# Process Design of Aluminum Tailor Heat Treated Blanks

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

_{2}and NO

_{x}emissions of the products. An auspicious approach within this context is the substitution of conventional deep drawing steel by precipitation hardenable aluminum alloys. However, based on the low formability, the application for complex stamping parts is challenging. Therefore, at the Institute of Manufacturing Technology, an innovative technology to enhance the forming limit of these lightweight materials was invented. The key idea of the so-called Tailor Heat Treated Blanks (THTB) is optimization of the mechanical properties by local heat treatment before the forming operation. An accurate description of material properties is crucial to predict the forming behavior of tailor heat treated blanks by simulation. Therefore, within in this research project, a holistic approach for the design of the THTB process in dependency of the main influencing parameters is presented and discussed in detail. The capability of the approach for the process development of complex forming operations is demonstrated by a comparison of local blank thickness of a tailgate with the corresponding results from simulation.

## 1. Introduction

**Figure 1.**Principal integration of Tailor Heat Treated Blanks (THTB) technology in the process chain.

## 2. A Material Model for Tailor Heat Treated Blanks

#### 2.1. General Approach to Describe the Plastic Behavior of Tailor Heat Treated Blanks (THTB)

_{V}and a flow curve σ

_{w}[11]. The yield surface provides the onset of plastic deformation depending on the stress state and a yield parameter YS

_{ref}. Thereby, the stress state is defined by the normalized components of the stress tensor σ

_{i}

_{= 1,2 j = 1,2}, while the yield parameter is an experimental value, e.g., the uniaxial yield strength under load parallel to the rolling direction. The yield surface is typically modeled by a function based on experimental input. The number of experiments necessary for the calibration varies depending on the chosen yield criterion, e.g., 3 for Hill48 [12] or 8 for BBC2005 (Banabic-Balan-Comsa) [13]. The flow curve describes the hardening of the material as soon as plastic deformation is reached and is commonly described with a hardening law, which is a function of true plastic strain ε

_{w}. Over the last decades, various phenomenological yield functions and hardening laws have been published that can be used to define the mechanical behavior of materials [14]. What all of these models have in common is that they require experimental input and are dependent on functional parameters k

_{i}that are often determined by an iterative algorithm, e.g., minimizing the sum of squared residuals. Vogt used this in the context of THTB and showed for the Hockett-Sherby hardening law [15] that all its functional parameters can be expressed based on the maximum temperature [16]. During the investigations, the parameters of the Hockett-Sherby law were replaced with polynomial equations that represented the change with maximum temperature. However, this simple model is not able to describe the onset of plastic deformation and the failure behavior of the material in dependency of the heat treatment. Moreover, the storage of the blanks and thereby the ageing of the blanks is not taken into account. An overview of the suggested approach to model the material behavior of THTB is given in Figure 2.

_{n}which influence the mechanical properties e.g., maximum temperature, ageing time, heating time, cooling conditions, etc. In the next step, a particular solution is found for each of these combinations using a specific yield function and hardening law. As a result, a point cloud is obtained for each functional parameter in the n-dimensional space spanned by the process variables. By fitting a suitable equation to this data, an analytical expression depending on the process variables is determined for each functional parameter of the yield function and hardening law. By reinserting these solutions into the original equations, all functional parameters are replaced and a formulation of the THTB yield function and hardening law is obtained. It is obvious, that fitting of the equations must be treated with great precaution to ensure high conformity of the fit with the experimental input. The final THTB material model is obtained by combining the THTB yield function with the hardening law to ensure their compatibility. For example, if the yield parameter in the yield function is defined as one of the functional parameters of the hardening law, it must be ensured that the same polynomial equation is used in both expressions to guarantee consistency of the data. The resulting THTB material model then consists of scalable functions solely dependent on the process variables. The parameters show a quasi-linear correlation with saturation at the borders. Therefore, for the modeling, a quadratic trial function is recommended combining a low number of variables with the necessary accuracy. Based on the interpolation approach, very good agreement with the experimental results can be realized within the technical borders. For the post-forming analysis a forming limit curve is calculated with the MK model that requires a yield function and hardening law as input. The MK model is based on the idea that failure of a specimen under load occurs due to a structural or a geometrical inhomogeneity. In the model, this is idealized by a localized and abrupt decrease in blank thickness, e.g., a groove. The resulting thickness ratio is termed as the inhomogeneity parameter. Considering a plane stress state and that no tangential stresses occur, the load is iteratively increased and the strain state inside and outside of the groove is evaluated. As soon as the ratio of thickness change becomes infinitely large, the failure point of the specimen is reached. By varying the loading condition and tilting the groove, the forming limit is calculated for various strain paths. To ensure the consistency of the THTB model, it must be ensured that the same yield function and hardening law is used as before. The suggested approach provides an easy way to fully describe the material behavior of THTB and allows high flexibility regarding available yield functions and hardening laws.

#### 2.2. Application of the THTB Material Model to AA6014PX

#### 2.2.1. Analysis of the Yield Surface and Flow Curve of the State T4

_{1}-σ

_{2}stress space. The numerical solution of the BBC2005 yield function for the state T4 is given in Table C1 in the Appendix.

**Figure 3.**Overview of different yield functions to describe the yield surface of AA6014PX in state T4 and a comparison of the predicted change in r-value for Hill90 and BBC2005.

#### 2.2.2. Determination of the THTB Material Model

_{v}(σ

_{ij},k

_{i}) − YS

_{ref.}(T

_{max},t

_{storage}) = 0

_{v}(σ

_{ij},k

_{i}) is the normalized yield function and YS

_{ref.}is a polynomial describing the change of the reference yield strength with maximum temperature and ageing time. In other words, to represent the softening correctly, only the reference yield strength must be expressed by a polynomial. This is based on the assumption of isotropic work hardening. To consider a change in the shape of the yield locus as a function of plastic deformation, it is necessary to express all its input parameters by a polynomial equation based on the process variables. In this work the yield strength under load parallel to the rolling direction (σ

_{YS}

_{,0°}) is used as reference yield strength. The resulting polynomial function is illustrated in Figure 5 together with the experimental data that was used for creating the fit.

^{2}-value was used and presumed to be larger than 0.95. To further improve the accuracy of the fit, the dataset was divided at a maximum temperature of 275 °C and two separate fits were created. At a temperature of 275 °C, a change of the microstructural softening effects can be identified. In particular, the combination of the dissolution of GP-Zones in combination with the formation of the β’’-precipitations leads to a discontinuity in the mechanical property change [4]. With both fit functions the dataset could be described sufficiently accurate within the range of the experimental data points. Reinserting the polynomial fit for the reference yield strength into Equation (1), leads to a description for the THTB yield surfaces. In Figure 6, the results of the THTB model are plotted together with experimental values for various combinations of maximum temperature and ageing time. The model shows high conformity with the experimental data and describes the physical behavior of THTB in agreement to microstructural processes as given in literature. For example, the yield surface is shrinking with increasing maximum temperature due to softening of the material (cf. yield surface for state T4 and T

_{max}= 400 °C, t

_{storage}= 0.25 h), while for a constant maximum temperature prolonged ageing leads to an expansion of the yield surface (cf. T

_{max}= 325 °C, t

_{storage}= 0.25 and 6 h).

_{w}) = σ

_{sat.}− (σ

_{sat.}− σ

_{YS}

_{,0°})∙exp(−C∙ε

_{w}

^{D}).

_{sat.}, the yield strength σ

_{YS}

_{,0°}and two additional functional parameters C and D, which are mainly used to describe the hardening behavior. Again, all parameters must be expressed as a function of maximum temperature and ageing time. While it was possible to model the change in yield surface by only one parameter, the hardening law for THTB needs a more careful treatment. Firstly, to ensure consistency of the data, the yield strength σ

_{YS}

_{,0°}should be described by the same expression as used for the yield surface, cf. Figure 5. Furthermore, Vogt indicated that the parameters C and D are strongly interconnected with each other and thus suggested to set parameter D to a constant value defined by the flow curve of the state T4. This approach is also used in this work. Consequently, only the saturation strength and parameter C remain to be described by a suitable equation. As mentioned previously, the best fit to the experimental data is evaluated using the adjusted R

^{2}-value, which is presumed to be larger than 0.95. As for the yield strength, to improve the accuracy the dataset was again divided at 275 °C and two separate fit functions were created. Reinserting the solutions into Equation (2) leads to a scalable flow curve function for THTB which depends on the maximum temperature and ageing time. The prediction of the model and experimentally obtained values are shown in Figure 6. The detailed equations and fitting parameters are listed in Table C2 in the appendix. The model describes the flow curves for different combinations of maximum temperature and ageing time in high agreement with the experiment. Even small differences between the flow curves, like for T

_{max}= 325 °C, t

_{storage}= 4 h and T

_{max}= 250 °C, t

_{storage}= 1 h, are correctly reproduced.

## 3. Process Design of Aluminum Tailor Heat Treated Blanks

**Figure 8.**Press including the forming tool for production of the tailgate with 50% increased drawing depth in the area of the light fixture.

**Figure 9.**Overview of the tailgate without failure produced by forming of a THTB together with failure analysis results from simulation.

**Figure 10.**Heating tool and experimentally determined temperature distribution (non-discretized and discretized) of the blank at the moment that the maximum temperature is reached during the heating process.

**Figure 11.**Comparison of blank thickness from simulation with experimental data for the state T4 and THTB.

**Figure 12.**Overview of different geometries that have been used to demonstrate the enhancement of the forming limits by the THTB technology.

## 4. Summary and Outlook

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A: Yield Functions

Variable | T4 value | Description | Method |
---|---|---|---|

σ_{YS}_{,0°} | 115 ± 1 MPa | yield strength under uniaxial loading for 0°/45°/90° to the rolling direction | uniaxial tensile test [18] |

σ_{YS}_{,45°} | 116 ± 1 MPa | ||

σ_{YS}_{,90°} | 112 ± 2 MPa | ||

σ_{YS}_{,b} | 121 ± 3 MPa | yield strength under biaxial loading (σ_{1} = σ_{2}, σ_{3} = 0) | biaxial tensile test [19] |

r_{0°} | 0.65 ± 0.019 | anisotropy value under uniaxial loading for 0°/45°/90° to the rolling direction | uniaxial tensile test [18] |

r_{45°} | 0.45 ± 0.015 | ||

r_{90°} | 0.61 ± 0.015 | ||

r_{b} | 0.92 ± 0.025 | anisotropy value under biaxial loading (σ_{1} = σ_{2}, σ_{3} = 0) | layer compression test [38] |

## Appendix B: Flow Curves

## Appendix C

**Table C1.**Solution of the BBC2005 yield criterion for the state T4. Variables are named according to [13].

Variable | a | M | N | P | Q | R | S | T |
---|---|---|---|---|---|---|---|---|

T4-solution | 1.3758 | 0.2351 | 0.3990 | 0.4449 | 0.5115 | 0.5018 | 0.5395 | 0.5591 |

_{max}+ p01 t

_{storage}+ p02 T

_{max}

^{2}+ p11 T

_{max}·t

_{storage}+ p02 t

_{storage}

^{2}+ p30 T

_{max}

^{3}+ p21 T

_{max}

^{2}·t

_{storage}+ p12 T

_{max}·t

_{storage}

^{2}

_{max}+ p01 t

_{storage}+p02 T

_{max}

^{2}+ p11 T

_{max}·t

_{storage}+ p02 t

_{storage}

^{2}+ p30 T

_{max}

^{3}+ p21 T

_{max}

^{2}·t

_{storage}+ p12 T

_{max}·t

_{storage}

^{2}+ p03 t

_{storage}

^{3}

Parameter | σ_{YS}_{,0°} | σ_{sat.} | C | |||
---|---|---|---|---|---|---|

Fit 1 | Fit 2 | Fit 1 | Fit 2 | Fit 1 | Fit 2 | |

p00 | 117.3 | 215.2 | 314.7 | 335.0 | 6.067 | −27.36 |

p10 | −0.2086 | −1.365 | −0.2422 | 0.1494 | −0.01509 | 0.2996 |

p01 | 1.949 | −17.73 | 3.783 | −136.8 | 0.1234 | 1.666 |

p20 | 0002894 | 0.00475 | 0.005042 | −0.003417 | 3.536 × 10^{−9} | −8.428 × 10^{−4} |

p11 | −0.02748 | 0.07863 | −0.02099 | 0.7111 | −8.024 × 10^{−4} | −0.01783 |

p02 | −0.1993 | 2.775 | –0.4793 | 6.53 | −0.018 | 0.4022 |

p30 | −9.567 × 10^{−6} | −5.877 × 10^{−6} | −1.906 × 10^{−5} | 5.53 × 10^{−6} | 2.386 × 10^{−7} | 7.725 × 10^{−7} |

p21 | 8.671 × 10^{−5} | −2.659 × 10^{−5} | 5.829 × 10^{−5} | 8.257 × 10^{−4} | −2.521 × 10^{−6} | 3.06 × 10^{−5} |

p12 | 0.001369 | −0.009505 | 0.001415 | −0.0202 | 1.891 × 10^{−4} | −3.901 × 10^{−4} |

p03 | - | - | - | - | - | −0.02772 |

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**MDPI and ACS Style**

Kahrimanidis, A.; Lechner, M.; Degner, J.; Wortberg, D.; Merklein, M.
Process Design of Aluminum Tailor Heat Treated Blanks. *Materials* **2015**, *8*, 8524-8538.
https://doi.org/10.3390/ma8125476

**AMA Style**

Kahrimanidis A, Lechner M, Degner J, Wortberg D, Merklein M.
Process Design of Aluminum Tailor Heat Treated Blanks. *Materials*. 2015; 8(12):8524-8538.
https://doi.org/10.3390/ma8125476

**Chicago/Turabian Style**

Kahrimanidis, Alexander, Michael Lechner, Julia Degner, Daniel Wortberg, and Marion Merklein.
2015. "Process Design of Aluminum Tailor Heat Treated Blanks" *Materials* 8, no. 12: 8524-8538.
https://doi.org/10.3390/ma8125476