小型轧钢机(工作原理+设计手册+外文文献翻译+CAD图纸) 第3页
with opposite signs, and the absolute value of the tensile stress is larger than that of the compressive stress. There exist two cases to be analyzed as follow:
 　　1)When σγ>0, σθ<0 and |σγ|>|σθ|, according to Equation 1.2, 2σγ-σθ>0 and εγ>0.This result shows that in the plane stress state with opposite signs, if the stress with the maximum absolute value is tensile, the strain in the maximum stress direction is positive, that is, in the state of tensile forming.
Also because σγ>0, σθ<0 and |σγ|>|σθ|, therefore εθ<0. The strain in the compressive stress direction is negative, that is, in the state of compressive forming.
The range of σθ is 0>=σθ>=-σγ. When σθ=-σγ, then εγ>0,εθ<0 , and |εγ|=|εθ|;when σθ=0, then εγ>0,εθ<0, and εθ=-εγ/2, it is the uniaxial tensile stress state. This kind of deformation condition is in the region MON of the diagram of the stamping strain (see Fig.1.1), and in the region FOG of the diagram of the stamping stress (see Fig.1.2).
2)When σθ>0, σγ <0,σt=0 and |σθ|>|σγ|, according to Equation 1.2, by
means of the same analysis mentioned above, εθ>0, that is, the deformation zone is in the plane stress state with opposite signs. If the stress with the maximum absolute value is tensile stress σθ, the strain in this direction is positive, that is, in the state of tensile forming. The strain in the radial direction is negative （εγ<=0）, that is, in the state of compressive forming.
The range of σγ is 0>=σγ>=-σθ. When σγ=-σθ, then εθ>0,εγ <0 and |εγ|=|εθ|; when σγ=0, then εθ>0,εγ <0, andεγ=-εθ /2. This kind of deformation condition is in the region COD of the diagram of the stamping strain (see Fig.1.1), and in the region AOB of the diagram of the stamping stress (see Fig.1.2).
Although the expressions of these two cases are different, their deformation essences are the same.
(4) The deformation zone of the stamping blank is subjected to two stresses with opposite signs, and the absolute value of the compressive stress is larger than that of the tensile stress. There exist two cases to be analyzed as follows:
1)When σγ>0,σθ<0 and |σθ|>|σγ|, according to Equation 1.2, 2σθ- σγ<0 and εθ<0.This result shows that in plane stress state with opposite signs, if the stress with the maximum absolute value is compressive stress σθ, the strain in this direction is negative, or in the state of compressive forming.
Also because σγ>0 and σθ<0, therefore 2σγ- σθ<0 and εγ>0. The strain in the tensile stress direction is positive, or in the state of tensile forming.
The range of σγis 0>=σγ>=-σθ.When σγ=-σθ, then εγ>0,εθ<0, and εγ=-εθ;when σγ=0, then εγ>0,εθ<0, and εγ=-εθ/2. This kind of deformation is in the region LOM of the diagram of the stamping strain (see Fig.1.1), and in the region EOF of the diagram of the stamping stress (see Fig.1.2).
2)When σθ>0, σγ <0 and |σγ|>|σθ|, according to Equation 1.2 and by means of the same analysis mentioned above,εγ< 0.This result shows that in plane stress state with opposite signs, if the stress with the maximum absolute value is compressive stress σγ,the strain in this direction is negative, or in the state of compressive forming, The strain in the tensile stress direction is positive, or in the state of tensile forming.

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