CONTENTS vii 6.2 Extrusion and drawing 77 6.3 Deformation efficiency 18 6.4 Maximum drawing reduction 6.5 Effects of die angle and reduction 80 6.6 Swaging 81 REFERENCES..... 82 PROBLEMS 82 7 Slab Analysis.......... 。。。 85 7.1 Sheet drawing 85 7.2 Wire and rod drawing 87 7.3 Friction in plane-strain compression 88 7.4 Sticking friction 90 7.5 Mixed sticking-sliding conditions 90 7.6 Constant shear stress interface 91 7.7 Axially symmetric compression 92 7.8 Sand-pile analogy 93 7.9 Flat rolling 93 7.10 Roll flattening 95 7.11 Roll bending 99 7.12 Coining 101 7.13 Reducing the area of contact 101 NOTES OF INTEREST....·...··.·· .102 REFERENCES..............,... ...102 PROBLEMS ....102 8 Friction and Lubrication....... ·····..106 8.1 General 106 8.2 Experimental findings 109 8.3 Ring friction test 110 8.4 Galling 111 8.5 Ultrasonics 111 NOTE OF INTEREST ....... ...111 REFERENCES....................................................112 PR0 BLEMS...........112 9 Upper-Bound Analysis.············· ….113 9.1 Upper bounds 113 9.2 Energy dissipation on plane of shear 114 9.3 Plane-strain frictionless extrusion 115 9.4 Plane-strain frictionless indentation 119 9.5 Plane-strain compression 119 9.6 Another approach to upper bounds 122 9.7 A combined upper-bound analysis 123 9.8 Plane-strain drawing 124CONTENTS vii 6.2 Extrusion and drawing 77 6.3 Deformation efficiency 78 6.4 Maximum drawing reduction 79 6.5 Effects of die angle and reduction 80 6.6 Swaging 81 REFERENCES .................................................... 82 PROBLEMS ..................................................... 82 7 Slab Analysis .......................................... 85 7.1 Sheet drawing 85 7.2 Wire and rod drawing 87 7.3 Friction in plane-strain compression 88 7.4 Sticking friction 90 7.5 Mixed sticking-sliding conditions 90 7.6 Constant shear stress interface 91 7.7 Axially symmetric compression 92 7.8 Sand-pile analogy 93 7.9 Flat rolling 93 7.10 Roll flattening 95 7.11 Roll bending 99 7.12 Coining 101 7.13 Reducing the area of contact 101 NOTES OF INTEREST ..............................................102 REFERENCES ....................................................102 PROBLEMS ..................................................... 102 8 Friction and Lubrication .................................. 106 8.1 General 106 8.2 Experimental findings 109 8.3 Ring friction test 110 8.4 Galling 111 8.5 Ultrasonics 111 NOTE OF INTEREST .............................................. 111 REFERENCES ....................................................112 PROBLEMS ..................................................... 112 9 Upper-Bound Analysis ................................... 113 9.1 Upper bounds 113 9.2 Energy dissipation on plane of shear 114 9.3 Plane-strain frictionless extrusion 115 9.4 Plane-strain frictionless indentation 119 9.5 Plane-strain compression 119 9.6 Another approach to upper bounds 122 9.7 A combined upper-bound analysis 123 9.8 Plane-strain drawing 124