Formulation of Strain Fatigue Criterion Based on Complex Numbers

In the case of many low-cycle multiaxial fatigue criteria, we encounter a mathematical problem of adding vectors of normal and shear strains. Typically, the problem of defining an equivalent strain is solved by weighting factors. Unfortunately, this ignores the fact that these vectors represent other physical quantities: the normal strain is a longitudinal strain, and the shear strain is a rotation angle. Therefore, the goal of the present work was to propose a method of combining different types of strains by adopting a system of complex numbers. The normal strain was defined as the real part and the shear strain was defined as the imaginary part. Using this approach, simple load states, such as pure bending and pure torsion, have been transformed into an expression for equivalent strain identical to the previously proposed criteria defined by Macha.

Using Signal Detection Theory to Better Understand Cognitive Fatigue

When we are fatigued, we feel that our performance is worse than when we are fresh. Yet, for over 100 years, researchers have been unable to identify an objective, behavioral measure that covaries with the subjective experience of fatigue. Previous work suggests that the metrics of signal detection theory (SDT)—response bias (criterion) and perceptual certainty (d’)—may change as a function of fatigue, but no work has yet been done to examine whether these metrics covary with fatigue. Here, we investigated cognitive fatigue using SDT. We induced fatigue through repetitive performance of the n-back working memory task, while functional magnetic resonance imaging (fMRI) data was acquired. We also assessed cognitive fatigue at intervals throughout. This enabled us to assess not only whether criterion and d’ covary with cognitive fatigue but also whether similar patterns of brain activation underlie cognitive fatigue and SDT measures. Our results show that both criterion and d’ were correlated with changes in cognitive fatigue: as fatigue increased, subjects became more conservative in their response bias and their perceptual certainty declined. Furthermore, activation in the striatum of the basal ganglia was also related to cognitive fatigue, criterion, and d’. These results suggest that SDT measures represent an objective measure of cognitive fatigue. Additionally, the overlap and difference in the fMRI results between cognitive fatigue and SDT measures indicate that these measures are related while also separate. In sum, we show the relevance of SDT measures in the understanding of fatigue, thus providing researchers with a new set of tools with which to better understand the nature and consequences of cognitive fatigue.

PREVENTING PROCESS FATIGUE WHEN FINISHING A PART

Possibilities of preventing the appearance of fatigue cracks during finishing processing of a part by changing the elastic–mechanical characteristics of the workpiece due to the accumulation of fatigue defects preceding the appearance of a crack are considered. Modules of elasticity and shear are considered as characteristics to be controlled under the assumption that the material of the part is isotropic. To control these values, the equation of vibrations of the part is used, which is solved by the numerical method, and the values of E and G are selected, corresponding to the measured displacements of surface points that occur during a given movement of the processing tool. The movements are proposed to be measured remotely. The obtained sequences of estimates of the elasticity and shear moduli form two time series, according to which a long–range forecast is made, and the limiting values of the sequences are calculated with an unlimited increase in time. The fatigue criterion is the reduction of these values at the present or future points in time below a preset value. Depending on the degree of reduction, a decision can be made to reject the part or to correct the technological process with a change in the law of the machining tool motion. The proposed control method can be used in the construction of flexible production systems.