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Figure 3 is the FLD ⁽¹⁷⁾ of 7075 aluminum alloy at forming rate of 5 mm/s, and forming temperatures of 20, 140, 180 and 220 °C, respectively. As can be seen from the diagram, the lowest point of the curve is not at the plane-strain axis. As temperatures decrease, its lowest point is constantly moving toward the plane-strain axis. This is because in the hot stamping process, not only will the equivalent stress affect the damage, the maximum principal stress and hydrostatic stress will also affect the damage. The FLD of aluminum alloys cannot be accurately predicted only using the uniaxial damage constitutive equations. Therefore, in the viscoplastic damage formula (20), established under plane-stress state and based on the uniaxial constitutive equations, Dijkl is the material's elasticity. Formula (21) is derived based on the uniaxial damage formula (4), and taking into consideration the effect of different stress states on the damage accumulation. The parameters σ₁, σʜ and σₑ are the maximum principal stress, hydrostatic stress and equivalent stress, respectively, while α₁, α₂ and α₃ are the weighted factor of the above-mentioned stresses, respectively. They express the magnitude of the damaging effect of the individual stress. For example, α₁ = 0 indicates that the maximum principal stress has no effect on the damage parameters. The parameter ϕ is the plane-stress damage index, which represents the effect of plane-stress on the damage evolution. The parameter Δ is the correction factor for the uniaxial tensile test data.
3.3.2 Determining damage equation parameters
As for the plane-stress problem, consider the stress σ₃, along the thickness direction of a metal plate to be 0. Perform numerical analysis for the plane-stress damage constitutive equations to obtain a fitting FLC. Compare the experimental FLC and the fitting FLC to determine the 5 parameter values of the damage Equation (21). The main steps are as follows:
(1) Define the principal strains ԑ₁ and ԑ₂, based on the strain rate and strain ratio β, with β = ԑ₂ / ԑ₁, as shown in Figure 1. In this case ԑ₁ = ԑ₁₁, ԑ₂ = ԑ₂₂.
(2) Solve the viscoplastic constitutive equations using the numerical analysis method, and calculate the principal stresses σ₁ and σ₂ by Formula (20). At this time, σ₁ = σ₁₁, σ₂ = σ₂₂. At the same time, calculate the plastic strains ԑⁿ₁₁ and ԑⁿ₂₂.
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