1 Die Design in Drawing with Drawbeads and Spacers Thesis

Die Design in Drawing with Drawbeads and Spacers

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in

the Graduate School of The Ohio State University

Advaith Narayanan

Graduate Program in Mechanical Engineering

The Ohio State University

2019

Thesis Committee

Dr. Taylan Altan, Advisor

Dr. Blaine Lilly

Copyrighted by

Advaith Narayanan

2019

Abstract

Challenges faced by the automotive industry in the areas of weight reduction, fuel

efficiency and crash worthiness have necessitated the increasing use of Advanced High

Strength Steels (AHSS), which have a higher strength but lower formability than

conventional mild steels and low carbon steels. Hence, the quality of parts formed with

AHSS is of primary concern. Some of the common defects in AHSS include occurrence of

splits, wrinkles and springback in the part.

Drawing is a process in which a sheet metal is drawn into a die cavity by the mechanical

action of the punch. It is termed as ‘deep drawing’ when the draw depth of the final part

exceeds its width or the diameter, depending on the shape of the final part. Deep drawing

(or drawing in general) finds a variety of applications like kitchen sinks, inner automotive

body panels, cooking pots, beverage cans, oil pan etc. The major defects occurring in drawn

parts are wrinkling and splitting due to fracture. While many publications deal with fracture

issues in drawing small parts, most of the large automotive components are drawn with the

tools having drawbeads in them to exert additional restraining forces. Additionally, spacers or kiss blocks are also employed to minimize elastic deflection of the dies in the press. It is important to prevent fracture in the part when using drawbeads and spacers, as failure to

do so will increase the scrap production, large number of experimental die tryouts and

repeated modification of drawbeads by grinding.

This study aims to propose simple guidelines using FE simulations, to predict and prevent

fracture and wrinkles in a drawing process containing drawbeads and spacers, thus

reducing the need for experimental die tryouts and scrap production. First, the existing fracture criteria in the literature for AHSS under deformation modes of bending and superimposed bending and stretching will be explored. Subsequently, using some of the aforementioned criteria, the effect of blank optimization, spacer height and lubrication conditions on possible fracture will be investigated, using a die set built by Honda as an example. Furthermore, the effect of drawbead geometry and change in material on possible fracture and wrinkling will be investigated. Lastly, a set of guidelines based on the studies conducted will be proposed for making a defect free part which is drawn with drawbeads and spacers.

Dedication

I dedicate this work to my family and my friends

iii

Acknowledgments

I am very grateful to my advisor Dr. Taylan Altan, director of Center for Precision Forming

(CPF) for giving me the opportunity to pursue my Masters’ degree under his guidance. His

intellectual support, encouragement and enthusiasm are the primary reasons for this research work to be possible.

I would like to thank Dr. Blaine Lilly for his inputs and comments. I would like to acknowledge the financial support by the Center for Precision Forming (CPF) and its consortium members.

I am indebted to my colleagues: Ali Fallahiarezoodar, David Diaz Infante, Berk Aykas,

Tanmay Gupta, Hitansh Singhal and Cliff Goertemiller. Their constant inputs, discussions contributed immensely to my research work. I am grateful to Mrs. Linda Anastasi for her administrative and logistical support.

Finally, I am thankful to my family and friends for all their support in this endeavor.

Vita

2017 ……… BE. Mechanical Engineering, Birla Institute of Tech & Science, Goa, India

2017 - Present………MS. Mechanical Engineering, The Ohio State University

Publications

1. Diaz-Infante, D., Narayanan, A., & Altan, T. (2019). Estimation of Cutting Parameters

in Two-Stage Piercing to Reduce Edge Strain Hardening (No. 2019-01-1092). SAE

Technical Paper.

2. Narayanan, A., Diaz, D., and Altan, T., "Edge Fracture in Hole Extrusion and Flanging

- Part I - Process Variables", Stamping Journal, July/August 2018, p. 16, 17.

3. Narayanan, A., et al, "Edge Fracture in Hole Extrusion and Flanging - Part II - Effect of

Shaving in Reducing Fracture in Collar Forming"/ Stamping Journal, Sept./Oct., 2018, p.

18-20.

Fields of Study

Major Field: Mechanical Engineering

Table of Contents

Abstract ...... i

Dedication ...... iii

Acknowledgments ...... iv

Vita ...... v

Table of Contents ...... vi

List of Tables...... ix

List of Figures ...... xi

Chapter 1. Introduction ...... 1

1.1 Advanced High Strength Steels (AHSS)...... 1

1.2 Drawing of AHSS ...... 4

1.3 Restraining forces in drawing ...... 7

1.4 Location of drawbeads ...... 14

1.5 Drawbead design requirements ...... 17

Chapter 2. Research Objective and Outline ...... 19 vi

2.1 Research objective ...... 19

2.2 Outline ...... 19

Chapter 3. Literature Review ...... 21

3.1 Fracture under Bending ...... 21

3.2 Fracture under simultaneous bending and stretching (drawing) ...... 30

Chapter 4. Determining limits for fracture under bending ...... 37

4.1 Introduction to critical major strains ...... 37

4.2 FE model setup for determining critical major strains...... 38

4.3 Effect of Coefficient of Friction on strain distribution ...... 43

4.4 Determination of critical major strains ...... 44

Chapter 5. Determining limits for fracture under drawing ...... 46

5.1 Critical R/t ratio under stretch bending ...... 46

5.2 Thinning at fracture...... 48

Chapter 6 Effect of Blank optimization, Spacer height and Friction on drawing with drawbeads and spacers ...... 51

6.1 Introduction ...... 51

6.2 FE model setup ...... 53

6.3 Effect of blank optimization ...... 57

vii

6.4 Effect of spacer height ...... 61

6.5 Effect of Coefficient of Friction (CoF) ...... 66

Chapter 7 Effect of material and drawbead design on Drawing with Drawbeads and

Spacers ...... 71

7.1 Effect of change in material ...... 71

7.2 Modified rectangular drawbead design ...... 77

7.3 Modified Circular Drawbead Design ...... 81

7.4 Effect of modified circular drawbead design on possible fracture under bending .. 83

7.5 Effect of modified circular drawbead design on possible fracture during drawing 85

Chapter 8. Summary, Conclusions & Future Work ...... 88

8.1 Summary ...... 88

8.2 Conclusions ...... 89

8.3 Future Work...... 90

8.4 Proposed guidelines for successful drawing ...... 91

References ...... 93

Appendix A: Comparison of tool forces between edge bead and rectangular drawbead designs ...... 96

viii

List of Tables

Table 1 Material properties for various 1.2 mm thick DP780s (designated as A, B and C) and TRIP780 sheet. Adapted from Dykeman et al. (2009)...... 22

Table 2 Results obtained after 900 experiments by Dykeman et al. (2009)...... 23

Table 3 Description of some materials for which limiting bend ratio data was obtained from literature...... 27

Table 4 Limiting bend ratios for some materials obtained from literature review and industry recommendations...... 28

Table 5 Material properties and Limiting bend ratios for DP980/1.6 mm from Sriram et al. (2012) and Hance (2016) ...... 30

Table 6 Geometric parameter values for 900 V-bending of DP780A/1.2 mm ...... 40

Table 7 Critical R/t ratio for various materials to prevent shear fracture ...... 48

Table 8 Thinning at fracture under drawing for various materials from literature and personal correspondence with industry ...... 50

Table 9 Material properties and anisotropy parameters of Al5182-O/1.2 mm obtained from tensile test ...... 54

Table 10 Material properties for DP780/1 mm and DP980/1.6 mm ...... 73

Table 11 Max. Major strain after bending for DP780/1.2 mm and DP980/1.2 mm ...... 74

Table 12 Evaluating possibility of fracture for different spacer heights when A) No drawbead and B) Original drawbead design by Honda is used (Optimized blank used) .. 75

Table 13 Rectangular drawbead geometric parameters at various points ...... 78

Table 14 Max. major strain after bending for various drawbead designs ...... 79

Table 15 Circular drawbead geometric parameter values at various points illustrated in

Figure 60 ...... 81

Table 16 Effect of drawbead parameters on severity of drawbead design ...... 82

Table 17 Original and modified drawbead design parameters (Values reported at point 2

in Figure 60) ...... 83

Table 18 Comparison of calculated major strain values from various deformation

conditions ...... 84

Table 19 Possibility of fracture in the part for original and modified circular drawbead designs ...... 85

Table 20 Geometric parameter values for the considered fictitious part ...... 97

Table 21 Geometric parameter values for a) Rectangular and b) Edge drawbead ...... 98

Table 22 Max. die force for both drawbead designs after bending and after drawing .... 100

List of Figures

Figure 1 Trend of formability (represented by total elongation) versus the tensile strength of the materials (Billur et al., 2012) ...... 2

Figure 2 Changes to the Forming Limit Curve with different levels of pre-strain

(Stoughton et al., 2004)...... 3

Figure 3 An example showing how a) FLD fails to predict b) Fracture in the part.

Material: DP780/1.6 mm (Zeng et al., 2009) ...... 3

Figure 4 Schematic of drawing process (Altan et al., 2012) ...... 4

Figure 5 Various zones of deformation during drawing of a cup (Altan et al., 2012) ...... 6

Figure 6 An example of drawn part (Image Courtesy: GRABCAD) ...... 7

Figure 7 Allowable Blank Holder Force that can be applied for successful drawing (Altan et al., 2012)...... 8

Figure 8 Defects common in sheet metal parts (Altan et al., 2012) ...... 9

Figure 9 Varying BHF profile with time (Altan et al., 2012) ...... 10

Figure 10 Methods of restraining the material flow, Blank Holder Force and drawbeads

(Lekarczyk et al., 2018) ...... 11

Figure 11 Various drawbead designs a) Edge bead, b) Rectangular drawbead and c)

Circular drawbead ...... 12 xi

Figure 12 Automated tool to control material flow during stamping process Tool used by

Audi (Narayanan et al., 2019)...... 13

Figure 13 A schematic showing the stages involved in drawing with drawbeads and

spacers ...... 14

Figure 14 Plane strain like and axisymmetric like types of deformations occurring during

drawing at various locations of the die (example die built by Honda) ...... 15

Figure 15 Conventional location of drawbeads in the die ...... 16

Figure 16 Drawbeads run out towards the corners of the die ...... 16

Figure 17 Schematic of 900 V-bending experiments used by Dykeman et al. (2009) ...... 23

Figure 18 Schematic and tooling of wedge bend test. Adapted from Dykeman et al.

(2009) ...... 25

Figure 19 Results of wedge bend test from Dykeman et al. (2009) ...... 25

Figure 20 Schematic of tooling and sample geometry for ASB test. All dimensions were in mm (Sriram et al., 2003) ...... 31

Figure 21 Height at failure vs. R/t ratio at punch for various materials (Sriram et al.,

2003) ...... 32

Figure 22 Strain distribution with distance from punch radius for BH210 (Sriram et al.,

2003) ...... 33

Figure 23 Schematic of the Bending Under Tension (BUT) test (Shih, 2005) ...... 35

Figure 24 Schematic of Stretch Forming (SF) Fracture test (Shih et al., 2017) ...... 35

xii

Figure 25 Example illustrating the effect of improperly designed R/t ratio in a step bead

(Shih et al., 2017) ...... 36

Figure 26 Bending strains after drawbead closure represented by 900 V-bending

experiments. Figure adapted from Dykeman et al. (2009) ...... 37

Figure 27 Flow stress curve of DP780A/1.2 mm obtained from its engineering stress-

strain curve from tensile test (Dykeman et al, 2009)...... 39

Figure 28 Geometric parameters in 900 V-bending ...... 40

Figure 29 Modelling of blank with 7 elements along sheet thickness in DEFORM 2D ... 41

Figure 30 Sequence of 900 V-bending process from FE simulation (DEFORM 2D) ...... 42

Figure 31 Punch load vs. stroke in 900 V-bending process for different punch radius ( ).

Example material DP780A/1.2 mm (Dykeman et al., 2009) ...... 𝑅𝑅𝑝𝑝 42

Figure 32 Comparison of critical major strains and thinning for DP780A/1.2 mm between

two different CoFs ...... 43

Figure 33 Major strain and thinning distribution after 900 V-bending simulations ...... 44

Figure 34 Results of FE simulations replicating Bending Under Tests proposed by Shih.

(2005), left and right plots show major strain and thinning distribution respectively ...... 47

Figure 35 Shape and dimensions of the Honda die set ...... 52

Figure 36 Protrusion and drawbead dimensions in Honda die set ...... 52

Figure 37 Flow stress curve of Al5182-O from combined tensile and bulge test data ..... 54

Figure 38 Comparison of final part shape obtained from experiments and FE simulations

...... 56

xiii

Figure 39 a) Locations of flange length measurement and b) Comparison of flange length remaining between experiments and FE simulations ...... 56

Figure 40 Initial blank shape and dimensions for A) Original blank used by Honda (non-

optimized) and B) Optimized blank from AutoForm R8 ...... 58

Figure 41 Comparison of ‘optimized’ blank shapes from AutoForm R8 and PAM-

STAMP ...... 59

Figure 42 Comparison of final part shape and max. thinning obtained after using A)

Original or Honda blank and B) ‘Optimized’ blank ...... 60

Figure 43 Locations at which thinning, and thickening are calculated with stroke ...... 60

Figure 44 Thinning and thickening at various locations of the Honda part with stroke of

the die (Part formed from ‘Optimized blank’) ...... 61

Figure 45 Possibility of fracture for various spacer heights when using A) Original blank

and B) Optimized blank ...... 62

Figure 46 Effect of spacer height on die and binder (blank holder) forces (Optimized

blank used) ...... 63

Figure 47 Locations of draw-in calculations in FE simulation ...... 64

Figure 48 Draw-in at various locations for different spacer heights ...... 65

Figure 49 Effect of spacer height on wrinkling (optimized blank used) A) Spacer height=

1.15 , B) Spacer height= 1.25 ...... 65

Figure𝑡𝑡 50 Effect of CoF on possible𝑡𝑡 fracture in the part ...... 67

xiv

Figure 51 Effect of CoF on wrinkles in the formed part (only optimized blank considered)

...... 68

Figure 52 Die force vs. stroke curve variation with CoF for Honda part (‘Optimized’

blank only) ...... 69

Figure 53 Binder force vs. stroke curve variation with CoF for Honda part (‘Optimized’ blank only) ...... 69

Figure 54 Draw-in variation with CoF at various locations (optimized blank used) ...... 70

Figure 55 Flow stress curves for DP780/1.0 mm and DP980/1.6 mm ...... 72

Figure 56 Major strain distribution after bending under original drawbead built by Honda

...... 74

Figure 57 Location of max. thinning or fracture when A) No drawbeads and B) Original

drawbead design built by Honda are used ...... 75

Figure 58 Wrinkles in the part at a stroke of 135 mm, A) No drawbeads and B) Original

drawbead ...... 76

Figure 59 Geometric parameters for a rectangular drawbead ...... 77

Figure 60 A drawbead region marked with points (1-3) at which parameter values have

been reported ...... 78

Figure 61 Thinning distribution in the part during drawing, when using modified

rectangular drawbead. Fracture at a stroke of 20 mm based on 12 % thinning fracture

criterion for DP780/1.2 mm ...... 80

Figure 62 Geometric parameters for a circular drawbead ...... 80

Figure 63 Major strain distribution after drawbead formation in Honda part ...... 84

Figure 64 Die force vs. stroke curve for various drawbead configurations ...... 87

Figure 65 Binder (Blank Holder) force vs. stroke curve for various drawbead

configurations ...... 87

Figure 66 Half-model of the fictitious part to compare tool forces between rectangular and edge drawbead design ...... 97

Figure 67 a) rectangular and b) edge drawbead designs with their associated geometric parameters ...... 98

Figure 68 Comparison of die force vs stroke curves between edge and rectangular

drawbeads ...... 99

xvi

Chapter 1. Introduction

1.1 Advanced High Strength Steels (AHSS)

Automotive and steel companies are striving towards the weight reduction and

improvement of fuel economy through the search for new materials that have higher

strength and crash worthiness. Advanced High Strength Steels (AHSS) provide these

advantages and help in meeting the demand for lightweight vehicles. AHSS typically have

a yield strength above 550 MPa and tensile strength above 700 MPa (Sung et al., 2007).

However, AHSS come with their own set of challenges concerning their formability, or

their capability of form complex shapes without the occurrence of fracture. The trend of lower formability with increase in tensile strength of the material is shown in Figure 1.

This has led to taking strides towards improvements in the processes that manufacture these complex parts.

Figure 1 Trend of formability (represented by total elongation) versus the tensile strength

of the materials (Billur et al., 2012)

The success of any stamping process is typically validated by predicting the occurrence of

fracture after the part has been formed. Traditionally, the Forming Limit Curve (FLC) is

used in sheet metal forming to predict fracture in a part. However, FLC is not valid for

complex forming processes involving multiple strain paths, bending or shear fracture. An

example of changes to the FLC with strain paths is shown in Figure 2. Furthermore, it is

very expensive and time consuming to create FLC for various materials through

experiments. One such example of where the FLD fails to predict fracture is shown in

Figure 3 below.

Figure 2 Changes to the Forming Limit Curve with different levels of pre-strain

(Stoughton et al., 2004)

Figure 3 An example showing how a) FLD fails to predict b) Fracture in the part.

Material: DP780/1.6 mm (Zeng et al., 2009)

1.2 Drawing of AHSS

In drawing, a hollow part is formed by forcing a rectangular or a circular sheet metal

through a die cavity by the motion of a punch. The sheet metal or the blank is constrained at the ends by the Blank Holder whereas its central portion is pushed by a punch through the die opening. The term ‘drawing’ is used as there is a flow of the blank located in the

flange, and the depth of the part is greater than the maximum attainable depth if the part

was just stretched around the die corner radius. A schematic of drawing process is shown

in Figure 4 below.

Figure 4 Schematic of drawing process (Altan et al., 2012)

Drawing operations are typically performed over a double action press (for punch force and blank holder force).

There are several modes of deformation during drawing. The state of deformation is different in various zones shown in Figure 5:

Zone A-C: As the circumferential area of the round blank decreases during drawing, the law of volume constancy ensures that the blank thickens in this region.

Zone C-D: As the thick flange material is drawn towards the die cavity, it undergoes bending and unbending around the die corner radius region. The die corner radius is an important design parameter during drawing as an improper choice of die corner radius may result in fracture around the corner. There is a significant material flow around the die corner radius.

Zone D-E: This region undergoes tension due to stretching caused by the punch.

Zone E-F: This region is critical for fracture as the material near the punch corner does not experience much strain hardening due to lack of material movement. Hence, the blank is weakest in this region. The punch corner radius is another critical parameter that if chosen poorly may result in fracture of material. Typically, fracture around the punch corner radius is most common in drawing.

Figure 5 Various zones of deformation during drawing of a cup (Altan et al., 2012)

There are several parameters that affect the drawing process, irrespective of the shape of the blank:

1. Blank Holder Force/Pressure.

2. Material Properties and formability (uniform and total elongation, Yield Strength and Ultimate Tensile Strength etc.).

3. Coefficient of Friction/lubrication between the tools and blank.

4. Surface finish of the tools and blank (related to Coefficient of Friction and coating on tools).

5. Geometric parameter of the drawing process (punch corner and die corner radius, punch-die clearance).

6. Presence of drawbeads and spacers in the drawing process.

An example of drawing is shown in Figure 6.

Figure 6 An example of drawn part (Image Courtesy: GRABCAD)

Fracture in drawing may occur at the punch/die corner radius, or at the sidewall region due to excessive stretching.

1.3 Restraining forces in drawing

The restraining forces in drawing are applied through two methods:

a. Blank Holder Pressure/Force: For small parts, Blank holder Force (BHF) exerted

through nitrogen cylinders, springs or cushions control the flow of material into the 7

die cavity. However, there are limits to the BHF that can be applied. The limits of

drawability versus the BHF applied is shown in Figure 7 below.

Figure 7 Allowable Blank Holder Force that can be applied for successful drawing (Altan

et al., 2012)

The BHF limits are governed by the material/thickness and draw depth desired for

a sheet metal part. When applied incorrectly, wrinkles or splits may occur in the

part, examples of which are shown in Figure 8 below.

Figure 8 Defects common in sheet metal parts (Altan et al., 2012)

Precise control of metal flow is required during forming of AHSS as compared to

5XXX, 6XXX aluminum alloys and High Strength Low Alloy (HSLA) steels. The applied BHF profile can vary as follows:

I. Constant in magnitude with stroke and time.

II. Varying with ram displacement.

III. Varying with time.

IV. Varying with both ram displacement and time.

An example of varying BHF profile is shown in Figure 9 below.

Figure 9 Varying BHF profile with time (Altan et al., 2012) b. Drawbeads: For large automotive body parts, the Blank Holder Force required to

properly constrain the material flow would be very large, possibly beyond the

capacity of the cushion. In such cases, drawbeads of various shapes (circular,

rectangular etc.) are used. Figure 10 shows various methods of restraining the flow

of sheet material during drawing.

Figure 10 Methods of restraining the material flow, Blank Holder Force and drawbeads

(Lekarczyk et al., 2018)

Springback effects are prominent among AHSS, causing distortions to the final shape of the formed part. The use of drawbeads increases the tension imposed on blank and reduces the springback, thus forming the desired parts within allowable tolerances. Additionally, when forming non-symmetric parts where it is desired to control draw-in at certain locations, drawbeads allow for non-uniform draw-in along the sheet perimeter.

Drawbeads can be designed in several shapes. Some of the basic drawbead designs are shown in Figure 11 below.

Figure 11 Various drawbead designs a) Edge bead, b) Rectangular drawbead and c)

Circular drawbead

Overall, the rate of sheet metal flow into the die cavity can be controlled by the means of applying enough BHF or the use of drawbeads in the die and blank holder. The need for a

high BHF necessitates the use of hydraulic cushions. However, due to the cost of hydraulic

cushions, many stampers in North America use drawbeads. Furthermore, for large parts,

many stampers use ‘spacers’ or ‘distance blocks’ or ‘kiss blocks’. Some of the applications

of spacers are as follows:

1. Spacers control the material flow in the flange region.

2. Spacers enable the dies to close in parallel fashion, thus neutralizing the effect of

elastic deflection in the dies.

Shims are used to increase or decrease the height of spacers during production or stamping trials. Typically, the height of the shims varies from 0.02 mm to 0.08 mm. The spacer height may need to be adjusted manually or automatically to increase or decrease the material flow at the flange. One such example of an automatic method used by Audi is shown in Figure 12; a laser sensor detects the amount of material flow in the flange and

adjusts the spacer height accordingly.

Figure 12 Automated tool to control material flow during stamping process Tool used by

Audi (Narayanan et al., 2019).

The drawbead design depends on the material properties of the sheet being formed, sheet

thickness, and the stretching force desired during the drawing process. Some requirements

in a drawbead design are described below. A schematic of drawing process with drawbeads and spacers is shown in Figure 13.

Figure 13 A schematic showing the stages involved in drawing with drawbeads and

spacers

1.4 Location of drawbeads

Drawbeads and spacers are used when drawing large parts, however the drawbeads are not present throughout the periphery of the die or the blank holder. The various regions of the part undergo different deformations, as seen in Figure 14. Guidelines developed industry

illustrate that drawbeads do not extend to the corners of the die (which experience

axisymmetric like deformation, Figure 14). The corners of the sheet metal thicken during

drawing, thus exerting additional restraining force on the material. The presence of

drawbeads will further increase the restraining force, thus locking the sheet metal and

leading to splits or fracture in the part. The conventional locations of drawbeads in the die

are shown in Figure 15 and Figure 16. The drawbeads are either not built around the corners of the die, or they run-out towards the corners of the die.

Figure 14 Plane strain like and axisymmetric like types of deformations occurring during

drawing at various locations of the die (example die built by Honda)

Figure 15 Conventional location of drawbeads in the die

Figure 16 Drawbeads run out towards the corners of the die

1.5 Drawbead design requirements

The drawbead design for a given material and thickness should satisfy the following requirements:

a. No fracture should occur in the sheet metal when the die closes during formation

the drawbead, i.e. in stages 2-3 shown in Figure 13. The fracture mechanism during

drawbead formation is bending. This type of fracture is more pronounced for

Advanced High Strength Steels (AHSS) than mild steels, low carbon steels and

Aluminum.

b. No fracture should occur in the sheet metal during drawing/deep drawing of the

part, i.e. stages 3-4 shown in Figure 13. During drawing, the sheet metal is subjected

to stretching in addition to bending around the die and the punch corners.

c. The drawbead should exert adequate stretching on the part so that wrinkles are not

formed and do not enter the die cavity.

d. After drawing, the non-useful remaining flange is trimmed. The drawbead design

should minimize the amount of scrap material or the material that will be trimmed

after drawing.

In the subsequent chapters, the focus will be on points a-c listed in drawbead design

requirements, i.e. the drawbead design guidelines required to prevent fracture under bending and drawing and minimizing wrinkles in the part during drawing. The effect of

blank optimization on the remaining flange mentioned in point d will also be considered.

A die set built by Honda will also be considered as an example to illustrate the importance of drawbead design, spacer height and Coefficient of Friction in drawing.

Chapter 2. Research Objective and Outline

2.1 Research objective

The objective of this study is to propose simple guidelines to reduce the possibility of fracture and wrinkles in a given drawing process containing drawbeads and spacers, using

FE simulations.

2.2 Outline

The outline of this study is as follows:

1. Chapter 1 gives a brief introduction to AHSS, drawing, methods of applying

restraining forces in drawing and the use of drawbeads and spacers.

2. Chapter 3 deals with literature review of various existing methods to determine

fracture under bending and drawing.

3. Chapter 4 focuses on determination of fracture limits for a given material under

bending, using FE simulations replicating 900 V-bending experiments.

4. Chapter 5 discusses the appropriate fracture limits for a given material under

drawing based on literature review conducted in chapter 3 and ease of use in

industry.

5. Chapters 6 and 7 investigate the effect of blank optimization, spacer height,

lubrication conditions and drawbead design on process outputs (possible fracture,

wrinkling, tool forces and draw-in) for 1.2 mm thick Al5182-O and DP780.

Chapter 3. Literature Review

3.1 Fracture under Bending

As described in Chapter 1, the sheet metal undergoes bending and stretching plus bending modes during drawing process. When the die closes to form the drawbead (stages 2-3,

Figure 13), the sheet metal is bent around the drawbead radii. Hence, it is important to design the drawbead radii such that no cracking occurs during bending. Otherwise, during subsequent drawing, the sheet metal will tear.

Various researchers have developed fracture criteria in terms of bending angle at fracture and the critical bend radius at fracture, for a given material and thickness. Dykeman et al.

(2009) performed a set of 900 V-bending experiments to determine the minimum bend radius at fracture for various DP780 sheets and a TRIP780 sheet, each having 1.2 mm thickness and different material properties and microstructure. The material properties of the considered materials are shown in Table 1 and the schematic of tooling used to perform

900 V-bending experiments is shown in Figure 17. The tests were performed with the standard JIS Z 2248. The samples for V-bending experiments were created by trimming and the tests were performed in both longitudinal (L) and transverse (T) directions; longitudinal direction indicates that the bend direction is parallel to the longitudinal direction of the sheet metal.

Table 1 Material properties for various 1.2 mm thick DP780s (designated as A, B and C)

and TRIP780 sheet. Adapted from Dykeman et al. (2009)

The results for the 900 V-bending tests are shown in Table 2. It is interesting to note that although the material properties (listed in Table 1) do not change much with transverse and rolling directions for a given material, the minimum bend radius (at which no fracture is observed) is lower for transverse directions, for DP780A and DP780B. Hence, it is possible that the alignment of the grains may be the reason for the observed differences, as it is difficult to conclude based on the macroscopic properties of the materials. However, the differences in minimum bend radius among various materials can be correlated to the differences in their uniform elongations (Table 1), i.e. the material having a higher uniform elongation is observed to have a lower bend radius at fracture (Table 2).

Figure 17 Schematic of 900 V-bending experiments used by Dykeman et al. (2009)

Table 2 Results obtained after 900 experiments by Dykeman et al. (2009)

However, the 900 V-bending tests suffered from the drawback that the cracks could be observed only by visually inspecting the bent specimen at the end of the forming stroke. It is possible that fractures started before the samples were bent by 900. 23

In addition to the V-bending test, Dykeman et al. (2009), Walp (2007) and Kim (2009) also proposed a wedge bend test, as shown in Figure 18. A punch of very sharp radius pushes the blank in between two dies until a crack occurs in the sheet metal. The bend angle at which cracking started was determined by the stroke at which the load drop in the punch occurred. However, the magnitude of load drop was not specified in Dykeman et al. (2009), but Walp (2007) imposed a 15 N drop in punch load as the criterion for onset of cracking in the sheet metal. The advantage of this test over the 900 V-bending tests was that the bend angle could be set to more than 900 and the method of crack inspection was more reliable.

These advantages helped in characterizing the bendability of DP780C and TRIP780 (see

Figure 19), as these materials did not fracture for the lowest bend radius used in 900 V-

bending (0.5 mm, see Table 2).

The number of samples for which the wedge bend tests were run was not specified. Hence,

the test results obtained (i.e. bend angle at fracture) may be variable.

Figure 18 Schematic and tooling of wedge bend test. Adapted from Dykeman et al.

(2009)

Figure 19 Results of wedge bend test from Dykeman et al. (2009)

Other researchers like Sriram et al. (2012), Kovacs et al. (2017) and Hance (2016) also used 900 V-bending tests to characterize the bendability of various materials. Hance (2016)

performed 900 V-bending experiments using the standard ASTM E290 with the bend axis

parallel to the rolling direction. The smallest punch radius used was 0.5 mm. If fracture

was observed, using a stereoscope at 10x magnification, then a larger punch radius was

used (increments of 0.5 mm). Hance (2016) defined the limiting bend ratio ( ) for a given

material and thickness by considering the average of minimum bend radius𝑓𝑓 at which no

fracture and maximum bend radius at which fracture is observed for a given material of

thickness ( ), as shown in equation 1.

𝑡𝑡 , + , = (1) 2 �𝑟𝑟𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑚𝑚𝑚𝑚𝑚𝑚� 𝑓𝑓 Where, 𝑡𝑡

, is the minimum bend radius at which a material does not fracture, , is the

𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑚𝑚𝑚𝑚𝑚𝑚 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑚𝑚𝑚𝑚𝑚𝑚 maximum𝑟𝑟 bend radius at which a material fractures and is the sheet thickness𝑟𝑟 of the material (Adapted from Hance (2016)). 𝑡𝑡

A table of the list of materials for which the critical bend ratios from V-bending were obtained after literature review and industry recommendations are shown in Table 4 with the description of some of the materials in Table 3.

Table 3 Description of some materials for which limiting bend ratio data was obtained

from literature.

Table 4 Limiting bend ratios for some materials obtained from literature review and

industry recommendations.

An interesting observation was the discrepancy in the limiting bend ratios of a 1.6 mm thick DP980 reported by Sriram et al. (2012) and Hance (2016). The material properties of

DP980/1.6 mm from both Sriram et al. (2012) and Hance (2016) and their corresponding

limiting bend ratios are shown in Table 5. The possible reasons for the discrepancies are

as follows:

1. The coating on the DP980s under consideration may be different. The DP980 in

Hance (2016) was electro-galvanized, whereas the coating was not specified in

Sriram et al. (2012). It is possible that the coating affects the material behavior

during bending.

2. The procedure describing how the 900 V-bending experiments were conducted in

Sriram et al. (2012) was not specified. The increments in punch radius used in

Sriram et al. (2012) may be different, whereas a punch increments used in Hance

(2016) was 0.5 mm.

3. Even though the material properties of both DP980s are similar in terms of YS,

UTS and uniform elongation (Table 5), it is possible that they may be different in

terms of local formability, i.e. how the materials behave under bending, blanking

etc. Hence, the microstructural differences between the materials may be the reason

for the discrepancy in limiting bend ratios.

Hence, the above described factors need to be taken into consideration when performing

V-bending or any equivalent experiments. However, in the subsequent chapters and FE simulations, the concept of continuum mechanics will be used, thus it is not possible to incorporate microstructural differences among materials in FE simulations. The flow stress curves of the materials are derived solely from their macroscopic properties (Yield

Strength, Ultimate Tensile Strength and Uniform Elongation).

Table 5 Material properties and Limiting bend ratios for DP980/1.6 mm from Sriram et

al. (2012) and Hance (2016)

3.2 Fracture under simultaneous bending and stretching (drawing)

This section discusses about possible fracture during drawing, i.e. when the sheet metal goes into the die cavity by the action of the punch (stages 3-4, Figure 13) when drawbeads are used.

Shih (2005) described about shear fracture, a type of which fracture happens generally at the corners of the part radii when subjected to superimposed bending and stretching.

According to Zeng et al. (2009), shear fracture is prominent only in materials having a hard martensitic phase (Dual Phase and Complex Phase steels), as brittle fracture initiates in the martensitic region. Sriram et al. (2003) conducted a test called Angular Stretch Bend (ASB) test to predict the height at failure for different materials with a punch radius having different R/t ratios. The thickness of the materials considered were between 0.6 mm to 1.7 mm. The schematic of the tooling and sample geometry for ASB test performed by Sriram et al. (2003) is shown in Figure 20. The action of the drawbeads were such that the material 30

flow was prohibited. Teflon and lubrication were used on the punch nose to minimize the effect of friction on the test. The height at failure was determined by the punch displacement at maximum load.

Figure 20 Schematic of tooling and sample geometry for ASB test. All dimensions were

in mm (Sriram et al., 2003)

The results for height at failure vs the R/t ratio of the punch is shown in Figure 21. It was seen that the height at failure was very sensitive to the R/t ratio for lower values of R/t ratio, thus giving an indication that the bending strains limited the formability of the steels under consideration. As the R/t increased, then the height at failure saturated for all materials, thus exhausting the formability of the material. Furthermore, for lower R/t ratios

the cracks were seen at the punch radius, whereas for the larger R/t values the cracks were

seen at the sidewall.

Figure 21 Height at failure vs. R/t ratio at punch for various materials (Sriram et al.,

2003)

Additionally, the strains were measured by etching square grids on the samples (around

0.01 inches in size) in Sriram et al. (2003). After cracks were detected, the deformation of the grids was measured to calculate the major and minor strains. The strain distribution with distance from punch radius for an example material (BH210) was plotted by Sriram et al. (2003) and is shown in Figure 22. It was seen that for low R/t ratios (R/t=1.12), the strains at fracture were low, and could not be predicted by the conventional Forming Limit

Curve (FLC). For the higher R/t ratios (R/t=4.16 and 8.43) where the failure occurred at

the sidewall of the part, the strains were high and could be predicted by the FLC.

Figure 22 Strain distribution with distance from punch radius for BH210 (Sriram et al.,

2003)

Sriram et al. (2012) proposed a Draw Stretch test as an alternative to Bending Under

Tension (BUT) tests and Stretch Forming (SF) Fracture tests have also been proposed by

Shih (2005) and Shih et al. (2017) respectively to determine the critical R/t ratio for shear fracture of the part when subjected to simultaneous bending and stretching. The critical R/t ratio was defined as the bend ratio up to which shear fracture is exhibited by the sheet metal. Hence, fracture is expected to be seen near the part radii. For R/t values higher than

critical R/t, the location of fracture shifts towards the sidewall. The schematics of BUT and

SF fracture tests are shown in Figure 23 and Figure 24 respectively. The pin in both cases

are representative of die corner radius or the exit radius of the drawbead, the pulling end

was representative of drawing or stretching of the part into the die cavity and the Back

Tension Force ( , Figure 23) or the fixed end (Figure 24) represented the restraining end

1 (by Blank Holder𝐹𝐹 Force, drawbeads or lockbeads).

Figure 23 Schematic of the Bending Under Tension (BUT) test (Shih, 2005)

Figure 24 Schematic of Stretch Forming (SF) Fracture test (Shih et al., 2017)

The BUT test suggested by Shih (2005) suffered from the setback that the critical R/t ratio for a material depended not only on the coefficient of friction between the sheet and the pin, but also the magnitude of Back Tension Force Figure 23). The Shear Forming (SF) fracture test suggested by Shih et al. (2017) simulated the locking of the material through a lock bead or a step bead, used primarily to reduce springback in the part. However, the 35

critical R/t ratios could be used to design the die corner radius or drawbead radius in such a way that no shear fracture (or fracture at the die corner) is observed in the part. One example illustrating the importance of R/t ratio on design of bead is shown in Figure 25.

Figure 25 Example illustrating the effect of improperly designed R/t ratio in a step bead

(Shih et al., 2017)

It is important to note that fracture can still occur at the sidewall during drawing, based on the formability of the material, lubrication, draw depth and the restraining force applied etc.

The existing literature deals with fracture in drawing without the use of spacers. No literature pertaining to drawing with spacers was found to the best of the author’s knowledge.

Chapter 4. Determining limits for fracture under bending

4.1 Introduction to critical major strains

The minimum bend radius from 900 V-bending experiments was used as the basis for

determining the major strain at fracture. The major strain at fracture will henceforth be

referred to as the critical major strain. Possible fracture under bending (stages 2-3, Figure

13) for a given drawbead design will be evaluated by comparing the major strains at the

drawbead region with critical major strains for that material. The critical major strains are

obtained by performing FE simulations replicating the bending experiments. For

determining the critical major strain, the wedge bend tests were not used due to their

limitations in terms of variability in results and a non-adequate criterion for determining

onset of fracture in the sheet metal. Hence, 900 V-bending experiments were used within

its own limitations, as a guideline for determining the critical major strains (Figure 26).

Figure 26 Bending strains after drawbead closure represented by 900 V-bending

experiments. Figure adapted from Dykeman et al. (2009) 37

4.2 FE model setup for determining critical major strains

The procedure implemented for determining the critical major strains will be shown for an example material. The materials chosen were DP980/1.6 mm (Sriram et al., 2012) and

DP780A/1.2 mm (Dykeman et al., 2009). However, the procedure followed will be illustrated for DP780A/1.2 mm only. The flow stress curve of DP780A/1.2 mm was extrapolated using its engineering stress-strain curve obtained tensile test using the procedure described in Kardes et al. (2011), as seen in Figure 27. The punch radius at fracture for 1.2 mm thick DP780A was determined from its limiting bend ratio ( =1.5, see

Table 4) and the thickness of the material ( ) using equation 2: 𝑓𝑓

= × = 1.5 × 1.2𝑡𝑡 = 1.8 (2)

𝑝𝑝 However, the size of𝑅𝑅 900 V𝑓𝑓-bending𝑡𝑡 tooling and𝑚𝑚𝑚𝑚 samples𝑚𝑚𝑚𝑚 were not specified in Sriram et al.

(2012) and in standard ASTM E290. Hence, these dimensions were adapted from Sever et al. (2012) and are shown in Figure 28 and Table 6.

Figure 27 Flow stress curve of DP780A/1.2 mm obtained from its engineering stress-

strain curve from tensile test (Dykeman et al, 2009)

The 900 V-bending operation was modelled in DEFORM 2D with the assumption of plane strain, i.e. the length of the sheet in the bend direction is very large. DEFORM 2D employs elements along the thickness of the sheet. Hence, the modelling of strains/stresses and thinning during bending would be better than software like AutoForm and PAM-STAMP, which use shell elements. The blank was modelled as plastic, as the strains obtained after

900 V-bending did not change significantly (about 2 % change) when the sheet was modelled as elasto-plastic. A springback analysis was not deemed necessary for this study, hence the strains after bending without unloading the tools were approximately the same for plastic and elasto-plastic brick elements. The number of elements along the sheet thickness was kept as 7, as shown in Figure 29.

Figure 28 Geometric parameters in 900 V-bending

Table 6 Geometric parameter values for 900 V-bending of DP780A/1.2 mm

Figure 29 Modelling of blank with 7 elements along sheet thickness in DEFORM 2D

The sequence of 900 V-bending process is shown in Figure 30. The forming stroke of the

punch was 20 mm. As seen from the sequence of the process, the blank was only in contact

with the punch radius and the die corners from the start to a stroke of 19 mm. The blank

surface was in complete contact with both the punch and die only at the final stroke. Hence,

the punch load increase towards the end of bending process was significantly higher than

during the initial stages (i.e. a punch stroke of 0 mm to 19 mm). An example of punch load

vs. stroke curve and its variation with punch radius ( ) is shown in Figure 31. It was seen

𝑝𝑝 that the punch load did not change significantly with𝑅𝑅 change in punch radius ( ). The

𝑝𝑝 effect of Coefficient of Friction (CoF) on strain distribution after 900 V-bending𝑅𝑅 was analyzed.

Figure 30 Sequence of 900 V-bending process from FE simulation (DEFORM 2D)

Figure 31 Punch load vs. stroke in 900 V-bending process for different punch radius ( ).

𝑝𝑝 Example material DP780A/1.2 mm (Dykeman et al., 2009) 𝑅𝑅

4.3 Effect of Coefficient of Friction on strain distribution

Two different Coefficient of Friction (CoF) values were chosen: 0.1 and 0.15 to assess the

effect of lubrication conditions on strains obtained under 900 V-bending. The material

chosen for this study was DP780A/1.2 mm (Dykeman et al., 2009) and the punch radius

( ) was 2 mm. It is important to note that this punch radius does not correspond to the

𝑝𝑝 limiting𝑅𝑅 bend ratio of DP780A/1.2 mm and was chosen solely to estimate the effect of CoF.

The other geometric parameters for 900 V-bending and FE model setup were same as mentioned previously in Table 6. A comparison of the critical major strain and thinning distribution obtained after 900 V-bending simulations was made and is shown in Figure 32.

It was observed that the CoF values did not affect the strains and thinning significantly for

900 V-bending operation. This is expected as the sliding between the tools and the blank is

minimal during the operation (see Figure 30 for sequence of operation).

Figure 32 Comparison of critical major strains and thinning for DP780A/1.2 mm between

two different CoFs 43

4.4 Determination of critical major strains

The CoF was assumed to be 0.1, as it does not affect the strain distribution during 900 V- bending. The maximum major strain at the tensile region of the bent sheet after 900 V-

bending simulations with punch radius ( ) corresponding to limiting bend ratio ( ) of the

𝑝𝑝 material was considered as the critical major𝑅𝑅 strain for that material, as shown in𝑓𝑓 Figure

33. The maximum thinning after bending was not considered as a fracture criterion as the

material thinning during bending only operations is negligible. Additionally, the effective

strains were not considered as they represent a combination of strains in all directions,

whereas the major strains only represent the direction of maximum deformation.

Figure 33 Major strain and thinning distribution after 900 V-bending simulations

The critical major strain for DP780A/1.2 mm was found out to be 0.287 after replicating the experiments with FE simulations. Similarly, the critical major strain obtained for

DP980/1.6 mm (Sriram et al., 2012) was obtained to be 0.240, after choosing a punch radius

( ) of 2.8 mm, based on limiting bend ratio in Table 5. The above computed values of

𝑅𝑅𝑝𝑝

critical major strains will be used in subsequent chapters for evaluating possible fracture

under bending in drawbeads.

A similar procedure can be adopted to estimate the critical strains at fracture for various materials. It is assumed in this study that the critical major strain for a given material is independent of its thickness. The effect of thickness change for a given material on critical major strains will not be evaluated as limiting bend ratios for different thicknesses of the

same material was not available from literature to the best of the author’s knowledge.

Chapter 5. Determining limits for fracture under drawing

Two fracture criteria will be used to evaluate possible fracture during drawing. One

criterion deals with evaluating the possibility of shear fracture and the other criterion

evaluates the possibility of fracture due to excessive deformation.

5.1 Critical R/t ratio under stretch bending

As described in Chapter 3, shear fracture during drawing cannot be predicted with the help

of Forming Limit Diagram (FLD) as it is a bending dominated failure. No necking is

observed in the sheet metal during shear fracture. It is important to design drawbead exit

radius ( ,Figure 62) and die corner radius (11 mm, Figure 36) such that shear fracture is

3 avoided.𝑅𝑅 In order to obtain the major strains at shear fracture, FE simulations replicating the Bending Under Tests (BUT) described by Shih. (2005) were conducted using

DEFORM 2D with brick elements. The geometry was approximated to be a plane strain condition. The major strains and thinning distribution after FE simulations are shown in

Figure 34. The maximum thinning and major strain values were obtained near the pulling end of the sheet and not at the pin radius, thus illustrating the inability of FE simulations to predict shear fracture. The critical R/t ratios under stretch bending for some materials from literature are shown in Table 7. The critical R/t ratio obtained from literature will be used as shear fracture criterion during drawing in chapters 6 and 7. The critical R/t ratios

under stretch bending for CRDP800 (5 6 ) and CRDP1000 (6 ) will be used for estimating shear fracture in chapter 7. 𝑡𝑡 − 𝑡𝑡 𝑡𝑡

Figure 34 Results of FE simulations replicating Bending Under Tests proposed by Shih.

(2005), left and right plots show major strain and thinning distribution respectively

The critical R/t ratio for any material under stretch bending is higher than the critical R/t ratio for that material under bending, as fracture occurs under superimposed stretching and bending in stretch bending. Hence, the critical stretch bend ratio can be used as a conservative criterion for evaluating possible fracture under bending for a given material, if the critical bend ratio for that material is not available.

Table 7 Critical R/t ratio for various materials to prevent shear fracture

5.2 Thinning at fracture

If the die design (i.e. die corner radius and drawbead radii) is such that no shear fracture is expected, then possible fracture during drawing can be evaluated by using thinning or 48

Forming Limit Curve (FLC). However, determination of FLC is time consuming and

expensive due to the experimentation involved. Due to lack of FLC for the materials considered in the subsequent chapters, the inability of Keeler-Brazier equation to generate accurate FLCs for Advanced High Strength Steels, and the variation of FLCs with the thickness of the materials make thinning as the primary choice as a fracture criterion under drawing. Thinning can be measured easily after the part is taken out of the die set, using micrometer, caliper or ultrasonic thickness gauge measurement devices. Other criteria like major strain, stresses etc. at fracture were not considered due to difficulties in procuring these values during experiments.

Measuring the maximum thinning or thinning at fracture of the drawn part is an approximate method, as the thinning depends on the deformation path of the material, i.e. the thinning at fracture is different for states of uniaxial tension, biaxial tension, edge

fracture etc.

Table 8 shows the thinning at fracture under drawing for various materials available from

literature as well as personal communication with industry (thickness specified only if

available). It is important to note that these are approximate values as variations exist

within the same grade of material due to difference in microstructure, thus leading to

differences in formability.

Table 8 Thinning at fracture under drawing for various materials from literature and

personal correspondence with industry

Chapter 6 Effect of Blank optimization, Spacer height and Friction on drawing with

drawbeads and spacers

6.1 Introduction

An example die set built by Honda was used as an example to simulate the effect of various

process parameters on drawing a part free of defects (fracture and wrinkling). The die set

was built by Honda to emulate the drawing process in inner door panel of the car. The

shape and dimensions of the Honda die set are shown in Figure 35. The Honda die set also

consisted of protrusions and circular drawbeads (which are symmetric), as shown in Figure

36. The effect of the following parameters was considered in drawing of the considered

part:

1. Blank optimization

2. Spacer height

3. Coefficient of Friction (CoF)

4. Drawbead design

The effect of the above process parameters on possible fracture in the part (when forming the drawbead and during drawing) and wrinkling were investigated.

Figure 35 Shape and dimensions of the Honda die set

Figure 36 Protrusion and drawbead dimensions in Honda die set

6.2 FE model setup

Experiments were previously conducted using the Honda die set using the blank shape suggested by Honda. The geometry of the blank used to form the Honda part is shown in

Figure 40. The material used was Al5182-O/1.2 mm. The flow stress curve and the anisotropy parameters of Al5182-O/1.2 mm were obtained from tensile tests previously conducted at Center for Precision Forming (CPF) and are shown in Figure 37 and Table 9 respectively. An IRMCO lubricant with code 080-00B was used. The lubricant was found to have a CoF of 0.07 based on thinning comparisons between experiments and FE simulations. However, the spacer height used by Honda when conducting experiments was unknown. A spacer height of 1.25 = 1.5 was assumed in FE simulations based on comparison of flange length remaining𝑡𝑡 between𝑚𝑚𝑚𝑚 experiments and FE simulations. The draw depth of the Honda part was 155 mm.

Figure 37 Flow stress curve of Al5182-O from combined tensile and bulge test data

Table 9 Material properties and anisotropy parameters of Al5182-O/1.2 mm obtained

from tensile test

The blank was meshed using the new Thickness Shell (TS11) elements, available in the new version of AutoForm (AutoForm R8). TS11 elements can simulate the thickening and ironing of blank as opposed to the conventional Elasto-plastic shell (EPS11) elements in

AutoForm. The tools (punch, die and the blank holder) were modelled as rigid and the

elastic deflection of the tools were neglected in the FE simulations. Additionally, the FE simulations were run using the ‘gap controlled’ option, which models a constant gap between the die and the blank holder. The gap was set equal to the spacer height (1.5 mm) and the blank holder applied enough force to prevent opening of the tools due to thickening of the blank around the corners. However, in reality, the spacer height at different locations may be different depending on material flow and the heights can be adjusted by adding or removing shims (usually with a gage of 3-5 % of sheet thickness).

The final part shape and maximum thinning obtained after forming the original blank using the Honda die set is shown in Figure 42 (using FE simulations). Additionally, a comparison of final part shape and flange length (between experiments and FE simulations) is shown in Figure 38 and Figure 39 respectively. The experimental and FEM flange lengths agreed except at locations 1, 7 and 8. These differences may be due to elastic deflection of the tools during the experiments. It was assumed that no fracture occurs under bending in drawbead region for Al5182-O/1.2 mm, as the experimental part did not show any splits.

Similarly, the die corner radius and the drawbead exit radius (11 mm and 10 mm, Figure

36) are assumed to high enough ( / 8) such that no shear fracture occurs for Al5182-

O/1.2 mm. 𝑅𝑅 𝑡𝑡 ≅

Figure 38 Comparison of final part shape obtained from experiments and FE simulations

Figure 39 a) Locations of flange length measurement and b) Comparison of flange length

remaining between experiments and FE simulations

6.3 Effect of blank optimization

The ‘Formchk’ feature in AutoForm R8 ‘optimizes’ the blank based on the desired stretching in the part during drawing and the desired shape of the final part, which is the punch shape for this case. The optimization was performed with zero stretching imposed on the part as the die and binder had drawbeads, which would create the necessary stretching on the part. The process parameters (drawbead design, spacer height=1.5 mm and CoF=0.07) were kept the same as before.

The ‘optimized’ blank shape and how it compared to the initial blank shape used by Honda is shown in Figure 40. To check for variation in optimized blank shape among various FE software, the optimization feature in PAM-STAMP was also used. The blank shapes obtained from both software were similar with small differences in their dimensions, as shown in Figure 41.

Figure 40 Initial blank shape and dimensions for A) Original blank used by Honda (non-

optimized) and B) Optimized blank from AutoForm R8

Figure 41 Comparison of ‘optimized’ blank shapes from AutoForm R8 and PAM-

STAMP

The final part shapes obtained (from FE simulation) using original blank and optimized

blank from AutoForm is shown in Figure 42. The fracture criterion for Al5182-O was chosen as 20% thinning, based on industry recommendations. Forming Limit Diagram

(FLD) was not considered as it was not readily available for Al5182-O/1.2 mm and the expense involved in experiments to generate FLD being high. Furthermore, the thinning could be measured easily after the experiments using micrometer, caliper etc. The optimized blank had a lower max. thinning, and thus a lower possibility of fracture as compared to the original blank. Additionally, the final flange shape was uniform in FE simulation, which is a contrast to the uneven flange shape for the original blank.

Figure 42 Comparison of final part shape and max. thinning obtained after using A)

Original or Honda blank and B) ‘Optimized’ blank

The thinning and thickening variation with stroke of die at various locations of the part

(seen in Figure 43) is shown in Figure 44.

Figure 43 Locations at which thinning, and thickening are calculated with stroke

Figure 44 Thinning and thickening at various locations of the Honda part with stroke of

the die (Part formed from ‘Optimized blank’)

Blank shape optimization is the first step towards modification of process parameters for

successful forming (minimal wrinkles and no fracture) in a given drawing process. The optimized blank shape can be cut using laser, or a simplified rectangular blank with chamfers can be cut out by blanking.

6.4 Effect of spacer height

The effect of spacer height on possible fracture in the part, draw-in and die forces was investigated for both the original and optimized blank shapes (Figure 40). Three different spacer heights were considered:1.10 ,1.15 and 1.25 , where is the sheet metal

𝑡𝑡 61𝑡𝑡 𝑡𝑡 𝑡𝑡

thickness. Only lower spacer heights were considered in the study as increasing the spacer

height led to excessive wrinkling in the part.

The effect of spacer height on possible fracture in the final formed part (based on 20 % thinning as fracture criterion) is shown in Figure 45 below. It was assumed that Al5182-

O/1.2 mm will not fracture under bending, as no fracture was observed in experiments when forming the Honda part with this material. Fracture is expected under drawing for a

spacer height of 1.10 irrespective of the blank shape used. Hence, it is not recommended

for forming the Honda𝑡𝑡 part based on the FE simulations.

Figure 45 Possibility of fracture for various spacer heights when using A) Original blank

and B) Optimized blank

Interestingly, the optimized blank was able to form successfully for a larger range of spacer heights (i.e. 1.15 to 1.25 ) as compared to the original blank shape, thus highlighting the importance of blank𝑡𝑡 optimization𝑡𝑡 before drawing any part.

The vertical die and binder forces vs. stroke of die for various spacer heights are shown in

Figure 46. It is important to note that the binder or blank holder force is variable as the FE simulations were run with ‘gap controlled’ option in AutoForm.

The binder and die forces increase significantly with decrease in spacer height. FE simulations can provide an estimation of the forces required to form a part beforehand.

Hence, the press and cushion capacities required can be taken into consideration before tryouts.

Figure 46 Effect of spacer height on die and binder (blank holder) forces (Optimized

blank used)

Subsequently, the effect of spacer height on draw-in at various locations of the Honda part

was investigated. The locations of measurement of draw-in are shown in Figure 47. The

draw-in values for various spacer heights are shown in Figure 48. The draw-in for spacer height=1.10 is not reported as fracture is observed in the material based on thinning criterion for 𝑡𝑡Al5182-O/1.2 mm (20 % thinning). The spacer height seems to affect the draw-in at locations 4 and 8 only for the Honda part. The spacer height can have a variable effect of the draw-in depending on the shape and size of the part being formed and the drawbead design used.

Figure 47 Locations of draw-in calculations in FE simulation

Figure 48 Draw-in at various locations for different spacer heights

The spacer height significantly affected wrinkling in the part as shown in Figure 49. The wrinkles were visualized using ‘zebra lines’ feature in AutoForm. The wrinkles for spacer height = 1.10 is not reported as fracture is observed. Heavy wrinkling was observed when a spacer height𝑡𝑡 of 1.25 was used.

𝑡𝑡

Figure 49 Effect of spacer height on wrinkling (optimized blank used) A) Spacer height=

1.15 , B) Spacer height= 1.25

𝑡𝑡 65 𝑡𝑡

Hence, a spacer height of 1.15 or slightly larger is recommended for forming the Honda part based on the wrinkling observed𝑡𝑡 in the part. However, the ‘best’ spacer height depends on the following factors:

1. Metal flow (forming the part without wrinkles and fracture)

2. Press and cushion force capacities.

It is possible to estimate the ‘best’ spacer height using FE simulations within certain limitations (i.e. neglecting elastic deflection of the tools and non-uniformity of spacer height around the part).

6.5 Effect of Coefficient of Friction (CoF)

The effect of Coefficient of Friction (CoF) was investigated on both the original and the optimized blank shapes. The spacer height for this study was chosen as 1.15 as no fracture and minimum wrinkles were observed for this spacer height, thus making𝑡𝑡 this the appropriate spacer height for simulation purposes. Three values of CoF were considered:

0.07, 0.10 and 0.12. One major assumption in this study was that the CoF was constant in the entire part and throughout the forming process. However, this does not reflect the real- life forming conditions as uneven distribution of lubricant on the sheet metal, temperature and pressure variation during forming affect the lubricant performance. Research is being conducted at Center for Precision Forming (CPF) and other companies to quantify the

lubricant performance with changes in temperature and pressure. A constant CoF has been assumed for simplicity.

Figure 50 shows the effect of CoF on possible fracture in the formed part at the final stroke.

It is seen that the original blank shape does not form the part successfully for the lowest considered CoF value. Hence, FE simulations were not conducted for higher CoF values.

The optimized blank was able to form successfully (without fracture) for a larger range of

CoF values or lubrication conditions than the original blank.

Figure 50 Effect of CoF on possible fracture in the part

The die and binder forces did not change much with change in CoF between the tools and

the blank when forming the Honda part, as shown in Figure 52 and Figure 53. This may be because force is an integrated value, and not that sensitive to CoF for drawing. CoF has a

localized effect, hence affecting only the deformation of the sheet. Similarly, the CoF did

not affect the wrinkling (Figure 51) and draw-in (Figure 54) in the Honda part significantly.

It is important to note that even though the effect of CoF on forces and wrinkling may not be significant, it plays a very important role on possible splitting in a drawn part.

Figure 51 Effect of CoF on wrinkles in the formed part (only optimized blank considered)

Figure 52 Die force vs. stroke curve variation with CoF for Honda part (‘Optimized’

blank only)

Figure 53 Binder force vs. stroke curve variation with CoF for Honda part (‘Optimized’

blank only) 69

Figure 54 Draw-in variation with CoF at various locations (optimized blank used)

Chapter 7 Effect of material and drawbead design on Drawing with Drawbeads and

Spacers

7.1 Effect of change in material

The possibility of forming different materials using the Honda die set was investigated using FE simulations. The materials considered were 1.2 mm thick DP780 and DP980, as the materials had a significantly higher strength and lower formability compared to

Al5182-O/1.2 mm. The ‘optimized’ blank shape for DP780/1.2 mm and DP980/1.2 mm were similar to the ‘optimized’ blank shape for Al5182-O/1.2 mm. The flow stress curve

and the material properties for DP780 and DP980 are shown in Figure 55 and Table 10

respectively. It is assumed that the material properties and flow stress curve for a 1.0 mm and 1.2 mm thick DP780 are the same, as only small differences in properties are observed

at low strain rates and temperatures for different thicknesses. Additionally, the materials

were assumed to be isotropic.

Two drawbead designs were considered:

1. The original drawbead built by Honda (Figure 36).

2. No drawbeads.

The reason for considering a case where no drawbead exists in the Honda part is because of lower formability and higher strength of DP780 and DP980 as compared to Al5182-O.

Hence, if a material like DP980 or DP780 does not form successfully (i.e. fracture in the

part) without drawbeads, then it cannot be formed with the Honda die set, irrespective of 71

the drawbead design. Like previous study, a constant of 0.07 was assumed. The FE

model setup was the same as the setup described in chapter𝐶𝐶𝐶𝐶𝐶𝐶 6.

Figure 55 Flow stress curves for DP780/1.0 mm and DP980/1.6 mm

The major strain at fracture under bending for DP780/1.2 mm and DP980/1.2 mm were chosen as 0.287 and 0.240 respectively, based on inverse analysis of 900 V-bending

experiments, covered in chapter 4. The major strain at fracture for DP780/1.2 mm

considered in this study and DP780A/1.2 mm, covered in chapters 3 and 4 was assumed to

be the same, as data under 900 V-bending experiments was not available for DP780

considered in this study and the material properties (YS, UTS and uniform elongation) for

both materials were similar. The fracture criterion under drawing for DP780/1.2 mm and

DP980/1.2 mm were 12 % and 10 % thinning respectively, based on industry

recommendations. Only ‘optimized’ blank shape was considered in this study. The

optimized blank shape and dimensions were observed to not change with change in

material.

Table 10 Material properties for DP780/1 mm and DP980/1.6 mm

The original drawbead design (built by Honda) was observed to not be severe during

drawbead formation, i.e. no cracking was observed for both 1.2 mm thick DP780 and

DP980 under bending (Figure 56 and Table 10). For the ‘no drawbead’ case, fracture under

bending was not a concern. Furthermore, the die corner radius (Figure 36) was high enough

to not cause any shear fracture for both the materials, 10 (critical stretch bend ratios 𝑅𝑅 𝑡𝑡 for DP780 and DP980 are listed in Table 7). DP980/1.2≅ mm could not be drawn

successfully with the Honda die set as the deformation conditions occurring in the part

were too severe for this material, irrespective of whether the drawbead was present or not.

Hence, DP980 will not be considered subsequently in this study.

Figure 56 Major strain distribution after bending under original drawbead built by Honda

Table 11 Max. Major strain after bending for DP780/1.2 mm and DP980/1.2 mm

The location of max. thinning or fracture after drawing remained the same irrespective of the presence of drawbeads in the tools, as seen in Figure 57. It was observed that a 1.2 mm thick DP780 could be drawn successfully (no fracture in the part) when no drawbeads were used, Table 12. The original drawbead design was found to be severe for DP780/1.2 mm.

Figure 57 Location of max. thinning or fracture when A) No drawbeads and B) Original

drawbead design built by Honda are used

Table 12 Evaluating possibility of fracture for different spacer heights when A) No

drawbead and B) Original drawbead design by Honda is used (Optimized blank used)

A spacer height of 1.15 is not recommended for forming the Honda part with DP780/1.2 mm, based on investigation𝑡𝑡 of possible fracture in the part for various spacer heights, Table 75

12. The stroke at fracture is higher for the case when no drawbeads are used in the die set, which is expected. A comparison of wrinkles was made at a stroke of 135 mm (Figure 58), between A) no drawbeads and B) original drawbeads. This is because of material fracture observed at a stroke of 137 mm for case B, Table 12.

Figure 58 Wrinkles in the part at a stroke of 135 mm, A) No drawbeads and B) Original

drawbead

Even though fracture was observed when the original drawbead was used, the wrinkles at the flange were reduced as compared to the case when no drawbeads were used (Figure

58). Furthermore, small wrinkles were observed in the drawn portion of the part when no drawbeads were used. Hence, a modification in drawbead design was proposed, to

simultaneously reduce the probability of fracture (under both bending and drawing) and

wrinkling in the part. The spacer height was subsequently kept as 1.25 in this study, as a lower spacer height led to fracture in the part for DP780/1.2 mm, Table𝑡𝑡 12.

7.2 Modified rectangular drawbead design

The drawbead design was modified to exert less restraining force on the sheet metal, as

fracture was observed on the original drawbead design built by Honda.

Initially, a change in the shape of the design from a circular to a rectangular drawbead was

considered. The rectangular drawbead parameters were chosen based on industry recommendations for AHSS. However, due to issues in the drawbead geometry at the corners, it was decided to keep the drawbead geometry circular. The geometric parameters of the rectangular drawbead is illustrated in Figure 59. The locations at which parameter

values are reported is shown in Figure 60 and the values have been reported in Table 13.

Figure 59 Geometric parameters for a rectangular drawbead 77

Figure 60 A drawbead region marked with points (1-3) at which parameter values have

been reported

Table 13 Rectangular drawbead geometric parameters at various points

The radii ( , ) and horizontal clearance ( ) in the rectangular drawbead become less

1 2 than the sheet𝑅𝑅 𝑅𝑅thickness (=1.2 mm) at points𝑋𝑋 1 and 3, shown in Figure 60. Hence, the possibility of fracture near the corners of the drawbead increased during bending

(Table 14). Moreover, the low drawbead radii ( , ) and clearance ( ) near the corners

1 2 of the rectangular drawbead region created additional𝑅𝑅 𝑅𝑅 restraining force𝑋𝑋 on the part during drawing, thus leading to early fracture (Figure 61).

Table 14 Max. major strain after bending for various drawbead designs

Thus, it was decided to use a modified circular drawbead as this eliminates the issues at the corners. The circular drawbead parameters (shown in Figure 62) do not pose problems at the corners. The parameter values of the original circular drawbead design at various points illustrated in Figure 60 is reported in Table 15.

Figure 61 Thinning distribution in the part during drawing, when using modified rectangular drawbead. Fracture at a stroke of 20 mm based on 12 % thinning fracture

criterion for DP780/1.2 mm

Figure 62 Geometric parameters for a circular drawbead

Table 15 Circular drawbead geometric parameter values at various points illustrated in

Figure 60

7.3 Modified Circular Drawbead Design

The drawbead parameters for a circular drawbead design are shown in Figure 62. The effect

of the geometric parameters on the severity of the circular drawbead are listed in Table 16

below. The severity of the drawbead is expressed qualitatively by the restraining force

exerted by the drawbead.

The bead radius ( ) and the groove depth ( ) do not affect the restraining force exerted

2 by the drawbead 𝑅𝑅for Honda part as the blank𝐷𝐷 is not in contact with these regions, both during bending (stages 2-3, Figure 13) and drawing (stages 3-4, Figure 13). When the drawbead height ( ) increases, the bending of the sheet in the drawbead region increases, hence increasing theℎ severity of the drawbead. Increasing the drawbead radius ( ) or the

1 drawbead entry/exit radius ( ) reduces the restraining force imposed by drawbead𝑅𝑅 region

3 due to bending of the sheet, 𝑅𝑅hence decreasing its severity.

Table 16 Effect of drawbead parameters on severity of drawbead design

The modified drawbead parameters and how it compares to the original drawbead parameters is shown in Table 17. The parameters highlighted in green were modified. The drawbead radius ( ) was increased to reduce the severity of the drawbead so that the

1 chances of forming𝑅𝑅 a 1.2 mm thick DP780 without fracture in the Honda part increase. The radius ( ) was decreased due to geometric restrictions imposed by the CAD model,

2 however𝑅𝑅 it did not affect the simulation results as the blank did not contact that portion of the drawbead.

Table 17 Original and modified drawbead design parameters (Values reported at point 2

in Figure 60)

7.4 Effect of modified circular drawbead design on possible fracture under bending

The major strain distribution after bending due to drawbead formation is shown in Figure

63. The cross section (A-A’) was chosen based on the location of maximum major strain in the part as observed from FE simulation. The maximum major strain after bending for the original and modified circular drawbead designs and how they compare to the major strain calculated at fracture is reported in Figure 63 and Table 18 respectively.

Figure 63 Major strain distribution after drawbead formation in Honda part

Table 18 Comparison of calculated major strain values from various deformation

conditions

It was seen from FE simulations that the sheet had approximately bent by 250 around the

drawbead region. This observation coupled with the fact that the drawbead radii (12

84 𝑚𝑚𝑚𝑚

for original drawbead design and 15 for modified drawbead design) were larger than

the bend radius at fracture (2 for𝑚𝑚𝑚𝑚 DP780A/1.2 mm for 900 V-bending), no fracture is expected during drawbead formation.𝑚𝑚𝑚𝑚

7.5 Effect of modified circular drawbead design on possible fracture during drawing

The spacer height and CoF values were kept as 1.25 and 0.07 respectively in FE simulations. 12 % thinning was considered as the fracture criterion𝑡𝑡 under drawing for a 1.2 mm thick DP780. The results obtained for modified circular drawbead geometry and how it compares with possibility of fracture for original drawbead geometry is reported in Table

19.

Table 19 Possibility of fracture in the part for original and modified circular drawbead

designs

The max. thinning in the part at the final draw depth (11.9 %, Table 19. See Figure 45 for

location of max. thinning/fracture) is very close to the fracture criterion for DP780/1.2 mm

(12 % thinning). Fracture may or may not occur in the part using the modified geometry, considering the variation in material properties for DP780/1.2 mm. However, an improvement is expected over the original drawbead design built by Honda. Additionally, negligible differences in wrinkling were observed when using original and modified drawbeads.

A comparison of tool (die and binder) forces among various drawbead configurations was obtained from FE simulations and are shown in Figure 64 and Figure 65 below. Higher tool forces were observed when drawbeads were used because of additional force required to bend the sheet metal under the drawbead continuously throughout the stroke.

The drawbead design can also be modified to affect the tool forces in a given process. An example of this effect is shown in Appendix A where the tool forces during drawing using two different drawbead configurations (edge bead and a rectangular drawbead) are compared for an example part. Edge bead is also called the half bead, representing one half of a rectangular drawbead. Edge beads are typically used in large parts where saving tonnage is a requirement. The effect of edge bead design on possible fracture, lock forces and wrinkling in Honda part is not within the scope of this study.

Figure 64 Die force vs. stroke curve for various drawbead configurations

Figure 65 Binder (Blank Holder) force vs. stroke curve for various drawbead

configurations

Chapter 8. Summary, Conclusions & Future Work

8.1 Summary

This document included a literature review of the existing criteria to determine possible

fracture under bending and stretch bending (superimposed bending and stretching) when

drawing with drawbeads and spacers. Subsequently, a study was conducted on an example die set to suggest possible improvements on spacer height, lubrication and drawbead design. A list of the tasks performed are described below:

1. A literature review summarizing the existing fracture criteria like limiting bend ratio

under 900 V-bending test, bend angle at fracture from wedge bend test and the modes

of fracture in a material subjected to drawing and their criteria was performed.

2. ‘Critical major strain’ for some example materials were evaluated using their limiting

bend ratios using FE simulations conducted in DEFORM 2D. These values were

subsequently used to evaluate possible fracture under bending in drawbeads.

3. The critical R/t under stretch bending and thinning at fracture were used among other

criteria to evaluate possible fracture at die corner radius and drawbead exit radius under

drawing.

4. The effect of blank optimization, spacer height and Coefficient of Friction (CoF) on

possible fracture, wrinkling, draw-in and tool forces were investigated for an example

part built by Honda.

5. The effect of changes in material and drawbead design on the aforementioned variables

were investigated for the die set built by Honda.

8.2 Conclusions

The main conclusions for this study are as follows:

1. Fracture limits for a given material under bending can be evaluated through a

combination of 900 V-bending experiments and FE simulations.

2. The Coefficient of Friction (CoF) does not affect the strain and thinning distribution in

900 V-bending.

3. Critical R/t under stretch bending (obtained from Bending Under Tension (BUT) and

Shear Fracture (SF) Forming tests) can help in designing of drawbead exit radius and

die corner radius.

4. Maximum thinning can be used to predict possible fracture under drawing, assuming

no shear fracture is observed.

5. FE simulations can predict with reasonable accuracy the draw-in of the material (i.e.

flange length).

6. Blank shape optimization can lead to more uniform flange shape and reduced thinning

in the drawn part.

7. Optimizing the blank using software like AutoForm or PAM-STAMP allows to have

more flexibility when it comes to choosing a spacer height or a lubricant for a drawing

operation containing drawbeads and spacers (i.e. a larger range of Coefficient of

Friction values and spacer heights are acceptable).

8. The ‘best’ spacer height depends on:

a. Metal flow (forming the part without fracture and wrinkles) and

b. Press and cushion capacities.

9. A larger drawbead radius reduces the possibility of fracture in drawing, while having a

similar effect on wrinkling, die and blank holder forces. However, a change in

drawbead design may significantly affect the tool forces, in Appendix A.

8.3 Future Work

The following studies can be considered for future work:

1. The effect of change in thickness for a given material on critical major strains under

bending can be investigated. 900 V-bending experiments coupled with FE simulations

for two different thicknesses of the same materials can be conducted and compared.

2. The effect of bend direction (parallel or perpendicular to rolling direction) and coating

on limiting bend ratio ( ) of a material needs to be investigated, as the differences in

cannot be explained by𝑓𝑓 the macroscopic material properties (YS, UTS and uniform𝑓𝑓

elongation).

3. The effect of lubrication conditions (or coefficient of friction) on critical R/t under

stretch bending needs to be investigated. Additionally, the effect of sheet direction

(rolling or transverse) on the Shear Fracture (SF) Forming tests should be explored. 90

4. The effect of individual drawbead parameters (drawbead radii, drawbead height etc.)

on fracture, wrinkling, tool forces and draw-in can be investigated so as to make

modifications in the drawbead design (if required) based on the desired stretching, force

or flange length requirements.

5. The possibility of considering elastic deflections on the die and the press, thus

accommodating different spacer heights on different locations of the part can be

explored. The tools were assumed to be rigid in the FE simulations for this study. The

elastic deflections on the die will lead to using different spacer heights at different

locations of the part.

6. The effect of binder/blank holder slope on possible fracture, tool forces, wrinkling and

draw-in of a part containing drawbeads and spacers can be analyzed. In some cases, the

binder is allocated a slope to allow for thickening of the sheet metal.

7. The possibility of optimizing the restraining forces at different locations of the part by

variable drawbead penetration using Multiple Point Cushions (MPC) cushion

technology can be explored.

8.4 Proposed guidelines for successful drawing

This study aims to propose some guidelines for successful drawing of any given material and final part geometry, containing drawbeads and spacers. These simple guidelines can be implemented using FE software like AutoForm and PAM-STAMP and seeks to reduce

the time and costs associated with die try-outs, die and drawbead design. The proposed

guidelines are as follows:

1. Given the part geometry and the material/thickness, the blank shape needs to be

optimized. This ensures that the part formed has a lower possibility of fracture and a

uniform flange shape, thus making it easier to trim the extra flange region.

2. Once the blank shape is optimized, the ‘best’ spacer height and lubrication conditions

for forming the part (no fracture/splits in the part and no wrinkles on the sidewall)

should be estimated. Even though FE simulations assume a constant spacer height and

CoF throughout the part and neglect elastic deflections, they help in providing an

estimate.

3. If a given material still fractures or wrinkles at the sidewall after estimating the ‘best’

spacer height and CoF for a given die set, then it is proposed to modify the drawbead

design to alter the severity of stretching imposed on the part.

References

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formability characterization of various types of high strength dual phase steel (No.

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May/June 2019, pg. 20,22.

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guideline (No. 2005-01-0499). SAE Technical Paper.

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Appendix A: Comparison of tool forces between edge bead and rectangular drawbead

designs

A fictitious example part was simulated in AutoForm to estimate the effect of edge bead

design on tool forces. The geometry of the part is shown in Figure 66 and the geometric parameter values are shown in Table 20. At the time when this study was conducted,

AutoForm did not have ‘Thickness Shell’ elements (TS-11) available. Hence, Elasto-

Plastic Shell elements (EPS-11) were used to model the blank. The tools were modelled as

rigid. The blank holder was modelled using the ‘gap controlled’ option with a constant gap of 1.32 mm (1.1 ).

The material considered𝑡𝑡 for this study was DP780/1.2 mm. The flow stress curve and material properties for DP780 are described in Figure 55 and Table 10 respectively. The length of the blank was 440 mm and the width of the blank was set to 120 mm, to achieve a plane-strain like deformation. The CoF value was assumed to be 0.1 as the CoF did not affect the strains and thinning values for this specific case. Additionally, the clearance ( ,

Figure 66) was equal to the sheet thickness ( ) as there are no corners in this fictitious part,𝑐𝑐 hence no thickening. The draw depth was chosen𝑡𝑡 as 40 mm.

Figure 66 Half-model of the fictitious part to compare tool forces between rectangular

and edge drawbead design

Table 20 Geometric parameter values for the considered fictitious part

The two drawbead designs and their corresponding geometric parameters are shown in

Figure 67 and the geometric parameter values are shown in Table 21.

Figure 67 a) rectangular and b) edge drawbead designs with their associated geometric

parameters

Table 21 Geometric parameter values for a) Rectangular and b) Edge drawbead

Both the drawbead geometric parameters were chosen based on industry recommendations, such that a horizontal restraining force of 40% of the Ultimate Tensile Strength of DP780.

Hence, a comparison of die force was made between edge bead and rectangular drawbead geometries which exert a similar stretch on the drawn part.

The die force vs stroke curves for both considered drawbead geometries are shown in

Figure 68. The values of max. die force after bending and drawing are shown in Table 22.

During bending, the die force on the edge bead is more than the rectangular drawbead (by around 20 %). This may be because of smaller drawbead radii in the edge bead, thus requiring more force to bend the sheet in the drawbead. However, after drawing, the die force when the edge bead design is used is lower (by around 16 %).

Hence, the edge bead design may be useful when drawing large parts containing drawbeads and spacers, as saving tonnage becomes very important for large parts. Furthermore, an investigation of the effect of drawbead design on draw-in of the material (indirectly related to material savings) may need to be conducted in the future.

Figure 68 Comparison of die force vs stroke curves between edge and rectangular

drawbeads

Table 22 Max. die force for both drawbead designs after bending and after drawing

100