Influence of temperature on the formability of an aluminum alloy

Abstract. Warm forming is widely used as increasing the temperature is a solution to improve the formability of aluminum alloys. The stress (or strain) state is one of the most important factors affecting the formability of metals. In warm forming, the temperature and strain rate also play an important role on the deformation and fracture behavior. Figuring out the relationship between formability, temperature, strain rate and stress state is of great importance for providing more understanding of ductile fracture in warm forming conditions. Therefore, the objective of this work is to investigate the influence of temperature on the ductile fracture of a 6000 series aluminum alloy sheet metal under different stress states. Dogbone specimens, notched tensile specimens with different radius, tensile specimens with a central hole and shear specimens are used to cover a wide range of stress states. The hybrid experimental-numerical approach is used to identify the fracture strain and the corresponding stress state parameters (i.e. stress triaxiality and Lode parameter). To this end, fracture tests are carried out at 200°C using a tensile machine to determine the instant of fracture. Numerical simulations of the tensile tests are performed in 3D with the finite element code Abaqus to predict the strain field and calculate the evolution of the stress state. To accurately model the material behavior the positive strain rate sensitivity in the flow stress response at elevated temperature is considered. The results show a strong dependency of the ductile fracture on the temperature, strain rate and stress state.


Intr Introduction oduction
Light materials are increasingly used in automotive industry to satisfy the growing demand for higher fuel efficiency and lower environmental impact. Especially, aluminum alloys are widely used in modern lightweight car concepts due to their good strength-to-weight ratio. However, when compared with steels, their formability at room temperature is much lower. Warm forming has been used as a solution to improve the formability.
It is well known that the stress state is one of the most important factors affecting the formability of metals. The stress state is mainly characterized in terms of the stress triaxiality and the Lode parameter. Bao and Wierzbicki [1] evidenced, via a series of tests on 2024-T351 aluminum alloy, the strong influence of the stress triaxiality on the ductility. Gao et al [2] showed the strong stress state effects on the plastic response and the ductile fracture behavior. Zhang et al [3] found that besides stress triaxiality the Lode parameter related to the third invariant of the deviatoric stress tensor has also an influence on the ductile fracture of metallic materials. They claimed that the use of the Lode parameter, with stress triaxiality, gives a complete description of the stress state.
Besides stress state, temperature and strain rate are major factor affecting the formability of metals. Shehata et al [4] investigated the formability of aluminum/magnesium alloys at temperatures from 20 to 300°C, for several strain rates, in both uniaxial and biaxial tension. They showed that, in the biaxial tension deformation mode, the material is less sensitive to temperature and strain rate than in uniaxial tension. Li and Ghosh [5] investigated the formability of three automotive aluminum sheet alloys (AA5757, AA5182 and AA6111-T4) in the temperature range 200-350°C using biaxial warm forming test. It was found that all tested alloys exhibit a significant improvement of their formability. Moreover, the strain hardened alloys AA5757 and AA5182 show considerably greater improvement ESAFORM 2021. MS14 (Formability Metals), 10.25518/esaform21.1511 1511/1 than the precipitation hardened alloy AA6111-T4. Mahabunphachai and Koç [6] investigated the formability of AA5052 and AA6061 sheets at different temperatures and strain rates through tensile and bulge tests. It was found that the formability increases with temperature and decreases with strain rate. Similar observations are made by Chu et al [7] for AA5086 using a Marciniak test setup. However, the above-mentioned studies mostly refer to a stress state range between uniaxial and biaxial tension, whereas the extension to a wider stress state range including shear is scarcely reported. Recently, Wang et al [8] investigated the ductile fracture of AZ31 magnesium alloy sheets as a function of the temperature from shear to biaxial tension. Similarly, the objective of the current research paper is to determine the fracture locus of AA6061-T6 alloy at an elevated temperature and for a wide stress state range (i.e triaxiality in the range [0 -0.6] and Lode parameter in the range [-1 -0]). To this regard, an experimental campaign is carried out including uniaxial tensile tests on dog-bone shaped specimen, notched specimens with different radius, specimens with a central hole and shear specimens at 200°C. The hybrid experimental-numerical approach [9] is used to measure the fracture strain and record the stress state evolutions during test. However, this method needs both an accurate modeling of the material behavior until fracture and a reliable numerical analysis. To this end, the positive strain rate sensitivity of the flow stress at elevated temperature is taken into account in the modeling and attention is paid to accurately constrain the FE model by using the real experimental boundary conditions.    To insure a homogenous temperature on the specimen during test, the tensile load is applied when the temperature recorded by both thermocouples reaches the testing temperature within ±2°C. Two tests among three are selected for each specimen geometry for post-processing.  Isotropic hardening coupled with Hill48 yield criterion is chosen to model the mechanical behavior. The Hill 48 quadratic yield function is given by:

FE models FE models
where ̅ is the Hill48 equivalent stress that is defined as follow, from the components of the Cauchy stress tenor: The Hill's coefficients (F, G, H, L, M and N) are related to the plastic anisotropy ratios (r0, r45 and r90) which are the ratios of the width to thickness incremental plastic strain during a tensile test at 0, 45 and 90°to the rolling direction, respectively: Due to the lack of available data regarding the mechanical behavior in the thickness of the sheet, L and M are kept equal to their isotropic value (i.e L = M = 1.5).
σy( ̅ ) denotes the isotropic hardening function that is chosen with a saturation form of Hockett-Sherby. At warm temperatures, the strain rate influences the hardening curve. This strain rate dependency is commonly introduced as a power law, e.g. [11,12]. Thus, the yield stress Y evolves with strain rate ε̇ as follow: where ̅ P is the equivalent plastic strain, σ0 the initial yield stress, represents the maximum change in the size of the yield surface, b defines the growth rate of the yield surface, n is the strain hardening coefficient, ε0 is a constant strain rate normalization factor and m is the strain rate sensitivity coefficient.   To determine the fracture strain ε̅ f, it is assumed that the fracture initiates in the element with the highest equivalent plastic strain at the displacement at fracture uf, which is taken as the fracture strain. The fracture stroke uf is determined at the instant of the sudden drop in the measured load-displacement curve as shown in Fig.5. For shear specimen, since it is difficult to pinpoint the onset of fracture in this way, a novel method that makes use of the load first derivative is adopted [8]. In this case the fracture stroke is identified at the minimum of this curve as shown in Fig.6. The critical element is located within the thickness for N-R5, N-R15 and H-R4. In the case of shear specimen, due to edge effects, the maximum equivalent plastic strain at uf is found at the edge rather than at the center. Therefore, the equivalent plastic strain at the center of the shear gauge is chosen as the fracture strain, as an underestimation of the rupture strain in shear.

Eff Effect of t ect of temper emperatur ature e
The effect of the stress triaxiality and Lode parameter on the fracture strain of the same material at room temperature has been recently studied by Kacem et al. [10]. Fig.9 compares the results obtained in the present study at 200°C with the ones reported in [10]. Only the triaxiality is considered in Fig.9 since it was found that this material exhibits a weak Lode parameter dependency. It can be seen that the testing temperature has a high effect on the fracture strain with an increase from room temperature to 200°C between 42% (in the case of SH specimen) and 107% (in the case of N-R5 specimen). It can be seen that the temperature influence on the formability depends on the stress state. Indeed, the effect of temperature is more significant at high stress triaxiality. Furthermore, it can be seen that, in the case of notched specimens, the average stress triaxiality also increases with the raise of temperature since the localization becomes more pronounced.

Conclusions Conclusions
The stress state dependent facture behavior of AA6061-T6 aluminum alloy is investigated at 200°C. Wide range of stress state is tested by using different specimen geometries. Fracture strain and stress state parameters are determined by a hybrid experimentalnumerical approach. For this purpose, a strain rate dependent anisotropic material model for finite element analysis is used. Attention is paid to accurately constrain the FE model by using the real experimental boundary conditions. The model parameters are identified using the experimental data obtained from ductile fracture tests by comparing load-displacement curves between experiments and simulations. The FE model accuracy is verified by also comparing the numerical and experimental evolution of major strain in critical zone for all fracture specimens.
The analysis shows that the stress state has a high influence on the formability of material. In addition, due to the extremely ductile nature of the fracture at elevated temperature, notched specimens show a high variation of stress state during the test. Besides, it is found that the fracture strain is highly influenced by the temperature. The high stress triaxiality states show considerably greater influence on the fracture than the low stress triaxiality state.
Influence of temperature on the formability of an aluminum alloy 1511/10