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.

A Practical Micro Mechanical Model Based Local Approach Methodology for the Analysis of Ductile Fracture of Welded T-Joints

This thesis concentrates on developing a practical local approach methodology based on micro mechanical models for the analysis of ductile fracture of welded joints. Two major problems involved in the local approach, namely the dilational constitutive relation reflecting the softening behaviour of material, and the failure criterion associated with the constitutive equation, have been studied in detail. Firstly, considerable efforts were made on the numerical integration and computer implementation for the non trivial dilational Gurson Tvergaard model. Considering the weaknesses of the widely used Euler forward integration algorithms, a family of generalized mid point algorithms is proposed for the Gurson Tvergaard model. Correspondingly, based on the decomposition of stresses into hydrostatic and deviatoric parts, an explicit seven parameter expression for the consistent tangent moduli of the algorithms is presented. This explicit formula avoids any matrix inversion during numerical iteration and thus greatly facilitates the computer implementation of the algorithms and increase the efficiency of the code. The accuracy of the proposed algorithms and other conventional algorithms has been assessed in a systematic manner in order to highlight the best algorithm for this study. The accurate and efficient performance of present finite element implementation of the proposed algorithms has been demonstrated by various numerical examples. It has been found that the true mid point algorithm (a = 0.5) is the most accurate one when the deviatoric strain increment is radial to the yield surface and it is very important to use the consistent tangent moduli in the Newton iteration procedure. Secondly, an assessment of the consistency of current local failure criteria for ductile fracture, the critical void growth criterion, the constant critical void volume fraction criterion and Thomason's plastic limit load failure criterion, has been made. Significant differences in the predictions of ductility by the three criteria were found. By assuming the void grows spherically and using the void volume fraction from the Gurson Tvergaard model to calculate the current void matrix geometry, Thomason's failure criterion has been modified and a new failure criterion for the Gurson Tvergaard model is presented. Comparison with Koplik and Needleman's finite element results shows that the new failure criterion is fairly accurate indeed. A novel feature of the new failure criterion is that a mechanism for void coalescence is incorporated into the constitutive model. Hence the material failure is a natural result of the development of macroscopic plastic flow and the microscopic internal necking mechanism. By the new failure criterion, the critical void volume fraction is not a material constant and the initial void volume fraction and/or void nucleation parameters essentially control the material failure. This feature is very desirable and makes the numerical calibration of void nucleation parameters(s) possible and physically sound. Thirdly, a local approach methodology based on the above two major contributions has been built up in ABAQUS via the user material subroutine UMAT and applied to welded T joints. By using the void nucleation parameters calibrated from simple smooth and notched specimens, it was found that the fracture behaviour of the welded T joints can be well predicted using present methodology. This application has shown how the damage parameters of both base material and heat affected zone (HAZ) material can be obtained in a step by step manner and how useful and capable the local approach methodology is in the analysis of fracture behaviour and crack development as well as structural integrity assessment of practical problems where non homogeneous materials are involved. Finally, a procedure for the possible engineering application of the present methodology is suggested and discussed.

A Micromechanics-Based Damage Model for [± θ / 90n ]s Composite Laminates

A new damage model based on a micromechanical analysis of cracked [± θ / 90n ]s laminates subjected to multiaxial loads is proposed. The model predicts the onset and accumulation of transverse matrix cracks in uniformly stressed laminates, the effect of matrix cracks on the stiffness of the laminate, as well as the ultimate failure of the laminate. The model also accounts for the effect of the ply thickness on the ply strength. Predictions relating the elastic properties of several laminates and multiaxial loads are presented

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.

Atomic diffusion induced by stress relaxation in InGaAs/GaAs epitaxial layers

The origin of the microscopic inhomogeneities in InxGa1-xAs layers grown on GaAs by molecular beam epitaxy is analyzed through the optical absorption spectra near the band gap. It is seen that, for relaxed thick layers of about 2.8μm, composition inhomogeneities are responsible for the band edge smoothing into the whole compositional range (0.05elastic energy. An additional support to this hypothesis is given by a clear proportionality between the magnitude of the composition variations and the mean strain

Avaliação de géis obtidos a partir da acetilação da quitosana em meio heterogêneo

Chitosan was acetylated during 2, 5 and 10h and physical gels were obtained at different polymer concentrations in N,N-dimethylacetamide containing 5% of LiCl. Acetylation was confirmed by infrared spectroscopy and 13C NMR, and degrees of acetylation in the range of 0.82-0.91 were determined by NMR. The O-acetylation degree (0.12-0.15) was exclusively determined by a volumetric method. Rheological studies showed that the storage modulus values were smaller for the more acetylated samples and increased with the temperature and the polymer concentration. All the gels presented storage modulus superior to loss modulus, evidencing more elastic than viscous characteristics. The results obtained in this work suggest a gelation process based on a balance between O and N-acetylation and intermolecular bonds.

Propriedades eletrônicas, estruturais e constantes elásticas do ZnO

The electronic, structural properties and elastic constants of the wurtzite phase of zinc oxide, ZnO, was investigated using computer simulation at Density Functional Theory level, with B3LYP hybrid functional and Hartree-Fock methodology. The electronic properties as well the band energy was investigated through the analysis of the band structures and density of states (DOS), and the mechanical properties was studied through the calculus of the elastic constants C11, C33, C44, C12 e C13. The results are in good agreement with experimental data found in the literature and in accordance with results obtained by another theoretical methodology.

Rheological and thermal characteristics of wheat gluten biopolymers plasticized with glycerol

The objective this work was to obtain bioplastics from mixtures of wheat gluten and glycerol by two different processes and evaluate their respective rheological properties. The mixtures and their respective bioplastics were obtained through direct batch mixing under approximately adiabatic and isothermal conditions. The bioplastics showed high values for the storage (G') and loss (G") moduli, suggesting a stronger protein network formed in both processes. The temperature onset and the percentage of weight loss to be estimated were found to be near in both bioplastics. The bioplastics have demonstrated to be materials of interesting potential of use as biodegradable barrier materials.

A NOVEL POLYACRYLAMIDE-BASED HYDROGEL CROSSLINKED WITH CELLULOSE ACETATE AND PREPARED BY PRECIPITATION POLYMERIZATION

The synthesis of polyacrylamide-cellulose acetate hydrogels by precipitation polymerization in acetone solution is reported herein. These hydrogels exhibit smaller swelling ratios and larger compression moduli than homo polyacrylamide hydrogels. For cellulose acetate concentrations above 20 wt.%, hydrogels with N,N'-methylenebisacrylamide as a crosslinker exhibit swelling ratios and compression moduli similar to those of the hydrogels without the crosslinker. A possible explanation for this behavior is that cellulose acetate crosslinks polyacrylamide via free-radical reaction. The hydrogels obtained without the N,N'-methylenebisacrylamide crosslinker exhibit compression moduli up to 1.7 MPa, making them suitable for tissue engineering applications such as cartilage replacement.

Conformal invariants

This master thesis investigates the moduli of families of curves and the capacities of the Gr¨otzsch and Teichm¨uller rings, which are applied in the main parts of this master thesis. The extremal properties of these rings are discussed in connection with the spherical symmetrization. Applications are given to the study of distortion of quasiconformal maps in the euclidean n-dimensional space.

Natural and synthetic fibres improving tensile strength and elongation of paper products

The theory part of the Master’s thesis introduces fibres with high tensile strength and elongation used in the production of paper or board. Strong speciality papers are made of bleached softwood long fibre pulp. The aim of the thesis is to find new fibres suitable for paper making to increase either tensile strength, elongation or both properties. The study introduces how fibres bond and what kind of fibres give the strongest bonds into fibre matrix. The fibres that are used the in manufacturing of non-wovens are long and elastic. They are longer than softwood cellulose fibres. The end applications of non-wovens and speciality papers are often the same, for instance, wet napkins or filter media. The study finds out which fibres are used in non-wovens and whether the same fibres could be added to cellulose pulp as armature fibres, what it would require for these fibres to be blended in cellulose, how they would bind with cellulose and whether some binding agents or thermal bonding, such as hot calendaring would be necessary. The following fibres are presented: viscose, polyester, nylon, polyethylene, polypropylene and bicomponent fibres. In the empiric part of the study the most suitable new fibres are selected for making hand sheets in laboratory. Test fibres are blended with long fibre cellulose. The test fibres are viscose (Tencel), polypropylene and polyethylene. Based on the technical values measured in the sheets, the study proposes how to continue trials on paper machine with viscose, polyester, bicomponent and polypropylene fibres.

The Effects of Some Furnish and Paper Structure Related Factors on Wet Web Tensile and Relaxation Characteristics

The objective of this thesis was to identify the effects of different factors on the tension and tension relaxation of wet paper web after high-speed straining. The study was motivated by the plausible connection between wet web mechanical properties and wet web runnability on paper machines shown by previous studies. The mechanical properties of wet paper were examined using a fast tensile test rig with a strain rate of 1000%/s. Most of the tests were carried out with laboratory handsheets, but samples from a pilot paper machine were also used. The tension relaxation of paper was evaluated as the tension remaining after 0.475 s of relaxation (residual tension). The tensile and relaxation properties of wet webs were found to be strongly dependent on the quality and amount of fines. With low fines content, the tensile strength and residual tension of wet paper was mainly determined by the mechanical interactions between fibres at their contact points. As the fines strengthen the mechanical interaction in the network, the fibre properties also become important. Fibre deformations caused by the mechanical treatment of pulp were shown to reduce the mechanical properties of both dry and wet paper. However, the effect was significantly higher for wet paper. An increase of filler content from 10% to 25% greatly reduced the tensile strength of dry paper, but did not significantly impair wet web tensile strength or residual tension. Increased filler content in wet web was shown to increase the dryness of the wet web after the press section, which partly compensates for the reduction of fibrous material in the web. It is also presumable that fillers increase entanglement friction between fibres, which is beneficial for wet web strength. Different contaminants present in white water during sheet formation resulted in lowered surface tension and increased dryness after wet pressing. The addition of different contaminants reduced the tensile strength of the dry paper. The reduction of dry paper tensile strength could not be explained by the reduced surface tension, but rather on the tendency of different contaminants to interfere with the inter-fibre bonding. Additionally, wet web strength was not affected by the changes in the surface tension of white water or possible changes in the hydrophilicity of fibres caused by the addition of different contaminants. The spraying of different polymers on wet paper before wet pressing had a significant effect on both dry and wet web tensile strength, whereas wet web elastic modulus and residual tension were basically not affected. We suggest that the increase of dry and wet paper strength could be affected by the molecular level interactions between these chemicals and fibres. The most significant increases in dry and wet paper strength were achieved with a dual application of anionic and cationic polymers. Furthermore, selectively adding papermaking chemicals to different fibre fractions (as opposed to adding chemicals to the whole pulp) improved the wet web mechanical properties and the drainage of the pulp suspension.

Uusia kirjoja

Kirjallisuusarvostelu

The position effect of structural Eucalyptus round timber on the flexural modulus of elasticity

Round timber has great use in civil construction, performing the function of beams, columns, foundations, poles for power distribution among others, with the advantage of not being processed, such as lumber. The structural design of round timber requires determining the elastic properties, mainly the modulus of elasticity. The Brazilian standards responsible for the stiffness and strength determination of round timber are in effect for over twenty years with no technical review. Round timber, for generally present an axis with non-zero curvature according to the position of the element in the bending test, may exhibit different values of modulus of elasticity. This study aims to analyze the position effect of Eucalyptus grandis round timber on the flexural modulus of elasticity. The three-point bending test was evaluated in two different positions based on the longitudinal rotation of the round timber element. The results revealed that at least two different positions of the round timber element are desired to obtain significant modulus of elasticity.

Static tests of constructive tires using hydraulic press on the soil

ABSTRACT The power consumption and load capacity of agricultural machines have grown and the effects of pressure on the soil by tires have been still little investigated. In concern with sustainable development, the relationship machine-tire-soil must be in balance to give more consistency on the best use of tires for a given load. This study aimed to evaluate four tires of two constructive types, the bias belted tires and radial tires, both with respective rim diameters of 22.5 and 26.5 inches with variables measuring the footprint, elastic deformation, sinkage and resistance to penetration. A hydraulic press with an attachment shaft for tire mounting and a box of soil in which the tire has been imposed on a load of 53.00 kN using nominal pressures recommended by the tire manufacturer. The radial construction tire with rim diameter of 26.5 inches obtained less sinkage and resistance to penetration; however, greater elastic deformation and footprint compared to other tires. The bias-belted tire with 22.5-inch rim presented the highest resistance to penetration and the lowest elastic deformation.