INDEX. forging Axisymmetric isothermal forging, cabbaging, compression of cylinders,

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1 INDEX Accuracy of simulation, 333 Air bending, 21, Air rounding, 21 ALPID program, 136 Analysis in metal forming, closed-die forging, 34, 35-36, 37 cold extrusion, cold forging, drawing of rod, wire, shapes, and tubes, equations for, 73 flow stress of metals, friction in metal forming, hot extrusion of rods and shapes, hot forming, 28-29, impression, 35-36, 37 methods of. See Methods of analysis objectives of, 26 rolling of strip, plate, and shapes, sheet-metal forming, temperatures, 28, 29, variables in, Anisotropy, 189 plastic, Area-weighted averaging, , 129, 255 Assemblage, element, Automobile wheel center, Axisymmetric forging of flange-hub shapes, , 257 in preform design, of pulley blank, See also Axisymmetric isothermal forging Axisymmetric isothermal forging, cabbaging, compression of cylinders, compressor disk forging, finite-element formulation, flashless forging, 170, 171, 172 friction, evaluation of, , 166 heading of cylindrical bars, ring compression, , spike forging, 163, 165 Backward extrusion forging, 14 Backward tracing, , in hot forming, in plane-strain rolling, in shell nosing, in symmetric forging, Bar drawing, multipass, Bar extrusion, multipass, Beverage cans, 46 Block compression, rectangular blocks, wedge-shaped blocks, Blocker operation, 35 Bore-expanding, , 196 Boundary conditions, 86-87, with hemispheric punch, Boundary lubrication, 31 Brake-bending, 21 Cabbaging, CAD. See Computer-aided design Can ironing press, Cauchy stress, 56, 57, 58, 208, 324 Closed-die forging analysis, 35-36, 37 load vs displacement curves in, 34 metal forming system using, 9 with flash, 14, without flash, 12 Coining operation, 13 Cold extrusion, 39-41

2 372 Cold forging, Compaction, Compatibility conditions, 73 Compression block, of cylinder, 75-78, 80-83, , , , flat-tool, 314 of porous metals, ring, , , , 333 square-ring, See also Hot compression; Planestrain compression Compression test, 29 Compressor disk forging, Computer-aided design (CAD), 35-36, Computer-aided techniques, 1, 186. See also Extrusion dies, computer-aided design of Connectivity, element, 115 Constitutive equations, 73 Cup drawing, 48 square, Cylinders compression of, 75-78, 80-83, , , , steel, compression of, Cylindrical bars, heading of, Index square-cup, of tubes, of wire, Dry conditions, 30 Effective strain, interpolation of, Effective strain-rate matrix, 107 Effective stress, Efficiency of simulation, 333 Element assemblage, Element connectivity, 115 Element strain-rate matrix, Equilibrium, with tractions, 62 Equilibrium equations, 61-62, 73 Equipment, l0 Equivalent stress, 66 Euler equation, 86 Extremum principles, 68-70, 71-72, 74 Extrusion, 19 bar, bar, multipass, cold, direct and indirect, 19 hot, 20, of rods, of shapes, Extrusion dies, computer-aided design of, 186 Deep-drawing processes, Deformation mechanics, 10. See also Plasticity Deformation speed, Die bending, 21 Die rounding, 21 Direct iteration method, Disk forging, 311,312 Distortion energy criterion, 59 Drawbead, 50, 51 Drawing, 20 bar, bar, multipass, cup, defects in, 48 deep, 23, flange, , 197 of rod, of shapes, FEM. See Finite-element method FEM code. See SPID Finite deformation, 56 Finite-element method (FEM), 83-87, 88, , admissibility requirement for velocity field, advantages of, 4 alternative approach, 84 assemblage, element, 115-I 16 axisymmetric isothermal forging, axisymmetric out-of-plane deformation, basic concept of, 3 basic equations, comments on, basic equations, derivation of, 83

3 Index 373 basic principles and concepts in, basis of, 4 boundary conditions, 86-87, computer-aided, construction of model, 3-4 direct iteration method, discretization of problem, 90 element strain-rate matrix, elemental stiffness equation, l0 geometry updating, history of, 90 in-plane deformation processes, introduction to, 3-4 Lagrange multiplier method, 110 linear matrix solver, linearization, 92 metal forming and, 5-6 nodal point velocities, 91 notation, 101 numerical integrations, l penalty function method, 110 plane-strain problems, porous metals, procedures, rectangular element family, , rezoning, rigid region, treatment of, 87 ring compression, sheet-metal forming of general shapes, stiffness equations, 92 three-dimensional brick element, , three-dimensional problems, time-increment, triangular element family, 95-97, , 113 variational approach, 83-84, 86 Flange drawing, , 197 Flange-hub shapes, axisymmetric forging of, , 257 Flashless forging, 170, 171, 172 Flat-face die, 36, 38 Flat-tool compression, 314 Flat-tool forging, 293,294, 295 Flow formulation, 4-5 Flow rule, 63-66, plasticity and, porous metals, Flow stress, 28-30, 66 Folding, 153 Forging. See also Axisymmetric forging; Closed-die forging classification of, 151 disk, 311,312 flashless, 170, 171, 172 flat-tool, 293, 294, 295 forward extrusion, 13 hot-die disk, 237, 238, 239 isothermal, 237, 238, 239. See also Axisymmetric isothermal forging open-die, 15 orbital, 16 process design objective, 35 process design steps, 35, 36 radial, 314 titanium alloy Ti6242, Forward extrusion forging, 13 Friction, 10, at tool-workpiece interface, , 166 Friction coefficient, 206 Friction hill, Friction shear stress, 32 Frictional stress, Gaussian elimination, Gaussian quadrature formula, Gear blank forging, 172 Generalized stress, 66 Geometry updating, H cross sections, preforms for, 309 Hasek method, 50 Heading of cylindrical bars, Heat transfer in porous metals, in thermo-viscoplastic analysis, Hexahedral element, 276 Hill's general method, 3, 78-83, 88 Hobbing, 14 Hooke's law, 63

4 374 Hot compression, of steel cylinder, Hot-die disk forging, 237, 238, 239 Hot extrusion, 20 of rods and shapes, Hot forming, 28-29, preform design, Hot nosing, Hot pressing, under plane-strain compression, Huber-Mises criterion, 59 Hydrodynamic conditions, 31 Impression, 35-36, 37 Infinitesimal deformation theory, Infinitesimal plastic strain, In-plane deformation processes, Integration points, 111 Ironing, 21 Ironing press, Isoparametric elements, 96, 98, 99 Isothermal forging, 237, 238, 239. See also Axisymmetric isothermal forging Jauman derivative, 324 Kirchhoff stress, definition of, 324 Lagrange multiplier method, 110 Lagrangian description, Lagrangian family, 98 Lagrangian strain, 208 Levy-Mises equations, 66 Limiting drawing ratio, 205 Lubrication, basic types of, Lubricity, Maximum plastic work principle, Maxwell-Heuber-Mises criterion, 59 Mechanics of deformation, 10. See also Plasticity Metal flow, 27 in non-steady-state upset forging, 27 in rolling, 42 in steady-state extrusion, 27 Index Metal forming and finite-element method, 5-6 Metal-forming processes, See also specific processes backward extrusion forging, 14 brake-bending, 21 classification of, closed-die forging, 9, 12, 13 closed-die forging, without flash, 12 coining operation, 13 deep drawing, 23 deformation mechanics, 10. See also Plasticity description of, drawing, 20 extrusion process, 19, 20 forward extrusion forging, 13 friction, 10 hobbing, 14 ironing, 21 material variables, 9-10 nosing, 15 open-die forging, 15 orbital forging, 16 product properties, 10 radial forging of shaft, 16 ring rolling, 18 roll bending, 22 roll forming, 22 rolling, 17 rotary tube piercing, 18 rubber-diaphragm hydroforming, 24 rubber-pad forming, 24 shear forming from plate, 19 sheet-metal, 11, 12 spinning, 23 systems approach in, 8-10 tooling and equipment, I0 upsetting with flat-heading tool, 17 Metal powders. See Porous metals Methods of analysis, equations for, 73 finite-element method, 83-87, 88. See also Finite-element method Hill's general method, 3, 78-83, 88 for non-steady-state processes, for steady-state processes, upper-bound method, 3, 74-78, 88 yon Mises criterion, 59

5 Index 375 Modeling, process, 1-3 Multipass bar drawing and extrusion, Nakajima method, 50 Necking, 47 Newton-Raphson method, 92, 93, 121 Nominal stress, 324 Nonquadratic yield criterion, Non-steady-state flow, 27 Nosing, 15 hot, shell, Open-die forging, 15 Orbital forging, 16 Parent element, 97 Penalty function method, 110 Piola-Kirchhoff stress, 208, 324 Piola-Kirchhoff stress tensor, 57 Plane plastic flow, 131. See also Plane-strain problems Plane-strain compression, hot pressing under, Plane-strain problems, closed-die forging with flash, finite-element formulation, plate bending, sheet roiling, side pressing, Plane-strain rolling, Plastic anisotropy, Plastic strain-rate, Plasticity, effective strain, effective stress, equilibrium equations, extremum principles, 68-70, flow rule, infinitesimal deformation theory, Lagrangian description, maximum plastic work principle, plastic potential, strain, strain-hardening, strain-rate, stress, virtual work-rate principle, viscoplasticity, yield criterion, Plastometers, 29 Plate bending of, , rolling of, Porous metals, axisymmetric forging of flange-hub shapes, , 257 axisymmetric forging of pulley blank, compaction, discretization, finite-element modeling, flow rules, fully dense materials, 248 heat transfer in, hot pressing under plane-strain condition, numerical procedures, simple compression, updating relative density, 248 volume integration, yield criterion, Powder compaction, Powder forming, 244. See also Porous metals Prandtl-Reuss equations, Preform design, axially symmetric forging, backward tracing, , , , , , See also Backward tracing definition of, 298 H cross sections, 309 hot forming, method for design, plane-strain rolling, shell nosing, Pressing, hot, Process modeling, 1-3 Product properties, 10 Pseudoconcentrations, 334 Pulley blank, axisymmetric forging of, Punch loads/displacements, , 146

6 376 Punch-stretching, Radial forging, 314 of shaft, 16 Rectangular block compression, Rectangular element family, strain-rate matrix, Reliability of simulation, Rezoning, Rigid-plastic formulation, disadvantages of, 330 solid formulation vs., Ring compression, , , 333 axisymmetric isothermal forging, friction and, solid formulation, , 333 Ring rolling, 18 Ring test, 33 Rods, 36-39, drawing of, hot extrusion of, Roll bending, 22 Roll forming, 22 Rolling, 17 analysis of spread in, metal flow in, 42 plane-strain, plate, 17, ring, 18 of shapes, sheet, 17, strip, 42-43, 45 Rotary tube piercing, 18 Rubber-diaphragm hydroforming, 24 Rubber-pad forming, 24 Shaft, radial forging of, 16 Shapes drawing of, flange-hub, axisymmetric forging of, , 257 hot extrusion of, rolling of, sheet-metal forming of, Shear forming from plate, 19 Shear strength of deforming material, 32 Index Shear stress criterion, 59 Sheet rolling, Sheet-metal forming, 47-52, axisymmetric out-of-plane deformation, axisymmetric punch-stretching, bore expanding, , 196 classification of processes, 11, 12 deep-drawing processes, flange drawing, , 197 general shapes, in-plane deformation processes, nonquadratic yield criterion, plastic anisotropy, square-cup drawing, Shell nosing, Side pressing, Simple compression, , of cylinder, of porous metals, Simple plastic incremental deformation. See SPID Simpson's formula, 114 Simulation of forming processes, Slab method, 1 Slip-line field method, 1-3, 138 Small-strain solid formulation, Smooth entry dies, 38 Solid formulation, 4-5, large deformation: incremental form, large deformation: rate form, plate bending, rigid-plastic (flow) solutions vs., ring compression, , 333 small-strain, three-dimensional analysis with, 334 SPID (simple plastic incremental deformation), description of major variables, example solution,

7 Index 377 input and output files, 340 input preparations, program listings, program structure, simulation conditions, Spike forging, 163, 165 Spinning, 23 Springback angle, 330 Square-cup drawing, Square-ring compression, Steady-state flow, 27 Steady-state processes, applications to process design, bar drawing, bar drawing, multipass, bar extrusion, bar extrusion, multipass, method of analysis, Steel cylinder, compression of, Stiffness equations, 120 assembled, elemental, Strain, effective, Strain-hardening, Strain-rate, in Cartesian coordinate system, 101 Strain-rate matrix, element, Strain-rate vector, 103, 153 Stress, effective, Stress measures, 324 Strip, rolling of, 42-43, 45 Swift test, 205 Temperature in metal forming, 28, 29, See also Thermoviscoplastic analysis Thermal conductivity. See Heat transfer Thermo-viscoplastic analysis, applications of, compression of cylinder, , computational procedures for, forging titanium alloy Ti6242, heat transfer analysis, hot nosing, hot-die disk forging, 237, 238, 239 isothermal forging, 237, 238, 239 Three-dimensional brick element, strain-rate matrix, Three-dimensional problems, block compressions, brick element, , finite-element formulation, flat-tool forging, 293, 294, 295 hexahedral element, 276 rolling, analysis of spread in, simplified elements, solid formulation, 334 square-ring compression, Time increment, Titanium alloy Ti6242, Tooling, l0 Tresca criterion (shear stress criterion), 59 Triangular elements, 95-97, , 113 strain-rate matrix of, True stress, 56, 57, 58 Tubes, drawing of, Upper-bound method, 3, 74-78, 88 Upsetting, with flat-heading tool, 17 Virtual work-rate principle, Viscoplasticity, See also Thermo-viscoplastic analysis definition of, 222 Visioplasticity method, 3 Volume strain-rate matrix, 107 von Mises criterion, 59 Wedge-shaped blocks, Wheels, automobile, Wire, drawing of, Wrinkling, 47, 50 Yield criterion nonquadratic, plasticity, porous metals,

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