MASTER’S THESIS IN ENGINEERING PHYSICS1217561/FULLTEXT01.pdf · Master’s thesis, Civilingenj orsprogrammet i teknisk fysik, Ume a University. Evelina Salomonsson, [email protected]

MASTER’S THESIS IN ENGINEERING PHYSICS

Investigation of factors affecting crackingduring forming of truck cab body parts

Evelina Salomonssonhejhejhej

June, 2018

Master’s thesis, Civilingenjorsprogrammet i teknisk fysik, Umea University.Evelina Salomonsson, [email protected].

Investigation of factors affecting cracking during forming of truck cab body parts is a project done in thecourse Master’s thesis in engineering physics, 30.0 ECTS at the Department of Physics, Umea University.

External supervisor: Par Myrlund, Pressing & Part Production, Volvo GTO EBM Umea.Internal supervisor: Alexandr Talyzin, Department of Physics, Umea University.Examiner: Ove Andersson, Department of Physics, Umea University.

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”If you can’t explain it simply, you don’t understand it well enough”- Albert Einstein

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To my beloved parents

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AbstractSheet metal forming is a technique widely used in todays industries as it enables fast transformation ofmetal sheets into parts of various shapes and sizes. Volvo GTO EBM in Umea uses sheet metal formingin their production of truck cab body parts, and a challenge common for all industries using this techniqueis to avoid cracking in the formed metal. The present study has been conducted in order to increasethe understanding of why produced articles sometimes crack, so that cracking can be prevented in futureproduction. This has been done by studying how different variations in the production process are affectingthe robustness of produced articles, partly by investigating variations in material properties and partly byrunning robustness simulations of a chosen article prone to crack. Material properties have been gatheredfor both cracked and non-cracked details of different articles, and thereafter been compared to each otherusing multivariate analysis. Furthermore, simulations have been run using the software AutoForm with thepurpose to investigate factors such as feeding direction of metal sheets, variations in material propertiesand different forces and velocities used during forming. Experiments have also been conducted in order tocompare the simulation model and simulation results with reality. From the material property analysis itcould be seen that differences in material properties do exist between cracked and non-cracked materials, butthat these differences vary between different articles. The robustness simulations indicated that a certainforce called draw cushion force do affect the final robustness of an article the most, compared to the otheraffecting factors investigated in this study. Moreover, the simulation set-up did seem to agree with reality,while the simulated material thinning deviates more than 20 % from the real one. This may result froman inadequate modeling of friction in the simulations. In conclusion, material properties are importantconcerning cracking during sheet metal forming, and the draw cushion force seems to have the strongestinfluence on article’s final robustness.

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SammanfattningPlatformning ar en teknik som anvands i stor utstrackning i dagens industrier da den mojliggor en snabbomvandling av metallplatar till produkter av olika former och storlekar. Volvo GTO EBM i Umea anvanderplatformning i deras produktion av karossdetaljer till lastbilar, och en utmaning som ar gemensam for allaindustrier som anvander denna teknik ar att undvika sprickbildning i den formade metallen. Denna studiehar genomforts till syfte att oka forstaelsen for varfor producerade artiklar ibland spricker, sa att sprickorkan forebyggas i framtida produktion. Detta har gjorts genom att studera hur olika variationer i produk-tionsprocessen paverkar hallfastheten hos producerade artiklar, delvis genom att undersoka variationer imaterialegenskaper och delvis genom att simulera hallfasthet hos en utvald artikel benagen att spricka.Materialegenskaper har sammanstallts for bade spruckna och icke-spruckna material, varefter de jamfortsmed varandra med hjalp av multivariat analys. Vidare har simuleringar korts i programvaran AutoFormmed syfte att undersoka faktorer sasom valsriktning pa platar, variationer i materialegenskaper samt olikakrafter och hastigheter som anvands under formning. Experiment har dessutom genomforts for att mojliggorajamforelser mellan simuleringar och verklighet. Fran materialanalysen kunde ses att det finns skillnader i ma-terialegenskaper mellan spruckna och icke-spruckna material, men att dessa skillnader varierar mellan olikaartiklar. Hallfasthetssimuleringarna indikerade att en viss kraft kallad mothallskraft paverkar den slutgiltigahallfastheten hos en artikel mest, jamfort med ovriga faktorer undersokta i denna studie. Vidare verkadeuppstallningen i simuleringen overensstamma med verkligheten, medan den simulerade materialfortunnin-gen avviker mer an 20 % fran den verkliga. Detta kan resultera fran en bristfallig modellering av friktioni simuleringarna. Sammanfattningsvis verkar materialegenskaper vara en viktig paverkande faktor gallandesprickbildning vid platformning, samt verkar mothallskraften ha storst inflytande pa en artikels slutgiltigahallfasthet.

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AcknowledgementAs an engineering physicist who has spent a big part of the last years diving into abstract theorems andequations, I have really enjoyed the mixture of theoretical and practical work with this thesis. I have feltlike a true engineer. During this thesis work I have learned incredibly much about sheet metal forming anddifferent material properties, but also encountered many challenges. I hereby invite you to follow me throughmy journey in the search of factors affecting cracking during forming of truck cab body parts.

Before we start, I would like to send a couple of thanks to the people who have made this thesis possible.First and foremost I would like to thank my supervisor and colleagues at the Pressing & Part Productiondepartment at Volvo GTO EBM in Umea for introducing me to the world of sheet metal forming. I deeplyappreciate your will to help and all the time you spend on, with great enthusiasm, sharing your knowledge.Finally, a big thank you to my beloved family who always has supported me through thick and thin andmakes sure I always have something to look forward to. You constantly fill me with energy and joy.

Let the journey begin.

Evelina Salomonsson,Umea, Sweden,12 June, 2018.

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Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theory 32.1 Material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Tensile testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Visualizing multivariate data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Mechanical sheet metal forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 Deep drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3.2 Forming window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Robustness analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4.1 Forming limit diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4.2 Robustness requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Method 93.1 Material analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.1 Feeding directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.2 Draw cushion forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.3 Real variation in material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.4 Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3.1 Tool balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3.2 Actual thinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Results 144.1 Material analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.2.1 Feeding directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.2.2 Draw cushion forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2.3 Real variation in material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.4 Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

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CONTENTS CONTENTS

4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Discussion 265.1 Material analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2.1 Feeding directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2.2 Draw cushion forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.2.3 Real variation in material properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.2.4 Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6 Conclusions & future improvements 30

Appendix A Simulations IA.1 Press settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IA.2 Motion curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV

Appendix B Matrix scatter plots V

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Chapter 1

Introduction

1.1 Background

Sheet metal forming plays a vital role in todays industries. The process is for example used in the productionof both soda cans and airplane wings and transforms metal sheets into parts of various shapes and sizesthrough something that is called plastic deformation. How this plastic deformation is achieved varies, asthere exists a number of different forming techniques. Air, liquids and mechanical tools are some examplesof what is used to achieve the desired geometry of a metal product [1].

One of many industries dependent on sheet metal forming is the trucking industry, where the metalforming is used in the manufacturing of truck cab body parts. Currently, Volvo Trucks is one of theworld leading truck brands and manufactures a large proportion of their truck cabs at Volvo Group TrucksOperations Europe & Brazil Manufacturing (GTO EBM) in Umea. Their truck cab manufacturing processconsists of the three main sub-processes metal processing, part assembly and surface treatment, and it is inthe metal processing part of the production that we find sheet metal forming. Volvo GTO EBM in Umeauses mechanical presses and tools in their production of truck cab body parts, whereupon one step in theirprocess is to send metal sheets through a number of presses. During this process cracks are sometimes formedin the processed metal, and their cause is currently unknown.

1.2 Purpose

The purpose of this master’s thesis is to study factors affecting cracking during forming of truck cab bodyparts, in order to find out how their variations affect the robustness of produced articles. This work increasesthe understanding of why articles crack, so that the cracking can be prevented in future production.

1.3 Objectives

There are two goals with this master’s thesis. The first goal is to investigate potential connections betweencracking and material properties. The second goal is to investigate, using simulations, how different variationsin the production process are affecting the robustness of articles prone to crack. More specifically, these goalscan be described by the following objectives:

i Compile data regarding material properties of articles prone to crack. This includes ordered and deliveredmaterial specifications, together with actual material properties obtained from tensile testing.

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1.4. DELIMITATIONS CHAPTER 1. INTRODUCTION

ii Perform a material analysis where the different material properties are to be compared between crackedand non-cracked materials.

iii Investigate the variation in material properties for an article prone to crack.

iv Plan and run simulations of the robustness of the chosen article prone to crack. This includes definingnoise variables of interest and their ranges.

v Perform robustness analysis based on the simulation results and compare with performed material ana-lyzes.

vi Conduct experiments with purpose to investigate if the simulations are consistent with reality.

1.4 Delimitations

Creating new specifications for material or equipment is not included in this thesis. Furthermore, the materialanalysis is delimited to investigating potential differences between expected and actual material quality ofcracked and non-cracked details. Only one specific article is considered when investigating the robustness ofarticles prone to crack and only the deep drawing operation is taken into account in the simulations. Thedeep drawing operation is described in chapter 2.

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Chapter 2

Theory

This chapter starts with treating important material properties of metals and how they can be determined.Thereafter the chapter gives a brief introduction to sheet metal forming, with focus on mechanical formingprocesses which are used at Volvo GTO EBM in Umea. Finally, descriptions of the software used to performthe robustness analysis and methods for visualizing multivariate data are described.

2.1 Material properties

The first step towards an understanding of sheet metal forming is to get familiar with the concepts stress andstrain. Stress is a physical quantity defined as the force per unit area of a material, while strain describesa material’s deformation. Stress consists of several components and a force acting normal to a plane resultsin either tensile or compressive stress. On the other hand, a force acting parallel to the plane will give riseto shear stress [2, ch. 1]. The strain, which can be described as the ratio between extension and originallength of an element, describes the deformation of a material, and this deformation can be either elastic orplastic. An elastic deformation is a deformation where the material returns to its original shape after theapplied stress is removed, while a plastic deformation is permanent. Exactly how much stress a materialcan manage without beginning to deform plastically is called the yield strength of the material and it variesbetween materials. This and five other material properties are described further below.

In sheet metal forming, it is crucial to understand the mechanical properties of sheet metals since theseproperties strongly affect the final formability and strength of a produced product. At Volvo GTO EBM inUmea, several material properties are taken into consideration before ordering a material. Which character-istics are desired depend on application and can be everything from high strength to smooth surface. Thefollowing six properties are taken into consideration when ordering materials at Volvo GTO EBM.

Strain hardeningThe strain hardening exponent n of a material describes the increase in strength and hardness that resultfrom a plastic deformation. The exponent is used to describe tension as a function of plastic strain in LudwikHollomon’s equation

σ = Kεn, (2.1)

where σ is the tension, K is a material constant and ε is the plastic strain [3, p. 2:2]. The exponent has avalue below 1 but above 0, and an increase in n leads to greater strain hardening. n can thus be describedas a material’s ability of distributing strains.

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2.2. VISUALIZING MULTIVARIATE DATA CHAPTER 2. THEORY

Plastic strain ratioA material’s ability to resist thinning or thickening can be described by its plastic strain ratio r - also calledLankford coefficient. This value is a measure of the plastic anisotropy of a material and r is defined as theratio of the true strain in the width direction to the true strain in the thickness direction when a materialis pulled in uniaxial tension beyond its yield point (point at which the yield strength is reached). Assumingthat the specimen volume remains constant during the test, the plastic strain ratio can be described by

r =ln(w0/wf )

ln(Lfwf/L0w0), (2.2)

where w0 and wf are the initial and final widths of the specimen and L0 and Lf its initial and final lengths [4].A higher plastic strain ratio of a material thus means a better ability to resist thinning or thickening.

ElongationThe elongation, sometimes denoted A80, is a measure of how much a material is elongated before it breaks.This value is often measured in mm for a material sample with a length of 80 mm, whereof the denotation.

Tensile strengthTensile strength, Rm, is the maximum stress a material can sustain before breaking [5] and is usually givenin MPa.

Yield strengthAs mentioned in previous section, the yield strength of a material is a measure of the maximum stress thematerial can manage without beginning to deform plastically. The point at which this transition betweenstates occur is referred to as the yield point of the material, and is considered to be the most importantproperty of a material’s strength [6]. The yield strength is often measured in MPa as the stress causing 0.2% plastic deformation in the material and is therefore denoted Rp0.2.

Surface roughnessSurface roughness, Ra, is often given in µm and is as the name implies a measure of smoothness of amaterial’s surface. A higher value of the surface roughness means greater deviations in the surface structureand hence a rougher surface [7].

2.1.1 Tensile testing

So how do we determine all these material properties for a specific material? One powerful method thatis commonly used is tensile testing. In tensile testing, a material test specimen is put into a testing ma-chine where it is stretched until it breaks. During this process tension, stress and strain are measured [8].Elongation, tensile and yield strength can thus be obtained from a tensile test, together with the strainhardening coefficient and plastic strain ratio by using eqs. (2.1) and (2.2). The last material property,surface roughness, is measured by instruments made for measuring the surface topography of a material.

2.2 Visualizing multivariate data

Multidimensional data sets, such as material properties for different materials, can be described and ana-lyzed using multivariate analysis - different statistical methods used for analyzing multivariate data. Thesemethods have a number of different purposes, one is to visualize potential differences or connections betweendata sets [9]. One way to achieve this visualization is to make use of the built in functions in the software

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2.3. MECHANICAL SHEET METAL FORMING CHAPTER 2. THEORY

MATLAB developed by MathWorks®. This software has, among a wide variety of other features, a numberof functions able to visualize high dimensional data. The functions used in the work with this thesis aredescribed below.

Matrix scatter plotPotential correlations between variables can be visualized by a matrix scatter plot. Given an n×m matrixwhere n is the number of observations in the data set and m is the number of variables for each observation,the MATLAB function plotmatrix generates m ×m pairwise plots for the variables of all observations inthe data set [10].

Parallel coordinates plotA parallel coordinates plot visualizes multidimensional data by representing each observation in a data setby a polygonal curve. Each curve is specified by the coordinate values for corresponding observation as afunction of coordinate indices. This is a function called parallelcoords in MATLAB [11].

2.3 Mechanical sheet metal forming

As mentioned in previous chapter, there exists a number of different sheet metal forming techniques. Onecommon technique, which is used at Volvo GTO EBM in Umea, is to use mechanical tools and presses inthe forming process of an article. When producing a detail in this kind of process, multiple operations aremostly needed in order to achieve the final product. These operations can be divided into two main groups;forming operations and cutting operations [3]. A forming operation can include everything from bendingand flanging to deep drawing and restrike. Bending and flanging operations bend parts of a detail whiledeep drawing operations are used to achieve more complex shapes of a product. Restrike operations areforming operations used for compensating potential deviations in the shape of a detail resulting from otheroperations such as cutting operations. Cutting operations punches holes in a detail and cuts off any excessmaterial.

When it comes to cracks, they are usually formed during the deep drawing operations. That is whenthe material is subjected to the greatest stress. Below follows a more detailed description of a deep drawingoperation.

2.3.1 Deep drawing

An illustration of the main components of a deep drawing tool can be seen in fig. 2.1. The tool, also calleddie, consists of an upper part called matrix and a lower part containing a blankholder and a punch. Thedeep drawing tools at Volvo GTO EBM in Umea has a fixed punch, while the blankholder and matrix arefree to move up and down. During the forming operation, the matrix is lowered down and met up by theblankholder after which they together hold the blank sheet metal in place as they finally pull it down overthe punch. The drawbeads placed on the blankholder is used to control the material flow into the tool duringforming. By varying their size and number, the resulting friction can be optimized so that a desired materialstretch can be obtained for the produced article [2, ch. 17].

Tools at Volvo GTO EBM in Umea also have components called balancing blocks. These are mounted onthe blankholder and are used for tuning the contact between blankholder, sheet metal and matrix. By addingsmall spacers called shims between the blankholder and the balancing blocks, contact and force distributioncan be optimized.

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2.3. MECHANICAL SHEET METAL FORMING CHAPTER 2. THEORY

Figure 2.1: Illustration of the main components of a deep drawing tool.

The blankholder is pushed upwards by a pressure cushion placed in the bottom of the press. The forceby which the pressure cushion is pushing the blankholder can be varied and is hereinafter referred to asthe draw cushion force. The part of the press to which the matrix is attached is called the press slide andthe force with which this press slide is lowered down is simply called slide force. Furthermore a formingoperation, hereinafter called cycle, involves several different velocities. At the beginning of the cycle, thepress slide and attached matrix are lowered down with a downward speed specific for the press. Then, duringthe forming motion, the slide and matrix are traveling at a certain percentage of an operating velocity thatvaries depending on cylinders used in the press and on article. Finally when the forming motion is complete,the slide and matrix stay fixed at the bottom during a set bottoming time and then travels back to theiroriginal positions at a return speed, which also depends on the press. Neglecting variations in velocity dueto acceleration, the total time for one cycle can be described by

ttot =s↓v↓

+sfvf

+ tb +s↑v↑, (2.3)

where s↓ is the distance the slide and matrix travels at downward speed v↓, sf is the distance they travel ata certain operating velocity vf , tb is the bottoming time and s↑ is the distance they travel at upward speedv↑.

2.3.2 Forming window

Before an article enters production, the press settings for corresponding press tools need to be specified.This is done by a number of try-outs, where the article is formed and examined using a number of differentpress settings. Guidelines for the slide- and draw cushion forces are obtained from simulations made in thedevelopment phase of the article, but the values then need to be tuned and adapted to the real-life presses.The last step in this try-out process is to create a forming window in a so called home line try-out. This isthe final tuning needed in order to make the tools work as good as possible in the presses that are going tobe used in the production of the article. By reducing the draw cushion force until wrinkles appears on thearticle and then increasing it until cracks occur, critical lower- and upper force limits are obtained for thearticle. The forming window is then, according to Volvo GTO EBM standard, defined as the window holding

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2.4. ROBUSTNESS ANALYSIS CHAPTER 2. THEORY

a 10 % margin to these limits. During production, it is allowed to vary the draw cushion force within thiswindow, and this is generally the approach used when cracks occur.

2.4 Robustness analysis

Important tools in modern industries are simulation softwares which enable fast analysis of processes andequipment, together with the possibility to generate and evaluate new solutions and setups. AutoFormEngineering GmbH provides such software for the sheet metal forming industries. Their products range fromsolutions for product development and production planning to tool manufacturing and part production [12].With help of the AutoForm software the whole forming process can be simulated - from a blank metal sheetto a finished article. One of the AutoForm modules is called AutoForm-Sigma®plus and enables thoroughanalysis of how the robustness of an article is affected by different parameters in the forming process.Resulting properties such as formability and thinning of a produced article can be investigated by specifyingvariables of interest and their ranges.

2.4.1 Forming limit diagram

An important starting point in robustness analysis is the forming limit diagram. A forming limit diagramshows the strains that lead to failure during forming of a material. By etching a circular grid on the materialsurface prior to forming, the principal strains can be obtained by measuring the minor and major diametersof the, after forming, outstretched circles. Failure conditions can then be obtained by measuring these valuesat necking [2, ch. 16]. Necking is a name for the localized thinning that appears right before rupture [3,p. 5:7]. An illustration of a forming limit diagram can be seen in fig. 2.2 below. The three dotted ellipsesin the figure represents the different deformations of a circle exposed to uniaxial tension, plane strain andbiaxial stretching respectively [13].

Figure 2.2: Schematic of a forming limit diagram with major strain on the y-axis and minor strain on the x-axis.The dotted ellipses illustrate different deformations of a circular grid etched on a material surface which has beenexposed to forming. The circles are, from left to right, exposed to uniaxial tension, plane strain and biaxial stretchingrespectively.

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2.4. ROBUSTNESS ANALYSIS CHAPTER 2. THEORY

2.4.2 Robustness requirements

At Volvo GTO EBM in Umea there are certain requirements for the robustness of a produced article. Onegeneral requirement is that the material is allowed to undergo a maximum thinning of 20 % during theforming process. Another requirement is that a safety margin of 40 % must be held to the failure limitgiven in the forming limit diagram in question, i.e. the major strains on a formed material are allowed tobe maximum 60 % of the major strains of the failure limit for the material. This limit is called maximumfailure in AutoForm.

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Chapter 3

Method

Potential factors affecting cracking have been investigated partly through a material analysis, partly throughrobustness simulations. Furthermore physical experiments have been carried out in order to verify that thesimulations are consistent with reality. This chapter starts with a description of the material analysis andcontinues with a description and explanation of the simulations. Finally, the methodology for the experimentsis clarified.

3.1 Material analysis

3.1.1 Data collection

Articles prone to crack were identified from an existing summary presenting so called work orders resulting incracked details produced during the beginning of the production year 2017. A work order holds informationabout the articles that should be produced, how many and out of which materials they should be made.From the summary it could be seen in which work order cracks had appeared and at which date. Dependingon the work order size, more than one sheet metal coil can be needed to produce the specified amount of anarticle. However, from which coil a cracked detail originated could neither be seen in the summary, nor betraced in any other way. As a result, the material properties of details belonging to a work order extendingover more than one coil could not be traced. These details could thus not be included in the study - witha few exceptions where the specific coils could be localized with help of documented dates. Work ordersthat contained details that had cracked during the end of the production year 2017 were identified fromproduction reports from the same year, and their corresponding sheet metal coils were identified as earlier.Considering these articles that had cracked during 2017, details produced during 2016 and the first threemonths of 2018 were also included in the analysis.

After summarizing all details that could be traced to specific coils, the material properties of each coilwere compiled. First, material properties were gathered from ordered material specifications containingthe recommended upper- and lower limits of each property. Secondly corresponding properties were takenfrom the delivered material specifications, i.e. values specified by the material suppliers. Lastly, availableinformation obtained from tensile tests was gathered. This included values of tensile strength, yield strengthand elongation.

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3.2. SIMULATIONS CHAPTER 3. METHOD

3.1.2 Analysis

All material properties were imported to the computing environment MATLAB, where they were comparedwith each other. Since different articles are of varying shapes and made out of different materials, thematerial properties of an article were not compared to those of other articles. Furthermore, the materialsummary did contain limited amounts of data for some articles, whereby only articles made out of at leastfive different cracked materials were included in the following analysis.

First, potential correlations between properties were investigated by generating a matrix scatter plotfor each article using the MATLAB function plotmatrix. Both cracked and non-cracked materials wereincluded in each plot. Then median values of the non-cracked material properties were calculated for eacharticle. These were then used to calculate quotas between all properties and their corresponding medianvalue, in order to easier be able to compare different variations within the data. This was also done forthe ordered lower- and upper limits for each property. Parallel coordinates plots were thereafter made fromthese quotas using the function parallelcoords, to be able to examine all the material properties at once.The plots were made displaying median values together with 25- and 75 percentiles for both cracked andnon-cracked materials.

Thereafter, quotas were calculated between the material properties obtained from tensile tests and corre-sponding delivered properties. This was done to be able to compare values between different articles, whichwas needed since few data obtained from tensile testing were available. These quotas were then compiled ina parallel coordinates plot displaying median values together with 25- and 75 percentiles for both crackedand non-cracked materials. All available tensile test data were included in the plot.

Finally, the variation in material properties was investigated for a chosen article prone to crack - articleA. This was done by taking the compiled data for that specific article and calculating mean, max and minvalues together with standard deviations for all properties.

3.2 Simulations

The robustness of article A was chosen to be simulated since this article has been, and still is, prone to crack.Moreover, the variation in material properties was investigated for this article. Article A is formed togetherwith the mirrored article B, whereupon also this article is included in the simulations. Both articles do crackfrom time to time.

The simulations were based on existing scans of the deep drawing tool for the articles and current presssettings retrieved from the presses. Screen shots of these settings can be found in figs. A.1 and A.2 inAppendix A.1. Furthermore a material file provided by the material supplier was used as material model inthe simulations.

3.2.1 Feeding directions

First, two simulations were run with the settings found in Appendix A.1. The friction, draw cushion force,tensile and yield strength, plastic strain ratio and sheet metal position in x- and y-direction were chosenas noise variables with ranges specified according to AutoForm-Sigmaplus application guidelines. How thesevariables and their ranges were specified in AutoForm can be found in tab. 3.1 below. Furthermore, thesimulations were run with different feeding directions of the sheet metal; one with current feeding directionand one with a feeding direction perpendicular to the current one. This was done since it has been changedhow the article is cut out from the sheet metal and because some material properties, such as the plasticstrain ratio described in sec. 2.1, are directionally dependent.

10

3.2. SIMULATIONS CHAPTER 3. METHOD

Table 3.1: Shows how the noise variables friction, draw cushion force, tensile and yield strength, plastic strain ratioand blank position in x- and y-direction were specified in AutoForm-Sigmaplus.

Variable Min Max SDlube -10.00 % 10.00 % 3.33 %preloadForce -10.00 % 10.00 % 3.33 %Rm -10.00 % 10.00 % 3.33 %Sigma0 -10.00 % 10.00 % 3.33 %rm -20.00 % 20.00 % 6.67 %yPos -1.00 mm 1.00 mm 0.33 mmxPos -1.00 mm 1.00 mm 0.33 mm

Secondly, two new simulations were run as earlier but with a draw cushion force of 2100 kN instead of1200 kN. This partly because 2100 kN is the specified lower limit of the draw cushion force according to thepress setting instructions for the article, and party to be able to investigate if different feeding directions havedifferent effects when different draw cushion forces are used during forming. Moreover the draw cushion forceused during production of these articles usually varies between 1200 kN and 2100 kN. Lastly formability,thinning and maximum failure were investigated and compared between the different simulations.

3.2.2 Draw cushion forces

Considering the current feeding direction, two different draw cushion forces have until now been simulated;1200 kN and 2100 kN. According to the press setting instructions, the forming window for the articles liesbetween a draw cushion force of 2100 kN and 3000 kN while the nominal value is specified as 2500 kN. Twomore simulations were hence run as earlier, but with draw cushion forces 2500 kN and 3000 kN. After that,differences in formability, thinning and maximum failure between the different simulations were investigated.

3.2.3 Real variation in material properties

Two simulations were thereafter run using the real variation in material properties obtained for article A.In AutoForm, the strain hardening coefficient is automatically changed when the tensile strength is varied,whereby plastic strain, tensile and yield strength were set to the desired values while the strain hardeningcoefficient was defined by AutoForm. Two different draw cushion forces were used, 1200 kN and 2100 kN,and as earlier formability, thinning and maximum failure were investigated.

3.2.4 Velocities

As can be seen from the press settings shown in fig. A.1 in Appendix A.1, the forming motion used for thearticles chosen to be simulated is divided into two parts; one where the velocity is set to 70 % of the operatingvelocity and another where it is set to 100 %. A specific value of this operating velocity was not available,but it was needed in order to make the simulations as realistic as possible. In previous simulations, thisvelocity was set to a default value specified by AutoForm where it was constant during the whole formingmotion. To improve the simulations, an approximated motion curve was calculated by first approximatingthe operating velocity vf using eq. 2.3. Distances, cycle time and bottoming time were taken from availablepress settings described in Appendix A.1. Values of the press specific downward- and return speeds are,according to Volvo GTO EBM standard, 800 mm/s and 850 mm/s respectively. Taking the two differentforming velocities into consideration, eq. 2.3 can be rewritten as

ttot =s↓v↓

+s1

0.7vf+s2vf

+ tb +s↑v↑,

11

3.3. EXPERIMENTS CHAPTER 3. METHOD

where sf = s1 + s2. Solving for vf , the equation can be rearranged as follows.

ttot − tb −s↓v↓− s↑v↑

=1

vf

( s10.7

+ s2

)⇐⇒

vf =(s1/0.7 + s2)

ttot − tb − s↓/v↓ − s↑/v↑

Inserting values of all parameters gives the approximated operating velocity

vf =35/0.7 + 89.6

3.8− 0.2− 690/800− 814.6/850≈ 78.5 mm/s. (3.1)

Using the approximated operating velocity, a scaled motion curve was then calculated taking the twodifferent forming velocities into account. The cycle time was scaled from 0 to 1 and divided into 20 timesteps, as this was done in an example provided by AutoForm. Then, corresponding positions were calculatedfor each of the 20 points in time using the press downward speed and the approximated velocity obtainedin eq. 3.1. The positions were scaled such that the top position of the press slide corresponded to 1 and itsbottom position to 0. After that, the unscaled approximated motion curve was plotted in MATLAB andcompared to a motion curve obtained from the press computer during forming of articles A and B. Lastly,the scaled motion curve was imported to AutoForm and two simulations with draw cushion forces 1200 kNand 2100 kN respectively were set up and run.

To be able to investigate potential differences between current settings for the forming velocity and onewhere the operating velocity is set to 100 % during the whole forming motion, a new motion curve was madein the same way as earlier but with a constant forming velocity set to 100 % of the operating velocity. Asearlier, the motion curve was imported to AutoForm and two simulations with draw cushion forces 1200 kNand 2100 kN respectively were set up and run. Finally, the formability, thinning and maximum failure wereinvestigated and compared with the simulations made with varying forming velocity. The two motion curvesare described in tabular form in Appendix A.2.

3.3 Experiments

3.3.1 Tool balancing

The tool model in AutoForm on which the simulations are based, are made under the assumption thatnone of the balancing blocks are in contact with the matrix during forming. To check if this is true in thereal forming process, the contact surfaces for the balancing blocks were painted with a blue color prior toforming. Blue color on the balancing blocks after forming hence indicates that the blocks and matrix havehad contact.

3.3.2 Actual thinning

To be able to compare the real material thinning with the simulated one, four different deep drawingoperations for the article were run with different draw cushion forces; 1200 kN, 2000 kN, 2100 kN and 3000kN. The resulting thinning was then measured using a micrometer at three different locations of each rundetail. These locations, shown in fig. 3.1 below, were chosen at points where cracks usually occur. Eachof the measurements was repeated three times, after which the lowest value was noted. Quotas betweenthese lowest values and the original thicknesses of the sheets were then finally calculated in order to obtainpercentage thinning for all forces. The original thicknesses were assumed to be 2.00 mm.

12

3.3. EXPERIMENTS CHAPTER 3. METHOD

Figure 3.1: Image of a CAD model of the deep drawn articles A and B, with marked points at which thicknessmeasurements have been performed. The measurements were done both on real and simulated details.

13

Chapter 4

Results

In this chapter, results from the material analysis, robustness simulations and experiments are given in theform of illustrative figures and tables. The chapter starts with presenting the results obtained from thematerial analysis, after which the simulation results are explained. Finally, the results from the experimentsare presented.


Regarding the data collection, all cracked details listed in the summary were not available in correspondingproduction reports. Everything is not documented in these reports, whereupon the details listed in thesummary and not in the reports still were included in the analysis. Moreover only articles A, C, D and Ewere made out of at least five different traceable cracked materials, whereby these are the articles includedin the material analysis. Their corresponding matrix scatter plots for cracked and non-cracked materialproperties are described in Appendix B, and in these plots no clear differences can be seen between thecracked and non-cracked materials for any of the above articles. It seems like an elongation and yieldstrength above 43 % and 228 MPa respectively for article A result in no cracking. This also seems to be thecase for a plastic ratio above 2 and an elongation above 36 % for article D. Furthermore neither a plasticstrain ratio above 1.45, nor a tensile strength above 306 MPa for article E tend to result in any cracking ofthe materials.

Parallel coordinates plots for the four articles can be seen in fig. 4.1 below. As explained in previouschapter, median values of the non-cracked material properties were calculated and then used to calculatequotas between all properties and corresponding median value. The plots in fig. 4.1 displays median valuesand corresponding 25- and 75 percentile values for these quotas, together with ordered recommended lowerand upper limits for each property. The number of properties with specified limits varies between materials,whereby the length of these limit lines differ between the articles represented in fig. 4.1. As can be seen inthe figure, cracked details seem to have lower plastic strain ratio than non-cracked details for articles C, Dand E. The median value of this property is however larger for cracked materials than for non-cracked oneswhen considering article A. Considering the different yield strengths in fig. 4.1, the median value is lower forcracked details than for non-cracked ones when it comes to articles A and D. The opposite holds for articles Cand E. Furthermore, all median values together with their 25- and 75 percentiles lie within the recommendedlower- and upper limits for articles A, D and E for both cracked and non-cracked materials. For article C,the 75 percentile for surface roughness of non-cracked materials lies above its recommended upper limit.Common for all articles is that the values of plastic strain ratio, elongation and surface roughness vary themost between the different materials.

14

4.1. MATERIAL ANALYSIS CHAPTER 4. RESULTS

Figure 4.1: Parallel coordinates plots of material properties for articles A, C, D and E. The coordinate values onthe y-axes are quotas between delivered material properties and median values of non-cracked delivered materialproperties. Six different material properties are shown on the x-axes; the strain hardening exponent n, the plasticstrain ratio r, the elongation A80, the tensile strength Rm, the yield strength Rp0.2 and the surface roughness Ra.

Differences between delivered material properties specified by the material suppliers and actual propertiesobtained from tensile tests can be seen in fig. 4.2. The figure shows median values together with 25- and75 percentiles for quotas between properties obtained from tensile tests and delivered material properties.Considering the cracked materials, all mean values lie below one, which also holds for the tensile and yieldstrengths of non-cracked materials. Looking at the 25- and 75 percentiles, they lie further apart for crackedmaterials than for non-cracked ones. Common for all materials however, is that the elongation valuesobtained from tensile tests seem to have the largest deviations from corresponding delivered values whenconsidering the different properties presented in fig. 4.2.

15

4.1. MATERIAL ANALYSIS CHAPTER 4. RESULTS

Figure 4.2: Parallel coordinates plot of quotas between material properties obtained from tensile tests and corre-sponding properties specified by the material suppliers. Three different material properties are shown on the x-axis;the elongation A80, the tensile strength Rm and the yield strength Rp0.2. Visible in the figure are median valuestogether with 25- and 75 percentiles for both cracked and non-cracked materials.

The variation in material properties for article A is shown in tab. 4.1. As seen in the table, the plasticstrain ratio has the largest deviation from mean and also the largest standard deviation. Looking at thesurface roughness, this property has the second largest values for both deviation from mean and standarddeviation. Tensile strength shows the smallest deviation from mean, while the strain hardening exponenthas the smallest standard deviation.

Table 4.1: Real variation in material properties for article A. The table shows mean values, min and max values aspercentages of mean values, together with the standard deviation (SD) of each property. The properties presentedin the table are the strain hardening exponent n, the plastic strain ratio r, the elongation A80, the tensile strengthRm, the yield strength Rp0.2 and the surface roughness Ra.

Material property Mean Min (%) Max (%) SD (%)n 0.209 -9.15 9.97 2.73r 1.96 -13.18 106.83 12.00A80 40.24 % -13.01 16.81 5.46Rm 346.52 MPa -12.56 5.04 3.22Rp0.2 220.92 MPa -21.24 8.64 5.90Ra 1.28 µm -14.32 32.42 11.78

16

4.2. SIMULATIONS CHAPTER 4. RESULTS

4.2 Simulations


Formability plots of the simulated deep drawn articles A and B are shown in fig. 4.3 below. The left detailis simulated with current feeding direction, and the right detail with a feeding direction perpendicular tothe current one. Both simulations were run with a draw cushion force of 1200 kN. As seen from the figure,purple and blue color represents thickening and compression while the gray areas of the details representsinsufficient stretch. Splits is the name used for cracks in AutoForm. Comparing the two details, it is visiblethat current feeding direction results in more compression and thickening. There is however a small spotof compression between the two immersions at the top of the right detail that is not visible in the left one.Furthermore the center of the left detail is slightly greener than the right one.

Figure 4.3: Formability plots of the simulated deep drawn articles A and B. The left detail was simulated withcurrent feeding direction, while the right was simulated with a feeding direction perpendicular to the current one.Both details were simulated with a draw cushion force of 1200 kN.

The same plots as above but with a draw cushion force of 2100 kN instead of 1200 kN are presented infig. 4.4. In addition to that larger parts of the details are green, slightly more compression can be seen inthe left detail than in the right one.

17


Figure 4.4: Formability plots of the simulated deep drawn articles A and B. The left and right details were simulatedwith current feeding direction and a feeding direction perpendicular to the current one respectively. A draw cushionforce of 2100 kN was used for both details.

Maximum thinning and maximum failure limit for the different feeding directions and draw cushion forcesare presented in figs. 4.5 and 4.6 respectively. The figures display close ups of the two immersions in thedetail, and values of thinning and maximum failure at specific points are given in form of text labels in eachfigure. Generally, the current feeding direction seem to have both greater maximum thinning and highervalues of maximum failure for each of the different draw cushion forces. Furthermore all values for the drawcushion force 2100 kN are higher than corresponding values obtained from the simulations run with a drawcushion force of 1200 kN. All values of the maximum failure lie below the required limit of 60 %, while onlythe maximum thinning resulting from a draw cushion force of 1200 kN stays below the required limit of 20%.

18


(a) Simulation run with current feeding direction anddraw cushion force 1200 kN.

(b) Simulation run with a feeding direction perpendicularto the current one and a draw cushion force of 1200 kN.

(c) Simulation run with current feeding direction anddraw cushion force 2100 kN.

(d) Simulation run with a feeding direction perpendicularto the current one and a draw cushion force of 2100 kN.

Figure 4.5: Values of maximum thinning at locations prone to crack on simulated articles A and B. Each label inthe figure shows the thinning at a specific point, where -0.500 corresponds to a 50 % material thinning. The smallervalues to the right in each label correspond to the maximum and minimum thinning obtained at that point duringthe simulation.

19


(a) Simulation run with current feeding direction anddraw cushion force 1200 kN.

(b) Simulation run with a feeding direction perpendicularto the current one and a draw cushion force of 1200 kN.

(c) Simulation run with current feeding direction anddraw cushion force 2100 kN.

(d) Simulation run with a feeding direction perpendicularto the current one and a draw cushion force of 2100 kN.

Figure 4.6: Values of maximum failure limit at locations prone to crack on simulated articles A and B. Each labelin the figure shows values at a specific point, where 0.500 corresponds to a 50 % margin to the forming limit diagrampresented in section 2.4.1. The smaller values to the right in each label correspond to the maximum and minimumvalues of the failure limit obtained at that point during the simulation.


Formability plots of the two articles simulated with draw cushion forces 2500 kN and 3000 kN respectivelycan be seen in fig. 4.7. Both details are simulated with current feeding direction and from the figure it isvisible that a draw cushion force of 2500 kN results in slightly more compression than the higher force of3000 kN. Moreover, the gray areas in the right detail are slightly smaller than corresponding areas in theleft detail.

20


Figure 4.7: Formability plots of the simulated deep drawn articles A and B. The left detail was simulated with adraw cushion force of 2500 kN, while the right was simulated with a draw cushion force of 3000 kN. Both details weresimulated with current feeding direction.

Maximum thinning and maximum failure limit for the different draw cushion forces are, in the same wayas earlier, presented in figs. 4.8 and 4.9. From the figures it is visible that the higher draw cushion force of3000 kN results in greater maximum thinning and higher values of maximum failure, compared to the lowerdraw cushion force of 2500 kN. All values of maximum thinning exceed the required limit of 20 %, while novalues of maximum failure are greater than the maximum failure limit of 60 %.

(a) Simulation run with draw cushion force 2500 kN. (b) Simulation run with draw cushion force 3000 kN.

Figure 4.8: Values of maximum thinning at locations prone to crack on simulated articles A and B. Each label inthe figure shows the thinning at a specific point, where -0.500 corresponds to a 50 % material thinning. The smallervalues to the right in each label correspond to the maximum and minimum thinning obtained at that point duringthe simulation.

21



Figure 4.9: Values of maximum failure limit at locations prone to crack on simulated articles A and B. Each labelin the figure shows values at a specific point, where 0.500 corresponds to a 50 % margin to the forming limit diagrampresented in section 2.4.1. The smaller values to the right in each label correspond to the maximum and minimumvalues of the failure limit obtained at that point during the simulation.


Fig. 4.10 shows formability plots of two details simulated with draw cushion forces 1200 kN and 2100kN respectively and the real variation in material properties for article A given in tab. 4.1. Since thestrain hardening coefficient was automatically specified by AutoForm, the simulations were run with n =0.176 instead of n = 0.209 specified in tab 4.1. As earlier, purple and blue color represent thickening andcompression while the gray and green areas of the details represent insufficient and sufficient stretch. Asseen in the figure, the right detail is significantly more stretched than the left one.

Figure 4.10: Formability plots of the simulated deep drawn articles A and B. The left and right details weresimulated with draw cushion forces 1200 kN and 2100 kN respectively and with the real material property dispersionobtained from the material analysis. Both articles were simulated with current feeding direction.

Values of maximum thinning and maximum failure limit at locations prone to crack on the two simulated

22


articles are presented in figs. 4.11 and 4.12. As earlier, both properties are greater for the higher drawcushion force than for the lower one. Moreover, the maximum thinning resulting from the higher drawcushion force do not fulfill the set requirement of a maximum 20 % material thinning.


Figure 4.11: Values of maximum thinning at locations prone to crack on simulated articles A and B. Each label inthe figure shows the thinning at a specific point, where -0.500 corresponds to a 50 % material thinning. The smallervalues to the right in each label correspond to the maximum and minimum thinning obtained at that point duringthe simulation. Both simulations were run with the real variation in material properties obtained from the materialanalysis.


Figure 4.12: Values of maximum failure at locations prone to crack on simulated articles A and B. Each label inthe figure shows values at a specific point, where 0.500 corresponds to a 50 % margin to the forming limit diagrampresented in section 2.4.1. The smaller values to the right in each label correspond to the maximum and minimumvalues of the failure limit obtained at that point during the simulation. The real variation in material propertiesobtained from the material analysis was used in both simulations.

4.2.4 Velocities

The approximated motion curve including two different forming velocities can be seen in fig. 4.13a. Corre-sponding real curve for the whole cycle, rather than just the downward motion of the slide, is shown in fig.4.13b. According to the approximated curve, the slide reaches its bottom position after approximately 2.65seconds. Corresponding time obtained from the real motion curve is roughly 2.20 seconds.

23


(a) Approximated motion curve for the downward motion of the slide.

(b) Real slide motion curve during one cycle. The y-axis represents the slide position and the x-axis represents time.

Figure 4.13: Motion curves for the press slide during forming of articles A and B.

24

4.3. EXPERIMENTS CHAPTER 4. RESULTS

When investigating formability and maximum thinning limit of the articles simulated with differentforming velocities, no differences could be seen neither for a draw cushion force of 1200 kN nor 2100 kN.This was also the case for maximum failure, considering a draw cushion force of 1200 kN. The differences inmaximum failure resulting from a draw cushion force of 2100 kN and different forming velocities are shownin fig. 4.14. The figure displays close ups of the two immersions in the detail, and the left and right imagecorrespond to varying and constant forming velocity respectively. The labels in the figure display values ofmaximum failure limit at specific points prone to crack and as seen, some values are slightly greater in theleft image than in the right and vice versa.

(a) Simulation run with a varying forming velocity; 70%and 100% of the operating velocity.

(b) Simulation run with a constant forming velocity of100% of the operating velocity.

Figure 4.14: Values of maximum failure at locations prone to crack on simulated articles A and B. Each label inthe figure shows values at a specific point, where 0.500 corresponds to a 50 % margin to the forming limit diagrampresented in section 2.4.1. The smaller values to the right in each label correspond to the maximum and minimumvalues of the failure limit obtained at that point during the simulation. Current feeding direction and a draw cushionforce of 2100 kN were used in both simulations.

4.3 Experiments

After performing the deep drawing operation of the articles A and B with colored contact surface for thebalancing blocks, no blue color could be seen on the balancing blocks after forming. Therefore, the matrixand balancing blocks did not have contact during the forming operation.

Thinning resulting from different draw cushion forces is presented in tab. 4.2 below. Visible in the tableis that higher draw cushion force results in a greater material thinning and that measurement points 1 & 3,shown in fig. 3.1, seem to be more exposed to thinning than measurement point 2.

Table 4.2: Measured thinning at three different locations of article A formed using four different draw cushion (DC)forces.

DC force (kN ) \Measurement 1 (%) 2 (%) 3 (%)1200 -22.5 -20.5 -22.52000 -26.0 -21.5 -26.52100 -26.0 -21.5 -27.03000 -27.0 -23.5 -28.0

25

Chapter 5

Discussion

This chapter starts with a discussion about the material analysis and its results; the differences in materialproperties between cracked and non-cracked materials and also the real material property dispersion obtainedfor a specific article. Thereafter the different simulations are analyzed, after which finally the experimentsare evaluated.


The work with the material analysis was strongly affected by the lack of documentation regarding crackedmaterials. As mentioned in ch. 3, many materials could not be traced to specific sheet metal coils, wherebyall such materials were excluded from the study. Furthermore, some of the work orders documented in thesummary containing cracked details could not be found in corresponding production reports, which indicatesthat not all cracks were documented in these reports.

The tendencies seen in the matrix scatter plots described in Appendix B are mostly speculative andmore material data are needed in order to conduct a proper analysis. Considering the different materialproperties presented in fig. 4.1, similar behaviors can be seen for cracked details of articles C and E. Thecracked details of these articles have lower values of plastic strain ratio, elongation and surface roughness thannon-cracked details, while values of tensile and yield strengths exceed those of non-cracked materials. Thedifferences between cracked and non-cracked materials are however small for some properties - for examplethe tensile and yield strengths for article E. A somewhat different behavior can be seen for article D, wherethe median values of all properties are less or equal to corresponding values obtained from the non-crackedmaterials. Values of the plastic strain ratio and yield strength are lower, while the median values of theremaining properties are the same for cracked and non-cracked materials. This suggests that using materialswith inferior ability to resist thinning or thickening, and which begins to deform plastically at lower forces,may with higher probability cause article D to crack. The difference in yield strength between cracked andnon-cracked materials is small, whereby the inferior ability to resist thinning or thickening can be seen as acharacteristic for cracked details of article D. On the other hand, article A stands out as its cracked detailsbehave in an opposite way compared to articles C and E. For article A, cracked details have higher valuesof plastic strain ratio, elongation and surface roughness than non-cracked details, while the tensile and yieldstrengths lie below those for non-cracked materials. A better ability to resist thinning or thickening anda rougher surface seem to negatively affect the robustness of article A. In summary, a behavior of crackedmaterial properties common for all four articles can not be seen from fig. 4.1. Maybe different articles aresensitive to different kinds of variations in material properties as they have different geometries.

26

5.2. SIMULATIONS CHAPTER 5. DISCUSSION

Looking at the differences between delivered and actual material properties in fig. 4.2, values of tensileand yield strengths obtained from tensile tests generally seem to be lower than those specified by the materialsuppliers. The 75 percentiles for the properties of cracked materials do however indicate that not all tensiletests result in lower property values. The median values of the elongation in fig. 4.2 suggest that tensile testsperformed on cracked materials generally result in smaller elongations than those specified by the suppliers.According to the different percentile values for the elongation however, the tests generate both higher andlower values than those specified. More specifically, these values are everything between roughly 6 % smallerto approximately 27 % greater than the delivered values. Corresponding values for non-cracked materialsare approximately 23 % and 28 % respectively. The delivered materials can hence either have incorrectvalues on their delivered specifications, be wrongfully tensile tested or both. Assuming that the tensile testsare correct suggests that smaller elongation and slightly greater values of tensile and yield strengths arecharacteristics for materials prone to crack. This complies with the material property behavior for crackeddetails of articles C and D shown in fig. 4.1.

The real variation in material properties for article A, presented in tab. 4.1, can be compared to thedispersion in tab. 3.1 recommended by AutoForm. Considering the tensile and yield strengths and plasticstrain ratio, which are the common variables for the two tables, several differences can be seen for both maxand min values and corresponding standard deviations. For starters the real spans for the plastic strain ratioand the tensile strength both exceed the spans specified in tab. 3.1. The real span for the tensile strengthis smaller than recommended, which also holds for the corresponding standard deviation. The standarddeviations of the real plastic strain ratio and yield strength are both higher than recommended, where thevalue for the plastic strain ratio is almost 80 % higher than the recommended one. Looking at the materialproperties for article A, shown in fig. 4.1, it is visible that the plastic strain ratio has bigger variations thanthe yield strength, which in turn varies more than the tensile strength. As a conclusion, the dispersion ofsome material properties for article A does hence not comply to the general recommendation of ± 10 % setby AutoForm.

5.2 Simulations


The differences in formability for different feeding directions, shown in figs. 4.3 and 4.4, suggest that thedetails of articles A and B are less stretched now than when they were produced with a feeding directionperpendicular to the current one. The current feeding direction and a draw cushion force of 1200 kN resultin thickening above the two immersions in the simulated detail, which means that the material is held tighterat those points. This results in more stretching in the surrounding areas of the detail, which in turn canbe the reason why compression is shown in the middle of the right detail in fig. 4.3 and not in the left.Important to add is that big parts of the details are not sufficiently stretched.

Looking at the maximum thinning in fig. 4.5, both feeding directions fail to fulfill the required limit whena draw cushion force of 2100 kN is used. All values visible in the figure are however not exceeding the limit,and as the maximum thinning represents the worst case scenario this may explain why details sometimes canbe run with this draw cushion force without cracking. The reason why the current feeding direction resultsin both greater material thinning and higher values of maximum failure than the old feeding direction, isprobably the extra compression and thickening visible in figs. 4.3 and 4.4.


The formability resulting from higher draw cushion forces, presented in fig. 4.7, indicates a more completematerial stretch, but the differences between draw cushion forces 2500 kN and 3000 kN are not as prominent

27

5.2. SIMULATIONS CHAPTER 5. DISCUSSION

as the differences between the lower forces shown in figs. 4.3 and 4.4. The resulting maximum thinningpresented in fig. 4.8 exceeds the required limit for both forces, whereby the upper limit of the formingwindow for the articles may be set too high. No signs of failure can be seen from the maximum failure visiblein fig. 4.9, but according to Volvo GTO EBM standard, none of the draw cushion forces of 2500 kN and3000 kN fulfill the requirements set on material thinning.


Comparing the formability plots in fig. 4.10 resulting from simulations run with real variation in materialproperties with corresponding plots in figs. 4.3 and 4.4, slightly more compression can be seen on the detailssimulated with real variation of material properties. This difference is however clearer for the lower drawcushion force of 1200 kN than the higher one of 2100 kN. When comparing maximum thinning betweenreal material properties and those obtained from the material file, the real properties result in less materialthinning for the draw cushion force 1200 kN while no specific behavior can be seen for a force of 2100 kN.Both simulations run with the force 1200 kN fulfill the limit of maximum thinning, while the ones run withthe draw cushion force 2100 kN do not. Moreover, a clear difference between the values of maximum failurefor a draw cushion force of 1200 kN can not be seen. For a force of 2100 kN, the real variation in materialproperties results in somewhat higher values than the one obtained from the material file. All values ofmaximum failure do however stay below the required limit. The fact that the simulations using the realvariation were run with a too low value of the strain hardening coefficient, means that a slightly poorerability of distributing strains was implemented. This could in turn have negatively affected the robustness ofthe simulated articles. In summary, only small differences can be seen between the real variation in materialproperties and the one obtained from the material file, and no clear patterns are visible between the twodifferent material implementations. The material file provided by the material supplier does hence seem tobe a good approximation to the real variation. Important to keep in mind however is that the simulationsrun using the material file did result in slightly better stretched details than the simulations run using thereal variation in material properties.

5.2.4 Velocities

The approximated motion curve shown in fig. 4.13a differs slightly from the real curve displayed in fig.4.13b. The fast downward motion of the slide at the beginning of the cycle is basically the same for the twocurves, while the forming motion is slower in the approximated curve than in the real one. Looking at thereal motion curve, the slide stays at its bottom position during approximately 0.5 seconds. This is morethan twice the time specified in the press setting instructions for the articles. As the calculations of theapproximated curve are based on the specified bottoming time 0.2 seconds, this is probably the main reasonwhy the two forming motions differ. Looking at the press slide settings shown in fig. A.1 in Appendix A.1,the bottoming time is set to 0.2 seconds in the presses. This does not seem to agree with the real motioncurve, whereby this function of the press may need to be reviewed. The fact that no acceleration was takeninto account during the calculations of the approximated curve does also contribute to the differences seenin fig. 4.13.

Considering the simulations run with varying and constant forming velocity, no differences could be seenfor neither formability nor maximum thinning for either of the two draw cushion forces. This was also thecase for the maximum failure resulting from the lower draw cushion force. Furthermore, the differences seenfor the maximum failure and the higher draw cushion force in fig. 4.14 are small - only a few tenths of apercent. No significant differences can thus be seen between the two forming velocities, which also is theconclusion drawn when comparing the simulations run with default forming velocity, visible in fig. 4.3, withthe optimized varying forming velocity presented in fig. 4.14. In summary according to simulations, it seem

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5.3. EXPERIMENTS CHAPTER 5. DISCUSSION

to be possible to change the press settings for articles A and B from having a varying forming velocity toconstant 100 % operating velocity during the forming motion, without affecting the final robustness of theproduced articles.

5.3 Experiments

Since the balancing blocks and matrix did not have contact during forming of articles A and B, the toolset-up used in the simulations seems to be reasonable.

Comparing the real material thinning in tab. 4.2 to the thinning obtained from the simulations, it isclear that a greater material thinning occurs in real life than in the simulations. The differences are quite bigsince the maximum thinning resulting from a draw cushion force of 3000 kN is according to the simulationsroughly 22 %, while it in real life is approximately 28 %. For a force of 1200 kN, the corresponding valuesare 18 % and 23 %, respectively. The simulated values of the maximum thinning are hence more than 20 %smaller than the real ones, and this phenomenon can be caused by a number of different things. For examplethe friction acting on the material during forming is constantly varying in the real life processes due to e.g.different speeds of the press slide and different temperatures in the tools. These kind of variations are notall taken into consideration in the AutoForm simulation model, whereby the simulated friction is somewhatsimplified. This simplification may affect the final robustness results, as friction strongly affects how tightor how loose a material is held. Furthermore, the surface roughness of a material does vary a lot betweendifferent metal sheets. As seen in tab. 4.1, this property varies more than ± 20 % from its median value forarticle A. This together with eventual coatings of the tools and different lubrications on the metal sheets isalso something that greatly affects how tight a material is held during forming of an article. In AutoForm,some of these friction variations is handled by the variable lube introduced in tab. 3.1. However, in thesimulations this noise variable was only allowed to vary ± 10 %, which is probably not enough to covervariations in speed, temperature, different surface topographies and so on.

Moreover the general recommended limit for maximum thinning does not seem to fit articles A and B.First and foremost, the thinning resulting from both forces creating the forming window for the articlesexceeds the specified limit of 20 %, but also the lower force of 1200 kN results in a too great thinning.This suggests that the limit should be changed and perhaps adapted to each of the articles produced in thefactory. This would give more accurate guidelines to base the simulations on, which in turn could reducethe existing gap between simulated and actual robustness results.

29

Chapter 6

Conclusions & future improvements

During the work with the material analysis, it became visible that more data have to be documentedregarding cracked materials, and this with greater regularity. First and foremost, the specific sheet metalcoils need to be documented for each cracked material, as this lack of traceability was the main problemencountered during the performed material analysis. Furthermore, there is a need of performing more tensiletests, both for cracked and non-cracked materials. Tensile tests are a good way of controlling materialquality in daily production, but more data, especially non-cracked material data to compare with those ofthe faulty materials, are needed in order to get reliable results. I would also recommend controlling theaccuracy of the tensile tests since the property values, especially for the elongation, differ significantly fromcorresponding values specified by the material suppliers. Of course this problem can also originate from faultymeasurements performed by the suppliers. Moreover, an automatic documentation of material propertieswould partly reduce potential human errors, partly ensure that data are indeed being documented. Perhapseach sheet metal coil identification number could be linked to corresponding material specifications, whichthen automatically are being registered in the systems at the same time as the coils. Important then is, asmentioned earlier, that each produced article always can be traced to a specific coil.

Considering the material analysis, different articles seem to be sensitive to different kinds of variations inmaterial properties. I therefore recommend to perform a more thorough study of this when more data areavailable. Thereafter the recommended limits can be optimized for each article, which probably is neededconsidering how wide these tolerated spans currently are.

Conclusion drawn from the simulations run with different feeding directions is that a material withcurrent feeding direction, together with a low draw cushion force, may be more prone to crack due to extracompression and thickening around the immersions in articles A and B. Moreover, considering the resultingpoor material stretch, low draw cushion forces of around 1200 kN should only be used when really necessary.A possible future study is to investigate how different draw cushion forces are affecting the final geometryof different articles.

When it comes to the real variation in material properties, the material file provided by the materialsupplier does seem like a good approximation to the real variation. However, for an article formed with alow draw cushion force and that has a wide spread among property values, I recommend to implement thereal variation in material properties.

As mentioned in previous chapter, it should be possible to change the real press settings for articles Aand B from having a varying forming velocity to have a constant maximum forming velocity, without alteringthe final robustness of the articles. This is advantageous since it decreases the cycle time for the articles,which in turn improves the production efficiency.

From the experiments it became clear that big differences could be seen between real and simulated

30

CHAPTER 6. CONCLUSIONS & FUTURE IMPROVEMENTS

material thinning, but also that the specified limit for maximum thinning does not fit articles A and B. Aninadequate modeling of the friction may be causing this difference in material thinning whereby I thereforesuggest to investigate alternative ways of handling friction in the simulations. Moreover, as explained in ch.5.3, I think that the specified limit of maximum thinning needs to be individually adapted to each article,rather than having one limit applying to all details.

Another potentially affecting factor concerning cracking, is varying temperatures in the tools, wherebyyet another future study could be to measure the temperatures in the tools during forming and investigateif details may be more prone to crack at certain temperatures. This should be possible to do with, as asuggestion, infrared temperature sensors mounted near each press.

In conclusion no general pattern that applies to all articles has been seen between cracked and non-cracked material properties. Differences in material properties do exist, but these differences seem to varybetween different articles. It does however seem possible that varying material properties are an importantfactor concerning cracking. Furthermore the simulations indicate that variations in draw cushion force areconsiderably more influential on a detail’s robustness, than variations in material properties, forming velocityand feeding direction of the metal sheets. Therefore there are several factors affecting the final robustnessof an article, and further potential affecting factors need to be investigated before all causes of cracks canbe determined.

31

Bibliography

[1] ”Sheet Metal Forming”, AutoForm [Online] Available:https:\\www.autoform.com\en\glossary\sheet-metal-forming\. [Retrieved: 11 April 2018].

[2] W. F. Hosford and R. M. Caddell, Metal Forming: Mechanics and metallurgy, 4th ed. New York:Cambridge University Press, 2011.

[3] H. Lundh, B. Carlsson, G. Engberg, L. Gustafsson and R. Lidgren, Formningshandboken: Styckskarandebearbetning och plastisk formning, 2nd ed. Borlange: SSAB Tunnplat AB, 1997.

[4] R. Gedney, ”Measuring the plastic strain ratio of sheet metals”, The FABRICATOR, June 2006.

[5] ”Brottgrans”, Nationalencyklopedin [Online] Available: http://www.ne.se.[Retrieved: 26 March, 2018].

[6] ”Strackgrans”, Nationalencyklopedin [Online] Available: http://www.ne.se.[Retrieved: 27 March 2018].

[7] J-E. Stahl, F. Schultheiss and S. Hagglund, ”Analytical and Experimental Determination of the Ra

Surface Roughness during Turning”, Procedia Engineering, nr 19, p. 351, 2011 [Online] Available:ScienceDirect, http://www.sciencedirect.com. [Retrieved: 27 March 2018].

[8] S. Lonnelid and R. Norberg, ”Dragning” in Grundlaggande Hallfasthetslara, 4th ed. Stockholm: Stif-telsen Kompendieutgivningen, 2009.

[9] ”Multivariat analys”, Nationalencyklopedin [Online] Available: http://www.ne.se.[Retrieved: 3 April, 2018].

[10] ”plotmatrix”, MathWorks [Online] Available: https:\\se.mathworks.com. [Retrieved: 3 April 2018].

[11] ”parallelcoords”, MathWorks [Online] Available: https:\\se.mathworks.com.[Retrieved: 3 April 2018].

[12] ”AutoForm Solution Overview”, AutoForm [Online] Available:https:\\www.autoform.com\en\products\solution-overview\. [Retrieved: 28 March 2018].

[13] C. Maier, ”Failure prediction in sheet metal forming using fea of Nakazima test”, Machines, technologies,materials, nr 7, 2013 [Online] Available: StumeJournals,http:\\stumejournals.com\mtm\Archive\2013\7\DOKLADI\1\3 9 Maier.tech-tes13.pdf.[Retrieved: 28 March 2018].

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Appendix A

Simulations

A.1 Press settings

Figure A.1: Different press settings for the press slide during forming of articles A and B.

I

A.1. PRESS SETTINGS APPENDIX A. SIMULATIONS

Figure A.2: Press settings for the draw cushion during forming of articles A and B.

II

A.1. PRESS SETTINGS APPENDIX A. SIMULATIONS

Figure A.3: Screen shot taken at the press computer screen during forming of articles A and B.

III

A.2. MOTION CURVES APPENDIX A. SIMULATIONS

A.2 Motion curves

Table A.1: Approximated motion curves for the press slide during forming of articles A and B. The left tablecontains a motion curve where the forming motion are divided into two different parts; one with a 70 % operatingvelocity and another with a 100 % operating velocity. In the right table the forming motion consists of a constant100 % operating velocity.

Step Time [s] Position [mm]0 0.00 1.0001 0.05 0.8702 0.10 0.7413 0.15 0.6114 0.20 0.4815 0.25 0.3516 0.30 0.2227 0.35 0.1498 0.40 0.1409 0.45 0.13110 0.50 0.12211 0.55 0.11312 0.60 0.10213 0.65 0.08914 0.70 0.07615 0.75 0.06416 0.80 0.05117 0.85 0.03818 0.90 0.02519 0.95 0.01320 1.00 0.000

Step Time [s] Position [mm]0 0.00 1.0001 0.05 0.8802 0.10 0.7593 0.15 0.6394 0.20 0.5195 0.25 0.3986 0.30 0.2787 0.35 0.1538 0.40 0.1429 0.45 0.13010 0.50 0.11811 0.55 0.10612 0.60 0.09413 0.65 0.08314 0.70 0.07115 0.75 0.05916 0.80 0.04717 0.85 0.03518 0.90 0.02419 0.95 0.01220 1.00 0.000

IV

Appendix B

Matrix scatter plots

Figure B.1: Matrix scatter plot of material properties for article A. The blue dots represent property values fornon-cracked details, while the red circles show material properties of cracked details. The six material propertiesvisible in the figure are the strain hardening exponent n, the plastic strain ratio r, the elongation A80, the tensilestrength Rm, the yield strength Rp0.2 and the surface roughness Ra.

V

APPENDIX B. MATRIX SCATTER PLOTS

Figure B.2: Matrix scatter plot of material properties for article C. The material properties of cracked and non-cracked details are represented by red circles and blue dots respectively. The six material properties visible in thefigure are the strain hardening exponent n, the plastic strain ratio r, the elongation A80, the tensile strength Rm,the yield strength Rp0.2 and the surface roughness Ra.

VI


Figure B.3: Matrix scatter plot of material properties for article D. The blue dots represent property values fornon-cracked details, while the red circles show material properties of cracked details. The six material propertiesvisible in the figure are the strain hardening exponent n, the plastic strain ratio r, the elongation A80, the tensilestrength Rm, the yield strength Rp0.2 and the surface roughness Ra.

VII


Figure B.4: Matrix scatter plot of material properties for article E. The material properties of cracked and non-cracked details are represented by red circles and blue dots respectively. The six material properties visible in thefigure are the strain hardening exponent n, the plastic strain ratio r, the elongation A80, the tensile strength Rm,the yield strength Rp0.2 and the surface roughness Ra.

VIII

Documents

MASTER’S THESIS IN ENGINEERING PHYSICS1217561/FULLTEXT01.pdf · Master’s thesis, Civilingenj orsprogrammet i teknisk fysik, Ume a University. Evelina Salomonsson, [email protected]