TABLE OF CONTENTS Slab analyses are based on making a force balance on a differentially thick slab of material. It is useful in estimating the role of friction on forces required in drawing, extrusion, and rolling. The important assumptions are these:
The principal axes are in the directions of the applied loads.
The effects of friction do not alter the directions of the principal axes or cause internal distortion. The deformation is homogeneous so plane sections remain plane.
Figure 7.1 illustrates sheet or strip drawing. A force F pulls a strip through a pair of wedges. The strip width w is much greater than the thickness t so the width doesn t change and plane strain prevails. The drawing stress is ? d =F/wt e.
Figure 7.2 shows the differential slab element. Pressure normal to the die, P, acts on two areas of w d x/cos ?, and the corresponding component of force in the x-direction is 2 Pw d x(sin ?/cos ?). The normal pressure also causes a frictional force on the work metal, 2 ?wP dx/cos ?, with a horizontal component 2 ?wP d x(cos ?/cos ?), where ? is the coefficient of friction. Both of these forces act in the positive x-direction. The drawing force, ? x wt, acts in the negative x
