# Analysis of TRIP Steel HCT690 Deformation Behaviour for Prediction of the Deformation Process and Spring-Back of the Material via Numerical Simulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. TRIP Steel HCT690 (EN 10346)

#### 2.2. Methodology of Calculation the Sheet-Metal-Forming Numerical Simulation in PAM-STAMP 2G Software

#### 2.3. Selected Material Computational Models of Numerical Simulation in PAM-STAMP 2G Software

_{3}is neglected. Thus, the yield criterion takes a planar expression and can be defined by an ellipse (see Figure 4), which forms the yield criterion boundary within the plane of the main stresses σ

_{1}and σ

_{2}. The shape of the ellipse, which represents the relevant yield criterion, can be controlled by the mathematical expressions used to calculate the anisotropy or by the external material characteristics obtained from the experimental material testing. In order to compile the yield criterion using the experimental inputs to describe the material anisotropy, so-called reference (control) points of the ellipse are needed. These points represent the individual mechanical tests of the material. For the common yield criteria (e.g., Hill 48), it is sufficient to perform only a static tensile test. However, to define advanced materials models that work with more accurate yield criteria (e.g., Vegter yield criterion), more input material characteristics are required, which leads to the need to carry out additional material tests such as biaxial tests, compression tests, shear tests, etc. (see Figure 4) [2,3,46].

- C—strength coefficient (MPa),
- n—strain hardening exponent (-),
- φ
_{0}—offset true strain (-).

**Figure 5.**Illustration of the stress–strain curve approximation for isotropic hardening law definition.

_{0}can be defined by Equation (2), where function Φ denotes the yield surface and Y is its boundary [46].

^{p}. Finally, C represents a material parameter that controls the rate of kinematic hardening [46].

_{sat}is the saturated value of the isotropic hardening stress at infinitely large plastic strain and m is a material parameter that controls the rate of isotropic hardening [46].

_{sat}is a material parameter [46].

_{σ}(see Figure 7) [46].

_{σ}. Then, Equation (14) must be valid [46].

_{0}[46].

_{kin}is the rate of kinematic hardening as shown in Equation (16) [46].

_{0}and E

_{a}stand for the Young’s modulus for virgin (original) and infinitely large pre-strained materials, respectively [46].

_{1}, σ

_{2}and angle of the coordinate system rotation Φ in the Vegter yield criterion are defined using the following Equations (18)–(20) [46].

- σ
_{1}—principal stress (direction 1) (MPa), - σ
_{2}—principal stress (direction 2) (MPa), - σ
_{xx}—stress in the direction 0° (MPa), - σ
_{yy}—stress in the direction 90° (MPa), - σ
_{xy}—shear stress (MPa), - ϴ—angle of the coordination system rotation (°).

#### 2.3.1. Vegter Lite Yield Criterion

- Young’s modulus E;
- Poisson’s ratio μ;
- Density ρ.

- Static tensile test;
- Hydraulic bulge test.

**Figure 8.**Vegter Lite Yield Criterion [3].

- Isotropic hardening law;
- (Yoshida) Kinematic hardening law.

#### 2.3.2. Vegter Yield Criterion

- Young’s modulus E;
- Poisson’s ratio μ;
- Density ρ.

- Static tensile test;
- Hydraulic bulge test;
- Plane strain tensile test;
- Shear test.

**Figure 9.**Vegter Yield Criterion [3].

- Isotropic hardening law;
- (Yoshida) Kinematic hardening law.

## 3. Experimental Part

#### 3.1. Static Tensile Test

_{e}(even. proof yield strength R

_{p}

_{0.2}) and ultimate tensile strength R

_{m}as well as the uniform ductility A

_{g}and total ductility A

_{80mm}and Young’s modulus E were determined. In order to take into account the anisotropy of the material, the test must be carried out with specimens taken in the directions 0°, 45° and 90° with respect to the rolling direction of the material. The test was carried out in a standard way according to EN ISO 6892-1 [47]. A schematic diagram of the specimen loading during the static tensile test is shown in Figure 10. The dimensions of the testing samples were as follows: L

_{0}= 80 mm, w

_{0}= 20 mm and t

_{0}= 1 mm.

#### 3.2. Hydraulic Bulge Test

_{EF}vs. effective (true) strain ϕ

_{EF}under the equi-biaxial loading. These values are obtained by substituting the measured parameters and quantities into Equations (21)–(23).

- σ
_{EF}—effective stress [MPa], - p—hydraulic pressure [MPa],
- φ
_{EF}—effective strain [-], - R—radius of curvature [mm],
- φ
_{1,2,3}—principal strains [-], - t, t
_{0}—actual and initial thickness [mm].

#### 3.3. Plane Strain Test

- φ
_{1}—principal strain (length) [-], - φ
_{2}—principal strain (width) [-], - φ
_{3}—principal strain (thickness) [-], - L—actual length [mm],
- L
_{0}—initial length [mm].

#### 3.4. Shear Test (Slotted Shear Test)

#### 3.5. Cyclic Test (Fully Reversed Alternating Cycle)—Stress Ratio R = −1

#### 3.6. Preparation of the Real Stamping Corresponding to the Process Set in Numerical Simulation

## 4. Results

#### 4.1. Mechanical Testing of TRIP Steel HCT690

_{0}.

_{0}. These are summarised in Table 3, together with the normal anisotropy coefficient from the equi-biaxial test.

_{0}. These are summarised in Table 4 with respect to rolling direction.

_{0}. These are summarised in Table 5 with respect to rolling direction.

#### 4.2. Definition of the Used Yield Criteria in the Numerical Simulation Environment of the Software PAM-STAMP 2G

_{0}obtained from the Krupkowski approximation of the static tensile test in the reference direction 0°. In Figure 34 is subsequently shown so-called data “fitting” in the software MatPara v2.1.0.0 to determine parameters for the proper definition of the Yoshida kinematic hardening model.

#### 4.3. Numerical Simulation of the Sheet Metal Forming Process

## 5. Discussion

#### 5.1. Comparison of the Yield Criteria Used in the Numerical Simulation

_{1}and σ

_{2}.

#### 5.2. Comparison of the Results from the Numerical Simulation and the Real Stamping

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Illustration of the structure change of TRIP steel during deformation [36].

**Figure 2.**Schematic diagram of TRIP steel production process after hot rolling (

**a**) and after cold rolling (

**b**) [39].

**Figure 3.**Examples of using TRIP steel on car body [36].

**Figure 7.**Definition of the non-isotropic hardening (non-IH) in the deviatoric stress space [46].

**Figure 11.**Realisation of the static tensile test by TIRA Test 2300 testing device (

**a**) and the detail of the measured specimen (

**b**).

**Figure 14.**Realisation of the hydraulic bulge test on a CBA 300/63 hydraulic press (

**a**) and the detail of the measuring device (

**b**).

**Figure 27.**Stress–strain curve of the material HCT690 from the static tensile test (

**a**) and Krupkowski approximation of the stress–strain curve in the rolling direction 0° (

**b**).

**Figure 28.**Stress–strain curve of the material HCT690 from the equi-biaxial test (

**a**) and Krupkowski approximation of the stress strain curve (

**b**).

**Figure 29.**Stress–strain curve of the material HCT690 from the plane strain test (

**a**) and Krupkowski approximation of the stress–strain curve in the rolling direction 0° (

**b**).

**Figure 30.**Stress–strain curve of the material HCT690 from the shear test (

**a**) and Krupkowski approximation of stress–strain curve in the rolling direction 0° (

**b**).

**Figure 31.**Stress–strain curve of the material HCT690 from the cyclic test in the rolling direction 0°.

**Figure 32.**Definition of the yield criterion: Hill 48 (

**left**), Vegter Lite (

**middle**) and Vegter Standard (

**right**) for material HCT690.

**Figure 33.**Definition of the isotropic hardening law in the PAM-STAMP 2G software for material HCT690.

**Figure 37.**Comparison of the selected material models representing the yield criteria in the planes σ

_{1}and σ

_{2}for material HCT690.

**Figure 38.**Comparison of the resulting contour obtained by numerical simulation of Hill 48, Vegter Lite and Vegter Standard with isotropic hardening law for material HCT690.

**Figure 39.**Difference between the sheet contour from Hill 48 isotropic hardening law and the real contour of the given stamping.

**Figure 40.**Comparison of the resulting contour obtained by numerical simulation of Hill 48, Vegter Lite and Vegter Standard with kinematic hardening law for material HCT690.

**Figure 41.**Difference between the sheet contour from Vegter Standard kinematic hardening model and the real contour of the given stamping.

Rolling Direction (°) | R_{p0,2} (MPa) | R_{m} (MPa) | A_{g} (-) | A_{80mm} (-) | E (MPa) |
---|---|---|---|---|---|

0 | 456.90 ± 1.05 | 695.09 ± 1.10 | 0.3086 ± 0.0022 | 0.3745 ± 0.0038 | 181.718 ± 112 |

45 | 457.65 ± 0.94 | 704.43 ± 1.22 | 0.2787 ± 0.0028 | 0.3258 ± 0.0034 | 194.229 ± 136 |

90 | 431.64 ± 1.12 | 694.32 ± 1.06 | 0.2896 ± 0.0018 | 0.3378 ± 0.0042 | 188.768 ± 123 |

**Table 2.**Approximation constants determined by the Krupkowski approximation of the stress–strain curve from the static tensile test for material HCT690.

Rolling Direction (°) | C (MPa) | n (-) | ϕ_{0} (-) | R (-) |
---|---|---|---|---|

0 | 1285.9839 ± 0.08008 | 0.28330 ± 5.23372 × 10^{−5} | 0.02572 ± 1.79626 × 10^{−5} | 0.8180 ± 0.012 |

45 | 1262.0275 ± 0.11845 | 0.25529 ± 6.89821 × 10^{−5} | 0.01914 ± 2.14572 × 10^{−5} | 0.7490 ± 0.009 |

90 | 1235.1558 ± 0.15673 | 0.25001 ± 9.10215 × 10^{−5} | 0.01647 ± 2.71825 × 10^{−5} | 1.1310 ± 0.014 |

**Table 3.**Approximation constants determined by the Krupkowski approximation of the stress–strain curve from the equi-biaxial test for material HCT690.

Rolling Direction (°) | C (MPa) | n (-) | φ_{0} (-) | R (-) |
---|---|---|---|---|

- | 1257.7543 ± 6.08372 | 0.25056 ± 0.00307 | 0.00887 ± 6.79748 × 10^{−4} | 1.1960 ± 0.015 |

**Table 4.**Approximation constants determined by the Krupkowski approximation of the stress-–strain curve from the plain strain test for material HCT690.

Rolling Direction (°) | C (MPa) | n (-) | φ_{0} (-) |
---|---|---|---|

0 | 1224.6926 ± 6.87837 | 0.19513 ± 0.00250 | 0.01066 ± 4.26765 × 10^{−4} |

45 | 1138.8545 ± 5.55614 | 0.16041 ± 0.00178 | 0.00219 ± 1.83297 × 10^{−4} |

90 | 1216.7021 ± 4.07405 | 0.17219 ± 0.00129 | 0.00274 ± 1.44064 × 10^{−4} |

**Table 5.**Approximation constants determined by the Krupkowski approximation of the stress– strain curve from the shear test for material HCT690.

Rolling Direction (°) | C (MPa) | n (-) | φ_{0} (-) |
---|---|---|---|

0 | 609.8419 ± 0.45077 | 0.17484 ± 8.38446 × 10^{−4} | 0.02078 ± 5.00940 × 10^{−4} |

45 | 600.7655 ± 0.29863 | 0.18977 ± 7.81576 × 10^{−4} | 0.03279 ± 6.37659 × 10^{−4} |

90 | 598.0089 ± 0.53662 | 0.15590 ± 8.80404 × 10^{−4} | 0.01462 ± 4.52226 × 10^{−4} |

Young Modulus E (GPa) | Poisson Ratio ν (-) | Density ρ (kg.m^{−3}) |
---|---|---|

181.718 | 0.3 | 7.8 × 10^{−6} |

Direction 0 (-) | Direction 45 (-) | Direction 90 (-) | Biaxial (-) |
---|---|---|---|

0.818 | 0.749 | 1.131 | 1.19596 |

Rolling Direction (°) | Uniaxial (-) | Plane (-) | Shear (-) | Biaxial (-) |
---|---|---|---|---|

0 | 1 | 1.14184 | 0.55473 | |

45 | 1.02201 | 1.14100 | 0.54075 | 1.00661 |

90 | 1.00420 | 1.17442 | 0.56076 |

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**MDPI and ACS Style**

Koreček, D.; Solfronk, P.; Sobotka, J.
Analysis of TRIP Steel HCT690 Deformation Behaviour for Prediction of the Deformation Process and Spring-Back of the Material via Numerical Simulation. *Materials* **2024**, *17*, 535.
https://doi.org/10.3390/ma17030535

**AMA Style**

Koreček D, Solfronk P, Sobotka J.
Analysis of TRIP Steel HCT690 Deformation Behaviour for Prediction of the Deformation Process and Spring-Back of the Material via Numerical Simulation. *Materials*. 2024; 17(3):535.
https://doi.org/10.3390/ma17030535

**Chicago/Turabian Style**

Koreček, David, Pavel Solfronk, and Jiří Sobotka.
2024. "Analysis of TRIP Steel HCT690 Deformation Behaviour for Prediction of the Deformation Process and Spring-Back of the Material via Numerical Simulation" *Materials* 17, no. 3: 535.
https://doi.org/10.3390/ma17030535