Master of Science in Mechanical Engineering May 2020
Friction and material modelling in
Sheet Metal Forming Simulations
Herman Bentsrud
The thesis is equivalent to 20 weeks of full time studies.
The author declare that he is the sole author of this thesis and that he has not used any sources other than those listed in the bibliography and identified as references. He further declares that he has not submitted this thesis at any other institution to obtain a degree.
Contact Information: Author: Herman Bentsrud E-mail: hebg15@student.bth.se University advisor: Md Shafiqul Islam, Ph.D.
Department of Mechanical Engineering
Company/University advisor: Mats Sigvant, Ph.D, Volvo Cars
Department of Mechanical Engineering
Faculty of Engineering Internet : www.bth.se Blekinge Institute of Technology Phone : +46 455 38 50 00 SE–371 79 Karlskrona, Sweden Fax : +46 455 38 50 57
Abstract
In today’s car manufacturing industry, sheet metal forming is a important process that takes preparation, which is time consuming and complex when new processes are made. When new metal grades and alloys are provided to the industry, tests are conducted to determine it’s behaviour and strengths. This gives the data for complex material models that can approximate the metal behaviour in an accurate way in a simulation environment. One of the unknown factors from tests is the fric-tion coefficient on the sheet metal. The software Triboform is able to provide an adaptable friction coefficient model that depends on multiple simulation and user input conditions. The problems that occur when acquiring data for the material model is that testing is time consuming and the friction model has to be adjusted to give accurate results. At Volvo Cars there are two material models used with their different advantages, BBC 2005 and Vegter 2017.
The purpose with this work is to compare the two material models using the Tri-boform friction models implemented to see if any combination provides accurate simulation results and then create recommendations for which model is best suited for different cases. Some side studies is also done with an older Vegter model, a strain rate sensitive BBC 2005 model and a Triboform model on all simulation parts. The purpose is achieved by implementing the Triboform model in Autoform and run a simulation of a Limiting Dome Height (LDH) test with both material models and compare the results with experimental data for several different materials. The data that is directly compared from the LDH test is the major and minor strain from two perpendicular sections at four different stages and also the force from the punch tool. The material models will be evaluated by how it manages to mimic the strain behaviour of the metals and how it estimates the punch force.
The results point towards an improvement of the accuracy for most of the met-als tested and BBC 2005 is the better model if there’s available biaxial data from tests, Vegter 2017 is decent if there’s not. However Vegter 2017 is not a good option for aluminum alloys simulations when the punch force is compared. Side study also shows that Vegter 2017 is bit of a downgrade when it comes to strain values, com-pared to the old Vegter.
The work, in summary shows a dynamic friction model can improve the accuracy for strain predictions in the simulation process. If there’s biaxial yield data available for the metal or if it’s an aluminum alloy, BBC 2005 is the superior choice, but if only tensile tests are available for metals, Vegter 2017 is a decent choice for some cases.
Keywords: Sheet metal forming, Material model, Triboform, Autoform
I dagens bilindustri är plåtmetalformning en viktig process som kräver förberedelser som är tidskonsumerande och komplex när nya processer tillkommer. När nya met-allslag kommer in till industrin, så utförs tester för att avgöra dess egenskaper och styrka. Denna testdata används till materialmodeller som kan approximera metal-lens beteende på ett noggrant sätt i en simuleringsmiljö. Den okända faktorn från dessa test är friktionskoefficienten på plåten. Programvaran Triboform är kapabel att göra en dynamisk friktionsmodel som beror på användar- och simuleringsdata. Problemen som uppstår vid framtagning av data är att det är tidskonsumerande och flera simuleringar måste göras för att bestämma friktionen. Volvo Cars använder sig av två modeller med olika fördelar, BBC 2005 och Vegter 2017.
Syftet med detta arbete är att jämföra de två materialmodellerna med Triboform modeller implementerat för att se om de påverkar noggrannheten i simuleringar och sedan förse rekommendationer för vilken modell passar bäst för olika fall. Några sidojobb i studien som görs är en jämförelse med gamla Vegter modellen, ett test med en modell som är känslig för töjningshastighet och test med att implementera Triboform modellen på alla pressverktyg.
Detta utförs med att implementera Triboform modellerna i Autoform och köra en simulering på ett LDH-test med båda materialmodeller och jämföra resultaten med experimentell data för flera olika metaller. Data som skall jämföras från LDH-testet är första och andra huvudtöjningen i två vinkelräta sektioner i fyra processsteg och stämpelkraften genom hela processen. Modellerna kommer evalueras genom hur de lyckas imitera töjningens beteende och hur den estimerar stämpelkraften.
Resultaten pekar mot en förbättring när Triboform är implementerat i simuleringar för de flesta metaller som ingår i testen och BBC 2005 är den model som föredras om det finns tillgänglig biaxiel spänning data från tester, Vegter 2017 är en duglig modell om dessa data inte finns. Vegter 2017 är dock inte ett bra alternativ när det kommer till jämförelse av töjning och stämpelkraften för aluminium. Sidojobb med gamla Vegter visar att den nya Vegter 2017 inte är en direkt förbättring med hänsyn till noggrannheter av krafter och töjningar.
Arbetet visar att en dynamisk friktionsmodel kan förbättra prediktering av töjningar i simuleringar. Om det finns biaxiel data för metallen eller om det gäller att simulera aluminium är BBC 2005 det bättre altermativet, om det endast finns dragprovsdata för metallen så är Vegter 2017 duglig för vissa fall.
Nyckelord: Plåtmetalformning, Materialmodell, Triboform, Autoform ii
Acronyms
BBC Banabic Balan Comsa. DIC Digital Image Correlation. FE Finite Element.
FEA Finite Element Analysis. FLC Forming Limit Curve. FLD Forming Limit Diagram. HSLA High Strength Low Alloy. LDH Limiting Dome Height. RMS Root mean square. SMF Sheet Metal Forming. SRS Strain Rate Sensitivity. TF Triboform.
VCBC Volvo Cars Body Components. VPB Viscous Pressure Bulge.
Abstract i Sammanfattning ii 1 Introduction 1 1.1 Background . . . 1 1.2 Aim . . . 2 1.3 Questions . . . 2 1.4 Hypothesis . . . 2 1.5 Delimitations . . . 2
2 Calibration of material models 3 2.1 Stamping terminology . . . 3
2.2 Input in AutoForm . . . 4
2.2.1 Material models . . . 4
2.2.2 Experimental input for material models . . . 9
2.2.3 Triboform and friction Input . . . 11
2.3 Inverse modelling . . . 12
2.4 MATLAB . . . 12
3 Related Work 13 4 Method 15 4.1 Main approach . . . 15
4.2 The simulation setup . . . 16
4.3 Materials . . . 17
4.3.1 Process for Triboform models . . . 18
4.3.2 Work process in Autoform . . . 19
4.3.3 Comparison . . . 20
4.3.4 Adjustments . . . 20
4.3.5 Evaluation . . . 20
4.4 Approach for different cases . . . 21
5 Results 22 5.1 BBC 2005 and Vegter 2017 . . . 22
5.1.1 Strains . . . 22
5.1.2 Punch force . . . 34
5.2 Heavily modified friction model . . . 37
5.3 BBC 2005 SRS . . . 39
5.4 Full Vegter . . . 40
5.5 Global friction model . . . 41
6 Analysis and Discussion 42 6.1 BBC 2005 and Vegter 2017 . . . 42
6.2 Full Vegter . . . 43
6.3 SRS BBC 2005 . . . 43
6.4 Global friction model . . . 43
7 Conclusions and Future Work 44 References 45 A Tables 47 A.1 Autoform and Triboform material settings . . . 47
A.2 RMS Force difference . . . 48
A.3 BBC 2005 RMS strain difference . . . 49
A.4 Vegter 2017 RMS strain difference . . . 50
2.1 Sectionviewofthesimulation model... 3
2.2 Exampleofa material model. TheHardeingcurve(left)(Truestrain [-], Truestress[MPa]), Yieldsurface(middle)(σx[MPa],σy[MPa]) andtheFLD(right)(Minorstrain[-], Majorstrain[-])areplottedin Autoform... 4
2.3 Yieldsurfacesforthesamematerialwithhigh(thinline)andlow(thick line) M-valueforBBC2005... 6
2.4 YieldsurfacecomparisonbetweenBBC2005(thick)andVegter2017 (thin)ontwo materials... 7
2.5 YieldsurfacecomparisonbetweenVegter2017(thick)andFullVegter (thin)ontwo materials... 8
2.6 HardeningcurvesinBBC2005SRSmodelforCR4.Strainrates(from top):10,1,0.1and0.0067s1 ... 9
2.7 Stampsetupandpunchtool... 10
2.8 TestblanksfromNakazimaandbulgetests... 11
4.1 Workflowforthestudyoffrictionand material models... 15
4.2 SectionviewoversimulationstepsoftheLDH-testinAutoform... 16
4.3 ExampleofsettingsforTF-models ... 18
4.4 ManipulatedTriboformfrictionmodelsdependingonpressureandstrain19 4.5 Sectioncapturefromsimulation... 19
5.1 StraincomparisonforBBC2005withthesteelCR3... 23
5.2 StraincomparisonforVegter2017withthesteelCR3... 24
5.3 Majorandminorstraincomparisonforbothmaterialmodelswiththe steelCR4 ... 25
5.4 MinorstraincomparisonwiththesteelCR5... 26
5.5 Minorstraincomparisonwiththe metalCR210BH ... 27
5.6 Majorandminorstraincomparisonforbothmaterialmodelswiththe metalCR270LA... 28
5.7 Majorandminorstraincomparisonforbothmaterialmodelswiththe aluminumalloyAdvanze170... 29
5.8 MajorandminorstraincomparisonforBBC2005withthealuminum alloyAdvanzs118... 30
5.9 MajorandminorstraincomparisonforVegter2017withthealuminum alloyAdvanzs118... 31
5.10 Majorand minorstraincomparisonforboth models withthea lu-minumalloyEcolite160ST... 32
5.11 Major and minor strain comparison for Vegter 2017 with the aluminum
alloy Superlite 160ST . . . 33
5.12 Punch force comparison for the mild steel family . . . 34
5.13 Punch force comparison for the CR270LA and CR210BH . . . 35
5.14 Punch force comparison for Aluminum alloys . . . 36
5.15 Manipulated Triboform friction models. Blue: One reference point. Red: Multiple points . . . 37
5.16 Strain and force comparison for CR440Y78T for both material models with constant and heavily modified friction model. . . 38
5.17 Strain and force comparison between normal BBC 2005 model and SRS with different settings. . . 39
5.18 Full Vegter and 2017 model comparison for metals CR4 and Advanz e170 . . . 40
5.19 Comparison between friction model implemented globally and sheet metal only. . . 41
4.1 Material list . . . 17 A.1 Settings for Triboform and material thickness . . . 47 A.2 RMS of force difference between the models and experiments . . . 48 A.3 RMS difference between major strains of BBC 2005 simulations and
experiments . . . 49 A.4 RMS difference between minor strains of BBC 2005 simulations and
experiments . . . 49 A.5 RMS difference between major strains of Vegter 2017 simulations and
experiments . . . 50 A.6 RMS difference between minor strains of Vegter 2017 simulations and
experiments . . . 50
Chapter 1
Introduction
1.1
Background
Sheet Metal Forming (SMF) is a complex manufacturing process which is heavily used in the car industry. Considering the process contains several complexities, the feasability check is often made in an Finite Element Analysis (FEA) software. The FEA results are notably influenced by the material models that is used by the software. The material model BBC 2005 has been used by Volvo Cars Body Components (VCBC) in Olofström, Sweden for approximately 10 years and has been proven to be viable for their sheet metal forming simulations. There is also another candidate model called Vegter 2017, that has been developed by Tata steel to increase the accuracy for different grades and alloys [1].
When VCBC receives new materials, they need to make additional tests to validate the material data for the models and then fine adjust them by comparing the strain results from a standard LDH-test and simulations. One of the biggest causes for the simulation to be inaccurate, is the friction coefficient between the metal sheet and the tools. The standard for newly received materials are a constant (Coulomb) friction coefficient, which can considerably limit the accuracy for the simulations, as it has been shown in a master thesis work from 2019 [2]. The problem is the conditions change and therefore can change the friction coefficient. VCBC has done work to implement advanced friction models from Triboform (TF) into their sheet metal forming simulations for better accuracy for new materials. In simulations, Triboform enables the FE-software to use a multi-scale model of a friction coefficient that can change during time and position under multiple process conditions [3, 4, 5, 6, 7, 8]. The reason to strive for accuracy in the simulations, is if the simulation will predict the metal behavior accurately, it’ll require less calibration and testing when the real tools are made for the SMF-process. This report presents a study of a standardised test for model calibration to increase the quality of sheet metal forming simulations with different materials, using Triboform with the two aforementioned material models. The study will also test on a few materials, a model that considers the strain rate and the old Vegter model (mentioned in Chapter 2.2.1).
1.2
Aim
The objective of this study is to use TriboForm friction models with the two different material models, BBC 2005 and Vegter 2017 for seven steel grades and four aluminum alloys in simulations to adjust the models so the results are near the experimental data. This will give an insight if the friction models will make the simulations more accurate with the different material models for different materials.
1.3
Questions
The work is evolving around these questions:
• How will the friction models affect the force, major and minor strains on sim-ulations and what parameters could change for improved accuracy?
• Will Triboform friction models improve the accuracy for sheet metal forming? • What material model is best suited for the different materials?
• How does the accuracy of Vegter 2017 compare with the Full (old) Vegter model when Triboform friction is applied? (only for a few materials tested)
• How will a Triboform friction model affect a BBC 2005 model with strain rate considered? (Only for one metal).
• If the same friction model is implemented on all tool surfaces, what effect will it have?
1.4
Hypothesis
The material models require different input parameters and the friction models can be adjusted, which gives different strain results. Therefore, there should be combi-nations of material models and friction models that fits each material.
1.5
Delimitations
The delimitations for this work are:
• The models that will be studied are BBC 2005 and Vegter 2017. However the SRS and full Vegter will be included for only a few metals.
• Only the punch force, major and minor strain from LDH-tests will be consid-ered for the comparisons.
• Velocity and temperature is assumed to be constant for the friction models, since the velocity is too low to be considered and there’s no temperature chang-ing process in the tests.
• Autoform is the software that is used in the industry and is compatible with Triboform, so no other simulation platform will be used for the study.
• The values acquired from the experiments will not be investigated or verified with other FE-software, since they calculate in different ways and therefore can give different results.
• Due to the complexity of the simulation model, no analytical comparison will be made, since it wouldn’t give any comparable results.
Chapter 2
Calibration of material models
2.1
Stamping terminology
The terms used for this specific setup are illustrated and labeled in Figure 2.1. The sheet metal(or blank) lies on blank holder before the die presses down and holds the sheet in place. The draw radius is keeping the sheet from getting an angular bend, which would give greater risk for fracture and cracks. This is a single action process, which means the punch is the static part in this setup. The die and the draw radius is moving downwards, against the blank holder and the punch, giving the sheet metal a rounded shape. The specific name of this test is Limiting Dome Height (LDH) which is described in Chapter 2.2.2.
Die
Draw radius Sheet metal
Blank holder Punch
Figure 2.1: Section view of the simulation model.
2.2
Input in AutoForm
2.2.1
Material models
The accuracy of Sheet Metal Forming simulations are heavily dependent on the ma-terial models, which are theoretical descriptions of the mama-terial properties and are acquired by multiple tests and mathematical formulations that have a large emphasis on the hardening and yield criteria for thin metal sheets. The models have different mathematical models and take experimental data for it’s calculations. The exper-imental inputs that is common among the studied models are the uniaxial plastic anisotropy coefficients in the directions 0°, 45° and 90° in reference to the rolling di-rection of the sheet metal. They are denoted as r0, r45 and r90. This data is acquired
from tensile tests, which also gives the yield stresses (when it starts to deform plasti-cally) (Chapter 2.2.2) [9, 10]. The other experimental data that all models require is from the Nakazima tests (Chapter 2.2.2) which are used to make the Forming Limit Curve (FLC). These experimental data points, along with the differing data depend-ing on the model, are used to determine coefficients in the mathematical model which then builds the material model, as shown in Figure 2.2.
Figure 2.2: Example of a material model. The Hardeing curve (left) (True strain [-], True stress [MPa]), Yield surface (middle) ( x[MPa], y[MPa]) and the FLD (right)
(Minor strain [-], Major strain [-]) are plotted in Autoform.
The Forming Limit Diagram (FLD) is a tool used to describe material responses when the sheet metal reaches critical strain values under deformation. The FLC shows limiting major and minor strains. The FLD is plotted to indicate the defor-mation limits for the metal. When simulating, the strain combinations on the sheet metal will be positioned in the FLD and if the values has crossed the FLC, the sheet metal has a risk for fracture.
For isotropic material behaviour, the Tresca and Von mises are widely known yield criterias (describes when materials goes from elastic to plastic deformation). But for most metals, this is not an adequate description due to the material being orthotropic and sheet metal forming requires precise descriptions. For these cases advanced yield criteria has been developed for taking orthotropy into consideration [10].
Chapter 2. Calibration of material models 5 The hardening curve is used for describing how the sheet metal gains strength when it deforms. The hardening curve provides data for a scalar function that’s used to equate how the yield condition will be changed during plastic deformation. The yield surface will grow outwards normal to the slope of the yield surface depending on the strain and stress conditions given by the hardening curve. This is called the associated flow rule [10]. This implies, if the yield surface looks different in the models or the curves has different slopes, they will grow differently and therefore give differing strain results. This could lead to the models requiring different friction coefficients to be able to mimic the strain data.
BBC 2005
This model is the one that has been most used by VCBC. Along with the r-values, this model requires following data from experiments [9, 10]:
• Three yield stresses in the directions 0°, 45° and 90° in reference to the rolling direction of the sheet metal. These are acquired by tensile tests (2.2.2) and are denoted as 0, 45 and 90.
• The biaxial yield stress wich is acquired by bulge tests (2.2.2) • The biaxial plastic anisotropy coefficient, denoted as rb
These data points are then used to calculate unknown coefficients called anisotropy parameters. These parameters and the exponent M is what builds the yield criterion. The exponent M, also denoted as 2k in some articles [9, 11] is a parameter that is associated with the crystallic structure of the sheet metal and has to be manually chosen accordingly by the user. Some sources that Banabic mentions in his book [10] says M has a similar value among a lot of metals, but experments performed by VCBC and RISE has shown it differs notably among materials the company has received. The exponent M changes the yield surface and as shown by LDH-tests, the major and minor strain results in process simulations. Practical experience in VCBC has shown that the exponent M can be estimated for BBC 2005 and has proven to describe strain results accurately, the problem is that it takes time and needs multiple simulations until a favorable value of the exponent M is found. What makes it more time consuming and costly of simulations is that the exponent M doesn’t have to be an integer [11]. Figure 2.3 shows what happens to the yield surface when coefficient M is changed.
x
[MPa]
y [MPa]
Figure 2.3: Yield surfaces for the same material with high (thin line) and low(thick line) M-value for BBC 2005.
Vegter 2017
This model has been developed by Tata Steel in the Netherlands. This model takes more information from the tensile tests and uses it to predict the yield surface. This is based on the work of Vegter [1]. Along with the r- and -values acquired from the tensile tests, it utilizes the uniform elongation, denoted as A0, A45 and A90. It
also utilizes the tensile strengths denoted as R0, R45 and R90. What this model
does is that it predicts the yield surface points that is usually determined by shear, plane strain, bulge and stack compression tests. For this to be a reliable model, a correlation was found between the mechanical properties of tensile parameters and the advanced parameters. This gave a set of equations that could predict the yield surface accurately. The model was validated by comparing the predicted model with the yield surface derived from test data. The conclusion from this work supports the model predicts the yield surface accurately. However, a LDH-test shows for some metals the punch force magnitude in a simulation deviates greatly for large forces compared with the test data. What differs this model from BBC 2005 is that it doesn’t need data from a bulge test or a user input factor to finalize the material model, and tests conducted by Tata steel supports that it predicts the yield surfac for a wide range of steel grades and aluminum alloys [1].
The Vegter 2017 and BBC 2005 model can deviate in the biaxial points for some ma-terials (as shown in Figure 2.4), which will affect the simulation results in Autoform. That will give the need to compensate with different friction coefficients [2].
Chapter 2. Calibration of material models 7 x [MPa] y [MPa] (a) Steel: CR5 x [MPa] y [MPa] (b) Aluminum: Advanz s118
Figure 2.4: Yield surface comparison between BBC 2005 (thick) and Vegter 2017 (thin) on two materials
Full (Old) Vegter
The older Vegter version is based on a wider range of tests to better determine the yield surface. The model uses 17 inputs that’s derived from a total of nine tests. Three tensile, three plane strain, two shear tests and one biaxial (bulge or compression) test [1, 12]. The problem with this model is the amount of test input it needs to function. Since Vegter 2017 only needs three tensile tests to work, it becomes a more attractive choice for usage when new materials are given to the industry. However, the yield surface for some materials are different in the equibiaxial point as shown in 2.5, which will give different strain results that in turn will need different friction coefficients to compensate. The biaxial data used for Full Vegter in this study is from the bulge test used for BBC 2005, the pure shear and plane strain test data is from Tata steel. It’s assumed BBC 2005 predicts the biaxial point correctly.
x [MPa] y [MPa] (a) Steel: CR4 x [MPa] y [MPa]
(b) Aluminum: Advanz e170
Figure 2.5: Yield surface comparison between Vegter 2017 (thick) and Full Vegter (thin) on two materials
Chapter2. Calibrationof material models 9 Strain RateSensitivity(SRS) BBC2005
Insheetmetalformingsimulations,therealprocesstimeisn’toftenconsidered,which couldleadtoproblemsfurtherintheproduction. Theproblemwithsomematerials is whentheyarestrainedatahighspeed,theygetstronger. Which meansthe hardeningcurveintheorywouldchangeandthereforeshiftinthestressaxis. For thesecases,Tatasteelhasdevelopedhardeningcurveswithdifferentstrainratesfor the materialCR4(showninFigure2.6)totesthowthesheet metalbehaveswhen simulatingtheprocessinrealtime[4,13]. Thiscouldintheoryleadtoaneedfor adjustmentsinthe materialdatasincetheSRShardeningcurveswillgivedifferent conditionsfortheyieldsurface.
Figure2.6: HardeningcurvesinBBC2005SRS modelforCR4.Strainrates(from top):10,1,0.1and0.0067s1
2
.2
.2 Exper
imenta
linputfor mater
ia
l mode
ls
VCBCreliesonexperimentalinputandinversemodelling(Chapter2.3)forcal ibra-tionandverificationofthe material models. Thesetestsareconductedby RISE IVF,Olofström,Sweden:
Tensiletest
ThetensiletestsareperformedbasedonthestandardEN10002-1.Theyieldstresses, r-values,tensilestrengthsanduniformelongationaredeterminedintherollingd irec-tion(0°),thetransversedirection(90°)and45°totherollingdirectionofthesheet metal.SamplecutoutsusedfortensiletestsareshowninFigure2.8c. Thedatais evaluatedbyusingtheARAMISDigitalImageCorrelation(DIC)system. Tensile testsalsogivesthefirstpartoftheplastichardeningcurve(uptoultimatetensile stress)whichisabout20%ofthetotalcurvewhiletheother80%iscalculatedfrom bulgetests[10,11].
Nakazima test (FLC and LDH)
The Nakazima test are conducted as shown in Figure 2.1 with the die and blank holder being static with the sheet metal while the punch being the static tool. The die is moving downwards to the punch with the sheet metal, giving it a rounded shape. The die moves until fracture occurs in the sheet metal. The setup and the punch are shown in Figure 2.7. The Nakazima test setup used by RISE is based on ISO 12004 with the modification of a hydraulic press with the ram speed of 25 mm/s to reduce friction between the punch and the blank. The punch has a diameter of 100 mm and is made of steel. The LDH-test is carried out with a prelubricated or as recieved in production, 200 mm circular blank that will yield unknown friction levels through the test. The strains are measured by painting the blank with a dotted pattern. Cameras watching the blank from above catches the change of the pattern, which then is used to calculate the strains. This test is what gives the strain and punch force data for inverse modelling that will determine the appropriate friction coefficient (Chapter 2.3). The FLC tests are carried out with lubrication conditions to give a friction coefficient close to zero. The blanks are varied between a 200 mm circular blank and a 25 mm wide dog bone sample, Figure 2.8a shows a few samples. This gives the look of the Forming Limit Curve, which determines when the blank will reach critical strains in simulations [10, 11].
Bulge test
A Viscous Pressure Bulge (VPB) test is used to acquire the equibiaxial yield stress, the equibiaxial r-value and the extension of the plastic hardening curve. This test is based on the work of M. Sigvant and K. Mattiasson [14]. The setup is similar to the LDH-test, the main difference is the punch is made of silicone with sensors inside and the draw radius is smaller. This test gives data which is used for calculations to extend the hardening curve. The first part of the bulge curve test is therefore not used and the curve from tensile tests is used instead. The curves are joined where they overlap. A sheet from a gulge test is shown in Figure 2.8b.
(a) Nakazima stamp setup (b) Punch tool
Chapter 2. Calibration of material models 11
(a) FLC Samples (from left): 75, 100, 125 and 200 mm
(b) Bulge sample (c) Tensile cutout samples
Figure 2.8: Test blanks from Nakazima and bulge tests
2.2.3
Triboform and friction Input
Triboform software is based on Johan Hol’s PhD thesis that describes a way to make an advanced friction model for SMF [15]. One of the biggest factors that affect the FE-results are the friction conditions on the sheet material and the tools. What affects the tribological conditions are the process and lubrication conditions that emerges locally on the sheet material, it also depends on the loading and strain conditions. The Triboform software enables to make a dynamic friction model that varies over time due to varying process conditions in simulations [16]. The condi-tions that Triboform depends on to predict the friction coefficient in the model is the contact pressure, plastic deformation, sliding velocity and temperature [4]. For usage, the software requires information input from the user, i.e. the sheet material and tool roughness, coating, the lubrication type and amount and also the process conditions. This information can either be accessed from a library in the software or entered by the user. The software manages to calculate the friction coefficient for conditions that can’t be measured from experiments e.g. straining and high pressure [7]. The generated friction model can then be imported from Triboform as a plug-in file for FE-software, i.e. Autoform.
2.3
Inverse modelling
Since there are uncertainties evolving around the accuracy of material models and new materials give the need for data tests, VCBC is using the data acquired from LDH-tests to calibrate its material models for adjustments and getting assurance that the simulations show accurate depictions of the material behaviour. What is acquired from the test is the major and minor strain in four process steps in two perpendicular sections, also the time related force from the punch tool. Since the unknown friction is present in the LDH-test and it has a correlation with the major and minor strain on the sheet material, the friction coefficient can be adjusted in the simulation until it is similar to the test results. Since the friction coefficient can change due to pressure and strain conditions [15], a Triboform friction model should provide an improvement in accuracy for the major and minor strains. This could also imply the exponent M in the model BBC 2005 needs to be changed. The process for Vegter 2017 is less complicated since none of the data in the model shall be manipulated.
2.4
MATLAB
MATLAB is a programming language developed by Mathworks. In this language, variables is based on matrices and the software has a wide range of applications [17]. The main use for this study is to plot, compare and evaluate the data curves and to compute the test and simulation differences. The data from ARAMIS is extracted as text files and the data from Autoform is exported as Excel files. MATLAB can read and plot the data from these files in one graph at the same time, ARAMIS can’t compare data from multiple files at the same time, which is time consuming. The reason to use MATLAB for the comparison is due to MATLAB’s ability to handle multiple files, being able to plot multiple graphs and is able to calculate the data differences. Being able to compare multiple simulations with the experimental data saves time.
Chapter 3
Related Work
There’s a reasonable amount in studies about implementing Triboform friction mod-elling to SMF in the automotive industry. Most of it has been made in collaboration between Tata Steel, Triboform Engineering from the Netherlands and VCBC. One of the earlier works are "Friction modeling in sheet metal forming simulations: Ap-plication and validation on an U-bend product" [7] is about implementing the model in a test that involves high sliding velocity on the sheet metal. It is concluded in this study that the prediction of the punch force, from this specific U-bend test was notably more accurate when compared with data from experiments and simulations using a Coulumb friction coefficient. It was also noted that using Triboform to test several friction conditions for simulations reduces the need of experimental tests. Later studies are about implementing Triboform friction models in the simulation process of making a car component e.g. "Friction and lubrication modeling in sheet metal forming simulations of a Volvo XC90 inner door" [3]. They concluded in a draw-in comparison (which is looking at the dimensions of the component by 3D-scanning) of the final part from a full scale production process with the simulation and concluded that the accuracy of the stamping simulation improves substantially if the advanced friction model and realistic lubrication conditions were used instead of a Coulomb friction coefficient. This study involved one material that came from Tata Steel and the process involved a notable sliding velocity between the tools and the sheet metal.
Another similar study is the "Friction in Sheet Metal Forming: Forming Simulations of Dies in Try-Out" [5]. The focus in this study was to implement the friction model to the aforementioned stamping tool and study the influence of different lubricants. In the article "Friction in Sheet Metal Forming Simulations: Modelling of New Sheet Metal Coatings and Lubricants" [6], they used Triboform to test new coatings and lubricants to see how it affects simulations. The conclusions from both of these stud-ies is that using Triboform gives more accurate results since the settings allow users to consider the mentioned conditions.
Since Triboform allows the user to control a wide range of parameters e.g. the surface roughness and lubrication conditions, it gives opportunity to investigate how those parameters affect the simulation results when the model is implemented. In "Friction in sheet metal forming: Influence of surface roughness and strain rate on sheet metal forming simulation results" [4] it is acknowledged that the tool surface roughness on the punch, die and the binder have a significant effect on the simulation accuracy, depending on the sheet metal. It was also noted that an SRS model was used for the simulations and that it had an effect on the strain values on some parts of the door component. In these articles, the BBC 2005 were used and they all can conclude that Triboform enables simulations to consider a wide range of conditions that can have an effect on the accuracy.
The master thesis "Material modeling in Sheet Metal Forming Simulations: Quality comparison between commonly used material models" [2] attempted to compare material models with a constant friction coefficient. In this study, the major and minor strain were compared at one time step and four models were tested. It was concluded that only two models gave decent strain results, BBC 2005 and Vegter 2017 and they should be chosen according to what material data is available. However, Vegter 2017 gave insufficient results when used for aluminum and the punch force magnitude was often overestimated.
In another work produced by J. Pilthammar [11], they attempted to automate the procedure to find a proper friction coefficient and the exponent M for the BBC 2005 model. However the method only worked when the data from FLC-tests (where the friction is close to 0) is considered and LS-dyna FE-software was used instead, however the problem with using the FLC-test is there are thick layers of lubrication that are difficult to consider in simulations. The report mentioned the problem with by only using the LDH-test for inverse modelling. There could be more than one combination of a suitable exponent M and friction coefficient. However it showed those factors are linearly dependent of each other.
Chapter 4
Method
4.1
Main approach
For most of the materials, the process will follow a main approach. For some cases it required a different approach to get satisfactory results which is mentioned in Chapter 5.2. The main approach to acquire optimal friction models for each material and both material models, is visualised in Figure 4.1. This is the only method that is used for this study, due to Volvo Cars giving certain restrictions and due to lack of time.
Make Triboform models Run in Autoform with a material model Compare simulations with experi-mental data Adjustments Are the results near? Evaluate yes no
Figure 4.1: Workflow for the study of friction and material models
4.2
The simulation setup
The setup in Autoform is a simulation of the LDH-test. The simulation will acquire strain and force data in four different process steps depicted in Figure 4.2, that re-sembles the experimental steps. Step one is when the punch is starting to notably deform the sheet metal, step two is when it’s starting to deform more, yet it’s still not going to fracture, step three and four is when most metals will start or getting close to fracture. The strain and the force will change notably over the whole process. The reason to look at all four steps, is to gain accuracy over the whole deforming process.
(a) Step 1 (b) Step 2
(c) Step 3 (d) Step 4
Chapter 4. Method 17
4.3
Materials
The study will be conducted on seven steel grades and four aluminum alloys listed in Table 4.1.
Family Material name
Mild steel CR3 CR4 CR5 Bake hardening CR210BH HSLA CR270LA
Dual phase CR330Y590T-DP
CR440Y780T-DP AA6014 Low strength (Advanz s118)
High strength (Advanz e170) AA6016 Unexposed (Ecolite 160ST)
Exposed (Superlite 160ST) Table 4.1: Material list
CR5, CR210BH and the DP family are provided by Tata steel, the other suppliers will stay anonymous. Data for the materials were made within the years of 2010-2016 and the material that isn’t used in VCBC-production when this study is conducted, is Superlite 160ST.
4.3.1
Process for Triboform models
While making the triboform model, it’s sought to recreate the conditions from the real LDH-test. Some of the materials are similar chemically and in their behaviour, therefore a couple materials is using the same friction models. This is listed in Table A.1. Some of the settings, for example the lubrication amount is assumed to be the same on all the Triboform models. Figure 4.3 shows the settings for a general case. When the conditions has been selected, the friction model can be adjusted by specifying a point (or multiple) and give a set friction coefficient value. This results in the coefficient among all the conditions change in parallel. In previous works mentioned in Chapter 3, they implemented the friction model from the Triboform library unchanged with known production conditions. In these cases, the velocity is so low it doesn’t apply for LDH-tests. The model has to be manipulated by the user to compensate to a lack of higher velocity. This is made by manually changing a point in the friction model. In most of the cases, the coefficients for the strain and pressure will change proportionally. This is then assumed to be within a reasonable range of 0.20 - 0.40, which gives the need to make multiple friction models for one metal to test which one gives the most accurate results. Figure 4.4 shows a few examples how the friction models looks in Triboform.
Chapter 4. Method 19
Figure 4.4: Manipulated Triboform friction models depending on pressure and strain
4.3.2
Work process in Autoform
The friction model is then implemented in Autoform R 8.01 along with the material model. The settings presented are standard at Volvo Cars. The mesh grid is trian-gular. The radius penetration is 0.1 mm and the element size is limited to 0.5 and 2 mm in the 50 mm radius of the blank to keep computational time within a range of 20 - 30 minutes. The captured moments from the tests are the correlating time steps in the simulations. From these time steps, the strain data are exported to compare. The data is from drawn sections that are 100 mm in length and crosses the center of the blank. Figure 4.5 shows the sections named as 1 and 2. In the results, section 1 called X and section 2 is called Y.
4.3.3
Comparison
The comparison between the simulation and experimental strains has usually been done in ARAMIS in most cases at Volvo Cars. However in this study it will be done in MATLAB since it gives the ability to plot and compare multiple simulations simultaneously and visualise the process steps in a manner that makes it clearer of what happens with the strain values. The code made for this also makes the data export from Autoform less tedious. Since the comparison is done with both the major and minor strain, in four process steps and in two different sections. This makes up to a total of sixteen exported CSV-files from one simulation. The punch force process gives a seventeenth CSV-file.
4.3.4
Adjustments
Most of the materials only need to have the friction models changed for better strain values, this is the only factor that can change for the Vegter 2017 model. Since BBC 2005 also has the M-value that affects the yield criterion, this value is also a subject to change for making the strain results to fit better with the experimental data. For some cases, changing the friction model won’t be enough to give decent results. Some materials behaves too differently from each other, so the friction coefficient on the holding tools (that is usually assumed to be constant) has to be changed. Some friction models has to be manipulated more drastically.
4.3.5
Evaluation
The evaluation will be made in two ways, visually and numerically. Both will be made with MATLAB code. For most of the comparison work, visual evaluation will be made to ensure the simulation strain and punch force graphs are near the exper-imental data. Usually that would be made with ARAMIS, however the MATLAB code enables to compare data from multiple simulations.
When a satisfactory setting for each material has been found. The difference will be calculated by using the experimental points to interpolate between simulation strain values, then taking the difference between the experimental strain and the interpo-lated simulation strain values.
The simulations and experimental data is the two strains, major and minor in four different time steps which will give eight RMS-values. This data is captured from two sections over the bulging area of the sheets, which gives eight more RMS-values. The punch force is also included for estimation. This makes up a total of seventeen different RMS-values to give an estimation of the difference between test data and a simulation for one model. The RMS estimation will be done for all the materials, with both models. This is done in MATLAB where it calculates the values from a vector. The RMS-equation is [18]:
xRM S = v u u t 1 N N X n=1 |xn|2 (4.1)
Chapter 4. Method 21 Where N is the amount data points, n is the data point and xn is the value in the
vector place n. This equation is rewritten to determine the rms-difference:
∆RM S = v u u t 1 N N X n=1 |"sim;n− "exp;n|2 (4.2)
Where "sim is the interpolated simulation strain and "exp is the experimental strain
data.
4.4
Approach for different cases
For some cases the standard work steps mentioned in previous sections won’t suffice. For some cases (e.g the dual phase family) the settings in the friction model or Autoform have to be adjusted for getting sufficient results. One of them are to manually change the friction model in a way to get proper strain results that agree with the experiment.
The second case is to make the friction model global, which means the friction model is applied to all the tools that are in contact with the sheet metal. This is tested for all metals in this study.
Results
What is important to note with the results, is when the experiments and the simula-tions are compared and the first ([X1] or [Y1]) and fourth ([X4] or [Y4]) experimen-tal step won’t agree well with the simulations, the second ([X2]/[Y2]) and the third ([X3]/[Y3]) simulation steps are prioritized to fit best. These steps are most impor-tant to get good accuracy for, when the models are used for other SMF-simulations. Another note is that some of the experimental data for the Y-section is not present in the report due to some of the data being obscured and inconsistent which doesn’t provide any clear information. The sections are as shown in Figure 4.5. The ex-perimental data is always the blue graph in the results figures, so if the simulation graphs are near, the prediction of the simulation is accurate.
5.1
BBC 2005 and Vegter 2017
5.1.1
Strains
When analyzing the strain comparison for all the metals between the material models, it is rather difficult to determine any consistency, since the results can differ heavily depending on the metal.
For the mild steel family, the consistency that could be determined is that both BBC 2005 and Vegter 2017 could predict the major strain accurately, however the minor strain differed quite heavily depending on the material models and the metal itself. When looking at CR3 the TF-model predicted the higher peaks better than the constant coefficient for major strain. However the minor strain prediction starts to give odd shapes for time step three (X3) and four (X4) in Figure 5.1. By looking at the results from using Vegter 2017 (Figure 5.2), the prediction for minor strain got overestimated in later time steps (X3 and X4) while in major strain, it got slightly worse than BBC 2005 but kept being within reasonable range of the experiment.
Chapter 5. Results 23
Chapter 5. Results 25 For CR4 it got underestimated in the first timestep while it got overestimated in the later steps for both models in the major strain path, however Vegter 2017 got closer than BBC 2005 in prediction, as shown in Figure 5.3.
Figure 5.3: Major and minor strain comparison for both material models with the steel CR4
For CR5, the major strain shows the same trend as CR3 and CR4, so it’s excluded in Figure 5.4. The minor strain showed the same wrongful predictions for later steps, the strains are overestimated, however BBC 2005 got a better prediction.
Chapter 5. Results 27 For CR210BH, the Vegter 2017 prediction was decent in the first step but got worse in later steps. BBC 2005 was able to follow the experimental data better. The major strain shows the same trend as CR3, CR4 and CR5, so it’s also excluded for CR210BH in Figure 5.5.
The most notable difference by using the TF-model on Vegter 2017 was found on CR270LA as shown in Figure 5.6. It was also able to predict the minor strains better than BBC 2005. Vegter without constant coefficient doesn’t predict the strain well, however with a TF-model it follows the experimental curve notably well.
Figure 5.6: Major and minor strain comparison for both material models with the metal CR270LA
Chapter 5. Results 29 For the aluminum alloy Advanz e170 there was no big improvement by using TF-models, however BBC 2005 got slightly improved accuracy with it. As can be seen in Figure 5.7, Vegter 2017 estimates the strains poorly.
Figure 5.7: Major and minor strain comparison for both material models with the aluminum alloy Advanz e170
For Advanz s118 both models made a relatively good prediction, since they both are predicting the strains close to the experimental data. Figure 5.8 shows BBC 2005 results and Figure 5.9 shows Vegter 2017.
Figure 5.8: Major and minor strain comparison for BBC 2005 with the aluminum alloy Advanz s118
Chapter 5. Results 31
Figure 5.9: Major and minor strain comparison for Vegter 2017 with the aluminum alloy Advanz s118
For Ecolite 160 ST, both models estimates a relatively accurate major strain path, however the minor strain from Vegter 2017 is giving a notably different shape, as seen in Figure 5.10.
Figure 5.10: Major and minor strain comparison for both models with the aluminum alloy Ecolite 160ST
Chapter 5. Results 33 For Superlite 160ST TF gave Vegter 2017 an improvement for both strains and is at the same area as BBC 2005, as seen in Figure 5.11.
Figure 5.11: Major and minor strain comparison for Vegter 2017 with the aluminum alloy Superlite 160ST
5.1.2
Punch force
When directly comparing the punch force from both the models and the test data, the TF friction model have no significant effect on the force. When it comes to the models for the mild steel family, simulations using BBC 2005 is following the test data curve perfectly, while Vegter 2017 is underestimating it in greater punch depths (after step two), as seen in Figure 5.12.
(a) BBC 2005 comparison for CR3 (b) Vegter 2017 comparison for CR3
(c) Comparison for CR4, both models (d) Comparison for CR5, both models
Chapter 5. Results 35 CR270LA and CR210BH have relatively good estimations of the force as seen in Figure 5.13.
(a) BBC 2005 comparison for CR270LA (b) Vegter 2017 comparison for CR270LA
(c) Comparison for CR210BH, both models
When it comes to aluminum, both models manages to overestimate the force in punch depths greater than approximately 15 mm. However Vegter 2017 seems to make the bigger error (Figure 5.14).
(a) Comparison for Advanz s118, both models (b) Comparison for Advanz e170, both models
(c) Comparison for Superlite, both models (d) Comparison for Ecolite 160ST, both mod-els
Chapter 5. Results 37
5.2
Heavily modified friction model
With the cases of the dual phase steel family, the friction model based of the DP800 library, wouldn’t give a parallel shift when one reference point was determined, which would give obscure strain results. In the usual cases the strain dependent direction in the friction model would be influenced in a way that would move the coefficient in a parallel trend. However for this metal type, it would depend more on the referenced strain values from the default library. With recommendations from Johan Hol, which is the person who wrote the PhD thesis mentioned in Chapter 2.2.3, multiple reference points had to be manually determined in the model to give a parallel shift. This in turn gives simulation results that could mimic the test data. Figure 5.15 shows the difference between friction models that are modified with one and multiple reference points. The heavily modified model is based of the CR4 library, since it gave the best parallel shift (based from the original DP800 model). Figure 5.16 shows the results with the heavily modified friction model for the steel CR440Y780T, both models predict the strains and the punch force accurately. Figures for CR330Y590T are excluded, since they show similar results compared to CR440Y780T.
Figure 5.15: Manipulated Triboform friction models. Blue: One reference point. Red: Multiple points
Figure 5.16: Strain and force comparison for CR440Y78T for both material models with constant and heavily modified friction model.
Chapter 5. Results 39
5.3
BBC 2005 SRS
With the dynamic hardening curve, the yield surface will give different results for the force as shown in Figure 5.17 (TF BBC SRS), the force will be overestimated and the strain is slightly changed. The force can be adjusted by changing the biaxial yield point, however this will give odd strain results (TF BBC SRS Test 1). To compensate the strains, the M-value and the friction coefficient has to be increased to decently give more accurate results (TF BBC SRS Test 2).
Figure 5.17: Strain and force comparison between normal BBC 2005 model and SRS with different settings.
5.4
Full Vegter
By the two materials that the full Vegter was tested for shows a significant difference in accuracy in both force and strains. Full Vegter is more accurate for both of the metals CR4 and Advanz e170 shown in Figure 5.18, in both strain and punch force.
Figure 5.18: Full Vegter and 2017 model comparison for metals CR4 and Advanz e170
Chapter 5. Results 41
5.5
Global friction model
When using a global friction model, no notable change was found at most of the metals, however a change was found among three aluminum alloys, Ecolite 160ST, Advanz e170 and Advanz s118 shown in Figure 5.19. The strains were moved pro-portionally and the force was unchanged.
Figure 5.19: Comparison between friction model implemented globally and sheet metal only.
Analysis and Discussion
6.1
BBC 2005 and Vegter 2017
When looking at the simulation punch force in comparison with the experimental data, it is clear that BBC 2005 has a better accuracy than Vegter 2017 for most cases. This is an effect from the difference in the biaxial yield points that are generated in the models. Since Vegter 2017 estimates the biaxial point and doesn’t take input data as BBC 2005 does, it runs the risk of varying in the yield surface. The reason could depend on the different methods Tata steel and RISE use for their tests for acquiring equibiaxial stress data, or that the pattern Vegter mention in their report [1] doesn’t apply for these metals. This was also known before that the punch force was inaccurate with the Vegter 2017 model.
While comparing the strains from using a constant friction coefficient and a multiscale TF friction model, some improvements can be seen e.g. the simulation curve moves closer to the test data curve and the curve shapes start to mimic the test data more. However some material simulations in the third and the fourth time steps, the minor strains are overestimated.
In the cases for CR270LA and Advanz s118 the Vegter 2017 model was predicting the strain better than BBC 2005 in some areas, the reason behind this is because the model managed to predict the biaxial yield point closely to the bulge test data. However it can’t be concluded that Vegter 2017 is an improved model when it badly estimates strains and forces on other metals.
For some metals, the models would often wrongly predict the max strain-tips in major strains, even when using the TF-models. An occurring theme was also the different strain shapes between Vegter 2017 and BBC 2005 in the same sections and time steps. This is caused by the associated flow rule, since the yield surfaces have different biaxial points and are calculated differently, they expand differently during plastic deformation and therefore give different strain results.
The difference between the models and test data can also be determined by looking at the RMS differences (A.2 - A.4), most of the values for Vegter 2017 are higher than BBC 2005.
Chapter 6. Analysis and Discussion 43 When it comes to inverse modelling for BBC 2005 there could be a range of combinations between the friction models and the coefficient M that could give a good fit for the strains, but for some metals the variable could be changed drastically to make them able to fit, for example one metal got a good fit with one friction model when the coefficient M was turned to the maximum value AUTOFORM allowed. This could probably be investigated further by lowering the exponent M and finding another friction model.
6.2
Full Vegter
By the limited tests with full Vegter shows a significant difference between it and Vegter 2017, the punch force is more accurately estimated by the full model and the simulation strains follow the test data more closely under the process steps. The punch force mostly depends on full Vegter having input data from biaxial tests, which means the assumption of BBC 2005 being accurate with the bulge test data is correct. The strain values are more accurately predicted, since the model has shear and plane strain tests and therefore manages to predict the strains better.
6.3
SRS BBC 2005
When implementing the SRS-model, it is shown that the biaxial factor have a signif-icant influence on both the strains and force. This further shows the perk of being able to adjust the biaxial data point for inverse modelling. It also shows the signif-icance of the biaxial yield point for the strains. A slight adjustment on that point shifted the strains greatly, wich has to be compensated with the coefficient M and friction coefficients.
6.4
Global friction model
Since the steel alloys strains were mostly unchanged and the aluminum showed a parallel decrease, it could depend on the characteristics of aluminum being more elastic. This would mean the simulation estimates the sheet to be straining and gliding between the tools depending on the friction coefficient. However, a global friction model work as a simplification for the mentioned steel grades.
Conclusions and Future Work
There are several conclusions that can be drawn from this. One conclusion is that adjusted Triboform friction models can improve the accuracy for SMF-simulations for both material models used in this study. The strains can be heavily affected by the friction coefficient, however the punch force is unaffected.
Another conclusion is that the Vegter 2017 is a good model only if it has managed to calculate a biaxial yield point similar that has been determined from a bulge test. BBC 2005 has the edge as a better model in this regard.
Another conclusion is that the Vegter 2017 is a slight downgrade from it’s predecessor in a sense that multiple yield points can’t be used as calibration input as it could be done in the older Vegter-model.
Conclusions that could be drawn from the singular test with the SRS-model is that it becomes more challenging to inverse model when both the strains and the punch force are considered. When the hardening curve is dynamic, it’ll then affect how the yield surface is calculated which will in turn affect the force. As the biaxial yield point is determined to acquire an accurate force the M-value and friction coefficient has to compensate to give decent strain which will be a balancing act.
Another conclusion is that using a global friction model in Autoform can be used as a simplification for steel grades, however Aluminum alloys has to be investigated further.
There’s a couple of recommended future works that can be conducted based from the results of this work. One suggestion is to use TF-models to investigate the BBC 2005 and Vegter 2017 difference for more materials from the same families to find if Vegter 2017 could be a better option for specific metal families.
Another recommendation for future work is trying to model the linear relation be-tween the coefficient M and TF-friction models for BBC 2005 to find optimal settings for several metals.
Another work is to further investigate the SRS-models for more materials to see how the friction and M-coefficient has to be changed when the biaxial yield point needs to be adjusted.
Another work is to find optimal settings for using global friction model in simula-tions, which would be a reasonable simplification that would remove the need for testing the tools friction coefficient.
References
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Appendix A
Tables
A.1
Autoform and Triboform material settings
Lubrication Friction modelsheet type Material thicknessSheet (mm) Sheet roughness ( m) Fuchs Anticorit RP4107S CR4-GI CR3 0.790 1.4 CR4 0.810 CR5 0.750 CR210BH 0.810 CR270LA 1.530 CR4-GI (modified) CR330Y590T-DP 1.200 0.9 CR440Y780T-DP 1.220 Fuchs Anticorit PL39SX AA6014 (AC118NG) Advanz s118 1.000 Walter Zepf AL200WL AA6014 (AC170PX) Advanz e170 1.020 Ecolite 160ST 1.010 Superlite 160ST 0.990
Table A.1: Settings for Triboform and material thickness
A.2
RMS Force difference
Force RMS difference [kN] BBC 2005 Vegter 2017 CR3 0.2103 1.3361 CR4 0.2848 2.4076 CR5 0.3208 1.5924 CR210BH 0.3408 0.4432 CR270LA 0.6578 2.2004 CR330 0.6264 0.9837 CR440 1.4574 1.6246 Ecolie160ST 0.5487 1.4696 Superlite 0.4297 1.0437 Advanz s118 0.3405 1.0963 Advanz e170 0.4672 1.6939Appendix A. Tables 49
A.3
BBC 2005 RMS strain difference
Strain Major BBC 2005 Section X Y Step 1 2 3 4 1 2 3 4 CR3 0.0033 0.0046 0.0167 0.0216 0.0035 0.0061 0.0124 0.0166 CR4 0.0073 0.0071 0.0091 0.0135 0.0056 0.0056 0.0216 0.028 CR5 0.0058 0.005 0.009 0.0092 0.0054 0.0059 0.0177 0.0244 CR210BH 0.0051 0.0052 0.0154 0.0178 0.0064 0.0082 0.0195 0.0241 CR270LA 0.0055 0.0084 0.0133 0.0154 0.0049 0.0088 0.0092 0.0176 CR330 0.0047 0.0095 0.0105 0.0125 0.0054 0.0124 0.017 0.0223 CR440 0.0061 0.0106 0.0124 0.0126 0.0074 0.0133 0.0172 0.0209 Ecolite 0.0118 0.013 0.0143 0.0157 0.0099 0.0107 0.0114 0.0118 Superlite 0.009 0.0095 0.0106 0.0135 0.0071 0.0074 0.0076 0.0144 Advanz s118 0.0064 0.008 0.0103 0.0195 0.0082 0.0122 0.015 0.0208 Advanz e170 0.0108 0.0119 0.0133 0.0156 0.0091 0.0095 0.0102 0.0156 Table A.3: RMS difference between major strains of BBC 2005 simulations and experiments Strain Minor BBC 2005 Section X Y Step 1 2 3 4 1 2 3 4 CR3 0.0036 0.0015 0.006 0.0064 0.0023 0.0027 0.007 0.0069 CR4 0.0057 0.0026 0.0068 0.007 0.0074 0.0051 0.01 0.0104 CR5 0.004 0.0009 0.0085 0.0089 0.006 0.0021 0.0085 0.0096 CR210BH 0.0044 0.0031 0.0023 0.0026 0.0048 0.0038 0.0047 0.0059 CR270LA 0.0067 0.009 0.0076 0.0095 0.0054 0.0054 0.0029 0.0041 CR330 0.0023 0.0051 0.006 0.0059 0.0025 0.005 0.0055 0.0049 CR440 0.0029 0.0048 0.0056 0.0065 0.0027 0.0041 0.0039 0.0039 Ecolite 0.005 0.0049 0.005 0.005 0.003 0.0032 0.0034 0.0034 Superlite 0.0064 0.0066 0.0073 0.0097 0.0057 0.0063 0.0065 0.0092 Advanz s118 0.0041 0.0044 0.0045 0.0043 0.0041 0.0033 0.0032 0.0033 Advanz e170 0.0081 0.0086 0.0088 0.0076 0.0086 0.0061 0.0058 0.0054 Table A.4: RMS difference between minor strains of BBC 2005 simulations and experiments
A.4
Vegter 2017 RMS strain difference
Strain Major Vegter 2017
Section X Y Step 1 2 3 4 1 2 3 4 CR3 0.0061 0.0055 0.0244 0.0281 0.0039 0.0061 0.0129 0.0182 CR4 0.0048 0.0045 0.0105 0.0141 0.0047 0.0065 0.0225 0.0292 CR5 0.0035 0.0059 0.0182 0.0212 0.0074 0.0113 0.0266 0.0335 CR210BH 0.0072 0.0086 0.0218 0.0251 0.0066 0.0087 0.0216 0.0268 CR270LA 0.003 0.0049 0.0135 0.0089 0.0028 0.005 0.0126 0.021 CR330 0.0053 0.0087 0.0092 0.0118 0.0053 0.0123 0.0157 0.021 CR440 0.0066 0.0098 0.0113 0.0109 0.007 0.0127 0.0161 0.0196 Ecolite 0.0114 0.0125 0.0138 0.0158 0.006 0.0065 0.007 0.0076 Superlite 0.0044 0.0043 0.0068 0.0097 0.0041 0.0048 0.005 0.0117 Advanz s118 0.0047 0.0082 0.0136 0.0242 0.0076 0.0117 0.0157 0.0227 Advanz e170 0.0089 0.0289 0.0343 0.0384 0.0103 0.0314 0.0368 0.0409 Table A.5: RMS difference between major strains of Vegter 2017 simulations and experiments
Strain Minor Vegter 2017
Section X Y Step 1 2 3 4 1 2 3 4 CR3 0.0035 0.0054 0.0132 0.014 0.0019 0.0024 0.0062 0.006 CR4 0.0028 0.0041 0.013 0.0138 0.0048 0.0045 0.0116 0.0124 CR5 0.0022 0.0064 0.0173 0.0194 0.0022 0.0041 0.0155 0.0181 CR210BH 0.0024 0.005 0.0116 0.015 0.0027 0.0046 0.0104 0.0135 CR270LA 0.0018 0.0019 0.0044 0.0033 0.0015 0.0044 0.0078 0.0064 CR330 0.003 0.0027 0.0031 0.0045 0.0034 0.0039 0.0034 0.0046 CR440 0.0025 0.0057 0.0063 0.0068 0.0027 0.0037 0.0035 0.0036 Ecolite 0.012 0.0129 0.014 0.0153 0.0082 0.0086 0.0092 0.0099 Superlite 0.0063 0.0069 0.0079 0.0106 0.0063 0.007 0.0075 0.01 Advanz s118 0.0031 0.003 0.0031 0.0038 0.0032 0.0031 0.0037 0.0045 Advanz e170 0.0103 0.0275 0.0296 0.0306 0.0090 0.0269 0.0287 0.0296 Table A.6: RMS difference between minor strains of Vegter 2017 simulations and experiments
