Plastic Deformation of Metals
Part of the International Centre for Mechanical Sciences book series (CISM, volume 46)
The classical theory of plasticity is based on the concept of a yield criterion f(б ij )= k , where б ij is the stress tensor and k is a material constant, which is in general a function of the previous strain history. For an isotropic material, the function f may be expressed in terms of the three invariants I1, I2, I3, of the stress tensor. Experimentally, it is found that the hydrostatic component of stress does not affect plastic flow, so that the stress may be replaced by the stress deviationwhere б = бkk and δ ij is the Kronecker delta. The yield criterion thus reduces to f(J2, J3) = k , where J2 , J3 are the second and third invariants of s ij (J1 being identically zero). In the von Mises criterion this is further simplified to J 2 1/2 = k where k is now identified with the yield stress in simple shear.
KeywordsPlastic Strain Mild Steel Applied Stress Plastic Flow Yield Criterion
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© Springer-Verlag Wien 1970