UTEX0145297
`
`McGraw Hill Series in
`MATERIALS
`SCIENCE AND
`ENGINEERING
`
`McGraw Hill Series in Materials Science and Engineering
`
`Editorial Board
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`Ronald Gibala
`University of Michigan
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`University of Minnesota
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`Wert Physics of Solids
`
`MECHANICAL
`METALLURGY
`
`Third Edition
`
`George E Dieter
`
`University of Maryland
`
`1
`
`11
`
`Mc
`Gravy
`Hill
`Education
`
`McGraw Ain EducatIon India Private Limited
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`

`

`UTEX0145298
`
`518 PLASTIC FORMING OF METALS
`
`FUNDAMENTALS
`
`OF METALWORKING 519
`
`into
`
`particle
`
`Figure
`
`at
`
`of
`
`are reduced considerably The matrix method has been incorporated
`requirements
`a computer code called ALPID1 analysis of large plastic incremental deforma
`limo It assumes a rigid viscoplastic material in which the flow stress is a function
`strain rate and temperature ALP1D predicts stress strain strain rate
`of strain
`velocity and temperature at any location within a deforming material
`1510 shows the distortion calculated
`by ALP1D after a 70 percent
`reduc
`at each point and displayed as contours
`ion Effective strain has been calculated
`the large deformations in many
`the bottom of
`the figure Because of
`metalworking processes the initial FEM mesh may become too distorted to give
`reliable information When this happens it
`is necessary to remesh by generating a
`the deformed material and interpolate the
`mesh within the boundary of
`of e è v and T to the new grid system
`FEM analysis can be used to simulate deformation very effectively when
`combined with real time computer graphics output The influence of die geome
`try preform design friction and material properties on such important factors as
`quickly and reliably While ALP1D
`formation can be investigated
`die fill and defect
`been applied to twodimensional metal deformation processes
`it will surely
`be expanded to simulate threedimensional deformation operations
`
`new
`
`values
`
`has
`
`153 FLOW STRESS DETERMINATION
`
`The various expressions that will be developed in succeeding chapters
`the forming stress or pressure in a particular metalworking process invariably
`consist of three terms
`
`to describe
`
`P = c70gfhc
`
`where
`
`strain rate
`
`i= the flow resistance of the material for the appropriate stress state ie
`is a function of strain temperature and
`uniaxial plane strain etc It
`g f = an expression for the friction at
`the toolworkpiece interface
`hc= a function of
`the tooling and the geometry of
`the geometry of
`deformation This term may or may not
`include a contribution from
`redundant deformation
`
`the
`
`It
`
`is obvious from the above
`
`if we are to make accurate
`relationship that
`and stresses we need accurate
`values of
`flow
`forming loads
`of
`predictions
`resistance flow stress The experimental problems in measuring the flow curve
`under metalworking conditions are more severe than in the usual stress strain test
`for structural or mechanical
`design applications Since metalworking
`determined
`is desirable to measure the flow curve out
`
`processes
`
`involve large plastic strains it
`
`S I Oh Int J Mech Set vol 17 pp 479493 1982 S I Oh G D Lahoti and T Altan
`Proc NAMRCX 1982 T Altan 11 L Gegel and S I Oh Metal Farming chap 20 American
`Society for Metals Metals Park Ohio 1983
`
`Radius mm
`
`20
`
`40
`
`60
`
`80
`
`100
`
`a Undeformed grid
`
`2
`
`3
`
`Radius
`
`inches
`
`b Grid distortion at 70 percent
`
`reduction
`
`100
`
`120
`
`110
`
`08
`n on
`n oh if uiu
`
`MI
`
`01
`
`0552
`
`
`050050
`I
`
`40
`
`20
`
`IP
`
`0
`
`20
`
`0
`
`20
`
`15
`
`10
`
`05
`
`0
`
`10
`
`05
`
`inch
`
`Height
`
`inch
`
`Height
`
`c Predicted effective strain distribution at 70 percent
`Figure 1510 Distortion of FEM grid in forging of a compressor disk Because of symmetry only
`onequarter of the cross section need be considered From T Allan S I Oh and H L Gegd
`Metal Forming p 336 American Society for Metals Metals Park Ohio 1983
`
`reduction
`
`on elastic plastic solutions Because these problems re
`problems concentrated
`increments of strain with elastic calculations made at
`quire the use of very small
`each increment a very large amount of computer capacity
`A practical adaptation of the FEM to metalworking analysis was achieved
`by
`in a technique called the matrix method This method neglects elastic
`Kobayashi
`strains compared with the larger plastic strains and assumes rigid plastic behav
`ior Therefore relatively large strain increments can be used and the computer
`
`is required
`
`I C H Lee and S Kobayashi Trans ASME Ser B J Eng Ind vol 93 pp 445454 1971 S
`Kobayashi and S N Shah Advances
`in Deformation Processing J 3 Burke and V Weiss eds
`pp 5198 Plenum Press New York 1978
`
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`
`

`

`UTEX0145299
`
`520 PLASTIC
`
`FORMING OF METALS
`
`FUNDAMENTALS
`
`OF METALWORKING 521
`
`I
`
`I
`
`1
`
`i
`
`1 411141161WW
`
`i
`
`I
`
`i
`
`r
`
`1
`
`1
`
`Figure 1511 Undeformed regions shaded due to friction at ends of a compression specimen
`
`high
`
`e
`
`to a true strain of 20 to 40 In addition many of
`these processes involve
`100 s1 which may not be obtained easily with ordinary test
`strain rates E
`facilities Further many metalworking
`processes are carried out at elevated
`temperatures where the flow stress is strongly strain rate sensitive
`but
`nearly
`independent of strain Thus tests for determining flow stress must be carried out
`under controlled conditions of temperature and constant
`truestrain rate
`The
`true stress true strain curve determined from the tension test
`is of
`limited usefulness because necking limits uniform deformation to true strains less
`than 05 see Sec 83 This is particularly severe in hot working where the low
`01 The formation of a
`rate of strain hardening allows necking to occur at
`necked
`region in the tension specimen
`introduces a complex stress state and
`locally raises the strain rate
`The compression of a short cylinder between anvils is a much better test for
`measuring the flow stress in metalworking applications There is no problem with
`necking and the test can be carried out
`to strains in excess of 20 if
`the material is
`ductile However
`the friction between
`and anvils can lead to
`the specimen
`unless it
`is controlled In the homogeneous upset
`diameter D and initial height h0 would be compressed in height to h and spread
`out in diameter to D according
`to the law of constancy of volume
`Djho = Dh
`
`difficulties
`
`test a cylinder of
`
`During deformation as the metal spreads over
`the compression anvils to increase
`its diameter
`the outward flow of metal This
`forces will oppose
`frictional
`frictional resistance occurs in that part of the specimen in contact with the anvils
`while the metal at specimen rnidheight can flow outward undisturbed This leads
`to a barreled specimen profile and internally a region of undeformed metal
`the anvil surfaces Fig 1511 As these cone shaped zones approach
`created near
`and overlap they cause an increase in force for a given increment of deformation
`and the load deformation curve bends upward Fig 1512 For a fixed diameter
`H J McQueen and J J Jonas Hot Workability Testing Techniques in A L Hoffnnanner ed
`Metal Forming Interrelation
`Between Theory and Practice Plenum Publishing Corporation New
`York 1971
`
`is
`
`Reduclion
`
`in heighi
`
`Figure 1512 Load deformation curves
`values of DOho
`tests with different
`
`for compression
`
`percentage
`
`force to produce the same
`require a greater axial
`a shorter specimen will
`reduction in height because of the relatively larger undeformed region
`Fig 1511 Thus one way to minimize the barreling and nonuniform deforma
`tion is to use a low value of Doho However
`limit of
`there is a practical
`05 for below this value the specimen buckles instead of barreling The
`p0h0
`friction can be obtained by plotting load
`true flow stress in compression without
`versus D0h0 for several values of reduction and extrapolating each curve to
`D0h0 = 0
`the specimen platen interface can be minimized by using
`The friction at
`smooth hardened platens grooving the ends of
`the specimen to retain lubricant
`in increments so that the lubricant can be replaced at
`the test
`and carrying out
`intervals Teflon sheet for cold deformation and glass for hot deformation are
`especially effective lubricants With these techniques it
`is possible to reach a strain
`e = 10 with only slight barreling When
`the
`friction is not present
`of about
`uniaxial compressive force required to produce yielding is
`P
`
`o0A
`
`The true compressive stress p produced by this force P is
`4P
`
`P=
`
`and using the constancy of volume relationship
`
`P
`
`4Ph
`
`TrNh
`
`1523
`
`M Cooke and E C Larke J Inst Met vol 71 pp 371390 1945
`2 G T van Rooyen and W A Backofen Int J Mech Scivoll pp 1271960 0 W Pearsall
`and W A Backofen Trans ASME Ser D J Basic Eng vol 85 p 68 1963
`3 Standard Methods of Compression Testing of Metallic Materials at Room Temperature ASTM
`temperature compression tests see ASTM E209
`Standards pt 31 Designation E970 for elevated
`T C Hsu Mater Res Stand vol 9 pp 2025 4753 1969
`
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`

`

`UTEX0145300
`
`522 PLASTIC FORMING OF METALS
`
`FUNDAMENTALS
`
`OF METALWORKING 523
`
`It has been found that the axial compressive
`plane strain compression test
`stress
`simply is the applied load divided by the contact area of the platens so long as the
`to platen width tb is in the range
`indentation thickness
`ratio of
`By
`changing platens to maintain this tb range it
`is possible to achieve deformations
`of about 90 percent An additional
`to maintain the plane strain
`requirement
`condition is that wb must be greater than 5
`True stress and true strain determined in the plane strain compression test
`may be expressed by
`
`to
`
`pE =in
`
`wb
`
`Pe
`
`to
`
`Figure 1513 Plane strain compression test
`
`where Do and ho are the initial diameter and height and h is the height of the
`cylindrical sample at any instant during compression The true compressive strain
`is given by
`
`The mean pressure on the platens is 155 percent higher than it would be in the
`corresponding uniaxial compression test see Prob 158 The true stress true
`strain curve in uniaxial compression ao versus cc may be obtained from the
`corresponding plane strain compression curve p versus epe by the following
`
`relations
`
`Ec= In
`
`ho
`
`Fr
`
`1524
`
`a =
`
`speed the true strain rate
`In a compression test at constant
`crosshead
`increases with deformation see Eq 9331 At strain rates up to
`continuously
`10 s1 a servocontrolled testing machine can be modified to maintain a constant
`true strain rate For metalworking strain rates of 1 to 103 s1 the only equipment
`truestrain rate is the earn plastometer
`capable of providing a constant
`A compression test such as that shown in Fig 1511 would be very difficult
`to conduct on a thin sheet since it might be impossible to machine the specimens
`A much more suitable test for sheet metal
`is the plane strain compression test In
`this test a narrow band across the width of a strip is compressed by narrow
`than the strip Fig 1513 The constraints of
`platens which are wider
`the
`undeforrned shoulders of material on each side of the platens prevent extension of
`in the width dimension There is deformation in the direction of platen
`the sheet
`motion and in the direction normal
`
`the platen as occurs in the
`to the length of
`rolling process In addition to its suitability with thin sheet other advantages of
`this test are that it simulates the stress state in rolling eliminates problems with
`barreling and because the area under the platen is constant
`the total deformation
`force does not rise as rapidly as in the compression of a cylinder On the other
`hand unless good lubrication is maintained a dead metal zone will
`form in the
`specimen next to the face of the platens Therefore the test usually is carried out
`thickness after each increment and relubricat
`incrementally measuring the sheet
`ing for the next higher load Slip line field theory has been used to analyze the
`
`I J F Alder and V A Phillips J Inst Met vol 83 pp 8086 19541955 J E Hocken Am
`Soc Test Water Proc vol 59 pp 13091319 1959
`2 A B Watts and Fl Ford Proc Inst Mech Eng vol 169 pp 11411156 1955
`
`1525
`
`1526
`
`p =1155
`
`2 2
`
`e = cP = 1155epc
`
`c
`
`if
`
`The hot torsion test see Sec 106 is capable of producing very large strains
`of the order of 20 Since the dimensions of the specimen do not change the strain
`for a constant rpm Strain rates varying from 10 5 to
`rate remains constant
`103 s 1 are readily achieved The chief difficulty with this test
`is the fact
`stress and strain vary with radial distance in the specimen Usually the maximum
`the surface are reported but this may lead to problems in interpretation
`values at
`the surface strain hardens more than the core The problem of nonuniform
`stress and
`strain is largely eliminated by using a tubular specimen2 but care
`must be exercised to use a short specimen or buckling will occur Also because of
`reorientation that may occur at large strains the torsion test
`the excessive material
`is not an accurate
`simulation of metalworking processes This affects the use of
`the test for workability studies but not for flow stress determination The uniaxial
`stress and strain are obtained from the torsional shear stress T and shear strain y
`by the following relations based on the von Mises criterion
`
`that
`
`00 =
`
`E =
`
`The variation of flow stress with strain can be neglected for true hot working
`see Fig 108 or for a highly cold worked metal In cases where strain hardening
`to selecting a flow stress for use in forming load
`the best approach
`is present
`
`I J A Bailey and S L Haas J Mater vol 7 pp 813 1972
`2 F Hodierne J Inst Met vol 91 pp 267273 1963
`
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`

`

`UTEX0145301
`
`524 PLASTIC FORMING OF METALS
`
`FUNDAMENTALS
`
`OF METALWORKING 525
`
`It
`
`deformation that is possible without causing fracture is less for cold working than
`for hotworking unless the effects of cold work are relieved by annealing
`the distinction between
`is important
`cold working and
`to realize that
`hot working does not depend on any arbitrary temperature of deformation For
`most commercial alloys a hot working operation must be carried out at
`a
`be
`that a rapid rate of
`relatively high temperature in order
`recrystallization
`obtained However
`lead and tin recrystallize rapidly at room temperature after
`room temperature
`large deformations so that
`the working of
`these metals at
`constitutes hot working Similarlyworking tungsten at 2000°F in the hot working
`for steel constitutes cold working because this high melting metal has a
`range
`recrystallization temperature above this working temperature
`in metalworking depends on 1 the initial
`The temperature of the workpiece
`the tools and the material 2 heat generation due to plastic
`temperature of
`deformation 3 heat generated by friction at
`interface and 4
`
`heal
`
`the diematerial
`the deforming material and the dies and surrounding
`transfer between
`environment For a frictionless deformation process the maximum increase in
`temperature is
`
`Figure 1514 Definition of mean flow stress
`
`calculations is to use the mean flow stress as given by
`
`1
`
`ao=
`
`E
`
`eb
`
`Eh
`
`a de
`
`1527
`
`Figure 1514 shows the interpretation of this equation This is considered a better
`choice than the flow stress based on E = Ea eb2 When analytical expressions
`the data to either Eq
`for the flow curve are required it
`is usually possible to fit
`821 or Eq 824 Extensive data for flow stress under metalworking conditions
`for large strains e > I it has been proposed2
`have been published However
`that the flow stress is best given by
`Go = A + BE
`
`1528
`
`where A = K1 n
`B= Kn
`
`154 TEMPERATURE
`
`IN METALWORKING
`
`into hot working and cold working
`Forming processes are commonly classified
`operations Hot working is defined as deformation under conditions of
`tempera
`ture and strain rate such that recovery processes take place simultaneously with
`the deformation On the other hand cold working is deformation carried out
`under conditions where recovery processes are not effective In hotworking the
`strain hardening and distorted grain structure produced by deformation are very
`rapidly eliminated by the formation of new strain free grains as the result of
`recrystallization Very large deformations are possible in hot working because the
`recovery processes keep pace with the deformation Hot working occurs at an
`flow stress and because the flow stress decreases with
`essentially constant
`increasing temperature the energy required for deformation is generally much
`less for hot working than for cold working Since strain hardening is not relieved
`in cold working the flow stress increases with deformation Therefore the total
`
`1 T Altan S I Oh and H L Gegel Metal Forming pp 5672 American Society for Metals
`Metals Park Ohio 1983
`2 M C Shaw Ini J Mach Tool Des Res vol 22 no 3 pp 215226 1982
`
`U
`P
`
`cief3
`
`Td
`
`1529
`
`pcJ
`pcJ
`where Up the work of plastic deformation per unit volume
`p= the density of workpiece
`c= the specific heat of the workpiece
`J= the mechanical equivalent of heat 778 ftlbBtu or 4185 Jkcal
`3= fraction of deformation work converted into heat Typically p = 095
`The remainder is stored in the material as energy associated with the
`defect structure
`
`The temperature increase due to friction is given by
`
`1530
`
`pvA At
`
`pcVJ
`
`TI
`
`where it=
`p =
`=
`A=
`Ai=
`V=
`
`friction coefficient
`
`stress normal
`
`at materialtool interface see Sec 157
`to interface
`
`velocity at the materialtool interface
`surface area at
`the materialtool interface
`time interval of consideration
`volume subjected to the temperature rise
`
`Usually
`
`interface where
`the materialtool
`the temperature is highest at
`and
`the heat and it
`falls off toward the inside of the workpiece
`friction generates
`into the die For simplicity we can neglect
`these temperature gradients and
`the deforming material to be a thin plate between a workpiece
`consider
`initially at
`
`T Attan S I Oh and H L Gegel op cit p 90
`
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`