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.

On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.

Testiohjelmiston kehittäminen väsytyskokeiden suorittamiseksi mielivaltaisilla kuormituksilla

Väsytyskokeita on väsymisilmiön keksimisestä lähtien tehty pääasiallisesti vakioamplitudisella kuormituksella. Paremmin todellisuutta kuvaavaan testitilanteeseen päästään kuitenkin vain käyttämällä testattavan rakenteen reaalikuormitusta simuloivaa muuttuva-amplitudista kuormitusta. Tällaisen kuormituksen testaaminen käytännössä on kuitenkin huomattavasti vaikeampaa kuin perinteisen vakioamplitudisen kuormituksen, koska muuttuva-amplitudisen kuormituksen spektri on ensin kehitettävä jostain – joko käytännön mittausten kautta tai rakenteen käyttötilaa analysoimalla. Myöskään tiedossa olevan spektrin tuottaminen käytännön kokeissa ei ole aivan yksinkertaista. Tässä kandidaatintyössä pyrittiin ratkaisemaan näitä ongelmia suunnittelemalla ja toteuttamalla testiohjelmisto, joka pystyy sekä generoimaan että käytännössä toistamaan käyttäjän haluaman kuormitusspektrin laboratoriokokeissa. Jälkimmäistä varten oli olemassa ohjelma, jota haluttiin hyödyntää tässä työssä. Tehtävä jaettiin kolmeen osioon: kuormitusspektrien generoiminen, kuormitusspektrien yhdistäminen ja lopuksi spektrien toistaminen itse väsytyskokeessa. Kahdessa ensimmäisessä osiossa käytettiin ohjelmointiympäristönä Matlab-ohjelmaa; kolmannessa käytettiin pohjana olemassa olevaa väsytyskoeohjelmaa ja käytännön ohjelmointi suoritettiin näin ollen ANSI C –kielellä käyttäen kääntäjänä Microsoft Visual Studio 6.0:aa. Alkuperäinen väsytyskoeohjelma vaati useita merkittäviä muutoksia, ennen kuin se soveltui käytettäväksi tässä yhteydessä. Työssä on kuvattu periaatetasolla ohjelmien suunnittelu- ja toteuttamisvaiheet. Lisäksi työn on tarkoitus toimia yksinkertaisena käyttöohjeena ja opastuksena koko ohjelmiston käyttöön.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Considerations on corrosion and weld repair effects on the fatigue strength of a steel structure critical to the flight-safety

The aim of this study is to analyze the effects of corrosion and successive tungsten inert gas (TIC) welding repairs on the reverse bending fatigue strength of AISI 4130 steel used in components critical to the flight-safety. The tests were performed on hot-rolled steel plate specimens, 1.10 mm and 1.60 mm thick, by means of a SCHENK PWS equipment, with load ratio R = -1, constant amplitude, 30 Hz frequency and room temperature. It was observed that the reverse bending fatigue strength of AISI 4130 steel decreases due to the corrosion and the TIC welding and re-welding processes. (C) 2010 Elsevier Ltd. All rights reserved.

Repair Welding Effects on the Bending Fatigue Strength of AISI 4130 Aeronautical Steel used in a Critical to the Flight-Safety Structure

The aim of this study was to analyze the effect of successive TIG (tungsten inert gas) welding repairs on the reverse bending fatigue strength of AISI 4130 steel, which is widely used in components critical to the flight-safety. In order to simulate the abrupt maneuvers, wind bursts, motor vibration and helixes efforts, which generate cyclic bending loadings at the welded joints of a specific aircraft component called motor cradle, experimental reverse bending fatigue tests were carried out on specimens made from hot-rolled steel plate, 1.10 mm (0.043 in) thick, by mean of a SCHENK PWS equipment, with load ratio R = -1, under constant amplitude, at 30 Hz frequency and room temperature. It was observed that the bending fatigue strength decreases after the TIG (Tungsten Inert Gas) welding process application on AISI 4130 steel, with subsequent decrease due to re-welding sequence as well. Microstructural analyses and microhardness measurements on the base material, heat-affected zone (HAZ) and weld metal, as well as the effects of the weld bead geometry on the obtained results, have complemented this study.

Effects of several TIG weld repairs on the axial fatigue strength of AISI 4130 aeronautical steel-welded joints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Considerations about the welding repair effects on the structural integrity of an airframe critical to the flight-safety

Structures critical to the flight-safety are commonly submitted to several maintenance repairs at the welded joints in order to prolong the in-service life of aircrafts. The aim of this study is to analyze the effects of Tungsten Inert Gas (TIG) welding repair on the structural integrity of the AISI 4130 aeronautical steel by means of experimental fatigue crack growth tests in base-material, heat-affected zone (HAZ) and weld metal. The tests were performed on hot-rolled steel plate specimens, 0.89 mm thick, with load ratio R = 0.1, constant amplitude, at 10 Hz frequency and room temperature. Increase of the fracture resistance was observed in the weld metal but decreasing in the HAZ after repair. The results were associated to microhardness and microstructural changes with the welding sequence. (C) 2010 Published by Elsevier Ltd.

Fatigue strength of tungsten inert gas-repaired weld joints in airplane critical structures

In this work the effect of Gas Tungsten Arc Welding (GTAW) repairs on the axial fatigue strength of an AISI 4130 steel welded joint used in airframe critical to the flight-safety was investigated. Fatigue tests were performed at room temperature on 0.89 mm thick hot-rolled plates with constant amplitude and load ratio of R = 0.1, at 20 Hz frequency. Monotonic tensile tests, optical metallography and microhardness, residual stress and weld geometric factors measurements were also performed. The fatigue strength decreased with the number of GTAW repairs, and was related to microstructural and microhardness changes, as well as residual stress field and weld profile geometry factors, which gave origin to high stress concentration at the weld toe. (C) 2011 Elsevier B.V. All rights reserved.

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

Formation of bright solitons and soliton trains in a fermion-fermion mixture by modulational instability

We employ a time- dependent mean- field- hydrodynamic model to study the generation of bright solitons in a degenerate fermion - fermion mixture in a cigar- shaped geometry using variational and numerical methods. Due to a strong Pauli- blocking repulsion among identical spin- polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Modelling of fatigue crack growth following overloads

In variable-amplitude loading there are interaction effects between the loading history and the crack propagation rate. The most important of these effects is the retardation in the crack propagation, which may raise the life of the cracked structureconsiderably. The main objective of this research is to analyse and quantify the retardation of crack propagation in a thin plate of the high-resistance aluminium alloy 2024-T3, comparing the results obtained from the mathematical models proposed to account for the retardation effect. The specimens were tested under high-low loading sequences, for different crack sizes and overload ratios. A simplified model was developed, based on crack closure theory, that could represent the crack behaviour during retardation very well. © 1991.

Fatigue Behavior of Weld Repaired AISI 4130 Aeronautic Steel Used in Critical Flight Safety Structures

Since the 1950s, fatigue is the most important project and operational consideration for both civil and military aircrafts. For some aircraft models the most loaded component is one that supports the motor: the Motor Cradle. Because they are considered critical to the flight safety the aeronautic standards are extremely rigorous in manufacturing them by imposing a zero index of defects on the final weld quality (Safe Life), which is 100% inspected by Non-Destructive Testing/NDT. This study has as objective to evaluate the effects of up to four successive TIG welding repairs on the axial fatigue strength of an AISI 4130 steel. Tests were conducted on hot-rolled steel plate specimens, 0.89 mm thick, with load ratio R = 0.1, constant amplitude, at 20 Hz frequency and in room temperature, in accordance with ASTM E466 Standard. The results were related to microhardness and microstructural and geometric changes resulting from welding cycles.

Estudo do efeito do processo de shot peening na taxa de propagação de trinca por fadiga na liga aeronáutica 2024 - T3

Pós-graduação em Engenharia Mecânica - FEG