Non-Linear Probabilistic Modification of Miner’s Rule for Damage Accumulation

A non-linear modification to Miner’s rule for damage accumulation is proposed to reduce the scatter between experimental fatigue life and fatigue life predicted according to the original Miner’s sum. Based on P-s-n probability distribution and design s-n curves, the modification satisfies the assumption of equality between the mean damage degree (at the critical level) and fatigue life random variables, which is not covered in the original formulation. The adopted formulation shows the discrepancies between the fatigue lives predicted according to the design s-n curves and the estimated probability distribution. It also proves that it is inappropriate to apply a normal distribution to fatigue life analysis and that the model becomes non-linear only for non-normal distributions. The predictions according to the established model were compared to the predictions obtained with Miner’s rule.

EXPLORATION OF CUMULATIVE DAMAGE EVOLUTION UNDER VARIABLE AMPLITUDE FATIGUE LOADING BASED ON WÖHLER CURVE

How to predict the residual strength of polymer matrix composites (PMCs) after a fatigue cycle at multiple stress levels, based on the fatigue or Wöhler (S-N) curves, remains unsatisfactorily tackled. The Miner’s Rule is a widespread example of a simple way to account for damage accumulation under different fatigue cycles. Under certain combinations of stress levels, Miner’s Rule accurately predicts the lifetime of PMCs, but it fails in other cases. The reason is the simple assumption of linear cumulative damage, not accounting for sequence effects in the loading history. Several researchers have proposed modifications to Miner’s Rule. However, due to its simplicity, Miner’s Rule is still used by structural designers. Recent research work proposed compatibility conditions for fatigue damage functions in the S–N plane, leading to a simple model that fulfils those conditions contrary to the previous models, the Miner’s Rule and the Broutman and Sahu linear model. These models predict fatigue life at variable amplitude loading based on constant amplitude fatigue data. Forcibly, the analytical form of SıN influences the model lifetime predictions. Experimental data obtained in the literature serves to illustrate the models' predictions at different loading conditions. Although this work focused on composite materials, we foresaw extension to other materials.

Fatigue Life Assessment for Variable Strain in a Mixing Tee by Use of Effective Strain Range

Mixing flow causes fluctuations in fluid temperature near a pipe wall and may result in fatigue crack initiation. Movement of the hot spot, at which the pipe inner surface was heated by hot flow from the branch pipe, causes thermal stress fluctuations. In this study, the effect of the loading sequence on thermal fatigue in a mixing tee was investigated. In addition, the prediction method of the fatigue life for the variable thermal strain in the mixing tee was discussed. The time histories of the strain around the hot spot were estimated by finite element analysis for which the temperature condition was determined by wall temperature measured in a mock-up test. The accumulated fatigue damage around the hot spot obtained by Miner's rule was less than 1.0. Since the strain around the hot spot had waveforms with periodic overload, the loading sequence with periodic overload caused reduction of the fatigue life around the hot spot. Crack growth tests showed that a single overload decreased crack opening strain and increased the effective strain range. The increment of the effective strain range accelerated the crack growth rate after the overload. The accumulated fatigue damage for the strain in the mixing tee was calculated using Miner's rule and the strain ranges which added the maximum increment of the effective strain range. The accumulated fatigue damage was larger than 1.0 under most conditions. The proposed procedure is suitable to predict the conservative fatigue life in a mixing tee.

Low-Cycle Fatigue Lifetime Estimation and Predictive Maintenance for a Gas Turbine Compressor Vane Carrier under Varying Operating Conditions

In the age of Industry 4.0, the capability of health management is critical to the design and maintenance of gas turbines. This work presents a probabilistic method to estimate the low-cycle fatigue (LCF) life of a gas turbine compressor vane carrier (CVC) under varying operating conditions. Sensitivity analysis based on finite element analysis (FEA) indicates that an operating cycle can be characterized by three predominant contributors to the LCF damage of the CVC among multiple parameters of an operating cycle. Two surrogate models mapping these three features to equivalent stresses are then built for fast computation of the LCF damage. Miner's rule is applied in a probabilistic way to calculate the distribution of accumulated LCF damage over varying operating cycles. Finally, the probabilistic LCF life of the CVC is assessed using real operational data. The proposed approach includes two novel solutions: 1) a new data processing technique inspired by the cumulative sum (CUSUM) control chart to identify the first ramp-up period as well as the shutdown period of each cycle from noisy operational data; 2) the sequential convolution strategy adapted from Miner's rule to compute the probability distribution of accumulated LCF damage (and hence LCF life) from the single-cycle damage distribution, and an approximative quick estimation method to reduce computational expense. Both the offline application for design and online implementation for predictive maintenance show that the expected LCF life at a critical location of the CVC is significantly longer than the deterministically assessed life.

Fatigue

This chapter introduces methods for analysing fatigue failure of materials under repeated loads. The notions of defect-free and defect-tolerant failure analysis are discussed. For defect free analysis the notion of S-N curves is introduced and Coffin-Mason low cycle as well as Basquin high cycle relations are discussed. Miner’s rule is also introduced. For a defect-tolerant approach Paris’s law for fatigue crack growth is presented.

A practical nonlinear damage accumulation method to predict the life and crack propagation of blade subjected to multilevel cyclic fatigue loads

An accurate life prediction is important to the design of a high-speed rotary blade subjected to multilevel cyclic loads. The widely used Miner’s rule and uniaxial stress prediction method always deviate from actual life of the blade. A prediction method based on Chaboche’s nonlinear damage evolution model is utilized to predict the multilevel cyclic fatigue life of a compressor blade subjected to start-up centrifugal force and working aerodynamic force. Chaboche’s model is verified by comparing with experimental data of different materials. The blade life predicted by Chaboche’s rule and Miner’s rule are compared, and it is found that Miner’s rule might overestimate the blade life under the typical loading spectrum of start-up centrifugal force and working aerodynamic force. To study the impact of multiaxial stress state on the blade life, the life predicted by uniaxial stress method is compared to that predicted by multiaxial stress method, and it demonstrates that the multiaxial stress state of the blade should not be neglected. Finally, the crack propagation of the blade under multiaxial fatigue loads is simulated successfully by element deletion technique, which is conducted by translating Chaboche’s multiaxial model into a user defined UMAT program in ABAQUS. The predicted crack propagation life is compared with that predicted by an approximate Paris law method plate model. This research proves that the method to predict the blade life subjected to multilevel cyclic loads based on multiaxial Chaboche’s model could provide a valuable reference for engineering blade fatigue design.

Variable Loading Sequence Effect for Thermal Fatigue at a Mixing Tee

Mixing flow causes fluctuations in fluid temperature near the pipe wall and may result in fatigue crack initiation. In a previous study, the authors reported the characteristics of the thermal stress to cause thermal fatigue at a mixing tee. A large stress fluctuation was caused by movement of the hot spot, at which the pipe wall was heated by hot flow from the branch pipe. According to a general procedure, fatigue damage is calculated by the linear damage accumulation rule. However, it has been reported that Miner’s rule does not always predict the fatigue life conservatively for variable stress amplitude. In this study, we investigated the change in fatigue life due to variable strain around the hot spot. The time histories of the strain around the hot spot were estimated by finite element analysis (FEA) for which the temperature condition was determined by wall temperature measured in a mock-up test. Strain-controlled fatigue tests were conducted using smooth cylindrical specimens made of stainless steel. The fatigue damage at failure of the specimen was calculated using Miner’s rule. The calculated fatigue damage around the hot spot became less than unity and the minimum value was 0.18. Therefore, Miner’s rule predicted non-conservative fatigue life. In addition, the calculated fatigue damage inside the hot spot was larger than those outside the hot spot and at the position of maximum stress fluctuation. Fatigue tests using strain with periodic overload were also conducted in order to investigate the effect of the loading history on fatigue life. It was shown that the strain with periodic overload reduced the fatigue life. The calculated fatigue damage for the strain at the maximum position of stress fluctuation range seemed to be smaller than those at other positions. This implies that the fatigue life can be estimated conservatively from the viewpoint of the loading sequence effect by calculating the fatigue damage using Miner’s rule for the strain at the maximum position of stress fluctuation range.

Improved Fatigue Design of SCR Modified Miner’s Rule

The Aasta Hansteen floating production system is the first SPAR platform with steel catenary risers (SCR) at the Norwegian Continental Shelf (NCS). The water depth is 1300 msw. The weather conditions with respect to wave loading are more severe than any offshore installation completed so far. Under such environmental conditions, it is vital to verify the design of the SCR’s with respect to extreme loading and fatigue life. A fatigue verification program has been executed for ground OD welds of both clad and carbon steel riser materials. The objective was to determine the effect of weld defects in combination with the effect of variable amplitude loading using the actual fatigue stress distribution experienced by critical parts of the SCR. The stress distribution is based on the local wave spectrum and estimated from hydrodynamic analysis of the riser and the long-term wave statistics. Two clad pipes and one carbon steel pipe was exposed to rotation bending fatigue testing with artificially imposed defects. One clad pipes gave fracture after more than 1.0 × 109 cycles. The carbon steel pipe gave fracture after 4.56 × 108 cycles. A modified Miner’s summation rule is proposed for variable amplitude fatigue design. The procedure is based on a verification of variable amplitude testing against constant amplitude testing. The results indicate that load amplitudes below a fatigue limit defined at 107 cycles are not contributing significantly to fatigue crack initiation and growth from a weld defect. The proposed method suggests an engineering approach to this by a modification of the Miner’s rule for VA loading.

Fatigue of Composite Materials Subjected to Variable Loadings

In the present work, a model describing the fatigue behaviour of composite materials under spectrum loading is presented. The approach is based on a two-parameter model describing the strength degradation kinetics for fibre-reinforced materials subjected to cyclic loadings, both with constant and variable amplitudes. The point of strength of the presented approach is that it allows to consider cyclic loadings as they are, without simplifications or reductions. In particular, the analytical background of the model is based on the statements that govern the composites behaviour and focused on the issues related to this class of materials when subjected to fatigue. Then, the final step is the definition of a damage accumulation rule that goes over Miner’s rule unreliability when applied to fibre-reinforced materials. As a matter of fact, it allows to take into account the effects of different loading histories, underlining the importance of the sequence of loads application in the framework of the presented approach.