Rain-flow Method Research Articles

Low-cycle fatigue of a medium carbon steel under variable strain cycling (Application of the rain flow method to the prediction of microcrack propagation life)

The rain flow method for counting fatigue damage was applied to predict microcrack propagation life under varying strain amplitudes. Low-cycle fatigue tests were conducted on a medium carbon steel under block-random and pseudo-random strain cycling as well as constant strain cycling. Through continual observation of the microcrack initiation and propagation behaviours of plain specimens and holed specimens with a small drilled hole, the results obtained are summarized as follows : (1) For a microcrack propagating under varying strain amplitudes, a fatigue damage calculated by means of the rain flow method can be fairly well correlated with a cycle ratio under constant strain amplitude. (2) The rain flow method is shown to be suitable in predicting microcrack propagation life as well as in evaluating fatigue failure life. (3) The essential conditions for Miner's rule to hold under variable strain cycling conditions are that the microcrack propagation law shows a relation of the linear type, dl/dN=Cl, and that prior fatigue damage hardly influences the subsequent microcrack growth rate.

COMPUTER SIMULATION STUDIES ON THE FATIGUE LOAD AND FATIGUE DESIGN OF HIGHWAY BRIDGES

The live loads for fatigue design and maintenance of highway bridges are studied based on computer simulations. Simulations of traffic live loads are carried out under various traffic volumes and constitutions of vehicle types. The type of vehicle, the vehicle weight and the array and headway of vehicles are cosidered as random variables. Bending moment responses of simply-supported one-lane girders of various lengths are calculated under usual traffic conditions. Moment ranges are analysed by using the rain flow method. For the evaluation of fatigue damage, the equivalent moment range and the reduced number of L-20 or T-20 live load are presented.

Fatigue Reliability for Offshore Structures

The results of a four‐year project, sponsored by the American Petroleum Institute, to investigate the fatigue design process in the welded joints of steel offshore structures are summarized. Fatigue damage expressions were formulated. A simple analytical expression for damage based on the rainflow method of cycle counting in a wide band process was constructed. Because fatigue design factors have significant uncertainty, a reliability approach, using the lognormal format, was developed. The performance of Miner's rule was characterized statistically, as was modeling error associated with the process of computing fatigue stresses in a joint from oceanographic data. Procedures of S‐N data analysis were developed, and characteristic S‐N data sets were presented. The reliability format was employed to construct a design rule for low period structures. It is argued that the new design rule is more discriminating in that it can account for service life, wave spectra, water depth, platform dynamics, as well as t...

Probabilistic analysis of deposit liquefaction : Fardis, M N; Veneziano, D J Geotech Engng Div ASCE, V108, NGT3, March 1982, P395–417

This paper presents a procedure to perform the risk analysis for ground failure by liquefaction. The liquefaction is defined as the result of cumulative damage caused by seismic loading. The fatigue life of soil can be determined on the basis of the N-S relationship and Miner`s cumulative damage law. The rain-flow method is used to count the number of cycles of stress response of the soil deposit. Finally, the probability of liquefaction is obtained by integrating over all the possible ground motion and the fragility curves of liquefaction potential.

Fatigue under Wide Band Random Stresses

A method for predicting high cycle fatigue under stationary gaussian wide band stress processes is developed. The rainflow cycle counting method is used as the basis for predicting fatigue damage. Stress simulations from various spectral density models were analyzed using the rainflow method. Statistical analysis of these results provided a closed form expression for fatigue damage. A principal application of the method is to predict fatigue in the welded joints of offshore structures, an example of which is provided. A long term nonstationary sea state is modelled as a sequence of stationary sea states. Thus the example also illustrates how fatigue under certain types of nonstationary stress processes can be analyzed.

Fatigue reliability in welded joints of offshore structures

Metal fatigue in welded joints in offshore structures is considered. Due to the considerable variability of conditions, a probabilistic approach is used. Theoretical studies of various aspects of the fatigue reliability problem in welded joints are presented. These include a study of the Palmgren-Miner rule, a modified linear model on S/N data, the use of the rainflow method of counting, and a closed form expression for the probability of fatigue failure. A probability model is derived as a suggested basis for an approach to fatigue design.

CUMULATIVE FATIGUE DAMAGE UNDER RANDOM LOADS

Abstract This paper presents a simple algorithm of hysteresis loop counting to make on‐line data processing much easier. It involves a modification of the range pair counting method and the rain flow method and yields practically the same result as these methods. In addition, the applicability of the present method to cumulative damage estimation is examined in experiments on fatigue crack growth rates under stationary random loads and low cycle fatigue lives under stationary random loads together with non‐stationary random loads such as seismically excited loads.

Fatigue Under Wide Band Random Stresses Using the Rain-Flow Method

A fatigue design procedure is proposed for the structural elements subjected to a stress process, modeled as stationary wide-band gaussian. This procedure, restricted to high cycle fatigue design, uses available constant amplitude material fatigue data and a modified, probability based, Palmgren-Miner (PM) rule. Statistical uncertainty in fatigue behavior and nonstatistical uncertainty in the PM rule are implicitly accounted for by treating the PM index at failure as a random variable. The rain flow method of counting stress cycles is used. The fatigue design algorithm requires only that the RMS and irregularity factor of the stress process be specified in addition to the constant amplitude S-N curve for the material.

Computational Fatigue Life Assessment Of Components Exposed To Non-stationary Loading

Non-stationary loads appear as a result of operating conditions or of non-linear structural behaviour. They are analysed either by the Rain Flow Method giving a macroblock of sinusoidal cycles or they can be split into segments for which quasi stationary characteristics are computed and further used as inputs to fatigue damage accumulation hypotheses. In order to verify the influence of non-stationarities on fatigue life 24 processes with various statistical characteristics were simulated and the fatigue lives were mutually compared for low carbon steel specimens with one surprising result: various non-stationarities do not substantially effect the resulting fatigue life. This was also confirmed by experiments.