Spectral method for fatigue damage estimation with non-zero mean stress E-Book

Pedro H. Alves Corrêa

• Herausgeber: Editora Dialética
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 47

Veröffentlichungsjahr: 2022

Beschreibung

This thesis consists of a fatigue study carried out on an aluminum alloy 2024-T3 in both time domain and frequency domain. Non-zero mean random signals of strain and stress are analyzed in time domain using usual Rainflow method and the damage is accumulated with the Palmgren-Miner rule, according to mean stress equations. The signals are analyzed in frequency domain using the power spectral density and the probability density function. The spectral domain analysis does not consider the negative effect of the mean stress in metal life under fatigue, so the correction factors for mean stresses developed by Goodman, Morrow, and Smith-Watson-Topper are used to change the power spectral density and, thus, the damage calculated by the probability density functions postulated by Dirlik and Tovo and Benasciutti. It is found that both Dirlik and Tovo and Benasciutti are non-conservative for a non-zero mean stress signal when comparing the damage to the one obtained in time domain analysis. When the spectral method is corrected, the results vary from Rainflow 4.9% for wide band and 6.8% for narrow band signals, always in the conservative zone, therefore predicting more damage. Tovo and Benasciutti 2 method is found to be the spectral function with the closest results when compared to the usual Rainflow method in time domain.

Leseprobe

Esse livro é dedicado ao meu avô Hugo Caetano Alves, a primeira pessoa para quem eu contei que ia publicá-lo e que infelizmente não teve tempo de lê-lo. Nunca me esquecerei do seu entusiasmo quando ficou sabendo que teria um livro publicado pelo seu neto. Tenho muita sorte de tê-lo como avô e me sinto muito honrado de ter dado orgulho ao senhor.

Esse estudo é também dedicado aos meus pais Evyania e Carlos que sempre me apoiaram, minha irmã Vanessa e sobrinha Bárbara e minhas avós Vânia e Vera. Vocês servem de inspiração diária para minha vida e continuam provendo suporte emocional, moral e espiritual. E dedico um pedaço especial ao dono do meu coração, Osvaldo Gaspar.

Gostaria também de agradecer o professor Jorge Durán por ter me sugerido essa linha de estudo e proposto o desafio. Gostaria de agradecer também os professores Gláucio Soares da Fonseca e Alberto Paiva por terem me apoiado e seguido todos os meus estudos na graduação e mestrado.

Um agradecimento especial ao meu parceiro de Mestrado Renner Egalon com quem dividi boa parte dos estudos de fadiga espectral no mestrado e todos os desafios da graduação.

Gostaria de agradecer também a Universidade Federal Fluminense por todo o suporte durante a graduação e a CAPES por fomentar esse estudo de mestrado.

List of Symbols

– Stress range

– Maximum stress

– Minimum stress

– Mean stress

– Stress amplitude; alternating stress

– Number of cycles until fatigue failure

, – Fitting parameters for fatigue curve

- Fatigue Strength

– Fatigue exponent

– Stress ultimate strength

– Real fracture strength from tensile test

E – Young’s modulus

– All reversed alternating stress

– Walker’s coefficient

K – Constant factors for mean stress correction

– Fatigue damage

– Number of cycles

– Stress or strain signal in time domain

– Mean value or the expected value of X

– Variance of X

– Root mean square of X

– Instant of time in data

– total time of data acquisition or total time of fatigue test

– Power spectral density (PSD) of X from time domain to frequency domain

– Frequency

– Amount of data

– Spectral moment of order i

– Number of zero level crossings with positive slope expected

– Number of Peaks expected

– Irregularity factor

PDF – Probability Density Function

– Parameters of Tovo-Benasciutti 2 Method

– Parameters of Dirlik Method

– Global Mean Stress

– Probability value from PDF function for a value

k – Stiffness of the cantilever bean

– Moment of Inertia

– System’s mass

Table of Contents

Capa

Folha de Rosto

Créditos

1. Introduction

1.1 Motivation

1.2 Objectives

2. Theoretical Fundamentals

2.1 Cyclic Loading

2.2 Fatigue of Materials

2.3 Mean Stress Correction

2.4 Rainflow Cycle Counting

2.5 Palmgren-Miner Rule

2.6 Spectral Fatigue

2.7 Random Loading

2.7.1. Stationary Random Loading

2.7.2. Ergodic Stationary Random Loading

2.7.3. Gaussian distribution

2.8 Power Spectral Density

2.9 Wide Band and Narrow Band Processes

2.10 Moments of the PSD

2.11 Fatigue Analysis Within Frequency Domain

2.11.1. The Rayleigh Method

2.11.2. Tovo-Benasciutti Method

2.11.3. Dirlik Method

2.12 Global Mean Stress Value

3. Materials and Methods

3.1 Materials and Equipment

3.1.1. Material

3.1.2. Specimen

3.1.3. Data Acquisition

3.2 Experimental Set

3.3 Signal generation

3.4 Fatigue Damage

3.5 Considering the Mean Stress

3.6 Paper Algorithm

4. Numerical and Experimental Results and Discussion

4.1 Impact test

4.2 Numerical results

4.3 Experimental Results

5. Conclusion

6. Suggestion for Future Researches

7. Appendix 1 Free Vibration of a Cantilever Bean

8. References

Landmarks

cover

titlepage

copyright-page

Table of Contents

bibliography

1. Introduction

The effect of variable loading on materials causing mechanical fatigue is one of the main reasons of failure. The usual technics to estimate fatigue damage are based on signals of strain or stress (KERR et al., [s.d.]) in time domain, followed by a cycle counting and damage estimation. The study in the frequency domain, often called Spectral Fatigue, is a procedure to calculate fatigue damage and life for random vibrations, which are complicated to be analyzed within the time domain, through usual Rainflow.

The Rainflow cycle counting was introduced in 1968 by Matsuishi and Endo (MATSUISHI; ENDO, 1968)

This counting procedure is still used nowadays but it can be dispendious for long time signals because the whole set of data, during the whole test, must be used to compute the damage generated in the material due to the loading. Most of real mechanic behaviors are non-stationary random processes. Nevertheless, as the signal varies slowly or almost constantly, in the majority of cases, the load is considered stationary for any time sample. To analyze the fatigue life and damage, the loading must be considered random, stationary and Gaussian.(BISHOP; SHERRATT, 1989)

The Spectral analysis is carried out in the frequency domain. For this reason, it’s possible to calculate the damage through statistic properties of the Power Spectral Distribution (PSD) of the time signal. These properties are equal for the whole signal as well for smaller samples, due to the ergodic feature of the signal. (NEWLAND; NEWLAND; NEWLAND, 1993)