Random Variable Amplitude Loading Research Articles

Research on Damage Mechanism and Performance-Based Design Process of Reinforced Concrete Column Members

In order to understand the seismic damage assessment of reinforced concrete column members, the coupling relationship between the capacity degradation and the accumulated hysteretic energy and the displacement history was considered. The energy-based damage index under the random variable amplitude loading history was proposed. On the basis of preliminary research, the corresponding relationship between the damage index and the construction member parameters and seismic parameters was established, the damage mechanism was analyzed according to the damage index, and then the performance-based design process was proposed. It was found that increase in the stirrup ratio can slow down the damage, and the slowing effect was initially fast and then slows. When the reinforcement ratio is doubled, the damage index decreased by 0.063. The longer the earthquake duration was, the more serious the damage was, and this phenomenon was more obvious when the ductility coefficient was larger. With the increase in the ductility coefficient, the damage continuously increased. Therefore, it is an effective way to decrease the damage by controlling the ductility coefficient. Among all the influencing factors, the fundamental period and seismic intensity contributed more significantly to the damage indicators. When the damage index (performance objective) was determined, the target stirrup ratio can be obtained according to the proposed performance design process, that is, this design process can be used in the performance-based design. The design method based on damage index can make up for the deficiency that the design method based on the ductility coefficient does not consider the earthquake duration.

Sequence effect of as-welded and HFMI-treated transverse attachments under variable loading with linear spectrum

It has been shown in several studies that methods to improve the fatigue strength of welded structures, such as high-frequency impact treatment (HFMI), can increase the fatigue life of welded joints [1–6]. The results of these investigations led to current guidelines and recommendations for the fatigue assessment of HFMI-treated welded joints. Nevertheless, in practice, there are reservations regarding the efficiency of HFMI-treated welded steel joints under variable amplitude loading. Recent results [7] from studies on transverse attachments of the material S355 and S700 under variable amplitude loading show that the fatigue strength increasing effect of the HFMI-treatment is maintained compared to the as-welded state. The aim of this study is to analyse the sequence effect on the fatigue strength of HFMI-treated transverse attachments and to validate the applicability of linear damage accumulation hypotheses for the design of as-welded and HFMI-treated welded details. In this paper, fatigue test results with random variable amplitude loading (VAL) and high-low VAL and low–high VAL with linear spectrum for the two states as-welded (AW) and HFMI-treated joints will be presented.

Investigation on low cycle fatigue crack propagation in steel under fully random variable amplitude loading

Investigation on low cycle fatigue crack propagation in steel under fully random variable amplitude loading

Evaluating the use of rate-based monitoring for improved fatigue remnant life predictions

The ability to perform accurate remnant life predictions is crucial to ensure the integrity of engineering components that experience fatigue loading during operation. This is conventionally achieved with periodic inspections, where results from non-destructive evaluation and estimation of the operating conditions are obtained to perform remnant life predictions using empirical crack growth laws. However, remnant life predictions made with this approach are very sensitive to their input parameters; uncertainty in each parameter would aggregate and result in great uncertainty in the final prediction. With the increasing viability of permanently-installed systems, it is proposed that the rate of damage growth can be used to more accurately and confidently gauge the integrity of an engineering component and perform remnant life predictions using the Failure Forecast Method. A statistical analysis of an example fatigue crack growth test was performed to compare the uncertainties of the remnant life predictions made using the conventional inspection approach and the proposed rate-based monitoring approach. It is shown that the Failure Forecast Method produces significantly more accurate and confident predictions compared to the inspection approach. The use of the Failure Forecast Method under non-constant amplitude loading conditions was also investigated. An equivalent cycles method is introduced to accommodate step changes in operating conditions. The effect of load interactions was also studied through a fatigue test with isolated overloads and a random variable amplitude loading test. Overall, the study has shown that the frequent data obtained from permanently installed monitoring systems provides new opportunities in remnant life estimates and potentially opens the way to increasing the intervals between outages and safely reducing conservatism in life predictions.

Durability assessment of automotive structures under random variable amplitude loading

Durability assessment is essential for assuring the reliability and safety of automotive structures, which subjects to complex random variable amplitude loadings. In this article, the application o...

Time-based subcycle formulation for fatigue crack growth under arbitrary random variable loadings

A time-based subcycle fatigue crack growth (FCG) formulation and validation are proposed to calculate the fatigue crack growth under general random variable amplitude loadings. The intrinsic difficulties of the classical cycle-based formulation for general random variable loadings are discussed first. Several typical spectrums that are not appropriate for cycle-based FCG are illustrated, such as the “Christmas tree” spectrums. A time-based subcycle formulation is then proposed to address this difficulty. The proposed model includes three major component: (1) a time-based crack growth kinetics function at the subcycle (time) scale; (2) an efficient crack tip opening displacement (CTOD) estimation method; (3) a crack tip plasticity zone tracking algorithms for crack opening level determination of a growing crack. Detailed derivation and calculation procedures are given. Following this, several numerical examples are illustrated for the proposed model under different loading spectrums for the crack growth and CTOD calculation. Randomly generated loading spectrums are used to illustrate the capability of the proposed method under arbitrary loadings. Next, in-house testing for “Christmas tree spectrum” and literature data on several representative variable loading spectrums are used for model validation. Finally, some conclusions and future work are drawn based on the proposed study.

Equivalent Stress Transformation for Efficient Probabilistic Fatigue-Crack Growth Analysis under Variable Amplitude Loadings

AbstractA general probabilistic fatigue-crack growth prediction methodology for accurate and efficient damage prognosis is proposed in this paper. The methodology is based on an equivalent stress transformation and the inverse first-order reliability method (IFORM). The equivalent stress transformation aims to transform the random variable amplitude loading to an equivalent constant amplitude loading spectrum. The proposed transformation avoids the cycle-by-cycle calculation under general random variable amplitude loadings. An IFORM is used to evaluate the probabilistic fatigue-crack growth behavior and to further enhance the computational efficiency. The computational cost of the proposed study is significantly reduced compared with the direct Monte Carlo simulation. Thus, the proposed method is very suitable for real-time damage prognosis because of its high computational efficiency. Numerical examples are used to demonstrate the proposed method. Various experimental data under variable amplitude loadin...

A simple analytical crack tip opening displacement approximation under random variable loadings

A simple analytical approximation is proposed in this paper to calculate the crack tip opening displacement under general random variable amplitude loadings. This approximation is based on a modified Dugdale model for cyclic loadings. The discussion is first given under constant amplitude loading and is extended to several simple cases under variable amplitude loadings. Following this, a general algorithm is proposed under general random variable loadings. Numerical examples are verified with finite element simulations. Following this, hardening effect is included by including a hardening correction function. The proposed analytical approximation is very efficient compared to the direct finite element simulation. The solution can be used for detailed fatigue crack growth analysis under random variable amplitude loadings.

Small time scale fatigue crack growth analysis

A new fatigue crack growth formulation at the small time scale is proposed in this paper. This method is fundamentally different from the classical reversal-based fatigue analysis and is based on the incremental crack growth at any time instant within a cycle. It can be used for fatigue analysis at various time and length scales and is very convenient for the fatigue analysis under random variable-amplitude loadings without cycle-counting. Stress ratio effect is intrinsically considered in the proposed fatigue model since the stress state is directly used instead of using the cyclic stress range. In the proposed methodology, the reverse plastic zone concept is adopted to determine the lower integration limit during the time integral for crack length calculation. Model validation is performed using extensive experimental observations for various metallic materials under both constant amplitude and variable-amplitude loadings. Statistical error analysis is used to compare the proposed model with existing fatigue crack growth codes. Generally, very good correlations are observed between model predictions and experimental observations.

Stochastic fatigue crack growth in steel structures subject to random loading

Uncertainty in fatigue crack growth under service load conditions arises from the statistical characteristics of crack growth under constant amplitude loading and from random variable amplitude loading. This study generalizes previous stochastic fatigue crack growth models by incorporating a time-dependent noise term described by arbitrary marginal distributions and autocorrelations to model the uncertainty in the crack growth under constant amplitude loading. A computationally efficient approach for handling wide-band random loadings based on the rainflow method of stress cycle identification also is developed. The method is illustrated with a fatigue reliability analysis of a steel miter gate at a lock and dam facility operated by the US Army Corps of Engineers.

High-cycle, long-life fatigue behavior of welded steel details

Abstract Results from laboratory fatigue tests of large-scale welded attachments under random variable-amplitude loading have indicated that the existence of a fatigue limit below which no fatigue cracks develop is assured only if none of the stress cycles exceeds the constant-amplitude fatigue limit. In the extreme life region of fatigue behavior, the contribution of the lower cycles of a stress range spectrum to crack propagation is a function of the larger stress cycles. However, the value of the constant-amplitude fatigue limit is not precisely known and in some cases will differ from the assumed value. As a consequence of the variability in the fatigue limit, the lower bound variable-amplitude fatigue resistance on large-scale welded steel details is defined by the straight-line extension of the S-N design curves below the constant-amplitude fatigue limit. A summary of the test data is given and the effect of the variability on the fatigue behavior of welded steel details in the high-cycle, long-life regime is discussed.