# On the Prediction of Material Fracture for Thin-Walled Cast Alloys Using GISSMO

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Studied Material

#### 2.2. Experimental Methodology

#### 2.3. Experimental Results

## 3. Characterization of Plasticity and Fracture Behaviors with GISSMO

#### 3.1. Shell-Based Model

#### 3.2. Tetrahedral-Based Models

## 4. Discussion

## 5. Conclusions

- With the well-calibrated parameters, GISSMO could reproduce the test results with good agreement for the multiple stress states.
- Optimization with LS-OPT was a feasible way to calibrate the parameters for GISSMO and avoid the requirement of practical skills.
- The part structures tests and simulations should be conducted in future work to evaluate whether the tetrahedral-based model with GISSMO is suitable.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Specimen configuration for the tests (unit: mm): (

**a**) Tensile, (

**b**) R5 notched, (

**c**) Center hole, (

**d**) R20 notched, (

**e**) Shear, and (

**f**) Tensile-shear.

**Figure 5.**True stress–plastic strain curves and hardening-law fittings before necking: (

**a**) MAT 1, (

**b**) MAT 2, and (

**c**) MAT 3.

**Figure 6.**Isotropic hardening-law fittings before necking using R5 test results: (

**a**) MAT 1, (

**b**) MAT 2, and (

**c**) MAT 3.

**Figure 8.**Optimized failure and instability loci using GISSMO for shell-based models: (

**a**) MAT 1, (

**b**) MAT 2, and (

**c**) MAT 3.

**Figure 9.**Shell-based model simulation vs. experiments for MAT 1 using GISSMO: (

**a**) shear specimen, (

**b**) tensile specimen, (

**c**) center hole specimen, and (

**d**) R5 specimen.

**Figure 10.**Shell-based model simulation vs. experiments for MAT 1 using GISSMO: (

**a**) shear specimen, (

**b**) tensile–shear specimen, (

**c**) tensile specimen, (

**d**) center hole specimen, (

**e**) R20 notched specimen, and (

**f**) R5 notched specimen.

**Figure 11.**Shell-based model simulation vs. experiments for MAT 3 using GISSMO: (

**a**) shear specimen, (

**b**) tensile–shear specimen, (

**c**) tensile specimen, (

**d**) center hole specimen, (

**e**) R20 notched specimen, and (

**f**) R5 notched specimen.

**Figure 12.**Mesh-dependency regularization factors for shell-based models: (

**a**) Mesh dependency regularization factors, (

**b**) Simulation results and (

**c**) Tensile specimen models with different mesh sizes.

**Figure 13.**Tetrahedral elements comparisons for MAT 2: (

**a**) element formulas, (

**b**) extrapolating curves, (

**c**) R5 model with a recalibrated weighting factor, and (

**d**) R5 model with the shell-based GISSMO.

**Figure 15.**Optimized failure and instability loci using GISSMO for tetrahedral-based models: (

**a**) MAT 1, (

**b**) MAT 2, and (

**c**) MAT 3.

**Figure 16.**Mesh-dependency regularization factors for tetrahedral-based models: (

**a**) Mesh dependency regularization factors, (

**b**) Simulation results, and (

**c**) Tensile specimen models with different mesh sizes.

**Figure 17.**Recalibrated results for one-layer models: (

**a**) MAT 1, (

**b**) MAT 2, (

**c**) MAT 3 and (

**d**) One-layer tensile specimen models.

Test # | Specimen | Desired $\mathit{\eta}$ | Desired $\overline{\mathit{\theta}}$ |
---|---|---|---|

a | Tensile | 0.33 | 1 |

b | R5 notched | 0.5 | 0.35 |

c | Center hole | 0.38 | 0.85 |

d | R20 notched | 0.40 | 0.80 |

e | Tensile–shear | 0.10 | 0.25 |

f | Shear | 0.0 | 0.0 |

# | ${\mathit{A}}_{\mathit{s}}$ | ${\mathit{B}}_{\mathit{s}}$ | ${\mathit{C}}_{\mathit{s}}$ | ${\mathit{A}}_{\mathit{v}}$ | ${\mathit{B}}_{\mathit{v}}$ | ${\mathit{C}}_{\mathit{v}}$ | ${\mathit{D}}_{\mathit{v}}$ | $\mathit{w}$ |
---|---|---|---|---|---|---|---|---|

MAT 1 | 383.143 | 0.09532 | 2.20 × 10^{−5} | 267.504 | 94.2477 | 40.0521 | 0.68908 | 0.5 |

MAT 2 | 319.5 | 0.15532 | 1.2 × 10^{−5} | 267.504 | 186.023 | 6.12133 | 0.41562 | 0.5 |

MAT 3 | 488.515 | 0.22313 | 1.9 × 10^{−5} | 306.092 | 221.370 | 11.5027 | 0.68509 | 0.39 |

ELFORM 4 | ELFORM 10 | ELFORM 13 | ELFORM 16 |
---|---|---|---|

149 s | 43 s | 49 s | 205 s |

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**MDPI and ACS Style**

Ge, Y.; Dong, L.; Song, H.; Gao, L.; Xiao, R.
On the Prediction of Material Fracture for Thin-Walled Cast Alloys Using GISSMO. *Metals* **2022**, *12*, 1850.
https://doi.org/10.3390/met12111850

**AMA Style**

Ge Y, Dong L, Song H, Gao L, Xiao R.
On the Prediction of Material Fracture for Thin-Walled Cast Alloys Using GISSMO. *Metals*. 2022; 12(11):1850.
https://doi.org/10.3390/met12111850

**Chicago/Turabian Style**

Ge, Yulong, Liping Dong, Huibin Song, Lechen Gao, and Rui Xiao.
2022. "On the Prediction of Material Fracture for Thin-Walled Cast Alloys Using GISSMO" *Metals* 12, no. 11: 1850.
https://doi.org/10.3390/met12111850