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.

Membrane properties of structurally modified ceramides : effects on lipid lateral distribution and sphingomyelin-interactions in artificial bilayer membranes

Ceramides comprise a class of sphingolipids that exist only in small amounts in cellular membranes, but which have been associated with important roles in cellular signaling processes. The influences that ceramides have on the physical properties of bilayer membranes reach from altered thermodynamical behavior to significant impacts on the molecular order and lateral distribution of membrane lipids. Along with the idea that the membrane physical state could influence the physiological state of a cell, the membrane properties of ceramides have gained increasing interest. Therefore, membrane phenomena related to ceramides have become a subject of intense study both in cellular as well as in artificial membranes. Artificial bilayers, the so called model membranes, are substantially simpler in terms of contents and spatio-temporal variation than actual cellular membranes, and can be used to give detailed information about the properties of individual lipid species in different environments. This thesis focuses on investigating how the different parts of the ceramide molecule, i.e., the N-linked acyl chain, the long-chain sphingoid base and the membrane-water interface region, govern the interactions and lateral distribution of these lipids in bilayer membranes. With the emphasis on ceramide/sphingomyelin(SM)-interactions, the relevance of the size of the SMhead group for the interaction was also studied. Ceramides with methylbranched N-linked acyl chains, varying length sphingoid bases, or methylated 2N (amide-nitrogen) and 3O (C3-hydroxyl) at the interface region, as well as SMs with decreased head group size, were synthesized and their bilayer properties studied by calorimetric and fluorescence spectroscopic techniques. In brief, the results showed that the packing of the ceramide acyl chains was more sensitive to methyl-branching in the mid part than in the distal end of the N-linked chain, and that disrupting the interfacial structure at the amide-nitrogen, as opposed to the C3-hydroxyl, had greater effect on the interlipid interactions of ceramides. Interestingly, it appeared that the bilayer properties of ceramides could be more sensitive to small alterations in the length of the long-chain base than what was previously reported for the N-linked acyl chain. Furthermore, the data indicated that the SM-head group does not strongly influence the interactions between SMs and ceramides. The results in this thesis illustrate the pivotal role of some essential parts of the ceramide molecules in determining their bilayer properties. The thesis provides increased understanding of the molecular aspects of ceramides that possibly affect their functions in biological membranes, and could relate to distinct effects on cell physiology.

A modified structural stress method for fatigue assessment of welded structures

Fatigue life assessment of weldedstructures is commonly based on the nominal stress method, but more flexible and accurate methods have been introduced. In general, the assessment accuracy is improved as more localized information about the weld is incorporated. The structural hot spot stress method includes the influence of macro geometric effects and structural discontinuities on the design stress but excludes the local features of the weld. In this thesis, the limitations of the structural hot spot stress method are discussed and a modified structural stress method with improved accuracy is developed and verified for selected welded details. The fatigue life of structures in the as-welded state consists mainly of crack growth from pre-existing cracks or defects. Crack growth rate depends on crack geometry and the stress state on the crack face plane. This means that the stress level and shape of the stress distribution in the assumed crack path governs thetotal fatigue life. In many structural details the stress distribution is similar and adequate fatigue life estimates can be obtained just by adjusting the stress level based on a single stress value, i.e., the structural hot spot stress. There are, however, cases for which the structural stress approach is less appropriate because the stress distribution differs significantly from the more common cases. Plate edge attachments and plates on elastic foundations are some examples of structures with this type of stress distribution. The importance of fillet weld size and weld load variation on the stress distribution is another central topic in this thesis. Structural hot spot stress determination is generally based on a procedure that involves extrapolation of plate surface stresses. Other possibilities for determining the structural hot spot stress is to extrapolate stresses through the thickness at the weld toe or to use Dong's method which includes through-thickness extrapolation at some distance from the weld toe. Both of these latter methods are less sensitive to the FE mesh used. Structural stress based on surface extrapolation is sensitive to the extrapolation points selected and to the FE mesh used near these points. Rules for proper meshing, however, are well defined and not difficult to apply. To improve the accuracy of the traditional structural hot spot stress, a multi-linear stress distribution is introduced. The magnitude of the weld toe stress after linearization is dependent on the weld size, weld load and plate thickness. Simple equations have been derived by comparing assessment results based on the local linear stress distribution and LEFM based calculations. The proposed method is called the modified structural stress method (MSHS) since the structural hot spot stress (SHS) value is corrected using information on weld size andweld load. The correction procedure is verified using fatigue test results found in the literature. Also, a test case was conducted comparing the proposed method with other local fatigue assessment methods.