Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

Calculation of the critical crack size for cold form rectangular hollow section tube (CRHS) under bending load at -40º C temperature

To predict the capacity of the structure or the point which is followed by instability, calculation of the critical crack size is important. Structures usually contain several cracks but not necessarily all of these cracks lead to failure or reach the critical size. So, defining the harmful cracks or the crack size which is the most leading one to failure provides criteria for structure’s capacity at elevated temperature. The scope of this thesis was to calculate fracture parameters like stress intensity factor, the J integral and plastic and ultimate capacity of the structure to estimate critical crack size for this specific structure. Several three dimensional (3D) simulations using finite element method by Ansys program and boundary element method by Frank 3D program were carried out to calculate fracture parameters and results with the aid of laboratory tests (loaddisplacement curve, the J resistance curve and yield or ultimate stress) leaded to extract critical size of the crack. Two types of the fracture which is usually affected by temperature, Elastic and Elasti-Plastic fractures were simulated by performing several linear elastic and nonlinear elastic analyses. Geometry details of the weldment; flank angle and toe radius were also studied independently to estimate the location of crack initiation and simulate stress field in early stages of crack extension in structure. In this work also overview of the structure’s capacity in room temperature (20 ºC) was studied. Comparison of the results in different temperature (20 ºC and -40 ºC) provides a threshold of the structure’s behavior within the defined range.

Horizontal Grid Size Selection and its Influence on Mesoscale Model Simulations

The use of two-dimensional spectral analysis applied to terrain heights in order to determine characteristic terrain spatial scales and its subsequent use for the objective definition of an adequate grid size required to resolve terrain forcing are presented in this paper. In order to illustrate the influence of grid size, atmospheric flow in a complex terrain area of the Spanish east coast is simulated by the Regional Atmospheric Modeling System (RAMS) mesoscale numerical model using different horizontal grid resolutions. In this area, a grid size of 2 km is required to account for 95% of terrain variance. Comparison among results of the different simulations shows that, although the main wind behavior does not change dramatically, some small-scale features appear when using a resolution of 2 km or finer. Horizontal flow pattern differences are significant both in the nighttime, when terrain forcing is more relevant, and in the daytime, when thermal forcing is dominant. Vertical structures also are investigated, and results show that vertical advection is influenced highly by the horizontal grid size during the daytime period. The turbulent kinetic energy and potential temperature vertical cross sections show substantial differences in the structure of the planetary boundary layer for each model configuration

Size distribution of atmospheric particulate ionic species at a coastal site in Portugal

A Berner impactor was used to collect size-differentiated aerosol samples from March to August 2003 in the city of Aveiro, on the Portuguese west coast. The samples were analysed for the main water-soluble ion species. The average concentration of sulphate, nitrate, chloride and ammonium was 6.38, 3.09, 1.67 and 1.27 µg m-3, respectively. The results show that SO4(2-) and NH4+ were consistently present in the fine fraction < 1 µm, which represents, on average, 72 and 89% of their total atmospheric concentrations, respectively. The NO3-particles were concentrated in the coarse size. Chloride presented the characteristic coarse mode for marine aerosols. During some spring/summer events, an ammonium surplus was observed (NH4+/SO4(2-) molar ratios > 2), possibly due to greater availability of ammonia coming from agricultural activities or from the neighbouring chemical industrial complex. During the remaining periods, the aerosol was found to be somewhat acidic and predominantly in the form of ammonium bisulphate (NH4+/SO4(2-) molar ratios = 0.5-1.25). Samples collected under a major or exclusive influence of maritime air masses were essentially constituted by coarse particles with enrichment in sea salt, while for air masses of continental origin the contribution of water-soluble ionic species in the fine mode was more pronounced.

Operador dipolo-dipolo na base de momento angular: um complemento ao estudo de ressonância magnética nuclear

The relationship between the magnetic dipole-dipole potential energy function and its quantum analogue is presented in this work. It is assumed the reader is familiar with the classical expression of the dipolar interaction and has basic knowledge of the quantum mechanics of angular momentum. Except for these two points only elementary steps are involved.

Brain size and evolutionary diversification in birds

The role of behavior in evolution remains controversial, despite that some ideas are over 100 years old. Changes in behavior are generally believed to enhance evolution by exposing individuals to new selective pressures and by facilitating range expansions. However, this hypothesis lacks firm empirical evidence. Moreover, behavioral changes can also inhibit evolution by hiding heritable variation from natural selection. Taking advantage of the complete phylogeny of extant birds, a new species-level measure of past diversification rate and the best existing measures of brain size (n = 1326 species), I show here that relative brain size is associated (albeit weakly) with diversification rates. Assuming that brain relative size reflects behavioral flexibility, an assumption well-supported by evidence, this finding supports the idea that behavior can enhance evolutionary diversification. This view is further supported by the discovery that the most important factor influencing diversification rates is ecological generalism, which is believed to require behavioral flexibility. Thus, behavioral changes that expose animals to a variety of environments can have played an important role in the evolution of birds.

Aerosol particle size distributions at a traffic exposed site and an urban background location in Oporto, Portugal

Aerosol size distributions from 6 to 700 nm were measured simultaneously at an urban background site and a roadside station in Oporto. The particle number concentration was higher at the traffic exposed site, where up to 90% of the size spectrum was dominated by the nucleation mode. Larger aerosol mode diameters were observed in the urban background site possibly due to the coagulation processes or uptake of gases during transport. Factor analysis has shown that road traffic and the neighbour stationary sources localised upwind affect the urban area thought intra-regional pollutant transport.

An undergraduate level experiment on the synthesis of Au nanoparticles and their size-dependent optical and catalytic properties

The synthesis of gold nanoparticles (Au NPs) 15, 26, and 34 nm in diameter, followed by the investigation of their size-dependent optical and catalytic properties, is described herein as an undergraduate level experiment. The proposed experiment covers concepts on the synthesis, stabilization, and characterization of Au NPs, their size-dependent optical and catalytic properties at the nanoscale, chemical kinetics, and the role of a catalyst. The experiment should be performed by groups of two or three students in three lab sessions of 3 h each and organized as follows: i) synthesis of Au NPs of different sizes and investigation of their optical properties; ii) evaluation of their catalytic activity; and iii) data analysis and discussion. We believe that this activity enables students to integrate these multidisciplinary concepts in a single experiment as well as to become introduced/familiarized with an active research field and current literature in the areas of nanoparticle synthesis and catalysis.

Herança da resistência à mancha-angular do feijoeiro e identificação de marcadores moleculares flanqueando o loco de resistência

A mancha-angular, cujo agente causal é o fungo Phaeoisariopsis griseola, é uma das principais doenças do feijoeiro comum (Phaseolus vulgaris). Os marcadores moleculares disponíveis ainda não são suficientes para monitorar todos os genes de resistência a essa doença. Por isso, objetivou-se neste trabalho estudar a herança da resistência aos patótipos 63.39 e 31.23 de P. griseola, em populações derivadas de 'Ouro Negro' (ON) e 'US Pinto 111' (PT), e identificar marcadores moleculares ligados a genes de resistência presentes nessas cultivares. Quando inoculadas com o patótipo 63.39, as plantas ON, F1 (ON x PT) e 3/4 da população F2 mostraram-se resistentes enquanto que PT e 1/4 da população F2 foram suscetíveis. Quando inoculadas com o patótipo 31.23, as plantas PT e 1/4 das famílias F2:3 foram resistentes e todas as demais, suscetíveis. Esses dados indicam que a resistência proveniente de ON é conferida por um gene dominante enquanto que a de PT, por um recessivo. Esses dois genes segregaram independentemente. Amostras de DNA das plantas F2 foram amplificadas pela técnica de RAPD (random amplified polymorphic DNA) de acordo com a estratégia de análise de bulks segregantes. Foram identificados os marcadores OPM02(460C) e OPAA19(600C,) respectivamente a 5,3 e 10 centimorgans (cM) do loco de resistência proveniente de ON. Eles flanqueiam este loco e, quando empregados simultaneamente, proporcionam uma eficiência de seleção de 97,4%. Não foram identificados marcadores para o loco de resistência proveniente de PT.

Resistência de cultivares de feijoeiro-comum à ferrugem e à mancha-angular em condições de casa de vegetação

Foram inoculadas 17 cultivares de feijoeiro-comum (Phaseolus vulgaris) recomendadas para plantio em Minas Gerais com cinco patótipos (6, 7, 9, 10 e 12) de Uromyces appendiculatus e cinco (63.55, 31.23, 63.39, 31.55 e 63.23) de Phaeoisariopsis griseola. Foi conduzido um ensaio separadamente para cada um dos patótipos dos dois patógenos, totalizando 10 ensaios. Nos ensaios de ferrugem foi avaliada a freqüência de infecção (FI) e estimado o tamanho médio das pústulas (TMP) e, nos ensaios de mancha-angular foram avaliados os sintomas utilizando uma escala de notas variando de 1 a 9. A maioria das cultivares se mostrou suscetível a pelo menos três dos cinco patótipos de ferrugem. As cultivares mais suscetíveis foram Roxo 90 e Meia Noite e a mais resistente foi a Ouro Negro, a qual apresentou proteção completa aos cinco patótipos testados. Com relação à mancha angular, além do Roxo 90, as cultivares Carioca MG, Pérola, Carioca 1030 e Aporé, extensivamente plantadas em Minas Gerais, foram altamente suscetíveis. As cultivares Ouro Negro e EMGOPA 201-Ouro apresentaram genes de resistência a diferentes patótipos e a combinação desses genes em uma nova cultivar resultaria em resistência a todos os patótipos testados.

Mapeamento de genes de resistência do feijoeiro à ferrugem, antracnose e mancha-angular usando marcadores RAPD

A organização de diferentes genes de resistência da cultivar Ouro Negro de feijoeiro-comum (Phaseolus vulgaris) à ferrugem, antracnose e mancha-angular foi estudada com o auxílio de marcadores moleculares. Uma população de 154 linhas endogâmicas recombinantes (RIL's) obtidas do cruzamento entre as cultivares Ouro Negro e Rudá foram inoculadas com sete raças fisiológicas de Uromyces appendiculatus, três de Colletotrichum lindemuthianum, e quatro de Phaeoisariopsis griseola. Amostras de DNA de cada uma das RIL's foram amplificadas via PCR utilizando 70 diferentes primers. A análise da segregação da resistência à ferrugem, antracnose e mancha-angular na população de 154 RIL's revelou diferentes modos de herança para a resistência a cada uma das raças fisiológicas. A análise de ligação genética revelou que os diferentes genes de resistência à ferrugem e à antracnose estão no mesmo grupo de ligação. Os genes de resistência à mancha-angular também foram mapeados juntos, porém em outro grupo de ligação. Verificou-se neste trabalho que a utilidade dos marcadores RAPD, previamente identificados como ligados a genes de resistência do feijoeiro a doenças foi restrita. Apenas cinco dos 38 marcadores moleculares testados foram validados na população de RIL's como ligados aos genes de resistência à ferrugem e à antracnose. Três novos marcadores (OBA16(669) e OBA16(583) a 10,4 cM em acoplamento e OAD9(3210) a 13,9 cM em repulsão) ligados ao bloco gênico de resistência da cultivar Ouro Negro à mancha-angular foram identificados.

Quantificação de componentes monocíclicos da mancha angular do feijoeiro

Foram realizados experimentos em ambiente controlado, em câmaras de crescimento, com duas cultivares de feijoeiro (Phaseolus vulgaris), Rosinha e Carioca, para a quantificação de componentes monocíclicos da mancha angular. Os componentes monocíclicos avaliados foram: período de incubação, severidade da doença e taxa de crescimento das lesões, sob as temperaturas de 6, 10, 14, 17, 21, 25, 29 e 33 ºC. Nenhum sintoma da mancha angular ocorreu em 6 e 33 ºC. A severidade da mancha angular foi elevada na faixa de temperatura entre 20 e 25 ºC e o período de incubação foi favorecido pela temperatura de 25 ºC, para as duas cultivares testadas. Esta temperatura também proporcionou a maior taxa de crescimento das lesões e estes dados foram ajustados, em função da temperatura por uma equação do primeiro grau. O efeito do período de molhamento foliar (5, 6, 12, 18, 24, 30, 36, 42, 48 e 54 h) na severidade da doença também foi avaliado. A severidade da mancha angular do feijoeiro aumentou com o aumento da duração do molhamento foliar até o máximo de 54 h. As variações de severidade da mancha angular do feijoeiro, em relação ao número de horas de molhamento foliar, foram explicadas pelo modelo de Richards. A função Beta-Richards explicou o efeito combinado da temperatura e da duração do molhamento foliar na severidade da mancha angular do feijoeiro para ambas as cultivares.

Determinação das condições climáticas que favorecem o desenvolvimento da ferrugem e da mancha angular do feijoeiro

Este trabalho objetivou estudar o efeito da temperatura e do molhamento foliar no desenvolvimento da ferrugem e da mancha angular do feijoeiro (Phaseolus vulgaris). Foram conduzidos ensaios em condições de campo durante os plantios das águas (outubro a dezembro), de inverno (maio a agosto) e da seca (fevereiro a maio). Os ensaios foram instalados em blocos casualizados com três repetições e dois tratamentos. Os tratamentos consistiram de: 1) inoculação com Uromyces appendiculatus e 2) inoculação com Phaeoisariopsis griseola. No inverno, a ferrugem ocorreu com maior intensidade, atingindo um valor máximo de severidade (Ymax) igual a 1,3 e as maiores taxas de crescimento (0,09, 0,04 e 0,07 aos 34, 55 e 62 dias, respectivamente), devido à predominância, nessa época, de temperaturas inferiores a 21,1 °C, e de maior número de horas diárias com temperaturas menores ou iguais a 16 °C, quando ocorreu molhamento foliar. Nos plantios das águas e da seca, a mancha angular ocorreu com maior intensidade, atingindo Ymax iguais a 2,6 e 3,5, respectivamente e as maiores taxas de crescimento (0,06, 0,02 e 0,15 aos 46, 60 e 67 dias, respectivamente, no plantio das águas, e 0,13 e 0,38 aos 51 e 58 dias, respectivamente, no plantio da seca), devido à predominância, nessa época, de temperaturas superiores a 21,1 °C, quando ocorreu molhamento foliar e não ocorrência de temperaturas menores ou iguais a 16 °C. Com esse estudo pôde-se caracterizar, em função das condições climáticas, o plantio de inverno como favorável à ocorrência da ferrugem e os plantios da água e da seca como favorável à ocorrência da mancha angular.