98 K. Sakaue and S. Higuchi Fig. 13.5 Upper images are of the photographs of the specimen surface, middle images are the maximum strain distribution, and the bottom images are the minimum strain distribution. (a) As received material, (b) cutting angle of 0 deg., (c) 15 deg., (d) 30 deg., (e) 45 deg., (f) 60 deg., (g) 75 deg., and (h) 90 deg. Fig. 13.6 Relationship between elastic modulus and cutting angle deformation-induced anisotropy appears in the necking part by plastic deformation. The elastic modulus E 1 in the direction of angle θ is given by coordinate transformation of the anisotropic elastic constitutive equation and is expressed by 1 E 1 = cos4 θ E1 − 2ν12cos 2 θsin 2 θ E1 + sin4 θ E2 + cos2 θsin 2 θ G12 (13.1) whereE1 andE2 are the elastic modulus in the direction of 0 and 90 degrees, respectively, andG12 is shear modulus. Thus, E1, E2, andG12 are determined by Newton-Raphson method using the elastic modulus E 1 in arbitrary directions. Here, the value of Poisson’s ratioν12 is supposed to be 0.35. The solid line in Fig. 13.6 is calculated elastic modulus in arbitrary directionθ from determinedE1, E2, andG12. The anisotropic elastic constitutive equation is in good agreement with the elastic modulus evaluated by the experiments. Therefore, the anisotropic elastic constitutive equation can represent the elastic modulus in arbitrary direction caused by plastic deformation-induced anisotropy. Figure 13.7 shows the relationship between the maximum stress in the stress-strain curve and the cutting angles. Figure 13.7 also indicates the maximum stress evaluated from the material as received. As shown in Fig. 13.7, the tensile strength in the material as received is isotropic. On the other hand, the maximum stress in the necking part decreases with increasing
RkJQdWJsaXNoZXIy MTMzNzEzMQ==