Viscoplastic constitutive equations for modeling fluid loading and damage evolution during warm medium forming

Highlights

• Relationship between pressure rate, strain rate and equivalent strain is obtained.

• The stress triaxiality function is introduced to feature the liquid pressure.

• The constitutive model is established coupling pressure rate and damage evolution.

• The proposed constitutive model is applied to the WMF process of AA7075-O sheet.

• Prediction accuracy of new model is significantly improved compared with ref. [10].

Abstract

A unified viscoplastic constitutive model is proposed coupling fluid pressure rate control and damage evolution for warm medium forming (WMF), which also includes flow stress function, hardening law and dislocation density evolution. The pressure rate and damage behavior are investigated based on the experimental data of Ref. (Lang et al., 2013) [10] and the fracture morphology observations of specimens. The constitutive equations are discretized and derived through the fourth-order Runge-Kutta method. Meanwhile, the material constants of this model are determined using the Genetic Algorithm. The proposed constitutive model is applied to the WMF process of AA7075-O sheet and compared with the results of Ref. [10]. The error between calculated and experimental data is quantified using the average absolute relative error (AARE). Results indicate that the prediction accuracy of the proposed constitutive model is significantly improved compared with Ref. [10], also, the predictions compare well with the experimental results. The new constitutive model can effectively predict the flow behavior of AA7075-O in WMF.

Introduction

Warm medium forming technology (WMF), which uses warm liquid as the transmission medium of power to act on the sheet metal instead of rigid dies, shows a huge advantage for effective improving forming accuracy and reliability of parts, and has been widely used to manufacture very complex shapes and structures in aerospace industry. WMF typically controlled by pressure rate and conducted at appropriate temperature can remarkably improve the forming limit and formability of low plasticity light alloy compared to conventional cold hydroforming. WMF is a non-linear coupled thermal-mechanical process with large elastoplastic deformation, which is complicated by the interaction of temperature, pressure rate and liquid medium load [1], [2]. In order to accurately describe the process, it is of great importance to obtain the exact process model since it is directly related to the accuracy of the critical WMF parameters optimization analysis and the production prediction process of complex shape parts. However, a major limitation to the process model is the lack of accurate constitutive model that can describe the typical characteristic of pressure rate control from warm liquid medium and damage evolution under warm liquid pressure during forming.

Work on constitutive relations for the warm / hot deformation of metals and alloys has been extensively reported, many researchers (Zener and Hollomon [3]; Kocks and Maddin [4]; Vinh et al. [5]; Johnson and Cook [6], [7]; Lin et al. [8] and others) have developed different advanced constitutive models to analyze the plastic flow of metals and improve the applicability in different process and various materials [9]. But, up to now, there are very few research reports about the constitutive modeling for the WMF process controlled by pressure rate, only Lang et al. [10] developed a rate dependent constitutive model coupling pressure rate, dislocation density and isotropic hardening, however, this model don’t take account of the influence of microstructure damage evolution on deformation process.

The damage in plastic deformation is manifested as the growth and closure of micro-cracks and micro-voids at the microscopic level and the expansion of cracks and fractures at the macroscopic level [11]. Teodosiu et al. [12] first proposed a physical model based on dislocation theory, and described the anisotropic characteristics of sheet metal under the large blank deformation. Sluys et al. [13] established a distribution fracture model of rate dependent materials by assuming that the fracture stress is a function of the fracture strain and its strain rate, and obtained the law of fracture dissipation energy. Khelifa et al. [14] proposed a local approach based on the strong coupling between anisotropic elastoplasticity with mixed nonlinear work hardening and an isotropic ductile damage, and verified its efficiency and the potential interest by Swift's benchmark deep-drawing test. Lin et al. [8], [15] first used genetic algorithm to optimize the parameters of unified constitutive model of superplastic metal materials, and found that the grain growth mechanism plays an important role in the superplastic deformation process of titanium alloy. Meanwhile, the typical constitutive equations of modeling damage evolution were summarized and the schematic diagrams were designed to explain the major types of damage mechanisms. Khaleel et al. [16] developed a viscoplastic constitutive model for superplastic materials based on the continuum mechanics, which revealed that the damage evolution was due to void nucleation and growth. Mohamed et al. [17] researched the damage feature of AA6082 in hot stamping based on the different temperature, strain rate and strain, and obtained a coupled constitutive model for damage evolution and deformation. Yang et al. [18] modeled the flow law of TA15sheets in hot forming based on flow softening and ductile damage evolution. Yan et al. [19] developed a novel unified model coupling defects evolution and stress responses under high strain rate forming. The model was successfully applied to predict aluminum alloys the stress responses, adiabatic shear bands evolution and low or negative strain rate sensitivity. However, these models are not enough to reflect the characteristic of damage failures under warm liquid pressure, in which the thickness normal stress is induced and produced, and the damage law of the sheet metal is different from other forming modes under the three-dimensional stress state. Therefore, modeling microstructure damage evolution under warm liquid pressure is of paramount significance for determining the constitutive relationship of WMF.

Because the pressure rate control law in WMF had not been deeply analyzed and the microstructure damage evolution had not been researched in the Ref. [10]. Therefore, this work focus on building a new viscoplastic constitutive relationship coupling pressure rate control and microstructure damage evolution for WMF as a supplement to the existing research. Firstly, the pressure rate and damage behavior are investigated based on the experimental data of Ref. [10] and the fracture morphology observations of specimens. Secondly, the unified constitutive model also including flow stress function, hardening law and dislocation density evolution is established. The constitutive equations are discretized and derived through the fourth-order Runge-Kutta method. Meanwhile, the material constants of this model are determined using the Genetic Algorithm. Finally, the proposed constitutive model is applied to the WMF process of AA7075-O sheet and compared with the results of Ref. [10]. The error between calculated and experimental data is quantified using the average absolute relative error (AARE).