Sheet Metal Forming Simulations with Elastic Dies: Emphasis on Computational Cost

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Master of Science in Mechanical Engineering June 2019

Sheet Metal Forming Simulations with

Elastic Dies: Emphasis on

Computational Cost

Degree Project for Master of Science in Engineering

with Emphasis on Applied Mechanics

Sara Allesson

Supervisor: Johan Pilthammar, Lic. Eng. & Mats Sigvant, Ph.D.

Volvo Cars Body Components & Department of Mechanical Engineering, BTH Faculty of Engineering, Blekinge Institute of Technology, 371 79 Karlskrona, Sweden

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This thesis is submitted to the Faculty of Engineering at Blekinge Institute of Technology in par-tial fulfilment of the requirements for the degree of Master of Science in Mechanical Engineering. The thesis is equivalent to 20 weeks of full time studies.

The authors declare that they are the sole authors of this thesis and that they have not used any sources other than those listed in the bibliography and identified as references. They further declare that they have not submitted this thesis at any other institution to obtain a degree.

Contact Information: Author: Sara Allesson E-mail: saai14@student.bth.se University advisor: Mats Sigvant, Ph.D.

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

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Abstract

The car industry produces many of their car parts by using sheet metal forming, where one of the most time-consuming phases is the development and manufactur-ing of new formmanufactur-ing tools. As of today, when a new tool is to be evaluated in terms of usability, a forming simulation is conducted to predict possible failures before manu-facturing. The assumption is then that the tools are rigid, and the only deformable part is the sheet metal itself. This is however not the case, since the tools also deform during the forming process. A previous research, which is the basis of this thesis, included a model with only elastic tools and showed results of high accuracy in com-parison to using a rigid setup. However, this simulation is not optimal to implement for a daily based usage, since it requires high computational power and has a long simulation time.

The aim and scope for this thesis is to evaluate how a sheet metal forming simula-tion with elastic tool considerasimula-tion can be reduced in terms of computasimula-tional cost, by using the software LS-DYNA. A small deviation of the forming result is acceptable and the aim is to run the simulation with a 50-75 % reduction of time on fewer cores than the approximate 14 hours and 800 CPUs that the simulation requires today. The first step was to alter the geometry of the tools and evaluate the impact on the deformations of the blank. The elastic solid parts that only has small deformations are deleted and replaced by rigid surfaces, making the model partly elastic. Later, different decomposition methods are studied to determine what kind that makes the simulation run faster. At last, a scaling analysis is conducted to determine the range of computational power that is to be used to run the simulations as efficient as pos-sible, and what part of the simulation that is affecting the simulation time the most. The correlation of major strain deviation between a fully elastic model and a partly elastic model showed results of high accuracy, as well as comparison with production measurements of a formed blank. The computational time is reduced by over 90 % when using approximately 65 % of the initial computational power. If the simula-tions are run with even less number of cores, 10 % of the initial number of CPUs, the simulation time is reduced by over 70 %.

The conclusion of this work is that it is possible to run a partly elastic sheet metal forming simulation much more efficient than using a fully elastic model, without re-liability problems of the forming results. This by reducing the number of elements, evaluate the decomposition method and by conducting a scaling analysis to evaluate the efficiency of computational power.

Keywords: Elastic Sheet Metal Forming Simulation, Computational Cost, Decom-position, LS-DYNA

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Sammanfattning

Bilindustrin producerar många av sina bildelar genom att tillämpa plåtformning, där en av de mest tidskrävande faserna är utveckling och tillverkning av nya formningsverktyg. Idag, när ett nytt verktyg ska utvärderas med avseende på användbarhet, genomförs en formningssimulering för att förutsäga eventuella fel innan tillverkning. Antagandet är då att verktygen är stela och den enda deformerbara delen är själva plåten. Det är dock inte så, eftersom verktygen också deformeras under formningsprocessen. Tidigare forskning, som ligger till grund för detta examensarbete, inkluderade en modell med endast elastiska verktyg och visade resultat med hög noggrannhet i jämförelse med att använda stela verk-tyg. Simuleringen med elastiska verktyg är emellertid inte optimal att implementera för daglig användning, eftersom den kräver hög beräkningskraft och har en lång simuleringstid. Syftet och omfattningen av detta examensarbete är att utvärdera hur en plåtformn-ingssimulering med elastiska verktyg kan minskas med avseende på beräkningskostnaden, genom att använda programvaran LS-DYNA. En liten avvikelse från formningsresultatet är acceptabelt, och målet är att köra simuleringen med en 50-75 % minskning av tiden på färre kärnor än ungefär 14 timmar och 800 processorer som simuleringen kräver idag. Det första steget är att ändra verktygets geometri och utvärdera inverkan på deforma-tionerna av plåten. De elastiska solida verktygsdelarna som endast har små deformationer raderas och ersätts av stela ytor, vilket gör modellen delvis elastisk. Senare studeras olika dekompositionsmetoder för att avgöra vilka som gör simuleringen snabbare. Till sist ut-förs en skalningsanalys för att bestämma antalet processorer som ska användas för att köra simuleringen så effektivt som möjligt.

Korrelationen av huvudtöjningarna mellan en helt elastisk modell och en delvis elastisk modell visade resultat av hög noggrannhet, såväl som jämförelse med produktionsmät-ningar av en format plåt. Beräkningstiden minskar med över 90 % när man använder ungefär 65 % av den ursprungliga beräkningskraften. Om simuleringarna körs med färre antal kärnor, cirka 10% av ursprungligt antal CPUer, minskar simuleringstiden med 70 %. Slutsatsen av detta arbete är att det är möjligt att köra en delvis elastisk plåtformn-ingssimulering mycket effektivare än att använda en helt elastisk modell, utan att de re-sulterar i pålitlighetsproblem. Detta genom att minska antalet element, utvärdera dekom-positionsmetoden och genom att genomföra en skalningsanalys för att utvärdera effek-tiviteten av beräkningskraften.

Nyckelord: Elastisk plåtformningssimulering, beräkningskostnad, dekomposition, LS-DYNA

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Acknowledgments

This thesis is my last step towards a Master’s Degree in Mechanical Engineering with Emphasis on Applied Mechanics, conducted at Blekinge Institute of Technol-ogy (BTH) in Karlskrona, Sweden. This thesis has been carried out at Volvo Cars Body Components (VCBC) in Olofström, Sweden.

First and foremost, I would like to express my sincere gratitude and appreciation towards Lic. Eng., Johan Pilthammar and Ph.D., Mats Sigvant from BTH/VCBC who has been my supervisors during this project. Your impeccable knowledge, sup-port and valuable insights have helped and guided me throughout this thesis, thank you!

I would also like to extend my gratitude towards the CAE IT Department at Volvo Cars, especially Anton Persson. Without all of Your help and support, I would still be trying to figure out the simulation settings.

Ph.D. Mikael Schill, David Aspenberg, among others, from DYNAmore Nordic AB, Linköping. Thank you for letting me take part in the introduction course and taking Your time to answer all of my questions regarding the software LS-DYNA.

To Ph.D. Ansel Berghuvud, my examiner. I appreciate all of your comments and remarks during this semester.

This thesis was conducted within the project "Reduced Lead Time through Advances Die Structure Analysis", financed by the Swedish innovation agency Vinnova. The project is within the "Strategic Vehicle Research and Innovation (FFI) Programme", with the duration 2017-2019.

Last but not least, I would like to thank my wonderful parents, Pia and Kjell, for always believing in me and supporting me in everything I do. I love you.

Karlskrona, June 2019 Sara Allesson

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Nomenclature

Acronym Explanation

BTH Blekinge Institute of Technology CAD Computer-aided Design

CAE Computer-aided Engineering CPU Central Processing Unit FE Finite Element

FLD Forming Limit Diagram

GB Gigabyte

MPP Massive Parallel Processing RCB Recursive Coordinate Bisection SMF Sheet Metal Forming

SMP Shared Memory Parallel Processing VCBC Volvo Cars Body Components

2D Two Dimensional

3D Three Dimensional

File Format

.asc ASCII

.iges Natural CAD

.k Keyword

.txt Normal text

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List of Figures

1.1 Virtual and physical approach to die manufacturing . . . 2

2.1 General part setup and notation for deep drawing . . . 5

2.2 Simplified deep drawing process . . . 5

2.3 Schematic overview of a Single-action production press . . . 6

2.4 Hollow cylinder presented by different element types . . . 7

2.5 Distribution of integration points . . . 8

2.6 Three levels of adaptive mesh . . . 10

2.7 Two versions of computer setup for LS-DYNA simulations . . . 11

2.8 Theoretical FLD diagram showing major and minor strain . . . 13

4.1 Overview of general workflow . . . 17

4.2 General layout of a keyword from LS-PrePost interface . . . 18

4.3 Symmetry based LDH-tool from LS-PrePost . . . 19

4.4 Scaling analysis of LDH-tool with 4-25 CPUs . . . 20

4.5 Exploded view of the original model . . . 21

4.6 Representation of blank before and after gravity simulation . . . 22

4.7 Exploded view with scanned nominal surfaces . . . 23

4.8 Exploded view of model with scanned rigid surfaces . . . 24

4.9 Zoomed in version showing adaptive mesh level three . . . 25

4.10 Edited solid punch to surface . . . 26

4.11 Zoomed in version of die before and after remeshing . . . 27

4.12 Default decomposition . . . 28

4.13 Decomposition of models by using transformation . . . 29

4.14 Decomposition of models by using contacts . . . 30

4.15 Decomposition of models by using groupable algorithm . . . 31

4.16 First view: Major strain from production processed blank . . . 32

4.17 Second view: Major strain from production processed blank . . . 33

5.1 Draw in curve for model V.1.2 . . . 36

5.2 Major strain deviation - Model V.1.2 . . . 37

5.3 Second view: Major strain deviation - Model V.1.2 . . . 37

5.6 Second view: Major strain deviation - Model V.1.6 . . . 39

5.9 Second view: Major strain deviation - Model V.4.4 . . . 41 xi

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5.10 Major strain deviation between Model V.4.4 & Original model . . . . 42

5.11 Second view: Major strain deviation between Model V.4.4 & Original model . . . 42

5.12 Distribution of computational time and cost for model V.4.4 . . . 43

5.13 Filtered reaction force between solid blankholder and cushion . . . 44

5.14 Percentage distribution of time between 512 and 528 number of CPUs 45 5.15 Distributed time per CPU when using 512 cores . . . 46

5.16 Distributed time per CPU when using 528 cores . . . 46

A.1 Hardening curve for blank material . . . 60

A.2 Closing and forming velocities for the die . . . 62

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List of Tables

2.1 Values of integration point distribution . . . 8

2.2 Unit systems . . . 10

4.1 Type of element per part in original model . . . 21

4.2 Number of elements for model with nominal surfaces . . . 23

4.3 Number of elements for model with scanned surfaces . . . 24

4.4 Number of elements before and after remeshing of scanned die and punch. . . 28

4.5 Decomposition by transformation settings and versions . . . 29

4.6 Decomposition by contact settings and versions . . . 30

4.7 Groupable settings and versions . . . 31

5.1 Simulation time and adaptive mesh results for rigid surface models . . 35

5.2 Simulation time for the original model . . . 35

5.3 Reaction forces per forming stage . . . 44

A.1 Material card settings for rigid and elastic parts . . . 59

A.2 Material card settings for blank using *MAT_BARLAT_YLD2000 . 61 A.3 All types of contacts and their contact ID . . . 63

A.4 Material card settings for blank . . . 64

A.5 All model versions: Description and simulation time . . . 65

A.6 Simulation time with different number of CPUs - Model V.4.4 . . . . 66

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Chapter 1 Introduction

1.1 Background

Car manufacturing companies around the world have for many years used sheet metal forming (SMF) to produce components such as door panels, hoods and tailgates for their vehicles. Along with the constant aim of developing safer, lighter and sustain-able cars on a competitive market, the manufacturing procedures have become more advanced [1, p. 1]. In order to reduce the lead time for the entire project with the constant increase of complexity and introducing the next generation of cars on the market faster than the competitors, optimizations must be conducted within each step of the process.

There are many more parts of the car body than just the visible exterior which are produced by SMF. The average number of parts produced by this method for a Volvo XC90 at Volvo Cars Body Components (VCBC) is 120 pieces. Behind each component is a specific set of forming tool, made exclusively for that part. The num-ber of different car models that are in production simultaneously differ, but VCBC has the capacity of 20 press lines to their disposal. The SMF stage is, therefore, one of the most time-consuming processes within the car project. If the development of the SMF process could be optimized, there are significant savings to be made both financial and time-wise. By testing and evaluating the process for a single set of tools and implement the results throughout, the changes may result in a shorter lead time of the entire development of new cars.

If the risk of failure or crack propagation, along with other possible fatal er-rors, could be predicted by performing SMF simulations with highly accurate results within the virtual design process, the lead time could be reduced extensively. As of today, these simulations are performed with the assumption that the only deformable part is the sheet metal itself, and the tools are treated as rigid non-deformable bod-ies. However, this is not the case since the tools also deform during the forming process. The topic of introducing elastic deformable bodies is the main bulk of a previous study at Blekinge Institute of Technology (BTH) [2], which is going to be the basis of this master thesis. The results from the simulation in [2, p. 45] com-pared with real-life measurements from physical SMF tools are of high accuracy. It, however, requires high computational power and has a simulation time of approxi-mately 14 hours. This makes the usability of this type of simulations unsuitable to be implemented on a daily basis before the computational cost has been reduced.

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2 Chapter 1. Introduction

1.1.1 Company Organization

The background and content for which this thesis is based on were provided by VCBC, located in Olofström, Sweden. The company develops and manufactures the majority of the body components used for Volvo Cars. The computers, software and other necessary equipment used for this research were all provided by VCBC. The majority of the study was conducted via a laptop connected to Volvo Cars intranet and their cluster at Gothenburg, Sweden. If specific files or software were needed, the study took place at the office in Olofström. This also simplified the ability to discuss and ask questions to people with more knowledge about the subject.

1.1.2 Approach of Die Testing

The process of developing and manufacturing dies are today seen as non-optimal and time-consuming, where the workflow is shown in Figure 1.1, inspired by [1, p. 2]. When a new die is to be manufactured, the factory in Olofström receives the geometry of the car part as a 3D CAD-file from the design department.

Figure 1.1: Virtual and physical approach to die manufacturing

Before the physical die manufacturing process begins, the surfaces of the parts are imported to the software AutoForm, where an FE-simulation is run with rigid body assumption in order to detect possible failures. The die is later manufactured and arrives as a cast structure to the tool processing unit in Olofström. The surface of the die is rough and needs to be processed manually by either adding or removing material, often by using milling or welding methods. The manual rework of the tool leads to different appearance between the physical die and the virtual model that the CAE-engineers have to their disposal. The deviation causes problems, because there is no longer a virtual model that resembles the die that is to be used when manufac-turing the car part. This render communication and support problems between the two stages. If the same change is made in the virtual and physical environment, a positive impact during the simulation doesn’t necessarily improve the results on the physical die. If it is noticed that the sheet during testing of the stamping tools has failures, the process of manual work must continue. The estimated time for work and rework for a single tool is approximately five weeks [1, p. 2]. When taking the number of tools that are needed for manufacturing a car into consideration, it shows that a considerable amount of time is spent on this stage of the project.

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1.2. Aim and Objective 3

1.2 Aim and Objective

The aim and scope for this master thesis is to get a deeper understanding and knowl-edge about computational cost when conducting SMF simulations with elastic tool consideration. Computational cost includes both the computational power, i.e. num-ber of CPUs, as well as the computational time, which is referred to as total clock time. The aim is to reduce the computational time of the model used today by 50-75 %, while still providing major strain results which are comparable with real-life measurements, with a minor overall accepted deviation. Except for the need to reduce the simulation time, the computational power is also needed to be reduced. This to be applicable for a daily base usage, i.e. be run with a lower number of cores than used today. The efficiency of the number of used CPUs together with the simulation time is to be tested by conducting a scaling analysis, to determine the optimal number of cores to be used for this type of SMF simulations.

The contribution of this master thesis could render efficiency throughout the design and manufacturing process when designing components for the next generation of cars. The content of this thesis can be divided into objectives, where the first is to investigate and detect which possible settings that are affecting the computational cost. By changing these settings, the latter objective is to evaluate the efficiency of the changes conducted for the model.

1.3 Research Questions

1. How can a structural analysis model with elastic body consideration used for SMF simulations be reduced with regards to simulation time?

2. How can different settings within a SMF simulation be evaluated in order to directly be connected to computational cost?

3. How is a scaling analysis evaluated with regards to the efficiency of the utiliza-tion of computautiliza-tional power?

1.4 Hypothesis

1. Considering the elastic behavior only for effective areas of the stamping die and treating remaining parts as rigid, the simulation time can be reduced by increasing the element size.

2. If a specific change of setting is individually implemented on different models, the results of the changed and unchanged models can be compared with regards to computational cost.

3. By running a model with the exact same setup with multiple numbers of CPUs, the efficiency and computational power can determine the usability with respect to the user’s needs.

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4 Chapter 1. Introduction

1.5 Delimitation

The following listed aspects will not be considered in this master thesis:

• None other geometry information than the presented figures of the model will be included

• No financial aspects are to be studied

• The only SMF tool that is to be studied is the front inner door for the model Volvo XC90

• No lubrication aspects in the SMF simulation is to be studied

• No other FE-analysis software than LS-DYNA will be used when simulating the model

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Chapter 2 Theory

2.1 Sheet Metal Forming Process

The SMF process that is to be studied in this thesis is deep drawing. The general setup for this forming method includes the parts die, blank, blankholder and punch, see Figure 2.1 inspired by [2, p. 4]. The process begins with the blank placed between the punch/blankholder and die. Later, the blankholder moves towards the die and clamps the blank, see Figure 2.2a, which prevents wrinkles and keeps the blank positioned. In the forming stage, the punch starts to move with a prescribed motion and presses the blank into the die, see Figure 2.2b. The blank is exposed to forces that stress the material beyond its yield point and is forced to be shaped into a new form, without adding or removing any material.

Figure 2.1: General part setup and notation for deep drawing

(a) Closing stage (b) Forming stage

Figure 2.2: Simplified deep drawing process

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6 Chapter 2. Theory

2.1.1 Production Setup

In production, the setup includes more parts than previously described in section 2.1, see Figure 2.3 inspired by [3, p. 1]. Each production line must have the ability to change tools depending on what car part that is to be manufactured, preferably with short lead time. Therefore, the entire set och tools are stored together and can be transferred in a single move. The cushion in Figure 2.3 is hydraulic and is a part of the single-action press. It controls the pressure when in contact with the blankholder since a smooth forming process is desired without sudden impacts.

Figure 2.3: Schematic overview of a Single-action production press

In deep drawing, the two most common setups are single and double action pressing. When using double action press, the die is stationary and the punch is set in motion. The main difference between the two processes is that for the double-action, no hydraulic cushion is usually used.

2.1.2 Hot- and Cold-Forming

There are various reasons why different temperatures of the metal are used when performing SMF. Cold forming is referred to forming processes in room tempera-ture, while hot forming is carried out at temperatures higher than the materials recrystallization point [4]. The main difference between these two processes is the behavior of the metal during and after forming. In cold forming, where the sheet is plastically deformed, it is strengthened because of strain hardening [5]. By using this method, the limit of how much the metal can deform until necking or cracks occur is lower than using hot forming. When the temperature is increased, the yield point is lowered and less force is needed when forming. Depending on the type of metal and

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2.2. LS-DYNA Software 7 its material properties, the forming temperature has a direct impact on how complex the geometry of the sheet can alter. The type of SMF that is to be studied in this thesis is cold forming with a single-action press process.

2.2 LS-DYNA Software

LS-DYNA is a multiphysics code based software package developed by Livermore Software Technology Corporation (LSTC) and its origins date back to mid-1970s. The core of the software is based on highly nonlinear transient dynamic FE-analysis, and is often used by automotive industries because of its ability to simulate crashes, airbags and SMF [6]. The software in the package that is to be used is LS-PrePost and LS-DYNA. The pre-processing is for example where the meshing, loads and boundaries are specified by connecting parts, segments, elements or nodes to a specific keyword. When the material properties and the contact between parts, among others, have completed the setup for the simulation, the model is solved by LS-DYNA. The results, such as stresses, strains and reaction forces can later be studied by importing the results back to LS-PrePost.

2.2.1 Element Types

The types of elements that mainly are going to be used are solid and shell elements. Solid elements represent the complete geometry of a structure and could be explained as a full 3D imitation of a model. For shell elements, only the mid-surface of the structure is modeled and a thickness is assigned [7], see Figure 2.4 for comparison.

(a) Shell elements (b) Solid elements

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8 Chapter 2. Theory

2.2.1.1 Integration Points

Integration points through the thickness of shell elements are were the stress, nodal displacement etc. are calculated within the element. Depending on the type of inte-gration method that is used, the placement of the points differ. The two inteinte-gration methods tested in this thesis are shown in Figure 2.5 with associated location values in Table 2.1. The values in Table 2.1 corresponds to the percentage offset from the dashed mid surface [8, p. 2334-2335], shown in Figure 2.5.

0 20 40 60 80 100 -1 -0.5 0 0.5 1 (a) Gauss - 3 0 20 40 60 80 100 -1 -0.5 0 0.5 1 (b) Gauss - 5 0 20 40 60 80 100 -1 -0.5 0 0.5 1 (c) Lobatto - 3 0 20 40 60 80 100 -1 -0.5 0 0.5 1 (d) Lobatto - 5 Figure 2.5: Distribution of integration points

Method Int. points [Nr] Value

Gauss 3 0.775, 0

Gauss 5 0.9062, 0.539, 0

Lobatto 3 1, 0

Lobatto 5 1, 0.655, 0

Table 2.1: Values of integration point distribution

2.2.2 Implicit and Explicit Methods

LS-DYNA is by default using explicit time integration when solving the simulations, but can be changed to implicit by the user if wanted. An implicit solution strategy is often used for pre-loads [9], such as gravity or pre-tension of a bolt, where dynamics in the solution is unwanted. The explicit method is preferable when solving complex problems, such as SMF and impacts. The difference between explicit and implicit is depending on the time steps and integration method. When solving the equation of

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2.2. LS-DYNASoftware 9 state,theexplicitapproachisthatthetimestepisdeterminedbythesmal lestde-formableelementinthe model. Whensolvingananalysiswiththeexplicit method, verysmalltimestepsaretaken,thistoavoidinstabilitiesinthesolution. When solvingtheequationofstateforthenexttimestep,theexplicittimeintegration isbasedonearlierconﬁgurationsandcalculatesadirectsolution. This makesthe explicit methodconditionallystableanddoesnothaveconvergenceproblems. See Eq.2.1foranexplicittimeintegration.

xn+1=f(x_n,xn 1,...,tn+1,tn,...) (2.1)

Implicittimeintegrationisaniterativeprocess,whichisbasedonﬁndingequil ib-riumwhenusingknownandunknownconﬁgurations.Thetimestepfortheimplicit methodisvaryingandcantherebybemuchlarger,whichoftenmakesthesimulation runfaster. However,thedrawbackisthatth isstrategycanhaveconvergenceprob-lemsandcanbeunconditionallystable.SeeEq.2.2foranimplicittimeintegration. 0=f(x_n+1,xn,xn 1,...,tn+1,tn,...) (2.2)

2 .2

.3 MassSca

l

ing

As mentionedinsection2.2.2,thesmallestdeformableelementhasadirectimpact onthesolutionstrategyforexplicittimeintegration.Ifa modelconsistsof many largeelements,andonlyafewthatisconsiderablysmaller,thetimestepcanbe alteredtobelargerandtherebyspeedupthesimulationbyusing massscaling[10]. ThecriticaltimestepisdeﬁnedbyEq.2.3[11].

∆tcritical=_cle

e (2.3)

Where leisthelengthofthesmallestelementandceisdeﬁnedbyEq.2.4.

ce∼ E_ρe

e (2.4)

Where Eeis Young’s modulusandρeisthedensityofthe material.Inorderto

increasethecriticaltimestep,thedensityisincreasedforthesmallestelements. Thisrenderthatthesmallestelementshaveamassincrease,andleadstoanincrease ofthe model’sinertiaproperties,whichtheuser mustbeawareof,sinceitcanhave animpactontheendresult.

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10 Chapter2. Theory

2 .2

.4 Un

itsystem

LS-DYNAisasoftwarewheretheusermustbeconcisewhendefin ingthemassprop-ertiesand measurementsforthe model. Whendefiningtheseparameters,thereare nooptionsforpersayenteringthelengthin metersor millimeters,or massinki lo-gramsorgrams. ThisisbasedonNewton’ssecondlaw,whichrequiresaconsistent unitsystem.Iftheunitsaren’tcohesive,thesimulationscangiveinaccurateand misleadingresults.ThemostcommonunitsystemsarelistedinTable2.2,whereS2 ischosentobeusedwhendefiningthepropertiesinLS-PrePost.

UnitSystem S1 S2 S3

Length meter millimeter millimeter

Time second second millisecond

Mass kilogram tonne kilogram

Force Newton Newton kiloNewton

Young’s Modulus Pa MPa GPa

Density kg/m tonne/mm kg/mm

Gravitation m/s mm/s mm/ms

Table2.2: Unitsystems

2 .2

.5 Adapt

ive Mesh

Whenperformingsimulationswithlargedeformations,itcanbedifficu lttodeter-minethesizeofthe meshtogetaccurateresults,especiallyiftheplacementofthe deformationscan’tbepredicted. Afinemeshovertheentiremodelcanbeseenasa quickfix,butcanrenderunnecessarilylongsimulationtime. Amethodthatcouldbe implementedisadaptivemesh,wheretheusercanchoosetolettheoriginalmeshbe refinedthroughoutthesimulationiterativelywithinacertainrange. Acomparison betweena meshwithoutadaptivity,seeFigure2.6a,andanadaptive meshwitha meshrefinementleveloftwoandthreecanbeseeninFigure2.6b-c. Arefinement levelisthemaximumamountoftimesameshcanbedivided,includingtheoriginal sizeofthe mesh.

(a)Level1 (b)Level2 (c)Level3

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2.2. LS-DYNA Software 11

2.2.6 Parallelization Strategies of SMP and MPP

When the model is sent to LS-DYNA for analysis, there are two different computer setups. The Shared Memory Parallel (SMP), is dividing the model within one com-puter on different cores (CPUs), see Figure 2.7a, and is often used when analyzing smaller models. For the Massively Parallel Processing (MPP) version, a multiple sets of computers must be available and connected [12], such as a cluster, where the model is divided between interconnecting computers, see Figure 2.7b. Within MPP, there are numerous different settings to partition the model, called decomposition which is discussed in section 2.2.6.1. For large and multi-physic models, the MPP version of LS-DYNA is highly recommended to greatly reduce the simulation time.

(a) SMP (b) MPP

Figure 2.7: Two versions of computer setup for LS-DYNA simulations

2.2.6.1 Decomposition

There are multiple ways of partitioning the model before the analysis is started, and has a direct impact on the simulation time with regards to what type of model that is to be solved. Depending on the decomposition method, the model is partitioned between the cores in different ways. Recursive Coordinate Bisection (RCB) is the recommended partitioning algorithm and is based on the global coordinate system of the model [8, p. 1105]. The default setting is that the algorithm is partitioning the model in the direction which has the largest dimension [13, p. 3]. There is a keyword in LS-DYNA called *CONTROL_MPP_DECOMPOSITION_SHOW which graph-ically shows the decomposition before the simulation is started. This can be helpful when evaluating if the partitioning is seen as acceptable. Another keyword, called *CONTROL_MPP_DECOMPOSITION_TRANSFORMATION, lets the user de-fine an axis of which the model is scaled along, both by translation or rotation. It is to be stated that the decomposition only scales or divides the model before analysis, and should not have an impact on the output results such as stresses, strains and displacement.

*CONTROL_MPP_DECOMPISITION_CONTACT_DISTRIBUTE is a decom-position method where, the user defines a specific contact for which the connected parts are distributed between all the cores. The main purpose of this method is to divide the parts in contact equally between all the cores, so that they all will solve

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12 Chapter 2. Theory the model within the same time range. If the decomposition is made poorly, it can result in that a few cores are taking a lot longer time to solve their individual part of the model the others. If so, it affects the computational time since the simula-tion cant be finished before the entire model is analyzed. Another method, that is not based on decomposition, but could improve the simulation time significantly, is *CONTROL_MPP_CONTACT_GROUPABLE. This is by using an algorithm that especially is used for surface contacts were the contacts, based on their configu-ration, are processed differently than the normal MPP algorithm [8, p.1093]. There are four different options within the keyword, where the user either can turn on or off the algorithm if the contact type is tied or non-tied based.

2.2.7 Scaling Analysis

If the simulation time is longer than intended, the easiest attempt to speed up the process is to increase the number of CPUs. However, this implementation doesn’t always work as intended, because of the scalability. For linear scaling, the simulation time is reduced by half if the number of CPUs is doubled. If this statement always were true, all models could be solved within seconds as long as the user has access to a considerable amount of CPUs. The MPP scaling is affected by both the software and hardware, were one or the other, or a combination, has influence on the simulation time. A scaling analysis, that is, solving the same model with a varying number of cores, often gives a good indication of how many CPUs that are needed. There is no easy way of knowing beforehand, but a guideline is to use one CPU per 100.000 deformable element. In some cases, the solution time can increase if the number of cores increases, and clearly indicates that the scaling have a negative impact on the simulation time. It is often up to the user to evaluate if the increase of cores is acceptable with regards to the simulation time, and how many CPUs that are to be used.

2.3 GOM Inspect

GOM Inspect is a free software that often is used for inspection and re-meshing of scanned measured surfaces and CAD-models. The software provides a preview of the installations before accepted, which is helpful to visualize the changes.

2.3.1 GOM Inspect SVIEW

SVIEW is an add on to the software GOM and lets the user import FE results such as stress, strain and thickness. The software accepts a variety of different output files, such as .k files from LS-DYNA and .asc files from ABAQUS. The ability to compare simulation and measured results to detect deviation with a variety of input file options, makes the software SVIEW easy to use when comparing or verifying SMF results.

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2.4. MathWorks MATLAB 13

2.4 MathWorks MATLAB

MATLAB is a programming language were variables are based on arrays and is developed by MathWorks. The software is used worldwide and has many areas of application. The primary use is for numerical computing, but can also be used to plot and evaluate data from other software.

2.5 Forming Limit Diagram

One of the most commonly used measurements for deformations in SMF is major and minor strain, which often are presented in a forming limit diagram (FLD). The diagram is primarily used for evaluating and predicting failure such as necking or cracks in the formed blank [14]. If a circle is mapped on a sheet before the forming process has started, and the same area is later evaluated, the major and minor strains can be determined. Regardless of the coordinate system prior to the forming, the major strain is always specified along the axis which has the largest deformation, while the minor strain is in the direction perpendicular to the major strain axis. Figure 2.8 is inspired by [14] and shows a simplified FLD, where the directions of drawing and stretching are specified.

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Chapter 3 Related Work

3.1 Preparatory Work

The importance of including elastic die deformations and friction modeling when performing SMF simulations was addressed by J. Pilthammar et al. in [15]. A vari-ety of methods are developed and investigated, were one setup was to combine two FE-models. This by first performing structural analysis to detect tool deformations on 3D solids, where some of the tools were elastic and other rigid. Later, the die de-formations were imported to the scanned 2D surfaces which were used for the SMF simulations. By using this type of setup, J. Pilthammar et al. showed that tool deformations can and should be implemented when using 2D surfaces for SMF. The result of this implementation showed that the model with die deformations had high resemblance when comparing with a production stamped die. In order to improve and make the method more efficient, they suggest combining the two models into one while still evaluate the influence of the simulation time.

The ability to introduce a SMF model with only elastic body consideration was studied by Lind and Sjöblom in their master thesis [2] from BTH in collaboration with VCBC. They showed, by using the software LS-DYNA, that one can implement elastic solid bodies when performing SMF simulations and obtain results that are of high accuracy. The main focus of Lind and Sjöblom’s thesis was not only to in-vestigate if elastic die consideration was feasible. They also compared the difference between the results from the usage of nominal and scanned die geometry, as well as using rigid dies. The presentation of the results was by draw-in curves that showed the offset of the edges of the formed blank, and major strain comparison between the simulations and reality. The conclusion of the work from Lind and Sjöblom was that the combination of scanned surface geometry with elastic solid dies gave the most ac-curate results, and that there was a deviation between the use of rigid and elastic dies.

3.2 LS-DYNA

The use of modal methods for reducing the simulation time considerably for transient dynamic analysis was investigated by Benson and Maker [16]. By using flexible rigid bodies and extracting the mode shapes by using modal methods, a representation of the deformations and strains can be obtained. It is however stated that the method only supports small changes in the model. Benson and Maker presented one of their

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16 Chapter 3. Related Work results by comparing a traditional explicit approach with modal analysis, and that the time savings for a model with 10.000 fully integrated shell elements was 300 times faster. The implementation of modal methods aren’t restricted to the entire model, but can be used for a single, or more parts within a model that is solved using default settings for explicit analysis.

A SMF simulation with various settings and blank thickness is studied by He and Du Bois in [17]. They attempted to find the most suitable implementation to lower the computational cost without having reliability problems of the results. The main three sections that were studied were mass scaling, tool traveling speed and adaptive mesh. They raise the importance of having a fine mesh at the end of performing SMF, since the deformations at that stage are large. For their study, they don’t see any advantages from having a uniform mesh at the start, without adaptive mesh selected. He and Du Bois concluded that the results from different blank thicknesses with the same settings shows some deviation. And, that it is difficult to determine a specific setup that works in general for SMF. They have noticed that the slightly different results could depend on the MPP-code, and that the results from the two thicknesses were comparable when only running the simulations on a single CPU.

3.3 VCBC and Universities

Topology optimization of an integrated solid blankholder was studied by Sudda-palli and Tatipala [18] at BTH in collaboration with VCBC. By using the software Optistruct, the shape and structure were optimized to increase the stiffness of the blankholder. By using the results from the topology optimization and implement the results on a CAD model, a structural analysis of a simplified press model was implemented. The results showed that a weight increase of 17% for the blankholder reduced the levels of stress in the tool extensively, and showed a more uniform stress distribution than with the original structure.

A comparison between SMF simulations and traditional try-out methods when new tools are to be manufactured was studied by Andersson in [19], a collaboration with VCBC and Lund University, Sweden. His aim was to investigate the benefits of implement simulations at VCBC in comparison with try-out methods. As the forming simulations in this stage of time are far more accurate than a decade ago, the use of try-out methods i.e. physically build a prototype and test the die design, is very time- and cost consuming. Andersson claims that the advantages of SMF simulations are seen throughout the process, from early stages in the tool design to the end stage of when the tool is running in production. However, Andersson also states that in order to go towards simulations for testing of die designs, the user must be very conscious when evaluating the results.

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Chapter 4 Method

4.1 General Workflow

An overview of the general workflow is shown in Figure 4.1. The pre-study is referred to as section 4.2-4.4 and the workflow from section 4.5. The grey areas in the figure represent evaluation procedures, the orange areas represent decision making and blue areas mostly involves model- or simulation-setup.

Figure 4.1: Overview of general workflow 17

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18 Chapter 4. Method

4.2 Introduction to LS-DYNA

In LS-PrePost, where the model is set by applying loads, boundary conditions, ma-terials, etc., they are all set by using keywords. From this stage and forward, all significant keywords are to be presented by the notation [*] followed by the name of the keyword in capital letters. An example is *MAT_RIGID, which is a mate-rial card used for defining rigid matemate-rials, see Figure 4.2 for a general outlay of a keyword. Each and every keyword can be found in the LS-DYNA Keyword User’s Manual Volume I [8], with a short explanation and in some cases implementation examples.

Figure 4.2: General layout of a keyword from LS-PrePost interface

4.2.1 Settings and Guidelines for Simulations

It is very important to be concise with settings when running simulations that later are to be compared by their computational cost. When using any kind of CAD- or FE-software, there will most likely occur problems if models are opened or simulated with different versions of the software. Therefore, the chosen versions for LS-PrePost is Linux V.4.5 and R9.3.0 for LS-DYNA. As described in section 2.2.6, there are two options when solving models in LS-DYNA. Since the models are complex and include many elements and settings, the MPP version is chosen.

The server in Gothenburg consists of several clusters, where all of them have a different number of cores per node. If a specific setting is not chosen each time a simulation is to be sent for analysis, the user can’t decide which the assigned cluster will be. If the number of chosen CPUs for running the model is not evenly dividable with the number of CPUs per node, the simulation time can be increased. A setting was therefore selected to each time run the simulations on the same cluster with even number of CPUs.

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4.2. Introduction to LS-DYNA 19

4.2.2 LDH-Tool

A simple model of an LDH-tool was provided by VCBC for understanding the SMF process when using LS-DYNA. The model is used for biaxial testing with a variety of thicknesses for the blank in order to determine the material properties, such as Yield- and Ultimate-strength. Since the LDH-tool is symmetric, only a quarter is modeled with the use of symmetry boundary conditions in x- and y-direction, see Figure 4.3. The die, blankholder and punch are rigid and the blank is deformable with adaptive mesh.

This model was mainly used for evaluating and testing settings and changes that were to be implemented on the larger model with elastic dies. The LDH-model had a simulation time of approximately three minutes, which was desirable when wanting to evaluate if the settings worked as intended.

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4.2.2.1 Scaling Analysis of LDH-Tool

A scaling analysis was set up for the LDH-model, which usually is run with a sim-ulation time of 3m15s when using 15 CPUs. As a start, the model was run with two CPUs and increased with steps of two until the scaling leveled out, then larger steps were taken. From Figure 4.4, one can see that the simulation time decreased considerably between four to ten CPUs, to later even out. The two last points to the right-hand side of the figure only differ by one second. When increasing the cores from 20 to 25, the simulation time saving is only 0.6%. The simulation time when using two CPUs differed between each run and will be excluded from the plot.

4 6 8 10 12 14 16 18 20 22 24 26 CPU [Quantity] 0 1 2 3 4 5 6 7 8 Time [min]

LDH-model - Computational time per CPU

Figure 4.4: Scaling analysis of LDH-tool with 4-25 CPUs

4.3 Original Model

The setup of the model from [2, p. 24] is presented in an exploded view, see Fig-ure 4.5. It consists of 11 parts where five are solid, five are scanned and the deformable blank. All of the solids are assigned with elastic material properties and are thereby deformable. The solid- die, blankholder and punch are CAD geometries and are con-nected to their scanned surfaces to represent the true geometry of the tools in produc-tion. The surfaces are assigned a null material and are tied to the solids by *CON-TACT_TIED_NODES_TO_SURFACE_CONSTRAINED_OFFSET, which can be explained as the solids have extended surfaces. Null material doesn’t have ma-terial properties, but can transfer pressure, forces, etc. to the solid. The cushion and guide rails are not presented as they appear in production, but serves the same purpose. The model consists of approximately 10.000.000 elements, see Table 4.1 for the specific number of elements per part. There are several die velocities tested in [2, p. 34], were the model with 2500 mm/s is chosen as reference for this thesis.

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4.3. Original Model 21

Figure 4.5: Exploded view of the original model

Part Element Type Nr of Elements

Solid Die Solid 1.519.259

Scanned Die Shims Shell 9.570

Scanned Die Shell 2.947.989

Scanned B.H. Shims Shell 109.928

Blank Shell 1.817.747

Scanned B.H. Shell 781.648

Scanned Punch Shell 1.793.429

Solid Blankholder Solid 280.665

Solid Punch Solid 641.526

Cushion Solid 64.078

Guide Rails Solid 6.712

Total 9.972.551

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22 Chapter4. Method

4 .3

.1 OtherSpec

iﬁcSett

ings

Theblankfortheoriginalmodelwascreatedwithanadaptiveleveloffour,andwas settohaveﬁveintegrationpointswiththeGaussmethod.Thethicknessoftheblank foreachandevery modelis0.7 mm. Massscalingisusedforall modelsbysetting theparameter DT2MSto-1.2e6_{in*CONTROL_TIMESTEP}_.Th_{is masssca}_l_ing

parameterisnottobechanged,sinceanincreaseoftheparametercouldresultin dynamicbehavioroftheparts. Thedensityofthesolidblankholderandcushionis settobeunrealisticallylow,7.85kg/m3_asdescr_ibedin[2_,p_.35_]_.

4 .4 SMF w

ithSurfaces

Inordertounderstandthesetupoftheoriginal model,thescannedsurfaceswhere exportedandsavedasindividualparts. Sincetheoriginal modelisquitelargein termsoffilesizeandinvolvesapproximately120differentkeywords,itissomewhat challengingtodeterminewhateffectsthesettingshaveontheendresult. Thein-dividuallysavedpartswereimportedtoLS-PrePosttocreate modelsbyonlyusing surfaces. Whenthesurfacesaren’tconnectedtoasolidgeometry,they mustbe definedbyrigid materialinordertobeapplicableforformingsimulations. There wheretwo modelsthatwerecreated,onewithnominalandonew ithscannedsur-faces. Togetaperceptionoftherequiredcomputationalpowerforonly movingthe rigidparts,theblankwasremoved. Theresultswillthengiveanindicationofhow fastthe modelcanberun. Thesettingsforadaptive meshwasalsotestedbyusing these models,whereadaptiveleveltwo,threeandfourweretestedfortheblank.

4 .4

.1 Grav

ityLoad

ing

Beforethenewmodelscouldbecreated,anothermodelprovidedbyVCBCfrom[2, p.11]hadtoberun. This modelconsistsoftwoparts,thenominalsurfaceofthe blankholderandtheblankbeforeusingadaptive mesh,seeFigure4.6. Thepurpose ofthissimulationistoshapetheblanktoﬁtontothesurfaceoftheblankholder. Implicittimeintegrationisusedbecausedynamicsintheblankisunwanted,were theonlyforceactingontheblankisgravity. A.dynainﬁleiscreatedthatconsistof thereshapedblankandtheinitialstresses.

(a)Before (b)After

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4.4. SMF with Surfaces 23

4.4.2 General Setup with Nominal Surfaces

The nominal surfaces of the die, blankholder and punch were imported to LS-PrePost where the material was set as *MAT_RIGID, see Appendix A.1. No tilting of the tools are included, and the parts were only allowed to move in negative z-direction, see Figure 4.7. The blank is deformable and assigned an elastic material card using *MAT_BARLAT_YLD2000, see Appendix A.2-A.3. A prescribed motion was set for the die using *DEFINE_CURVE and consists of two stages, the closing and forming stage, see Appendix A.4. During the closing stage, the die is moving towards the blankholder and clamps the blank in between to prevent the blank from sliding or moving. In order to clamp the blank during the entire simulation, a force of 1.5 MN is assigned. During the forming stage, the die and blankholder are moving forcing the blank to adopt the shape of the punch, which is stationary during the entire simulation.

Figure 4.7: Exploded view with scanned nominal surfaces

When an SMF model is set up in LS-PrePost, the most common keyword to use when determining which parts that control the deformation of the blank is *CON-TACT_FORMING_(OPTIONS). This contact is based on a master/slave relation-ship in combination with a hierarchic setup. The master/slave setup is based on that the part which is set as slave must follow the motion and shape of the master. It is very important to determine these relationships correctly so that there aren’t any conflicts, since the simulation otherwise is terminated. A conflict that can cause termination is that a part is set as master in one keyword and a slave in another. The easiest way to set these master/slave relationships is to begin with the part that has the prescribed motion, and continue throughout the model. The number of elements per part before using a pre-adapted mesh is seen in Table 4.2.

Part Nr of Elements Blank 63.734 Blankholder 41.299 Die 152.435 Punch 108.912 Total 366.380

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24 Chapter4. Method

4 .4

.3 ScannedSurfaces

Themodelsetupforusingscannedtoolsurfacesarethesameasfornominalsurfaces, seesection4.4.2. Sincethesurfacesarescanned,theyconsistofalotsmallerand thereby moreelements,seeTable4.3. Theelementsdifferinsizeduetothatfiner measurementsaretakenwhenthegeometrychanges,asforexamplearoundfillets andholes. The maindifferencefromusingnominalsurfacesisthattheshimsofthe dieandblankholderareappliedseparately,seeFigure4.8.

Part NrofElements

Blank 63.734 Blankholder 781.648 Shims 109.928 Die 2.947.989 Shims 9.570 Punch 1.793.429 Total 5.706.298

Table4.3: Numberofelementsfor modelwithscannedsurfaces

Figure4.8:Explodedviewof modelwithscannedrigidsurfaces

4 .4

.4 Adapt

ive Mesh

Theundeformedblankconsistof63.734elementswiththeapproximatesizeof 36mm perelement.Figure4.9showsazoomedinversionoftheadaptivemeshwith threelevels. Astheformingprocesshasreacheditsterminationtime,thenumber ofelementshasbeenincreasedtoapproximately730.000. Whentheadaptivelevel issettofour,thenumberofelementsisincreasedtoapproximately1.800.000. The purposeofreducingtheadaptiveleveltothreeistoseeiftheresultsdiﬀerwhen importedtothemodelwithelasticdies. Amodelwithleveltwowasalsotested,but concludedincracksintheblankduetoanerrorinmassscalingandisthereforenot used.

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4.5. Modifications of Original Model 25

Figure 4.9: Zoomed in version showing adaptive mesh level three

4.5 Modifications of Original Model

The first step towards a model with reduced computational cost was to remove settings, nodes and elements that were present in the original model, but not used. A tool in LS-PrePost called Model Checking was used, which evaluates each keyword, part, node, among others, to detect possible errors before the simulation is started. The checking indicated that there were approximately 650.000 unreferenced nodes in the model, which can be explained as nodes that are placed arbitrarily in space, but isn’t connected to a part or keyword. The original file size is 1.5 GB, and was reduced with 0.15 GB when all unreferenced nodes were deleted. The changed model was sent for analysis to see if the reduced file size and unreferenced nodes had an impact on the simulation time. All keywords, curves, sets and other settings were renamed and checked to enhance the comprehension of the model. From this stage and forward, the version for the newly created models is listed in the caption, as for example in the upcoming section 4.5.1.

4.5.1 Remove Solid Die and Punch - Model Version V.1.1

It is known from [1, p. 32] that the solid part that deforms the most during the forming operation is the solid blankholder. The solid die was therefore deleted and replaced with it’s scanned null surface and assigned with a rigid material. The con-tact *CONTACT_TIED_NODES_TO_SURFACE_CONSTRAINED_OFFSET between the solid and scanned die was removed and the forming contact *CON-TACT_FORMING_SURFACE_TO_SURFACE_ONE_WAY was set between the surface of the die and the blank.

The second step was to remove the solid punch, in the same way as for the die. During the forming process, there is a contact between the solid punch and blankholder, that guides the blankholder in the right position of the punch. Since the scanned surface of the punch only is available for the area which is in contact with the blank, the contact areas were added by using mesh by plane in LS-PrePost, see Figure 4.10 for the newly created model. The total number of deleted solid elements was 2.160.785 and the file size is now reduced to 1.3 GB.

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Figure 4.10: Edited solid punch to surface

4.5.2 Updating Contact Keywords - Model Version V.1.2

There are multiple options for each of every used contact keyword in the model, see Appendix A.5 for all contact keywords used for all versions of the new models. Since two null surfaces and solid parts were replaced by rigid surfaces, the settings for the forming contacts in these regions were changed. It is known from [2, p. 31] that the contacts were set to update more frequently when contact keywords with null material were used. The value of Bucket was therefore reset to the default value of 200, instead of the former 10. This means that the forming contacts updates less frequently. As a start, the Bucket option was only changed for the forming contacts between the die/blank and punch/blank. This to evaluate if the change made the simulation run faster and to see if it had an impact on the end result of the formed blank. Later, all of the four forming contacts were set to have the value set to 200.

4.5.3 Change of Blank Material

The material card previously used for the blank is *MAT_BARLAT_YLD2000. There are over 150 different material cards to the user’s disposal when using LS-PrePost, each with the option of implement a variety of material data. If a lot of data is included, the material card takes a longer time to read when simulating the model, but often render simulation results that are of higher accuracy. A new material card is tested, called *MAT_TRANSVERSELY_ANISOTROPIC_ELASTIC_PLASTIC, see Appendix A.6. This card is especially used for blank materials, but only considers

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4.6. RemeshingofScannedSurfaces-V.3.1-2 27 transverseanisotropyofthematerial[20,p.320].Ifthesimulationtimeisdecreased andtheblankhasacceptableresults,theprevious materialcardwillbereplaced. 4.5.3.1 Von Mises R - Model Version V.1.3

IftheR-valueusedinthemateria lcard*MAT_TRANSVERSELY_ANISOTROPIC-_ELASTIC_PLASTICissettoR =1,the materialisreferredtoasaVon Mises material.Thismeansthattheyieldsurfacehasanellipticformbasedonsymmetry. 4.5.3.2 Hill’48 R - Model Version V.1.4

ThethreeR-valuesforthe00-,45-and90-directionsfromAppendixA.3wasused inEq.4.1tocalculatetheanisotropichardeningparameter. As ment ionedinsec-tion4.5.3.1,thisvaluechangestheyieldsurfaceofthematerialandisreferredtoas Hill’48.Itisstillsymmetric,buttheshapeoftheouteredgediﬀerfromwhenusing R.

R =R +2R +R

4 (4.1)

4.5.3.3 NumberofIntegration Points- Model Versions V.1.5-7

Thenumberofintegrationpointsfortheblankwaschangedtothreeinsteadofthe initialﬁvepoints,bothfortheoriginal*MAT_BARLAT_YLD2000materialandthe previous mentioned materialinsection4.5.3.2. Thenullsurfaceoftheblankholder previouslyhadthreeintegrationpoints,butsincethesurfaceonlyactsasanextended surfaceoftheblankholder,theintegrationpointwaschangedtoone.

4 .6 Remesh

ingofScannedSurfaces- V

.3

.1-2

ThesurfacesofthedieandpunchwasremeshedbyusingthesoftwareGOMInspect. Thesizeoftheelementswaschangedbyusingthetool OPERATION/Mesh/Thin wheretheoption"Numberofnodes"wasusedincollaborationwith"Max. edge length",seeTable4.4andFigure4.11forresultsandsettings. Whenenteringthe numberofnodes,thatistheamountofnodesthe modelgetsassignedafterthe remeshing. Theselectedsettingswereprimarilysettoincreasetheelementsizefor thesmallestelements,butkeepthesizeofthelargerones. Boththeelementsfor thedieandpunchwassettobedecreasedtoapproximatelyhalfofthenumberof elementsfromtheoriginal model. Theﬁlesizeisnowreducedto800 MB.

(a)Before (b)After

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Part Die Punch

Nr of Elements [Before/After] 2.957.559/1.594.026 1.793.429/997.777 Deleted elements [Nr/%] 1.363.553/46.1 795.652/44.4 Number of nodes 800.000 500.000

Max. edge length [mm]

1.5 4

Table 4.4: Number of elements before and after remeshing of scanned die and punch.

4.7 Decomposition

A variety of different decomposition methods are studied in order to evaluate the computational time with regards to the method. There are other decomposition methods available, but the ones in section 4.7.2 to 4.7.4 are recommended when work-ing with models which include many elements and contacts. By uswork-ing the keyword *CONTROL_MPP_DECOMPOSITION_SHOW, the partitioning of the models are shown by importing the model back into LS-PrePost. The number of parti-tions is depending on the number of cores that are used when sending the model for analysis, where all the partitions in Figure 4.12-4.15 are run with 32 CPUs.

4.7.1 Default

The default version of the decomposition is shown in Figure 4.12, and is based on partitioning the model in the direction with the largest dimensions throughout. The coordinate system showed in Figure 4.12 is the same for all further displayed decom-position figures. As the model is partitioned by shell and solid element separately, a total of 64 partitioned parts can be found in the model, if 32 CPUs are assigned when analyzing.

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4.7. Decomposition 29

4.7.2 Decomposition by transformation

By scaling the model along axes, a value less than one shrinks the model and a value greater than one expands the model. When using rotational transformation, the value chosen for the rotation is the rotation in degrees and is by default clock-wise. The key-word used for this decomposition is *CONTROL_MPP_DECOMPOSITION_TR-ANSFORMATION. See Table 4.5 for model versions and settings where S denotes transformation and R rotation and Figure 4.13 for decompositions.

Model Version Transformation setting Value

V.2.1 SY 1000

V.2.2 SZ 0.001

V.2.3 SX & SY 1000 & 2000

V.2.4 RY 200

Table 4.5: Decomposition by transformation settings and versions

(a) y-direction (b) z-direction

(c) x- and y-direction (d) y-rotation

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30 Chapter4. Method

4 .7

.3 Decompos

it

ionby Contacts

Thekeyword*CONTROL_MPP_DECOMPOSITION_CONTACT_DISTRIBUTE isusedtopartitionthe modelbycontactinterfaces. Thecontactsthatinclude the mostelements wereusedfordecomposition werethecontacttypeis*CON-TACT_FORMING_ONE_WAY_SURFACE_TO_SURFACE. Thefourdiﬀerent models withtheiruniquesettingsand modelversionarelistedin Table4.6and showedinFigure4.14. A modelwiththesamesetupasV.4.4butwiththeblank materialchangedtoR werealsosimulatedwith modelversionnameV.4.5.

ContactID Parts Model Version Used ContactID’s

1 Die/Blank V.4.1 1,2&3

2 Punch/Blank V.4.2 1&2

3 Blankholder/Blank V.4.3 1&3

V.4.4 1

Table4.6: Decompositionbycontactsettingsandversions

(a)ID1,2and3 (b)ID1and2

(c)ID1and3 (d)ID1

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4.7. Decomposition 31

4.7.4 Groupable Algorithm

There is a total of 17 contacts in the model that are tied-based, where all are con-nected to the null surface of the blankholder, see Appendix A.5. By using the groupable algorithm, the contacts that are tied or non-tied based are processed differ-ently depending on what type of setting is used in the keyword *CONTROL_MPP_ -CONTACT_GROUPABLE. The model versions and settings are listed in Table 4.7 with the decomposition displayed in Figure 4.15.

Model Version Groupable setting Turned ON/OFF

V.4.6 All non-tied contacts ON

V.4.7 All tied contacts ON

V.4.8 All non-tied contacts OFF

V.4.9 All tied contacts OFF

Table 4.7: Groupable settings and versions

(a) Non-tied ON (b) Tied ON

(c) Non-tied OFF (d) Tied OFF

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4.8 Final Models

The models chosen to validate was based on the percentage reduction of computa-tional time with regards to what had been changed in the model. As a start, the models where geometry changes have been made was validated, primarily to see how large of an impact the changes had on the blank. If it was seen that a change had a poor impact on either the simulation time or geometry of the formed blank, no further analysis was conducted. On the other hand, if a change concluded a sig-nificant reduction of computational time, the change was implemented throughout when new models were constructed. All models with elastic tool consideration along with a brief explanation and the simulation time when using 800 CPUs can be seen in Appendix A.7. The major strain comparison was conducted for the models V.1.2, V.1.6 and V.4.4.

4.8.1 Result Comparison Setup

The comparison of major strain results was conducted for the blank. The measure-ment for the blank formed in production was provided by VCBC, where the upper surface was scanned. The blank was scanned in separate segments to later be assem-bled, which means that the entire surface of the simulated results can’t be verified. Figure 4.16 and 4.17 shows the major strain of the scanned blank, which are com-pared in GOM SVIEW with three of the simulated results. When comparing the results, the deviation of major strain was calculated with Eq. 4.2.

"Deviation = "Simulation "M easurement (4.2)

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4.8. Final Models 33

Figure 4.17: Second view: Major strain from production processed blank

4.8.2 Draw-in Curves

The outer edges of the model from Figure 4.16 and 4.17 was provided by VCBC as an .iges file. The so-called, draw-in curve is imported together with the three simulated blanks in LS-PrePost in order to see the possible deviation of the placement of the blank. No other than visual comparison between the draw-in curve and outer edges of the model will be conducted.

4.8.3 Integration Method

The integration method used throughout is set to be Gauss, which is discussed in section 2.2.1.1. The Lobatto method is implemented on the model which had the overall most pleasing results. Two models were set up with this method, one with three and one with five integration points, to later be compared with the model using the Gauss integration method.

4.8.4 Scaling Analysis

A scaling analysis was carried out of the model with the results that were most similar to the validation model with the fastest simulation time. The number of used CPUs started at eight to later be increased to a value evenly dividable with 16. In the beginning, when the simulation time drops fairly quick, each step of 16 was taken. When the simulation time even out, the step size increased to each 128th CPU. No simulation will be run with over 1024 number of CPUs, since it is uninteresting to run the simulation on that many cores.

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4.8.5 Distribution of Contacts and Reaction Force

When a simulation is terminated without errors, two files are automatically created which includes the timing information for all the CPUs and contacts. The file which contains the time per CPU and contact ID is called .cont_profile, while the more general distribution file is called .load_profile. In the later named file, the simulation time is divided into categories like, contact, rigid body, time-step and element pro-cessing. This file specifies how much time is spent analyzing each part of the model, and can be helpful when evaluating what type of changes that can be implemented to improve the computational cost. These files are edited and converted to .txt files and evaluated by using the software MATLAB.

To get a better understanding of how the model behaves with regards to the applied clamping force of 1.5 MN, the resultant force between the blankholder pins and cushion are exported and plotted in MATLAB.

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Chapter5

Resu

lts

5 .1 S

imu

lat

ionT

ime- R

ig

idSurfaces

Theresultsfromthe modelswithrigidsurfacesareshowninTable5.1. Modelswithoutblank,only movementofrigidsurfaces

*Errorterminationduetocorrupted meshfortheblank **Terminatedsuccessfullybuttheblankhascracks

Model Type Adapt.level Adapt.elements[Nr] SimulationTime

Nominal N/A N/A 1m39s

Scanned N/A N/A 38m32s

Scanned Remeshed N/A N/A 19m18s

Nominal 2 N/A *

Nominal 3 733.928 1h7m

Nominal 4 1.817.747 2h46m

Scanned 2 214.346 2h50m**

Scanned 3 739.349 3h31m

Scanned 4 1.887.932 5h0m

Table5.1:Simulationtimeandadaptive meshresultsforrigidsurface models

5 .2 S

imu

lat

ionT

ime- Or

ig

ina

l Mode

l

Theoriginal modelwasrunwithavarietyofcorestogetabriefunderstandingof thescalingforthis model,seeTable5.2.

Nrof CPUs Simulation Time

96 23h20m

208 15h13m

400 11h38m

608 15h7m

800 13h43m

Table5.2:Simulationtimefortheoriginal model

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36 Chapter 5. Results

5.3 Major Strain Comparison and Draw-in Curves

The following four subsections include a comparison between draw-in curves and major strain deviation calculated with Eq. 4.2.

5.3.1 Deleted Solids - Model Version V.1.2

The dark red outline represents the draw-in curve from the production formed blank which is imported with the same coordinate system as the simulated model into LS-PrePost, see Figure 5.1. Model V.1.2 is the first model chosen to validate and include the changes of deleted unreferenced nodes, updated bucket settings an removed solid die and punch.

Figure 5.1: Draw in curve for model V.1.2

The major strain deviation between the validation model and model V.1.2 is shown in Figure 5.2 and presented from a different view in Figure 5.3. The red areas imply that the major strain is overpredicted in comparison with the measurements, while the blue areas are underpredicted. Green areas imply that there only are small deviations between the measured and simulated results.

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5.3. Major Strain Comparison and Draw-in Curves 37

Figure 5.2: Major strain deviation - Model V.1.2

Sheet Metal Forming Simulations with Elastic Dies: Emphasis on Computational Cost