# Weibull S-N Fatigue Strength Curve Analysis for A572 Gr. 50 Steel, Based on the True Stress—True Strain Approach

^{*}

## Abstract

**:**

^{3}and 10

^{6}cycles. In the application, published experimental data for the CSA G40.21 Gr. 350W steel is used to derive the true stress and true strain parameters of the A572 Gr. 50 steel. Additionally, the application of the S-N curve, its probabilistic percentiles and the Weibull parameters that represent these percentiles are all determined step by step. Since the proposed method is flexible, then it can be applied to determine the probabilistic percentiles of any other material.

## 1. Introduction

## 2. Fatigue Strength Behavior of the A572 Gr. 50 Steel

#### 2.1. True Stress-True Strain Analysis for the A572 Gr. 50 Steel

#### 2.2. S-N Fatigue Strength Analysis for A572 Gr. 50 Steel

#### 2.3. Proposed Method to Determine the A572 Gr. 50 S-N Curve

**Note 1:**Remember that ${\u03f5}_{ut}=n$ holds only on the ${S}_{ut}$ coordinate. For any other coordinate, the corresponding ${\u03f5}_{i}$ value must be estimated.

## 3. Weibull/S-N Fatigue Strength Analysis for A572 Gr. 50 Steel

#### 3.1. Fatigue Strength Analysis Based on Weibull Approach

**Note 2:**from Equation (7), as mentioned by Piña-Monarrez (2019), the Weibull scale parameter does not depend on unknown variables, therefore it completely represents the ${({S}_{f}^{\prime})}_{{10}^{3}}$ and ${({S}_{f}^{\prime})}_{{10}^{6}}$ values.

**Note 3:**Notice that, in Equation (9), $R({t}_{n})$ represents the reliability of the analysis. It does not represent the reliability of the designed material.

#### 3.2. Proposed Fatigue Strength Based Weibull Method

## 4. Probabilistic S-N Fatigue Strength Curve

#### 4.1. Generalities of S-N Percentiles Formulation

#### 4.2. Proposed Method to Determine the Probabilistic S-N Fatigue Curve

## 5. Fatigue Strength S-N Curve Application Case

^{3}and 10

^{6}are ${({{S}^{\prime}}_{f})}_{{10}^{3}}=$220.10 MPa and ${({{S}^{\prime}}_{f})}_{{10}^{6}}={S}_{e}=$131.72 MPa.

^{3}and 10

^{6}the standardized S-N diagram is given in the Figure 2.

**Note 4:**By following this proposed method, let us present the analysis of the fatigue strength ${({{S}^{\prime}}_{f})}_{{10}^{6}}$ cycles. The estimated data is given (all strength data is given in MPa):

#### 5.1. Stress-Strength Analysis for a Given Structural Component Based on the Probabilistic S-N curve

#### 5.2. Failure Theory Analysis by Using Probabilistic S-N curve

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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STEP 10. EQ. 9: N | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

STEP 10. EQ. 10: y_{i} | −3.4034833 | −2.4916620 | −2.0034632 | −1.6616459 | −1.3943983 | −1.1720537 | −0.9793812 |

STEP 10. EQ. 9: N | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

STEP 10. EQ. 10: y_{i} | −0.8074473 | −0.6504921 | −0.5045088 | −0.3665129 | −0.2341223 | −0.1052851 | 0.0219284 |

STEP 10. EQ. 9: N | 15 | 16 | 17 | 18 | 19 | 20 | 21 |

STEP 10. EQ. 10: y_{i} | 0.1495258 | 0.2798450 | 0.4159621 | 0.5625020 | 0.7276158 | 0.9293107 | 1.2296598 |

STEP 10. ∑y_{i} − μ_{Y} | −0.5456241 | ||||||

STEP 10. ∑y_{i} − σ_{Y} | 1.17511694 |

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**MDPI and ACS Style**

Molina, A.; Piña-Monarrez, M.R.; Barraza-Contreras, J.M.
Weibull S-N Fatigue Strength Curve Analysis for A572 Gr. 50 Steel, Based on the True Stress—True Strain Approach. *Appl. Sci.* **2020**, *10*, 5725.
https://doi.org/10.3390/app10165725

**AMA Style**

Molina A, Piña-Monarrez MR, Barraza-Contreras JM.
Weibull S-N Fatigue Strength Curve Analysis for A572 Gr. 50 Steel, Based on the True Stress—True Strain Approach. *Applied Sciences*. 2020; 10(16):5725.
https://doi.org/10.3390/app10165725

**Chicago/Turabian Style**

Molina, Alejandro, Manuel R. Piña-Monarrez, and Jesús M. Barraza-Contreras.
2020. "Weibull S-N Fatigue Strength Curve Analysis for A572 Gr. 50 Steel, Based on the True Stress—True Strain Approach" *Applied Sciences* 10, no. 16: 5725.
https://doi.org/10.3390/app10165725