Ratcheting Behavior of a Titanium-Stabilized Interstitial Free Steel

Engineering stress-control ratcheting behavior of a titanium-stabilized interstitial free steel has been studied under different combinations of mean stress and stress amplitude at a stress rate of 250 MPa s^?1. Tests have been done up to 29.80 pct true ratcheting strain evolution in the specimens at three maximum stress levels. It is observed that this amount of ratcheting strain is more than the uniform tensile strain at a strain rate of 10^?3 s^?1 and evolves without showing tensile instability of the specimens. In the process of ratcheting strain evolution at constant maximum stresses, the effect of increasing stress amplitude is found to be more than that of increasing the mean stress component. Further, the constant maximum stress ratcheting test results reveal that the number of cycles (N) required for 29.80 pct. true ratcheting strain evolution exponentially increases with increase of stress ratio (R). Post-ratcheting tensile test results showing increase of strength and linear decrease in ductility with increasing R at different constant maximum stresses indicate that stress parameters used during ratcheting tests influence the size of the dislocation cell structure of the steel even with the same amount of ratcheting strain evolution. It is postulated that during ratcheting fatigue, damage becomes greater with the increase of R for any fixed amount of ratcheting strain evolution at constant maximum stress.     

Exact tolerance interval with specified tail probabilities and a control chart for the sample variance

A β-content tolerance interval (TI) is a statistical interval which contains at least some fraction (proportion) β of the population with a given confidence level. When we are interested in the precision of a quality characteristic, a TI for the sample variance is useful. In this paper, we consider an exact two-sided β-content TI for the sample variance from a normal distribution with a specified ratio of the tail probabilities. The proposed tolerance interval allows the practitioner more control over how the probabilities in the tails are distributed, which may be useful in certain applications. A comparison with an existing two-sided β-content TI shows that the proposed TI is better on the basis of expected coverage and standard deviation of the coverage. In addition, the proposed TI is shown to require fewer subgroups to achieve a specific accuracy level. Moreover, a phase II control chart with guaranteed performance is obtained from the proposed TI. Finally, a real and a simulated data are used for illustration.