Inﬂuences of the Forming Process on the Crash … · Inﬂuences of the Forming Process on the Crash Performance - - Finite Element Analysis Abstract The objective of this thesis

se

Influences of the Forming Proceson the Crash Performance - Finit

Element AnalysisAleksandra Krusper

Göteborg, May 2003

Analysis Report no. 03-013

MSc. Thesis

Department of Structural MechanicsChalmers University of Technology

andVolvo Car Corporation

Volvo Car Corporation

CHALMERS

Influences of the Forming Process on the Crash Performance -

- Finite Element Analysis

Abstract

The objective of this thesis work has been to transfer metal forming simulationparameters (effective plastic strain distribution, thickness and residual stresses)into the crash simulation of a structural component. In order to reach thisobjective, a simple hat profile with two triggers near the front end and a weldedflat lid, has been chosen as suitable component. The simulation procedureconsisted of:

- design of the hat profile which has to be produced by a stamping process,

- forming simulations of the component (stamping, coarsening, trimming andtwo different springback simulations),

- transferring the forming parameters into the crash simulation,

- crash simulation.

Two different solutions of the springback process have been tested in order tohandle the problem which occurs when the welding between the flat lid anddeformed flanges of the hat profile (as a consequence of the springback) isdefined.

Different inputs of the forming parameters have been transferred into the crashsimulations and their particular importance has been analysed. The resultsindicates that all forming parameters should be considered. The effective plasticstrains makes the structure stiffer, and their influence is the most eminent. Thethinning of the structure makes its response weaker. Considering the influenceof the residual stresses two different cases have been obtained. When thethickness reduction is not included, the influence of the stresses is minor. Withthe thinning included, the residual stresses preserve a deformation modewithout buckling.

The finite element program, used for the simulations was LS-DYNA. Itsimplicit solver was used for the springback simulations, while the rest of thesimulations were computed by the explicit solver.

Keywords: sheet metal forming simulation, crash simulation, springback,residual stresses, effective plastic strain, thickness thinning.

Influences of the Forming Parameters on the Crash Performance -

- Finite Element Analysis

s

Acknowledgment

The Master’s Thesis is the final task of the International Master’s Programme inEngineering Mathematics at Chalmers University of Technology. The thesis hasbeen carried out at Volvo Car Safety Centre in Göteborg in co-operation withDepartment for Virtual verification, Volvo Car Corporation, Body Componentsin Olofström.

I would like to thank my supervisors Lic. Eng. Edin Omerspahic for hispatience and for spending hours on reviewing the manuscript; Lic. Eng. MatsSvensson for indispensable help in the first part of the work which refers to theforming process and for his great encouragement and support; Dr. Johan Jergeufor always being available for a discussion and for his almost unboundedknowledge in UNIX applications that he has generously shared with me. I wantto thank my examiner Dr. Adj. Prof. Kjell Mattiasson for his concise and preciseanswers (in any time) on my questions which made me think on the right way.

I also want to express my special gratitude to the people at Volvo Safety Centrewho helped me in many ways.

Göteborg, May 2003

Aleksandra Krusper

Influences of the Forming Parameters on the Crash performance - Finite Element Analysis

3.3.4.4.77.8

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33

Table of Contents

1 Introduction ............................................................................ 12 Methodology ............................................................................

2.1 Planned Work ................................................................................2.2 Extract from the theoretical background .......................................

2.2.1 Elastoplastic material behaviour ............................................2.3 Numerical and computation tool ...................................................

2.3.1 Finite Element Method ...........................................................2.3.2 FE-software ...........................................................................

3 Forming to crash procedure ................................................ 113.1 Design ..........................................................................................3.2 Forming process ...........................................................................

3.2.1 Stamping process ..................................................................3.2.2 Coarsening ............................................................................3.2.3 Trimming of the formed hat profile ......................................153.2.4 Springback phase ..................................................................3.2.5 Crash of the component ........................................................

4 Results and discussion .......................................................... 14.1 Influence of the different geometry on the crash response ..........4.2 Influence of the forming parameters on the crash response .........

4.2.1 Influence of the effective plastic strain ................................24.2.2 Influence of the effective plastic strain and the stress tensor 24.2.3 Influence of the thickness .....................................................2

5 Conclusions and the further work ...................................... 315.1 Conclusions ..................................................................................5.2 Further work .................................................................................3

References ................................................................................Appendix A LS-DYNA insufficiency ..................................... 35Appendix B Simulations ......................................................... 41

Chapter 1 Introduction

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1 IntroductionAn overview of Master Thesis’ background, purpose and outline.

In today’s industry applications, Finite Element Method (FEM) is commonly used in oto simulate different processes based on different FE analyses. In Volvo Cars Corpoparticularly, the metal forming process and the crash process, among others, are resimulated to lower costs in an early construction phase and to evaluate real phprocesses in a later construction phase.

The metal forming FE analysis is used to simulate production of car components adevelop the corresponding dies. Usually, the physical process involves many iterativebut the final result could be seen only during and after the prototype production. Uforming simulations, these steps can be done in a faster and cheaper way. The crashanalysis is used to evaluate different car designs in order to find the one that gives thcrash safety. Also, in this application, the FE analysis can save both time and money.

So far, there has been no coupling between these two analyses, i.e. the crash aassumes virgin properties of the material. The reality is that during the forming of msheets, numerous effects influence the later crash response. The most obvious effethickness variation (which induces some variations in stresses), residual stresses,hardening, damage, etc. Therefore it is of interest to link these two analyses.

With this link it will be possible to predict the crash behaviour of a component maccurately. This can be a further step towards a more reliable FE analysis.

Another interesting observation is how large the influence of each of the above menteffects is. Including into the crash simulation only those which significantly influencecrash performance, transferring of data will be simplified.

Some work in this area have already been done. In Jergeus [1], the effect of forming ocrash response of an energy-absorbing simplified frontrail was studied. The forming odata: thickness, stress, and effective plastic strain distribution, were included in thesimulations. The data were taken from simple forming simulations without springbrelaxations. The influence-importance study indicated that some of the forming effecteffective plastic strain and a thickness) should be included in the crash simulation.

Another simple example was used for a short investigation of transferred data fromforming into the crash simulation, see Dagson [3]. The same procedure as in [1] wasfor the simple geometry. Then, a more complicated geometry, a roof rail componentexposed to the same analysis. The conclusion was that only effective plastic strain mawas done successfully in LS-DYNA Version 960.

Both works were simulating elasto-plastic deformation processes with isotropic hardeNone of these studies have tried to explore how the kinematic hardening of a forprocess simulation influences the crash response. Therefore, one purpose of this wofind out a way to transfer the effects of both kinematic and isotropic hardening.

1

Influences of the Forming Process on the Crash Performance - Finite Element Analysis

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To reach the goal described above, the Master’s Thesis procedure is divided in the follosections:

• Design of the component

• Forming simulation, including springback

• Mapping of the forming effects

• Crash simulation

• Analysis of the results

• Conclusions

• Further work

A comparison with real crash test has not been done since the experimental study hbeen performed before this work was started as it had been planned.

2

Chapter 2 Methodology

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2 MethodologyAn overview of planned work, an extract from the theoretical background, and ucomputation tools.

2.1 Planned WorkAs usual, when the mapping frommetal formingto crash is investigated, the geometry othe example component is simple, a hat profile with a welded flat lid. First, the hat prshould be formed and then the lid should be added by welding. Maximum enabsorption is a requirement that is leading the design process of the tested componenhaving a hat profile with the maximum energy absorption, the design of the correspoforming tools can be started. In this way, moving from the final process phase to theone, conditions for the real process sequence are created. In addition, it should be sain this early design phase there is a possibility to see whether or not a structural compis formable. To conclude, by designing the forming tool the process of coupling the mforming with the crash operation (with the simulations of trimming, coarsening,springback, in between) can be performed.

Within Department for Virtual Verification, non-linear finite element analysis software,DYNA, is used for the forming simulations, while RADIOSS is used for the crasimulations within Crash Simulation group. In order to avoid problems of transferringfrom one software to the other one, LS-DYNA has been chosen as a suitable tooperforming the both simulations.

The choice of material model depends on the particular process which is simulatetransversely anisotropic material model (nr. 37 in LS-DYNA) is usually used to modedeformable material in the forming simulations, while the rigid (nr. 20 in LS-DYNA)used for modelling the forming tools. An elastoplastic (isotropic) material model (nr. 2LS-DYNA) suits properties of steel-based materials for the crash simulations. Both moaccounts for only isotropic hardening of the materials. In order to include even kinemhardening, a material model with mixed hardening has been considered (nr. 103 inDYNA). The idea was to use this material model for the whole sequence of simulatfrom the forming to the crash.

The analysis has been planned to be performed as follows: The forming parametershave to be transferred are geometry, shell thickness, stresses, and effective plasticDifferent combinations of the forming parameters have to be made and included as anfor the crash simulation. By comparing differences between the crash simulations,with different input data, the significant forming parameters have to be chosen.

LS-DYNA can generate a few different types of output. One of them is the file “dynawhich can be used as an input file (The DYNAIN File Method) for the next process. Theincludes all information mentioned above. It is a simple text file, easy to manipulate wConsidering the material model 103, the backstress tensor should be included i“dynain” file (for the crash simulations) as the information about kinematic hardeningnew, unofficial version of LS-DYNA, 970, is supposed to include the backstress tensthe “dynain” file. Another possibility to include backstress tensor in the crash simulatioto use the “old” LS-DYNA version 960 and “d3dumpnn” files for the data transferring.

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Although much effort has been made, it was not possible to use the material model 1simulations due to LS-DYNA code insufficiency. Transferring of the forming parametincluding the backstress tensor could not be performed. For more information about thAppendix A. Therefore, the analysis has been performed using the material model 3the forming (including springback) simulations, and the material model 24 for the csimulations.

For the sake of simplicity the material is considered strain rate independent.

The planned work is illustrated in Figure 2.1

Figure 2.1The planed steps, in order to map the forming simulations and the crashsimulations

2.2 Extract from the theoretical backgroundThe presented theory is limited to the part of theory which describes a behaviour of mematerial under “repeated” loading, i.e. hardening, which occurs during both the formingthe crash process.

2.2.1 Elastoplastic material behaviourExposed to a loading, a metallic material goes through an elastic range. When the stexceeds the elastic level, the material is said to be in the plastic range (uniaxial elastoploading as in Figure 2.2, see also Doltsinis [8]). Due to such material responselastoplastic analysis is necessary. For this reason, a short description of the elastoanalysis and hardening rules are given.

At a given strain levelε, the elastic stress can be determined by one-dimensional Hoolaw as

where E is the Young’s modulus. For a general case of loading this equation can be giv

formingphase springback phase

F O R M I N G S I M U L A T I O N S

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As said, a uniaxial elastoplastic material response is presented in Figure 2.2. The poincalled the linearity limit and it is taken as the yield point. The associated stress is thestress, noted by .

If the material is loaded under point A, a strain occurs in the material. When it is unloa

the strain completely vanishes. This strain is called elastic strain, . If the material isstressed to a state well beyond point A (point B in Figure 2.2 a)) and then unloadedstrain follows the dashed line. When the stress is removed the strain restores partial

elastic strain ) and some amount of strain (the plastic strain ) remains in the matThe existence of both kinds of strain is a characteristic for the elastoplastic regime.

general case of loading, the total strain may be presented as . For the locase in Figure 2.2, the maximum stress reached under plastic deformation is “remembby the material. For a further stress increase and additional plastic straining (line BD)maximum stress , becomes the actual yield limit. Since the yield stress increase

material is said to strain-harden and the function describes the harde

characteristic with .

When the plastic deformation occurs, it is called the plastic flow. Each increase of theproduces increase of the plastic strain, while unloading, i.e. a decrease of the stress,the plastic strain unaffected. In general, the plastic flow is described by the yield cond

(2.1)

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2.2.1.1 Hardening rulesDuring the forming performed in our case (see Section 3.2.1), a metal sheet hassubjected twice to bending in the different directions which caused that the upper surfathe metal sheet is subjected first to tension and later to compression. The lower surfthe metal sheet is subjected first to compression and later to tension. This is called aloading. This type of loading rises the question of isotropic and kinematic hardeninorder to explain the hardening rules, it is necessary to introduce hydrostatic and devistresses. Generally, the stress can be decomposed into a hydrostatic , and a de

stress :

(2.2)

where , and is the Kronecker delta. While represents the rest of

stress. The isotropic hardening assumes the expansion of plastic yield surface.principal stress space, the yield surface is represented by cylinder and the increase ofstrain causes expansion of the cylinder around the hydrostatic axis (Figure 2.3).

Experimental observations shows that the cyclic loading diminish the yield stress. Thcalled Bauschinger effect (Figure 2.4 a)). The kinematic hardening accounts for this eby assuming that the yield surface keeps the same form but is translated when thedeformations occur. Translation is defined by thebackstress tensor (Figure 2.4). Themixed hardening is a combination of isotropic and kinematic hardening.

Figure 2.3Isotropic hardening of the yield surface. The expansion of yield surface a) in theprincipal stress space and b) in the effective stress - effective plastic strain curve (hardeningcurve)

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2.3 Numerical and computation toolMathematical modelling is commonly done by using differential equations. Usually,considered problem is too complicated to be solved analytically. The numerical mewhich is used for solving these, is the Finite Element Method (FEM). It is well suiteddigital computers and used in different fields of science. Many softwares, based onmethod, have been developed. An analysis by means of the method demandsupplementary softwares for a problem preparation (pre-processing) and a visualizatsolution (post-processing). The next subsections introduce a short description of theElement Method applied on the forming and crash simulations. The FE software, usthe work, is presented as well.

2.3.1 Finite Element MethodThe Finite Element Method requires that a domain is divided into finite number of elem(a mesh). The elements are connected at points called nodes. When the load is appthe structure, deformation occurs in the element. It invokes nodal displacement. Thedisplacement is related to the strains and the stresses. FEM calculates thedisplacement so that the stresses are in equilibrium (approximately) with the applied

There are two general schemes for calculating an approximate solution (here, thedisplacement): explicit and implicit method.

2.3.1.1 Explicit methodIf it is possible to find a dependent variable upon known quantities, the computation isto be explicit. The explicit method has the form:

where {D} is a displacement vector, and indexes n+1, n, and n-1 refers to the solution onext, current, and the previous step, respectively. Hence, the solution

determined by already known information.

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This is the method which has been developed for solving transient dynamic problemscrash process, but it can also be used for quasi-static analysis, like the forming procdoes not demand assembling and inverting of the stiffness matrix which then leads tmemory requirement. Instead a few different explicit methods can be used. Thepopular is the central difference method (see Svensson [12]), which is used by LS-Dexplicit solver. In general, there is no problems (convergence difficulties) in the conimplementation within the explicit method. A disadvantage of explicit method is thatconditionally stable, i.e. the time step size is restricted. It is the smallest element wdetermines the time step. This can cause a long calculation time.

2.3.1.2 Implicit methodThere are two methods which are used for the implementation of the springback simu(static solution, free from dynamic oscillations): The explicit dynamic relaxation andstatic implicit method. The second one is preferred.

The implicit method evaluates solution upon unknown quantities at the next time stepimplicit method has the form:

The solution requires the knowledge of time derivatives of the solution, which

unknown. An iterative procedure must be used to compute new quantities. Invematrices in each time step demands high memory requirements. The advantagemethod is an accurate solution and unconditional stability, i.e., there is no limit on theof time step.

2.3.2 FE-softwareSoftware used for FE-analysis includes a pre-processor, a finite element solver and aprocessor.

The pre-processor is used for the mesh generation of domain. The post-processosoftware which is used for the visualization of results. A choice of pre- and post-procedepends on the finite element solver which is used, i.e. on their compatibility.

For the reasons explained in 2.1, LS-DYNA has been chosen as a suitable solver. Itexplicit finite element code for analysing non-linear dynamic problems in three dimenswhich also includes an explicit dynamic relaxation and a static implicit solver. Tsimulation model is defined by an input deck, which is an ordinary text file. It is basethe cards, defined within keywords, which represents corresponding characteristicsmodel. LS-DYNA generates different types of output. “d3plot” file contains data for vispresentation of results. “d3dumpnn” (in Shared Memory Parallel - SMP version ofDYNA) or “d3fullnn” (in Distributed Memory Parallel - MPP version of LS-DYNA) filescontain all information about calculation course and solution. Moreover, there are Afiles which contain additional information about solution which is made on requesspecial keyword. A “dynain” file, is also made on request. It contains the geometry datathickness, the stress tensor, the effective plastic strain, and the strain tensor at the lastep. Then, there are few text files which give information about calculation course.

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ANSA has been used as the corresponding pre-processor for the crash models and INhas been used as the corresponding pre-processor for the stamping models. ANSA is(Computed Aided Engineering) pre-processing software, which includes somefunctions (2D and 3D definitions), part assembly and connections, shell mesh and vomesh generation, etc. INGRID is a pre-processor that can read in meshes on difformats and then create an LS-DYNA input file.

LS-POST has been used as a post-processor. It can read most of listed LS-DYNA figives the possibilities to check the input data, visualize a deformed geometry per timeplotting variables by different ways of visualization (fringles, diagrams, vectors), etc.

Depending on whether a forming or a crash process is simulated, different types of mamodel and element are usually used. LS-DYNA offers over 80 material models and a delement types. The material models and element types used in the simulations are expin the following subsections.

2.3.2.1 Material modelsMaterial model type 37,Transversely Anisotropic Elastic-Plastic, (LS-DYNA Manuals [5],[6]), is a fully iterative elasto-plastic model that assumes plane stress conditions aavailable only for shell elements. Transversely anisotropic materials has the same stin all directions in the sheet plane but it differs in the transverse direction, while isotrmaterials have the same stiffness in all directions.

For this model an arbitrary dependence of the effective stress and the effective plasticcan be defined via a load curve. The input parameters for this model are: the mass d

, Young’s modulus E, Poisson’s ratio , the yield stress , the tangent modulus

the hardening curve is linear), and the anisotropic hardening parameter R. Theparameter is used to define anisotropy input. By setting R=1.0, the isotropy is assuComparing the isotropic case where R=1.0 with other isotropic models available inDYNA, differences in the results are expected, but they are usually insignificant.

Material model type 24,Piecewise Linear Isotropic Plasticity(LS-DYNA, Manuals [5], [6])is an isotropic, three dimensional, elasto-plastic (von Mises) material model. “Piecelinear” implies the piecewise linear hardening curve. A required input data is the samfor the material type 37, with additional information for the strain rate dependence wcan be defined for this model.

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The material model 103 was planned to replace these two models, for the reasconsistent use of one material model, which includes the mixed hardening possiMaterial type 103,Anisotropic Viscoplastic(LS-DYNA, Manuals [5], [6]) is applied to shelland brick elements. The basic input parameters are: the mass density, Young’s moPoisson’s ratio, the initial yield stress, viscous material parametres ( and

anisotropic hardening parameters in three directions ( , and ). The vis

material parameters controls the strain rate dependence. Setting them to zero, adependent behaviour in solution is disabled. For the isotropy, all three R variable shouset to one. Dependence of the effective stress and the effective plastic strain can be dby one of three ways. Their implementation is specified by variable FLAG. By setFLAG=0, isotropic hardening parameters and kinematic hardening parameters, requiran equation of uniaxial strress-strain curve and a yield criteria (see LS-DYNA, Man[6]), must be defined by the input. By setting FLAG=1, the dependence is found by thecurve fitting. More precisely, all isotropic hardening parameters are determined by thefitting and the kinematic hardening parameters are found by scaling of these isothardening parameters. The scaling is defined by variable . Setting gives

kinematic hardening, while gives pure isotropic hardening. When FLAG is set tthe load curve is used directly.

The last option has been considered as the most suitable. Unforunately it was not coimplemented in the LS-DYNA code (see Figure A.4).

2.3.2.2 Type of elementsIf the thickness of a structure is small compared to its radius of curvature, the structudivided into shell elements.

Within the Crash Simulation group, crash simulations are usually performed usingBelytschko-Tsay, one point integrated shell elements (type 2), based on the Mindlin shelltheory. This is a default shell element in LS-DYNA. They are simple but efficiunderintegrated elements which satisfy most engineering applications. Disadvantathese elements is that they give a wrong result in problems where the elements are w(twisted). Underintegrated elements permit zero-energy modes (hourglassing). To cthese modes, artificial hourglass stabilization is used.

Within Department for the Virtual Verification, forming simulations are usually performby using theBelytschko-Leviathan shell elements (type 8). Warping stiffness has been addeto the formulation of these elements, which made them applicable for the problemstwisted elements, but calculation time is longer compared to the elements type 2.

Fully integrated shell elements (type 16)are recommended for the forming process whethe springback should be performed. Four Gauss point integration is used which givesintegration but too stiff solution for a coarse mesh. A disadvantage is that the amoustored data is increased nearly four times and the computation time increases threetimes.

This type of element does not cause problems in the crash simulations, except thcalculation time is increased. Therefore the type 16 has been used for all simulations

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3 Forming to crash procedureA description of the steps which have been done in order to map the forming resultscrash simulation. The steps are divided into a design, a forming and a crash proDetailed information about the simulations is given in Appendix B.

3.1 DesignThe objective of the design process was to get the geometry of the component which iwas used for the design of forming tool. As this step is necessary but not directly connto the purpose of the work, only a short description of the step is given.

A simple geometry - a top hat profile with a welded flat lid has been chosen as the sucomponent. The component has to satisfy the following conditions:

• It has to be able to absorb as much kinetic energy as possible during the cras

• It has to be produced by stamping in one operation.

The first condition is satisfied if the component deforms in an acceptable deformationduring the crash process. To invoke this deformation mode, two triggers have been mathe component. In the process of designing the trigger, the second condition has beein the mind, i.e., the trigged hat profile has been made formable by stamping, inoperation. In order to check the deformation mode of the component with the trigiterative steps (design - crash simulation - design) were involved in the process of desigAccepted shape of the triggers and dimensions of the component are shown in Figur

11


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Figure 3.1Designed component

3.2 Forming processForming is divided into two phases: a forming phase, and a springback phase. Furtherthe forming phase includes simulations of stamping, coarsening and trimming.stamping is a process of the sheet metal forming which is done by relative motion of asheet caused by parts of tool (punch and die).

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The coarsening is performed after the stamping, and includes remeshing, i.e., increasthe element size.

The trimming is a process where the uneven deformed edges after stamping and excmaterial are cut off.

The springback is a process of relaxation of elastic residual stresses obtained aftstamping process.

All the forming simulations and the crash simulations have been performed by the exsolver. The springback simulation have been performed by the implicit solver.

3.2.1 Stamping processIn order to get the desired form of the hat profile the corresponding forming tool has

created. The forming tool consist of: a die, a punch, two blank holders, and two drawbe1.(Figure 3.2).

Figure 3.2The forming tool with the blank

The fixed part of the forming tool is called the die and the punch is a movable part otool. The blank (metal sheet) is placed between them. The punch and the die, togethethe blank. By the punch’s movement, the blank is forced into the die for creating the deshape (see Figure 3.3). The shape of the tool and their relative position in the last simu

1. The drawbeads are defined by LS-DYNA input deck

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step define the final shape of the blank. The objective of having drawbeads is to increastraining in the material. It is easy to see that the most strained parts are vertical sideshat profile (see Figure B.5). In the part of material which passes the drawbeads a reforce occurs as the consequence of bending and unbending over drawbead surfacethere is an additional resisting force acting on the blank (see detail in Figure 3.3) dfriction in the contact between the blank and the die and the blank holder respectively

Figure 3.3Relative placement of tool parts and blank. I) Position before the forming isstarted II) Beginning of the forming III) Continuation of the forming IV) End of the forming.Tool is in the closed position. Detail shows the motion of blank over the drawbeads, thepunch, and the die. F is the blankholder force.

After the tool was created the mesh has been generated. The initial mesh size of 2.5 mbeen applied on the blank in the forming phase. One springback simulation has thenrun with output, obtained from the stamping simulation. For this case the shape oprofile, after the springback simulation, was unacceptable. Since the springback depethe stamping data, the problem is usually found in the forming phase simulation. Hereproblem was that the fully integrated shell elements caused too stiff solution aftestamping. This has been avoided by using finer mesh. The mesh size was thedecreased to 1.25 mm.

3.2.2 CoarseningThe mesh coarsening is used to decrease the calculation time and needed CPU memlater steps, and improve convergence behaviour during a nonlinear equilibrium iter

die

blank holder

drawebad

punch

blank

T=0 s I T=0.006 s II

drawbeads

dieA blank

punch

T=0.014 s III T=0.026 s IV

Detail A

F

14


r. Thistry), theure 3.4.fileern hasbackween

quiteds can

(springback). During the coarsening, four small elements are connected to one biggeis a selective process, i.e. where a better accuracy is needed (over the curved geomemesh size remains the same. An example of the coarsen mesh can be seen in the FigAll information about previous connection between elements is kept in a “dynain”(within keyword CONSTRAINED_ADAPTIVITY), after the coarsening is done. In ordto investigate how the coarsening influence the springback, one springback simulatiobeen run with the fine mesh (without coarsening) and compared with the springsimulation with coarsening. No differences in the solution have been obtained betthese two simulations.

Figure 3.4Mesh of the hat profile a) before and b) after the mesh coarsening

3.2.3 Trimming of the formed hat profileDuring the stamping the edge area of material is unevenly stretched (the edge line iscurved), especially when the drawbeads are used. Sometimes, usage of drawbea

A

a)

Mesh size: 1.25mmNo. of el.: 64000No. of nodes: 642525

B

b)

Mesh size: 2.5mm and1.25mmNo.of el.: 24007No. of nodes: 22276

A

B

15


tions ind, theys thed, at

efore,, the

toolbeentwo

d the

emainn ise part,arped

ancesamen LS-een

tbeen

cause even wrinkles in the edge area. In order to avoid appearance of these deformathe final product, the blank is made longer than demanded. If the drawbeads are useshould be placed in such position that this additional length of the material containmost of deformations. The additional length is removed by the trimming operation anthe same time, the wanted dimensions of the final product are obtained.

In the case of the hat profile the deformed part is placed at the edge of flanges. Therthe edge part of flanges is removed by the trimming (see Figure 3.5). In this casetrimming curve is defined by rectangle. Direction of the trimming is negative z-axis.

Figure 3.5The trimming of deformed part of the flanges

In reality, the trimming is performed after the springback. Usage of the trimmingcauses again additional stresses in material. Then, later, since the trimming tool hasremoved, a relaxation of stresses is performed (springback). In order to avoidspringback simulations, the trimming simulation is performed between the stamping anspringback simulations.

3.2.4 Springback phaseThe springback is a process of residual stress relaxation. After the forming, stresses rin the material. When the formed part is moved from the tool, the stress distributiochanged in order to reach an equilibrium. This causes the changes in the shape of thespecially close to the edges. Here, the flanges are mostly deformed. They are w(twisted) and it is not possible to connect them to the flat lid in a later phase. Distbetween the lower surfaces of flanges and the upper surface of lid is not theeverywhere. Somewhere the distance is too large for available contact algorithms iDYNA. To avoid this problem, two different cases of the springback simulation have brun.

The first case- The common springback simulation.All data from the forming phase of haprofile have been transferred to the springback simulation and a full relaxation hasperformed.

trimming curve x

yz

16


nesstions.fter the

eno getofile.uses antionhas

n hastion,voiddenthe

rash

m thecrasher to

onnessrstICK.

withsed.

ss of has

d forthe

rt oft part

pact

he haters autareeshhe

Only the forming parameters (stress tensor, effective plastic strain and thickdistribution) from this springback simulation have been used for the later crash simulaThe geometry that has been used in combination with these parameters is obtained aforming phase. The lid has been added with virgin material properties.

The second case- In reality, the full relaxation is performed since the hat profile has bemoved from the tool. After that, the hat profile can be subjected to bending in order tthe wanted form and position of the flanges. Finally, the lid can be welded to the prThis procedure causes (again) the appearance of residual stresses, which in turn caadditional deformation of the hat profile and the lid together. In order to get a soluwhich is closer to reality and at the same time to avoid the problem with flanges, the lidbeen added to the hat profile after the forming phase. Then the springback simulatiobeen performed with the whole structure. To include the spotwelds in the implicit solutwo types of contact have been used: CONTACT_SURFACE_TO_ SURFACE (to apenetration between two surfaces) and a mesh indepenCONTACT_TIED_NODES_TO_ SURFACE_OFFSET (for the spotwelds modelling). Tlast one was the only spotweld modelling method accepted by the implicit solver.

All data from this springback simulation have been transferred to the later csimulations.

3.2.5 Crash of the componentThe crash simulations have been performed with an input, which is the output data froforming simulation (the geometry and the forming parameters) and compared to thesimulation for the component with ideal geometry (the component designed in ordconstruct the tool). Three different modelling cases are considered:

1. The geometry of the hat profile has been taken after the forming phase simulatiwith the later welded lid. The forming parameters (stress tensor, strain and thickdistribution) after springback simulation, performed with only the hat profile (the ficase of springback), have been used. This crash simulation has been called TR

2. Both the geometry and the forming parameters after springback simulation, runthe lid welded to the hat profile (the second case of the springback) have been uThis crash simulation has been called FlSB (Forming, lid, SpringBack).

3. Geometry of the designed component with virgin material properties, the thickne1 mm and the element mesh size of 5 mm has been used. This crash simulationbeen called VIRGIN.

The computer model is done according to a real crash test which is usually performethis kind of structure. During the real test, the back end of the component is fixed tounmovable part of the test equipment. The front end (near the triggers) is the pastructure that is exposed to the initial force of the impact body. The impact body is a flaof test equipment which moves along the y-axis (see Figure 3.6). The surface of the imbody is perpendicular to the axis.

The fixed part of component is modelled by constrained nodes on the back edge of tprofile and the lid. The nodes are constrained in translation and rotation. LS-DYNA offspecial keyword (RIGIDWALL), for the impact body modelling. By means of inpparameters, only motion of the rigid wall along the y-axis is allowed. Initial conditionset by the mass and velocity of the rigid wall. The spotwelds are modelled by a mindependent contact keyword CONTACT_TIED_SHELL_EDGE_TO_SURFACE. T

17


E_3.6.

keyword used in the implicit calculation, CONTACT_TIED_NODES_TO_SURFACOFFSET, is not accepted by the explicit solver. The crash model is illustrated in Figure

Figure 3.6Crash model. The back part of component is fixed and the front one is exposed tothe impact body which moves in the direction of the Y axis.

fixed end

spotweldsY

ZX

impact body(modelled by

(modelled by constrainednodes along the edge)

the rigid wall)

F

18

Chapter 4 Results

eterstures,eters

:

oints’Figure

, i. e.

lobalactionndingched,icates

cess.

4 Results and discussionResults of the crash simulations, performed with the transferred forming param(thickness, stress tensor, and effective plastic strain) are presented. Two different strucobtained after the forming, have been considered. The influence of the forming paramon the crash response is discussed.

The results obtained from the crash simulations are presented by three diagramsaxialdeformation of the front end, force-displacement response, andenergy absorptiondiagram.

The axial deformation is presented by adisplacement of the front endvs time curve. Thedisplacement of the front end has been calculated as the mean value of seven pdisplacement along the Y-axis. These points lie on the front edge of the structure (see4.1).

Figure 4.1Seven points which have been used to calculate the displacement of the front endin Y-direction

The displacement of the front end reaches its maximum when the rigid wall is stoppedwhen the kinematic energy of the rigid wall is absorbed by the structure.

The force-displacement response shows how the rigid wall force acts at different gdisplacement. When the rigid wall hits the component, the impact force causes a reforce of the component. This reaction force, and thereby the impact force, vary depeon the stiffness of the component. When the equilibrium between the two forces is reathe plastic deformation of the structure is stopped. Therefore, this response curve indthe deformation mode of the structure.

The energy absorption is given by arigid wall work vs displacement of the front endcurve.It indicates the value of kinetic energy absorbed by the structure, during the crash pro

19


f the

haseters

e

ingctures

ialin the

Performed simulations are listed in Table 4.1. For the sake of clarity, an explanation osimulations (represented by the listed abbreviations) follows one more time:

• TRICK - The geometry of the hat profile, as obtained after the forming phase,been used, and the flat lid has been welded to the profile. The forming param(the thickness, the stress tensor, and the effective plastic strains) after thespringback process (applied only on the hat profile), have been included in thcrash simulations. The lid is considered as a virgin material.

• FlSB - The flat lid has been welded to the hat profile, as obtained after the formphase. Then, the springback simulation has been performed on the whole stru(the hat profile and the welded lid). The geometry and the forming parameterobtained after such springback have been included in the crash simulations.

• VIRGIN - Geometry of the designed component with virgin properties of materthe thickness of 1 mm and element mesh size of 5 mm has been used directlycrash simulation.

Table 4.1:Performed simulations

run # run name

linetypeinfig.

thicknessvariationincluded

eff. pl.strainsincluded

stress ten-sor in-cluded

LS-DYNA960, revi-sion:

1 TRICK-0 k- N (1mm) N N 1488/1647

2 TRICK-e b- N (1mm) Y N 1488

3 TRICK-es c- N (1mm) Y Y 1488

4 TRICK-te g- Y Y N 1488

5 TRICK-tes r- Y Y Y 1488

6 FlSB-0 k-- N (1mm) N N 1647

7 FlSB-e b-- N (1mm) Y N 1647

8 FlSB-es c-- N (1mm) Y Y 1647

9 VIRGIN b*- N (1mm) N N 1488/1647

εffp σ

20

Chapter 4 Results

andin

largen. Theaxialor thee 4.4

Since all simulations could not be performed by the same revision of LS-DYNA 960since two revisions (1488 is installed in Olofström on the IBM and 1647 is installedGöteborg on the SGI) give different solutions for the same model for the case ofnumber of elements (see A.2), the results are grouped depending on the used revisioFlSB simulations where the thickness is included could not be performed at all. Thedeformations, the force-displacement responses, and the energy absorptions fsimulations performed by two revisions are shown in Figure 4.2 and Figure 4.3, Figurand Figure 4.5, and Figure 4.6 and Figure 4.7, respectively.

Figure 4.2Axial deformation of the front end (simulations performed by the revision 1488)

0 0.02 0.040

50

100

150

200

250

Time [s]

Dis

plac

emen

t [m

m]

VIRGIN TRICK−0 TRICK−e TRICK−es TRICK−te TRICK−tes

1488 revision

21


Figure 4.3Axial deformation of the front end (simulations performed by the revision 1647)

Figure 4.4Force-displacement response (simulations performed by revision 1488)

0 0.02 0.040

50

100

150

200

250

Time [s]

Dis

plac

emen

t [m

m]

VIRGIN TRICK−0FlSB−0 FlSB−e FlSB−es

Göteborg 1647revision

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 104

Displacement [mm]

Rig

id w

all f

orce

[N]


1488revision

22

Chapter 4 Results

Figure 4.5Force-displacement response (simulations performed by the revision 1647)

Figure 4.6Energy absorption of the structure (simulations performed by the revision 1488)

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 104

Displacement [mm]

Rig

id w

all f

orce

[N]


1647 revision

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

Displacement [mm]

Rig

id w

all w

ork

[J]


1488revision

23


ases,d as

ts isere it

Forix A

sttion is

te hasgiveforceone

ctureted tois not. Butrence

Figure 4.7Energy absorption of the structure (simulations performed by the revision 1647)

The VIRGIN simulation which contains a smaller number of elements than the other cwas performed with both revisions and results do not differ between the two. It is usethe reference solution, for the comparison of the other results.

The force-displacementdiagrams are not smooth, since the number of calculating pointoo small. Therefore, these diagram are only used for the additional investigation whhas been shown that some differences or similarities clearly exist.

The computation time give important information about the performed simulations.detailed information about performed simulations and computation time see Appendand Appendix B.

4.1 Influence of the different geometry on the crash response

VIRGIN, TRICK-0, and FlSB-0. A first look at the diagrams shows that the weakestructures are the structures where the forming parameters are not included. This situaapparent since the deformations governed by thestress-strain curve begin from the stateplaced at the origin of the curve. Hence, the hardening first occurs when the plastic stabeen entered. By comparing TRICK-0, FlSB-0, and VIRGIN it can bee seen that theydifferent crash response. In the FlSB-0 case, the axial deformation is larger, the impactvanishes further away from the impact point, and the energy is absorbed slower. Inword, the FlSB-structure is the weakest structure. The VIRGIN is an idealized struwith larger elements (5 mm) used to design the triggers and therefore it can be expecshow a stiffer response. The difference between the TRICK-0 and FlSB-0 structuresvery large (in the deformation mode) for the displacement of the front end 0-100 mmafter this displacement, direct influence of the triggers disappears and the diffe

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

Displacement [mm]

Rig

id w

all w

ork

[J]


1647revision

24

Chapter 4 Results

onselSB

in theling ofe FlSBcture

ed thatfterationses a

after

becomes significant. It is probable that the flat lid in the TRICK case gives a stiffer respthan the lid (and the hat profile) deformed during the springback simulation in the Fcase.

On the other hand, the springback simulation in the FlSB case also causes changesshape around the spotwelds on the lid, see Figure B.6, which then influences the buckthe FlSB-structure, see Figure 4.8. These deformations also cause the buckles in thcase to be more compressed than in the TRICK structure. All this makes the FlSB struweaker but also more stable than the other cases, see Figure B.7. It should be noticthe solution obtained by the 1647 revision shows buckling of the TRICK structure adisplacement of 200 mm has been reached. That is the reason why the axial deformfor the TRICK-0 and FlSB-0 cases in further steps is are similar. The revision 1488 givstiffer TRICK-0 structure, which seems realistic since it is the structure obtainedforming phase.

25


Figure 4.8The deformation modes of VIRGIN, TRICK and FlSB-structures. The influenceof the spotwelds on the forming of buckles on the FlSB-structure is bigger than on theTRICK and VIRGIN structures.

VIRGIN

FlSB-0

TRICK-0(rev. 1647)

TRICK-0(rev. 1488)

26

Chapter 4 Results

iaxialin theas an

(theheffectiveth theith an andstiffer.

ce inlSB

plasticand

astic

ectse the

4.2 Influence of the forming parameters on the crash responseIn order to explain influence of the forming parameters on the crash response, the unstress-strain diagram is used. The diagram does not represent the real situationmaterial since the real state refers to a plane stress state, but it still can be usedapproximate explanation.

4.2.1 Influence of the effective plastic strainWhen only the effective plastic strains have been transferred from the formingsimulationsTRICK-e andFlSB-e), the initial state in the crash simulation is defined by ttransferred effective plastic strains and the zero stresses (see Figure 4.9). Since the eplastic strain effects the yield stress, a new material response (during the crash) wiupdated (higher) yield stress, matches the situation when having a virgin material wstress-strain curve moved to the left. The diagrams representing the axial deformatiothe energy absorption show that this (higher) material hardening makes the structureFurthermore, by comparing the difference between0 ande-simulation (i.e. effective plasticstrains are included) for two different types of geometry, we can see that the differenobtained results for the TRICK structure is greater than the difference for the Fstructure. Since the springback implies only changes of the stresses (the effectivestrains remains the same), this difference can be explained only by the different TRICKFlSB geometry caused by differently performed springback simulations.

Figure 4.9The effective plastic strains after the springback simulation are mapped into thecrash simulation.

4.2.2 Influence of the effective plastic strain and the stress tensorIt is interesting to compare the structural response with included only effective plstrains to the response with also stresses included (TRICK-e andTRICK-es, andFlSB-eandFlSB-es). Since the springback simulations for TRICK and FlSB differ, we can expsomewhat different crash response caused by different stress distribution. In any cainfluence of the stresses should be minor.

σs

ε

σ

forming with the springback crash (with only eff. pl. strains included)

σ

ε

new yieldstresses

initialstates afterspringback states

1

2

3

321

27


onsebvioussmall.7. Theeters

haveplicity,l case,) have

eachedgreender tociselyferringsents

phase.t that itning of

rce-eviouste andn the

, wein theonse

curvehasd thene is arptionntly

gramtion

If we look at the axial deformations, we can see that TRICK-es gives a weaker respthan TRICK-e, see Figure 4.2 and Figure 4.6. The influence of the stresses is not so oin the FlSB case. The difference between FlSB-e and FlSB-es displacement is veryand here the stresses have a somewhat stiffening effect, see Figure 4.3 and Figure 4energy absorption confirmes this observation, i.e. the combination of these two paramgives a stiffer structure especially for the TRICK case, at the end of simulation.

Let us look again at Figure 4.9. After the springback process, some of the elementsresidual tensile stresses, some of them have cmpressive stresses. For the sake of simthey are represented by three elements. From the stress-strain diagram for the uniaxiawe can see that new yield stresses for e-simulations for each element (magenta linesthe same values as they should have if the crash simulation continues from the state rafter the forming (with included effective plastic strains and stresses: es-simulations,lines). The difference between these cases is in the work that have to be done in orreach the new yield stress. By means of this explanation, we can not explain preinfluence of the stresses on the crash response, but we can be sure that only by transthe effective plastic strains, we can not expect that the crash simulation exactly reprethe real crash process.

4.2.3 Influence of the thicknessThe thickness has been changed during the stamping but not during the springbackTherefore, the thickness distribution is same on the both structures and we can expecinfluences both structures in the same way. In our case, the stamping has caused thinthe material which then causes a weaker crash response of the structures (TRICK-et,TRICK-tes ). This is clearly shown by the diagrams (the axial deformation and the fodisplacement response). The same influence of the thickness was noticed in the prworks, see Jergeus [1] and Dagson [3]. Therefore, we can expect that also the FlSB-FlSB-tes (that could not be performed) would have shown a weaker response thaperformed FlSB-e and FlSB-es simulations.

One interesting observation is that comparing the TRICK-e and TRICK-es simulationscan see that TRICK-es gives weaker response than TRICK-e, but including thicknessmodels the situation becomes the opposite. TRICK-tes simulation gives stiffer respthan TRICK-te. This seems contradictory.

Let us include the force-displacement response (Figure 4.4) in the explanation. TheTRICK-te differs from the other curves after displacement of approximately 120 mmbeen reached, i.e. after 0.01 s. At this position the curve has the last sharp peak anquickly goes down, which is not the case with the other curves. This shows that therdifference in the deformation mode in comparison to the other cases. The energy absodiagram (Figure 4.6) shows that the lines TRICK-te and TRICK-tes become significadifferent after displacement of 135 mm is reached, and in the axial deformation dia(Figure 4.2) this difference is visible after 160 mm, i.e. after 0.015 s. The deformamodes for all five TRICK models are shown in Figure 4.10.

28

Chapter 4 Results

Figure 4.10Deformation modes of the TRICK structure for the different inputs of formingdata.

A A

line color:run name: 0te es etes

Time=0.006 s

Time=0.010 s

Time=0.015 s

Time=0.040 s

view A

29


herecase,eforethe

ictionn seee andn alsoibutione that.

We can see that the TRICK-0 and TRICK-e have the most regular deformation mode, wTRICK-e is a hardened structure and therefore gives stiffer response. In the TRICK-essome global buckling occurs but considerably less than in the TRICK-te case. TherTRICK-es gives a stiffer response than TRICK-te. The considerable buckling inTRICK-te case occurs around time of 0.01 s and that is the reason for the contraddescribed above. By looking at the deformation mode for the TRICK-tes case, we cathat stresses influence the deformation mode in such way that it becomes stabltherefore gives a stiffer response that in TRICK-te case. At least for this case, we castate that even if the stresses weaken the structure locally, they preserve an even distrof buckles, which makes a better energy absorption. In other words, we shall concludthe residual stresses may prevent an unwanted buckling of some unstable structures

30

Chapter 5 Conclusions and the further work

ainedds, are

ns ofs fromblems

ons.ently

nd theective

antlyf thewhichnessn onlyo theas nottes

cantlyidualckled.

uence

veryns ofot

5 Conclusions and the further workThis chapter contains conclusions based on the performed simulations and the obtresults. Some suggestions, according to the present studies and the future demanoutlined.

5.1 ConclusionsThe springback simulations have successfully been performed. Two different solutiothe springback process has generated two different structures. The forming parameterthese simulations have been transferred to the crash simulations. Due to numerical prothe thickness distribution for one structure (FlSB) could not be included into simulatiThe results indicates that the influence of the different geometry, obtained by differperformed springback simulations is significant.

Thinning of the material causes a somewhat weaker response of the structure aeffective plastic strains always hardens the material response. The influence of the effplastic strains is the most eminent.

Considering the influence of the residual stresses, the question was if they significinfluence the crash simulation. The results show that a parameter combination ostresses, the effective plastic strain and thickness distribution, gives a crash responsenotably differs from the crash response when only effective plastic strains and thickchanges are transferred into the crash simulation. Since the response of material whethe effective plastic strains are included does not differ very much from one when alsstresses obtained after springback are included, the influence of the stresses wconsidered to be significant. But in the combination with thinning simulation indicaanother conclusion. The residual stresses added to the strains with thinning significhange the deformation mode. It is likely that some softening, introduced by the resstresses, preserve a stable deformation without global buckling, compared to a budeformation induced by the thinning. These observations must be further investigated

The available code does not support mapping of the back stress tensor so that the inflof the kinematic hardening could not be investigated.

The computation time for the stamping simulation as well as for the crash simulation islong using only one CPU. Differences in the solutions between SMP and MPP versiothe LS-DYNA and impossibility to perform all crash simulations by MMP version did nallow usage of more CPUs.

31


Some

n of

aredorth

mme ofrisonsh

ntthe

ticalwsorth

5.2 Further workAs already stated, the influence of the residual stresses must be investigated further.other suggestions for the further work follow:

• Physical forming and crash tests should be performed and compared with thesimulated processes. This comparison should show which virtual structure(obtained with respective springback simulation) gives more accurate simulatiothe crash process and thereby govern the future usage of the springbacksimulations.

• An analysis on the influence of kinematic hardening should be done and compto physical test results. This comparison should show if mixed hardening is wof considering.

• The crash simulations have been performed with the element size of the 2.5 and 1.25 mm. This size was demanded by the springback simulation. The sizthe elements is quite small compared to common crash simulations. A compabetween crash simulations performed by RADIOSS (FE solver) and a real cratest (Eriksson and Jonsson [2]) has shown that the nominal size of the elemeshould be 5-7 mm. Therefore it would be useful to perform the coarsening afterspringback simulation.

• Since the simple structure (with the straight angle between the top and the versurfaces of the hat profile) which is used so far for this kinds of investigation shounstable behaviour in the crash simulations, some stable structure should be wof considering for future investigations.

32

References

ncal

Rail,

01

001

n

lid

References[1] Johan Jergeus,IVS course: Energy absorption in vehicle structures, Pages 4-12, Volvo

Car Corporation, March 2002

[2] Pär Eriksson and Patrik Jonsson,Automotive Component Testing for Crash SimulatioCalibration, Master Thesis, Division of Solid Mechanics, Department of MechaniEngineering Linköping University and Volvo Cars Corporation, December 2002

[3] Niclas Dagson,Influence of the Forming Process on the Crash Response of a RoofComponent, Master Thesis, Department of Solid mechanics, Linköping UniversityMarch 2001

[4] Malin Magnusson and Erik Torstenson, Overview of Sheet Metal Forming Theory andComparison of Simulation Results from Two Finite Element Programs,Department ofStructural Mechanics, Chalmers University of Technology, Göteborg, Sweden 20

[5] LS-DYNA Theoretical Manual, Livermore Software Technology Corporation, May1998

[6] LS-DYNA Keyword User’s Manual,Volume II (Material Models, References andAppendices), Version 960, Livermore Software Technology Corporation, March 2

[7] LS-DYNA Keyword User’s Manual, Volume I, Version 960, Livermore SoftwareTechnology Corporation, March 2001

[8] Ioannis Doltsinis,Elements of plasticity, Theory and Computation,Institute forComputer Applications, University of stuttgart, Germany, 2000

[9] David Roylance,Mechanics of Materials, John Wiley & Sons, Inc. 1996

[10] Abdel-Rahman Ragab, Salah Eldin Bayoumi,Engineering Solid Mechanics,Fundamental and Applications, CRC Press, 1999

[11] http://www.dynamore.de/download/papers/af02_v10_elsaesser_trw.pdf

[12] Mats Svensson,FE-Simulation of Hemming in the Automotive Industry,Department ofthe Structural Mechanics, Chalmers University of Technology, Göteborg, Swede2001

[13] Bradley N. Maker, Xinhai Zhu,Metal Forming Tutorial - 1, Livermore SoftwareTechnology Corporation, April 2000

[14] Bradley N. Maker, Xinhai Zhu,Metal Forming Tutorial - 2, Livermore SoftwareTechnology Corporation, June 2001

[15] www.ls-dyna.com

[16] C. W. Hirt, Implicit Versus Explicit Method, Flow Science, Inc. 2001

[17] Peter Hansbo,Beyond the Elements of Finite Elements: General Principles for Soand Fluid Mechanics Applications, Departemnt of Solid Mechanics, Chalmers

33


.

University of Technology, April 2002

[18] Robert D. Cook, David S. Malkus, Michael E. Plesha,Concepts and Applications ofFinite Element Analysis, University of Wisconsin-Madison, John Wiley & Sons, IncThird Edition, 1989

[19] Anders Johansson, Stefan Pauli,Modelling of Spot Welds with Failure nad MeshIndependency, Institute of technology, Dept of Mech Eng, SE-581 83 Linköping,Sweden, 2002

[20] Belytschko T., Liu W.K., Moran B.,Nonlinear Finite Elements for Continua andStructures, John Wiley & Sons, Ltd, Chichester, England, 2000

34

Appendix A LS-DYNA insufficiency

rk of. As ahe list

LS-ry488

one

er toable.SMPr was

oseay:

runcks

he

odeseir

t in

d inoc-osener tongigure

Appendix A LS-DYNA insufficiencyMany problems occurred during the work. Since they were caused by an improper wothe solver (LS-DYNA), it would be useful to give a short description of these problemsconsequence, the information about used versions of LS-DYNA is given, followed by tof perceived irregularities.

A.1 Used versions of LS-DYNA codeTwo versions of LS-DYNA have been used: LS-DYNA 960 and an unofficial version ofDYNA 970 beta. LS-DYNA 960 is available in a few revisions: 1106 (Distributed MemoParallel - MPP, on 5 to 15 CPUs, SGI), 1647 (MPP on 5 to 15 CPUs, SGI), and 1(Shared Memory Parallel - SMP on 1 CPU, IBM). Version 970 is available in onlyrevision - 2827 (SMP on 1 CPU, IBM).

Whenever it was possible the MPP revision of LS-DYNA 960 has been used in ordreduce the computation time. In the first part of the work, the Revision 1106 was availLater on, this revision has been replaced by the Revision 1647. In addition, therevision has been used for the springback simulations because the implicit solveavailable only in this revision.

A.2 Irregularities in the codeThere are some options in the LS-DYNA (all three revisions of the version 960) whusage is explained in LS-DYNA User’s Manual [7], but which do not work in a proper w

1. For a complex structure, neither the trimming nor the coarsening can betogether with the stamping or the springback simulations. The input demust be separated.

2. If the coarsening is performed after the stamping in the same file with ttrimming, the “dynain” file written by the keywordINTERFACE_SPRINGBACK_DYNA3D_ NOTHICKNESS is not correct(some lines are missing).

3. The coarsening does not work if seed nodes are not defined. The seed nare included in an optional keyword card (see Maker and Zhu [14] ). Thusage helps in finding an isolated region of mesh (which does not exisour case) that should be coarsened.

4. The first time when the coarsening was performed successfully and usethe later simulations, it was noticed that one single row of finer elementscurred at the edge of the profile. The reason was that the one of the chseed nodes was placed, by mistake, at the edge of the hat profile. In ordcheck if the coarsening would be done in different way, a new coarseniwas performed with new seed nodes. The results was the same (see FA.1 ).

35


-t beeenb-

nda-

how

rr-

Figure A.1 The coarsening performed with a) incorrectly and b) correctly chosen nodes.There is one single row of finer elements in the both coarsen mesh.

5. It is possible to simulate a springback process without any constrainednode.

6. When the forming simulations have been performed and the data transferred to the crash simulations, some of the crash simulations could noperformed by Revision 1647. The input deck of these simulations has brun in Revision 1488 and simulations have been performed without prolems.

7. The same input deck (TRICK-0) has been run by two revisions (1647 a1488) in order to compare the performed simulations. The axial deformtion of the front end and the energy absorption for these simulations, san unacceptable difference (see Figure A.2 ).This could be caused by us-ing different hardware! But, in more simple case (i.e. with smaller numbeof elements), like VIRGIN simulation, there was no difference in the peformed simulations.

badly chosenseed node

a)

b)

36


a- to

ing,imu-

minoringri-ele-d as-

areeene

rgerm -

Figure A.2 The axial deformation and the energy absorption for the simulations which wererun by two different revisions (1647 and 1488) with the same input deck (TRICK-0), showunacceptable difference.

8. When this result-difference (see point 7) was noticed, all forming simultions were run again, but this time in the Revision 1488, and comparedthe simulations which have been already performed in Revision 1647(stamping simulation) and the Revision 1488 (the coarsening, the trimmand the springback simulations). The difference between the forming slations is shown by the Forming Limit Diagram (FLD, see Figure A.3 ).The squares show the elements’ deformation states expressed by the and the major strains. The red line in the diagram represents the FormLimit Curve (FLC) obtained from experimental observations of the mateal. The area above FLC is the area of failure. In order to be sure that thements are distanced from the failure area, the yellow line is usually usethe failure boundary. FLD diagrams in the Figure A.3 show that the elements’ deformation, in the simulation performed by the Revision 1488,concentrated between -10% and 10% value of the minor strain, and betw-2% and 13% value of the major strain. The simulation performed by thRevision 1647, gives deformation of the elements which covers much laarea of the diagram (minor strains: from -24% to 11%, major strains: fro2% to 30%).This could be caused by using different hardware!

Figure A.3 FL diagrams obtained from the simulations performed by a) the Revision 1488and by b) the Revision 1647

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

50

100

150

200

250

Time [s]

Dis

plac

emen

t [m

m]

Rev. 1647Rev. 1488

0 50 100 150 200 2500

500

1000

1500

2000

2500

3000

3500

Displacement [mm]

Rig

id w

all w

ork

[J]

Rev. 1647Rev. 1488

Axial deformation Energy absorption

a) b)

37


thei-la-

(theontactrly

s ex-

n one

lcu-ingtestnylts

9. In order to be consistent, and because of the mentioned differences insimulations (see A.2 ), an attempt in performing all simulations by Revsion 1488 was made. This time the problem occurred in the crash simutions. Only simulation of the TRICK-0 case was possible to run (for theinformation about used revisions see Appendix B ). The reason for thisproblem might be smaller elements remains after performed coarseningerror message referred to those nodes) or/and the mesh independent cused for a definition of the spotwelds. This contact does not work propeif it happens that a node, which should be connected to an element, lieactly under the boundary between two elements.

A.2.1 Problems with an implementation of the material model 103Before the implementation was started, a simulation of tensile-compression test oelement (with material models 37 and 103 [withα=0 and α=1, see 2.3.2]) has beenperformed. The following irregularity was found:

10. Within the material card for implementation of the material model 103,there is a parameter called FLAG. When the FLAG is set to 2, the loadcurve “stress vs effective plastic strain” should be taken as an input to calations directly. The kinematic hardening should be implemented by settα=0. Figure A.4 shows the model of implemented tensile - compressionwith the corresponding results. The results show that we do not have akinematic hardening. This conclusion is obvious by comparing the resuof this simulation with the “isotropic” one (α=1). In the “d3hsp” file, thefLAG=2 did not exist as the offered option.

Figure A.4 Tensile - compression test performed on the one element with the materialmodels 37 (isotropic hardening), 103 withα=1 (isotropic hardening), and 103 withα=0(kinematic hardening) with parameter FLAG set to 2. a) Test model with the implemented“displacement vs time” curve. b) Test results. There is no any sign of the kinematichardening.

b)

Y

Z

X

Translation of all four nodesof the element are constrainedin the X - direction

a)

physical model

−0.1 0 0.1−600

−400

−200

0

200

400

600

Strain

Str

ess

[MP

a]

37−iso 103−iso103−kin

0 0.2 0.4 0.6 0.8 1−0.3

−0.2

−0.1

0

0.1

0.2

0.3

Time [s]

Dis

plac

emen

t in

Y d

irect

ion

[mm

]

38


pingentlation

e

la-the re-rds,noteenutitial

de a

tionsf theIBMnn”

ssing

When trying to implement the material model 103 in the simulations, only the stamsimulation was done successfully. Two different versions of LS-DYNA and differmethods were used in order to transfer data (with the backstress tensor) from one simuto the next one:

• Version 970 and thedynain method

• Version 960 and the restart input data method (by using d3dumpnn files). Thefullandsmall restart have been considered.

11. Unfortunately, the coarsening and the trimming is not yet included in thVersion 970. Therefore, it was not worth to continue using this version.

12. Thefull restart is used when some changes should be made in the simution which has already been performed. The “d3dump” file, obtained asoutput from the previous simulation, is used as the first input file for thestarting. A restart file, which contains changes and few necessary keywois the second input file used to perform the restarting. Coarsening couldbe performed at all. The best solution, obtained when the trimming has brun byfull restart, is shown in Figure A.5. It was a normal termination bwith an abnormal solution. One or a few nodes have been stuck at the inposition.

Figure A.5 Solution obtained when the trimming has been performed by a restart with thematerial model 103.

A.3 ConsequencesOne of the consequences caused by the LS-DYNA insufficiency is impossibility to inclukinematic hardening in the crash simulations.

Another one is connected to the computation time. The difference in the soluperformed by different revisions of the LS-DYNA 960 unable us to use advantage oshorter computation time of the 1647 (MPP) revision. The MPP-revision installed onplatform was not used since the code “dumpbdb” does not work properly with “dboutnnfiles (made by this revision) which had to be used to get output files for the post-proceof crash results.

39


d 54crashl run

d bymed

The CPU time for the stamping model by Revision 1106 (on 15 CPU’s) was 6 hours anminutes. The same model run by Revision 1488 took 90 hours and 14 minutes. Thesimulation performed by Revision 1647 took 6 hours and 58 minutes. Identical modeby Revision 1488 took 43 hours and 54 minutes.

It is worth noticing that the stamping simulation with the material model 103, performeLS-DYNA 970 (on 1 CPU) took 178 hours and 5 minutes. The same simulation perforby LS-DYNA 960, Revision 1647 (on 5 CPU’s) took 28 hours 56 minutes.

40

Appendix B Simulations

d steelrcialwith

n the

tablecess.

e later

Appendix B SimulationsThis appendix contains a detailed information about the simulations.

B.1 Material used in the simulationsThe real material whose behaviour has been simulated is rephosphorized, zinc coateincluded in the list of Volvo standard sheet metal steels by number 1437. A commename of material is SSAB Docol 260 RP. It is a strain rate dependent materialfollowing physical and mechanical properties given by a material supplier:

• Mass density

• Young’s modulus

• Poisson’s ratio

• Yield stress

They differs in Young’s modulus and yield stress from the standard properties given itable of material.

For simplicity, the material is considered a strain rate independent. Thestress-straincurve isgiven in Figure B.1 .

Figure B.1Stress-strain curve of the material 1437 given by supplier

B.2 DesignIn order to find a placement of the triggers on the component, leading to an accepdeformation mode during crash, crash simulation has been included in the design pro

Two different material have been considered in the design process: 1437 and 1464. Thone is a dual phase steel (DP 350/600).

ρ 7.8 kg dm3⁄[ ]=

E 2.1 105MPa[ ]⋅=

ν 0.3=

σy 293 MPa[ ]=

A

Detail A

41


ations
The following standard properties of material 1437 have been used for the crash simul(in the design phase):
• Mass density



• Yield stress

The properties of the material 1464:

• Mass density



• Yield stress

The crash model used in the simulations is described in Subsection 3.2.5 .

Basic input data for the simulation model:

• Geometry of the component

• Material data: Steel 1437 (and 1464)

• Thickness: 1mm

• Frictionless sliding after contact between the rigid wall and the component

• Rigid wall mass: 50 kg

• Rigid wall velocity: 54 km/h

ρ 7.8 kg dm3⁄[ ]=

E 2.05 105 MPa[ ]⋅=

ν 0.3=

σy 263 MPa[ ]=

ρ 7.8 kg dm3⁄[ ]=

E 2.05 105 MPa[ ]⋅=

ν 0.3=

σy 352 MPa[ ]=

42


art of

in2

t thede of

. Inf 7

Basic configuration in LS-DYNA:

• Termination time: 0.03 s

• Element type: 2 (Belytschko-Tsay)

• Element size on the hat profile: 5mm

• Element size on the lid: 3.51 and 5 mm

• Number of integration points through the element thickness: 5

• Material model: 24 (Piecewise Linear Isotropic Plastic)

• Number of constrained nodes: 26 welded nodes and fixed nodes at the end pthe component

• Contact: CONTACT_AUTOMATIC_SINGLE_SURFACE (to determine thecontact between the lid surface and the flanges) and CONSTRAINED_SPOTWELD (to define the spotwelds)

• The rigid wall and its moving is defined by keyword:RIGIDWALL_PLANAR_MOVING

• Strain rate dependence is presented by a table which contains the stress-stracurves for the corresponding strain rates. The curves are shown in Figure B.

Solver: LS-DYNA (explicit), Version 960, Revision 1106, Distributed Memory Parallel

Number of CPUs: 15;

Computation time (CPU time): 7-9 minutes

Figure B.2The strain-rate dependence for a) material 1437 and b) material 1464, given byten stress-strain curves

The difference between the deformation modes for components with and withoutriggers can be seen in Figure B.3 a) and b). Figure B.3 c) shows the deformation mothe component where the triggers are placed on both the lid and the hat profile.

1. The contact CONSTRAINED_SPOTWELD is a mesh dependent contact. In order to get the lidnodes placed exactly under the nodes of hat profile, mesh size of some elements had to be 3.5 mmthe design phase, the length of flanges was 14 mm, and spotwelds were placed on the distance omm from the edge of flanges.

0 0.2 0.4 0.6 0.8 1250

300

350

400

450

500

550

600

Strain

Str

ess

[MP

a]

0 0.2 0.4 0.6 0.8 1300

400

500

600

700

800

900

Strain

Str

ess

[MP

a]

a) b)

43


ed

Figure B.3Triggers influences on the deformation modes. a) Structure without the triggers,b) Structure with the triggers and c) Structure with badly placed triggers

B.3 Forming simulations

B.3.1 Stamping simulationBasic input data for the simulation model:

• Geometry of the tools and blank

• Material data: Steel 1437

• Blank thickness: 1mm

• Coefficient of friction: 0.1

• Maximum allowed drawbead retaining force when the bead is in the fully closposition: 200 kN

a)

b)

c)

44


Basic configuration in LS-DYNA:


• Element type on the tools: Belytschko-Lin-Tsay element, 2

• Element type on the blank: Fully integrated shell element, 16

• Element size on the blank: 1.25 mm

• Number of integration points through the sheet thickness: 5

• Material model: 37 for 1437 and rigid for the tools

• Contact: FORMING_SURFACE_TO_SURFACE and CONTACT_DRAWBEAD

• Punch speed: 2.5 m/s

• Movement function of the punch is given by a displacement-time curve (seeFigure B.4

Figure B.4Movement function of the punch

Output data:• Geometry of the hat profile

• Strain tensor

• Element thickness

• Stress tensor

• Effective plastic strain

Solver: LS-DYNA (explicit), Version 960, Revision 1106, Distributed Memory Parallel

Number of CPUs: 15.

Calculation time: 6 hours and 54 minutes.

The effective plastic strain distribution is shown in Figure B.5 .

0 0.005 0.01 0.015 0.02 0.025 0.030

10

20

30

40

50

60

70

Time [s]

Dis

plac

emen

t [m

m]

45


Figure B.5Effective plastic strain distribution after the stamping simulation

B.3.1.1:CoarseningBasic input data for the simulation model (“dynain” file from the stamping simulation):

• Geometry of the hat profile

• Strain tensor

• Thickness

• Stress tensor

• Effective plastic strain distribution

46


rd

red

):

Basic configuration in LS-DYNA


• Coarsening is performed by the keyword CONTROL_COARSEN including cawith the seed nodes

• Number of the elements: 64000

• Number of the nodes: 64525

• The rest is the same as for the stamping simulation.

Output data:

• Geometry of the hat profile (including information about the previous mesh,written within the keyword CONSTRAINED_ADAPTIVITY);

• Strain tensor

• Thickness distribution

• Stress tensor


• Number of the elements: 22276

• Number of the nodes: 24007

Finite element analysis software: LS-DYNA (explicit), Version 960, Revision 1488, ShaMemory Parallel

Number of CPUs: 1;

Calculation time: 1 minute 48 seconds

B.3.1.2:TrimmingBasic input data for the simulation model (“dynain” file from the coarsening simulation

• Geometry of the hat profile (and the keyword CONSTRAINED_ADAPTIVITY)

• Strain tensor


• Stress tensor





• Trimming is defined by the following keywords: ELEMENT_TRIM andDEFINE_CURVE_TRIM


47


ry

Output data (“dynain” file):

• Geometry of the hat profile (and the keyword CONSTRAINED_ADAPTIVITY,see Subsection 3.2.2 )

• Strain tensor


• Stress tensor


Solver: LS-DYNA (explicit), Version 960, Revision 1488, Shared Memory Parallel

Number of CPUs: 1;

Calculation time: 1 minute and 4 seconds.

B.3.2 Springback

B.3.2.1:The first caseBasic input data for the simulation model:


• Strain tensor


• Stress tensor





• Element type: Fully integrated shell element, 16

• Element size: 1.25 and 2.25 mm


• Material model: 37

• Number of constrained nodes: 3

Output data:


• Strain tensor


• Stress distribution

• Effective plastic strain d

Solver: LS-DYNA (non-linear implicit), Version 960, Revision 1488, Shared MemoParallel

Number of CPUs: 1;

48


d 10

ion

Computation time: 55 minutes (calculation time without mesh coarsening: 2 hours anminutes)

B.3.2.2:The second caseBasic input data for the simulation model (“dynain” file from the trimming simulation):


• Strain tensor


• Stress tensor


• Geometry of the lid

• Element thickness of the lid: 1 mm





• Element size on the hat profile: 2.25 and 1.25 mm

• Element size on the lid: 2.5 mm


• Material model: 37

• Number of constrained nodes: 3 + 26 spot welds

• Contact: CONTACT_SURFACE_TO_SURFACE andCONTACT_TIED_NODES_TO_SURFACE_OFFSET

Output data (dynain file):


• Geometry of the lid

• Strain tensor (on the lid and the hat profile)

• Thickness distribution (on the lid and the hat profile)

• Stress distribution (on the lid and the hat profile)

• Effective plastic strain distribution (on the lid [=0] and the hat profile)

Finite element analysis software: LS-DYNA (non-linear implicit), Version 960, Revis1488, Shared Memory Parallel

Number of CPUs: 1;

Calculation time: 17 minutes

Stress distribution on the lid is shown in Figure B.6.

49


ss dis-
Figure B.6 Stress distribution on the lid after second case of the springback was performed. The stretribution indicates the changes in the shape around the spotwelds.
a)

x st

ress

x

y z

b)

yt

zx

y st

ress

c)

z st

ress

50


tion

d part

t

P

min.

gure

other. Theith

B.4 Crash simulationsAll performed crash simulations are listed in the Chapter 4 . The general informafollows:

Basic input data for the simulation model:

• Geometry and the forming parameters (see the chapters 3 and 4 )


• Frictionless sliding after contact between the rigid wall and the component

• Rigid wall mass: 30 kg

• Rigid wall velocity: 54 km/h

Basic configuration in LS-DYNA for all simulations



• Element size on the hat profile: 2.25 and 1.25 mm

• Element size on the lid: 2.5 mm


• Material model: 24 (Piecewise Linear Isotropic Plastic)

• Number of constrained nodes: 26 welded nodes and the fixed nodes at the enof the component

• Contact: CONTACT_AUTOMATIC_SINGLE_SURFACE_TITLE (to determinethe contact between the lid surface and the flanges) andCONTACT_TIED_SHELL_EDGE_TO_SURFACE (mesh independent contacfor defining the spotwelds)

• The rigid wall and its moving is defined by the keyword:RIGIDWALL_PLANAR_MOVING

Solver: LS-DYNA (explicit), Version 960, Revision 1488, SMP and Revision 1647, MP

Number of CPUs: 1 (SMP), 5 and 15 (MPP).

Computation time: 44-45 hours (SMP),.9 hours and 11 min. (5 CPUs), 3 hours and 26(15 CPUs)

The deformation mode for the TRICK case is given in the Subsection 4.2.3 . FiB.7shows deformation mode for the VIRGIN and FlSB cases.

One simulation TRICK-0 has been performed with the lid that was shorter than in thecases. One row of elements (2.5 mm) has been removed from the front end of lidsimulation mode showed relatively big difference in comparison to the TRICK-o wregular length of the lid.

51


e-
Figure B.7 Deformation modes of VIRGIN and FlSB structure for the different inputs of forming paramters
A A

Time=0.006 s

Time=0.010 s

Time=0.015 s

Time=0.040 s

view A

line color:run name:

*VIRGIN FlSB-0 FlSB-e FlSB-es

52


e
Figure B.8Deformation mode for the TRICK-0 and TRICK-0 with the shorter lid. The difference in thlength of lid is 2.5 mm but it gives large difference in the deformation mode
TRICK-0 (shorter lid) TRICK-0

Time=0.0 s

Time=0.004s

Time=0.01s

53


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Documents

Inﬂuences of the Forming Process on the Crash … · Inﬂuences of the Forming Process on the Crash Performance - - Finite Element Analysis Abstract The objective of this thesis