# Ratcheting Strain and Microstructure Evolution of AZ31B Magnesium Alloy under a Tensile-Tensile Cyclic Loading

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## Abstract

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## 1. Introduction

^{7}cycles). In recent years, microstructure changes were reported only after fatigue test, however its evolution during the fatigue test was not found. In the present paper, cyclic deformation behaviors of (hot-rolled) AZ31B alloy under tensile-tensile cyclic loads are investigated at ambient temperature. The relationship between the ratcheting effect and microstructure change under a cyclic loading are discussed.

## 2. Experiments

^{7}cycles is 95.05 MPa, as shown in Figure 1b. The gage diameter of the fatigue specimens cut from the plate is 25 mm (Chinese Standard GBT 3075-2008 [22]). The specimens’ surfaces were polished using emery papers, which was to reduce the external effects.

_{min}/σ

_{max}) is 0.1 and the frequency is 1 Hz. The specimen tested at σ

_{max}140 MPa was investigated representatively, and its deformation and microstructure were analyzed during the whole fatigue process.

## 3. Results and Discussion

#### 3.1. Deformation Curves of the AZ31B Alloy under cyclic loading

_{0.2}=146.02 MPa), the irreversible deformation still occurred. During the initial loading process, the hysteresis loops’ change was unstable. The irreversible deformation increased with the cycles in the material. After 10,000 cycles, the hysteresis loops remained narrower and stable. This means that the clear ratcheting effect occurred during the cyclic loading. The ratcheting strain is defined as the strain ${\epsilon}_{\left(r,i\right)}$ at cycle “i” [23]:

_{(i,max)}is the maximum strain and ε

_{(i,min)}is the minimum strain at cycle “i”.

_{s}keep constant in the second stage. In Stage III, the ratcheting strain speed was accelerated by the crack open distance during the crack propagated in the material, causing the final fracture [24]. As noticed, most of the fatigue life was spend before the Stage III. Especially, the strain was almost unchanged in Stage II. Furthermore, the ratcheting curves have the same tendency under different stress levels [25]. Therefore, the relationship between the ratcheting strain and microstructure evolution is the main concern of current study.

#### 3.2. Microstructure Evolution

#### 3.3. Geometrically Necessary Dislocation (GND) Density Change with the Cycle Increase

_{i}is the local misorientation around the point ‘i’ (100 nm × 100 nm) and ${\theta}_{j}^{sur}$ is the misorientation at its neighboring point ‘j’. To calculate the GND density, a simple equation from the strain gradient theory is used [34,35]:

^{GND}represents the GND density in tested area; Δθ

_{i}means the local misorientation; u is the unit length of the point (100 nm); b is the Burgers vector. $\mathrm{B}=\frac{2}{ub}=2b\times {10}^{16}{\mathrm{m}}^{2}$, is a constant for specific material. The column charts of the calculated GND density and their change were given in Figure 6.

_{1}and l

_{2}are the dividing lines of the three stages. The GND density increased sharply in the first Stage and fluctuated in small range in Stage II. The evolution pattern of the GND density is consistent with that shown in the ratcheting curve in Figure 2b. That is, the deformation of the material under cyclic loading was strongly affected by the change of the dislocation density.

#### 3.4. The Microstructure at the Crack Tip Area

#### 3.5. The Fatigue Fracture Mechanism

## 4. Conclusions

- (1)
- There is the ratcheting effect for the alloy under a cyclic loading of 140 MPa. The development of the ratcheting strain includes three stages: rapid increase stage (Stage I); steady stage (Stage II); and final abrupt increase stage (Stage III). The change of Extra Geometrically Necessary Dislocations (GNDs) was found to have the same evolutionary tendency as that of the ratcheting strain.
- (2)
- Two deformation mechanisms, basal slip and {10−12} tensile twinning, are found to be dominant during a cyclic loading, which is stress-controlled. The {0001} basal slip dominates plastic deformation during the crack initiation (Stage I and II) and the 86° {10−12} tensile twinning is dominant in Stage III.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**The strength curves of AZ31B magnesium alloy: (

**a**) The tensile stress–strain curve; (

**b**) S–N curve.

**Figure 2.**The deformation curves under σ

_{max}of 140 MPa in AZ31B magnesium specimen: (

**a**) The hysteresis loops under different cycles; (

**b**) The ratcheting evolution curve under different cycles.

**Figure 3.**The grains change during cyclic loading: (

**a**) As-received material; (

**b**) cycles at 1000; (

**c**) cycles at 5000; (

**d**) cycles at 10,000; (

**e**) cycles at 20,000; (

**f**) cycles at 30,000.

**Figure 4.**Misorientation distributions in AZ31B magnesium alloy: (

**a**) as-received metal; (

**b**) cycles at 5000; (

**c**) cycles at 10,000; (

**d**) cycles at 15,000; (

**e**) cycles at 20,000; (

**f**) cycles at 30,000.

**Figure 6.**The mean GND density distributions under loading of 140 MPa (

**a**) as-received magnesium alloy; and in specimens (

**b**) cycles at 100; (

**c**) cycles at 1000; (

**d**) cycles at 5000; (

**e**) cycles at 10,000; (

**f**) cycles at 15,000.

**Figure 9.**The Schmid factor distribution in the as-received material. (

**a**) the distributions of the Schmid factor on the base metal; (

**b**) the crystal shifts from hard orientation to soft orientation

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**MDPI and ACS Style**

Yan, Z.; Wang, D.; Wang, W.; Zhou, J.; He, X.; Dong, P.; Zhang, H.; Sun, L.
Ratcheting Strain and Microstructure Evolution of AZ31B Magnesium Alloy under a Tensile-Tensile Cyclic Loading. *Materials* **2018**, *11*, 513.
https://doi.org/10.3390/ma11040513

**AMA Style**

Yan Z, Wang D, Wang W, Zhou J, He X, Dong P, Zhang H, Sun L.
Ratcheting Strain and Microstructure Evolution of AZ31B Magnesium Alloy under a Tensile-Tensile Cyclic Loading. *Materials*. 2018; 11(4):513.
https://doi.org/10.3390/ma11040513

**Chicago/Turabian Style**

Yan, Zhifeng, Denghui Wang, Wenxian Wang, Jun Zhou, Xiuli He, Peng Dong, Hongxia Zhang, and Liyong Sun.
2018. "Ratcheting Strain and Microstructure Evolution of AZ31B Magnesium Alloy under a Tensile-Tensile Cyclic Loading" *Materials* 11, no. 4: 513.
https://doi.org/10.3390/ma11040513