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

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7335
Author(s):  
Łukasz Blacha
Keyword(s):  
Fatigue Life ◽  
Probability Distribution ◽  
Damage Accumulation ◽  
Normal Distributions ◽  
Damage Degree ◽  
Non Linear ◽  
Miner’S Rule ◽  
The Mean ◽  
Fatigue Life Analysis ◽  
Miner's Rule

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.

A First Investigation on Cumulative Fatigue Life for a Type 304-L Stainless Steel Used for Pressure Water Reactor

2009 ◽  
Author(s):  
A. Fissolo ◽  
J. M. Stelmaszyk
Keyword(s):  
Stainless Steel ◽  
Fatigue Life ◽  
Fatigue Tests ◽  
Operating Conditions ◽  
Damage Effect ◽  
Final Conclusion ◽  
Variable Loading ◽  
Miner’S Rule ◽  
Miner's Rule ◽  
Type 304

In order to estimate the crack initiation damage, and also the water leakage conditions on PWR pipes, uniaxial fatigue curves are often used. They were deduced from strain or stress load control tests using normalised cylindrical specimens. However, severe thermo-mechanical loading fluctuations are observed in operating conditions. Components may also be submitted to transient loadings. The purpose of the present work is to start investigation on the fatigue life with a variable loading, in order to examine cumulative damage effect in fatigue. In this frame, multilevel strain controlled fatigue tests have been performed on a Type 304-L stainless steel (elaborated in accordance with the RCC-M specifications). The experimental results show that linear Miner’s rule is not verified in our conditions. When the strains are applied in a decreasing order (High-Low strain sequence), the summation of cycle ratios is smaller than unity, whatever the number of applied levels, whereas this summation is higher than one for an increasing order (Low-High strain sequence). A loading sequence effect is clearly evidenced. Different cumulative fatigue damage theories, proposed in literature, have been also tested. Some of them have been given better estimation than the Miner’s rule. That is the case of the so-called “Hybrid Theory” proposed and tested before by Bui Quoc on a Type 304-L steel. Extension of a model proposed by S. Taheri would seem also promising. At this stage, final conclusion cannot be yet deduced, additional investigations are needed.

scholarly journals On the applicability of Miner’s rule for multiaxial fatigue life calculations under non-proportional load histories

2017 ◽  
Vol 11 (41) ◽  
pp. 98-105 ◽  
Author(s):  
Marco Antonio Meggiolaro ◽  
Jaime Tupiassú Pinho de Castro ◽  
Samuel Elias Ferreira ◽  
Hao Wu
Keyword(s):  
Fatigue Life ◽  
Multiaxial Fatigue ◽  
Miner’S Rule ◽  
Miner's Rule

Effect of Strain Amplitudes and Mean Strain Values on Fatigue Life at Elevated Temperature

2013 ◽  
Author(s):  
Shin-ichi Watanabe ◽  
Koh-ichi Imamura ◽  
Osamu Watanabe ◽  
Akihiro Matsuda
Keyword(s):  
Fatigue Life ◽  
Elevated Temperature ◽  
Strain Amplitude ◽  
Evaluation Method ◽  
Mean Value ◽  
Random Wave ◽  
Miner’S Rule ◽  
Miner's Rule ◽  
Number Of Cycles ◽  
Mean Strain

This paper shows randomness effects of loading amplitude and mean value of displacement-controlled loading history for perforated plates made of SUS304 stainless steel at elevated temperature of 550°C. Under the random wave of strain amplitude, the fracture behavior at elevated temperature environment is clarified by measuring the load-deflection curve at all cycles. The data of experiments were evaluated by Miner’s rule, which has been established as an evaluation method for load variation problem. Number of cycles to fracture is compared to show the good agreement with the Best Fit Fatigue curve (BFF). Peak count method also was used in calculating frequency of the strain in order to evaluate Miner’s rule, and the local strain concentration is calculated based on Stress Redistribution Locus (SRL) method. The other object of this study is to evaluate effect of mean value of strain in loading diagram on fatigue life. The mean strain were used for the cases of R = −0.0, −0.2, −0.4, −0.8 and −1.0. The crack length is measured by using photographs with the CCD video camera at a constant frequency. From the measurement, it is found that the number of cycles to failure is reduced when the absolute of value of mean strain is decreased. And cracks develop at both sides around the hole, but the growth of each crack may not be symmetric. By using these inelastic strain amplitude and crack initiation cycle, the experimented results are shown at the present study.

Fatigue Design of Machine Elements Under Cumulative Damage Effect, Using Bagci’s Fatigue Failure Surface Line

1984 ◽  
Vol 106 (4) ◽  
pp. 466-475
Author(s):  
C. Bagci
Keyword(s):  
Fatigue Life ◽  
Fatigue Strength ◽  
Material Properties ◽  
Cumulative Damage ◽  
Damage Effect ◽  
Stress Effect ◽  
Mean Stress ◽  
Fatigue Design ◽  
Miner’S Rule ◽  
Miner's Rule

A thorough review of the state-of-the-art of determining fatigue life of machine and structural members considering cumulative damage effect under varying stress amplitudes is given. Among the many proposed theories, Miner’s linear damage rule is seen to be as reliable as any other rule alleged to be an improvement for predicting fatigue life under cumulative damage effects. Its simplicity and amenability for easy modification have in fact been the basis for some other theories and used in design codes. In its original form, Miner’s rule, however does not account for fatigue strength reducing factors. Observing fatigue data on the effects of fatigue strength reducing factors, the article offers a modified form of the Miner’s rule to consider the effects of fatigue strength reducing factors, such as the notch, reliability, surface finish, size, and environmental factors. The mean stress effect and material properties are incorporated utilizing Bagci’s mean stress line and the S-N diagram. The safe fatigue life of a component subjected to stresses of varying magnitudes becomes Ns=df/∑i=1s(αi/10zi) where zi=A{B−log(pig/Rf)+log[1−(pi/mi)r]} in the ith block of stress range, Rf being the resultant of fatigue strength reducing factors; A, B, g are parameters defined by material properties, pi is the ratio of the basic alternating stress times the factor of safety (the failure value) to the yield strength of the material, and mi is the slope of the load line in the ith block of loading. Design charts for zi for steel and aluminum alloys for cases with and without basic mean stress for r=4 are given. Numerical examples are included. Therefore, the article offers the most general form of the Miner’s rule for designers’ use for fatigue design considering cumulative damage effect.

scholarly journals NUMERICALLY MODELING FATIGUE LIFE OF STRUCTURAL ELEMENTS UNDER THERMAL CYCLIC LOADING

2020 ◽  
Vol 82 (2) ◽  
pp. 168-188
Author(s):  
I.A. Volkov ◽  
L.A. Igumnov ◽  
D.N. Shishulin ◽  
V.A. Eremeev
Keyword(s):  
Plastic Deformation ◽  
Fatigue Life ◽  
Fatigue Damage ◽  
Damage Accumulation ◽  
Strength Criterion ◽  
Cyclic Fatigue ◽  
Defining Relations ◽  
Damage Degree ◽  
Fatigue Damage Accumulation ◽  
Main Effects

The paper considers processes of fatigue life of materials and structures in the exploitation conditions characterized by multiparametric nonstationary thermal-mechanical effects In the framework of mechanics of damaged media, a mathematical model is developed that describes processes of thermal-plastic deformation and fatigue damage accumulation in materials with degradation according to low- and high-cycle fatigue mechanisms (accounting for their interaction). The model consists of three interconnected parts: relations determining cyclic thermal-plastic behavior of a material, accounting for its dependence on the failure process; equations describing kinetics of fatigue damage accumulation; a strength criterion of the damaged material. The version of the defining relations of thermal plasticity is based on the notion of the yield surface and the principle of orthogonality of the plastic strain rate vector to the yield surface at the loading point and reflects the main effects of the process of cyclic plastic deformation of the material for arbitrarily complex trajectories of combined thermal-mechanical loading. The version of kinetic equations of fatigue damage accumulation is based on introducing a scalar parameter of damage degree and on energy-based principles, and takes into account the main effects of the nucleation, growth and merging of microdefects under arbitrarily complex loading regimes. A generalized form of an evolutionary equation of fatigue damage accumulation in low-cycle and high-cycle fatigue regions is introduced. The condition when the damage degree reaches its critical value is taken as the strength criterion of the damaged material. To assess the reliability and the scope of applicability of the developed defining relations of mechanics of damaged media, processes of thermal-plastic deformation and fatigue damage accumulation have been numerically analyzed, and the numerical results obtained have been compared with the data of full-scale experiments for a particular applied problem. The effect of the dropping frequency of a distillate on thermal cyclic fatigue life of the material of a heated surface of a tube has been numerically analyzed. The computational results for the fatigue damage accumulation processes under thermal pulsed loading are compared with experimental data. It is shown that the developed model describes both qualitatively and, accurately enough for engineering purposes, quantitatively the experimental data and can be effectively used for evaluating thermal-cyclic fatigue life of structures working in the conditions of multiaxial non-proportional regimes of combined thermal-mechanical loading.

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

2021 ◽  
Author(s):  
Koji Miyoshi ◽  
Masayuki Kamaya
Keyword(s):  
Fatigue Life ◽  
Crack Growth ◽  
Fatigue Damage ◽  
Hot Spot ◽  
Effective Strain ◽  
Strain Range ◽  
Life Assessment ◽  
Miner’S Rule ◽  
Loading Sequence ◽  
Miner's Rule

Abstract 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.

Variable Loading Sequence Effect for Thermal Fatigue at a Mixing Tee

2019 ◽  
Author(s):  
Koji Miyoshi ◽  
Masayuki Kamaya
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
Pipe Wall ◽  
Hot Spot ◽  
Fatigue Tests ◽  
Stress Fluctuation ◽  
Fluctuation Range ◽  
Miner’S Rule ◽  
Loading Sequence ◽  
Miner's Rule

Abstract 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.

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