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Effect ofPre-Drawing on Formability During Cold Heading
by
Lianzhong Ma
Department of Mechanical Engineering McGiII University Montreal, Canada
A thesis submitted to Mc Gill University in partial fulfillment of the requirements of the degree of
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ABSTRACT
One of the most common indus trial cold forging processes is cold heading of steel wire
or rod to produce screws, bolts, nuts and rivets. The process is limited by a complicated
interplay of many factors. The cold work (pre-drawing) is one of them. Although several
investigations into the effects of pre-drawing ~m the formability of metals during cold
heading processes have been conducted, so far no attention has been given to the
numerical simulations of this phenomenon. The CUITent work aims at examining effects of
pre-drawing on formability during cold heading through numerical simulations.
Physieal tests in the literature investigating the effects of pre-drawing on the formability
of three metals are simulated using ABAQUS 6.4, with three successive FE models: the
drawing model, the cutting model and the upsetting model. A new combined linear
kinematic/nonlinear isotropic hardening constitutive model is proposed and derived to
aecount for the Bausehinger effect existing in reverse plastic deformation. The new model
is implemented into ABAQUS/Explicit v6.4 by a user subroutine VUMAT, which is
verified by one-element numerical tests under tension, compression and reverse loading
conditions. In addition, for the purpose of comparison, the Johnson-Cook isotropie
hardening model is also applied for the materials. The Cockroft and Latham criterion is
employed to predict surface fracture.
Although considerable discrepancies between the experimental and simulation results are
observed, the proposed combined hardening model is more accurate in predicting material
behavior in the reverse loading than the Johnson-Cook isotropie hardening model. In
addition, the simulation results show that the proposed combined hardening material
mode! has the potential to correctly predict the material behavior in the reverse loading
process.
RÉSUMÉ
Un des processus industriels les plus communs de forge à froid est la formation à froid du
bout du fil d'acier ou de la tige pour produire des vis, des boulons, des écrous et des
rivets. Le processus est limité par des effets compliqués de beaucoup de facteurs. Le
travail à froid (pré-drawing) est l'un d'entre eux. Bien que plusieurs recherches sur les
effets du pré-drawing sur la formabilité des métaux pendant des processus de la formation
à froid du bout aient été conduites, aucune attention n'a été donnée aux simulations
numériques de ce phénomène. Le travail présent vise à examiner des effets du pré
drawing sur la formabilité pendant la formation à froid du bout par des simulations
numériques.
Des essais physiques dans la littérature étudiant les effets du pré-drawing sur la
formabilité de trois métaux sont simulés en utilisant ABAQUS 6.4, avec trois modèles
successifs de FE : le modèle de drawing, le modèle de découpage et le modèle de
dérangement. Un nouveau modèle constitutif du durcissement combiné de kinematique
linéaire/isotrope nonlinéaire est proposé et formulé pour expliquer l'effet de Bauschinger
existant dans la déformation plastique inverse. Le nouveau modèle est mis en application
dans ABAQUSlExplicit v6.4 par un sous-programme VUMAT d'utilisateur, qui est
vérifié par les essais numériques d'un élément sous une tension, une compression et les
conditions de chargement inverse. En outre, pour la comparaison, le modèle du
durrcissement isotrope de Johnson-cook est également appliquée pour les matériaux. Le
critère de Cockroft et de Latham est utilisé pour prévoir la rupture superficielle.
Bien qu'on observe des différences considérables entre les résultats expérimentaux et de
simulation, le modèle combiné du durcissement proposé est plus précis en prévoyant le
comportement matériel sous le chargement inverse que le modèle du durcissement
isotrope de Johnson-cook. En outre, les résultats des simulations montrent que le modèle
matériel combiné du durcissement proposé a le potentiel de prévoir correctement le
comportement matériel dans le procéssus de chargement inverse.
11
ACKNOWLEDGEMENTS
l would like to first thank my supervisor, Professor James A. Nemes, for his guidance,
encouragement, patience and support.
l gratefully acknowledge the financial support of the Natural Sciences and Engineering
Research Council of Canada and Ivaco Rolling Mills through the Strategie Grants
Program.
l would also like to thank aIl the group members under the supervision of Prof. Nemes,
specifically Christine EI-Lahham for her initial help with the simulation modeling, Amar
Sabih for his help with the documentation, Wael Dabboussi for his proofreading of the
thesis, and Desheng Deng for his translation of the abstract.
Finally, l thank my family, my wife, and my daughter for their love and support.
111
TABLE OF CONTENTS
Abstract ........................................................................................................................................... i
Résumé ........................................................................................................................................... ii
Acknowledgments ........................................................................................................................ iii
Table of Contents .......................................................................................................................... iv
List of Figures .............................................................................................................................. vii
List of Tables ................................................................................................................................. xi
Glossary ...................................................................................................................................... xiii
3.2 Identification of the Corresponding Material Constants for the Johnson-Cook Hardening Model ................................................................................................... 40
3.2.1 Typical Procedures to Determine the Corresponding Material Constants for the Johnson-Cook Hardening Model ................................ .40
3.2.2 Determination of the Corresponding Material Constants for the Johnson-Cook Hardening Model in this Work ....................................... .42
3.3 A Proposed New Combined Linear KinematiclNonlinear Isotropie Hardening Model ...................................................................................................................... 47
3.4 Implementation of the Proposed Combined Linear KinematiclNonlinear Isotropie Hardening into ABAQUS ...................................................................... 52
3.4.1 Overview of User Subroutine ................................................................... 52
3.4.2 The Goveming Equations ......................................................................... 53
3.4.3 Integration of the Goveming Equations ................................................... 54
3.4.4 Derivation of Temperature Increment for an Adiabatic Analysis ........... 57
3.4.5 Flow Chart and Code ofVUMAT and UMAT ........................................ 58
3.5 Verification of the User Subroutine VUMAT ...................................................... 59
3.5.1 One-Element Tests under Uniaxial Loading Conditions ......................... 60
3.5.2 One-Element Tests under Reverse Loading Conditions .......................... 62
5.2.1.2 Results for the Material Point with the Highest Principal Stress on the Exterior Surface of the Upset Rod ..................... 93
5.2.1.3 Calculations of Reduction in Height from Simulation Results .................................................................................... 1 03
5.2.2 Results of Simulations for Mn Steel ....................................................... 110
5.2.2.1 Results for the Material Point with the Highest Principal Stress on the Exterior Surface of the Upset Rod ................... 110
5.2.2.2 Calculations of Reductions in Height from Simulation Results .................................................................................... 114
5.3 Results of Simulations of Tests in Gill and Baldwin's Paper ............................ 117
Appendix A 2-D Subroutine ..................................................................................................... 130
vi
Number
Figure 2-1
Figure 2-2
Figure 2-3
Figure 2-4
Figure 2-5
Figure 2-6
Figure 2-7
Figure 2-8
Figure 2-9
Figure 2-10
Figure 2-11
Figure 2-12
Figure 2-13
Figure 2-14
Figure 2-15
Figure 2-16
Figure 2-17
Figure 2-18
Page
4
6
8
8
12
LIST OF FIGURES
Tille
Schematics of the cold heading on an unsupported bar in a horizontal machine. (a) Head formed between punch and die. (b) Head formed in punch. (c) Head formed in die. (d) Head formed in punch and die. (adapted from Davis, 1988)
Conventional procedure for the manufacturing of CHQ steel wire (adapted from Sarruf, 2000)
Drawing ofrod or wire (adapted from Davis, 1988)
Cross section of a typical wire die for drawing 5.5mm (0.218 in.) diameter rod to 4.6mm (0.18 in.) diameter wire (adapted from Davis, 1988)
he ad diameter Cold heading limit ( .. ) versus percentage reduction of area by
Wlre dzameter
drawing by 7°,15° and 30° dies (adapted from Gill and Baldwin, 1964)
13 Plot of fracture true axial strain versus pre-strain by drawing (adapted from Luntz, 1969/1970)
14
15
16
16
17
18
19
19
20
20
21
21
A -A o Ir, on the upsetting limit,
Ao Effect of the reduction of area in drawing,
ho - hlr -----""- (adapted from Tozawa and Kojima, 1971) h
Effect of approach die angle at constant reduction on the reduction in height for two steels (adapted from Tozawa and Kojima, 1971)
S45C. Average axial stress versus average axial strain curves for upsetting with different reductions of area (adapted from Tozawa and Kojima, 1971)
Mn steel. Average axial stress versus average axial strain curves for upsetting with 40% reduction of area (adapted from Tozawa and Kojima, 1971)
Schematic Bauschinger effect curve
The effect of pre-drawing on strength in compression. Material K1020. Only the homogeneous drawing strain is shown (adapted from Havranek, 1984)
The effect of pre-drawing on strength in compression. Material K1020. (adapted from Havranek, 1984)
The effect of 29% pre-drawing on strength in compression. Material K1020, spheroidised 700°C/24h (adapted from Havranek, 1984)
The effect of pre-drawing on strength in compression. Material KI040 (adapted from J. Havranek, 1984)
The effect of 29% pre-drawing on strength in compression. Material K1040, spheroidised 700°C/24h (adapted from Havranek, 1984)
Fracture limits in K1020 and K1040 determined in the support upset tests (adapted from Havranek, 1984)
Fracture limits in spheroidised K1020 and K1040 determined in the support upset tests (adapted from Havranek, 1984)
VIl
Figure 3-1
Figure 3-2
Figure 3-3
Figure 3-4
Figure 3-5
Figure 3-6
Figure 3-7
Figure 3-8
Figure 3-9
Figure 3-10
Figure 3-11
Figure 4-1
Figure 4-2
Figure 4-3
Figure 4-4
Figure 4-5
Figure 4-6
Figure 5-1
Figure 5-2
Figure 5-3
Figure 5-4
Figure 5-5
42
43
44
45
46
50
59
60
61
62
63
64
66
69
72
73
74
80
81
83
83
84
Stress versus strain in simple tension and compression tests (adapted from Tozawa and Kojima, 1971)
Stress versus plastic strain in the simple tension and compression tests
Comparison of the stress versus plastic strain curves calculated from the Johnson-Cook hardening model with the corresponding values of the material parameters obtained from tension curve fitting and those from tension tests in the literature
Comparison of stress versus plastic strain curves calculated from the JohnsonCook hardening model with the corresponding values of the material parameters obtained from tension curve fitting and those from compression tests in the literature
Comparison of stress versus plastic strain results from compression tests in the literature and those calculated from the Johnson-Cook hardening model with the corresponding values of the material parameters obtained from compression curve fitting
Symmetric strain cycle experiment (adapted from HKS Inc., 2004)
Flow chart for VUMAT
S45C. Mises stress versus equivalent plastic strain results from uniaxial tension simulations with H = 100 (MPa) and isotropie hardening
S45C. Mises stress versus equivalent plastic strain results from uniaxial compression simulations with H = 100 (MPa) and isotropie hardening
S45C. Axial stress versus axial plastic strain results from reverse loading testing models with H = 0 (MPa) and isotropie hardening
S45C. Axial stress versus axial plastic strain results from reverse loading testing models with H = 100 (MPa)
The procedure of Tozawa and Kojima's test
Geometry and mesh for FEM drawing model
The end shape ofthe eut rod (a) with adaptive mesh and (b) without adaptive mesh
History of ratio of kinematic energy to internaI energy
(a) Configuration of the drawn rod at the final increment of the drawing simulation and (b) The initial configuration of the rod in cutting model.
Initial configuration of the upsetting model
Force versus displacement curves for the simulations of upsetting after 20% pre-drawing by a 30° die for S45C
Simulation and experimental average axial stress versus average axial strain curves for upsetting after 20% pre-drawing by a 30° die for S45C
Force versus displacement curves for the simulations of upsetting without predrawing for S45C
Force versus displacement curves for the simulations of upsetting after 40% pre-drawing by a 30° die for S45C
Simulation and experimental average axial stress versus average axial strain curves for upsetting without pre-drawing for S45C
viii
Figure 5-6
Figure 5-7
Figure 5-8
Figure 5-9
Figure 5-10
Figure 5-11
Figure 5-12
Figure 5-13
Figure 5-14
Figure 5-15
Figure 5-16
Figure 5-17
Figure 5-18
Figure 5-19
Figure 5-20
Figure 5-21
Figure 5-22
Figure 5-23
Figure 5-24
Figure 5-25
84
86
86
87
87
88
88
91
92
95
95
96
96
97
97
99
99
100
100
101
Simulation and experimental average axial stress versus average axial strain curves for upsetting after 40% pre-drawing by a 30° die for S45C
Force versus displacement curves for the simulations of upsetting after 40% pre-drawing by a 30° die for Mn steel
Simulation and experimental average axial stress versus average axial strain curves for upsetting after 40% pre-drawing by a 30° die for Mn steel
Force versus displacement curves for the simulations of upsetting after 40% pre-drawing by a 15° die for Mn steel
Force versus displacement curves for the simulations of upsetting after 40% pre-drawing by a 60° die for Mn steel
Simulation and experimental average axial stress versus average axial strain curves for upsetting after 40% pre-drawing by a 15° die for Mn steel
Simulation and experimental average axial stress versus average axial strain curves for upsetting after 40% pre-drawing by a 60° die for Mn steel
Contour of the equivalent plastic strain of the rod obtained from the simulations with H equal to 300 (MPa) for the process with 20% pre-drawing by a 30° die for S45C
Contour plot of maximum principal stress (MPa) of the rod obtained from the simulations with H equal to 300 (MPa) for the process with 20% pre-drawing by a 30° die for S45C
History of hoop (0 (J(J)' axial (0 zz), shear (0 rz) and radial stress (0 rr )
components of the element with the highest principal stress from the simulation with H equal to 300 (MPa)
History of hoop (Et(J ) and axial (E~) plastic strain components of the element
with the highest principal stress from the simulation with H equal to 300 (MPa)
Time history of hoop (0 (J(J)' axial (0 zz), shear (0 r(J ) and radial stress (0 rr)
components of the element with the highest principal stress from the simulation with the isotropie hardening
History of hoop (E:(J ) and axial (E ) plastic strain components of the element
with the highest principal stress from the simulation with isotropie hardening
History of the maximum principal stress, hoop stress and axial stress of the element with the highest principal stress from the simulations with H equal to 300 (MPa)
History of the maximum principal stress, hoop stress and axial stress of the element with the highest principal stress from the simulations with isotropie hardening
History of maximum principal stress for simulations with 10% pre-drawing
History of maximum principal stress for simulations with 20% pre-drawing
History of maximum principal stress for simulations with 40% pre-drawing
History of equivalent plastic strain for simulations with H equal to 300 (MPa)
History of maximum principal stress for simulations with H of 300 (MPa).
IX
Figure 5-26
Figure 5-27
Figure 5-28
Figure 5-29
Figure 5-30
Figure 5-31
Figure 5-32
Figure 5-33
Figure 5-34
Figure 5-35
Figure 5-36
Figure 5-37
Figure 5-38
Figure 5-39
Figure 5-40
Figure 5-41
101 Maximum principal stress versus equivalent plastic strain for simulations with 10% pre-drawing
102 Maximum principal stress versus equivalent plastic strain for simulations with 20% pre-drawing
102 Maximum principal stress versus equivalent plastic strain for simulations with 40% pre-drawing
103 Maximum principal stress versus equivalent plastic strain curve of the element with the highest maximum principal stress for the simulation with the combined hardening model with H of 300 (MPa) without pre-draw
104
105
105
111
111
112
112
Evolution of the accumulated Cockroft and Latham parameter for simulations with the combined hardening model with H equal to 300 (MPa)
Evolution of the accumulated Cockroft and Latham parameter for simulations with the combined hardening model with H equal to 600 (MPa)
Evolution of the accumulated Cockroft and Latham Parameter for simulations with isotropic hardening model
History of equivalent plastic strain for simulations with pre-drawing of 10% reduction in area with the combined hardening model with H of 200 (MPa)
History of equivalent plastic strain for simulations with pre-drawing of 20% reduction in area with the combined hardening model with H of 200 (MPa)
History of equivalent plastic strain for simulations with pre-drawing of 40% reduction in area with the combined hardening model with H of 200 (MPa)
Maximum principal stress versus equivalent plastic strain results for simulations with pre-drawing of 10% reduction in area with the combined hardening model with H of 200 (MPa)
113 Maximum principal stress versus equivalent plastic strain results for simulations with pre-drawing of 20% reduction in area with the combined hardening model with H of 200 (MPa)
113 Maximum principal stress versus equivalent plastic strain results for simulations with pre-drawing of 40% reduction in area with the combined hardening model with H of 200 (MPa)
118 Contour plot of equivalent plastic strain for 20% reduction
118 Contour plot of maximum principal (MPa) stress for 20% reduction in area
119 Contour plot of temperature (oC) for 20% reduction in area
x
Number Page
Table 2-1 11
Table 2-2 14
Table 3-1 43
Table 3-2 45
Table 3-3 47
Table 4-1 65
Table 4-2 65
Table 4-3 67
Table 4-4 67
Table 4-5 76
Table 4-6 76
Table 4-7 78
Table 4-8 78
Table 5-1 106
Table 5-2 106
Table 5-3 106
Table 5-4 107
Table 5-5 107
Table 5-6 107
Table 5-7 108
Table 5-8 114
Table 5-9 115
Table 5-10 115
Table 5-11 115
Table 5-12 115
Table 5-13 116
LIST OF TABLES
Tille
Wire sizes for cold heading (adapted from Gill and Baldwin, 1964)
Mechanical properties oftwo steels (adapted from Tozawa and Kojima, 1971)
Values of material parameters obtained from tension curve fitting
Values of material parameters obtained from compression curve fitting
Values of material parameters for S45C and Mn steel
Chemical composition of materials used (adapted from Tozawa and Kojima, 1971)
Pre-drawing reductions in area and die approach angle for S45C and Mn steel.
Original geometry of the rod corresponding to finallength 12 mm
Original geometry of the rod for the FEM drawing model
Heights of compressed rods to fracture (a) for S45C and (b) for Mn steel
Chemical composition of AISI 1335 (adapted from EAD Inc., 1977)
Material properties of Mn steel
Corresponding heights at fracture from Gill' s paper
Predicted heights to fracture and reductions in height for simulations with H of 300 (MPa)
Predicted heights to fracture and reductions in height for simulations with H of 600 (MPa)
Predicted heights to fracture and reductions in height for simulations with isotropic hardening model
Heights to fracture and reductions in height from the experiments in the literature
Comparisons of heights to fracture between the simulation and experimental results
Comparisons of reductions in height between the simulation and experimental results
Differences of reduction in height
Reductions in height for the experiments in the literature
Calculated Cockroft and Latham constants
Comparison of the predicted and experimental heights to fracture for the process with 15°approach angle
Comparison of the predicted and experimental heights to fracture for the process with 300 approach angle
Comparison of the predicted and experimental heights to fracture for the process with 600 approach angle
Comparisons of reductions in height between the simulation and experimental results for the process with 15° approach angle
Xl
Table 5-14 116
Table 5-15 116
Table 5-16 116
Table 5-17 117
Table 5-18 117
Table 5-19 120
Table 5-20 120
Table 5-21 120
Table 5-22 121
Table 5-23 121
Table 5-24 121
Table 5-25 121
Table 5-26 122
Table 5-27 122
Comparisons of reductions in height between the simulation and experimental results for the process with 300 approach angle
Comparisons of reductions in height between the simulation and experimental results for the process with 60° approach angle
Differences of reduction in height between results from simulations and literature for 15° approach angle
Differences of reduction in height between resuIts from simulations and literature for 30° approach angle
Differences of reduction in height between results from simulations and literature for 60° approach angle
Radius of the rods to fracture for 7° approach angle
Radius of the rods to fracture for 15° approach angle
Radius of the rods to fracture for 30° approach angle
Comparisons of ratios of the fracture radius to the initial radius of the rod between the simulation and experimental resuIts for 7° approach angle
Comparisons of ratios of the fracture radius to the initial radius of the rod between the simulation and experimental resuIts for 15° approach angle
Comparisons of ratios of the fracture radius to the initial radius of the rod between the simulation and experimental resuIts for 30° approach angle
Differences between the predicted and experimental ratios for 7° approach angle
Differences between the predicted and experimental ratios for 15° approach angle
Differences between the predicted and experimental ratios for 30° approach angle
xii
a 2a 0.
gnew
dv aij
do.ij
Ë P
Ë f
t P
êl
1
. " é
. * ê axia/
!!.ê e
!!.ê P
!!'ËP
o al
am al
GLOSSARY
semi-angle approach angle backstress tensor
backstress tensor at the end of the time increment
backstress tensor at the beginning of the time increment
backstress rate tensor
components of a backstress tensor
deviatoric backstress tensor
components of a deviatoric backstress tensor
backstress increment components
equivalent plastic strain
equivalent plastic strain to fracture
uni axial plastic strain.
tensile plastic strain at yield point of cycle i .
compression plastic strain at yield point of cycle i .
total mechanical strain rate tensor
elastic strain rate tensor
plastic strain rate tensor
equivalent plastic strain rate
dimensionless equivalent plastic strain rate for Eo= 1.0 s-J
dimensionless axial plastic strain rate for Eo= 1.0 s-J
increment of uniaxial plastic strain.
equivalent plastic strain increment
components of a plastic strain increment
increment of strain tensor over a time increment
increment of elastic strain tensor over a time increment
increment of plastic strain tensor over a time increment
increment of equivalent plastic strain over a time increment axial stress
maximum principle tensile stress
hydrostatic stress
tensile and compression yield stresses of cycle i
compression and compression yield stresses of cycle i
equivalent stress
xm
o
d trial
(Y new
o new
o ISO
(Yiso new
do df.1 t;ij
2f.1 À
dÀ yP
1z 1]
P A Ao
AI
Ac
AI
AIr
A* B B*
C
Co
CI
C2
C3
C4
Cs Cz
Cz
components of a stress tensor
stress tensor
stress tensor rate
trial stress tensor at the end of the time increment
stress tensor at the end of the time increment
stress tensor at the beginning of the time increment
a measure of the size of the yield surface a measure of the size of the yield surface at the end of the time increment increment of uniaxial stress positive scalar
the Kronecker delta
Lames constant Lames constant a positive scalar heat flux per unit volume
a material scalar quantity the plastic heat fraction material density Johnson-Cook material constant
original cross-sectional area of the rod
Oyane fracture criterion constant
CUITent cross-sectional area of the rod
finishing cross-sectional area of the rod
cross-sectional area of the rod at fracture
Johnson-Cook material constant at the strain rate of 0.002 S-I
Johnson-Cook material constant Johnson-Cook material constant at the strain rate of 0.002 S-I
Johnson-Cook material constant
fracture criterion constant
Frudenthal fracture criterion constant
Cockroft and Latham fracture criterion constant
Brozzo et al. fracture criterion constant
Oh et al. fracture criterion constant
Oyane fracture criterion constant
a material scalar quantity
the rate of change of Cz with respect to temperature and field
variables
specific heat
XIV
c F F(oij)
J; g H
h
Q
/inew
striai _new
Tnew
Tmelt
Told
t
!!lt y
kinematic hardening material constant die reaction force
function of actual stress state
field variable
plastic potential anisotropic part of the plastic hardening modulus or kinematic hardening modulus material constant representing the isotropie part of the plastie hardening modulus
initial height of the rod
height of the rod at fracture
CUITent height of the rod
ratio of the stress at elevated temperature to that at the room temperature at the same strain rate, material constant in yie1d function
finallength of the rod
originallength of the rod
Johnson-Cook material constant Johnson-Cook material constant
normal to the Mises yield surface
original radius of the rod
finishing radius of the rod
coefficient of multiple determination fraction al drawing reduction in area deviatoric stress tensor
deviatoric stress tensor at the end of the time increment
trial deviatoric stress tensor at the end of the time increment
components of a deviatoric stress tensor
CUITent temperature increment of temperature over a time increment rate of temperature normalized temperature
reference temperature
temperature at the end of the time increment
melting temperature of the material
temperature at the beginning of the time increment
time time increment yield stress in uniaxial tension (or compression)
xv
1 Introduction
1.1 Motivation
One of the most common indus trial cold forging processes is cold heading of steel wire or
rod to produce screws, bolts, nuts and rivets (Billigmann, 1953). The major consumers of
the se products are automotive, construction, aerospace, railway, metallurgical industry
and electrical product sectors (Barret, 1997).
It is of great significance to assess the formability of cold heading materials (metals), a
major feature of forming processes, since failures, because of insufficient formability of
heading materials, result in expensive equipment downtime, material waste, tooling
damage, and unpredictable potential loss to end users. The forming process is limited by a
complicated interplay of several factors, namely, material microstructure, temperature,
deformation rate, tool and workpiece geometry, the friction at the interface of the
workpiece and tool (Sowerby et al., 1984), the surface quality of the workpiece (Muzaket
et al.,1996; Maheshwari et al., 1978) and the amount of cold work (pre-drawing)
performed on the workpiece prior to cold heading (Jenner and Dodd, 1981).
The ductility of a material, which can be defined as "the ability of a material to withstand
deformation without fracture" (NickoletopouIos, 2000), is strain-history dependent
(Rogers, 1962). Many researchers have shown that wire drawing after process annealing
can in sorne circumstances increase ductility in subsequent upsetting operations
(Billigman, 1951; Gill and Baldwin, 1964; Luntz, 1969/1970; Tozawa and Kojima, 1971;
Havranek, 1984). The Bauschinger effect has been observed in the upsetting of steel wire
following pre-drawing, which is regarded as the cause for increased ductility in the
subsequent upsetting (Havranek, 1984). Therefore, the quantitative evaluation of effects
of pre-drawing on fracture would be of considerable use to the cold heading industry
(Nickoletopoulos, 2000).
1
To evaluate the effects of pre-drawing on formability during cold heading for metals,
trial-and-error, by repeating the real physical process and taking measurements, is not a
feasible approach since it is time consuming, costly, difficult and sometimes even
impossible. Alternatively, estimating the effect of pre-drawing with the finite element
method (FEM) , which has proved to be a powerful tool to simulate a metal forming
operation, is far more cost-effective. However, although several investigations into effects
of pre-drawing on the formability of several metal materials during cold heading
processes have been conducted, no attention has been given to the numerical simulations
of this phenomenon so far. Most of the numerical simulations of bulk forming processes
simulated only a single process such as drawing, extrusion, or upsetting. Although one of
the simulations (Petrescu et al., 2002) involved both pre-drawing and subsequent
upsetting, the intent was not to evaluate the effects of pre-drawing, but to simulate as
accurately as possible the typical procedures employed in the fastener manufacturing
process. To address the above concerns, the present project was initiated.
1.2 Objective
The objective of this work is to examine effects of pre-drawing on formability during cold
heading through numerical simulations. In this work, physical tests from the literature
(Gill and Baldwin, 1964; Tozawa and Kojima, 1971) were simulated with finite element
software ABAQUS 6.4; a new combined linear kinematic/nonlinear isotropic hardening
constitutive model was proposed and implemented in the simulations. The Johnson-Cook
isotropic hardening constitutive model was also applied to make a comparison between
the isotropic hardening and combined linear kinematic/nonlinear isotropic hardening
models. The well-known Cockroft and Latham criterion (Cockroft and Latham, 1968)
was employed to prediet the surface fracture.
The material constitutive model is one of the cri tic al inputs required for an accurate
numerical simulation of a metal forming process. To date, most simulations of bulk metal
forming processes in literature are with isotropie plastic hardening material models as
material constitutive model inputs, whieh are reasonable for monotonic bulk forming
2
processes. To simulate reverse-loading processes, such as pre-drawing followed by cold
heading in this work, kinematic hardening material models must be used instead due to
the fact that isotropic plastic hardening material models are incapable of taking into
account the Bauschinger effect. Therefore, a combined linear kinematic/nonlinear
isotropic hardening constitutive model, which is able to account for the Bauschinger
effect, was proposed to simulate the inelastic behavior of three materials, Mn steel and
C45S, investigated by Tozawa and Kojima (1971), and AISI 1335 investigated by Gill
and Baldwin (1964). Since the chemical compositions of the Mn steel and AISI 1335 are
similar, in this work, they are treated as the same material.
1.3 Organization
This thesis is divided into the following chapters: Chapter 2 presents a literature review of
cold heading, pre-drawing processes, ductile fracture criteria, the Bauschinger effect,
constitutive relations and numerical simulations of met al forrning processes. Chapter 3
presents the determination of ductile fracture criteria, the identification of material
constants for the Johnson-Cook hardening model, the derivation of a new combined linear
kinematic/nonlinear isotropic hardening constitutive model and the implementation of the
combined constitutive model through user subroutines including the verification of the
user subroutines. Chapter 4 describes the numerical simulation models. Chapter 5
presents the simulation results and discussion. Finally, conclusions and recommendations
for future work are presented in Chapter 6.
3
2 Literature Review
2.1 Cold Heading
Cold heading is a cold-forging process in which the force developed by one or more
blows of punch( es) is used to upset the metal in a portion of a wire or rod blank contained
between the punch(es) and die(s) in order to form a section of a pre-determined contour.
(Davis, 1988). The cross-sectional area of the initial material is increased as the height of
the workpiece is decreased. Figure 2-1 illustrates the cold heading on an unsupported
bar in a horizontal machine (Davis, 1988).
(0) (b)
o (cl)
Figure 2-1: Schematics of the cold heading on an unsupported bar in a horizontal
machine. (a) Head formed between punch and die. (b) Head formed in punch. (c)
Head formed in die. (d) Head formed in punch and die. (adapted from Davis, 1988)
High production rates, low labor costs, and materials savings grant cold heading a
productive and economical process. Not only is cold heading widely used to produce
fasteners, su ch as bolts, rivets and nuts, but it can also successfully and economically
4
form a variety of other shapes. According to part size, production rates range from about
2000 to 50 000 pieces per hour. Many parts traditionally manufactured by machining
have been produced with cold heading (Janicek and Maros, 1996). Advantages of the
cold heading process over machining of the same parts from suitable bar stock include
less waste material, increased tensile strength from cold working, and controlled grain
flow (Davis, 1988).
2.1.1 Properties and Manufacturing Procedures for Cold Heading
Quality (CH Q) Steel Wire
There are two distinct sets of properties required for cold heading quality materials. One
is good cold headability required for cold forming processes; the other involves the
properties relating to product end use (Matsunaga and Shiwaku, 1980). Good cold
headability requires the materials to be adequately soft and ductile to aid the operation,
while product specification usually requires higher yield strength. There is a trade-off
between them. For exampIe, increased carbon content in the steel results in increase of
yield strength but the impact properties and toughness are adversely affected
(Maheshwari et al., 1978).
The very nature of the cold heading process demands that cold heading quality steel wire
should possess an essentially defect-free surface, an internaI soundness, a coating with
excellent lubricating properties and a ductile microstructure (Muzaket et al., 1996;
Maheshwari et al., 1978). To meet these requirements, several sophisticated processing
steps need to be carried out during the production of CHQ steel wire, as shown in Figure
2-2 (Muzaket et al.,1996; Sarruf, 2000).
5
SPHEROIDIZING & ANNEALING
CLEARING & COA TING
Figure 2-2: Convention al procedure for the manufacturing of CHQ steel wire
(adapted from Sarruf, 2000)
2.1.2 Parameters for Cold Heading
There are man y processing parameters influencing cold heading processes. The main
parameters include strain rate and temperature during deformation, friction between die
and workpiece, and pre-draw prior to cold heading (Nickoletopoulos, 2000). In this work,
these processing parameters are taken into account during simulations of the cold heading
processes.
Cold heading is a high-rate deformation process, in which the average strain rates usually
exceed 100 S-l (Yoo et al., 1997). There is a considerable difference between mechanical
behavior at high strain rates and at quasi-static or intermediate strain rates; therefore, it is
necessary to de termine the mechanical properties, such as flow stress, strength, and
ductility, at the deformation rate close to the ones observed during actual cold heading
(Kuhn et al., 2000).
6
Due to the high production rates and high speed, cold heading is essentially an adiabatic
process (Nickoletopoulos, 2000). During the forming process, approximately 90 to 95%
of the mechanicai energy required is transferred into heat (Farren et al., 1925), and as
much as 400 degrees of temperature rise in a workpiece is observed during cold heading
(Osakada, 1989). The flow stress decreases with . . mcreasmg temperature
(Nickoletopoulos, 2000). At constant temperature, increasing strain rate increases the
flow stress (Dieter, 1984A).
Friction conditions between the die and workpiece have a large influence on metai flow,
formation of surface and internaI defects, load of the die, and energy requirements
(Kobarashi et al., 1989). Friction at the die-workpiece interface can increase the
deformation force and may result in non-uniform or Iocalized deformation and surface
bulging (Dieter, 1984A; Nickoletopoulos, 2000).
The effect of pre-draw on cold heading will be reviewed in next section.
2.2 Pre-Draw
2.2.1 Pre-Drawing Process
Pre-draw, a common practice in the manufacture of fasteners (Havranek, 1984), is a cold
drawing process performed after annealing and prior to cold heading.
In the wire drawing process, the cross-sectional area of a wire is reduced by pulling
through a die, the geometry of which determines the final dimensions, the cross-sectional
area of the drawn wire, and the reduction in area. To avoid fracture or unstable
deformation during the drawing process, the pulling force cannot exceed the strength of
7
the wire being drawn (Davis, 1988). Figure 2-3 illustrates a procedure for drawing of rod
or wire.
Nib height 10nun
Die
Figure 2-3: Drawing of rod or wire (adapted from Davis, 1988)
Bell alogie Min at-gIe~2>tapplO.ElChat-gle
Back Ielief90
Figure 2-4: Cross section of a typical wire die for drawing 5.5mm (0.218 in.) diameter rod to 4.6mm (0.18 in.) diameter wire (adapted from Davis, 1988)
As one type of forming process, wiredrawing is a complex interaction of such main
parameters as material properties (flow stress, modulus of elasticity, work hardening),
strain rate (drawing speed), lubricant (friction, coatings), reduction in area, die geometry,
8
and temperature during the drawing process (Shemenski, 1999). The resulting mechanical
properties of drawn wire are controlled by the interplay of all these many factors. Hence,
in this work they are all taken into consideration in finite element simulations.
Figure 2-4 shows a typical carbide-drawing die. As can be seen, there are four functional
zones in a drawing die. The first zone, the bell zone, where a lubricant is introduced and
is pulled into the die-wire interface by a moving wire, is the entrance of the die. The
approach zone is the second zone, where the wire is forced to contact with the drawing
cone along the approach angle and is plastically reduced into the dimensions of the third
zone, bearing area. No further reduction occurs in the bearing area, but final dimensional
control and surface finish are established here. The final zone is the exit zone
distinguished by the back relief angle (Davis, 1988).
It is important to notice that there are two key parameters about a drawing die, an
approach angle and drawing reduction in area. The approach angle (2a) is the included
angle between the two sides of the approach zone. This angle is usually expressed by the
semi-angle (a), which is the angle between one side of the approach zone and the
longitudinal axis of the die (Shemenski, 1999). The fraction al drawing reduction in area
may be expressed as: (2.1)
where Ao and A f are the original and finishing cross-sectional area of the rod
respectively.
Wright (1979) pointed out that the die semi-angle (a) and the reduction per die (r)
control deformation of a drawing process because they determine the shape of the
deformation zone in a conical drawing die. Both parameters are incorporated into the tl.
parameter:
9
1
~=(a)[1+(l_r)2]2 r
(2.2)
A low ~ value indicates a long defonnation-zone shape and increased die contact,
resulting in excessive frictional work and heat generation requiring optimum lubrication
and lower coefficient of friction (Shemenski, 1999).
There are many advantages in cold drawing wire before gomg into cold heading.
Pre-draw serves to improve dimension al tolerances and the surface finish of the final
product (Havranek, 1984). Cold drawn wire is stiffer, feeds better and shears cleaner. One
of the more important effects of wiredrawing is its influence on the cold heading limit
(that is, the maximum head diameter to which a wire diameter can be upset), which is an
indication of material formability during cold heading (Gill and Baldwin, 1964).
2.2.2 Effect of Pre-Drawing on Formability during Cold Heading
It has been weIl demonstrated by many researchers that the ductility of a material is a
strain-history dependent parameter (Rogers, 1962). Surface ductility is a function of both
strain history and steel type (Brownrigg et al., 1981). Due to the fact that pre-draw can
change the strain history of CHQ wire steel, it is reasonable to corne up with the idea that
pre-draw should have an effect on cold headability in subsequent cold heading operations.
In fact, many researchers have observed that wire drawing after process annealing can
increase ductility in subsequent cold heading operations.
Gill and Baldwin (1964) carried out tests to investigate the effects of pre-drawing on cold
heading limits by cold heading more than 8000 bolts of AISI 1335, a common cold
heading steel, to a range of head diameter expansions from wire that had been drawn to
various reductions in area with 7°, 15° and 30° dies. During their investigation, first, the
10
wire, which was judged to be of cold heading quality, was fully spheroidized and drawn
into the "ready to finish" diameters listed in Table 2-1. After being re-annealed, the wire
was pre-drawn to different reductions, as shown in Table 2-1, through polished carbide
dies with three different die angles on a drawing machine at 150 ft per min (0.762 mis).
Then the wire was upset in a single blow on a cold header with a hammer speed of
approximately 1000 inch per min (0.423 mis). The cold heading limit was defined as "the
greatest expansion in diameter that could be made on the wire without the appearance of
45 shear cracks in the head" (Gill and Baldwin, 1964).
Ready to Finish Final
Diameter (in) Diameter* (in)
7° die
0.157 (1) 0.139
0.165 (1) 0.139
0.179 (2) 0.139
0.211 (3)0.139
0.241 (4) 0.139
5° die
0.213 (1) 0.211
0.220
0.226
0.241
0.266
0.278
0.304
0.304
0.157
0.165
0.179
0.211
0.241
(1) 0.211
(1) 0.211
(1) 0.211
(1) 0.211
(1) 0.211
(2) 0.211
(3) 0.l79
30° die
(1)0.139
(1) 0.139
(2) 0.139
(3) 0.139
(4) 0.139
Reduction
in Area (%)
23
29
40
57
67
7
12
23
37
42
52
65
23
29
40
57
67
* Numbers ln parentheses indicate number of
drawing passes to go from ready to finish size to
finish size.
Table 2-1: Wire sizes for cold heading (adapted from Gill and Baldwin, 1964)
Il
The results are shown in Figure 2-5. According to this graph, for 15° dies, pre-draw
reductions ranging from 35% to 40% improve heading limits significantly from 2.2 to
2.6; for 7° dies, the greatest cold heading limits are obtained at about 40% reduction in
area; however, drawing through 30° dies reduces the heading limit when reduction in area
is beyond 25%. Gill and Baldwin suggested that a pre-drawing with about 35% reduction
in area, through dies with any die angle in the range of 12° to 20°, should be adopted in
order to obtain a significant improvement in cold heading limits.
2.8
2.6
2.4 ;!::
E 2.2 :::i C)
2 c "0 cu Q) 1.8 J: "0
1.6 (5 ------ ---- -
0 1.4
1.2
0 10 20 30 40 50
Reduction by Drawing, %
-.-7 degree
. -lll-15degree
~30degree
60 70
F' 2 5 C Id h d' l' , head diameter) d ' f 19ure -: 0 ea mg ImIt ( " versus percentage re uchon 0 area Wlre dwmeter
by drawing by 7°,15° and 30° dies (adapted from Gill and Baldwin, 1964)
Luntz (1969/1970) has carried out wire drawing on annealed B.S.311/1 and B.S.311/2
steels. After drawing, the wires that had received three different drawing reductions were
cut into billets with a length-diameter ratio of 1. These billets were then upset at a mean
strain rate of approximately 2 s -J using lubricated platens. The obtained results, true axial
strain at the onset of shear cracking versus reduction in area, are shown in Figure 2-6. It is
12
obvious that Wlre drawing can have a marked effect on ductility during subsequent
upsetting, and ductility increases with increasing drawing reduction in area in terms of
true axial strain at the onset of shear cracking.
1.6 -,----------------------'--..., -o ... 1.4 Q) III c: o Q) C)
~ .5 ... .:.:: 1.0
1.2
... (,) cu cu .50 0.8 cu L-
b cu en Q) 0.6 -~ cu en ')( 0.4 « Q) :::s 0.2 L-I-
0.0 -f-----r----r----r----,....---..,...------l
o 5 10 15 20 25 30
Reduction by Drawing, %
---+- B.8.3111/2
~B.8. 3111/1
Figure 2-6: Plot of fracture true axial strain versus pre-strain by drawing (adapted
from Luntz, 1969/1970)
Tozawa and Kojima (1971) conducted an extensive investigation into the effects of
pre-deformation on the cold headabilities of three alloys: S45C, Mn steel and 17S. The
mechanical properties of these materials are shown in Table 2-2. In this investigation,
drawing dies with three different die angles, 15°,30°, and 60°, were used. After rods were
annealed, they were pre-drawn through the drawing dies to reductions as high as 40% to
get a constant finish diameter of 8 mm. Lubricants were applied during the drawing
process. Then they were cut to aspect ratio of 1.5 and were upset between flat dies
without lubrication. Both the drawing process and the upsetting process were performed
quasi-statically.
13
Yield (MPa) UTS (MPa) Elongation at Reduction in Break, % Area, %
Figure 4-4: History of ratio of kinematic energy to internai energy
The kinematie boundary condition is symmetric on the aXIS of the rod, having
ur = 0 described, and u z = 0 was prescribed on the bottom of the rod. The u z -
displacement of the rigid die was described using a displacement boundary condition
whose value was ramped up over step time to ensure the rod goes through the die totally
at the constant drawing speed of O.8m/s. The radial and rotation al degrees of freedom of
the rigid die were constrained.
4.1.2.2 Description of the Cutting Model
The cutting process was simulated using ABAQUS/Standard by importing the deformed
mesh and its associated material state of one-third of the whole drawn rod in the middle
from the final increment of the drawing simulation to this cutting simulation mode!. Then
the imported part underwent self-relaxation since no die or external loading is involved.
Therefore, the cutting model is actually a statie simulation without external loading or
contact. The reason for using ABAQUS/Standard in this model is that it can obtain a
72
static solution in just a few increments while ABAQUSlExplicit must solve a static
problem by obtaining a dynamic solution over a time period that is long enough for the
solution to reach a steady state; in addition, ABAQUS only provides the capability to
transfer results of simulations from ABAQUS/Standard into ABAQUSlExplicit or
ABAQUS/Standard and vice versa; ABAQUS cannot transfer results between
ABAQUSlExplicit (HKS Inc., 2004). Figure 4-5 shows the configuration of the drawn
rod at the final increment of the drawing simulation and the initial configuration of the
imported part of the rod in the cutting simulation.
o
(a) (b)
Figure 4-5: (a) Configuration of the drawn rod at the final increment of the drawing simulation and (b) The initial configuration of the rod in cutting model
It is important to notice that to import the material state from the drawing model
involving the Johnson-Cook isotropie hardening material model, the Johnson-Cook
hardening model has to be input into the drawing model in a discretized tabular format,
which both ABAQUSlExplicit analysis and ABAQUS/Standard analysis accept, since the
73
built-in Johnson-Cook hardening material model exists only in ABAQUSlExplicit's
materiallibrary, and not in ABAQUS/Standard's. In the case of the drawing model with
the Johnson-Cook hardening material model, no material definition need to be specified
in the cutting model as the material definition from the drawing model will be imported
as weB.
The initiaBy imported rod is approximately 12 mm long, with a radius of about 4 mm.
The imported mesh is the same type as in the drawing model. Since only elastic
springback was assumed to happen in this cutting process, the material model here was
assumed to be linear elastic for both materials with the same values of Young' s modulus
and Poisson' s ratio as in the drawing model. u = 0 was described on the axis of the rod
to ensure the symmetric kinematic boundary condition there, and the node at the bottom
of the axis of the rod was encastered to constrain the movement of the rod.
4.1.2.3 Description of the Upsetting Model
For a similar reason as the drawing model, the upsetting model was developed using
ABAQUSlExplicit. In this model, the deformed mesh and its associated material state
was imported from the final increment of the cutting simulation, and then was
compressed between two flat rigid dies. Figure 4-6 shows the initial configuration of this
model.
Figure 4-6: Initial configuration of the upsetting mode}
74
Geometry and model:
The imported initial rod is approximately 12 mm long, with a radius of about 4 mm; the
imported mesh type is CAX4R with 1188 elements in total. The material models defined
here are the same as in the drawing model since the upsetting process is also a quasi-static
process. However, when the drawing model is specified with the Johnson-Cook
hardening material model, no material definition needs to be specified, since the material
definition in the cutting model, which was imported from the drawing model, is imported
into this upsetting model. A Coulomb friction model with a friction coefficient of 0.13
(Nickoletopoulos, 2000) was used to model the friction between the top, bottom and
lateral surfaces of the rod and two flat rigid dies. The heat generated by the friction was
neglected since the process is quasi-static. The heat transfer between the dies and the rod
were also neglected, and the temperature of the dies and the rod were fixed to 25°C.
Boundary conditions:
The compression speed of this quasi-static process was chosen to be 0.5 mis according to
the procedure similar to the drawing model. The boundary condition is symmetric on the
axis of the rod i.e. u = o. The bottom die was encastered; the top die was constrained to
have no rotation and ur -displacement, and its Uz -displacement was prescribed using a
displacement boundary condition who se value was ramped up over time step until the
height of the deformed rod reached the height to fracture ensuring a constant compression
velocity of 0.5 mis. The heights to fracture (shown in Table 4-5) for the two materials
A -A were deterrnined according to Figure 2-7, w hich is the curves of 0 fr X 100% versus
Ao
ho - h fr -_.....::.- x 100%, where Ao and A ji- are the initial cross-sectional area and the crossho
sectional area at fracture of the rod, respectivel y; ho and h fr are the initial height and the
height at fracture of the rod, respectively.
75
Reduction in area 0% 10% 20% 40% Heights to fracture
3.81 3.38 3.03 3.47 (mm)
(a) For S45C
Height at fracture Height at fracture Height at fracture Reduction in area with 15° approach with 30° approach with 60° approach
Figure 5-19: History of the maximum principal stress, hoop stress and axial stress of the element with the highest principal stress from the simulations with H equal to
300 (MPa)
1500 --+- Maximum Principal Stress (MPa) - Hoop Stress (MPa) - Axial Stress (MPa)
Figure 5-20: History of the maximum principal stress, hoop stress and axial stress of the element with the highest principal stress from the simulations with isotropie
hardening
97
Figures 5-21 to 5-23 present plots of history of the maximum principal stress for the
elements with the highest principal stress from simulations with the isotropie hardening
and the combined hardening model with H equal to 300 and 600 (MPa) for pre-drawing
of 10%, 20% and 40% reductions in area, respectively. It is clear that in general, the
isotropie hardening model gives the highest maximum principle stress, while H equal to
600 (MPa) generates the lowest maximum principal stress, implying that increasing H
decreases the corresponding maximum principal stress regardless of different reductions
in area.
Figure 5-24 shows the history of equivalent plastic strain of the elements with the highest
maximum principal stress for simulations with H equal to 300 (MPa). lt is observed that
after the drawing, the element obtained the largest equivalent plastic strain for simulation
with 40% reduction in area, while the element for simulation with 20% reduction in area
had the smallest equivalent plastic strain. The order in terms of the magnitude of the
equivalent plastic strain maintained throughout upsetting stage. Therefore, increasing the
reduction in area increases the equivalent plastic strain of the element with the highest
principal stress.
Figure 5-25 illustrates the history of maximum principal stress from simulations with
H equal to 300 (MPa). It can be seen that at the end of the drawing stage, the maximum
principal stress decreases with increasing reduction in area, and the maximum principal
stress for 40% reduction in area has the lowest value at the upsetting stage.
Figures 5-26 to 5-28 show the comparison of maximum principal stress versus equivalent
plastic strain results among the simulations with the combined hardening model with
H of 300 and 600 (MPa), and the isotropic hardening model. In general, increasing the
value of H decreases the maximum principal stress, and the simulations with the
isotropie hardening mode! have the highest maximum principal stresses when the
Table 5-27: Differences between the predicted and experimental ratios for 30°
approach angle
It is obvious that in general, for the dynamie proeesses, results from simulations with the
combined hardening material model are mueh doser to those from the experiments in the
literature th an simulations with Johnson-Cook isotropie hardening material model. The
agreement for the case of 30° approaeh angle is the best with the differences in the range
of 3% to 9%. However, for the similar reasons to section 5.2.1.3, larger differences still
exist in the case of 7° and 15° approaeh angle.
122
6. Conclusions and Future Work
6.1 Conclusions and Summary
One of the most common industrial cold forging processes is cold heading of steel wire or
rod to pro duce screws, bolts, nuts and rivets. The forming process is limited by a
complicated interplay of many factors. The amount of cold work (pre-drawing) is one of
the factors. Although several investigations into effects of pre-drawing on the formability
of metal materials during cold heading processes have been conducted, so far no attention
has been given to the numerical simulations of this phenomenon. Most numerical
simulations of bulk forming processes in literature are limited to a single process such as
drawing, extrusion, or upsetting.
In this work, physical tests investigating the effects of pre-drawing on the formability of
three metals, S45C, Mn steel and AISI 1335, from two papers in literature (Gill and
Baldwin, 1964; Tozawa and Kojima, 1971) are simulated with finite element software
ABAQUS v6.4. Since the chemical composition of Mn steel and AISI 1335 are similar,
they are treated as the same material. The tests are simulated with three successive FE
numerical models: the drawing model, the cutting model and the subsequent upsetting
model. The drawing and upsetting models were performed using the finite element
software ABAQUS/Explicit v6.4 package, while the cutting model was performed using
finite element software ABAQUS/Standard v6.4 package. The cutting process was
modeled by the "import" function in ABAQUS, which imports the material state of the
one-third of the drawn rod in the middle from the last increment of the drawing
simulation. Then after elastic springback in the cutting simulation, it is imported into the
upsetting model to be upset between two flat dies.
A new combined linear kinematic/nonlinear isotropie hardening constitutive model is
proposed and derived to account for the Bauschinger effect existing in reverse plastic
deformation. It is implemented into the ABAQUS/Explicit v6.4 by a user subroutine
VUMAT, which is used as an interface to specify a new material model in the
123
ABAQUS/Explicit v6.4 package. The VUMAT is verified by single-element tests under
tension, compression and reverse loading conditions.
An elastic-plastic model is assumed for both S45C and Mn steel. The elastic behavior of
the material model is assumed to be linear and isotropic, while the plastic behavior of the
material model is described by the new combined linear kinematic/ nonlinear isotropic
hardening model since both materials in the literature undergo reverse loading conditions.
In addition, for the purpose of comparison, the Johnson-Cook isotropie hardening model
is also applied for both materials.
The material constants of the Johnson-Cook isotropie hardening model are determined
using the resuIts of the simple compression test, while the kinematic hardening modulus
H was determined by fitting the average axial stress versus average axial strain curves
from the resuIts of simulations with the proposed combined hardening model to those
from the experimental resuIts in Tozawa and Kojima's paper (1971).
The good agreement between the simulation and experimental average axial stress versus
average axial strain curves indicates that the Bauschinger effect is important in this
process and also provides evidence to validate the FE numerical models and the proposed
combined hardening material model.
The Cockroft and Latham criterion (Cockroft and Latham, 1968) is employed to predict
the surface fracture.
After examining the simulation resuIts and comparing them to the resuIts from the
experiments in the literature, the following points are concluded for both the quasi-static
and dynamic processes:
• Reverse plastic de formation occurs in both axial and circumferential directions.
Therefore, it is correct that the Bauschinger effect was accounted for in this work.
124
• The principal stress changes its direction from the axial direction to the
circumferential direction during the entire process (drawing, cutting and
upsetting).
• Increasing the kinematic hardening modulus, H , decreases the corresponding
maximum principal stress regardless of different reductions in area.
• Increasing the pre-drawing reduction in area increases the equivalent plastic strain
of the element with the highest principal stress in the entire process.
• Increasing the approach die angle increases the equivalent plastic strain; the
differences of the equivalent plastic strains between the simulations with different
approach die angles for the fixed reduction in area diminish
• The proposed combined hardening material model is more accurate in predicting
material behavior in this reverse loading process (drawing and cutting followed by
upsetting) than the Johnson-Cook isotropic hardening model.
• The proposed combined hardening material model has the potential to correctly
predict the material behavior in the reverse loading process.
• This work successfully examined the effects of pre-drawing on formability during
cold heading through numerical simulation.
6.2 Future Work
This work is the first step for investigation into effect of pre-drawing on formability
during cold heading through numerical simulations. Further study can be focused on the
applications of combined nonlinear kinematic hardening/nonlinear isotropic hardening
material models. The effect of the friction factor may be of great importance, and
therefore needs to be studied further. In addition, the validity of Cockroft and Latham
criterion in this type of processes needs to be investigated since the maximum principal
stress of the element of interest changes its direction from the axial direction to the
circumferential direction during this process, which is not accounted for in the criterion.
125
REFERENCE LIST
Barrett, R. (1997) Getting a Grip on Fasteners, Metal Bulletin Monthly, pp.38-43.
Behrens, A., H. Just, and D. Landgrebe (2000) Prediction of Cracks in Multistage Cold Forging Operations by Finite-Element-Simulations with Integrated Damage Criteria, Proceedings of the International Conference "Metal Forming 2000", Krakow Poland, pp. 237.
Billigman, J. (1951) Stahl Eisen, vol. 71, pp 252-262.
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