This paper presents a new algorithm to implement the Carpinteri–Spagnoli–Vantadori (CSV) multiaxial fatigue criterion for random loading and to shorten the computation time. This goal is achieved after calculating the exact expressions of stress spectral moments in every rotated plane, which allow the maximum variance and expected maximum peak of normal/shear stress to be computed directly. This permits the new algorithm to determine the five rotations of the critical plane without using ‘for/end’ loops (which represent a slow numerical operation), although some information on stress signals examined is lost. Two examples are presented to demonstrate the advantages of the new algorithm in comparison with its standard version, which are particularly remarkable when considering the stress output of all finite element model nodes. The approach behind the new algorithm can be extended to other multiaxial spectral criteria that use angular rotations or direction cosines to locate the critical plane or the direction of maximum stress variance.
This paper presents an overview of fatigue testing systems in high-cycle regime for metals subjected to uniaxial and multiaxial random loadings. The different testing systems are critically discussed, highlighting advantages and possible limitations. By identifying relevant features, the testing systems are classified in terms of type of machine (servo-hydraulic or shaker tables), specimen geometry and applied constraints, number of load or acceleration inputs needed to perform the test, type of loading acting on the specimen and resulting state of stress. Specimens with plate, cylindrical and more elaborated geometry are also considered as a further classification criterion. This review also discusses the relationship between the applied input and the resulting local state of stress in the specimen. Since a general criterion to classify fatigue testing systems for random loadings seems not to exist, the present review—by emphasizing analogies and differences among various layouts—may provide the reader with a guideline to classify future equipment.
The fatigue damage of a structure is usually estimated by calculating the damage values of a limited number of measured random time-histories. The limited damage values are generally not identical due to the sampling variability. In a recent work, confidence interval expressions have been proposed to bound the expected damage value. The method revealed a good agreement with simulations, thus suggesting its use also with real measurements. The present paper investigates the above-mentioned confidence intervals for expected damage by a real engineering application, in which few measured time-history records, or even only one, are available. This goal is achieved after measuring the random loadings acting on an instrumented Mountain-bike riding in a typical north Italian off-road track. As the whole ensemble of an infinite number of time-histories is not available and the expected damage is thus not known a priori, a sort of calibrator sample damage value, which is computed using a large number of measured time-history records, is used to estimate the expected damage. The obtained results confirm the accuracy of the proposed approach also with real measurements.
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