Effect ofPre-Drawing on Formability During Cold Heading

151 Pages·2012·8.03 MB·English

Effect ofPre-Drawing on Formability During
Cold Heading
by
Lianzhong Ma
Department of Mechanical Engineering
McGiII University
Montreal, Canada
A thesis submitted to McG ill University
in partial fulfillment of the requirements of the degree of
Master of Engineering
Un der the supervision of:
Professor J.A. Nemes
McGill University
© Lianzhong Ma
August, 2005
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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
1 Introduction ......................................................................................................................... 1
1.1 Motivation ................................................................................................................ 1
1.2 Objective .................................................................................................................. 2
1.3 Organization ............................................................................................................. 3
2 Literature Review .............................................................................................................. 4
2.1 Cold Reading ........................................................................................................... 4
2.1.1 Properties and Manufacturing Procedures for Cold Reading Quality
(CRQ) Steel Wire ........................................................................................ 5
2.1.2 Pararneters for Cold Reading ...................................................................... 6
2.2 Pre-Draw .................................................................................................................. 7
2.2.1 Pre-Drawing Process ................................................................................... 7
2.2.2 Effect ofPre-Drawing on Forrnability during Cold Reading .................. 10
2.2.3 The Bauschinger Effect ............................................................................. 17
2.3 Cold Readability and Ductile Fracture Criteria .................................................... 22
2.3.1 The Macromechanical Approach to Ductile Fracture .............................. 23
2.3.2 The Micromechanical Approach to Ductile Fracture ............................... 25
2.4 Constitutive Relations ............................................................................................ 26
2.4.1 Isotropie Hardening Material Models ....................................................... 27
2.4.2 Kinematic Rardening Material Models .................................................... 30
2.4.3 Combined Kinematic/Isotropic Rardening Material Models .................. 32
2.4.4 Flow Rules ................................................................................................. 34
2.5 Numerical Simulations of Metal Forrning Processes ........................................... 35
IV
2.5.1 Numerical Simulations of Drawing Processes ......................................... 35
2.5.2 Numerical Simulations of Cold Heading Processes ................................. 37
2.5.3 Numerical Simulations of the Fastener Manufacturing Process .............. 38
3 Model Development ........................................................................................................ 39
3.1 Failure Criterion Determination ............................................................................ 39
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
4 Numerical Simulations. .................................................................................................. 64
4.1 Numerical Simulations of Tozawa and Kojima's Tests ....................................... 64
4.1.1 Experimental Procedure ............................................................................ 64
4.1.2 Description of Simulation ......................................................................... 65
4.1.2.1 Description of the Drawing Model .......................................... 65
4.1.2.2 Description of the Cutting Model ............................................ 72
4.1.2.3 Description of the Upsetting Model ........................................ 74
4.2 Numerical Simulations of Gill and Baldwin' s Tests ............................................ 76
4.2.1 Experimental Procedure ............................................................................ 76
4.2.2 Description of Simulations ........................................................................ 77
5 Numerical Results and Discussion ............................................................................ 79
v
5.1 Determination of the Kinematic Hardening Modulus, H ................................... 79
5.1.1 Determination of the Kinematic Hardening Modulus, H, for S45C ...... 79
5.1.2 Determination of the Kinematic Hardening Modulus, H , for Mn steel. 85
5.1.3 Comments .................................................................................................. 89
5.2 Results of Simulations of Tests in Tozawa and Kojima' s Paper ......................... 90
5.2.1 Results of Simulations for S45C ............................................................... 90
5.2.1.1 Contour Plot lllustration .......................................................... 90
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 .................................................................................... 10 3
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
5.3.1 Contour Plot lllustration .......................................................................... 117
5.3.2 Calculations of Cold Heading Limit from Simulation Results .............. 119
6 Conclusions and Future Work ................................................................................. 123
6.1 Conclusions and Summary ................................................................................. 123
6.2 Future Work ........................................................................................................ 125
References .............................................................................................................................. 126
Appendix A 2-D Subroutine ..................................................................................................... 130
vi
LIST OF FIGURES
Number Page Tille
Figure 2-1 4 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)
Figure 2-2 6 Conventional procedure for the manufacturing of CHQ steel wire (adapted
from Sarruf, 2000)
Figure 2-3 8 Drawing ofrod or wire (adapted from Davis, 1988)
Figure 2-4 8 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)
Figure 2-5 12 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)
Figure 2-6 13 Plot of fracture true axial strain versus pre-strain by drawing (adapted from
Luntz, 1969/1970)
Figure 2-7 14 A -A
Effect of the reduction of area in drawing, o Ir, on the upsetting limit,
Ao
ho - h
lr
-----""- (adapted from Tozawa and Kojima, 1971)
h
Figure 2-8 15 Effect of approach die angle at constant reduction on the reduction in height
for two steels (adapted from Tozawa and Kojima, 1971)
Figure 2-9 16 S45C. Average axial stress versus average axial strain curves for upsetting
with different reductions of area (adapted from Tozawa and Kojima, 1971)
Figure 2-10 16 Mn steel. Average axial stress versus average axial strain curves for upsetting
with 40% reduction of area (adapted from Tozawa and Kojima, 1971)
Figure 2-11 17 Schematic Bauschinger effect curve
Figure 2-12 18 The effect of pre-drawing on strength in compression. Material K1020. Only
the homogeneous drawing strain is shown (adapted from Havranek, 1984)
Figure 2-13 19 The effect of pre-drawing on strength in compression. Material K1020.
(adapted from Havranek, 1984)
Figure 2-14 19 The effect of 29% pre-drawing on strength in compression. Material K1020,
spheroidised 700°C/24h (adapted from Havranek, 1984)
Figure 2-15 20 The effect of pre-drawing on strength in compression. Material KI040
(adapted from J. Havranek, 1984)
Figure 2-16 20 The effect of 29% pre-drawing on strength in compression. Material K1040,
spheroidised 700°C/24h (adapted from Havranek, 1984)
Figure 2-17 21 Fracture limits in K1020 and K1040 determined in the support upset tests
(adapted from Havranek, 1984)
Figure 2-18 21 Fracture limits in spheroidised K1020 and K1040 determined in the support
upset tests (adapted from Havranek, 1984)
VIl
Figure 3-1 42 Stress versus strain in simple tension and compression tests (adapted from
Tozawa and Kojima, 1971)
Figure 3-2 43 Stress versus plastic strain in the simple tension and compression tests
Figure 3-3 44 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
Figure 3-4 45 Comparison of 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 compression
tests in the literature
Figure 3-5 46 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
Figure 3-6 50 Symmetric strain cycle experiment (adapted from HKS Inc., 2004)
Figure 3-7 59 Flow chart for VUMAT
Figure 3-8 60 S45C. Mises stress versus equivalent plastic strain results from uniaxial tension
simulations with H = 100 (MPa) and isotropie hardening
Figure 3-9 61 S45C. Mises stress versus equivalent plastic strain results from uniaxial
compression simulations with H = 100 (MPa) and isotropie hardening
Figure 3-10 62 S45C. Axial stress versus axial plastic strain results from reverse loading testing
models with H = 0 (MPa) and isotropie hardening
Figure 3-11 63 S45C. Axial stress versus axial plastic strain results from reverse loading
testing models with H = 100 (MPa)
Figure 4-1 64 The procedure of Tozawa and Kojima's test
Figure 4-2 66 Geometry and mesh for FEM drawing model
Figure 4-3 69 The end shape ofthe eut rod (a) with adaptive mesh and (b) without adaptive
mesh
Figure 4-4 72 History of ratio of kinematic energy to internaI energy
Figure 4-5 73 (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.
Figure 4-6 74 Initial configuration of the upsetting model
Figure 5-1 80 Force versus displacement curves for the simulations of upsetting after 20%
pre-drawing by a 30° die for S45C
Figure 5-2 81 Simulation and experimental average axial stress versus average axial strain
curves for upsetting after 20% pre-drawing by a 30° die for S45C
Figure 5-3 83 Force versus displacement curves for the simulations of upsetting without pre
drawing for S45C
Figure 5-4 83 Force versus displacement curves for the simulations of upsetting after 40%
pre-drawing by a 30° die for S45C
Figure 5-5 84 Simulation and experimental average axial stress versus average axial strain
curves for upsetting without pre-drawing for S45C
viii