identification under sinusoidal excitation is studied first and proven to be effective. Then, the crack identification sensitivity under lower excitation frequencies is further improved by parametric optimization of sample entropy and WT. Finally, breathing crack identification under general random excitations are experimentally studied and realized using frequency response functions (FRFs) as an add-in tool with the proposed crack identification technique. / October 2016

Titanium alloys are major materials used in the airplane industry, and prospects show that airplane production will double in the next 20 years. Consequently, the demand for cutting tools for machining of titanium alloys will increase. The primary problem when machining titanium alloys is their low thermal conductivity. Crater wear is the main factor limiting tool life, and is generally caused by thermal diffusion due to high temperatures in the tool-chip interface. This master’s thesis was performed in collaboration with Sandvik Coromant, with the prospect to increase knowledge of how diffusion and chip formation influences crater wear progression. The aim was to study tool wear of cutting tools when turning Ti–6Al–4V. This was done by testing two different rake face geometries, both coated and uncoated, at cutting speeds of 30–115 m/min. Diffusion was investigated to learn about the impact it has on crater wear. Chips were examined to investigate chip formation and shear strain. The coated modified rake face insert showed less crater wear only for the initial few seconds of machining. Uncoated inserts with a modified rake face showed higher diffusion rate and faster crater wear progression than did standard inserts. The standard inserts showed twice as long tool life as did the modified inserts. No significant differences in the chip formation mechanism were found between modified and standard inserts. Cracks were found within shear bands that were thinner than usual, which suggest that the generation of cracks allows less shear deformation.