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.

Eri laskentamenetelmien vertailu hitsatun rakenteen väsymislaskennassa

Tässä työssä tutkittiin eri mitoitusmenetelmien soveltuvuutta hitsattujen rakenteiden vä-symislaskennassa. Käytetyt menetelmät olivat rakenteellinen jännityksen menetelmä, te-hollisen lovijännityksen menetelmä ja murtumismekaniikka. Lisäksi rakenteellisen jänni-tyksen määrittämiseksi käytettiin kolmea eri menetelmää. Menetelmät olivat pintaa pitkin ekstrapolointi, paksuuden yli linearisointi ja Dongin menetelmä. Väsymiskestävyys määritettiin kahdelle hitsiliitoksen yksityiskohdalle. Laskenta tehtiin käyttäen elementtimenetelmää rakenteen 3D-mallille. Tutkittavasta aggregaattirungosta oli olemassa FE-malli mutta alimallinnustekniikkaa hyödyntämällä pystyttiin yksityiskohtai-semmin tutkimaan vain pientä osaa koko rungon mallista. Rakenteellisen jännityksen menetelmä perustuu nimellisiin jännityksiin. Kyseinen mene-telmä ei vaadi geometrian muokkausta. Yleensä rakenteellisen jännityksen menetelmää käytetään hitsin rajaviivan väsymislaskennassa, mutta joissain tapauksissa sitä on käytetty juuren puolen laskennassa. Tässä työssä rakenteellisen jännityksen menetelmää käytettiin myös juuren puolen tutkimisessa. Tehollista lovijännitystä tutkitaan mallintamalla 1 mm fiktiiviset pyöristykset sekä rajaviivalle että juuren puolelle. Murtumismekaniikan so-veltuvuutta tutkittiin käyttämällä Franc2D särön kasvun simulointiohjelmaa. Väsymislaskennan tulokset eivät merkittävästi poikkea eri laskentamenetelmien välillä. Ainoastaan rakenteellisen jännityksen Dongin menetelmällä saadaan poikkeavia tuloksia. Tämä johtuu pääasiassa siitä, että menetelmän laskentaetäisyydestä ei ole tietoa. Raken-teellisen jännityksen menetelmällä, tehollisen lovijännityksen menetelmällä ja murtumis-mekaniikalla saadaan samansuuntaiset tulokset. Suurin ero menetelmien välillä on mal-linnuksen ja laskennan vaatima työmäärä.

Computational modelling of non-equilibrium condensing steam flows in low-pressure steam turbines

The steam turbines play a significant role in global power generation. Especially, research on low pressure (LP) steam turbine stages is of special importance for steam turbine man- ufactures, vendors, power plant owners and the scientific community due to their lower efficiency than the high pressure steam turbine stages. Because of condensation, the last stages of LP turbine experience irreversible thermodynamic losses, aerodynamic losses and erosion in turbine blades. Additionally, an LP steam turbine requires maintenance due to moisture generation, and therefore, it is also affecting on the turbine reliability. Therefore, the design of energy efficient LP steam turbines requires a comprehensive analysis of condensation phenomena and corresponding losses occurring in the steam tur- bine either by experiments or with numerical simulations. The aim of the present work is to apply computational fluid dynamics (CFD) to enhance the existing knowledge and understanding of condensing steam flows and loss mechanisms that occur due to the irre- versible heat and mass transfer during the condensation process in an LP steam turbine. Throughout this work, two commercial CFD codes were used to model non-equilibrium condensing steam flows. The Eulerian-Eulerian approach was utilised in which the mix- ture of vapour and liquid phases was solved by Reynolds-averaged Navier-Stokes equa- tions. The nucleation process was modelled with the classical nucleation theory, and two different droplet growth models were used to predict the droplet growth rate. The flow turbulence was solved by employing the standard k-ε and the shear stress transport k-ω turbulence models. Further, both models were modified and implemented in the CFD codes. The thermodynamic properties of vapour and liquid phases were evaluated with real gas models. In this thesis, various topics, namely the influence of real gas properties, turbulence mod- elling, unsteadiness and the blade trailing edge shape on wet-steam flows, are studied with different convergent-divergent nozzles, turbine stator cascade and 3D turbine stator-rotor stage. The simulated results of this study were evaluated and discussed together with the available experimental data in the literature. The grid independence study revealed that an adequate grid size is required to capture correct trends of condensation phenomena in LP turbine flows. The study shows that accurate real gas properties are important for the precise modelling of non-equilibrium condensing steam flows. The turbulence modelling revealed that the flow expansion and subsequently the rate of formation of liquid droplet nuclei and its growth process were affected by the turbulence modelling. The losses were rather sensitive to turbulence modelling as well. Based on the presented results, it could be observed that the correct computational prediction of wet-steam flows in the LP turbine requires the turbulence to be modelled accurately. The trailing edge shape of the LP turbine blades influenced the liquid droplet formulation, distribution and sizes, and loss generation. The study shows that the semicircular trailing edge shape predicted the smallest droplet sizes. The square trailing edge shape estimated greater losses. The analysis of steady and unsteady calculations of wet-steam flow exhibited that in unsteady simulations, the interaction of wakes in the rotor blade row affected the flow field. The flow unsteadiness influenced the nucleation and droplet growth processes due to the fluctuation in the Wilson point.