A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfiment of the requirements for the degree of Master or Science in Engineering. Johannesburg, 1993. / The stress concentration factors around rectangular holes in carbon-fibre reinforced epoxy plates, subject uniaxial loads, were investigated experimentally and theoretically. To obtain theoretical solutions, two approaches were adopted; the finite element method and the theory of elasticity using the method of complex variable functions. Reflective photoelasticity was used as the experimental method. The determination of the stress concentration factor around a rectangular hole in a glass-fibrereinforced plate was attempted using transmissive photoelasticity, but no meaningful results were obtained. [Abbreviated Abstract. Open document to view full version} / MT2017

[pt] No presente trabalho de tese, é analisado a distribuição de tensões na parte extrema de um cilindro de parede grossa, submetido a uma pressão exercida por outro cilindro. É feito o estudo da distribuição das tensões para diferentes posições do cilindro interno, utilizando uma mesma relação de diâmetros para o cilindro oco. Resina epoxi é usada como material fotoelástico para a construção dos modelos. O método de congelamento das tensões foi empregado. O modelo foi cortado em fatias e analisados no polariscópio. As tensões foram determinadas por integração numérica das equações diferenciais de equilíbrio, em coordenadas cilíndricas. Os resultados são apresentados em gráficos e analisados. / [en] The presented work deals with the problem of the state of the stress near the end of the two thick wall cylinders pressed together. The problem was for solved for various configurations of the cylinder by the three-dimensional photo elasticity using stress freezing method. The models were manufactured from the epoxy resin prepared by the special procedure and after stress freezing procedure sliced into the radial and meridial slices. The stresses were determined by numerical integration of the equations of the equilibrium of a elastically deformed body, using cylindrical coordinates.

[pt] Este trabalho se propõe a analisar o estado de tensões do fêmur humano, usando o método da fotoelasticidade tridimensional. O modelo de fêmur feminino foi construído, de um material oticamente sensível, desprezando as propriedades não homogêneas e anisotrópicas do osso real. O modelo do fêmur foi carregado por uma força vertical e o estado de tensões, foi analisado na região do colo onde ocorre com frequência a fratura do osso real. É discutido em detalhes o procedimento de confecção do modelo. O estado de tensão é determinado em um modelo sem considerar a medula óssea, e comparado com modelos onde esta é simulada usando fluidos viscosos. Este trabalho pode ser considerado como um primeiro, com o objetivo de analisar a distribuição de tensões em ossos humano, usando o método da fotoeslasticidade tridimensional. / [en] This work presents the attempt to analyse the state of stress of human femur using the method of three-dimensional photoelasticity. The model of woman’s femur was made from the optically sensitive material reglecting the non-homogenity and anisotropy of real bone. The model of femur was loaded by verticalforce and the state of the stresses was analysed within area of the neck, where the fracture of real bone frequently occurs. The special procedure of the manufacturing of the model is discussed in detail. The state of the stress of bollow bone and model filled by viscous fluid is compared. This work should be considered as a first step in the attempt to analyse the stress distribution of the stress in the human’s bones using the methods of three-dimensional photoelasticity.

Thesis (MEng.)-- University of Stellenbosch, 1992. 140 leaves on single pages, preliminary pages i-xi and numbered pages 1-113. Includes bibliography. Digitized at 600 dpi grayscale to pdf format (OCR),using an Bizhub 250 Konica Minolta Scanner and at 300 dpi grayscale to pdf format (OCR), using a Hp Scanjet 8250 Scanner. / Thesis (MEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 1992 / ENGLISH ABSTRACT: The large variety of turbo-machinery blade root geometries in use in industry prompted the question if a optimum geometry could be found. An optimum blade root was defined as a root with a practical geometry which, when loaded, returns the minimum fillet stress concentration factor. A literature survey on the subject provided guidelines but very little real data to work from. An initial optimization was carried out using a formula developed by Heywood to determine loaded projection fillet stresses. The method was found to produce unsatisfactory results, prompting a photoelastic investigation. This experimental optimization was conducted in two stages. A single tang defined load stage and a single tang in-rotor stage which modeled the practical situation. The defined load stage was undertaken in three phases. The first phase was a preliminary investigation, the second phase was a parameter optimization and the third phase was a geometric optimization based on a material utilization optimization. This material optimization approach produced good results. From these experiments a practical optimum geometry was defined. A mathematical model which predicts the fillet stress concentration factor for a given root geometry is presented. The effect of expanding the single tang optimum to a three tang root was examined. / AFRIKAANSE OPSOMMING: Die groot verskeidenheid lemwortelgeometrieë wat in turbomasjiene gebruik word het die vraag na 'n optimum geometrie laat ontstaan. Vir hierdie ondersoek is 'n optimum geometrie gedefineer as 'n praktiese geometrie wat, as dit belas word, die mimimum vloeistukspanningskonsentrasiefaktor laat ontstaan. 'n Literatuur studie het riglyne aan die navorsing gegee maar het wynig spesifieke en bruikbare data opgelewer. Die eerste optimering is met die Heywood formule, wat vloeistukspannings in belaste projeksies bepaal, aangepak. Die metode het nie bevredigende resultate opgelewer nie. 'n Fotoelastiese ondersoek het die basis vir verdere optimeering gevorm. Hierdie eksperimentele optimering is in twee stappe onderneem. 'n Enkelhaak gedefineerde lasgedeelte en 'n enkelhaak in-rotor gedeelte het die praktiese situasie gemodeleer. Die gedefineerde lasgedeelte is in drie fases opgedeel. Die eerste fase was n voorlopige ondersoek. Die tweede fase was 'n parameter optimering. 'n Geometrie optimering gebasseer op 'n materiaal benuttings minimering het die derde fase uitgemaak. Die materiaal optimerings benadering het goeie resultate opgelewer. Vanuit hierdie eksperimente is 'n optimum praktiese geometrie bepaal. 'n Wiskundige model is ontwikkel, wat die vloeistukspanningskonsentrasiefaktor vir 'n gegewe wortelgeometrie voorspel. Die resultaat van 'n geometriese uitbreiding van die enkelhaaklemwortel na 'n driehaaklemwortel op die spanningsverdeling is ondersoek.

This thesis details an experimental study on the determination of the fracture parameters for a crack located at the interface between two dissimilar materials using the method of photoelasticity. The interface is potential1y an inherent weak spot of any composite material, structure"or adhesively bonded joint. Accurate description of the state of stress at the crack tip is required for strength prediction. The concept of the complex stress intensity factor is used to characterise the elastic crack tip stress field for an interface crack. Complex stress intensity factors and their moduli have been measured experimental1y for standard bimaterial crack geometries using the wel1 established technique of photo elasticity. Bimaterial specimens comprising aluminium al10y and epoxy resin components were used. This creates a large material mismatch at the interface and al10ws data to be col1ected from the epoxy component of the specimen using transmission photoelasticity. An automated ful1 field photoelastic technique was developed to significantly reduce the data col1ection time. The technique comprises elements from the approaches of three wavelength and phase stepping photoelasticity and is a significant improvement on techniques previously available. Stress intensity factors were determined by fitting a theoretical stress field solution for the bimaterial crack to the experimental data. A computational routine automatical1y selects the region of best fit between the experimental data and the theoretical solution. This data is then used to determine the complex stress intensity factor and its modulus value. In order to provide a robust fit between the experimental data and the theoretical field solution a weighting function was incorporated into the routine. The measured bimaterial stress intensity factors are compared with those determined experimental1y for equivalent homogeneous specimens made from epoxy resin. The differences between the two are then discussed. The experimental results agree with the wel1 known concept that tension and shear effects are inherently coupled at the crack tip. However, the effects of changing the load angle with respect to the interface also demonstrate that some contrasts exist with known numerical solutions.

The application of fracture mechanics to engineering design has provided significant advances in understanding of the causes and mechanisms of failure and crack growth. Despite this, there are still some aspects that remain incompletely understood, such as the crack closure/crack shielding effect. The presence of crack closure/shielding acts to reduce . The mechanisms of crack closure/shielding are complicated, and have not been fully understood. This work focuses on the plasticity-induced crack tip shielding mechanism and presents a novel approach to characterise the elastic stress fields under the influence of the plastic enclave surrounding the crack tip. The model is successfully applied to determine the four stress parameters experimentally using full-field photoelastic stress analysis on polycarbonate CT specimens, following studies of the effect of the crack tip position and the valid data collection zone giving the best fit between the model predictions and the experimental data. The predicted values from the model demonstrate good data repeatability, and exhibit sensible trends as a function of crack length and load ratio that are interpretable in terms of physically meaningful changes to the plastic enclave. In addition, the model is proven to describe the stress field around a crack more accurately than classic Williams‟ stress solution. The model is also extended to AL 2024-T3 specimens using a full-field displacement measurement technique, digital image correlation. Using the Sobel edge detection method to identify the crack tip from the displacement fields with a rectangular shaped data collection zone employed in the current study, reasonable trends were again demonstrated in the experimental results as a function of crack length.

O objetivo deste estudo foi avaliar a distribuição de tensões na região peri-implantar de próteses fixas unitárias cimentadas com conexões protéticas em hexágono externo (HE), hexágono interno (HI) e cone morse (CM), substituindo o 2° pré-molar mandibular; utilizando análise fotoelástica. Foram confeccionados 3 modelos fotoelásticos com implantes de diferentes conexões protéticas (HE, HI e CM) suportando coroas metalocerâmicas unitárias, com dentes adjacentes (1° molar e 1° pré-molar mandibular). Foram aplicados 2 tipos de cargas com diferentes intensidades, oclusal fisiológica (15, 20 e 25 Kgf) e pontual (10 e 15 Kgf) na fossa mesial das coroas implantossuportadas. As imagens obtidas foram inseridas no programa Fringes® (Laboratório de Projetos Mecânicos, Universidade Federal de Uberlândia, Uberlândia, Brasil), e selecionados 12 pontos a serem analisados. Foram realizadas análises quantitativa e qualitativa das tensões observadas. Os resultados das tensões (KPa) medias da região peri-implantar, para cada tipo e intensidade de carga, foram: Cargas fisiológicas: 1) 15 Kgf: HE 107,42; HI 88,81; CM 182,63; 2) 20 Kgf: HE 185,60; HI 123,77; CM 226,44; e 3) 25 Kgf: HE 207,90; HI 176,88; CM 320,65; Cargas pontuais: 1) 10 Kgf: HE 115,94; HI 108,14; CM 64,78; e 2) 15 Kgf: HE 147,25; HI 143,88; CM 177,87. Foi observado que para os carregamentos fisiológicos a HI apresentou os menores valores de tensão e melhor distribuição entre implante e dentes adjacentes; a CM apresentou os maiores valores de tensão, contudo a distribuição entre implante e dentes adjacentes também foi adequada; a HE mostrou a distribuição menos favorável com tensões na crista mesial do implante. Nos carregamentos pontuais a CM apresentou melhor distribuição de tensões ao longo do implante seguido pela HI e HE. Conclui-se que a distribuição de tensões foi influenciada pelo tipo de conexão protética; sendo que as tensões foram melhor distribuídas na carga oclusal fisiológica. O HI apresentou melhor distribuição de tensões para a carga fisiológica e o CM para a carga pontual, evidenciando melhor desempenho das conexões internas / This study aimed to evaluate the peri-implant stress fields generated from 3 different implant- abutment interfaces external hexagon (EH), internal hexagon (IH) and morse taper (MT); supporting single crowns corresponding to the 2nd mandibular pré-molar via photoelastic analysis. 3 photoelastic models with different implant-abutment connections (HE, HI, CM) supporting metal-ceramic single crowns with adjacent teeth (mandibular 1st molar and 2nd pre-molar) were fabricated. The models were submitted to different loads: physiologic occlusion (15, 20, 25Kgf) and punctual (10, 15Kgf) in the implant-supported crown at the mesial fossa region. The images obtained were inserted in the software Fringes® (Laboratório de Projetos Mecânicos, Universidade Federal de Uberlândia, Uberlândia, Brasil). The maximum stresses were determined and observed at 12 selected points, qualitative and quantitative analysis were performed. The results of the stress (KPa) average of peri-implant regions with the 2 different loads and their respective intensities (Kgf) were: Physiologic occlusion: 1) 15 Kgf: HE 107,42; HI 88,81; CM 182,63; 2) 20 Kgf: HE 185,60; HI 123,77; CM 226,44; and 3) 25 Kgf: HE 207,90; HI 176,88; CM 320,65; Punctual loads: 1) 10 Kgf: HE 115,94; HI 108,14; CM 64,78; and 2) 15 Kgf: HE 147,25; HI 143,88; CM 177,87. With the physiological load the IH showed the lowest stress values and a favorable distribution among implant and adjacent teeth; the MT showed the highest stress values, however a favorable distribution with the adjacent teeth; the EH showed stress values in the cervical mesial point of the implant. For the punctual load the MT showed the best stress distribution within the implant, followed by the IH and EH. It was concluded that stress patterns were influenced by the connection design and were more favorable with the physiological occlusion load for all connections. The IH showed better stress distribution with the physiological occlusion load and the MT with the punctual load, showing better performance for internal connections

O sistema de fixação vertebral utilizando o parafuso pedicular é um dos métodos mais eficientes no tratamento de patologias da coluna vertebral. Quando o parafuso estiver submetido à força de arrancamento, ele gera tensões ao redor, principalmente próximo do canal medular, situação que pode ser analisada pela técnica da fotoelasticidade. O objetivo foi analisar as tensões internas geradas em modelos fotoelásticos de vértebras, utilizando diferentes medidas de parafusos do sistema de fixação vertebral, submetidos à força de arrancamento. Foi utilizado um modelo de vértebra lombar em material fotoelástico utilizando três medidas de diâmetros externos de parafusos pediculares (5, 6 e 7mm) do tipo USS1. As tensões internas ao redor do parafuso foram avaliadas em 18 pontos pré-determinados utilizando um polariscópio de transmissão plana. As regiões de maiores concentrações de tensões foram observadas entre o canal medular e as curvas do processo transverso. Nas comparações das médias das tensões cisalhantes entre os parafusos 5 e 7mm, e 6 e 7mm foram observadas diferenças estatísticas significativas, o que não ocorreu com os parafusos de 5 e 6mm onde não foram observadas diferenças estatisticamente significativas. Foi observado que as tensões internas são mais elevadas em áreas irregulares próximas do canal medular, o que sugere ser uma região crítica, em termos de esforços mecânicos. / The system of vertebrae fixation using the pedicular screw is one of the most efficient methods to treat vertebral spine pathologies. When the screw is submitted to pullout strength, it causes internal stress near the medullary canal and this situation can be analyzed using the photoelasticity technique. The objective of this study was to examine the internal stress of a photoelastic vertebrae model using different sizes of screws for the vertebral fixation submitted to pulling out. A lumbar vertebral model made of photoelastic material with three different pedicular screw sizes (5, 6 and 7mm), type USS1 was used. The internal stress around the screw were tested in 18 pre established points by a plain transmission polariscope. The areas of greater concentration of stress were placed between the medullary canal and the transverse process. Comparing the maximum average pulling out stress, statistical differences were observed between screws 5 and 7, and 6 and 7. On the other hand, when screws 5 and 6mm where compared no significant differences were found. This study identified that the internal stress are greater in irregular areas, near the medullary canal, suggesting that this may be a critical region.

A técnica da fotoelasticidade pode ser particularmente útil na análise de tensões em sistemas com geometrias complexas. Em um equipamento chamado polariscópio, um feixe de luz polarizada atravessa o modelo fotoelástico que representa o protótipo. Ao submeter este modelo a um carregamento, faixas de diferentes cores poderão ser visualizadas. Cada cor é associada a um nível de tensão. As tensões observadas no modelo fotoelástico podem ser comparadas com as tensões determinadas nos modelos numéricos ou analíticos. Em casos específicos, o problema da distribuição de tensões em uma fundação pode ser analisado com emprego da fotoelasticidade. A análise do comportamento de estacas helicoidais através da técnica da fotoelasticidade pode ser então de grande valia para estudos mais aprofundados deste sistema. O principal objetivo desta pesquisa foi viabilizar este método experimental para ser aplicado no Departamento de Geotecnia da EESC em análises de tensões em sistemas geotécnicos. Para validar as análises experimentais, tensões observadas em modelos de geometria simples foram comparadas com as tensões determinadas por meio de modelagem numérica com o método dos elementos finitos. O comportamento da fundação por estaca helicoidal observado pela técnica da fotoelasticidade mostrou semelhança ao observado na modelagem numérica. Por meio da distribuição de tensões, foi possível avaliar a influência da geometria helicoidal da lâmina e da profundidade de instalação da ancoragem no terreno. / The photoelastic method can be particularly useful for stress analysis with complex geometry systems. In equipment called polariscope, a polarized light beam crosses the photoelastic model that represents the prototype. Submitting this model to a load, fringes of different colors can be visualized. Each color is associated to a stress level. The stresses corresponding to the observed fringes on the photoelastic model can be compared to the stresses obtained through analytical or numerical models. In specific cases, the stress distribution problem can be analyzed with the use of photoelasticity. The photoelastic analysis of the helical pile behavior can then be valuable for further studies of this system. The main objective of this research was enabling this experimental method to be applied in the Department of Geotechnical Engineering of EESC in geotechnical systems stress analysis. To validate the experimental analysis, stresses observed in simple geometry models have been compared to those stresses determined by numerical modeling with the finite element method. The observed behavior of the helical pile foundation by photoelastic method showed similarity to that one observed through numerical modeling. Stress distribution analyses allowed evaluating the influence of helical blade geometry and the depth of installation.

O tratamento de deformidade espinhal, doença degenerativa, trauma, e tumores da coluna vertebral exigem freqüentemente a realização da fixação interna. O surgimento dos parafusos pediculares possibilitou a realização da instrumentação segmentar da coluna mais estável, tornando-se atualmente procedimento padrão para realização das cirurgias de correção, estabilização de deformidade e instabilidade da coluna em patologias torácicas, lombares e sacrais. O segmento vertebral mais favorável para a implantação do parafuso é a região lombar, devido ao maior diâmetro dos pedículos. A fotoelasticidade tem sido utilizada em estudos científicos a fim de determinar a distribuição de tensões/deformações em sistemas estruturais, pois permite uma análise qualitativa e quantitativa do estado de tensão, através da observação de efeitos óticos. Neste trabalho foi utilizada esta técnica para determinar e analisar as tensões internas de modelos fotoelásticos sob influência de parafusos pediculares tipo USS1, quando submetidos a esforços de arrancamento. Para realização das análises fotoelásticas foram confeccionados 12 modelos divididos em três grupos, contendo em cada 4 modelos fotoelásticos. O primeiro grupo, G1, inclui o parafuso com diâmetro externo de 5 mm, o segundo, G2, o parafuso com diâmetro externo de 6 mm e o terceiro, G3, o parafuso com diâmetro externo de 7 mm. A simulação foi feita utilizando cargas de 0,75 e 1,5 Kgf. As ordens de franjas foram avaliadas em torno dos parafusos, utilizando o método de compensação de Tardy. Em todos os modelos analisados foram determinadas as tensões cisalhantes. Os resultados mostraram que para a carga de 0,75 Kgf, a tensão cisalhante máxima no parafuso de 5 mm foi maior que no de 6 mm, que foi maior que no de 7 mm. Com a carga de 1,5 Kgf houve igualdade nos três diâmetros externos de parafusos, e comparando estas duas cargas prevaleceu o último resultado. De acordo com as análises realizadas nos doze modelos, observou-se que o local de maior tensão é no pico das cristas, principalmente próxima a ponta dos parafusos. Sendo assim, esta técnica é bastante eficiente, pois, através da análise quantitativa e qualitativa foi possível comparar os parafusos de fixação vertebral, verificando qual é o mais suscetível ao arrancamento. / The treatment of spinal deformities, degenerative disease, injuries and tumors on the vertebral column often demand the accomplishment of the internal fixation. The pedicular screws arising enabled the accomplishment of column segmental instrumentation more stable and became a standard procedure in accomplishing surgeries of correction, deformities stabilization and column instability in thoracic, lumbar and sacral pathologies. The best vertebral segment for the screw implantation is the lumbar area due to a larger diameter of the pedicles. The photoelasticity has been used in scientific studies in order to determine the stress/strain distribution in structural systems, because it allows a qualitative and quantitative analysis of the state of stress, through the observation of optical effects. In this work was used this technique to determine and analyze the internal stress of the photoelastic models under the influence of pedicular screws type USS1 submitted to pullout strength. In order to accomplish the photoelastic analysis 12 models divided in 3 groups were made. Each of them contained 4 photoelastic models. The first group, G1, was composed by the screw of 5 mm of external diameter, the second, G2, was composed by the screw of 6 mm external diameter and the third, G3, by a screw of 7 mm external diameter. The simulation was performed using loads of 0.75 Kgf and 1.5 Kgf. The fringe orders were evaluated around the screws using the Tardy compensation method. In all the models analyzed were calculated the shear stress. The results showed that using the load of 0.75 Kgf the shear stress in the 5 mm screw was bigger than in the 6 mm screw, which was bigger than in the 7mm screw. With a load of 1.5 Kgf there was equality among the three external diameter screws and comparing these two last loads, the last result prevailed. According to the analysis realized in the 12 models, we observed that the place of highest stress is at the peak of the crests mainly at the tips of the screws. Concluding, this technique is efficient enough because through the quantitative and qualitative analysis it was possible to compare the vertebral fixation screws, verifying witch one is more susceptible to pullout.