# The Reliability of SAC305 Individual Solder Joints during Creep–Fatigue Conditions at Room Temperature

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Test Vehicle

#### 2.2. Experimental Set-Up

#### 2.3. Test Profile

## 3. Results and Discussions

#### 3.1. Weibull Plots Analysis and Prediction Modeling

#### 3.1.1. Mechanical Fatigue Condition

#### Weibull Plots

#### Prediction Modeling

_{63}= C × P

^{−n}

_{63}is the characteristic life, P is the stress magnitude, C, n are material constants. n is called the ductility factor where lower value implies higher ductility. Figure 8 illustrates the fatigue life as a function of stress amplitude. Seven solder joints are cycled until complete failure with each stress level. The fatigue life is reduced drastically at higher stress levels.

#### 3.1.2. Dwelling (Creep–Fatigue) Condition

#### Weibull Plots

#### Prediction Modeling

_{d}) must be identified. The correlations to predict the power values of n and C value as a function of dwell time are shown in Figure 14 and Figure 15. From Equation (2), the characteristic life is predicted as a function of stress amplitude and dwell time as shown in Equation (3).

_{63}is the characteristic life, P is the stress amplitude, and t

_{d}is the dwell time. To find out the general reliability model of solder joints as a function of dwell time, parameters in Equation (1) must be determined. In our case, there is no observed trend for the shape parameter of the Weibull plot at different dwell times and stress amplitudes. The shape parameter values were found between 3.5 and 14 with an average of 6.66. For the scale parameter (θ); the finding of characteristic life from Equation (3) is substituted in Equation (1). As a result, the general reliability model as a function of dwell time is established as shown in Equation (4).

#### 3.2. Stress–Strain Analysis

#### 3.3. Creep Effect

#### 3.4. The Coffin–Manson and Morrow Energy Models

#### Coffin–Manson Model

_{d}

^{0.119}

_{d}is the dwell time. The D-value could also be formulated as a function of stress amplitude according to Figure 27. Thus, Equation (6) can be expressed as shown in Equation (6). The dwell time’s impact on the value of the plastic strain is depicted by the D coefficient in terms of its magnitude.

^{0.1248}

^{P}× t

_{d}

^{0.119}

_{63}is the characteristic fatigue life, Z is the fatigue ductility coefficient, PS is the plastic strain, and R is the fatigue exponent. Based on the Coffin–Manson equation, the general reliability model as a function of plastic strain could be developed under certain conditions. If there is no clear trend for the coefficient of fatigue ductility (Z) and the fatigue exponent (R) at various dwellings, this implies that dwelling does not affect the Coffin–Manson equation. Moreover, data points for all conditions should have a similar trend (slope) to be fitted to a global Coffin–Manson equation no matter what the dwelling time is. To establish such a model, the characteristic life as a function of plastic strain (Equation (7)) must be obtained. Then, the new equation is substituted in Equation (1) to obtain the reliability model. To examine the model applicability in our case, the above-stated conditions must be checked. Figure 28 demonstrates the characteristic life as a function of plastic strain for various dwelling periods. Data points have the same trend (slope) and could be fitted to a global Coffin–Manson equation. The values for Coffin–Manson equation constants at various dwellings are generated accordingly, as shown in Table 2. It is obviously shown that there is no clear trend in these constants regardless of the dwelling time. This means dwelling has no effect on the Coffin–Manson model, and a general model could be developed. The values of the coefficient of fatigue ductility (Z) and the fatigue exponent (R) for the global equation are 0.19 and 0.646, respectively. Moreover, the global Coffin–Manson model is illustrated in Figure 29.

_{63}= 0.0771 × PS

^{−1.546}

#### 3.5. Morrow Energy Model

_{d}

^{0.12}

_{d}is the dwell time. On the other hand, the H-value could also be formulated as a function of stress amplitude according to Figure 31. Thus, Equation (10) can be expressed as shown in Equation (11). The H coefficient illustrates the magnitude of the dwell time impact on the value of the inelastic work per cycle.

^{−6}× P − 7 × 10

^{−5}) t

_{d}

^{0.12}

_{63}is the characteristic fatigue life, G is the fatigue ductility coefficient, W is the inelastic work, and m is the fatigue exponent. In the same way as the Coffin–Manson model, the reliability model as a function of inelastic work based on the Morrow Energy model could be established under similar circumstances defined above. Our data show that fatigue ductility and fatigue exponent have no clear trend at various dwellings, as shown in Figure 32. Furthermore, the data points on a log–log scale demonstrate having a similar trend (slope) and could be fitted to the global Morrow Energy equation. The fatigue ductility and the fatigue exponent constants for all dwellings are specified accordingly, as shown in Table 3. It is obviously shown that there is no clear trend in these constants regardless of the dwelling time. This means dwelling has no effect on the Morrow Energy model, and the global model could be developed. Figure 33 shows the global model for Morrow Energy equation considering that the global constants for fatigue ductility coefficient and fatigue exponent are 0.0025 and 0.737, respectively.

_{63}= 0.0003 W

^{−1.356}

#### 3.6. Microstructure Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Weibull distributions for SAC305 joints cycled at different stress amplitudes at no dwelling.

**Figure 9.**Characteristic life as a function of stress amplitude for SAC305 solder joints at no dwelling.

**Figure 10.**Weibull distributions for SAC305 joints cycled at different stress amplitudes at 10 s dwelling.

**Figure 11.**Weibull distributions for SAC305 joints cycled at different dwellings with 16 MPa stress level.

**Figure 12.**Characteristic life as a function of dwell time for SAC305 solder joints cycled with various stress levels.

**Figure 13.**Characteristic life as a function of stress amplitude for SAC305 solder joints at various dwelling times.

**Figure 16.**The hysteresis loops for SAC305 joints cycled with different stress amplitudes at no dwelling.

**Figure 17.**The hysteresis loops for SAC305 joints cycled with different stress amplitudes at 10 s dwelling.

**Figure 18.**The hysteresis loops for SAC305 joints cycled at various dwellings with 24 MPa stress level.

**Figure 19.**Inelastic work vs. the number of cycles for SAC305 solder joints cycled at 16 MPa stress amplitude until failure.

**Figure 20.**Inelastic work vs. the number of cycles for SAC305 solder joints cycled at various stress amplitudes at no dwelling until failure.

**Figure 21.**Inelastic work vs. the number of cycles for SAC305 solder joints cycled at 20 MPa stress amplitudes at various dwellings until failure.

**Figure 22.**Hysteresis loops (

**right**) with no dwelling and with 10 s dwelling cycled at 16 MPa, and a bar chart (

**left**) for average inelastic work for both cases.

**Figure 28.**Characteristic life vs. plastic strain for SAC305 joints at various dwelling times on a log–log scale.

**Figure 29.**Characteristic life (global Coffin–Manson equation) vs. plastic strain for SAC305 joints at various dwelling times on a log–log scale.

**Figure 32.**Characteristic life vs. inelastic work for SAC305 joints at various dwelling times on a log–log scale.

**Figure 33.**Characteristic life (global Morrow Energy equation) vs. plastic work for SAC305 joints at various dwelling times on a log–log scale.

**Figure 34.**SEM images for tested joints under various dwelling periods compared with no dwelling condition (most left).

Load Amplitude (Mpa) | Fatigue Only Test | Creep–Fatigue Test | ||
---|---|---|---|---|

0 s Dwell | 10 s Dwell | 60 s Dwell | 180 s Dwell | |

16 MPa | 7 samples | 7 samples | 7 samples | 7 samples |

20 MPa | 7 samples | 7 samples | 7 samples | 7 samples |

24 MPa | 7 samples | 7 samples | 7 samples | 7 samples |

Dwelling Time | Fatigue Ductility (Z) | The Fatigue Exponent (R) |
---|---|---|

0 | 0.108 | 0.565 |

10 | 0.255 | 0.7 |

60 | 0.185 | 0.636 |

180 | 0.313 | 0.745 |

Global | 0.19 | 0.646 |

Dwelling Time | Fatigue Ductility (G) | The Fatigue Exponent (m) |
---|---|---|

0 | 0.0023 | 0.713 |

10 | 0.0055 | 0.85 |

60 | 0.0028 | 0.69 |

180 | 0.0085 | 0.96 |

Global | 0.0025 | 0.737 |

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## Share and Cite

**MDPI and ACS Style**

Abueed, M.; Al Athamneh, R.; Tanash, M.; Hamasha, S.
The Reliability of SAC305 Individual Solder Joints during Creep–Fatigue Conditions at Room Temperature. *Crystals* **2022**, *12*, 1306.
https://doi.org/10.3390/cryst12091306

**AMA Style**

Abueed M, Al Athamneh R, Tanash M, Hamasha S.
The Reliability of SAC305 Individual Solder Joints during Creep–Fatigue Conditions at Room Temperature. *Crystals*. 2022; 12(9):1306.
https://doi.org/10.3390/cryst12091306

**Chicago/Turabian Style**

Abueed, Mohammed, Raed Al Athamneh, Moayad Tanash, and Sa’d Hamasha.
2022. "The Reliability of SAC305 Individual Solder Joints during Creep–Fatigue Conditions at Room Temperature" *Crystals* 12, no. 9: 1306.
https://doi.org/10.3390/cryst12091306