THE TRIBOLOGY AND FORMABILITY OF ZINC COATED STEEL SHEETS

SUBJECTED TO DIFFERENT STRAIN STATES

by

YOHAN JANG

Submitted in partial fulfillment of the requirements

For the degree of Master of Science

Thesis Adviser: Professor. Gary M. Michal

Department of Materials Science and Engineering

CASE WESTERN RESERVE UNIVERSITY

May, 2010

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

candidate for the degree *.

(signed) (chair of the committee)

(date)

* We also certify that written approval have been obtained for any proprietary material contained therein.

Yohan Jang

Master of Science

Professor Gary M. Michal

Professor Gerhard E. Welsch

Professor John J. Lewandowski

03/ 24/ 2010

Copyright 2010 by Yohan Jang All rights reserved

iv

TABLE OF CONTENTS

Table of Contents ..............................................................................................................

List of Tables ....................................................................................................................

List of Figures ...................................................................................................................

Acknowledgement ...........................................................................................................

Abstract ...........................................................................................................................

1. Introduction ....................................................................................................................1

2. Background .....................................................................................................................4

2.1 Static Friction Theory ..............................................................................................4

2.1.1 Coulomb and Amontons Friction Theory ....................................................4

2.1.2 Bowden and Tabors Friction Theory ...........................................................5

2.1.3 Orowan and Shaws Friction Theory .............................................................7

2.2 Dynamic Friction Theory ........................................................................................8

2.2.1 Stribeck Friction Theory ..............................................................................10

2.2.2 Daltons Friction Theory ..............................................................................12

2.3 Fracture Mechanics of Coated Steel Sheet ............................................................15

2.3.1 Wedging Mechanism Causing Powdering ....................................................16

2.3.2 Buckling Mechanism Causing Powdering ....................................................17

3. Experimental Procedure ................................................................................................20

3.1 Material Properties .................................................................................................20

3.1.1 Special Treated Zinc Coated (STZC) Materials...........................................20

3.1.2 Hot- Dip Galvanized (GI) Material..............................................................23

v

3.1.3 Galvanneal (GA) Material............................................................................24

3.2 Measurement of Real Area of Contact .................................................................24

3.2.1 Systemic Manual Point Count Method ........................................................25

3.3 Mechanical Testing ..............................................................................................27

3.3.1 Measurement of Surface Friction Coefficient ..............................................27

3.3.1.1 Cup Test .......................................................................................28

3.3.1.2 Hemispherical Punch Test ...........................................................33

3.3.2 Measurement of Coating Adhesion Propensities ........................................38

3.3.2.1 Powdering Tests ...........................................................................38

3.3.3 Measurement of Formability ......................................................................40

3.3.3.1 Limiting Dome Height (LDH) Test ...........................................40

3.4 Surface Analysis ..................................................................................................40

3.4.1 Surface Analysis by SEM ..........................................................................42

3.4.2 Surface Analysis by ESCA ........................................................................42

3.5 Microstructural Characterization by SEM and EDS ............................................42

4. Results .........................................................................................................................44

4.1 Materials Characterization ...................................................................................44

4.1.1 Surface .......................................................................................................44

4.1.1.1 Surface Morphology ...................................................................44

4.1.1.2 Real Area of Contact ( Areal Fraction of Asperities ) ................51

4.1.1.3 Depth Profile of Alloying Elements ...........................................51

4.1.2 Microstructure ............................................................................................57

vi

4.1.2.1 Cross sectional Morphology .......................................................57

4.1.2.2 Phase Identification of Coating Layers ......................................60

4.2 Surface Friction ..................................................................................................69

4.2.1 The Coefficient of Surface Friction under Drawing Conditions ...............69

4.2.2 The Coefficient of Surface Friction under Stretching Conditions .............72

4.3 Coating Adhesion Properties ..............................................................................78

4.3.1 Powdering under Drawing Conditions ......................................................78

4.3.2 Powdering under Plane Strain & Stretching Conditions............................79

4.4 Formability .........................................................................................................85

4.4.1 Limiting Dome Height Value ....................................................................85

5. Discussion ...................................................................................................................88

5.1 Factors affecting Surface Friction .......................................................................88

5.1.1 Surface Morphology ..................................................................................88

5.1.2 Strain State .................................................................................................90

5.1.3 Microstructure ............................................................................................92

5.1.4 Galvanizing and Galvannealing Conditions ..............................................95

5.2 Factors affecting Coating Adhesion .....................................................................99

5.2.1 Microstructure ............................................................................................99

5.2.2 Strain State ...............................................................................................103

5.2.3 Galvannealing Conditions ........................................................................107

5.2.4 Steel Substrate ..........................................................................................108

5.2.5 Surface Friction ........................................................................................111

vii

5.3 Formability ........................................................................................................112

5.3.1 Surface Friction .........................................................................................112

5.3.2 Coating Adhesion ......................................................................................116

6. Conclusions ..............................................................................................................118

7. Appendix 1 ...............................................................................................................123 Appendix 2 ...............................................................................................................124 Appendix 3 ...............................................................................................................125

8. References ................................................................................................................126

viii

LIST OF TABLES

Table 3.1 Galvannealing condition and mechanical properties for the STZC Samples ................................................................................................... 23 Table 3.2 Mechanical properties for commercial IF-grade and IFP- grade .............23 Table 3.3 Mechanical properties for GI and GA material .......................................24 Table 4.1 Areal fraction of asperities at initial normal pressure( P ) = 0 .................52 Table 4.2 Atomic concentration, elemental ratio and zinc state ratio observed by XPS at 5nm depth in the surfaces of five different coated steel sheets .........................................................56 Table 4.3 Polynomial fits for punch load, P in kN, as a function of contact radius, cr in mm ..........................................................................77

Table 4.4 Calculated coefficient of friction, ,under stretching condition ............77

Table 5.1 Predominant factors affecting surface friction under specific conditions ................................................................................................97

Table 5.2 Calculated lattice misfit of interfacial layers [33,47,48].............................110

Table A.1 Prediction of the number of fields (n) to be observed as a function of the desired relative accuracy and of the estimated magnitude of the areal fraction of the constituent ........................................................................................123 Table A.2 95% Confidence interval multipliers .....................................................123 Table A.3 Data used for calculation of ratio of a shear stress due to friction to a shear yield strength of pure zinc coating and an interfacial shear strength of pure zinc coating ........................................................124

ix

LIST OF FIGURES

Figure 2.1 Comparison between hard/hard contact and hard/soft contact .................7 Figure 2.2 Various static friction models : (a) Coulomb and Amontons model ; (b) Bowden and Tabors model ; (c) Orowans model ; (d) Shaws model ........................................................................................................8 Figure 2.3 Examples of static Friction (a) and dynamic Friction (b,c). Figure (a) shows Coulomb friction which is independent of velocity. Figure (b) shows there is a pre-sliding regime by microscopic motion before gross sliding. Figure(c) shows both sliding velocity and frequency of velocity oscillation lead a friction force. Figure (b) and (c) suggest that friction is a function of either displacement or velocity........................................ 9 Figure 2.4 The Stribeck curve and the Stribeck effect by Stribeck model ...............11 Figure 2.5 Daltons friction model for coated steel sheet .........................................14 Figure 2.6 Trapped lubricant effect (a) no lubricant condition, (b) lubricant& trapped condition; y = the shear yield strength of surface material ........15 Figure 2.7 Crack initiation of GA under the lateral tension condition .....................16 Figure 2.8 The mechanism of interfacial crack propagation ....................................17 Figure 2.9 The buckling failure mechanism .............................................................18 Figure 3.1 Fe-Zn diffusion couple and principle of microstructure control .............22 Figure 3.2 Transparent test grid sheet ......................................................................27 Figure 3.3 Schematic diagrams of cup test (A) and important parameters in equation (3.2) (B) ................................................................................31

Figure 3.4 Preparations for cup test:(A-a) male die,(A-b) female die with 225mm diameter, respectively, (A-c) punch with 33mm diameter, (B-a) 74mm blank, and (B-b) fully formed cup ......................................32 Figure 3.5 Generalized stretching forming operation [25] .......................................34

x

Figure 3.6 Punch with 101.6mm diameter and die set with 225mm diameter and 132.6mm diameter draw bead for hemispherical punch test (A) and important parameters in equation (3.4) (B) .............................................37 Figure 3.7 Radius of the boundary of punch contact ( cr ) is plotted as a punch displacement, for three test materials under different test conditions [25] .........................................................................................38 Figure 3.8 Relationship between major engineering strain vs. minor engineering strain and limiting dome height vs. blank geometry ...........41 Figure 4.1 SEM plan view images (200 ) of the STZC1 steel (a) and STZC2 steel (b) ....................................................................................................47 Figure 4.1 SEM plan view images (200 ) of the STZC3 steel (c) and GI steel (d) ............................................................................................................48 Figure 4.1 SEM plan view images (200 ) of the GA steel (e) ................................49 Figure 4.2 SEM images of pattern (asperity) on the (a) STZC1, (b) STZC2, (c) STZC3 (d) GI and (e) GA steels. Yellow arrow indicates surface asperity ....................................................................................................50 Figure 4.3 Real area of contact of five coated steels at initial normal pressure=0 ...52 Figure 4.4 XPS (ESCA) Depth Profile of the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steel coatings .............................................................55 Figure 4.5 Cross sectional images of five types of coating layer captured by back scattered electron mode in SEM (2000 ) : (a) STZC1 (b) STZC2 (c) STZC3 (d) GI and (e) GA steels. Arrows from (a) to (e) indicate an Fe-Zn intermetallic phase formed through the thickness and its average vertical height. Circles and ellipse in (e) indicate vertical cracks and horizontal crack, respectively. ................................59 Figure 4.6 EDS element mapping through the thickness of the STZC 1 steel (a) and energy spectrum (b) and chemical composition (at.%) (c) from an Fe-Zn intermetallic phase (yellow arrow) in the steel coating ....................................................................................................63

xi

Figure 4.7 EDS element mapping through the thickness of the STZC 2 steel (a) and energy spectrum (b) and chemical composition (at.%) (c) from an Fe-Zn intermetallic phase (yellow arrow) in the steel coating ....................................................................................................64 Figure 4.8 EDS element mapping through the thickness of the STZC 3 steel (a) and energy spectrum (b) and chemical composition (at.%) (c) from an Fe-Zn intermetallic phase (yellow arrow) in the steel coating ....................................................................................................65 Figure 4.9 EDS element mapping through the thickness of the GI steel (a) and energy spectrum (b) and chemical composition (at.%) (c) from a pure zinc coating (yellow arrow) on the steel ............................66

Figure 4.10 EDS element mapping through the thickness of the GA steel (a) and energy spectrum (b) and chemical composition (at.%) (c) from a fully galvannealed zinc coating (yellow arrow) on the steel ......67

Figure 4.11 Fe-Zn-Al ternary phase diagram (isothermal section at 500C) [32] ....68

Figure 4.12 Punch load as a function of hold down load and punch displacement of the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steels.....74

Figure 4.13 Coefficient of surface friction calculated as a function of punch displacement for cups drawn from STZC1, STZC2, STZC3, GI and GA steels .........................................................................................75

Figure 4.14 Punch load as a function of punch displacement and radius of contact boundary of the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steels ...............................................................................76

Figure 4.15 Powdering weight under the condition of drawing of the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steels and (f) a comparison of the powering rate in the five zinc coatings ........................................83

Figure 4.16 Powdering weight calculated as a function of blank width from LDH tests of the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steels and (f) a comparison of the powdering rate in the five zinc coatings ..................................................................................................84

Figure 4.17 LDH curves for the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steels and (f) curves normalized by setting each plain strain condition as an origin .............................................................................87

Figure 5.1 Effect of surface morphology on surface friction ..................................89

xii

Figure 5.2 Effect of different strain state on surface friction. Note GI: galvanized, GA: galvannealed, P-GA: galvannealed and phosphate treated, and Bare: non-coated (Source: present study [0], Paik [24], Ghosh [25], Fox et al.[39], Siegert et al. [40], Hira et al.[41] ) .................................91

Figure 5.3 A microstructure of zinc coating where an Fe-Zn intermetallic phase was grown ideally ...................................................................................94

Figure 5.4 Effect of average vertical height of Fe-Zn intermetallic phase on surface friction ........................................................................................97

Figure 5.5 Effect of galvannealing temperature on shear yield strength of zinc coating [43, 44, 45] ..........................................................................98

Figure 5.6 Effect of average vertical height (a) and type (b) of Fe-Zn intermetallic phase on coating adhesion for a drawing strain ................101

Figure 5.7 The Fe-Zn intermetallic phases and surface oxides acting as initial crack sites ...............................................................................................102

Figure 5.8 Effect of strain state on coating adhesion in phase based (a) and phase based coating (b) based upon strain states generated during cup testing and LDH testing ..................................................................105

Figure 5.9 Schematic illustration of crack propagation of phase based- and phase based coating as fracture driving strains are subjected (Red line: crack initiation sites, blue line: crack propagation) ..............106

Figure 5.10 Effect of steel substrate on coating adhesion in the STZC steels ..........110

Figure 5.11 Effect of surface friction on formability in various zinc coated steel sheets .....................................................................................................113 Figure 5.12 Effect of a modification of strain state by frictional constraint on formability .............................................................................................115 Figure 5.13 Effects of coating layer and steel substrate on formability; a) effect of average vertical height of Fe-Zn intermetallic phase, b) effect of steel substrate (IF and IFP *) .................................................................117

xiii

ACKNOWLEDGEMENTS

The author would like to thank Professor Gary M. Michal for giving this research

opportunity and lending his insight and experience for long time to this project. His

guidance and support have always encouraged me to overcome various challenges. I am

proud to have the opportunity to work with him. Also, I would especially like to thank Dr.

Doojin Paik for all of his time and effort while being an invaluable help through the

length of this work. My thanks also to CMCM staff, Christopher J. Tuma, SCSAM staff,

Reza Sharghi and graduate colleague, Joshua Katz for all of their advice and help.

I would like to thank my wife, Yewon Lee and lovely son, Josiah Jang who kept on my

side and my parents who prayed for my ways.

Finally, I would like to glorify my god who guided my life and provided all supports for

my needs throughout this pursuit of a masters degree.

xiv

The Tribology and Formability of Zinc Coated Steel Sheets Subjected to Different Strain States

Abstract

by

YOHAN JANG

Five types of zinc coated sheet steels were evaluated for their surface friction,

coating adhesion properties and formability under different strain states. The coefficient

of friction values found under biaxial tensile strain were significantly larger than those

associated with the drawing strain states. It was found that surface morphology, strain

state, and shear yield strength of the zinc coating were direct factors affecting surface

friction. The - phase based coatings exhibited the lowest coating adhesion either at the

plane strain condition or at the stretching condition whereas the - phase based coating

exhibited that at the drawing condition. It was found that coating adhesion depends

directly on the microstructure of the zinc coating and the strain state. It was also found

that surface friction and coating adhesion could affect the formability of a zinc coated

steel sheet by influencing its strain state and fracture mechanism, respectively.

1

1. Introduction

Zinc coated sheet steels such as galvanized or galvannealed are gaining

importance in the automotive industry due to their good drawability and corrosion

resistance. The steel with a thin zinc layer can be produced by passing the steel through a

molten bath of zinc at a temperature of around 460 C and various kinds of heat

treatments through a cascade of furnaces can be applied after this. The coated sheet steels

consist of a coating layer (~10m thick on each side of the substrate) and steel that is

nominally 0.7mm thick. In spite of its modest thickness compared to the substrate, the

coating layer has a critical role in the whole performance of the coated sheet steel. It is

well known that the zinc based coating layer increases corrosion resistance because zinc

is anodic with respect to iron, the zinc acts as a sacrificial anode to protect the substrate

from corrosion. Another important role of the zinc layer which is not as well known is its

ability to increase formability. The outer zinc coating layer serves as a thin film of soft

metal on the substrate and it avoids hard metal to hard metal contact which greatly

increases friction. Usually, the coating layer increases the formability of the steel sheet by

lowering its surface friction. Additionally, the coating layer can improve paintability and

weldability through post heat treatments [1,2].

Formability is a key characteristic in the application of zinc coated steel sheet for

processes which avoid machining such as automotive panels, the outer body of

appliances, and parts for aircraft. Two key properties that contribute to formability are

surface friction and coating adhesion. The lower the surface friction, the higher the

formability that is possible. Surface friction is a characteristic of a particular system, used

2

to measure friction. Thus, it is very important to understand how friction is being

assessed and what system factors affect friction for different kinds of forming operations.

Coating adhesion affects formability and it depends upon the characteristics of the

coating layer. Usually, the better the coating adhesion, the higher the formability that is

possible. In the case of heat treated zinc coated steel sheets such as galvannealed steel,

the coating layer has several intermetallic phases and these can be fractured easily and

detached from the coating during a sheet forming operation. The process of brittle

fracture leads to mass loss commonly referred to as powdering. It results in reducing the

coating quality, causing damage to the forming tools or the steel sheet itself, and as a

result the lowering of formability. Coating adhesion should be taken into account to

optimize formability and it is very important to understand how the fracture takes places

on the substrate and what factors affect mass loss or powdering.

The objectives of this work are to evaluate surface friction and coating adhesion

of differently treated zinc coated sheet steels subjected to different strain states, to

analyze factors correlated with them, and subsequently to define optimal conditions in

terms of surface friction and coating adhesion for good formability

To do this, it is first required to understand how friction can be measured in major

sheet metal forming processes and what kind of coating fracture mechanisms occur

during such processes. A number of reviews of previous studies of surface friction

models and fracture mechanisms are presented as a part of the background in chapter 2.

Chapter 3 includes details associated with the experimental procedures. The

information regarding the materials used in this work is listed in section 3.1. The method

3

used to quantify the surface morphology of each material is described in section 3.2.

Several kinds of mechanical tests used for the measurement of friction, coating adhesion,

and formability are described in section 3.3. Several methods for microscopic surface

analysis and microstructural characterization are presented in section 3.4 and section 3.5,

respectively.

Chapter 4 includes the results of experiments described in chapter 3. The five zinc

coated materials are characterized in terms of both their surface and microstructural make

up in section 4.1. The surface frictional behavior of the five materials subjected to

different strain states is covered in section 4.2 and the coating adhesion behavior of the

materials subjected to different strain states is contained in section 4.3.

Chapter 5 discusses key issues uncovered through this study. Several factors

affecting surface friction and coating adhesion, empirical relationships among factors,

and fracture models for the five zinc coatings are discussed in section 5.1. The relevance

of surface friction and coating adhesion to formability, one of the biggest themes in this

study, is discussed in section 5.2.

Finally, chapter 6 presents the conclusions of this study about surface friction and

coating adhesion of zinc treated steel sheets subjected to different strain states and their

effects on formability.

4

2. Background

The friction between sheet metal and various tools is one of the most important

factors affecting the formability as well as the success of a sheet metal forming operation.

In this chapter, friction will be defined and categorized with models proposed from

various perspectives.

Friction is the tangential reaction force between two surfaces in contact. In other

words, if two bodies are placed in contact under a normal load, a finite force is required

to initiate or maintain sliding. This is the force of friction. This force is the result of many

different mechanisms, which depend on contact geometry and topography, properties of

the bulk, the material at the surfaces of the bodies, displacement, relative velocity of the

bodies, and the presence of lubrication. Many models have been developed to take into

account these various sources of friction. Important static friction models and dynamic

friction models that relate to sheet metal forming will be presented.

2.1 Static Friction Theory

2.1.1 Coulomb and Amontons Friction Theory

Static friction is the friction associated with sticking. It describes the friction force

at rest. The concept is opposed to dynamic friction. The early work concerning this form

of friction was done by Coulomb and Amontons. The main idea is that the frictional force

is independent of the area of contact of the sliding bodies and velocity (Coulombs law)

and proportional to the applied load (Amontons law). In general, contact occurred only

locally at the summit of the surface irregularities so that the real contact is very small and

the frictional force is almost independent of the apparent area of contact, but still

5

dependent on the real contact area. After Coulomb and Amontons had suggested the

postulates of frictional force, a conductivity measurement by Tabor proved their

postulates [3]. According to Tabors studies, the deformation of the surfaces is not elastic,

but mainly plastic and the metal flows under the applied load until the area of contact is

sufficient to support it. In the case of plastic flow, the area of contact, i.e. real contact

area, is directly proportional to the applied load, so that the frictional force is directly

proportional to the applied load. It is clear that the frictional resistance is determined

primarily by the real area of contact and that the load is important only insofar as it

affects this area from Coulomb, Amontons and Tabors friction theory. The Coulomb

friction can be described as

C NF F= (2.1)

where CF is coulomb friction force, NF is normal load and is coefficient of friction.

2.1.2 Bowden and Tabors Friction Theory

After Coulomb and Amontons work, Bowden and Tabor investigated the

deformation of surface asperities using the theory of plasticity [4]. They compared the

deformation of a single asperity with hardness testing, and obtained a very useful model

of the friction mechanism even if the influence of tangential stresses, interaction between

asperities, strain hardening, and elastic effects were neglected. According to their model,

the asperities each carry a part iF of the normal load NF . If the asperities start to be

deformed plastically when the contact area of each junction has grown large enough to

carry its part of the normal load, the contact area of each asperity junction is iiFaH

= ,

6

where H is the hardness of the weakest bulk material of the bodies in contact and the unit

for H is the Pascal. The total contact area ( rA ) can thus be written i

r i

FA a

H= = .

This relation holds even with elastic junction area growth, provided that H is adjusted

properly. For each asperity contact the tangential deformation is elastic until the applied

shear stress exceeds the shear strength y of the surface materials. The friction force, i.e.

plastic deformation forces of microscopical asperities in contact, is defined as C y rF A= .

As a result, the friction coefficient can be expressed as y r yCN r

AFF A H H

= = = . According

to this model, the friction coefficient is not dependent on the normal load or the velocity,

but on the properties of the surface material in the model.

The model implies that it is possible to manipulate frictional characteristics by

deploying surface films of suitable materials on the bodies in contact. As such a soft

coating layer on a coated sheet steel can be very important for decreasing the frictional

force. Figure 2.1 shows schematically how this is possible. (a) is hard/hard metal contact

and (b) is soft thin film layer/hard metal contact. For the case of (a), the high shear

strength of the hard metal makes the frictional force significant. However, in the case of

(b), the shearing takes place on the thin film which has a low shear strength. That is why

a coated steel sheet could have a low frictional force compared to non-coated steel sheet.

Even though the Bowden and Tabor model is close to understand the frictional

mechanism of coated steel sheets, it has still many limitations.

7

Figure 2.1: Comparison between hard/hard contact and hard/soft contact

2.1.3 Orowan and Shaws Friction Theory

Since Bowden and Tabor (Fig.2.2-b) established the adhesion theory based upon

the individual plastic deformation of the contact points, many authors have developed

new friction theories concerning metal forming processes using a similar idea to focus on

the deformation of surface asperities using the theory of plasticity. Whereas the friction

model from Bowden and Tabor is confined to frictional behavior at low normal stress,

Orowan (Fig.2.2-c) and Shaw (Fig.2.2-d) developed friction models at high normal

stresses. Because some metal forming operations such as forging, extrusion and

stretching occur under high normal stress and the zones from different asperities can

interact due to the high stress, a different model should be applied to understand frictional

behavior. They suggested that the friction stress ( c ) at low normal stresses is

proportional to the normal stress ( N ), but at high normal stress is equal to the yield stress

in pure shear ( y ) of the surface materials [5,6]. This implies that normal stress no longer

affects friction at sufficiently high stress because the ratio between real area of contact

and apparent area increases with increasing pressure and approaches one.

8

Figure 2.2: Various static friction models : (a) Coulomb and Amontons model ; (b) Bowden and Tabors model ; (c) Orowans model ; (d) Shaws model

2.2 Dynamic Friction Theory

Steel sheets experience various displacements within a die during metal forming

operations such as drawing and stretching. This means that static friction is no longer

valid in practice. Many studies have been started to understand the nature of dynamic

friction since the 1950s [Fig.2.3]. The concept is that surface friction is a function of

displacement or velocity. Rabinowicz studied the transition between sticking and sliding

in his early work [Fig.2.3(b)] [7] and found that the maximum frictional force typically

occurs at a small displacement from the starting point. Dalton proposed that the

coefficient of surface friction is a function of time or distance in his studies of the

frictional behavior of zinc-coated steel sheet [8]. Stribeck addressed the velocity

9

dependence of the frictional force in the early 19th century [9]. Hess et al. performed

experiments on the velocity dependence of friction with a periodic time-varying velocity

superimposed on a bias velocity and observed an unsteady sliding under high frequency

of velocity oscillation causes a multi-valued friction during acceleration and deceleration

[Fig.2.3 (c)] [10].

Figure 2.3: Examples of Static Friction (a) and Dynamic Friction (b,c). Figure (a) shows Coulomb friction which is independent of velocity. Figure (b) shows there is a pre-sliding regime by microscopic motion before gross sliding. Figure (c) shows both sliding velocity and frequency of velocity oscillation lead a friction force. Figure (b) and (c) suggest that friction is a function of either displacement or velocity.

10

2.2.1 Stribeck Friction Theory

Usually, sheet steel is formed with the aid of a lubricant. The understanding of the

effect of lubrication on surface friction is one of the most important aspects of practical

metal working. Based on friction experiments on bearings, Stribeck expressed the

relationship between the friction coefficient [ f ], viscosity of the lubricating oil [ ],

normal load [ NF ], and velocity [V ] in the Stribeck curve. According to his model, a

material undergoing a forming operation experiences three distinctive lubrication states

based upon increase in a factor, / NV F (oil viscosity sliding velocity / normal load)

known as Stribeck parameter. In hydrodynamic lubrication regime where the / NV F

factor is high, the fluid lubricant completely isolates the friction surfaces and internal

fluid friction alone determines the tribological characteristics. In other words, friction is

related to only viscous drag forces in the lubricating film. In this state, the friction

coefficient increases as the / NV F factor increases because the shear force of the fluid

increases due to the film thickness increase. In the elastohydrodynamic lubrication

regime where the / NV F factor is low, i.e. at low velocities and high pressure, the thin

lubricant is transformed into an amorphous solid phase due to the high pressure (pressure

effect) and an interaction between friction surfaces is significant (velocity effect). The

transformation of lubricant and significant interaction between surfaces lead to a high

friction coefficient because shear forces corresponding to a combination of solid lubricant

and solid surface are much higher than those corresponding to fluid lubricants. As a result,

the friction coefficient decreases as the / NV F factor increases in this state. In the

11

boundary lubrication regime where the / NV F factor is very low, lubricant thickness is

at a minimum and surfaces are in contact at microasperities. The friction coefficient is at

its highest value in this state because lubricant is not effective. Figure 2.4 shows the

Stribeck curve and the Stribeck effect which corresponds to the dip in the frictional force

at low velocities.

Figure 2.4: The Stribeck curve and the Stribeck effect by Stribeck model

12

2.2.2 Daltons Friction Theory

Recently, Dalton has suggested new surface friction models for sheet metal

forming [8]. Daltons model is the most practical and applicable one because it is a

hybrid model that includes possible events, which take care of certain aspects of the

friction force. It covers four cases with several factors, which are the sheet coating, tool

type, roughness, and lubricant additives. Figure 2.5 shows the new model schematically.

Region1 and 2 show a mixed film plateau. In this region, the lubricant forms a thin film

and this phenomenon has already been described by Stribeck. Model A is the case of

increasing surface friction and the contact of asperities is significant. In model B1 surface

friction stabilizes and then increases. The supply of surface film or lubricant is exhausted

in this region and stick-slip eventually occurs. In model B2 separation of surfaces allows

a decrease of surface friction. In this region surface damage is high. Model C is the case

of the formation of pressurized pockets by oil trapping as asperities continue to deform.

Surface friction is gradually decreased as the forming process continues. This model is

one of the ideal cases for metal forming. Wanheim and Bay [11] suggested that the

presence of trapped lubricant would result in a superimposed hydrostatic pressure acting

on the valleys of the asperities and could reduce friction in metal working processes

[Fig.2.6]. According to their theory, the lubricant pressure equals:

1

0 1

0 1 0

......

1 (1 2 ) 1

F

KF

K K K P

PK K h

= + +

=

(2.2)

13

where K is the bulk modulus of the lubricant, 0K is the initial bulk modulus of the

lubricant, 1K is a unitless coefficient of pressure sensitivity , FP is the hydrostatic

compression applied, is the displacement of an asperity after deformation, and 0h is the

height of an asperity. As a result, the effect of trapped lubricant equals:

0

02 2 2drytotal F qq KP

k K k k= + (2.3)

where totalq is the total pressure necessary to obtain a certain contact area, k is the bulk

modulus of the asperity, and dryq is the pressure necessary to obtain a certain contact area

without trapped lubricant. The first term corresponds to a contribution by lubricant

pressure and the second term corresponds to a contribution by applied pressure. Once

superimposed hydrostatic pressure is applied by trapped lubricant and the total normal

pressure required is constant, dryq decreases compared to the no lubricant trapped

condition. Because dryq is directly related to the real area of contact, a large reduction in

contact area could be achieved by trapped lubricant. It is evident that friction decreases as

real contact area decreases.

Daltons model and Bowden & Tabors model have directly contributed to the

understanding of the frictional behavior of coated sheet steel during forming operations.

Based on their fundamental model, extensive work has been done to modify the surface

coating layer and various lubricant have been used in order to obtain a low friction

coefficient, i.e. high formability. The frictional behavior of special treated zinc coated

14

material, one of the candidates to show high formability will be discussed in subsequent

chapters.

Figure 2.5: Daltons friction model for coated steel sheet

15

2.3 Fracture Mechanics of Coated Steel Sheet

Another key property that contributes to the formability of zinc coated steel sheets

is coating adhesion and fracture. Usually, heat treated coated steel sheets have a

deficiency in that the coating layer tends to powder and fall off when undergoing severe

press forming. The process of brittle fracture is referred to as powdering. It is possible

that powdering acts as a source of cracks which could induce local stress concentrations

and thus affect formability. Coated steel sheets have several intermetallic phases formed

after galvannealing. These phases act as the main source of powdering. The fundamental

fracture mechanisms associated with the coating layer will be discussed in this section.

Figure 2.6: Trapped lubricant effect (a) no lubricant condition, (b) lubricant& trapped condition ; y = the shear yield strength of surface material

16

2.3.1 Wedging Mechanism Causing Powdering

A. T. Alpas et al. [12] proposed that a decohesion of the interfaces between

substrate and coating could be followed by a propagation of through thickness cracks

under uniaxial compressive stress condition when the strength of the substrate-coating

boundary is higher that the intrinsic strength of the coating. This is referred to as the

wedging mechanism. The powdering phenomenon from galvanneal steel sheet (GA) is a

very good example of the wedging mechanism. The coating layer of GA may consist of a

thick layer of phase ( FeZn10 , 86.5~91.8 at.% Zn ), a thin layer of phase ( Fe3Zn10,

68.5~82.5 at.% Zn ), columnar crystals of 1 phase (Fe11Zn40 ,75~81 at.% Zn ) and

blocky crystals of (FeZn13, 92.8~94 at.% Zn). Initially, cracks are not created in the

interface. Many pre-existing cracks nucleated during cooling of the coated steel sheet

from the galvannealing temperature to room temperature. These grow in the phase as it

is subjected to a tensile stress [Fig.2.7]. Once the cracks are propagated adjacent to the

interface between coating and substrate under lateral tension, a crack propagation along

the interface can be triggered under lateral compression. The decohesion along the

substrate- coating interface under lateral compression directly results in powdering.

Figure 2.7: Crack initiation of GA under the lateral tension condition

17

Alpas et al. [12] stated that the driving force for interface crack propagation is an

inhomogeneous distribution of residual stress caused by the formation of the 1 phase

with a columnar morphology. Usually, the 1 phase is formed over the planar phase

and grows into the phase by forming a columnar morphology. The crystals cause

residual compressive stress and generate interfacial shear stresses along the -1 and -

phase boundaries. As a result, a crack can easily propagate through the interface when

subjected to lateral compression [Fig.2.8].

Figure 2.8: The mechanism of interfacial crack propagation

2.3.2 Buckling Mechanism Causing Powdering

Another mechanism by which a coating can fail under lateral compression is

buckling. Buckling failure occurs if the strength of the interface is less than that of the

coating itself so that decohesion of the substrate-coating interface precedes the formation

of the through thickness cracks in the lateral tension condition [Fig.2.9]. There are

18

various sources that can initiate buckling. In the case of hot dip galvanizing or electro

galvanizing, the substrate can be exposed to an unclean environment just before the

coating layer is deposited. The deposited defects on the substrate can reduce adhesion

energy between the substrate and coating layer equivalent to roughly 150J/m2 in the case

of a zinc-steel interface. During the electro galvanizing process,

some amount of hydrogen can be injected between the substrate and the coating layer.

S.L. Amey et al. [13] showed that approximately 9 22 10 /moles cm of hydrogen could

be absorbed into the steel in a commercial electro galvanizing line. A region debonded by

hydrogen could exhibit buckling when subjected to lateral compression.

Figure 2.9: The buckling failure mechanism

Janavicius P. V. et al. [14] modeled the growth of an initially buckled area and

derived an expected critical pressure equation as follows.

1/2

22 (1 )a

critEGP

a

= as a t (2.4)

19

1/21/2 3

2

32 43(1 1

acrit

G a aP at t

= +

as a t= (2.5)

1/43

44.8a

critG EtP

a

=

as a t (2.6)

where a = radius of debonded region, E = elastic modulus of layer, t = thickness of layer

and aG = adhesion energy. According to the model, the growth of an initially delaminated

area in the zinc coating depends on the size of the initial delamination, the adhesion

energy between the zinc and its steel substrate surface and the thickness and the elastic

modulus of the zinc layer. The thickness and elastic modulus of the zinc layer cannot be

varied significantly in practice. However, the size of the initial delamination and the

adhesion energy can vary substantially. The presence of irregularities in the steel

substrate can greatly influence both of those parameters. Such irregularities could include

microflaps, carbides, oxide inclusions not completely removed after the rolling process.

This means that the exposure of the substrate to an unclean environment before

galvanizing could affect both crack initiation and propagation according to the buckling

fracture mechanism.

20

3. Experimental Procedure

3.1 Material Properties

Special treated zinc coated (STZC) materials were tested in the current work.

These materials were produced by Pohang Iron and Steel Company and are material used

for automotive panel applications. The STZC steels were designed to investigate the

effects of surface morphology and an Fe-Zn alloy layer on the formability of coated steel

sheets. In addition to the three STZC steel sheets, conventional galvanized (GI) and

galvanneal (GA) coated steel sheets were also tested for comparison. Usually, galvanized

steel sheet has a low powdering rate and a high surface friction coefficient because its Fe-

Zn alloy layer is very thin so its coating does not exfoliate during forming operations and

the zinc coating layer on the steel sheets surface is continuous resulting in a contact area

that is very large. Thus, galvanized steel can be used as a standard for a high powdering

resistance and high friction material. Galvanneal steel sheet has a high powdering rate

and a low friction coefficient because its Fe-Zn alloy layer is mostly composed of phase

which is relatively thick and the alloyed coating surface morphology is in the form of

islands or mesas so that its contact area is very low. Thus, galvanneal steel can be used as

a standard for a low powdering resistance and low friction material during forming.

3.1.1 Special Treated Zinc Coated (STZC) Materials

The materials were modified differently in terms of surface texture and

microstructure. The surface texture is one of the key parameters that determines surface

friction and affects formability. After completing the galvanizing process, three types of

21

patterns were imprinted into STZC1, STZC2 and STZC3 via working rolls that were

patterned by an Electrical Discharge Texturing (EDT) method. Microstructure is one of

the key parameters that determines the powdering rate which in turn affects formability.

The main parameters that control the microstructure of a coating are galvannealing

temperature and time. Temperature controls diffusion length to a greater extent than time.

Thus, temperature was controlled to modify the thickness of the Fe-Zn alloyed layers.

STZC1,STZC2 and STZC3 were galvannealed in 452C, 465C and 516C , respectively

[Fig.3.1]. The Fe-Zn phases initially nucleate at the steel/coating interface and consume

the pure zinc phase, when the steel passes through the galvannealing furnace. The

initial Fe-Zn intermetallic compound grows rapidly. The phase grows at the expense of

the phase. Later, the phase can be consumed by the growing phase [15]. It is well

known that the brittle phase decreases the formability of galvannealed steel sheet. The

galvannealing time was controlled by the line speed of the rolling process and the short

time in the range of 1~5 seconds was designed to prevent transformation of phase to

phase. The galvannealing condition and mechanical properties for the STZC steels are

listed in Table 3.1. The substrates of the STZC materials are an interstitial free steel (IF

steel grade) and an interstitial free rephosphorized steel (IFP steel grade). Interstitial free

steels are a class of high formable steel with exceptionally low levels of interstitial

elements such as carbon and nitrogen (typically, total C 30ppm and total N 40ppm by

weight) and are mainly used for automotive application due to their high drawability [16].

Interstitial free rephosphorized steel provides a high yield and tensile strength. It has a

carbon content similar to an IF steel grade, but a much higher phosphate content

22

( 630ppm) leading to an increased yield strength and ultimate tensile strength due to

grain boundary hardening [17]. The rephosphorized steel grade was applied to only the

STZC3 material in order to evaluate how the substrate in a coated steel sheet affects its

total formability. The mechanical properties of a typical commercial IF-grade steel and a

IFP-grade are given in Table 3.2.

Figure 3.1: Fe-Zn diffusion couple and principle of microstructure control

23

Table 3.1 Galvannealing condition and Mechanical properties for the STZC samples

Material Grade GA heating temperature(C)

Yield Strength (MPa)

Ultimate Tensile Strength (MPa)

Elongation (%)

Line Speed (mpm)

STZC1 IF 452 160 306 45 110 STZC2 IF 465 152 310 46 138 STZC3 IFP 516 264 396 35 120

Table 3.2 Mechanical properties for commercial IF-grade and IFP- grade

Substrate Yield

Strength (MPa)

Ultimate Tensile Strength (MPa)

ef (%)

IF 150~200 300~350 35 IFP 260~320 350~410 23

3.1.2 Hot- Dip Galvanized (GI) Material

The galvanized steel sheet was intended to have the highest formability possible.

Basically, the interstitial free grade steel which has good drawability was used for the

substrate of the GI. Usually, the GI has a thin intermediate layer called the inhibition

layer between the steel substrate and the zinc coating. The layer consists of an Al-Fe

compound and acts as a diffusion barrier to suppress brittle intermetallic Fe-Zn

compound formation which affects negatively the adhesion quality of the coating layer

and subsequent formability [18]. To process the GI a high aluminum content was present

in the zinc bath in order to promote the formation of the inhibition layer. Mechanical

properties for the sheet are given in Table 3.3. After being coated with zinc, the material

was temper rolled.

24

3.1.3 Galvanneal (GA) Material

The galvanneal steel sheet was intended to have the lowest formability. The

interstitial free steel strip immersed in a zinc bath was immediately heated to 505C and

held for 20 sec in a galvannealing furnace in order to form a fully phase coating layer

containing around 10 wt. % Fe. The Al content of the zinc bath was maintained at a low

level of 0.126 wt. % to produce a relatively thin inhibition layer. After the galvannealing

process, the material was temper rolled. The mechanical properties for the GA sheet steel

are listed in Table 3.3.

Table 3.3 Mechanical properties for GI and GA material

Material Grade GA heating temperature(C)

Yield Strength (MPa)

Ultimate Tensile Strength (MPa)

Elongation (%)

Al content in the zinc bath (%)

GI IF - 156 291 47 0.236 GA IF 505 146 294 47 0.126

3.2 Measurement of Real Area of Contact

The real area of contact is made up of a large number of small regions of contact,

called asperities or junctions of contact, where atom-to-atom contact takes place as

Bowden and Tabor suggested in their inelastic adhesive theory [3]. The real area directly

affects the surface friction of a coated steel sheet [11]. The droplet like bumps in the

STZC steels and the GI steel imprinted by the texturing process creates what are

effectively asperities. In the case of the GA steel, islands or mesas are effectively the

asperities. Under the assumption that the change of real contact area is not significant

25

during a metal forming process, the initial real contact area, i.e. the sum of asperities was

calculated by a simple statistic method, called Systemic Manual Point Count [19].

3.2.1 Systemic Manual Point Count Method

The method is based upon the stereological principle that a grid with a number of

regularly arrayed points, when systematically placed over an image of a two dimensional

section through the microstructure, can provide, after a representative number of

placements on different fields, an unbiased statistical estimate of the volume fraction of

an identifiable constituent or phase. The method also can be used to measure the areal

fraction of asperities.

The systemic manual point count method requires a test grid and images obtained

from a scanning electron microscope. The test grid is in the form of a transparent sheet

where a specified number of equally spaced points formed by the intersection of very thin

lines is imprinted [Fig.3.2]. The scanning electron microscope provides excellent depth of

field and magnification high enough to adequately resolve the microstructure. It is

recommended to choose a magnification that gives an average constituent size that is

approximately one half of the grid spacing. The number of images or fields depends on

the desired degree of accuracy for the measurement. Table A.1 gives a guide to the

number of fields or images to be counted as a function of total number of points in the

test grid (PT), the relative accuracy which means a measure of the statistical precision,

i.e. 95%% 100P

CIRAP

= , and the magnitude of the areal fraction.

The measurement procedure is as follows. The test grid which has a total of 100

26

points was superimposed upon an image captured at 200 magnification in a scanning

electron microscope. The number of points ( iP ) falling within the microstructural

constituent of interest, i.e. asperities or mesas was counted and averaged for 20 fields.

The average number of points expressed as a percentage ( PP ) is an unbiased statistical

estimation of the areal fraction of the asperities or mesas, i.e. real contact area. After five

values of PP were obtained, the precision of the areal fraction measurement was

determined by calculation of the 95% confidence interval. The equations for calculating

these values are as follows:

11/2

2

1

1 ( )

1 [ ( ) ]1

95%

n

P Pi

n

p pi

P P in

s P i Pn

sCI tn

=

=

=

=

=

(3.1)

where ( )pP i is the percentage of grid points in field i , s is estimate of the standard

deviation, 95%CI is 95% confidence interval, i.e. 95%PP CI , t is 95% confidence

interval multiplier and n is number of fields. Table A.2 lists 95% confidence interval

multipliers (t).

27

Figure 3.2: Transparent test grid sheet

3.3 Mechanical Testing

Mechanical testing was conducted to determine how frictional and powdering

properties affect the formability of coated steel sheets. Surface friction coefficients were

measured by cup tests and hemispherical punch tests. These tests evoke drawing strain

states and stretching strain states, respectively. The deformed cups were subsequently

used to assess the degree of powdering by measuring the quantity of coating loss. Finally,

the plane strain formability was evaluated using a limiting dome height test.

3.3.1 Measurement of Surface Friction Coefficient

Punch-to-sheet friction plays an important role in determining formability and

28

subsequently determining the success or failure of sheet metal forming operations. The

friction depends strongly on what kind of forming conditions are operative. The friction

values need to be measured under different forming conditions. The cup test was

designed to determine surface friction values under conditions corresponding to drawing

strain states. The hemispherical punch test was designed to determine surface friction

values under conditions corresponding to biaxial stretching strain states.

3.3.1.1 Cup Test

In a deep drawing operation, friction exists in three regions. These regions are the

flange, the die radius, and the punch profile radius. The regions have different frictional

conditions. Throughout the flange region, in which the sheet is held with a normal force

exerted by a blankholder, sliding friction is predominant, and small amounts of strain are

present. In the die radius and punch profile regions, sliding is negligible, and stretching

due to the local plastic deformation of the sheet prevails [20]. The sliding friction in the

flange region is what needs to be measured in this test because the friction in the flange

region determines the ease of supply of material due to plastic flow and subsequently

drawability in a deep drawing operation [21].

Based upon modeling of the forming loads during drawing of a cup, the

relationship between maximum forming load, hold down load and sliding friction

coefficient has been developed. According to K. Langes Handbook of Metal Forming

[22], one of the relationships is that maximum forming load or drawing load is a linear

function of the hold down force and the coefficient of sliding friction is a simple multiple

of that slope. Swift et al. [23] found that the contact angle between the punch and the

29

drawn blank and the instantaneous blank radius are functions of the punch displacement

or forming load.

As a result, an equation (3.2) for the forming load, P , which takes into account

drawing stress (1), stress due to friction in the flange, stress due to friction over the die

radius (2) and stress due to bending and unbending (3) was obtained from the continuum

models by Swift et al.

1 20

2 1.1 ln exp( )2

Nm fm fm

m

FX tP R tR Xt r

= + +

(3.2)

In equation 3.2 is the coefficient of surface friction, is the contact angle, X is the

instantaneous blank radius, t is the blank thickness, mR is equal to the punch radius plus

0.75t , NF is the hold down load, 0r is die radius, 1fm is the average flow stress in the

flange area of the blank, and 2fm is the average flow stress when the blank undergoes

bending and unbending. The contribution to the forming load of 1fm and 2fm , which

depend on the work hardening coefficient ( n ), is very small compared to that of the

coefficient of surface friction ( ). The coefficient of surface friction can be obtained by

taking the derivative of P with respect to NF resulting in equation (3.3). The value of

is determined through this transcendental equation by measuring the slope of the forming

load versus hold down load for particular values of the parameter X and .

2 exp( )mN

RdPdF X

= (3.3)

(1) (2) (3)

30

The coefficient of surface friction, , for each of the five types of steel sheets

was determined through cup tests [Fig.3.3-A]. Initially about thirty blanks (74mm dia.)

were sheared from each type of steel using a shearing punch and hold down die set

mounted on a dual actuator hydraulic deformation press [Fig.3.4-B]. The punch and die

set was then replaced by a cup forming punch and male and female die set on the same

dual actuator hydraulic press [Fig.3.4-A]. Five of the thirty blanks for each steel were

used to determine the range of hold down loads where cups could be formed without

wrinkling their side walls or fracturing their bottoms. The acceptable range of hold down

loads ( NF ) for the STZC series steels and the GA steel was 2 to 11kN.The corresponding

range for the GI steel was 3 to 11kN. The remaining 25 blanks were used to measure the

punch load as a function of punch displacement for 5 different hold down loads and

subsequently to determine the slope, N

dPdF

. The blanks were formed into cups employing

a punch speed of 20mm/sec after a mill oil was applied to the blanks using a soft brush.

Once the slope,N

dPdF

was determined for a given punch displacement, the coefficient of

surface friction was calculated using equation (3.3) because the values for mR is constant

(17.03mm) and and X are well established functions of punch displacement [24].

31

Figure 3.3: Schematic diagrams of cup test (A) and important parameters in equation (3.2) (B)

32

Figure 3.4: Preparations for cup test:(A-a) male die,(A-b) female die with 225mm diameter, respectively, (A-c) punch with 33mm diameter, (B-a) 74mm blank, and (B-b) fully formed cup

0 3cm

33

3.3.1.2 Hemispherical Punch Test

In a stretching operation, deformation takes place in three distinct regions. These

are metal stretching in contact with the punch (region 1), metal stretching in the

unsupported region (region 2), and metal flowing through the blank holding areas

(drawing region 3 ) [Fig.3.5]. In contrast to the stretching mode of deformation in region

1 and 2, metal flow takes place through circumferential contraction in region 3. Thus,

region 1 is an optimal area to consider the surface friction under the condition of pure

stretching.

Amit K. Ghosh developed a model for friction measurement that is free from

material property inputs under the condition of stretching of sheets over punch surfaces

and a method to determine an average value of the coefficient of punch-to-sheet friction

in stretching over a 50.8mm hemispherical punch [25]. The model uses three assumptions

to simplify the complexity of the plastic deformation occurring in contact with the punch.

The first assumption is that interfacial pressure between the punch and sheet is uniform at

any stage of deformation. The assumption is very important because the pressure is

directly related to the surface friction. If the variation of the pressure during deformation

were large, the acquisition of a constant friction coefficient would be impossible.

According Wang [26], the pressure distribution shows a relatively small variation over

the punch contact area. Thus, the assumption is very reasonable. The second assumption

is that the frictional force is proportional to the applied load, i.e. Amontons law applies.

This means that frictional stress is proportional to the interfacial pressure, p = . The

third assumption is that the inflection point on the load-displacement plot corresponds to

34

the attainment of the maximum pressure. This means that the average pressure ( p )

exerted by the punch on the sheet surface reaches a maximum. Using these assumptions

and geometrical expressions for key parameters [Fig.3.6B] the following expression can

be derived to determine surface friction.

{ }

0

2 1 2 2 2 20 0 0 0 0

2

( / )sin ( / ) ( ) (2 / ( ))

Xr

X r r r r r

=

(3.4)

In equation 3.4, is the surface friction coefficient, cr is the radius of the punch-sheet

interface boundary, 0r is the value of cr at the inflection point in a plot of load-

displacement, is the punch radius, X is [ ]0

( / ) /c rdP dr P , and P is the punch load.

Figure 3.5: Generalized stretching forming operation [25]

35

The hemispherical punch test was used to obtain the coefficient of surface friction

under the condition of stretching based upon the work of Ghosh [25]. The hemispherical

punch employed had a standard diameter of 101.6mm, i.e. =50.8mm, and the blanks

were secured by a 132.6mm diameter draw bead [Fig. 3.6A]. The clearance between the

blank holder die set opening and the punch was 2.03mm. A hold down load of 170kN

was applied to completely eliminate metal flow into the die cavity. A constant punch

displacement rate of 25.4mm/min was maintained for all of the hemispherical punch

testing. The five different types of steels were sheared to form square shaped

(178mm178mm) blanks.

The independent variables in Figure 3.6(B) are X and 0r . Two procedures were

required in order to determine X . Initially, punch load ( P ) versus punch displacement

( x ) plots were obtained from the hemispherical punch tests of the five different types of

steels. Punch displacements continued until the blanks fractured. The punch load data

obtained was used to convert to plots of punch load ( P ) versus radius of the punch-sheet

interface boundary ( cr ). According to Ghosh [25] [Fig. 3.7], the radius of the boundary of

the punch contact ( cr ) can be reliably determined as a function of punch displacement

( x ) regardless of the material or the test conditions. The punch load ( P ) versus the

radius of the boundary of the punch contact ( cr ) data were fitted with a fourth order

polynomial with an index of fit of 0.9999 using ORIGIN 8.0 software in order to get a

fourth order equation ( ( )cP f r= ) from which the derivative value, / cdP dr could be

obtained. The next procedure was to determine an inflection point mathematically.

36

The punch load ( P ) versus punch displacement ( x ) plots were fitted with a fourth order

polynomial and fourth order equations were obtained from the fitting in a manner similar

to the first procedure. The specific punch loads and displacements at the inflection point

were determined after taking the second order derivative of the fourth order equations

( ( )P f x= ). The inflection point was found by solving for the value of X at which the

second derivative of plot was zero, i.e. 2 2/ 0d P dx = .

Once the punch load and displacement at the inflection point were determined, the

radius of the boundary of the punch contact at the inflection point ( 0r ) was obtained using

the first procedure. As a result, the coefficient of surface friction was calculated using

equation (3.4).

37

Figure 3.6: Punch with 101.6mm diameter and die set with 225mm diameter and 132.6mm diameter draw bead for hemispherical punch test (A) and important parameters in equation (3.4) (B)

0 3cm

38

Figure 3.7: Radius of the boundary of punch contact ( cr ) is plotted as a function of punch displacement, for three test materials under different test conditions [25]

3.3.2 Measurement of Coating Adhesion Propensities

Coating adhesion was assessed by determining the fracture characteristics of a

coating. Powdering tests were employed to measure the amount of coating fracture that

occurred due to a forming operation.

3.3.2.1 Powdering Tests

The powdering tests were conducted after the sheet steels were subjected to

drawing and stretching strain states. Cup testing was employed to measure the amount of

coating exfoliation under drawing conditions and hemispherical punch testing was

employed to measure the same quantity under stretching conditions.

39

The test sequence began by cleaning each blank (77mm diameter) with methyl

alcohol followed by weighing each blank. A mill oil was then applied using a soft brush.

The blank was weighed again after application of the oil to monitor and control the

amount of oil applied. Approximately 0.1g oil equivalent to a 12m oil film thickness

was applied to each blank. The oiled blanks were then formed into cups employing a

punch speed of 20mm/sec and hold down loads in the range from 2kN to 11kN. Each

fully formed cup was rinsed in solvent and dried. After cleaning, Scotch 3710 tape was

applied to all of the cups inside and outside surfaces to pull off any loose coating.

Finally, the cup was weighed in gram once more. The difference in weigh between the

initial weighing of the blank and the final weighing of the formed cup established the

extent of powdering of the coated steel caused by the drawing operation.

A similar experimental procedure was applied after hemispherical punch testing

to measure the amount of exfoliation of a coating that occurred under a stretching strain

state. Blanks 178mm long with widths that varied from 125mm to 140mm were designed

to define the plane strain stretching condition. Before the blanks were subjected to

deformation they were cleaned with methyl alcohol and weighed. After the blanks were

deformed they were again cleaned with methyl alcohol and then Scotch 3710 tape was

applied to both their convex and concave surfaces to pull off any loose coating. The

deformed blanks were weighed again and the difference in weight between the initial

weighing and the final weighing was used to measure the extent of powdering of the

coating caused by the stretching operation.

40

3.3.3 Measurement of Formability

In many automotive stampings the failure of steel sheets occurs under a condition

of plane strain (minor strain 0). A.K. Ghosh suggested a test procedure in which dome

heights are measured as a function of minor strain and the minor strain can be varied by

modifying the blank width [27]. The punch height where a blank fails under a plane strain

condition can be used as an effective predictor of formability. This test procedure is now

commonly known as the limiting dome height or LDH test.

3.3.3.1 Limiting Dome Height (LDH) Test

The first procedure associated with a LDH test was to establish the blank width

that would generate a plane strain deformation condition. The plane strain condition was

determined by conducting a series of hemispherical punch tests with blanks that were

178mm long and had widths that varied from 115 to 148mm in intervals of 3mm [Fig.

3.8]. The blank width at which the specimen fractured after experiencing the minimum

punch displacement corresponded to the case of plane strain deformation. After the plane

strain deformation blank width was established, five replicated LDH tests were run with

that blank width to determine average punch heights.

3.4 Surface Analysis

Scanning electron microscope was employed to characterize the texture, i.e.

roughness and patterns found on the outer surface of each of the five steels which

experienced the Electrical Discharge Texturing (EDT) process. Electron Spectroscopy for

Chemical Analysis, also known as X-ray Photoelectron Spectroscopy (XPS) was

employed to analyze the concentration and the distributions of the main elements and

41

Figure 3.8: Relationship between major engineering strain vs. minor engineering strain and limiting dome height vs. blank geometry

the phases in the extreme outer surface of each of the zinc coatings. There were two

objectives to the analysis of the extreme outer surface. First, the frictional behavior of the

sheet is tied to its extreme outer surface at contact, i.e. tangent points. Knowledge of the

phases and composition at the extreme outer surface could be useful for friction control.

Second, it is known that the aluminum in the coating layer controls the formation of Fe-

Zn phases. However, the diffusion of aluminum to outer surface where it forms alumina

could affect weldability negatively [28]. Thus, the outer surface analysis with ESCA

provides some information about the weldability of the five coated steels.

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3.4.1 Surface Analysis by SEM

A scanning electron microscope equipped with a field-emission gun (HITACHI

S4500) was employed to take images of the surface of the coating layers. The specimens

were sheared into pieces 10mm by 10mm and cleaned with acetone. Plan view images of

each zinc coating were taken at 250 to provide a global view of the surface features

and at 500 to resolve details of the surface structure. Detailed images of potential

contact points and particles were taken at 3000 .

3.4.2 Surface Analysis by ESCA

A PHI 5600 ESCA instrument with an aluminum x-ray source and an inert gas

sputtering source was employed to obtain depth profiles of the extreme outer surface of

each of the five steels. The specimens were sheared into pieces of 10mm by 10mm and

cleaned with acetone. Depth profiles including the elements zinc, oxygen, aluminum, iron

and carbon were obtained for a maximum sputtering depth of 40nm.

3.5 Microstructural Characterization by SEM and EDS

Scanning electron microscope (SEM) and energy dispersive x-ray spectroscopy

(EDS) analyses of cross sectional samples were used to identify the Fe-Zn phases present

in each of the steel coatings and evaluate the disposition of their inhibition layers.

Samples 10mm 10mm were sheared from each of the five steels and placed in standard

31.75mm diameter mounts. Samples of each steel were positioned to form a stack with

sheared edges parallel to one another. The stacks were assembled so that the sheared

edges were aligned and the samples in each stack were separated from each other by

placing a small piece of double sticky tape between each sample away from the sheared

43

edges. Epoxy resin was used as the mounting media. Grinding through 400, 600, and

1200 grit paper was carried out by hand making sure that back and forth motion over

each paper was performed with the interface between the mounting material and the zinc

coatings oriented parallel to the direction of motion. This procedure minimized smearing

of the coating. Polishing proceeded through 3m and 1m diamond slurries finishing

with a 0.05m alumina slurry. The polishing machine employed was adjusted to apply a

heavy, even pressure to each mount. After polishing the specimens were etched in a

solution consisting of 5% nitric acid and 95% methanol, i.e. Nital.

Cross sectional SEM images of the coating layer found on each of the five steels

were taken at 2000 using the back scattering electron (BSE) mode. Energy dispersive x-

ray spectroscopy (EDS) analyses were conducted at several location throughout the

thickness of the zinc coatings in order to investigate the compositions of the Fe-Zn phases.

Elemental maps of the zinc coatings for the elements zinc, iron and aluminum were

obtained to investigate the distribution of those elements through the thickness of the

coatings.

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4. Results

4.1 Materials Characterization

Five types of zinc coated materials were characterized with respect to surface and

microstructure. The surface is one of the most important factors affecting friction and the

microstructure of a coating is directly related to its adhesion propensities.

4.1.1 Surface

Surface morphologies were investigated by scanning electron microscopy at

various magnifications. Areal fraction of contact between a coated steel sheet and a die,

i.e. the sum of the contact with surface asperities when the normal pressure is roughly

zero was calculated using a systemic point count method with captured images taken with

a SEM. The depth profiles of alloying elements found in the outer surface of zinc coating

were investigated by ESCA.

4.1.1.1 Surface Morphology

Three different types of morphology were imprinted onto the STZC1, STZC2 and

STZC3 steels via a skin pass [Fig.4.1]. The first type of pattern imprinted on the STZC1

steel has a well rounded droplet-like shape [Fig. 4.1(a)]. The second type of pattern

imprinted on the STZC2 steel has a truncated droplet -like shape [Fig. 4.1(b)]. The last

type of pattern imprinted on the STZC3 steel has a elongated droplet- like shape [Fig.

4.1(c)]. The average distance between the pattern shapes decreases from the STZC1 steel

to the STZC3 steel. The GI and GA steels which underwent a temper rolling process

exhibited different surface morphologies. The temper rolling process flattened and

45

merged their surface patterns unlike the skin pass process and so formed a conglomerated

mesa-like surface morphology, i.e. hills with flat tops. The pattern on the GI steel has a

coarse mesa-like shape [Fig. 4.1(d)]. The pattern on the GA steel has a fine mesa-like

shape and the distance between pattern shapes is smaller than that found on the GI steel

[Fig. 4.1(e)].

A unit of pattern creates an asperity point, i.e. initial contact point with a die, and

its shape and distribution affect surface friction directly [29]. Figure 4.2 shows different

patterns formed via either the skin pass or the temper rolling process. An asperity point

on the STZC1 steel has a rounded droplet-like shape 20 m in diameter and it is

distributed very sparsely [Fig. 4.2(a)]. An asperity point on the STZC2 steel has a

truncated droplet -like shape with a 20m major axis and 10m minor axis [Fig. 4.2(b)].

The shape and distribution of its asperity points falls between those found on the STZC1

and STZC3 steels. An asperity point on the STZC3 steel has an elongated droplet- like

shape approximately 20m in size across its diagonal. Its asperity points are distributed

very densely [Fig. 4.2(c)]. An asperity point on the GI steel has a mesa-like shape with a

diagonal dimension of 50m and these form flat and large conglomerates that are

distributed sparsely [Fig. 4.2(d)]. An asperity point on the GA steel has a fine mesa-like

shape with a diameter of 6 to 7 m. These fine asperity points form flat and small

conglomerates densely distributed over the surface [Fig. 4.2(e)]. The matrix surrounding

these asperity points on the GA steel is comprised of rough valleys whereas those of the

STZC steels and the GI steel are fairly planar. These imply that the Fe-Zn intermetallic

crystals that comprise the GA steel affect the size of the asperity points, the size of

46

conglomerates, the spacing of conglomerates and the matrix structure surrounding the

asperity points.

47

Figure 4.1: SEM plan view images (200 ) of the STZC1 steel (a) and STZC2 steel (b)

a

b

48

Figure 4.1: SEM plan view images (200 ) of the STZC3 steel (c) and GI steel (d)

c

d

49

Figure 4.1: SEM plan view images (200 ) of the GA steel (e)

e

50

Figure 4.2: SEM images of pattern (asperity) on the (a) STZC1, (b) STZC2, (c) STZC3, (d) GI and (e) GA steels. Yellow arrow indicates surface asperity

a b

c d

e

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4.1.1.2 Real Area of Contact ( Areal Fraction of Asperities )

The real area of contact of the five coated steels at an initial normal pressure near

zero was calculated with the aid of equation 3.1. The areal fractions of asperities are

given in Table.4.1 and the real area of contact as a function of the steel type is shown in

Figure 4.3. According to these results, the real area of contact increases from the STZC1

steel to the STZC3 steel. This result is related to the curvature of the asperities and the

repeat of the asperities pattern rather than the size of the asperities. The shape of the

asperities on the STZC1 steel is hemispherical with a high curvature and a low contact

area. The shape of the asperities on the STZC3 steel is roughly that of a flat rectangle

which has a low curvature and a high contact area. The shape of the asperities found on

the STZC1 steel is more regular than those found on the STZC3 steel. As a result, the

asperities with the high curvature and the high regularity yield a lower real area of

contact. The values for the real contact area of the GI and GA steels are very high and

similar to the STZC2 and STZC3 steels. Asperity flattening by the temper rolling process

contributes to an increase in the real area of contact.

4.1.1.3 Depth Profile of Alloying Elements

The concentration profiles of the outer surfaces were acquired using a sputtering

proces