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.

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.

Estimation of standard enthalpy of formation of alkanes in gaseous state by calculating size, structural and electronic parameters in the molecules

A quantitative analysis is made on the correlation ship of thermodynamic property, i.e., standard enthalpy of formation (ΔH fº) with Kier's molecular connectivity index(¹Xv),vander waal's volume (Vw) electrotopological state index (E) and refractotopological state index (R) in gaseous state of alkanes. The regression analysis reveals a significant linear correlation of standard enthalpy of formation (ΔH fº) with ¹Xv, Vw, E and R. The equations obtained by regression analysis may be used to estimate standard enthalpy of formation (ΔH fº) of alkanes in gaseous state.

Germination of Caesalpinia leiostachya (benth.) ducke seeds classified by size and shape

Caesalpinia leiostachya (Benth.) Ducke (Caesalpiniaceae) is a Brazilian legumenous tree whose seeds present different sizes and shapes, with dormancy imposed by a waterproof coat. In order to improve that quality of lot, seeds were classified by width in sieves of circular meshes (13, 14, 15, 16 and 17) and manually separated by shape in elongate, round and angular. Masses of 1000 seeds were determined and the thickness of each width and shape seedclass was measured, and coat permeability of the seeds classified by the width was investigated. Seeds were scarified in concentrated sulphuric acid and submitted to the germination test. Both final percentage and speed of germination index were evaluated. The classification of the seeds improved the quality of the lot, and the coat permeability was not affected by seed width. Elongated-flat seeds are of low physiological quality and should be discarded. Masses of 1000 seeds, percentage final and speed of germination increased with the width of the seeds. Both elongated and angular seeds had similar germinative behavior, and round seeds are of greater thickness and of superior physiological quality.

SPECIES RICHNESS AND ABUNDANCE OF LOW-TRUNK HERB EPIPHYTES IN RELATION TO HOST TREE SIZE AND BARK TYPE, EASTERN AMAZONIA

ABSTRACTThe composition and structure of the low-trunk epiphytic herb assembly as well as its vertical distribution were studied. DBH of host tree and bark type influence species richness and abundance in a nonlooded lowland tropical rainforest in Eastern Amazonia (1º57’36"S 51º36’55"W). A total of 37 epiphytic herb species were identified, among which 60% were Araceae. Species richness and abundance of epiphytic herbs showed tendency of positive correlation with host tree size and no relationships with bark type. Low positive correlation may be a by-product of the predominance of trees with smaller diameter in our sample rather than a reflection of neutral relationship. The absence of relationships with bark type may be partially explained by the large number of secondary, generalist, hemi-epiphytes and also may reflect the absence of suitable substrate in trees with smaller diameter.

Coffea arabica (cv Catuaí) production and bean size under different population arrangements and soil water availability

The purpose of this research was to evaluate the effect of drip irrigation under different population arrangements on the phytometric features, coffee productivity and bean size classification according to sieve retention. The experiment with Coffea arabica L. cv Catuaí was carried out in Mococa, São Paulo, Brazil. The experimental design was a 6 x 2 factorial scheme in randomized blocks, with four replications. The six densities of plantation were E1 (1.60 x 0.50 m); E2 (1.60 x 0.75 m); E3 (1.60 x 1.00 m); E4 (3.20 x 0.50 m); E5 (3.20 x 0.75 m) and E6 (3.20 x 1.00 m), which were divided according to the availability of water (irrigated - I - or non-irrigated - NI - groups). Data were submitted to analysis of variance and averages compared by Tukey test at 1 and 5% of probability. Descriptive analysis of coffee beans according to sieve classification was performed. Irrigation promoted an increase in plant height, crown diameter and production of processed coffee when compared with the NI group. Interaction between population arrangement and irrigation was observed, with an increase in production and crown diameter as the spacing was decreased. Therefore, irrigation provided significant increase in coffee bean size.

Fragment size of corn silage according to the dry matter and forage harvester adjustments

In Brazil, the best results in milk production are found in the state of Paraná. Such results are reached through genetic selection of the animals and management of their diets, in which whole plant corn silage is widely used. Aiming the silage quality, it was evaluated the influence of dry matter content of the corn culture as forage and the harvester adjustments on the fragment size of whole plant corn silage. The fragment size of two corn hybrids silage (SPEED and 2B688) was evaluated using a 5x3 factorial, with 4 repetitions. The first factor was the harvest time of the plants (105, 108, 112, 118, and 123 days after sowing (DAS)), which determines the forage dry matter (DM) content. The second factor was the harvester adjustments (2, 6.5 and 11mm of theoretical fragment length (TFL)). The DM content did not affect the average fragment size of 2B688. For SPEED, however, the real fragment size decreased as the maturation of plants increased. The conclusion is that the DM content and harvester adjustments can affect the real fragment sizes, according to different plant genotypes. The alterations of the harvester adjustments resulted in different fragment sizes, however, it were different from those indicated by the manufacturer.