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two axial tensile stresses, if the tensile stress with the maximum absolute value is σγ, the principal strain in this direction must be positive, that is, the deformation belongs to tensile forming.
In addition, because σγ>σθ>0，therefore -（σt+σθ）<0 and εt<0. The strain in the thickness direction of the blankεt is negative, that is, the deformation belongs to compressive forming, and the thickness decreases.
The deformation condition in the tangential direction depends on the values ofσγ and σθ. When σγ=2σθ,εθ=0； when σγ>2σθ,εθ<0；and when σγ<2σθ ,εθ>0.
The range of σθ is σγ>=σθ>=0 . In the equibiaxial tensile stress state σγ=σθ ，according to Equation 1.2,εγ=εθ>0 and εt <0 . In the uniaxial tensile stress stateσθ=0，according to Equation 1.2 εθ=-εγ/2.
According to above analysis, it is known that this kind of deformation condition is in the region AON of the diagram of the diagram of the stamping strain (see Fig .1.1), and in the region GOH of the diagram of the stamping stress (see Fig.1.2).
2)When σθ>σγ >0 and σt=0, according to Equation 1.2 , 2σθ>σγ >0 and εθ>0,This result shows that for the plane stress state with two tensile stresses, when the absoluste value of σθ is the strain in this direction must be positive, that is, it must be in the state of tensile forming.
Also becauseσγ>σθ>0，therefore -（σt+σθ）<0 and εt<0. The strain in the thickness direction of the blankεt is negative, or in the state of compressive forming, and the thickness decreases.
The deformation condition in the radial direction depends on the values ofσγ and σθ. When σθ=2σγ,εγ0;when σθ>σγ,εγ<0;and when σθ<2σγ,εγ>0.
The range of σγ is σθ>= σγ>=0 .When σγ=σθ,εγ=εθ>0, that is, in equibiaxial tensile stress state, the tensile deformation with the same values occurs in the two tensile stress directions; when σγ=0, εγ=-εθ /2, that is, in uniaxial tensile stress state, the deformation characteristic in this case is the same as that of the ordinary uniaxial tensile.
This kind of deformation is in the region AON of the diagram of the stamping strain (see Fig.1.1), and in the region GOH of the diagram of the stamping stress (see Fig.1.2).
Between above two cases of stamping deformation, the properties ofσθandσγ, and the deformation caused by them are the same, only the direction of the maximum stress is different. These two deformations are same for isotropic homogeneous material.
(1)When the deformation zone of stamping blank is subjected to two compressive stressesσγandσθ(σt=0), it can also be divided into two cases, which are σγ<σθ<0,σt=0 and σθ<σγ <0,σt=0.
1）When σγ<σθ<0 and σt=0, according to Equation 1.2, 2σγ-σθ<0与εγ=0.This result shows that in the plane stress state with two compressive stresses, if the stress with the maximum absolute value is σγ<0, the strain in this direction must be negative, that is, in the state of compressive forming.
Also because σγ<σθ<0, therefore -（σt +σθ）>0 and εt>0.The strain in the thickness direction of the blankεt is positive, and the thickness increases.
The deformation condition in the tangential direction depends on the values ofσγ and σθ.When σγ=2σθ,εθ=0;when σγ>2σθ,εθ<0;and when σγ<2σθ ,εθ>0.
The range of σθ is σγ<σθ<0.When σγ=σθ,it is in equibiaxial tensile stress state, henceεγ=εθ<0; when σθ=0,it is in uniaxial tensile stress state, hence εθ=-εγ/2.This kind of deformation condition is in the region EOG of the diagram of the stamping strain (see Fig.1.1), and in the region COD of the diagram of the stamping stress (see Fig.1.2).
2）When σθ<σγ <0and σt=0, according to Equation 1.2,2σθ-σγ <0 and εθ<0. This result shows that in the plane stress state with two compressive stresses, if the stress with the maximum absolute value is σθ, the strain in this direction must be negative, that is, in the state of compressive forming.
Also becauseσθ<σγ <0 , therefore -（σt +σθ）>0 and εt>0.The strain in the thickness direction of the blankεt is positive, and the thickness increases.
The deformation condition in the radial direction depends on the values ofσγ and σθ. When σθ=2σγ, εγ=0; when σθ>2σγ,εγ<0; and when σθ<2σγ ,εγ>0.
The range of σγ is σθ<= σγ<=0 . When σγ=σθ , it is in equibiaxial tensile stress state, hence εγ=εθ<0; when σγ=0, it is in uniaxial tensile stress state, hence εγ=-εθ /2>0.This kind of deformation is in the region GOL of the diagram of the stamping strain (see Fig.1.1), and in the region DOE of the diagram of the stamping stress (see Fig.1.2).
(3) The deformation zone of the stamping blank is subjected to two stresses
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