# Failure Modelling of CP800 Using Acoustic Emission Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Flow Behaviour

#### 2.2. Failure Behaviour

^{−9}ton/mm

^{3}, 2.1 × 10

^{5}MPa and 0.3. For the flow behaviour, the extrapolated flow curve from the Swift approach and the parametrised Hill48 yield criterion were used. According to the loading angle, the RD of the butterfly specimen was adjusted in the material card. The calculation of the model was performed implicitly using the LS-Dyna Solver R12.0 (parallel multifrontal sparse solver) with double precision and hourglass control.

## 3. Results and Discussion

#### 3.1. Flow Behaviour

#### 3.2. Failure Behaviour

## 4. Summary and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Acronyms | Description |

AHHS | Advanced high-strength steels |

B | Bainite |

CP | Complex phase steel |

F | Ferrite |

JC | Johnson–Cook failure model |

M | Martensite |

ND | Normal direction |

RD | Rolling direction |

TD | Transverse direction |

Parameters | Description |

$A,B,C$ | Material parameters of the Swift extrapolation approach |

${D}_{1},{D}_{2},{D}_{3}$ | Material parameters of the JC failure model |

$F,G,H,L,M,N$ | Hill48 parameters |

${\epsilon}_{\mathrm{f},\mathrm{J}\mathrm{C}}$ | Equivalent plastic strain at failure |

${\epsilon}_{\mathrm{p}\mathrm{l}}$ | Equivalent plastic strain |

$\eta $ | Triaxiality |

${k}_{\mathrm{f},\mathrm{S}\mathrm{w}\mathrm{i}\mathrm{f}\mathrm{t}}$ | Flow stress of the Swift extrapolation approach |

${r}_{0},{r}_{45},{r}_{90}$ | Anisotropy coefficients |

${\sigma}_{11},{\sigma}_{22},{\sigma}_{33}$ | Tensile yield stresses |

${\sigma}_{12},{\sigma}_{23},{\sigma}_{31}$ | Shear yield stresses |

${\stackrel{-}{u}}_{\mathrm{x}}$ | Failure displacements in x-direction |

${\stackrel{-}{u}}_{\mathrm{y}}$ | Failure displacements in y-direction |

## References

- Fonstein, N. Dual-phase steels. In Automotive Steels—Design, Metallurgy, Processing and Applications; Elsevier: Amsterdam, The Netherlands, 2017; pp. 169–216. [Google Scholar] [CrossRef]
- Behrens, B.-A.; Uhe, J.; Wester, H.; Stockburger, E. Hot forming limit Curves for numerical Press Hardening Simulation of AISI 420C. In Proceedings of the 29th International Conference on Metallurgy and Materials, Brno, Czech Republic, 20–22 May 2020; pp. 350–355. [Google Scholar] [CrossRef]
- Bai, Y.; Wierzbicki, T. Application of extended Mohr–Coulomb criterion to ductile fracture. Int. J. Fract.
**2010**, 161, 1–20. [Google Scholar] [CrossRef] - Wilson-Heid, A.E.; Furton, E.T.; Beese, A.M. Contrasting the Role of Pores on the Stress State Dependent Fracture Behavior of Additively Manufactured Low and High Ductility Metals. Materials
**2021**, 14, 3657. [Google Scholar] [CrossRef] [PubMed] - Mohr, D.; Marcadet, S.J. Micromechanically-motivated phenomenological Hosford–Coulomb model for predicting ductile fracture initiation at low stress triaxialities. Int. J. Solids Struct.
**2015**, 67–68, 40–55. [Google Scholar] [CrossRef] - Erice, B.; Roth, C.C.; Mohr, D. Stress-state and strain-rate dependent ductile fracture of dual and complex phase steel. Mech. Mater.
**2018**, 116, 11–32. [Google Scholar] [CrossRef] - Hong, T.; Ding, F.; Chen, F.; Zhang, H.; Zeng, Q.; Wang, J. Study on the Fracture Behaviour of 6061 Aluminum Alloy Extruded Tube during Different Stress Conditions. Crystals
**2023**, 13, 489. [Google Scholar] [CrossRef] - Johnson, G.R.; Cook, W.H. Fracture Characteristics of three Metals subjected to various Strains, Strain Rates, Temperatures, and Pressures. Eng. Fract. Mech.
**1985**, 21, 31–48. [Google Scholar] [CrossRef] - Wang, H.; Sui, X.; Guan, Y. Prediction of Hot Formability of AA7075 Aluminum Alloy Sheet. Metals
**2023**, 13, 231. [Google Scholar] [CrossRef] - Xu, T.; Li, F.; Wang, X.; Zhang, G. Characterization of Anisotropic Fracture Behavior of 7075-T6 Aluminum Alloy Sheet under Various Stress States. J. Materi. Eng. Perform.
**2022**. [Google Scholar] [CrossRef] - Lou, Y.S.; Yoon, J.W. A User-friendly Anisotropic Ductile Fracture Criterion for Sheet Metal under Proportional Loading. Int. J. Solids Struct.
**2021**, 217, 48–59. [Google Scholar] [CrossRef] - Rice, J.R.; Tracey, D.M. On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Sol.
**1969**, 17, 201–217. [Google Scholar] [CrossRef] [Green Version] - Chuluunbat, T.; Lu, C.; Kostryzhev, A.; Tieu, K. Investigation of X70 line pipe steel fracture during single edge-notched tensile testing using acoustic emission monitoring. Mater. Sci. Eng. A
**2015**, 640, 471–479. [Google Scholar] [CrossRef] - Voestalpine Steel Division. Data Sheet Complex Phase Steels, 10/2022. Available online: https://www.voestalpine.com/ultralights/en/content/download/4638/file/Complex-phase-high-ductility-steels-voestalpine-EN-14102021.pdf (accessed on 7 February 2023).
- DIN EN ISO 10275:2020; Metallic Materials—Sheet and Strip—Determination of Tensile Strain Hardening Exponent. Beuth: Berlin, Germany, 2020. [CrossRef]
- DIN EN ISO 12004-2:2021; Metallic Materials—Determination of Forming-Limit Curves for Sheet and Strip. Beuth: Berlin, Germany, 2021. [CrossRef]
- Pelleg, J. Mechanical Testing of Materials. In Mechanical Properties of Materials; Springer: Berlin/Heidelberg, Germany, 2013; pp. 1–84. [Google Scholar] [CrossRef]
- DIN EN ISO 16808:2022-08; Metallic Materials—Sheet and Strip—Determination of Biaxial Stress-Strain Curve by Means of Bulge Test with Optical Measuring Systems. Beuth: Berlin, Germany, 2022.
- Sigvant, M.; Mattiasson, K.; Vegter, H.; Thilderkvist, H. A viscous pressure bulge test for the determination of a plastic hardening curve and equibiaxial material data. Int. J. Mater. Form.
**2009**, 2, 235–242. [Google Scholar] [CrossRef] - Behrens, B.-A.; Rosenbusch, D.; Wester, H.; Stockburger, E. Material Characterization and Modeling for Finite Element Simulation of Press Hardening with AISI 420C. J. Mater. Eng. Perform.
**2022**, 31, 825–832. [Google Scholar] [CrossRef] - Swift, H.W. Plastic instability under plane stress. J. Mech. Phys. Solids
**1952**, 1, 1–18. [Google Scholar] [CrossRef] - DIN EN ISO 10113:2020; Metallic Materials—Sheet and Strip—Determination of Plastic Strain Ratio. Beuth: Berlin, Germany, 2021. [CrossRef]
- Hill, R. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. A
**1948**, 193, 281–297. [Google Scholar] [CrossRef] [Green Version] - Stockburger, E.; Vogt, H.; Wester, H.; Hübner, S.; Behrens, B.-A. Evaluating Material Failure of AHSS Using Acoustic Emission Analysis. Mater. Res. Proc.
**2023**, 25, 379–386. [Google Scholar] [CrossRef] - Behrens, B.-A.; Dröder, K.; Hürkamp, A.; Droß, M.; Wester, H.; Stockburger, E. Finite Element and Finite Volume Modelling of Friction Drilling HSLA Steel under Experimental Comparison. Materials
**2021**, 14, 5997. [Google Scholar] [CrossRef] [PubMed] - Pathak, N.; Butcher, C.; Worswick, M.J.; Bellhouse, E.; Gao, J. Damage Evolution in Complex-Phase and Dual-Phase Steels during Edge Stretching. Materials
**2017**, 10, 346. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Behrens, B.-A.; Jüttner, S.; Brunotte, K.; Özkaya, F.; Wohner, M.; Stockburger, E. Extension of the Conventional Press Hardening Process by Local Material Influence to Improve Joining Ability. Procedia Manuf.
**2020**, 47, 1345–1352. [Google Scholar] [CrossRef]

**Figure 1.**Butterfly specimen with close-up of the investigation area as well as stochastic pattern (

**A**), and schematic representation of the test setup for butterfly specimen with optical as well as acoustical measuring system (

**B**).

**Figure 2.**Measured forming force—amplitude over time curve (

**A**) and used evaluation methods for determining failure of the butterfly specimen: mechanical (

**B**), optical (

**C**), as well as acoustical (

**D**).

**Figure 4.**Evaluation areas of the butterfly simulation models: mechanical as well as optical (

**A**) and acoustical evaluation method (

**B**).

**Figure 7.**Average failure displacement in x-direction ${\stackrel{-}{u}}_{\mathrm{x}}$ and in y-direction ${\stackrel{-}{u}}_{\mathrm{y}}$ of the butterfly tests for CP800.

**Figure 8.**Comparison of the experimental and numerical force—displacement curves for the three evaluation methods.

**Figure 9.**Comparison of the optically measured and numerically calculated equivalent plastic strain distributions of the butterfly tests for the optical evaluation method.

**Figure 10.**Equivalent plastic strain–triaxiality curves (

**A**) and equivalent plastic-strain-normalised Lode angle curves (

**B**) of the butterfly specimens for the three evaluation methods.

**Figure 11.**Stress state (

**A**) and equivalent plastic strain (

**B**) of the butterfly specimens for the three evaluation methods.

Element | C | Si | Mn | P | S | Al | Cr + Mo | Ti + Nb | B | V |
---|---|---|---|---|---|---|---|---|---|---|

Amount in mass-% | 0.18 | 1 | 2.5 | 0.05 | 0.01 | 0.5 | 0.74 | 0.07 | 0.001 | 0.1 |

Coefficient | A | B | C | |||

Value | 1123.7 MPa | 0.0022 | 0.1057 | |||

Coefficient | F | G | H | L | M | N |

Value | 0.495 | 0.531 | 0.469 | 1.5 | 1.5 | 1.634 |

Coefficient | D_{1} | D_{2} | D_{3} |
---|---|---|---|

Mechanical | 0.5158 | 0.2617 | −3.02 |

Optical | 0.3485 | 0.4664 | −3.03 |

Acoustical | 0.4691 | 0.2345 | −2.99 |

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**MDPI and ACS Style**

Stockburger, E.; Wester, H.; Behrens, B.-A.
Failure Modelling of CP800 Using Acoustic Emission Analysis. *Appl. Sci.* **2023**, *13*, 4067.
https://doi.org/10.3390/app13064067

**AMA Style**

Stockburger E, Wester H, Behrens B-A.
Failure Modelling of CP800 Using Acoustic Emission Analysis. *Applied Sciences*. 2023; 13(6):4067.
https://doi.org/10.3390/app13064067

**Chicago/Turabian Style**

Stockburger, Eugen, Hendrik Wester, and Bernd-Arno Behrens.
2023. "Failure Modelling of CP800 Using Acoustic Emission Analysis" *Applied Sciences* 13, no. 6: 4067.
https://doi.org/10.3390/app13064067