Numerical measures of the degree of non-proportionality of multiaxial fatigue loadings

The influence of the non-proportional loadings on the fatigue life depends on the material ductility. Ductile materials react with a shortening of lifetime compared to proportional loading conditions. For a semiductile material there is almost no difference between proportional and non-proportional loadings with respect to the fatigue life. Brittle materials show an increase of the lifetime under non-proportional loadings. If fatigue life assessment is performed using stress-based hypotheses, it is a rather difficult task to take into account material ductility correctly, especially the fatigue life reduction as displayed by ductile materials. Most stress-based hypotheses will compute a longer fatigue life under non-proportional loading conditions. There are also hypotheses, which already include quantitative evaluation of the non-proportionality (e.g. EESH, SSCH and MWCM). Anyway in order to improve assessment for ductile materials, some sort of numerical measure for the degree of non-proportionality of the fatigue loading is required. A number of measures of this kind (or non-proportionality factors) were proposed in the literature and are discussed here: - the factor used in EESH is a quotient of stress amplitudes integrals, - the factor according to Gaier, which works with a discrete stress tensor values in a scaled stress space, - the factor according to Kanazawa, which makes use of plane-based stress values, - the factor used in MWCM, which exploits stress values in the plane with the highest shear stress amplitude, a new non-proportionality factor, which is based on the correlation between individual stress tensor components, is proposed. General requirements imposed on the non-proportionality factors are discussed and each of the factors is evaluated with respect to these requirements. Also application with the stress-based hypotheses is discussed and illustrated using the experimental data for aluminum and magnesium welded joints under constant and variable amplitude loadings

Fatigue life assessment of thin-walled welded joints under non-proportional load-time histories by the shear stress rate integral approach

Fatigue life tests under constant and variable amplitude loadings were performed on the tube-tube thin-walled welded specimens made of magnesium (AZ31 and AZ61) alloys. The tests included pure axial, pure torsional and combined in-phase and out-of-phase loadings with the load ratio "R ",?"R "? ? ?1. For the tests with variable amplitude loads a Gaußdistributed loading spectrum with LS ? 5?104 cycles was used. Since magnesium welds show a fatigue life reduction under out-of-phase loads, a stress-based method, which takes this behavior into account, is proposed. The out-of-phase loading results in rotating shear stress vectors in the section planes, which are not orthogonal to the surface. This fact is used in order to provide an out-of-phase measure of the load. This measure is computed as an area covered by the shear stress vectors in all planes over a certain time interval, its computation involves the shear stress and the shear stress rate vectors in the individual planes. Fatigue life evaluation for the variable amplitudes loadings is performed using the Palmgren-Miner linear damage accumulation, whereas the total damage of every cycle is split up into two components: the amplitude component and the out-of-phase component. In order to compute the two components a modification of the rainflow counting method, which keeps track of the time intervals, where the cycles occur, must be used. The proposed method also takes into account different slopes of the pure axial and the pure torsional Wöhler-line by means of a Wöhler-line interpolation for combined loadings.&nbsp

The robustness, link-species relationship and network properties of model food webs

New results are collected using the Webworld model which simulates evolutionary food web construction with population dynamics (Drossel et al., 2001 [1]). We show that it supports a link-species relationship of neither constant link-density nor constant connectance, and new properties for the food webs are calculated including clustering coefficients and stability in the sense of community robustness to species deletion. Time-series for more than 40 properties of the taxonomic and trophic webs are determined over the course of individual simulations. Robustness is found to be positively correlated with connectance, but negatively with diversity, and we study the long-term development of model webs including the distribution of extinction events in a simulation with 108 speciation event

Spatial topologies affect local food web structure and diversity in evolutionary metacommunities

An important challenge in theoretical ecology is to better predict ecological responses to environmental change, and in particular to spatial changes such as habitat fragmentation. Classical food-web models have focused on purely ecological predictions, without taking adaptation or evolution of species traits into account. We address this issue using an eco-evolutionary model, which is based on body masses and diets as the key traits that determine metabolic rates and trophic interactions. The model implements evolution by the introduction of new morphs that are related to the existing ones, so that the network structure itself evolves in a self-organized manner. We consider the coupling and decoupling of habitats in multi-trophic metacommunities consisting of 2 or 4 habitats. Our model thus integrates metacommunity models, which describe ecosystems as networks of networks, with large community evolution models. We find that rescue effects and source-sink effects occur within coupled habitats, which have the potential to change local selection pressures so that the local food web structure shows a fingerprint of its spatial conditions. Within our model system, we observe that habitat coupling increases the lifetimes of top predators and promotes local biodiversity

Eine Methode zur Festigkeitsbeurteilung von laserstrahlgeschweißten Magnesium-Verbindungen unter mehrachsigen Beanspruchungen mit konstanten und variablen Amplituden

Im Rahmen der vorliegenden Arbeit wird das Schwingfestigkeitsverhalten der dünnwandigen laserstrahlgeschweißten Magnesium-Verbindungen unter mehrachsigen phasengleichen und phasenverschobenen Belastungen mit variablen Amplituden untersucht. Dies ermöglicht eine Überprüfung mehrerer bestehender Schwingfestigkeitshypothesen im Hinblick auf ihre Anwendbarkeit für Magnesium-Schweißungen. Es werden außerdem die tatsächlichen Schadenssummen abgeleitet und es wird eine zulässige Schadenssumme festgelegt. Diese ist für die Bauteilauslegung unter mehrachsigen Belastungen mit variablen Amplituden notwendig. Die meisten Mehrachsigkeitshypothesen können entweder das Werkstoffverhalten unter mehrachsigen nichtproportionalen Beanspruchungen sehr grob abbilden (Interaktionsgleichungen aus den Regelwerken) oder sie sind nur auf Beanspruchungen spezieller Art anwendbar (SSCH, WVS). In dieser Arbeit wird eine Mehrachsigkeitshypothese entwickelt, die in der Lage ist, das Werkstoffverhalten unter mehrachsigen phasengleichen und phasenverschobenen Belastungen mit variablen Amplituden zu beschreiben, und zwar bei beliebigen unkorrelierten lokalen Beanspruchungskomponenten

Testing of Multi-Axial Strength Behavior of Hard Foams

For modern applications of hard foams an appropriate description of the limit behavior under different stress states are required. So a newstrength hypothesis based on the stress-angle is proposed. In order to obtain the parameters of the model, relevant tests are discussed. The quality of approximation of the experimental data by a limit surface must be evaluated. Some evaluation criteria are discussed and applied to the measured data from the literature. The results of the fitting are presented in the BURZY´NSKI-plane and in the p-plane. The presented approach reduces the number of errors in fitting of the limit surface. Certain empiric restrictions help to obtain reliable fitting even for insufficient or unsure measurements

Study of Time-Dependent Properties of Thermoplastics

Simple tests carried out with a common tension/compression testing machine are used to obtain timedependent properties of non-reinforced thermoplastics. These tests include ramp loadings as well as relaxation and creep tests. Two materials (PBT Celanex 2002-2 and POM Hostaform C9021, Ticona GmbH, Kelsterbach) were taken for the experiments. The experiments show that an adequate description of the long-term material properties can be obtained from the short-time tests, namely from tests with constant traverse speed $L^.$. Below a model for the time-dependent mechanical behavior is presented and fitted to the obtained measured data. For the evaluation of the fitting quality long-term tests are used. Especially creep and relaxation tests with ”jumps”, i.e. rapid change of loading, are important for this purpose