TABLE OF CONTENTS With plane strain, all of the flow is in the x y plane. This means that d ? ya= ?d ? x and d ? z=0 so ? z = ? 2 =( ? x + ? y )/2. Therefore according to the von Mises criterion, ? z is always the mean or hydrostatic stress.
and
Thus plane-strain deformation can be considered as pure shear with a superimposed hydrostatic stress, ? 2.
Planes of maximum shear stress are mutually perpendicular. The projections of these planes form a series of orthogonal lines called slip lines. Figure 9.3 illustrates a section of a field of slip lines. The shear stress acting on these lines is k, while the mean stress, ? 2 , acts perpendicular to the slip lines. The slip lines are rotated at some angle 
to the x and y axes.
To develop the necessary equations it is necessary to adopt a convention for slip-line identification. The families of slip lines are labeled either ? and ?. The convention is that the largest principal stress (most tensile) lies in the first quadrant formed by ? and ? lines as illustrated in Figure 9.4. If all of the stresses are compressive, the least negative is ? 1.
