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

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

Experimental results and fatigue life evaluation of magnesium laserbeam-welded joints under proportional and non-proportional multiaxial fatigue loading with variable amplitudes

Fatigue life of magnesium laserbeam-welds (AZ31 and AZ61 alloys) was assessed experimentally under variable amplitude loadings. The specimens were subjected to load-controlled cyclic loadings. The tests were carried out using a Gauss-distributed amplitude sequence of length L-S = 5.10(4) cycles and loading ratio R = -1 under pure axial, pure torsion as well as in-phase and out-of-phase combined loadings. The notch stresses were obtained from a linear-elastic FE-model using the reference radius approach with r(ref) = 0.05 mm. The stress-based hypotheses were applied: Effective equivalent stress hypothesis (EESH), shear stress intensity hypothesis (SIH), Findley, and modified Gough-Pollard. A non-proportionality factor is introduced and steps required for computing are presented in order to improve fatigue life assessment under non-proportional 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  RR " ", " " 1  . For the tests with variable amplitude loads a Gaußdistributed loading spectrum with S L 4 5 10  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 loading

Extreme Yield Figures for Universal Strength Criteria

We propose a universal, generally applicable yield criterion that describes a single convex surface in principal stress space encompassing extreme yield figures as convexity limits. The novel criterion is derived phenomenologically exploiting geometrical properties of yield surfaces in principal stress space. It is systematically compared with known yield criteria using different forms of visualization. Using a I1-substitution the criterion is applicable to materials with pressure-sensitive behavior and contains well-known strength criteria. Introducing appropriate parameter restrictions, it can be applied for the modeling of ductile and brittle material behavior. The implementation of the present criterion eliminates the necessity of choosing a specific yield criterion for a particular material. The proposed criterion allows for excellent approximation of experimental data. It is applied to measured data of concrete and provides better accuracy than existing criteria from literature