# Experiments and Modeling of Fatigue Behavior of Friction Stir Welded Aluminum Lithium Alloy

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## Abstract

**:**

_{1}(Al

_{2}CuLi) and δ’(Al

_{3}Li) seen in the base metal were observed to coarsen and dissolve due to the FSW process. In order to evaluate the static and fatigue behavior of the FSW of the AA2099, monotonic tensile and fully-reversed strain-controlled fatigue testing were performed. Mechanical testing of the FSW specimens found a decrease in the ultimate tensile strength and fatigue life compared to the base metal. While the process parameters had an effect on the monotonic properties, no significant difference was observed in the number of cycles to failure between the FSW parameters explored in this study. Furthermore, post-mortem fractography analysis of the FSW specimens displayed crack deflection, transgranular fracture, and delamination failure features commonly observed in other parent Al–Li alloys. Lastly, a microstructurally-sensitive fatigue model was used to elucidate the influence of the FSW process on fatigue life based on variations in grain size, microhardness, and particle size in the AA2099 FSW.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Multistage Fatigue Model

_{total}is the total fatigue life, or the total number of cycles until failure. The incubation life, N

_{inc,}is the initial stage of the formation of fatigue cracks. The condensed small crack growth stage, ${N}_{\frac{MSC}{PSC}}$, represents the number of cycles necessary for the propagation of a microstructurally small, physical crack to reach a critical length. The last stage, N

_{LC}, is the number of cycles required for the advancement of a long crack to ultimate fracture. The MSF model has been modified and extended for a variety of materials and applications since its development [31,32,33,34,35,36,37,38,39,40].

#### 2.1.1. Incubation

_{in}

_{c}represents the number of cycles until the establishment of a fatigue crack, which is characterized by the occurrence of microscopic damage. The MSF model employs a revised Coffin–Manson law for crack incubation for enhanced micro-scale relationships:

_{inc}is the linear coefficient, q is a material dependent constant, N

_{inc}is the incubation life, α is the exponential coefficient, $\frac{\Delta {\gamma}_{max}{}^{p*}}{2}$ is the local average maximum plastic shear strain amplitude, ε

_{a}is the remote applied strain amplitude, and ε

_{th}is the micro-plasticity strain threshold. The expression $\psi ={\left[\frac{\left({MPS}^{2}\right)}{\left(NND\right)\left(GS\right)}\right]}^{\gamma}$ is a function of the maximum particle size (MPS), nearest neighbor distance (NND), grain size (GS), and the sensitivity exponent ($\gamma $). The term ψ is a relationship that integrates experimentally observed microstructure characteristics to enhance model receptiveness to microstructure variation.

_{lim}, which is dictated by the ratio of the size of the plastic zone to the size of the inclusion as a function of the applied strain amplitude.

_{1}and y

_{2}are model constants associated with the remote applied strain translation and local plastic shear strain, and R is the load ratio. Y = y

_{1}under fully reversed strain controlled loading. Additionally, when the previously discussed parameter $\mathit{l}/\mathit{D}$ reaches its limit $\left({\mathit{\eta}}_{\mathit{l}\mathit{i}\mathit{m}}<\frac{\mathit{l}}{\mathit{D}}\le \mathbf{1}\right),$ the parameter $\overline{\mathit{Y}}$ is enhanced to include geometric effects:

_{th}is the strain threshold, and ε

_{per}is the percolation limit. Through micromechanical simulations, the microplasticity constants ε

_{th}, ε

_{per}, and ${\epsilon}_{a}$ were established. The values can also be calculated by using the standard endurance limit calculations, ${\epsilon}_{th}=\frac{0.29{S}_{ult}}{E}\text{}\mathrm{and}\text{}{\epsilon}_{per}=\frac{0.7{\sigma}_{y}^{cyclic}}{E}$ ${S}_{ult}$ is the ultimate strength, ${\sigma}_{y}^{cyclic}$ is the cyclic yield stress, and E is the elastic modulus. The fatigue crack transitions into the next phase of fatigue damage when the localized plastic zone has been saturated.

#### 2.1.2. Small Crack Growth

_{i}is the initial crack length, as a function of inclusion size. The crack tip displacement threshold range $\left(\Delta {CTD}_{\mathrm{th}}\right)$ is defined by the Burger’s vector for pure face centered cubic (FCC) aluminum ($2.85\times {10}^{-4}$ µm). The χ parameter is typically less than unity and estimated as 0.35 for aluminum alloys [39]. Showing fluctuating degrees of influence, the crack tip displacement range is reasonably proportional to the length of the crack and applied stress amplitude (σ

_{a}) for high cycle fatigue and macroscopic, plastic shear strain range in low cycle fatigue. Equation (10) defines $\Delta CTD$ as a function of remote applied loading.

#### 2.1.3. Long Crack Growth

## 3. Results

#### 3.1. Microstructure

#### 3.1.1. Grain Structure

#### 3.1.2. Microhardness

#### 3.1.3. Secondary Phase Characterization

_{1}precipitates were Cu-rich and were seen as bright platelets, consistent with the literature [43]. These particles help to block dislocation movement within the material, and thus increase strength. The δ’ precipitates were Li-rich and were seen as dark, spherical (or dot-shaped) precipitates. Selected area diffraction (SAD) data from each corresponding region confirmed the identity of the T

_{1}and delta-prime precipitates.

_{1}precipitates coarsened due to the heat input from FSW and were much larger (103–258 nm) than the BM (29–104 nm). Figure 4c shows the HAZ of a Weld II produced at 700 rpm and 500 mm/min. Due to the lower heat input seen with higher transverse speeds, the number of T

_{1}strengthening precipitates seen was considerably higher than that of the previous weld. In addition, the precipitates had only coarsened slightly (37–125 nm) as compared to the BM (29–104 nm). The T

_{1}precipitates coarsened considerably during FSW process I, but only marginally in FSW process II. With the increase in precipitate size, an increase in the spacing between precipitates became noticeable. This increase in spacing will reduce the Orowan strengthening for the material. The diffraction patterns taken from both welds showed no precipitates other than T

_{1}. The heat input from FSW caused the dissolution of the δ’ precipitates, resulting in the reduction of strength observed in the welds. The coarsening and dissolution of strengthening precipitates is commonly seen in other FSW Al–Li alloys [21,25,44].

#### 3.2. Monotonic Stress–Strain Behavior

#### 3.3. Low-Cycle Fatigue Parameters

#### 3.4. Fracture Analysis

#### 3.5. MSF Model Correlation

_{y}), ultimate strength (σ

_{ult}), hardness, and grain size were determined through experimental data analysis and used in calibrating the model. The MSF model was able to accurately correlate the experimental data performed by varying the material parameters determined from material characterization efforts. To appropriately analyze the total fatigue life, the MSF model was discretized into estimations for the incubation and crack growth stages. As such, the MSF model reveals that small crack growth dominates total fatigue life for high-strain amplitudes, and the incubation stage is dominant in the total fatigue life for low-strain amplitudes. Figure 12d shows model fits for the base metal and both welding parameter sets, showing the model’s capability to capture the effects of FSW on the fatigue life.

## 4. Conclusions

- AA2099 was successfully friction stir welded free of large voids or welding defects. In both of the welds, four characteristic regions could be identified: the stir zone (SZ), the thermo-mechanical affected zone (TMAZ), the heat-affected zone (HAZ), and base metal (BM).
- The SZ in Weld II was considerably smaller than that of Weld I, yet the grain size in the SZ of Weld I was smaller than that of Weld II. These size effects were correlated to the heat inputs.
- Although Welds I and II displayed similar cross-section hardness profiles, the hardness values in the SZ of weld I were slightly lower than those of Weld II. Weld I was produced at a lower transverse speed, which increased the heat input in the material and further enabled the dissolution of strengthening precipitates resulting in these lower values.
- The heat input of the FSW process enabled the dissolution of the strengthening precipitate δ’ and the dissolution or coarsening of fine T
_{1}precipitates. Welds I and II had lower amounts of T_{1}particles than that in the BM. Although the sizes of the T_{1}precipitates in Weld II increased in relation to the BM, they were noticeably smaller than those of Weld I. - For strain amplitudes below 0.3%, the elastic strain amplitude was significant in the cyclic deformation. In contrast, at strains amplitudes above 0.1%, the plastic strain amplitude was the dominant factor.
- Overall, the base material demonstrated higher fatigue resistance in both high-cycle and low-cycle fatigue than the FSW specimens.
- For low-cycle fatigue, the two welded parameters displayed similar fatigue results.
- The high-cycle fatigue of Weld II (700 rpm and 500 mm/min) showed fatigue lives 1.5–2 times greater than that of Weld I (400 rpm and 100 mm/min).
- Fracture specimens displayed crack deflection, delamination failure features commonly observed in Al–Li alloys. Fatigue cracks initiated at particles located near the surface of the samples.
- The MSF model was successfully modified to account for competing effects of grain size and hardness variations within an FSW.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Welding schematic, (

**b**) pin tool schematic, and (

**c**) fatigue test specimen geometry (all dimensions are in mm).

**Figure 2.**Optical micrographs showing (

**a**–

**b**) macro views of the cross-section; (

**c**–

**d**) microstructures in the stir zone (SZ); and (

**e**–

**f**) heat affected zones (HAZs) of welds produced at (

**a**,

**c**,

**e**). Weld I: 400 rpm and 100 mm/min and (

**b**,

**d**,

**f**). Weld II: 700 rpm and 500 mm/min.

**Figure 3.**Microhardness profiles obtained from welds produced at (

**a**) Weld I: 400 rpm, 100 mm/min and (

**b**) Weld II: 700 rpm, 500 mm/min. Note that all values of hardness are shown in Vickers hardness (HV).

**Figure 4.**High-angle annular dark-field scanning transmission electron microscopy images of (

**a**) base metal viewed along the <112>

_{Al}zone axis, (

**b**) Weld I (400 rpm and 100 mm/min) viewed along the <011>

_{Al}zone axis, (

**c**) Weld II (700 rpm and 500 mm/min) viewed along the <011>

_{Al}zone axis, and (

**d**–

**f**) the corresponding selected area diffraction patterns from the regions shown in (

**a**–

**c**).

**Figure 5.**Monotonic stress–strain comparison of AA2099 base material and FSW AA2099 with parameters 700 rpm and 500 mm/min, and 400 rpm and 100 mm/min, respectively.

**Figure 6.**Hysteresis loops for welds produced at (

**a**,

**b**) 400 rpm and 100 mm/min and (

**c**,

**d**) 700 rpm and 500 mm/min for (

**a**,

**c**) 0.4% strain amplitude and (

**b**,

**d**) 0.8% strain amplitude first cycle and half life cycle.

**Figure 7.**Strain-life fatigue behavior of (

**a**) base metal, (

**b**) Weld I (400 rpm/100 mm/min), (

**c**) Weld II (700 rpm/500 mm/min), and (

**d**) comparison between the fatigue lives of the base metal and both welds.

**Figure 8.**Optical macrographs showing the failure locations at various strain amplitudes for (

**a**) Weld I and (

**b**) Weld II.

**Figure 9.**Optical micrographs showing the fracture surfaces for the Weld I processed at 400 rpm and 100 mm/min (

**a**,

**c**) and the Weld II processed at 700 rpm and 500 mm/min (

**b**,

**d**) and tested under cyclic loading at 0.3% (

**a**,

**b**) and 0.8% (

**c**,

**d**) strain amplitude.

**Figure 10.**(

**a**) Representative fracture surface for the weld produced at a tool rotational speed of 400 rpm and tested at 0.2% strain amplitude. (

**b**) Backscatter electron image showing the morphology of the fractured secondary particles in Region i. (

**c**) Magnified images of a crack initiation site in Region ii.

**Figure 11.**(

**a**) Representative fracture surface for the Weld II tested at 0.2% strain amplitude. (

**b**) Magnified image of a crack initiation site in Region i. (

**c**) Backscatter electron image showing the morphology of the fractured secondary particles in Region ii.

**Figure 12.**MSF model correlation for (

**a**) the BM, (

**b**) FSW AA2099 produced at 400 rpm and 100 mm/min, (

**c**) FSW AA2099 produced at 700 rpm and 500 mm/min., and (

**d**) MSF model fits for the BM and both welding parameter sets.

Chemical Composition Limits of Wrought AA2099 (Weight %) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Elements | Cu | Li | Zn | Mg | Mn | Zr | Ti | Fe | Si | Al |

Min | 2.40 | 1.60 | 0.40 | 0.10 | 0.10 | 0.05 | - | - | - | Remainder |

Max | 3.00 | 2.00 | 1.00 | 0.50 | 0.50 | 0.12 | 0.10 | 0.07 | 0.05 | Remainder |

Low Cycle Fatigue Parameters | Al–Li Alloy 2099 (BM) | Weld I (400 rpm 100 mm/min) | Weld II (700 rpm 500 mm/min) |
---|---|---|---|

Cyclic strain-hardening exponent n′ | 0.0601 | 0.123 | 0.147 |

Cyclic strength coefficient K′, MPa | 664 | 666.4 | 798.5 |

Fatigue strength coefficient ${\sigma}_{f}^{\prime}$, MPa | 1009 | 515 | 559 |

Fatigue strength exponent b | −0.126 | −0.084 | −0.089 |

Fatigue ductility coefficient ${\epsilon}_{f}^{\prime}$ | 0.648 | 0.1231 | 0.0884 |

Fatigue ductility exponent c | −0.899 | −0.684 | −0.604 |

Coefficients | AA 2099 Base Metal | Weld I: 400 rpm and 100 mm/min | Weld II: 700 rpm and 500 mm/min |
---|---|---|---|

Ultimate Strength (MPa) | 558 | 342 | 390 |

Yield Strength (MPa) | 510 | 245 | 284 |

Grain Size (µm) | 1000 | 20 | 35 |

Hardness (HV) | 155 | 83 | 98 |

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## Share and Cite

**MDPI and ACS Style**

Cisko, A.R.; Jordon, J.B.; Avery, D.Z.; Liu, T.; Brewer, L.N.; Allison, P.G.; Carino, R.L.; Hammi, Y.; Rushing, T.W.; Garcia, L.
Experiments and Modeling of Fatigue Behavior of Friction Stir Welded Aluminum Lithium Alloy. *Metals* **2019**, *9*, 293.
https://doi.org/10.3390/met9030293

**AMA Style**

Cisko AR, Jordon JB, Avery DZ, Liu T, Brewer LN, Allison PG, Carino RL, Hammi Y, Rushing TW, Garcia L.
Experiments and Modeling of Fatigue Behavior of Friction Stir Welded Aluminum Lithium Alloy. *Metals*. 2019; 9(3):293.
https://doi.org/10.3390/met9030293

**Chicago/Turabian Style**

Cisko, Abby R., James B. Jordon, Dustin Z. Avery, Tian Liu, Luke N. Brewer, Paul G. Allison, Ricolindo L. Carino, Youssef Hammi, Timothy W. Rushing, and Lyan Garcia.
2019. "Experiments and Modeling of Fatigue Behavior of Friction Stir Welded Aluminum Lithium Alloy" *Metals* 9, no. 3: 293.
https://doi.org/10.3390/met9030293