Bounds for the solution of hyperbolic problems

This article describes a newly developed and implemented method for computing guaranteed errorbounds for the solution of hyperbolic initial value problems. The basic concepts—modified fixed point theorems and approximated operators—allow an a posteriori error-estimation automatically. Therefore, no a priori knowledge of Lipschitz constants, monotonicity properties or additional error analysis is necessary.     

Biaxiale Ermüdung reibrührgeschweißter Strukturelemente

Biaxial fatigue of friction stir welded stiffened panels Within the framework of the European WelAir project, cruciform specimens made from stiffening FSW overlap joints were fatigued in the DLR biaxial test rig. To resemble the loading situation of pressurized fuselage structures, proportional loading without any phase shift, but with different load ratios λ between the loading components in both directions was applied.Natural crack initiation and subsequent crack growth were governed by the stiffness gradient caused by introducing the stringer. Cracks initiated and propagated at run‐in and run‐out locations in a direction perpendicular to the weld seam. The shortest fatigue life was observed for uniaxial loading in welding direction (λ = 0). An additional stress component perpendicular to the joint line (λ > 0) resulted in a higher number of cycles to failure. Similar to single stringer panels, increasing the load ratio also increased the number of cycles to failure for FSW clip‐stringer structural members, but additionally gives a different location of the fatal crack.     

Possibilities and extension of XRD material response analysis in failure research for the advanced evaluation of the damage level of Hertzian loaded components

Due to clearly distinguishable damage symptoms, it is differentiated between the surface and sub‐surface failure mode of rolling bearings. Material states red out by X‐ray diffraction (XRD) residual stress measurements point to a variety of loading conditions especially at raceway surfaces that are associated with several competing failure mechanisms. The corresponding lifetime reduction can range from the lower fatigue strength region to material ratcheting in extreme cases. Relevant position of the microstructural changes and nature of the failure mechanisms are characterized. The time alteration of the XRD material parameters measured at or near the surface and at the depth of the maximum equivalent stress correlates, in a different manner, with the statistical parameter of the 10 % bearing life. Both failure modes are illustrated by concrete examples. Contaminated lubricant and boundary lubrication, which represent practically important surface‐induced failures, are discussed in more detail. Gray staining, i.e. shallow pitting, often occurs without distinct indication of global material aging by means of XRD characteristics. Here, scanning electron microscopy observations and electron microprobe analyses point to corrosion fatigue as acting surface failure mechanism. The interaction between material and lubricant under complex loading regimes particularly of mixed friction and corrosion opens further failure research areas in the field of tribology.     

Radiale Wärmeleitung in durchströmten Schüttungsrohren

Heat Transport to the Wall of Packed Tubes. Radial conduction of heat in packed tubes has a crucial influence on yield and selectivity of many heterogeneously catalyzed reactions. In spite of many years of intensive research in the field, there are still tremendous discrepancies between correlations of different origin. Even the standard model using two constant heat transport parameters, which was introduced in the fifties and has since become most widely accepted, has been controversially discussed and called into question. The unsatisfactory state of the art has been an incentive for several groups of researchers to take up this old topic once again. Three parallel experimental investigations on heat transport with air flowing in packed tubes of similar dimensions, electrically heated, steam-heated, or water-cooled, were completed in 1991. Comparative evaluation of the results of these three investigations, together with other data from the relevant literature, now provides the first clear answers to some of the questions so controversially discussed in the past.