Engineering Plasticity E-Book

Z. R. Wang

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 835

Veröffentlichungsjahr: 2018

Beschreibung

An all-in-one guide to the theory and applications of plasticity in metal forming, featuring examples from the automobile and aerospace industries * Provides a solid grounding in plasticity fundamentals and material properties * Features models, theorems and analysis of processes and relationships related to plasticity, supported by extensive experimental data * Offers a detailed discussion of recent advances and applications in metal forming

Leseprobe

Table of Contents

Title Page

Copyright

Preface

Chapter 1: Fundamentals of Classical Plasticity

1.1 Stress

1.2 Strain

1.3 Yield Criteria

1.4 A General Yield Criterion

1.5 Classical Theory about Plastic Stress–Strain Relation

1.6 Effective Stress, Effective Strain, and Stress Type

References

Chapter 2: Experimental Research on Material Mechanical Properties under Uniaxial Tension

2.1 Stress–Strain Relationship of Strain-Strengthened Materials under Uniaxial Tensile Stress State

2.2 The Stress–Strain Relationship of the Strain-Rate-Hardened Materials in Uniaxial Tensile Tests

2.3 Stress–Strain Relationship in Uniaxial Tension during Coexistence of Strain Strengthening and Strain Rate Hardening

2.4 Bauschinger Effect

2.5 Tensile Tests for Automotive Deep-Drawing Steels and High-Strength Steels

2.6 Tensile Tests on Mg-Alloys

2.7 Tension Tests on Ti-Alloys

References

Chapter 3: Experimental Research on Mechanical Properties of Materials under Non-Uniaxial Loading Condition

3.1

P-p

Experimental Results of Thin-Walled Tubes

3.2 Results from

P-M

Experiments on Thin-Walled Tubes

3.3 Biaxial Tension Experiments on Sheets

3.4 Influences of Hydrostatic Stress on Mechanical Properties of Materials

3.5 Experimental Researches Other Than Non-Uniaxial Tension

References

Chapter 4: Yield Criteria of Different Materials

4.1 Predicting Capability of a Yield Criterion Affected by Multiple Factors

4.2 Construction of a Proper Yield Criterion in Consideration of Multifactor-Caused Effects

4.3 Anisotropic Materials

References

Chapter 5: Plastic Constitutive Relations of Materials

5.1 Basic Concepts about Plastic Deformation of Materials and Relevant Plastic Constitutive Relations

5.2 Equivalent Hardening Condition in Material Plastic Deformation

5.3 “Softening” and Strength Property Changes in Plastic Deformation of Materials

5.4 Influences of Loading Path on Computational Accuracy of Incremental Theory

References

Chapter 6: Description of Material Hardenability with Different Models

6.1 Plastic Constitutive Relations of Sensitive-to-Pressure Materials

6.2 Anisotropic Hardening Model of Rolled Sheet Metals Characterized by Multiple Experimental Stress–Strain Relations and Changeable Anisotropic Parameters

6.3 Plastic Constitutive Relation with the Bauschinger Effects

References

Chapter 7: Sequential Correspondence Law between Stress and Strain Components and Its Application in Plastic Deformation Process

7.1 Sequential Correspondence Law between Stress and Strain Components and Its Experimental Verification

7.2 Zoning of Mises Yield Ellipse and Typical Plane Stress Forming Processes on It

7.3 Stress and Strain Analysis of Plane-Stress Metal-Forming Processes

7.4 Spreading of Mises Yield Cylinder and Characterization of Three-Dimensional Stresses Therein

7.5 Zoning in Three-Dimensional Stress Yield Locus and Positioning Typical Forming Processes Thereon

References

Chapter 8: Stress and Strain Analysis and Experimental Research on Typical Axisymmetric Plane Stress-Forming Process

8.1 Incremental-Theory-Based Solution to Stress and Strain Distribution of Steady Axisymmetric Plane Stress-Forming Processes

8.2 Experimental Study on Thickness Distribution in Tube Necking and Tube Drawing

8.3 Experiments on Thin-Walled Tube under Action of Biaxial Compressive Stresses

References

Chapter 9: Shell and Tube Hydroforming

9.1 Mechanics of Dieless Closed Shell Hydro-Bulging

9.2 Dieless Hydro-Bulging of Spherical Shells

9.3 Dieless Hydro-Bulging of Ellipsoidal Shells

9.4 Dieless Hydro-Bulging of Elbow Shell

9.5 Tube Hydroforming

References

Chapter 10: Bulk Forming

10.1 Load Calculation in Tool Movement Direction

10.2 Upsetting of Cylinders and Rings

10.3 Characteristics of Die Forgings and Calculation of Required Loads

10.4 Isothermal Forging

10.5 Calculation of Required Load in Rolling

10.6 Extrusion and Drawing

10.7 Rotary Forging

10.8 Strain Distribution Measurement in Bulk Forming

References

Chapter 11: Sheet Forming

11.1 Deep Drawing

11.2 Sheet Hydroforming Process

11.3 Hole-Flanging

11.4 Viscous Pressure Forming

11.5 Multipoint Sandwich Forming

11.6 Formability of Sheet Metals

11.7 Improvements of Panel Stamping Process

References

Index

End User License Agreement

Pages

13

14

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

Guide

Cover

Table of Contents

preface

Begin Reading

List of Illustrations

Chapter 1: Fundamentals of Classical Plasticity

Figure 1.1 Directional forces acting on a unit element.

Figure 1.2 Relationship between forces and stresses on a plane cut out of a loaded body under uniaxial tension.

Figure 1.3 Stress components on three mutually perpendicular planes.

Figure 1.4 Stress components on an oblique plane.

Figure 1.5 Three principal stresses on an oblique plane.

Figure 1.6 Maximum shear stress and relationship among principal stresses.

Figure 1.7 Octahedral stress planes.

Figure 1.8 Different stress types.

Figure 1.9 Analyses of stress states in connection with three tensors of stress components: (a) simple tension, (b) drawing, and (c) extrusion.

Figure 1.10 Plane stress state at a point inside a stressed body.

Figure 1.11 Mohr circle for a plane stress state.

Figure 1.12 Mohr Circle for the three-dimensional stress state.

Figure 1.13 Generation of Mohr circle for the three-dimensional stress state.

Figure 1.14 Force equilibrium at a point inside a deforming body.

Figure 1.15 Change in length of a stretched bar.

Figure 1.16 Changes in length at different stretch stages.

Figure 1.17 Comparison between the true strain curve and the nominal strain.

Figure 1.18 Displacements of a point inside a deforming body.

Figure 1.19 Strains and displacements of the plane

XOZ

.

Figure 1.20 Spherical coordinate system.

Figure 1.21 A small hexahedron cut from a deforming body along the principal planes.

Figure 1.22 Three deformation types of a deforming body: (a) tension type, (b) plane state type and (c) compression type.

Figure 1.23 Yield behavior of three yield criteria in different stress spaces: (a) yield surfaces of three yield criteria in the principal stress space, (b) yield loci on the

π

plane, and (c) yield loci under plane stress state.

Figure 1.24 Distribution areas of the principal stress orders.

Figure 1.25 Yield loci with different material properties: (a) yield locus on the

π

plane and (b) yield loci under plane stress state.

Figure 1.26 Yield surfaces in the principal stress space: (a) material yield with hydrostatic stress effects and (b) material yield with stress type effects.

Figure 1.27 Yield loci under plane stress state without considering the effects of hydrostatic stress exerted on material yieldability.

Figure 1.28 Gradients of yield function and plastic potential.

Figure 1.29 Subsequent yield loci of Mises yield function on the π plane.

Chapter 2: Experimental Research on Material Mechanical Properties under Uniaxial Tension

Figure 2.1 Stress–strain curves.

Figure 2.2 Two methods for determining

m

values.

Figure 2.3 Effects of temperature on strain rate sensitivity index

m.

Figure 2.4 True stress–strain curves of fine-grained Ti-6Al-4V at different strain rates (775°C).

Figure 2.5 True stress–strain curves of AZ31 Mg-alloy at different strain rates (400°C).

Figure 2.6 True stress–strain curves of Nano-Ni at different strain rates (450°C).

Figure 2.7 Relationship between strain-hardening component

n

and inverse of absolute temperature. K

−1

.

Figure 2.8 Relationship between parameters

B

and logarithmic strain rates.

Figure 2.9 Relationship between strain rate sensitivity index

m

and inverses of absolute temperature.

Figure 2.10 Relationship between stress coefficient

C

and inverses of absolute temperature.

Figure 2.11 Comparison between flow stresses from empirical formula and those from experiments: (a) = 0.001 s

−1

; (b) = 0.01 s

−1

; (c) = 0.1 s

−1

.

Figure 2.12 Bauschinger effect.

Figure 2.13 Tensile test piece (DP590): (a) dimension of test piece; (b) test piece photo.

Figure 2.14 Engineering stress–strain curves of DP590 dual-phase steel.

Figure 2.15 True stress–strain curves of four materials.

Figure 2.16 Arc-shape tensile specimen.

Figure 2.17 True stress-true strain curves of AZ31B Mg-alloy tubes: (a) = 0.001 s

−1

; (b) = 0.01 s

−1

; (c) = 0.1 s

−1

.

Figure 2.18 Effects of temperature and strain rate on the yield strength and tensile strength: (a) ; (b) .

Figure 2.19 Effects of temperature and strain rate on breaking elongation and uniform elongation: (a) (b) .

Figure 2.20 Tensile specimens after fracture at: (a) 650°C; and (b) 800°C.

Figure 2.21 True stress–strain curves of Ti-3Al-2.5V alloy at various temperatures and strain rates: (a) ; (b) ; (c) .

Figure 2.22 Strengths of Ti-3Al-2.5V alloy at various temperatures and strain rates: (a) yield strength; (b) tensile strength.

Figure 2.23 Yield-to-tensile ratio of Ti-3Al-2.5V alloy at various temperatures and strain rates.

Figure 2.24 True stresses versus true strains in log-log scale: (a) 700°C; (b) 0.01s

−1

.

Figure 2.25 Variation of

n

with changes in temperature and strain rate.

Chapter 3: Experimental Research on Mechanical Properties of Materials under Non-Uniaxial Loading Condition

Figure 3.1 Lode experiment results.

Figure 3.2 Experimental results about Lode's verification of the relation of Lode parameter to .

Figure 3.3 A loading experiment on a thin-walled tube.

Figure 3.4 Different subsequent yield surfaces defined by different yield stresses for pure aluminum L2.

Figure 3.5 Subsequent yielding surfaces borne of different loading paths for low-carbon steels.

Figure 3.6 Work-hardening characteristic curves by adopting the

converted equivalent stress.

Figure 3.7 Sn-Pb binary phase diagram.

Figure 3.8 A thin-walled test piece.

Figure 3.9 A tensile test underway on a thin-walled tube.

Figure 3.10 Working principle of a recorder.

Figure 3.11 Test pieces after experiments: (a)

σ

z

/

σ

θ

= 2.9; (b)

σ

z

/

σ

θ

= 1; (c)

σ

z

/

σ

θ

= 0.46; (d)

σ

z

/

σ

θ

= −0.5; (e)

σ

z

/

σ

θ

= −1; (f)

σ

z

/

σ

θ

= −2.

Figure 3.12 Yield locus of Mises and Tresca yield criteria.

Figure 3.13 Stress state of a micro-body.

Figure 3.14

σ

i

−ϵ

i

relationship with different principal stress ratios at different strain rates: (a)

V

= 0.5 mm/min; (b)

V

= 1.0 mm/min.

Figure 3.15 Initial and subsequent yield surfaces at different loading speeds: (a)

v

= 0.5 mm/min; (b)

v

= 1.0 mm/min.

Figure 3.16 Influences of intermediate stress on yielding.

Figure 3.17 Distribution of data points and straight line of .

Figure 3.18 Photo of the testing machine.

Figure 3.19 Working principle of the testing machine.

Figure 3.20 Stress–strain relation predicted by second order functions and experimental relation coming of axial compression (a) stress–strain relation; (b) anisotropic parameter [10].

Figure 3.21 Bulging test results relating to an equivalent uniaxial tension in the circumferential direction: (a) stress–strain relation; (b) anisotropic parameter.

Figure 3.22 Linear stress-loading paths.

Figure 3.24 Equivalent strain-hardening work of different loading paths.

Figure 3.25 Points with same equivalent strain-hardening work of different loading paths (corresponding to plastic strain of axial compression).

Figure 3.26 Schematic of Taylor-Quinney experimental apparatus.

Figure 3.27 Taylor-Quinney results.

Figure 3.28 MTS809 testing machine.

Figure 3.29 The distribution of yielding points in

σ−τ

coordinate system.

Figure 3.30 Distribution of yield points on π plane.

Figure 3.31 Experimental equipment for biaxial tension of cruciform specimens.

Figure 3.32 Stress states in elbow bend corner zones with different shapes.

Figure 3.33 Cruciform specimen with long slots on arms.

Figure 3.34 Experimental yield loci of BH220 steel sheet.

Figure 3.35 Comparison between prediction and experimental loci of BH220 steel sheet.

Figure 3.36 A specimen of IC10 alloy on a fixture.

Figure 3.37 A fractured cruciform specimen of C/C composites.

Figure 3.38 Schematic diagram of a testing apparatus with liquid as pressure medium [31].

Figure 3.39 Types of strengthened high-pressure vessels: (a) self-strengthened; (b) multilayered; (c) hydraulic-supported; (d) with changeable external mechanical supporting.

Figure 3.40 Karman's experimental device [33].

Figure 3.41 Curves of marble borne of compression test under different liquid pressures [33].

Figure 3.42 Influences of hydrostatic pressure on yield stresses of metals [31].

Figure 3.43 Influences of hydrostatic pressure on yield stresses of bcc-structured metals [31].

Figure 3.44 Influences of hydrostatic pressure on yield stresses of NiAl [31].

Figure 3.45 Influences of hydrostatic pressure on yield stress of discontinuous reinforcing metal matrix composites [31].

Figure 3.46 Influences of hydrostatic pressure on strain-hardening exponent

n

of high strength Al-alloy 7075-T651 [31].

Figure 3.47 Influences of hydrostatic pressure on ultimate strengths of different steels [31].

Figure 3.48 Influences of hydrostatic pressure on ultimate strengths of different metals [31].

Figure 3.49 Influences of hydrostatic pressure on ultimate strengths of discontinuous reinforced metal matrix composites [31].

Figure 3.50 General categories of fracture processes in metallic materials: (a) transgranular cleavage, (b) intergranular fracture, (c) microvoid coalescence or dimpled rupture, (d) ductile rupture, (e) localized shear [31].

Figure 3.51 Influences of hydrostatic pressure on appearances of fracture of test bars [29].

Figure 3.52 Influences of hydrostatic pressure on fracture appearances of test sheets [35].

Figure 3.53 Experimental results of influences of hydrostatic pressure on fracture behavior of materials.

Figure 3.54 Comprehensive description of the influences of hydrostatic pressure on fracture strain [31].

Figure 3.55 Fracture locus of the ductile fracture criterion in a 3-D stress space .

Figure 3.56 Experimental device for plane compression experiments.

Figure 3.57 Working principle of an ungraded device for plane compression experiment.

Figure 3.58 Flow stress curves borne of uniaxial tension and plane compression of different materials: (a) 6022-T4 aluminum alloy; (b) IF steel.

Figure 3.59 Experiment device to evaluate Bauschinger effect on sheet metals [40].

Figure 3.60 Cyclic stress-strain curves of Al-alloy and low-carbon steel sheets [38].

Figure 3.61 Dual actuator loading system and dimension of the specimen: (a) schematic of the mechanical system; (b) schematic of the specimen geometry of the biaxial loading angle β [42].

Figure 3.62 Comparison between theoretical predictions and experimental results of stress-strain relationship for an Al-alloy: (a) normal stress α = 45°; (b) shear stress α = 45°;(c) normal stress α = −45°; (d) shear stress α = −45°.

Figure 3.63 Changes in initial and subsequent yield surfaces of a thin-walled tube due to tension, torsion, and tension plus torsion [46].

Chapter 4: Yield Criteria of Different Materials

Figure 4.1 Yield locus in a plane stress system.

Figure 4.2 Stress condition on the slip plane between slipping grains.

Figure 4.3 Possible yield loci predicted by Drucker-Prager criterion.

Figure 4.4 Yield loci characterized by three experimental results

σ

t

,

σ

c

,

σ

bt

.

Figure 4.5 Shearing stress strength affected by hydrostatic stress.

Figure 4.6 Yield loci characterized by four experimental stresses

σ

t

,

σ

c

,

σ

bt

,

σ

bc

.

Figure 4.7 Possible yield loci affected by different factors: (a) perfect isotropic yield; (b) yield with hydrostatic-stress-caused effect; (c) yield with stress-type-caused effect; and (d) general behavior of material yield.

Figure 4.8 Distribution of the parameter

λ

σ

against the Lode parameter

μ

σ

.

Figure 4.9 Concave form of the yield loci with different material properties.

Figure 4.10 Concavity on the yield loci predicted by Equation (4.28).

Figure 4.11 Concavity on the yield loci predicted by Equation (4.30).

Figure 4.12 Convexity of the yield loci with different material properties predicted by Equation (4.18): (a) yield loci with different

σ

bt

/

σ

t

; (b) yield loci with different

σ

bc

/

σ

t

.

Figure 4.13 Yield loci with different material properties with .

Figure 4.14 Yield loci on the

π

plane: (a) with a changing , (b) with a changing .

Figure 4.15 Yield loci in planes parallel to the

π

plane with a changing hydrostatic stress

σ

M

: (a) ; (b) .

Figure 4.16 model of the yield criterion with different

σ

c

/

σ

t

and

σ

bt

/

σ

t

: (a) ; (b) .

Figure 4.17 model of the yield criterion with different

σ

bc

/

σ

t

.

Figure 4.18 Yield surfaces with different material properties but without the stress-type-caused effects.

Figure 4.19 Yield loci not influenced by the hydrostatic stresses.

Figure 4.20 Yield surface in 3-D stress space.

Figure 4.21 Predicted yield loci in comparison with the Taylor-Quinney's experimental data: (a) yield loci; (b) predicted yield loci on the

π

plane.

Figure 4.22 Predicted yield loci in comparison with the Lode's experimental data.

Figure 4.23 Predicted yield loci for gray cast-iron.

Figure 4.24 Predicted yield loci and experimental data: (a) predictions in comparison with experimental results; (b) yield loci on the

π

plane for two kinds of materials.

Figure 4.25 Directions of the test pieces vs. rolling direction.

Figure 4.26 Experimental results of rolled dual phase steel sheet: (a) stress–strain relations in directions of rolling, perpendicular and diagonal to rolling; (b) ratios between strain in direction perpendicular to thickness and strain in through-thickness.

Figure 4.27 Dissimilar stress states with the same stress-type.

Figure 4.28 Profiles of the yield locus affected by the anisotropy of rolled sheet metals: (a) yield loci affected by the ratio of

σ

90

/

σ

0

; (b) yield loci affected by the ratio of

σ

b

/

σ

0

.

Figure 4.29 Yield loci in different principal stress directions vs. rolling laid out in the same coordinate system.

Figure 4.30 Yield loci in different directions of the principal stresses and the coordinate axes against the rolling.

Figure 4.31 Relationship between the uniaxial tension yield stress and the stretching direction against the rolling in coordinate system.

Figure 4.32 Yield loci of uniaxial tension in changing stretching direction.

Figure 4.33 Determination of the stresses and the strains in the thin-walled tube test.

Figure 4.34 Profiles of the plastic potential influenced by the strain ratios: (a) strain ratios with ; (b) strain ratios with ; (c) strain ratios with .

Figure 4.35 Plastic flow feature of rolled sheet metals expressed by the gradients of plastic potential.

Figure 4.36 Yield loci influenced by the yield stress ratio

σ

90

/

σ

0

.

Figure 4.37 Yield loci influenced by the yield stress ratio

σ

b

/

σ

0

.

Figure 4.38 Yield loci influenced by the plastic strain ratio

R

.

Figure 4.39 Predicted plastic flow feature influenced by experimental stress data.

Figure 4.40 Comparison between yield stresses of the uniaxial tension predicted by different yield criteria and experimental data.

Figure 4.41 Comparison between

R

predicted by different plastic potentials and experimental data.

Figure 4.42 Yield loci of high-strength steel in different directions of the principal stresses relative to the rolling.

Figure 4.43 Yield loci of aluminum alloy sheet in different directions of the principal stresses relative to the rolling.

Figure 4.44 Yield loci generated by two anisotropic yield criteria in the principal stress direction relative to the rolling and to the direction perpendicular to the rolling.

Figure 4.45 Distribution of the experimental data of aluminum alloy sheet Al-2.5 wt.% Mg compared with the predictions by Hill's yield criterion and Hu's yield criterion.

Chapter 5: Plastic Constitutive Relations of Materials

Figure 5.1 Effect of superimposed pressures on the material deformability.

Figure 5.2 Specimen subjected to material property transformation from one state to another.

Figure 5.3 Stress-strain relations affected by superimposed pressures or loading directions.

Figure 5.4 Convexity of yield function.

Figure 5.5 Subsequent yield loci complying with isotropic hardening model: (a) anisotropic material with principal stresses keeping in directions; (b) sensitive-to-pressure material under a constant superimposed pressure.

Figure 5.6 Subsequent yield loci complying with anisotropic hardening model: (a) hardening state with ; (b) hardening state with .

Figure 5.7 Subsequent hardening processes resulted from changes in superimposed pressures or loading directions.

Figure 5.8 Gradient directions of yield function and plastic potential.

Figure 5.9 physical interpretation of the gradient based constitutive model.

Figure 5.10 Uniaxial tension curves and subsequent yield loci for a special material: (a) stress–strain curves born of uniaxial tension in

x

and

y

directions; (b) subsequent yield loci.

Figure 5.11 Plastic strain increments represented by two different tensors.

Figure 5.12 Stress–strain relation curves affected by different superimposed pressures.

Figure 5.13 Mechanical models to imitate stress–strain relations of a material element (a) dynamic model unaffected by superimposed pressures; (b) dynamic model affected by superimposed pressures.

Figure 5.14 Dynamic model to imitate the stress–strain relation under a variable superimposed pressure.

Figure 5.15 Stress–strain relations in different stretching directions versus rolling.

Figure 5.16 A dynamic model to imitate stress–strain relations obtained in uniaxial tension of rolled sheet metals in different stretching directions against rolling.

Figure 5.17 Dynamic model to imitate uniaxial tension of anisotropic materials in a changing loading direction.

Figure 5.18 Stable and instable deformation defined by traditional plasticity.

Figure 5.19 Dynamic model imitating stable softening deformation.

Figure 5.20 Equivalent hardening state in softening.

Figure 5.21 Comparison between stable and instable softening.

Figure 5.22 Two changing loading processes under different strain boundary conditions.

Figure 5.23 Discontinuous stress paths meeting strain boundary condition: (a) discontinuous stress path; (b) strain boundary condition.

Figure 5.24 Two changeable loading processes under one stress boundary condition.

Figure 5.25 Discontinuous strain paths under a stress boundary condition: (a) stress boundary condition; (b) discontinuous strain paths.

Chapter 6: Description of Material Hardenability with Different Models

Figure 6.1 Comparison of experimental flow stresses in tension and compression with theoretically predicted results.

Figure 6.2 Yielding surfaces and plastic flow surfaces at planar stress state.

Figure 6.3 Normal directions at uniaxial tension and compression stress states by yield function and plastic potential.

Figure 6.4 Comparison of predicted volumetric plastic strains by using two different constitutive models.

Figure 6.5 Stress–strain relations of 4330 steel in compression affected by different superimposed pressures.

Figure 6.6 Initial and transformed equivalent stress states of an element unit with different normal stresses: (a) original stresses; (b) stresses after equivalent transformation.

Figure 6.7 A new 3D stress coordinate system.

Figure 6.8 Experimental results and related subsequent yield loci: (a) stress–strain relation curves borne of uniaxial tension in rolling and transverse-to-rolling direction; (b) effects of initial yield stresses

σ

0

and

σ

90

on subsequent yield loci; (c) effects of

σ

0

and

σ

b

on subsequent yield loci.

Figure 6.9 Subsequent yield loci influenced by anisotropic hardening behavior of material element: (a) flow stress–strain relations borne of uniaxial tension along rolling and equi-biaxial tension; (b) subsequent yield loci of the material characteristic of ; (c) subsequent yield loci of the material characteristic of .

Figure 6.10 Anisotropic parameters of materials with different hardenability: (a) anisotropic parameters of a dual-phase steel sheet; (b) anisotropic parameters of the 6A02 Al-alloy sheet.

Figure 6.11 Subsequent yield loci influenced by and declining during hardening: (a) ; (b) .

Figure 6.12 Subsequent yield locus influenced by declining and rising during hardening.

Figure 6.13 Subsequent yield locus influenced by rising during hardening process.

Figure 6.14 Experimental stress–strain relations borne of uniaxial tensions of a dual-phase steel sheet in different directions against rolling.

Figure 6.15 Distribution of flow stresses in uniaxial tension of a dual-phase steel sheet in different directions against rolling.

Figure 6.16 Experimental stress–strain relations borne of uniaxial tension of 6A02 Al-alloy sheet indifferent tensile directions other than rolling.

Figure 6.17 Distributions of flow stresses from uniaxial tensions of 6A02 Al-alloy sheet in different directions against rolling.

Figure 6.18

R

values of a dual-phase steel sheet in different directions against rolling: (a) anisotropic parameter

R

in different directions against rolling with progress of the stretching strain of uniaxial tension; (b) predictions of anisotropic parameters at several equivalent hardening states.

Figure 6.19 Distribution of

R

values of 6A02 Al-alloy sheet in different stretching directions against rolling: (a) anisotropic parameters in different stretching directions against rolling with progress of the stretching strain of uniaxial tension; (b) distribution of predicted anisotropic parameters in different stretching directions against rolling.

Figure 6.20 Correlation between the back stresses and the loading stresses.

Figure 6.21 Kinematic yield surface at

π

plane.

Figure 6.22 Gradient of yield surface influenced by kinematic hardening.

Figure 6.23 Exotic anisotropy induced by kinematic model based on associated flow rule.

Figure 6.24 Evolution of back stresses at new loading stress state.

Figure 6.25 Schematic illustration of the two-surface model.

Figure 6.26 Flow directions of plastic strain increments during reloading and changes in back-stress increments: (a) reloading after preloading and unloading processes without reyielding (case 1); (b) reloading after preloading and unloading processes with reyielding (case 2).

Figure 6.27 Changes in back-stress ratio under condition of given strain ratios.

Figure 6.28 Stress-state changing with increase in equivalent plastic strain with a constant strain increment ratio.

Figure 6.29 Predictions of plastic strain increments with changeable stress states and different hardening models: (a) flow directions of plastic strain increments involving different stress states and hardening models; (b) distribution of ratios of plastic strain increments at different stress states and under different predictions.

Figure 6.30 Plastic potentials and potential back stresses at different stress states.

Figure 6.31 Tensile and compressive stress types under loading and unloading conditions: (a) hardening at loading; (b) hardening at unloading.

Figure 6.32 Plastic deformation in loading and unloading at uniaxial stress state: (a) case 1; (b) case 2; (c) case 3.

Chapter 7: Sequential Correspondence Law between Stress and Strain Components and Its Application in Plastic Deformation Process

Figure 7.1 Compression type deformation during medium principal stress getting close to

σ

1

.

Figure 7.2 Elongation type deformation during medium principal stress getting close to

σ

3

.

Figure 7.3 Schematic diagram of a thin-walled tube subjected to an internal pressure and an axial load.

Figure 7.4 Variation of stress and strain against time under tension-compression stress state.

Figure 7.5 Variation of stress and strain against time under biaxial tension stress state.

Figure 7.6 Schematic diagram of upsetting and tension under hydrostatic pressure: (a) hydrostatic upsetting; (b) hydrostatic tension.

Figure 7.7 Sequence of strains and stresses at point A during indenting a punch in a semi-infinite space.

Figure 7.8 Zoning of Mises yield ellipse at typical plane stress state [6].

Figure 7.9 Stress change locus in tube drawing.

Figure 7.10 Stress change locus in the deep drawing process.

Figure 7.11 Optimal range of stress variation in tube hydroforming.

Figure 7.12 Spread diagram showing intersection of Mises cylinder and planes and .

Figure 7.13 Spread diagram showing lines generated when Mises cylinder intersects planes , , and .

Figure 7.14 Positions of three-dimensional stress state metal forming processes on the unfolded Mises cylinder [1].

Figure 7.15 Mohr's stress circle with (a) ; (b) ; (c) .

Figure 7.16 Mohr's stress circle with : (a) ; (b) .

Figure 7.17 Mohr's stress circle with : (a) ; (b) .

Chapter 8: Stress and Strain Analysis and Experimental Research on Typical Axisymmetric Plane Stress-Forming Process

Figure 8.1 Four types of steady thin-walled tube forming processes: (a) drawing; (b) necking; (c) flaring; (d) expanding.

Figure 8.2 Compressive stresses acting on the microelement: (a) stresses on the outer surface with diameter decreasing; (b) stresses on the inner surface with diameter increasing.

Figure 8.3 Yield locus of characteristic of axisymmetric plane stress state.

Figure 8.4 Stresses on the microelement in absence of friction.

Figure 8.5 Dimensionless bicompressive stress distribution on the tube during steady frictionless forming process.

Figure 8.6 Strain distribution in a tube in a steady frictionless forming process.

Figure 8.7 Strain rates of a tube in a steady frictionless forming process.

Figure 8.8 Strain distribution on the thin-walled tube in steady frictionless forming process.

Figure 8.9 Strain distribution on a tube in a steady frictionless forming process.

Figure 8.10 Thin-walled tube in conical die forming processes in presence of friction: (a) drawing; (b) necking; (c) flaring; (d) bulging.

Figure 8.11 Stress distribution in the necking process.

Figure 8.12 Strain distribution on a tube in a steady necking process in the presence of friction.

Figure 8.13 Final strain distribution on a tube in a steady necking process in presence of friction.

Figure 8.14 Dimensions of a necking die.

Figure 8.15 Thickness variation with different necking coefficients.

Figure 8.16 Thickness variation in deformation zone.

Figure 8.17 Thickness and stress variation in mandrel-free tube drawing.

Figure 8.18 Schematic view of experimental setup and specimen.

Figure 8.19 An undeformed test piece (left) and a piece subjected to ongoing deformation (right) in tube drawing.

Figure 8.20 After-test pieces.

Figure 8.21 Experimental apparatus and stress state in a microelement.

Figure 8.22 Dimension of an experimental tube.

Figure 8.23 Sketch of a tube-necking process.

Figure 8.24 Segmented loading process.

Figure 8.25 Theoretical and experimental results of the thickness variation.

Chapter 9: Shell and Tube Hydroforming

Figure 9.1 An element cut from a closed shell.

Figure 9.2 Loading analysis of a shell element.

Figure 9.3 A basketball-shaped shell preform before hydro-bulging.

Figure 9.4 Variation of curvature radii on pole and equator: (a) equator; (b) pole.

Figure 9.5 Diagrammatic sketch of the strain homogenization adjustment caused by deformation strengthening in shell hydro-bulging: (a) division according to strain; (b) diagrammatic sketch of deformation sequence.

Figure 9.6 Chief operations of spherical shell hydro-bulging process: (a) blanking; (b) roll-bending of petals; (c) assembling and welding; (d) hydro-bulging.

Figure 9.7 Types of polyhedral shell structures before hydro-bulging: (a) basketball; (b) football; (c) volleyball; (d) tennis.

Figure 9.8 A spherical tank and it's thickness distribution: (a) LPG tank; (b) thickness distribution (unit: mm).

Figure 9.9 Geometry of an ideal revolving ellipsoidal shell.

Figure 9.10 Relationship between stresses and axis length ratios for an internally pressurized ellipsoidal shell: (a) longitudinal stress; (b) latitudinal stress; (c) dividing line of latitudinal tension stresses and compression stresses.

Figure 9.11 Wrinkling on the equatorial plane of an ellipsoidal shell with during hydro-bulging.

Figure 9.12 structural design of a double generatrix ellipsoidal shell: (a) 2D schematic view; (b) 3D schematic view.

Figure 9.13 Shape changes of a double generatrix ellipsoidal shell with λ = 2.2: (a) 0.17

p

s

; (b)

p

s

; (c) 1.5

p

s

.

Figure 9.14 Variation of both axis lengths during hydro-bulging of a double generatrix ellipsoidal shell with λ = 2.2.

Figure 9.15 Dieless hydro-bulged elbow shells with wrinkles at inner sides.

Figure 9.16 A perfect dieless hydro-bulged elbow shell coming of optimized design.

Figure 9.17 Schematic diagram of tube hydroforming.

Figure 9.18 Stress state in a tube during hydroforming.

Figure 9.19 Schematic diagram of loading path during tube hydroforming.

Figure 9.20 Distribution of typical stress states on yield ellipse during tube hydroforming.

Figure 9.21 Effects of stress states on tube deformation characteristics: (a) wrinkling; (b) fracture; (c) sound part.

Figure 9.22 Wrinkles on 5A02 aluminum tubes produced under different internal pressures: (a) ; (b) ; (c) ; (d) ; (e) ; (f) .

Figure 9.23 Development of wrinkles under an internal pressure of 1.2

P

s

.

Figure 9.24 Analysis of the development of wrinkles.

Chapter 10: Bulk Forming

Figure 10.1 Directions of friction forces and applied pressures on contact surfaces between tool and workpiece.

Figure 10.2 Total load on punch in producing a ring by hydroforming.

Figure 10.3 Pressure distribution on an intricate workpiece being formed.

Figure 10.4 Drawing of a flat plate.

Figure 10.5 Projected area of a conical surface.

Figure 10.6 Metal flow and flow directions in a link forging.

Figure 10.7 Stress analysis by slab method in cylinder compression.

Figure 10.8 Balance of forces.

Figure 10.9 Distribution of unit upsetting pressure under the contact friction stress: (a) ; (b) .

Figure 10.10 Effects of cylinder diameter on pressure distribution.

Figure 10.11 Effects of friction coefficient and ratio d/h on unit pressure during cylinder upsetting: (a) Coulomb friction; (b) shear friction.

Figure 10.12 Grid deformation before and after upsetting.

Figure 10.13 Distorted grids in various zones after upsetting:(a) grids before upsetting; (b) distorted grids in zoneIafter upsetting; (c) distorted grids in zoneIIafter upsetting; (d) distorted grids in zone III after upsetting.

Figure 10.14 A sheathed test piece.

Figure 10.15 Grid deformation before and after compression with sheath.

Figure 10.16 Grid deformation before and after compression without sheath.

Figure 10.17 The effects of sheath on equivalent plastic strains in blanks: (a) with sheath; (b) without sheath.

Figure 10.18 Effects of sheath on temperature of blanks: (a) with sheath; (b) without sheath.

Figure 10.19 Effects of sheath on loads.

Figure 10.20 Metal flow in ring compression.

Figure 10.21 Theoretical curve for deciding friction coefficient

μ

in ring compression [3].

Figure 10.22 Pressure distribution on the contact surfaces during ring compression.

Figure 10.23 Various stages in disc forging: (a) before forging; (b) first stage; (c) second stage; (d) third stage.

Figure 10.24 Pressure distribution on flash land in die forging.

Figure 10.25 Division of metal flow in die cavity.

Figure 10.26 Pressure distribution in finish forging.

Figure 10.27 Schematic of isothermal forging apparatus.

Figure 10.28 Mock-up of a single rib forging.

Figure 10.29 Stress distribution on symmetrical cross section (reduction of upper die: around 13

mm

): (a)

σ

x

; (b)

σ

y

; (c)

σ

z

.

Figure 10.30 Division of zones in a piece according to stress states at filling stage.

Figure 10.31 A cross-rib forging.

Figure 10.32 The velocity field distribution of metal flow of a cross-rib forging during isothermal forming: (a) reduction around 3.04 mm; (b) reduction around 15.08 mm; (c) reduction around 18.04 mm; (d) reduction around 19 mm.

Figure 10.33 Deformation division in a cross-rib at filling stage.

Figure 10.34 Stress–strain states in a cross-rib at filling stage: (a) zone A and zone B; (b) zone D and zone E; (c) zone C.

Figure 10.35 A cross-rib forging.

Figure 10.36 Folds on ribs on cross-rib forgings with different cross points: (a) offset distance around 25 mm; (b) Offset distance around 45 mm.

Figure 10.37 Fold locations on ribs in relation to cross positions on isothermally forged cross-rib forgings: (a) Offset distance around 25 mm; (b) Offset distance around 45 mm.

Figure 10.38 Fold formation on a compressor blade: (a) before fold creation; (b) after fold creation; (c) fold-borne blade forging.

Figure 10.39 A way to avoid folds on compressor blades: (a) improved blade perform; (b) fold disappearing; (c) a fold-free blade forging.

Figure 10.40 Flow lines in a complex forging with high ribs and thin webs.

Figure 10.41 Effects of deformation degree on final distribution of flow lines in a forging during upsetting: (a) zero deformation degree; (b) 50% deformation degree; (c) 80% deformation degree.

Figure 10.42 Metal flow in a workpiece during compression between two inclined plates.

Figure 10.43 Stress state in a micro-element in rolling deformation zone.

Figure 10.44 Geometry of deformation in rolling.

Figure 10.45 Contact pressure distribution on arc with front and back tensions under Coulomb friction.

Figure 10.46 Contact pressure distribution on arc with variable reductions at D=200 mm, μ=0.5,

h

x

=1 mm.

Figure 10.47 Contact pressure distribution on arc with variable friction coefficients at , .

Figure 10.48 Contact pressure distribution on arc with variables

D

.

Figure 10.49 Pressure and friction force in roller's forward slip zone.

Figure 10.50 Relationships among

n

σ

,

δ

, and

ϵ

.

Figure 10.51 Rolling torque constituted of rolling force.

Figure 10.52 Bar extrusion.

Figure 10.53 Sheath extrusion with pure-Al sheath.

Figure 10.54 Coarse-grain ring on an extruded aluminum part.

Figure 10.55 Mesh deformation and equivalent strains in an extruded aluminum part in canned and sheath-free extrusions: (a) mesh deformation in canned extrusion; (b) mesh deformation in sheath-free extrusion; (c) equivalent strains in canned extrusion; (d) equivalent strains in sheath-free extrusion.

Figure 10.56 Drawing a rectangular bar.

Figure 10.57 Rod drawing.

Figure 10.58 Single-die hydrodynamic lubrication.

Figure 10.59 Dual-die hydrostatic lubrication. 1-high-pressure oil; 2-sealed die case; 3-front drawing die block; 4-rear die block.

Figure 10.60 Schematic diagram of rotary forging. 1-upper die; 2-billet; 3-sliding block; 4-pressure cylinder.

Figure 10.61 Mushroom-shaped workpiece during rotary forging [20].

Figure 10.62 FEM model of a cylinder billet during rotary forging [24].

Figure 10.63 Mushroom shape obtained from simulation [11].

Figure 10.64 Mushroom shape obtained from simulation.

Figure 10.65 Three meridional sections to be analyzed.

Figure 10.66 Distribution of stresses and strain rates in three meridional sections in the contact area: (a) section AB; (b) section CD; (c) section EF [20].

Figure 10.67 Positions of typical points on a meridional section of a workpiece.

Figure 10.68 Radial strains at typical points [24].

Figure 10.69 Circumferential strains at typical points [24].

Figure 10.70 FEM model in rotary forging of a disc [19].

Figure 10.71 Stress fields and strain rate fields atop surface of a workpiece: (a)

σ

θ

; (b)

σ

r

; (c) ; (d) .

Figure 10.72 Distribution of stresses and strain rates in a disc during rotary forging [25].

Figure 10.73 Contact region between top surface of a workpiece and upper die [25].

Figure 10.74 Strain measurement using plasticine method.

Figure 10.75 Grid method.

Figure 10.76 Deformation distribution indicated in terms of micro-hardness.

Figure 10.77 Section view of a screw-embedded cylinder.

Figure 10.78 An example of allocation of embedded screws.

Figure 10.79 Disappearance of interface under microscope.

Figure 10.80 Clean interface after oxidation treatment.

Figure 10.81 Cylindrical test piece with four screw holes within.

Figure 10.82 An oxidation-treated screw.

Figure 10.83 A test piece before and after upsetting.

Figure 10.84 Coordinates of four axial threads under microscope.

Figure 10.85 A micro-element for measurement of thread pitches.

Figure 10.86 Axial strains of thread Z1: (a) thread Z2; (b) thread Z3; (c) and thread Z4; (d) with screw method.

Figure 10.87 Magnified radial thread lines.

Figure 10.88 Radial strain from: (a) thread R1; (b) thread R2; (c) thread R3; (d) thread R4.

Chapter 11: Sheet Forming

Figure 11.1 Section views of billet and die during deep drawing: (a) before forming; (b) and (c) during forming; (d) after forming.

Figure 11.2 The variation of punch load

F

with punch stroke with different

k

d

.

Figure 11.3 Principle strains in flange area during deep drawing.

Figure 11.4 Thickness distribution in a deep-drawn cylindrical part made of 5A02 Al-alloy.

Figure 11.5 Changes in billet size during deep drawing.

Figure 11.6 Stress state in a severed element in flange area.

Figure 11.7 Variation of

σ

r

,

σ

θ

in flange area in deep drawing.

Figure 11.8 Stages of sheet hydroforming process: (a) filling liquid; (b) exerting blank holder force; (c) starting deep drawing; (d) continuing forming process; and (e) a finished part.

Figure 11.9 Suppression of wrinkling in SHP due to reverse bulging effect.

Figure 11.10 Stress state of the billet in SHP.

Figure 11.11 (a) The distribution of deformation zones on Tresca and Mises plane stress yield loci; (b) the typical deformation zones of cup-making SHP with stress and strain states; (c) the distribution of deformation zones on the locus in terms of Lode's parameter

μ

σ

, and hydrostatic stress

σ

, built up by unfolding von Mises cylindrical yield surface.

Figure 11.12 Process of pre-bulging-added SHP: (a) filling with liquid; (b) pre-bulging by blank holder force; (c, d) deep drawing; (e) formed part.

Figure 11.13 Comparison of strain distribution between: (a)SHP-formed part; (b) pre-bulging-added- SHP-formed one.

Figure 11.14 Thickness measurement on parts with different pre-bulging heights: (a) measuring points; (b) thickness distribution.

Figure 11.15 Principal strains at point №.10 at different punch strokes with 20% pre-bulging height: (a) pre-bulging; (b) flattening;(c) deep drawing.

Figure 11.16 Variation of micro-hardness in formed parts with different relative pre-bulging heights.

Figure 11.17 (a) The hole-flanging process; (b) the formed part.

Figure 11.18 Stress state during hole-flanging.

Figure 11.19 The variation of radial stresses and circumferential stresses with different R/r.

Figure 11.20 Variation of

ϵ

r

,

ϵ

θ

, and

ϵ

t

with different R/r (at the moment of

d =

1.1

d

0

).

Figure 11.21 Thickness distribution in a part after hole-flanging.

Figure 11.22 Forming mechanism of VPF: (1) viscous medium injection cylinder; (2) viscous medium cabin; (3) billet; (4) viscous medium; (5) lower die; (6) back viscous medium pressure cylinder; and (7) main pressure cylinder.

Figure 11.23 Al-alloy stepped disk.

Figure 11.24 BHP loading paths in experiments.

Figure 11.25 Al-alloy-madestepped disks via VPF: (a) without defects (Path b, BHP = 1.8 MPa followed by 10.5 MPa); (b) with wrinklings (Path a, BHP = 0.8 MPa); and (c) with fractures (Path c, BHP = 10.5 MPa).

Figure 11.26 Comparison of convex diameters obtained with different BHP loading paths: (a) Path a (BHP = 0.8 MPa); (b) Path c (BHP = 10.5 MPa); (c) Path b (BHP = 1.8 followed by 10.5 MPa).

Figure 11.27 Relation between leakage and BHP: 1. Upper die; 2. Sheet; 3. Sealing ring; 4. Viscous medium; 5. Lower die. (a) initial state; (b) working state; (c) viscous medium leakage; (d) specimen fracture.

Figure 11.28 Defects on superalloy-made parts: (a) wrinkles; (b) fracture in corrugated area; (c) fracture at edge; (d) a perfect piece.

Figure 11.29 A diagram of defect-free, wrinkle-induced and fracture-induced zones based on experimental results.

Figure 11.30 Comparison between MPF and MPSF: (a) conventional multipoint forming and; (b) multipoint sandwich forming.

Figure 11.31 Schematic of components for MPSF.

Figure 11.32 Deformation of polyurethane sheet and die sheet under pressure.

Figure 11.33 Schematic contracting section in a wind tunnel.

Figure 11.34 A panel of the contracting section is being processed by MPSF.

Figure 11.35 An MPSF-processed panel.

Figure 11.36 Assembling process of a contracting section for a wind tunnel.

Figure 11.37 MPSF is underway to produce a petal for a sphere.

Figure 11.38 FE simulation process of MPSF.

Figure 11.39 Mechanical model of MPSF according to constitutive relationship among component materials.

Figure 11.40 FE model of MPSF.

Figure 11.41 Schematic of a multipoint die.

Figure 11.42 Dimension of tool surface.

Figure 11.43 Workpieces processed with interpolators of different thickness: (a) dimples on a workpiece and; (b) a dimple-free workpiece with an interpolator 50 mm thick and an interpolator 10 mm thick.

Figure 11.44 Three shapes of polyurethane upper dies: (a) rectangular die; (b) 45°-borne pyramidal die and; (c) 30°-borne pyramidal die.

Figure 11.45 Mises stress distribution on elastic upper dies of different shapes: (a) rectangular die, (b) 45°-borne pyramidal die and (c) 30°-borne pyramidal die.

Figure 11.46 Locations of the typical points on the ellipsoidal workpiece.

Figure 11.47 Stress loci on typical points on upper and lower surfaces of ellipsoidal workpiece processed with different upper dies: (a) rectangular die; (b) 45°-borne pyramidal die; and (c) 30°-borne pyramidal die.

Figure 11.48 Saddle-shaped surface of a multi-point die.

Figure 11.49 Multistep forming method for forming saddle workpiece in MPSF: (a) pre-forming; and (b) finishing forming with an upper die with different shapes.

Figure 11.50 A dimple-deformed die sheet.

Figure 11.51 A saddle-type piece (Q235B steel sheet 3.7mm thick) formed with multistep method.

Figure 11.52 Effects of changing upper die shape on the sectional profiles of workpieces:(a) section AA′; and (b) section BB′.

Figure 11.53 A bulge-borne workpiece.

Figure 11.54 Forming process of bulge-borne workpiece without pre-forming: (a) flat; (b) bending with negative curvature; (c) compound bending with negative and positive curvatures; (d) bulging.

Figure 11.55 Deformation of a circular mark for strain analysis [36].

Figure 11.56 Forming limit curves for necking and for fracture [35].

Figure 11.57 Main factors affecting formability of sheet metals [35].

Figure 11.58 Schematic of Erichsen test method.

Figure 11.59 Swift's cup-drawing test method.

Figure 11.60 Notched and notch-free rectangular specimens [38].

Figure 11.61 Schematic of hydraulic bulging test with elliptical dies [39].

Figure 11.62 (a) Shape of the specimens used in the Nakazima test [40]; (b) photos of a set of specimens to determine a complete FLD (courtesy by GOM company).

Figure 11.63 Schematic diagram of tracking process in DIC analysis [43].

Figure 11.64 A setup for LDH test with DIC system and LDH specimen [43].

Figure 11.65 Strain paths for determining FLC and FFLC [43].

Figure 11.66 Theoretical models used in FLC determination [35].

Figure 11.67 FLCs of various instability models in strain space [50].

Figure 11.68 Geometrical model of the M-K theory [47].

Figure 11.69 Stress-based version of instability models [47].

Figure 11.70 Stress-based FLC of AA6111-T4 sheet: (a) predicted and measured FLDs; (b) predicted FLSD [56].

Figure 11.71 Development from FLC to generalized FLD: (a) influence of normal stress on FLC; (b) FLS showing influence of through-thickness shear stress [59].

Figure 11.72 Formability analysis of a panel stamping.

Figure 11.73 Wrinkling of stamping panel in drawing process: (a) wrinkling in the area 1; (b) wrinkling in the area 2; (c) wrinkling in the area 3.

Figure 11.74 Different designs of draw-bead (or draw-bar).

Figure 11.75 Change of draw-bead direction.

Figure 11.76 Changing draw-bead with draw-bar and locally deepening draw-beads.

Figure 11.77 Wrinkling close to addenda.

Figure 11.78 Forming defects on a downsized blank.

Figure 11.79 Forming defects varying with different addenda designs: (a) an original blank; (b) a downsized blank.

List of Tables

Chapter 1: Fundamentals of Classical Plasticity

Table 1.1 Comparisons between nominal strains and true strains

Chapter 2: Experimental Research on Material Mechanical Properties under Uniaxial Tension

Table 2.1 Test materials and their thicknesses

Table 2.2 Mechanical properties of DP590 sheet

Table 2.3 Mechanical properties of DP780 sheet

Table 2.4 Mechanical properties of DC56 sheet

Table 2.5 Mechanical properties of H180Y sheet

Table 2.6 Mechanical properties of HC340LA sheet

Table 2.7 Mechanical properties of TR780 sheet

Table 2.8 Mechanical properties of QP980 sheet

Table 2.9 Mechanical properties of DP980 sheet

Table 2.10 Mechanical properties of MS1180 sheet

Chapter 3: Experimental Research on Mechanical Properties of Materials under Non-Uniaxial Loading Condition

Table 3.1 Mechanical properties of test material at different tension speeds

Table 3.2 Diameters and thicknesses of the tube (unit: mm)

Chapter 7: Sequential Correspondence Law between Stress and Strain Components and Its Application in Plastic Deformation Process

Table 7.1 Numerical relationship among

θ

,

ω

and Lode parameter

μ

σ

Chapter 8: Stress and Strain Analysis and Experimental Research on Typical Axisymmetric Plane Stress-Forming Process

Table 8.1 Dimension variation and strain calculation

Table 8.2 Dimension variation and calculated strains in deformation zone

Table 8.3 Measured results of segmented steps and incremental strain values

Table 8.4 Total strains calculated by total strain theory and by incremental theory

Chapter 9: Shell and Tube Hydroforming

Table 9.1 Comparison of chief parameters of various types of polyhedral shells for a spherical shell 4 meters in diameter

Table 9.2 Comparison of main parameters of basketball type structures 4 meters in diameter composed of variable amounts of petals

Table 9.3 Structure parameters of the double generatrix ellipsoidal shells

Table 9.4 Stress states in a tube during hydroforming [23]

Engineering Plasticity

Theory and Applications in Metal Forming

Z. R.Wang

Harbin Institute of Technology

China

W. L. Hu

Troy Design & Manufacturing Co.

USA

S. J. Yuan

Harbin Institute of Technology

China

X. S.Wang

Harbin Institute of Technology

China

This edition first published 2018 by John Wiley & Sons Singapore Pte. Ltd under exclusive licence granted by Higher Education Press for all media and languages (excluding simplified and traditional Chinese) throughout the world (excluding Mainland China), and with non-exclusive license for electronic versions in Mainland China.

© 2018 Higher Education Press

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Z. R. Wang, W. L. Hu, S. J. Yuan and X. S. Wang to be identified as the authors of this work has been asserted in accordance with law.

Registered Offices

John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

John Wiley & Sons Singapore Pte. Ltd, 1 Fusionopolis Walk, \#07-01 Solaris South Tower, Singapore 138628

Editorial Office

1 Fusionopolis Walk, #07-01 Solaris South Tower, Singapore 138628

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging-in-Publication Data

Names: Wang, Zhongren, 1934- author.

Title: Engineering plasticity: theory and applications in metal forming / by Z.R. Wang, W.L. Hu, S.J. Yuan, X.S. Wang.

Description: First edition. | Hoboken, NJ, USA : Wiley, [2018] | Includes bibliographical references and index. |

Identifiers: LCCN 2017046173 (print) | LCCN 2017058494 (ebook) | ISBN 9781119237334 (pdf) | ISBN 9781119237327 (epub) | ISBN 9781119237303 (cloth)

Subjects: LCSH: Metal-work. | Metals-Plastic properties. | Metals-Formability.

Classification: LCC TS205 (ebook) | LCC TS205 .W37 2018 (print) | DDC 671-dc23

LC record available at https://lccn.loc.gov/2017046173

Cover design by Wiley

Cover images: (Background) © pawel.gaul/Gettyimages; (Back cover) - Courtesy of the authors

Preface

With enormous pleasures, I, on behalf of all of the authors of the book, feel deeply honored to contribute our years of attained experience of research and teaching work through the book in English version to the readers who are engaged in the engineering plasticity regarding metal forming.

This book makes detailed introductions of authors' academic contributions: the sequential correspondence law between stress and strain components, the zoning of yield graphics under plane stress states and three-dimensional stress states, the prediction of the dimensional variation tendency of work pieces, the general yield criterion,the graphical description of the anisotropic yield criterion and also shell hydro-forming for manufacturing large vessels.

This book performs mechanical analyses of a couple of special forming technologies, which include, rotary forging, viscous pressure forming, multipoint sandwich forming, and isothermal forging.

For decades, the authors of this book actively took part in the international academic exchanges and published a great number of academic papers. This book systematically summarized a number of scattered papers that were published on various periodicals, on conference proceedings and on the Journal of Material Processing Technology, in 2004 published a Special Issue dedicated to Professor Z. R. Wang on the occasion of his issued 70th birthday.

It is quite difficult to get real understanding of many concepts in the theory of plasticity, such as the concept that the values of stress are dependent on the orientation of the plane acted on, that the equivalent stresses and equivalent strains are the extension from the strength theory, that the yielding function is different from the plastic potential, and others. The book is meant to hammer them home.