By W. Johnson
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Extra info for Plane-Strain Slip-Line Fields for Metal-Deformation Processes. A Source Book and Bibliography
18, 371 (1951). Drucker, D. C , Prager, W. and Greenburg, H. , "Extended limit design theorems for continuous media". Q. Appi. Math. 9, 381 (1952) . , "Mechanik der festern Korper in plastisch deformablen Zustand". (1913). -phys. Klasse, 562 CHAPTER 3 Basic Theory of Plane Plastic Flow INTRODUCTION This chapter is concerned with the governing equations of the plane plastic flow of a rigid-perfectly plastic solid. In the plane of flow the velocity vector is everywhere parallel to a certain plane, say the (x^yjf plane, and is independent of the distance from the plane.
At any p o i n t in plane *E y %y plastic flow is known as the stress plane. For a rigid-perfectly plastic material the radius of this Mohr circle cannot exceed the yield shear stress k, and if the radius is less than k the material is not deforming. Pole Fig. 8. Strong and weak solutions in the stress plane. 40 BASIC THEORY OF PLANE PLASTIC FLOW Suppose^that for the plane flow of a rigid plastic material the stress vector T at a point P on an elemental plane normal to the plane of flow is known.
Plasticity. Massachusetts (19 59). , "The characteristic method of solution for the problem of plane plastic strain". Engineer, 207, 250 (1959). Green, A. , "On the use of hodographs in problems of plane plastic strain". J. Mech. Phys. Solids, 2, 73 (1954). , Johnson, W. and Samanta, S. , "The diamentral 1 compression of circular rings by 'point loads". Int. J. Mech. Sci. 10, 369 (1968). , "A geometrical discussion of the slip line field R. Inst. , Stockholm, No. 65 (1953). Bishop, J. F. , Green, A.