CONTENTS 年 13 Bending.··········· ...199 13.1 Sheet bending 199 13.2 Bending with super-imposed tension 202 13.3 Young's modulus on unloading 204 13.4 Reducing springback 204 13.5 Neutral axis shift 204 13.6 Bendability 206 13.7 Shape bending 207 13.8 Forming limits in bending 208 NOTE OF INTEREST.…· ..209 REFERENCES....................................................209 PR0 BLEMS...................209 14 Plastic Anisotropy············· ......212 14.1 Crystallographic basis 212 14.2 Measurement of R 214 14.3 Hill's anisotropic plasticity theory 214 14.4 Special cases of Hill's yield criterion 216 14.5 Nonquadratic yield criteria 217 14.6 Calculation of anisotropy from crystallographic considerations 220 N0TE0 F INTEREST........................221 REFERENCES...······· ...221 PROBLEMS.·… 221 15 Cupping,Redrawing,and Ironing...... 225 15.1 Cup drawing 225 15.2 Anisotropy effects in drawing 228 15.3 Effects of strain hardening in drawing 229 15.4 Analysis of assumptions 230 15.5 Effects of tooling on cup drawing 232 15.6 Earing 233 15.7 Redrawing 235 15.8 Ironing 236 15.9 Progressive forming 238 15.10 Tapered dies 238 15.11 Drawing boxes 240 15.12 Residual stresses 241 NOTES OF INTEREST...······ ...242 REFERENCES........... ....242 PROBLEMS.··· ....242 16 Forming Limit Diagrams.... ......245 16.1 Localized necking 245 16.2 Forming limit diagrams 249
CONTENTS ix 13 Bending ............................................. 199 13.1 Sheet bending 199 13.2 Bending with super-imposed tension 202 13.3 Young’s modulus on unloading 204 13.4 Reducing springback 204 13.5 Neutral axis shift 204 13.6 Bendability 206 13.7 Shape bending 207 13.8 Forming limits in bending 208 NOTE OF INTEREST .............................................. 209 REFERENCES ....................................................209 PROBLEMS ..................................................... 209 14 Plastic Anisotropy ...................................... 212 14.1 Crystallographic basis 212 14.2 Measurement of R 214 14.3 Hill’s anisotropic plasticity theory 214 14.4 Special cases of Hill’s yield criterion 216 14.5 Nonquadratic yield criteria 217 14.6 Calculation of anisotropy from crystallographic considerations 220 NOTE OF INTEREST .............................................. 221 REFERENCES ....................................................221 PROBLEMS ..................................................... 221 15 Cupping, Redrawing, and Ironing ........................... 225 15.1 Cup drawing 225 15.2 Anisotropy effects in drawing 228 15.3 Effects of strain hardening in drawing 229 15.4 Analysis of assumptions 230 15.5 Effects of tooling on cup drawing 232 15.6 Earing 233 15.7 Redrawing 235 15.8 Ironing 236 15.9 Progressive forming 238 15.10 Tapered dies 238 15.11 Drawing boxes 240 15.12 Residual stresses 241 NOTES OF INTEREST ..............................................242 REFERENCES ....................................................242 PROBLEMS ..................................................... 242 16 Forming Limit Diagrams..................................245 16.1 Localized necking 245 16.2 Forming limit diagrams 249
CONTENTS 16.3 Experimental determination of FLDs 250 16.4 Calculation of forming limit diagrams 252 16.5 Factors affecting forming limits 255 16.6 Changing strain paths 258 16.7 Stress-based forming limits 260 NOTE OF INTEREST ............ 260 REFERENCES.·········· .261 PROBLEMS ....261 17 Stamping········· ····.263 17.1 Stamping 263 17.2 Draw beads 263 17.3 Strain distribution 265 17.4 Loose metal and wrinkling 266 17.5 Springback 268 17.6 Strain signatures 269 17.7 Die design 270 17.8 Toughness and sheet tearing 272 17.9 General observations 274 N0TES0 F INTEREST.............275 REFERENCES.........................275 PROBLEMS.···· ....275 i8 Hydroforming,·············· ....277 18.1 General 277 18.2 Free expansion of tubes 277 18.3 Hydroforming into square cross sections 279 18.4 Bent sections 281 NOTE OF INTEREST ....................... 283 REFERENCES.··· .283 PROBLEMS.....................................................283 l9 Other Sheet Forming Operations.....··············· ......285 19.1 Roll forming 285 19.2 Spinning 286 19.3 Foldable shapes 288 19.4 Incremental sheet forming 288 19.5 Shearing 290 19.6 Flanging,hole expansion,and beading 291 19.7 Hemming 292 NOTE OF INTEREST .................... 293 REFERENCES………………·· .293 PROBLEMS.....................................................293
x CONTENTS 16.3 Experimental determination of FLDs 250 16.4 Calculation of forming limit diagrams 252 16.5 Factors affecting forming limits 255 16.6 Changing strain paths 258 16.7 Stress-based forming limits 260 NOTE OF INTEREST .............................................. 260 REFERENCES ....................................................261 PROBLEMS ..................................................... 261 17 Stamping ............................................ 263 17.1 Stamping 263 17.2 Draw beads 263 17.3 Strain distribution 265 17.4 Loose metal and wrinkling 266 17.5 Springback 268 17.6 Strain signatures 269 17.7 Die design 270 17.8 Toughness and sheet tearing 272 17.9 General observations 274 NOTES OF INTEREST ..............................................275 REFERENCES ....................................................275 PROBLEMS ..................................................... 275 18 Hydroforming ......................................... 277 18.1 General 277 18.2 Free expansion of tubes 277 18.3 Hydroforming into square cross sections 279 18.4 Bent sections 281 NOTE OF INTEREST .............................................. 283 REFERENCES ....................................................283 PROBLEMS ..................................................... 283 19 Other Sheet Forming Operations ............................ 285 19.1 Roll forming 285 19.2 Spinning 286 19.3 Foldable shapes 288 19.4 Incremental sheet forming 288 19.5 Shearing 290 19.6 Flanging, hole expansion, and beading 291 19.7 Hemming 292 NOTE OF INTEREST .............................................. 293 REFERENCES ................................................... .293 PROBLEMS ..................................................... 293
CONTENTS 20 Formability Tests..... ...294 20.1 Cupping tests 294 20.2 LDH test 294 20.3 Post-uniform elongation 297 20.4 OSU formability test 297 20.5 Hole expansion 298 20.6 Hydraulic bulge test 299 20.7 Duncan friction test 300 REFERENCES.·......·.··· ....301 PROBLEMS....······ ...301 21 Sheet Metal Properties.···· ,...304 21.1 Introduction 304 21.2 Surface appearance 305 21.3 Strain aging 305 21.4 Roller leveling and temper rolling 308 21.5 Properties of steels 309 21.6 Grades of low-carbon steel 309 21.7 Tailor-welded blanks 314 21.8 Special sheet steels 315 21.9 Surface treatment 315 21.10 Stainless steels 316 21.11 Aluminum alloys 317 21.12 Copper and brass 321 21.13 Hexagonal close-packed metals 322 21.14 Tooling 323 21.15 Product uniformity 323 21.16 Scrap 324 NOTES OF INTEREST.... ....324 REFERENCES.......... ...325 PROBLEMS.······· ..325 Index 327
CONTENTS xi 20 Formability Tests ....................................... 294 20.1 Cupping tests 294 20.2 LDH test 294 20.3 Post-uniform elongation 297 20.4 OSU formability test 297 20.5 Hole expansion 298 20.6 Hydraulic bulge test 299 20.7 Duncan friction test 300 REFERENCES ....................................................301 PROBLEMS ..................................................... 301 21 Sheet Metal Properties ................................... 304 21.1 Introduction 304 21.2 Surface appearance 305 21.3 Strain aging 305 21.4 Roller leveling and temper rolling 308 21.5 Properties of steels 309 21.6 Grades of low-carbon steel 309 21.7 Tailor-welded blanks 314 21.8 Special sheet steels 315 21.9 Surface treatment 315 21.10 Stainless steels 316 21.11 Aluminum alloys 317 21.12 Copper and brass 321 21.13 Hexagonal close-packed metals 322 21.14 Tooling 323 21.15 Product uniformity 323 21.16 Scrap 324 NOTES OF INTEREST ..............................................324 REFERENCES ....................................................325 PROBLEMS ..................................................... 325 Index 327
Preface to the Fourth Edition My coauthor,Robert Caddell,died in 1990,and I have greatly missed working with him. The most significant changes from the third edition are a new chapter on friction and lubrication and a major rearrangement of the last third of the book dealing with sheet forming.Most of the chapters in the last part of the book have been modified,with one whole chapter devoted to hydroforming.A new section is devoted to incremental forming.No attempt has been made to introduce numerical methods.Other books treat numerical methods.We feel that a thorough understanding of a process and the constitutive relations that are embedded in a computer program to analyze it are necessary.For example,the use of Hill's 1948 anisotropic yield criterion leads to significant errors. I wish to acknowledge my membership in the North American Deep Drawing Research Group from whom I have learned so much about sheet forming.Particular thanks are due to Alejandro Graf of ALCAN,Robert Wagoner of the Ohio State Uni- versity,John Duncan formerly with the University of Auckland,and Thomas Stoughton of General Motors. William F.Hosford xii
Preface to the Fourth Edition My coauthor, Robert Caddell, died in 1990, and I have greatly missed working with him. The most significant changes from the third edition are a new chapter on friction and lubrication and a major rearrangement of the last third of the book dealing with sheet forming. Most of the chapters in the last part of the book have been modified, with one whole chapter devoted to hydroforming. A new section is devoted to incremental forming. No attempt has been made to introduce numerical methods. Other books treat numerical methods. We feel that a thorough understanding of a process and the constitutive relations that are embedded in a computer program to analyze it are necessary. For example, the use of Hill’s 1948 anisotropic yield criterion leads to significant errors. I wish to acknowledge my membership in the North American Deep Drawing Research Group from whom I have learned so much about sheet forming. Particular thanks are due to Alejandro Graf of ALCAN, Robert Wagoner of the Ohio State University, John Duncan formerly with the University of Auckland, and Thomas Stoughton of General Motors. William F. Hosford xii
1 Stress and Strain An understanding of stress and strain is essential for the analysis of metal forming operations.Often the words stress and strain are used synonymously by the nonscientific public.In engineering usage,however,stress is the intensity of force and strain is a measure of the amount of deformation. 1.1 STRESS Stress o is defined as the intensity of force at a point. g=aF/8 A as A→0， (1.1) where F is the force acting on a plane of area,4. If the stress is the same everywhere in a body, G=F/A. (1.2) There are nine components of stress as shown in Figure 1.1.A normal stress component is one in which the force is acting normal to the plane.It may be tensile or compressive. A shear stress component is one in which the force acts parallel to the plane. Stress components are defined with two subscripts.The first denotes the normal to the plane on which the force acts and the second is the direction of the force.*For example,ox is a tensile stress in the x-direction.A shear stress acting on the x-plane in the y-direction is denoted by oy Repeated subscripts(e.g.)indicate normal stresses.They are tensile if both the plane and direction are positive or both are negative.If one is positive and the other is negative they are compressive.Mixed subscripts(e.g.,ox,oxy,oy=)denote shear stresses.A state of stress in tensor notation is expressed as Oxx Oyx Ozx Oij= Oxy Oyy Ozx (1.3) Oxz Oy 02z The use of the opposite convention should cause no problem because j=j
1 Stress and Strain An understanding of stress and strain is essential for the analysis of metal forming operations. Often the wordsstress and strain are used synonymously by the nonscientific public. In engineering usage, however, stress is the intensity of force and strain is a measure of the amount of deformation. 1.1 STRESS Stress σ is defined as the intensity of force at a point. σ = ∂F/∂ A as ∂ A → 0, (1.1) where F is the force acting on a plane of area, A. If the stress is the same everywhere in a body, σ = F/A. (1.2) There are nine components of stress as shown in Figure 1.1. A normal stress component is one in which the force is acting normal to the plane. It may be tensile or compressive. A shear stress component is one in which the force acts parallel to the plane. Stress components are defined with two subscripts. The first denotes the normal to the plane on which the force acts and the second is the direction of the force.∗ For example, σxx is a tensile stress in the x-direction. A shear stress acting on the x-plane in the y-direction is denoted by σx y . Repeated subscripts (e.g., σxx, σyy, σzz) indicate normal stresses. They are tensile if both the plane and direction are positive or both are negative. If one is positive and the other is negative they are compressive. Mixed subscripts (e.g., σzx , σx y , σyz) denote shear stresses. A state of stress in tensor notation is expressed as σi j = σx x σyx σzx σx y σyy σzx σx z σyz σzz , (1.3) ∗ The use of the opposite convention should cause no problem because σi j = σji . 1