# Low-Cycle Fatigue Behavior of Hot V-Bent Structural Components Made of AZ31B Wrought Magnesium Alloy

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hot Bending Process

#### 2.2. Microstructural Investigations

^{©}[24].

#### 2.3. Low-Cycle Fatigue Tests at Room Temperature

## 3. Numerical Simulation of the Novel Hot-Bent Structural Component

## 4. Results and Discussion

#### 4.1. Microstructural Analyses

#### 4.2. Low-Cycle Fatigue Tests

## 5. Conclusions

- In domains with high plastic deformation during the hot forming process of the specimen, a highly inhomogeneous microstructure with serrated grain boundaries can be observed. This is due to the low-temperature dynamic recrystallization.
- The hot forming process leads to the formation of BTG in the gauge area on the compressively loaded concave side of the specimen. These extend at a 45° angle to the sheet plane approx. 1 $\mathrm{m}$$\mathrm{m}$ in the direction of the center of the sheet wall thickness. The EBSD and light microscope investigations of the microstructure after applied cyclic loading showed that these BTGs are no longer detectable. The reason for this is that the occurrence of twins distributes evenly after cyclic loading. The information on how far the material twins toward the center of the sheet wall thickness was used to determine the highly strained volume to apply the CH$\epsilon $V.
- The study shows that fatigue models developed with data from uniaxial experiments and the CH$\epsilon $V can represent the fatigue life of the tested structural components made of the wrought magnesium alloy AZ31B. In particular, the model developed by using a dataset containing data from both as-received and hot-bent uniaxial specimens shows a satisfactory prediction of the fatigue life of the V-bent specimens. Nevertheless, every model examined tends to underestimate the life of the specimens.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BS | Bent specimen |

BTG | Band of twinned grains |

CH$\epsilon $V | Concept of highly strained volume |

DIC | Digital image correlation |

EBSD | Electron backscatter diffraction |

FEM | Finite Element Method |

LLL | Lower load level |

Mg | Magnesium |

ND | Normal direction |

RD | Rolling direction |

RMSE | Root Mean Square Error |

TD | Transverse direction |

ULL | Upper load level |

${V}_{\epsilon}$ | Highly strained volume |

Zn | Zinc |

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**Figure 1.**Variations of the structural component specimen: (

**a**) blank of the structural component specimen with a global $({x}_{1},{x}_{2},{x}_{3})$-coordinate system; (

**b**) the investigated versions of the structural component with a cylindrical coordinate system $(r,\phi ,{x}_{2})$ in the gauge area.

**Figure 2.**Forming tool and structural component specimen: (

**a**) setup of the forming tool with inserted structural component, thermocouple and modular exchangeable radius punches (blue) and dies (red); (

**b**) modular exchangeable radius punches and dies of the respective structural component variant.

**Figure 3.**Test setup for force-controlled LCF tests on V-bent structural components using 3D digital image correlation for strain measurement.

**Figure 4.**Numerical simulation of the structural component made of AZ31B with bending radius ${R}_{\mathrm{BS}12}=12\mathrm{m}\mathrm{m}$: (

**a**) stress field ${\sigma}_{\phi \phi}(r,\phi ,{x}_{2})$ of a FEM quarter model at a given load of $F=-275\mathrm{N}$ in ${x}_{1}$-direction; (

**b**) stress ${\sigma}_{\phi \phi}$ along the path ${L}_{{x}_{2}}$; (

**c**) stress ${\sigma}_{\phi \phi}$ along the path ${L}_{{x}_{3}}$; (

**d**) stress ${\sigma}_{\phi \phi}$ along the path ${L}_{\phi}$.

**Figure 5.**Numerical simulation of the structural component made of AZ31B with bending radius ${R}_{\mathrm{BS}12}=12\mathrm{m}\mathrm{m}$: (

**a**) stress field ${\sigma}_{22}(r,\phi ,{x}_{2})$ of a FEM quarter model at a given load of $F=-275\mathrm{N}$ in ${x}_{1}$-direction; (

**b**) stress ${\sigma}_{22}$ over the path ${L}_{{x}_{2}}$; (

**c**) stress ${\sigma}_{22}$ over the path ${L}_{\phi}$; (

**d**) stress ratio ${\sigma}_{22}/{\sigma}_{\phi \phi}$ over the path ${L}_{{x}_{2}}$; (

**e**) stress ratio ${\sigma}_{22}/{\sigma}_{\phi \phi}$ over the path ${L}_{\phi}$.

**Figure 6.**Gauge area and microstructure of the structural component specimen BS9-003 made of AZ31B after the bending process: (

**a**) overview of the gauge area with line-shaped BTG; (

**b**) band structure with high and low densities of twins due to the bending process; (

**c**) magnified view of areas of high and low density of twins.

**Figure 7.**EBSD measurement with view in TD of the structural component specimen BS9-003 made of AZ31B after the bending process: (

**a**) orientation map including a BTG with scanning step size of $1.00\mathsf{\mu}\mathrm{m}$ and reference view in ND; (

**b**) orientation map including a BTG with scanning step size of $1.00\mathsf{\mu}\mathrm{m}$ and reference view in RD; (

**c**) orientation map within the BTG with reference view in ND and scanning step size of $0.115\mathsf{\mu}\mathrm{m}$; (

**d**) band contrast with detected $\left\{10\overline{1}2\right\}$ tension twins marked with red lines and borders of BTG marked with green lines.

**Figure 8.**$\left(0002\right)$ pole figures of (

**a**) the as-received material with view in the ND [13] and (

**b**) the V-bent specimen BS9-003 made of AZ31B after the bending process with view in the TD.

**Figure 9.**Gauge area and microstructure of the structural component specimen BS9-008 made of AZ31B after cyclic loading with ${R}_{\mathrm{F}}=-1$ and ${F}_{\mathrm{a}}=1104\mathrm{N}$: (

**a**) overview of the gauge area with visible cracks; (

**b**) crack in the area of twinned grains in the center of the specimen at ${x}_{2}=0$; (

**c**) magnified view at the crack tip; (

**d**) magnified view at the origin of the crack with visible twins.

**Figure 10.**EBSD measurements of the structural component specimen BS9-008 made of AZ31B after cyclic loading: (

**a**) EBSD orientation map of the specimen BS9-008 with scanning step size of $1\mathsf{\mu}\mathrm{m}$ with reference direction in ND; (

**b**) EBSD orientation map of the specimen BS9-008 with scanning step size of $0.115\mathsf{\mu}\mathrm{m}$ with visible serrated grain boundaries and reference direction in ND; (

**c**) $\left(0002\right)$ pole figure of the specimen BS9-008 with view in TD.

**Figure 11.**Three-dimensional and two-dimensional ${\tilde{\overline{\epsilon}}}_{\mathrm{RD},\mathrm{a}}$-${V}_{\epsilon}$-${N}_{\mathrm{f}}$ fatigue diagrams by applying the CH$\epsilon $V with regression parameters from results of low-cycle fatigue tests of the as-received material specimens.

**Figure 12.**Three-dimensional and two-dimensional ${\tilde{\overline{\epsilon}}}_{\mathrm{RD},\mathrm{a}}$-${V}_{\epsilon}$-${N}_{\mathrm{f}}$ fatigue diagrams by applying the CH$\epsilon $V with regression parameters from results of low-cycle fatigue tests of the hot-bent uniaxial specimens.

**Figure 13.**Three-dimensional and two-dimensional ${\tilde{\overline{\epsilon}}}_{\mathrm{RD},\mathrm{a}}$-${V}_{\epsilon}$-${N}_{\mathrm{f}}$ fatigue diagrams by applying the CH$\epsilon $V with combined regression parameters from results of low-cycle fatigue tests of the as-received material specimens and hot-bent uniaxial specimens.

**Figure 14.**Comparison of the calculated and experimentally determined numbers of cycles to failure ${N}_{\mathrm{f}}$: (

**a**) model with the regression parameters of the as-received material specimens; (

**b**) model with the regression parameters of the hot-bent uniaxial specimens; (

**c**) model with the regression parameters of the combined as-received material specimens and hot-bent uniaxial specimens.

Mg | Al | Zn | Mn | Cu | Si | Fe | Ni | Ca | Other Impurities |
---|---|---|---|---|---|---|---|---|---|

balance | 2.75 | 1.08 | 0.368 | 0.00262 | 0.0187 | 0.00282 | 0.00038 | 0.00041 | <0.004 |

**Table 2.**Parameters of the LCF tests: Applied force amplitude ${F}_{\mathrm{a}}$, force ratio ${R}_{\mathrm{F}}$, the test frequency f, the highly strained volume ${V}_{\epsilon}$, the mean effective strain amplitude ${\tilde{\overline{\epsilon}}}_{\phi \phi ,\mathrm{a}}$ and the numbers of cycles to failure ${N}_{\mathrm{f}}$ of the force-controlled cyclic tests.

Specimen ID | ${\mathit{F}}_{\mathbf{a}}$ (N) | ${\mathit{R}}_{\mathbf{F}}$ (-) | f (Hz) | ${\mathit{V}}_{\mathit{\epsilon}}$ (mm${}^{3}$) | ${\tilde{\overline{\mathit{\epsilon}}}}_{\mathit{\phi}\mathit{\phi},\mathbf{a}}$ (%) | ${\mathit{N}}_{\mathbf{f}}$ (-) |
---|---|---|---|---|---|---|

BS12-011 | 750 | $-1$ | 1.0 | 335 | 0.421 | 11,427 |

BS12-003 | 900 | $-1$ | 1.0 | 486 | 0.542 | 4216 |

BS12-012 | 1200 | $-1$ | 0.2 | 298 | 1.03 | 424 |

BS9-010 | 690 | $-1$ | 1.0 | 248 | 0.416 | 12,592 |

BS9-009 | 828 | $-1$ | 0.5 | 419 | 0.513 | 3319 |

BS9-008 | 1104 | $-1$ | 0.2 | 526 | 0.879 | 554 |

BS6-008 | 615 | $-1$ | 1.0 | 219 | 0.390 | 8623 |

BS6-007 | 738 | $-1$ | 0.5 | 270 | 0.527 | 3329 |

BS6-009 | 984 | $-1$ | 0.2 | 311 | 0.849 | 470 |

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**MDPI and ACS Style**

Mader, F.; Nischler, A.; Huber, O.
Low-Cycle Fatigue Behavior of Hot V-Bent Structural Components Made of AZ31B Wrought Magnesium Alloy. *Crystals* **2023**, *13*, 184.
https://doi.org/10.3390/cryst13020184

**AMA Style**

Mader F, Nischler A, Huber O.
Low-Cycle Fatigue Behavior of Hot V-Bent Structural Components Made of AZ31B Wrought Magnesium Alloy. *Crystals*. 2023; 13(2):184.
https://doi.org/10.3390/cryst13020184

**Chicago/Turabian Style**

Mader, Florian, Anton Nischler, and Otto Huber.
2023. "Low-Cycle Fatigue Behavior of Hot V-Bent Structural Components Made of AZ31B Wrought Magnesium Alloy" *Crystals* 13, no. 2: 184.
https://doi.org/10.3390/cryst13020184