2006:068 CIV

M A S T E R ' S T H E S I S

Finite Element Simulationof Punching

Magnus Söderberg

Luleå University of Technology

MSc Programmes in Engineering Mechanical Engineering

Department of Applied Physics and Mechanical EngineeringDivision of Computer Aided Design

2006:068 CIV - ISSN: 1402-1617 - ISRN: LTU-EX--06/068--SE

Abstract This work is a study of a punching process using the ABAQUS/Explicit FE-code. Adamage model based on equivalent plastic strain has been used to describe crack initiationand propagation in the blank.

An axisymmetric model created in ABAQUS/CAE was used throughout the study. Themodel consists of a punch, blank holder, die and blank. In this work the punch, blankholder and die are modelled as rigid bodies while the blank is considered elastic-plastic.

The materials used in simulations are DC04, Docol 350 YP, Docol 800DP and DC1400M.This selection of steel qualities has a wide span in mechanical properties and fields ofapplication.

Material characterisation for simulation purposes has been done by conducting uniaxialtensile tests. The data from these tests have been extrapolated beyond the necking strain bydouble Voce extrapolation.

Punching experiments have been performed in an excenter driven press equipped withposition and force measurement devices. The experiments result in load curves for thedifferent steel qualities and gives information about the characteristic zones of the sheetedges.

The results from simulations have been evaluated by comparisons with experimentsconcerning load curves, characteristic zones of the sheet edge, work done during theoperation, maximum forces and stroke to failure.

A good compliance with experiments was found concerning maximum forces,characteristic zones and work done during the operation.

Table of Contents1. Introduction....................................................................................................................42. Influence of simulation parameters................................................................................5

2.1 FE-Model ...............................................................................................................52.1.1 Geometry........................................................................................................52.1.2 Element type ..................................................................................................62.1.3 Material data and model.................................................................................62.1.4 Contact and boundary conditions ..................................................................72.1.5 Failure criterion..............................................................................................8

2.2 Fe-Simulations .......................................................................................................92.2.1 Mesh density ..................................................................................................92.2.2 Adaptive mesh .............................................................................................142.2.3 Failure strain value.......................................................................................16

2.3 Comparison with results from DEFORM............................................................212.3.1 Failure criterion in DEFORM......................................................................212.3.2 Load curves..................................................................................................212.3.3 Simulated edge geometry.............................................................................22

2.4 Elastic tools..........................................................................................................232.5 Comments ............................................................................................................27

3. Material properties .......................................................................................................283.1 Materials ..............................................................................................................283.2 Tensile tests..........................................................................................................28

3.2.1 Mechanical properties..................................................................................283.2.2 Extrapolation of test data .............................................................................29

4. Experiments .................................................................................................................304.1 Experimental setup ..............................................................................................304.2 Data from experiments.........................................................................................31

5. Simulation model.........................................................................................................325.1 Geometry and mesh density.................................................................................325.2 Material model .....................................................................................................33

5.2.1 Strain rate dependency.................................................................................345.3 Failure criterion....................................................................................................345.4 Contact and boundary conditions ........................................................................35

5.4.1 Contact conditions .......................................................................................355.4.2 Boundary conditions ....................................................................................37

6. Comparison with experiments .....................................................................................386.1 Method of evaluating simulations........................................................................38

6.1.1 Evaluation of simulated characteristic edge zones ......................................386.1.2 Evaluation of work.......................................................................................396.1.3 Evaluation of stroke to failure......................................................................396.1.4 Evaluation of maximum punch force...........................................................40

6.2 Load curves and edge profiles .............................................................................406.2.1 DC04............................................................................................................406.2.2 Docol 350 YP...............................................................................................416.2.3 Docol 800 DP...............................................................................................426.2.4 Docol 1400M ...............................................................................................43

6.3 Characteristic zones .............................................................................................446.3.1 Rollover .......................................................................................................446.3.2 Shear zone....................................................................................................45

6.3.3 Fracture zone................................................................................................466.4 Maximum punch force.........................................................................................476.5 Work ....................................................................................................................486.6 Stroke to failure....................................................................................................49

7. Discussion....................................................................................................................508. Conclusions..................................................................................................................519. Future work..................................................................................................................5210. Acknowledgements..................................................................................................5311. References................................................................................................................54Appendix 1 Mechanical properties ......................................................................................55Appendix 2 Data from punching experiments .....................................................................57

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1. IntroductionPunching is a sheet metal forming procedure were material shearing mechanisms are usedto produce the desired geometry. The development today is focused against usingadvanced high strength steel qualities to make lighter products with sustained or increasedproduct durability. These steel qualities puts higher demands on the tooling used to cut orform the sheet steel, which makes the choice of process parameters even more importantthan with ordinary mild steels, because of the narrow process window when using highstrength steels. Identification of the process parameters is today mostly done by large seriesof experiments, which is costly and time-consuming [1]. In earlier work performed by D.Thunvik [2] and others [3], [4], the DEFORM FE-code has been used to simulate thepunching process with results close to experimental. Simulations with theABAQUS/Standard FE-code and damage implemented by means of a user subroutine havealso shown results in compliance with experiments [5], [6]. This shows the possibility ofusing FE-simulations to reduce the number of experiments that has to be conducted andgive a increased understanding concerning the influence of process parameters.

This work utilises the ABAQUS/Explicit FE-code and a failure criterion that is readilyimplemented in the code. The objective has been to resolve the capacity of this codeconcerning simulations of punching and establishment of a modelling procedure for thistype of problems. Simulations will be compared to experimental data concerning geometryof the edges, load curves, work done by the punch during the process, maximum forcesinvolved and stroke to failure of the blank.

The first section is devoted to finding a suitable modelling approach in ABAQUSconcerning mesh densities, failure criterion and features in the software such as adaptivemesh. The results from this section will be compared to simulations made in DEFORM [2].

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2. Influence of simulation parametersIn this section a FE model is created in ABAQUS to resolve the influence of the variationsin the mesh density, value of the failure criterion and the adaptive mesh function that isimplemented in the software. A single case of punching in Docol 800 DP will be simulatedusing the dimensions and material model as earlier in the DEFORM [2] simulations, tomake a comparison between the results from the two different software packages possible.Simulations with elastic tools have been made to study if it is possible to evaluate the stressstate in the tools during punching and the elastic response in the tools using this modellingapproach.

2.1 FE-Model

All FE-models evaluated in this study have been created using the ABAQUS/CAE pre-processor. The solution is obtained with the ABAQUS/Explict solver, which uses a directintegration scheme on the structural dynamic equations. This approach is suitable forhighly dynamic problems with non-linear behaviour, which is the case when simulatingfracture of metals.

2.1.1 GeometryThe tools and blank have been modelled using an axisymmetrical model that can be seen inFigure 2.1, values of the dimensions can be found in Table 2.1.

Figure 2.1: The axisymmetric FE-model in ABAQUS.

Table 2.1: Dimensions corresponding to the model in Figure 2.1r1 [mm] r2 [mm] r3 [mm] r4 [mm] c1 [mm] c2 [mm] t [mm]

2.44 0.01 0 0.01 0.5 0.06 1

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2.1.2 Element typeThe elements in the blank consist of four node bilinear axisymmetric quadrilateralelements with reduced integration (CAX4R) and three node axisymmetrical triangles(CAX3). The triangles are used to coarsen the mesh for increased computationalefficiency, see Figure 2.4. Both elements belongs to the family of solid elements and are ofthe first order, which means that the strain is computed as an average over the elementvolume instead of the first order gauss point. The feature of reduced integration used in theCAX4R element causes the integration order to be lower than full integration, in this caseonly one integration point in the centre of the element is used. By using reduced integrationthe numbers of constraints which are introduced by the elements are decreased, thisprevents “locking” in the elements causing a stiff response. The drawback of this techniqueis that for certain modes of deformation no energy is registered in the element integrationpoint. These modes are usually referred to as “hourglass modes”. This problem isaddressed in ABAQUS using a “hourglass control” algorithm [9].

2.1.3 Material data and modelThe blank material consists of Docol 800 DP in all simulations in this section. Yield datawere taken from [2] in an effort to make the simulations as comparable as possible, seeFigure 2.2. The yield data is extrapolated using the double Voce method, which is a way ofproducing reliable data at high strains. This procedure is explained in more detail in section3.2.2, which covers the topic of extrapolation of yield curves.

Double Voce extrapolated yield data

0200400600800

100012001400

0 0.2 0.4 0.6 0.8 1

True plastic strain

True

str

ess

[MPa

]

Yield stress Docol800 DP

Figure 2.2: Yield data for Docol 800DP extrapolated with the double Voce method.

The material model used is the isotropic von Mises hardening model. In this model thematerial is assumed to have similar properties in all directions. As no reversed loadingoccur during the simulations the hardening was described as isotropic i.e. the Bauchingereffect is not modelled. The yield criterion for this model can be expressed by means of theprincipal stresses as:

])()()[(21 2

322

212

21 σσσσσσσ −+−+−=y (1)

As can be seen from Equation (1) the criterion is independent from the hydrostatic stresscondition i.e. only the deviatoric part of the stress tensor influences the criterion. This can

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be interpreted by saying that yielding occurs at a certain level of deviatoric strain energy[10].

2.1.4 Contact and boundary conditionsContact between the tools and the blank is enforced by a kinematic contact condition,using pure master-slave surface pairs established in the first step of the solution. Themaster and slave designation must be chosen so the rigid tool forms the master surface andthe surfaces defined on the blank act as slave [11].

The formulation of this contact condition is of predictor/corrector type were the model isfirst advanced to a kinematic state without consideration to the contact condition. The slavenodes witch penetrates the master surface is then determined and the force to move theslave nodes on to the master surface is calculated. These forces are calculated based on thedepth of penetration, nodal masses and time increment. The acceleration correction for themaster and slave surfaces is then calculated based on the forces needed to opposepenetration and the inertia of the contacting bodies [11]. The surfaces which form thecontact pairs in this model are summarised in Figure 2.3 and Table 2.2.

Figure 2.3: The surfaces used in the contact pairs. 1) is the surface of the punch, 2) is the top nodesof the blank, 3) is an internal nodal based surface, 4) is the surface of the blank holder, 5) is thebottom nodes of the blank and 6) is the surface of the die

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Table 2.2: A summarisation of the contact conditions numbered as in Figure 2.3Master surface Slave surface/surfaces

1 2, 34 26 3, 5

Friction between the surfaces is implemented with a Coulomb model defined as:

nf µστ = (2)

Where τf is the friction shear stress, µ is the friction coefficient and σn is the normalpressure. A friction coefficient of 0.1 has been used in all simulations.

The punch displacement is applied as a prescribed velocity of 40 mm/s and the holderforce is set to be 1350 N which is about 15 percent of the maximum punch force. Thenodes at the symmetry line are locked in the radial direction by a displacement boundarycondition. When an axisymmetrical definition is adapted, no material flow in the angulardirection is presumed.

2.1.5 Failure criterionTo estimate the start and propagation of fracture, a local fracture criterion is used in thesimulations. The criterion used in this set of simulations is the shear failure model inABAQUS. This model is based on a value of equivalent plastic strain at elementintegration points and failure is assumed to occur when the damage parameter exceeds 1.The damage parameter, ω, is defined as:

plf

plpl

εεε

ω �∆+= 0 (3)

Where ε0pl is the initial value of the equivalent plastic strain, ∆εpl is an increment of plastic

strain and εfpl is the strain at failure [11].

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2.2 Fe-Simulations

2.2.1 Mesh densityBecause of the high strain gradients in the cut region, a sufficiently dense mesh must beapplied in this area. The mesh density will also affect the geometry of the cut edges as aresult of fracture being simulated with element deletion.

To resolve how the mesh density will affect the results four models with different meshdensities have been analysed. The number of elements was 656, 1488, 3901 and 7693 andthe plastic failure strain was set to 1.5. Mesh densities were chosen by starting out with 16through thickness (t in Figure 2.1) elements in the sheared zone and then dividing them by2 until 128 through thickness elements were reached. The maximum number of elementsthrough thickness will hereafter be used when referring to a mesh density i.e. 16, 32, 64and 128. For additional data about the different mesh sizes see Table 2.3. The differentmesh sizes are shown in Figure 2.4.

Table 2.3: Data about the different mesh densitiesMaximum number of throughthickness (t) elements

Number of elements Smallest characteristic lengthof elements [mm].

16 656 0.062532 1488 0.0312564 3901 0.01563

128 7693 0.007813

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Figure 2.4: a) 656 elements, 16 through thickness elements, b) 1488 elements, 32 through thicknesselements, c) 3901 elements, 64 through thickness elements and d) 7693 elements with 128 throughthickness elements. The number of through thickness elements stated is the maximum number in therefined zone.

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It can be seen from the load curves plotted in Figure 2.5 that the mesh density influencesthe rupture behaviour and stroke to failure to a greater extent than the maximum force.This is believed to be an effect of the more localised plastic deformation when the meshdensity is increased, which results in higher strains at an earlier stage of the simulation thustriggering the failure criterion with following element deletion, see Figure 2.6.

Mesh density Docol 800 DP

0

2000

4000

6000

8000

10000

0 0.2 0.4 0.6 0.8

Stroke [mm]

Forc

e [N

] 64 elements32 elements16 elements128 elements

Figure 2.5: Force versus stroke curves using the above mentioned mesh densities. The plasticfailure strain was set to 1.5 for all simulations.

Figure 2.6: Field plots of the equivalent plastic strain with a) 64 elements through thickness and b)128 elements through thickness.

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When coarser meshes are used the final rupture is delayed because of the cracks in theblank that originates from the punch and die miss each other, as shown in Figure 2.7. Thisbehaviour is not observed when using 128 elements through thickness because of thepossibility for cracks to initiate closer to the edges of the punch and die. Another effect ofthe increased mesh is that it seems to facilitate for the cracks to change columns in themesh as they propagate, see Figure 2.8 for the simulated edge geometry using differentmesh densities. The ability for the cracks to change column is of great importance if thecrack tips shall be able to meet each other and produce rupture behaviour similar to the oneobserved in experiments.

Figure 2.7: Crack tips missing each other during fracture of the blank. The mesh density is 64elements through thickness.

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Figure 2.8: The simulated sheet edges with a) 16 through elements, b) 32 through thicknesselements, c) 64 elements and d) 128 elements. The number of elements refers to the maximumnumber of elements through thickness as mentioned above A plastic failure stain of 1.5 was used inall simulations.

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2.2.2 Adaptive mesh

Adaptive meshing in ABAQUS is carried out in two steps: creating a new mesh andremapping of the solution variables from the old mesh to the new mesh by an advectionsweep. The adaptive meshing task is triggered at user specified intervals with a defaultvalue of 10 increments. During an adaptive mesh increment, the new mesh is created byone or many mesh sweeps, which moves nodes to reduce element distortion. The numberof mesh sweeps can be specified by user input and has a default value of one. This valuehas to be increased if the deformation rate is high because the numerical stability of theadvection sweep is maintained only if the difference between the new and old mesh issmall [11]. For the simulations in this section, the default values will be used.

In the section above the crack tips miss each other when using coarse meshes, whichcauses a section of elements between the two cracks to experience large distortion beforefinal rupture. This results in an increased stiffness causing a longer stroke to fracture. Toinvestigate if the adaptive mesh function in ABAQUS is able to improve the solution, thefour mesh densities used in the previous section were simulated using this function on theelements in the zone between the tool edges. The results of the simulations can be seen inFigure 2.9. The location of crack initiation is improved with adaptivity i.e. the cracks isstarting nearer to the tool edges which is an effect of the mesh ability to follow the toolgeometry closer. For 16 and 32 elements the cracks propagates in the same elementcolumn during the whole rupture process which gives a realistic load drop but fails torepresent the edge geometry by producing a very short sheared zone, see Figure 2.10. With64 elements the simulations produces results that are improved over the ones withoutadaptivity but still suffers from the fact that a element column is “trapped” between thetwo crack tips which results in a deviation from the simulation with 128 elements at astroke of 0.16 mm. This leads to the conclusion that between 64 and 128 through thicknesselements are needed for the simulations. For capturing the edge geometry, 128 elementswill probably be required but 64 elements can be used to study the influence of parametervalues on the force stroke curve to reduce the cpu time required to perform the simulations.

Mesh density Docol 800 DP

0

2000

4000

6000

8000

10000

0.00 0.10 0.20 0.30 0.40

Stroke [mm]

Forc

e [N

] 16 elements32 elements64 elements128 elements

Figure 2.9: Force versus stroke curves for different mesh densities using adaptive meshing. Theplastic failure strain was set to 1.5 for all simulations.

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Figure 2.10: The simulated sheet edges with a) 16 elements, b) 32 elements, c) 64 elements and d)128 elements in the thickness direction, using adaptive mesh.

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2.2.3 Failure strain valueTo investigate the influence of the failure strain value five models with the same meshdensity, 64 through thickness elements with adaptive meshing has been simulated. Thevalues of failure strain have been set to 1.5, 2.0, 3.0, 3.5 and 4. The results from thesimulations showed that the failure strain value mainly affected the stroke to fracture andhad a small influence on the maximum force, which can be seen in Figure 2.11.

Shear failure value Docol 800 DP

0

2000

4000

6000

8000

10000

0.00 0.10 0.20 0.30 0.40 0.50

Stroke [mm]

Forc

e [N

]

Shear 1.5Shear 2.0Shear 3.0Shear 3.5Shear 4.0Experiment

Figure 2.11: Force versus stroke curves for different values of plastic failure strain. A mesh densityof 64 through thickness elements with adaptive mesh was used in all simulations. The simulatedcurves are denoted with “Shear” and a corresponding value of the failure strain.

The influence of failure strain value on the characteristic zones have been investigatedusing a results from simulations in DEFORM[2] as a benchmark for a realistic edgegeometry. This was done because no experimental data for the edge geometry could befound for this set of process parameters.

Measurments of the characteristic zones were taken by using the distance query tool inABAQUS/CAE, which calculate the distance between nodes picked by the user. Defintionof the zones have been done by taking the rollover as the distance between the top of theblank and the first node at the transition to shear zone. The shear zone is measured betweenthe transition point until initiation of fracture and the remaining part down to the loweredge of the blank is considered to be the fracture zone. Burr is measured from the loweredge of the blank. See Figure 2.12 for details concerning how the zones are measured.

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Figure 2.12: a) Rollover is measured from the top of the sheet edge to the first node of the shearzone. b) The shear zone is measured from the end of rollover until the start of fracture. c) Thefracture zone is measured from the start of fracture until the lower edge of the sheet. d) Burr ismeasured from the lower edge of the sheet.

The characteristic zones were measured using the procedure outlined above and the resultsare presented together with results from DEFORM for comparison, see Figure 2.13. Themeasured edge profiles are presented in Figure 2.14.

Characteristic zones

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6

Leng

th o

f cha

ract

eris

tic z

ones

[mm

]

RolloverShear zoneFracture zoneBurr height

Figure 2.13: The characteristic zones measured with different values on the failure strain. Bar 1-5are measurements from simulations done in ABAQUS with failure strain: 1) 1.5, 2) 2, 3) 3, 4) 3.5,5) 4. Bar 6 is measurements from a reference case taken from DEFORM. All ABAQUS simulationswere done with 64 elements through thickness and adaptive mesh.

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Figure 2.14: Simulated sheet edges with value of strain at failure of a) 1.5, b) 2.0, c) 3.0, d) 3.5 ande) 4.0. The edges were simulated with 64 through thickness elements and adaptive meshing.

As the shear zone was considered to short to be realistic in the simulations made withABAQUS, an attempt to produce edge geometry closer to the one achieved with DEFORMwas made by increasing the mesh density to 128 elements through thickness. Failure strain

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values of 3.5 and 4 were used. The model with failure strain of 3.5 were simulated bothwith and without adaptive mesh but as can bee seen from Figure.2.15 the results withadaptive mesh were not as close to experimental results as the ones with a standardLagragian mesh definition. Because of the erroneous results produced with adaptivemeshing, it was discontinued for the simulations with a failure strain of 4, which produceda stroke to failure similar to experiments. The deterioration of the results with adaptivemesh can probably be explained by the large number of mappings of the solutions to a newmesh that has to be done when the failure strain value is set to high values, yielding aniteration count of about 5 million increments. Also some kind of incompatibility withadaptivity and failure combined is suspected. The simulated edge geometry for the modelswith 128 elements through thickness can be seen in Figure 2.16. Measurements of thecharacteristic zones are presented in Figure 2.17.

Docol 800 128 elements through thickness

02000400060008000

10000120001400016000

0 0.1 0.2 0.3 0.4

Stroke [mm]

Forc

e [N

]

Failure strain = 3.5

Failure strain = 4.0

Experimental

Failure strain = 3.5adap

Figure.2.15: Force versus stroke curves with 128 through thickness elements. “adap” indicatesthat adaptive mesh have been used.

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Figure 2.16: The simulated sheet edges with 128 through thickness elements with a failure strainvalue of a) 3.5, b) 4 and c) 3.5 with adaptive mesh.

Characteristic zones

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4Leng

th o

f cha

ract

eris

tic z

ones

[mm

]

RolloverShear zoneFracture zoneBurr height

Figure 2.17: Measurements of the characteristic zones with different values of failure strain. Bar 1-2 are measurements from ABAQUS using a failure strain of 1) 3.5 and 2) 4. Bar 3 is simulated inABAQUS using a failure strain of 3.5 and adaptive mesh. Bar 4 is a reference case from DEFORM.All simulations in ABAQUS used 128 elements through thickness.

The difference in the initial response in simulations and experiments can probably beexplained by the fact that the experimental punching setup has elastic properties whenloaded while the tools in the simulations are modelled as rigid. Another possible source oferror is that the material model used in the simulations is unable to predict the actualbehaviour of the material when subjected to this kind of deformation.

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2.3 Comparison with results from DEFORM

DEFORM is an implicit code that is mainly used to simulate different kind of metalforming operations such as forging, machining and rolling. To facilitate these kind ofsimulations it has a more advanced mesh updating function were an adaptive refinementprocedure is implemented in the code, which allows severe case of deformation withoutdistorting the mesh. The code also has more models for fracture initiation and propagationthan is implemented in ABAQUS today. A drawback with such a specialised code is thereduced capability to simulate more general problems were for example non-metalmaterials is included. Another issue is that DEFORM is not as commonly used in industryas ABAQUS. Therefore a comparison between the results produced with the two differentcodes is of interest to see if the process can be simulated with no mesh updating and theless advanced failure criterion used in ABAQUS.

2.3.1 Failure criterion in DEFORMThe Cockroft and Latham failure criterion were chosen to predict failure initiation andpropagation in the work used for comparison [2]. Other authors have also used this failurecriterion with acceptable results [4]. The formula for the Cockroft and Latham failurecriterion is given by:

Cdf

=� εσσε *

(4)

Where *σ is the maximum principal stress,σ is the effective stress, ε is the effective strain,fε is the effective strain at fracture and C is the damage value which is a material

parameter. When the damage value C reaches a critical value in an element, given as userinput, the element is deleted from the mesh. The interpretation of this criterion is that ahigh degree of triaxiality invokes fracture at a lower strain level compared to the uniaxialcase.

2.3.2 Load curvesTwo important results from the simulations are the maximum force and the stroke tofailure. ABAQUS and DEFORM shows good agreement in predicted maximum force andstroke to failure compared to experiments. The noise produced in the ABAQUS curve is aresult of mass scaling techniques being used to reduce the cpu time necessary to performthe simulations.

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ABAQUS vs DEFORM and experiment

-2000

0

2000

4000

6000

8000

10000

0 0.1 0.2 0.3 0.4 0.5

Stroke [mm]

Forc

e [N

]

Experiment

DEFORM C=1.5

ABAQUS Failurestrain=4

Figure 2.18: Comparison between load curves from ABAQUS, DEFORM and experiments.

2.3.3 Simulated edge geometryThe dimensions of the different characteristic edge zones have been compared earlier andcan be found in Figure 2.13 and Figure 2.17. The measured zones from the two codesdiffer somewhat but are in reasonably good agreement, keeping in mind that themeasurements are dependent on how the author chooses to define the limits of the differentzones. The appearance of the edges is presented in Figure 2.19. The edges simulated inABAQUS appear to be smoother than in DEFORM because of the higher degree ofdiscretization necessary to capture the geometry and fracture behaviour when a adaptivemesh refinement method are not available.

Figure 2.19: Simulated sheet edges in DEFORM (left) and ABAQUS (right). The ABAQUSsimulation has 128 elements through thickness with a plastic failure strain of 4,Adaptive meshingwas not used.

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2.4 Elastic toolsIn order to resolve the difference between using elastic and rigid tools, a simulation modelusing elastic tools were created see Figure 2.20. The boundary conditions is applied in thesame manner as the simulations using rigid tools except for the contact between the toolsand the blank, which is modelled as a pure master-slave contact pair with element-nodecontact surfaces. This contact condition prescribes that nodes on slave surfaces cannotpenetrate the master surfaces but nodes from master surfaces can penetrate slave surfaces.In this case, the blank is modelled as a nodal based slave surface and the tools are elementbased master surfaces. The motivation for the choice of master and slave surfaces is thatABAQUS requires parts that can fail to be modelled with nodal surfaces and nodalsurfaces is always slave using this contact definition [11].

Figure 2.20: The FE-model with elastic tools.

Figure 2.21 shows the difference between rigid and elastic tools using 128 throughthickness elements in the blank and a failure strain of 3.5. The elastic response in the toolscan be seen as a slight displacement of the curve to the right in the beginning of thesimulation and faster rupture of the blank. The faster rupture is assumed to be an effect ofthe elastic springback in the tools during load drop. A greater elastic response wouldprobably be achieved by using tools that are longer in the 2 direction in Figure 2.20.

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Elastic vs Rigid tools

-500

1500

3500

5500

7500

9500

11500

0 0.1 0.2 0.3Stroke [mm]

Forc

e [N

]

Shear 3.5 128 el elastShear 3.5 128 el

Figure 2.21: Force stroke curves with rigid and elastic tools. Both simulations had a plastic failurestrain of 3.5 and 128 elements through thickness.

The stress in the tools is shown for different levels of stroke in Figure 2.22-19. The VonMises stress, x-stress component (S11) and y-stress component (S22) is presented in thementioned order, the orientation of the directions can be seen in figure 2.22 (1 is the xdirection and 2 is the y direction). It can bee seen that the blank mesh is too coarse tocapture the sharp corner radius of the punch. This leads to that only a few nodes from theblank are in contact with the punch creating very high local stress levels (over 6500 MPa inFigure 2.23) and sharp gradients in the stress field. Severe penetration of the elements inthe slave surface by the punch master surface is also observed.

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Figure 2.22: Effective stress and components in the punch and blank at a stroke of 0.05 mm. Thestresses are given in MPa.

Figure 2.23: Effective stress and components in the punch and blank at a stroke of 0.15 mm. Thestresses are given in MPa.

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To resolve these problems the elements in the refined area was divided by 2 in the xdirection. This resulted in a better interaction between the punch and blank andsmoothened the gradients in the stress field see Figure 2.24. The effective stress level wasabout 1000 MPa evenly distributed around the radius instead of 2600 MPa directly underthe node contact points, which were the case in Figure 2.23. With these results in mind,conclusions can be made that a very high level of mesh refinement is needed to resolve thestate of stress in the punch during the cutting operation when using this type of contactcondition.

Figure 2.24: Effective stress and stress components in the punch and tool at a stroke of 0.05mm.The stresses are given in MPa.

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Figure 2.25: Effective stress and components in the punch and blank at a stroke of 0.15mm. Thestress is given in MPa.

2.5 CommentsIt has been shown in this section that simulations with ABAQUS using an axisymmetricalmodel can predict the maximum punch force and stroke to failure with good accuracy,using a plastic failure strain of 4. Calibrations against experiments have to be done todetermine the value of the plastic failure strain.

Comparisons with simulations made with the DEFORM FE-code showed good agreementin terms of the characteristic edge zones and stroke to failure when using a value on thefailure parameter that produces a stroke as measured in experiments.

Simulations using elastic tools showed that the elastic response had a small effect on theload curve (Figure 2.21), causing a delay in the rise of the punch force and a shorter stroketo failure. A greater difference is expected if simulations with tool dimensions similar tothe ones used in experiments would be made, this has not been done because of the longcpu time such a simulation would require. The tool stress could not be resolved using themesh density from the simulations with rigid tools because of the single sided contactcondition allowed penetration by the punch radius into the mesh of the blank. This wasimproved when the mesh density in the blank was increased in the radial direction,showing more reasonable stress levels, but further studies has to be made if estimations ofthe accuracy shall be possible.

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3. Material properties

3.1 MaterialsThe materials that will be used in the simulations are DC04, Docol 350 YP, Docol 800 DPand Docol 1400M. The Docol steels are cold reduced high and ultra high strength qualities.The corresponding numerical value to each Docol grade corresponds to the lowest yieldstrength for the YP qualities and lowest tensile strength for the DP and M qualities. DC04is a mild steel quality suitable for deep drawing.

3.2 Tensile testsTo generate the necessary input data for the simulations tensile tests have been performedfor the above mentioned materials. Specimens for each material have been created in therolling direction (0 degrees), 45 degrees and transverse to the rolling direction (90degrees). The tests were made and documented by SSAB Tunnplåt. True stress versus truestrain curves generated during the tests can be found in Appendix I.

3.2.1 Mechanical propertiesThe mechanical properties for the different materials in the directions mentioned earlier aregiven in Table 3.1. The parameter r is the plastic strain ratio that is used to assess theanisotropy of blank materials [7]. It can be expressed in terms of strains as:

t

wrεε

= (5)

Were εw is the strain in the width direction and tε is the strain in the thickness direction.Another parameter that is useful for determining the properties of sheet metal is r which ismeasure of the normal anisotropy i.e. the average anisotropy in the plane of the sheet. Ahigh r value shows that the preferred flow direction is in the plane of the sheet ( r >1)while a low value ( r <1) indicates a preferred flow direction in the thickness direction. Thenormal anisotropy parameter can be calculated from the plastic strain ratios with thefollowing formula [8]:

42 90450 rrrr ++

= (6)

Were the indices denote the orientation of the tensile direction given as the angle to therolling direction.

29

Table 3.1: Mechanical properties of the different sheet materials. r is the normal anisotropy.Materialdesignation

Direction Rp0.2 [MPa] Rm [MPa] r r n

Docol 350 YP 0° 363 423 0.67 0.1145° 369 416 0.97 0.1190° 403 432 1.05 0.92 0.11

Docol 800 DP 0° 653 873 0.70 0.1145° 645 862 0.98 0.1190° 659 887 0.87 0.88 0.11

Docol 1400 M 0° 1277 1486 0.75 0.1145° 1258 1459 0.61 0.1190° 1278 1496 0.62 0.65 0.11

DC04 0° 184 308 2.26 0.2145° 187 315 1.55 0.2090° 176 299 2.86 2.06 0.20

3.2.2 Extrapolation of test dataData produced with uniaxial tensile tests is only valid until the point of necking. Neckingcauses a triaxial stress state in the specimen that alters the strain hardening behaviour. Thestrain developed in the blank during a cutting operation exceeds the necking strain inuniaxial tension by far, which calls for other procedures to characterise the materialresponse under high strain. One way to overcome this problem is extrapolating the yielddata from the tensile test, starting with the point at the onset of necking. This has beendone using a method called double Voce extrapolation were the yield data is fitted to theexpression given by:

)1()1( 42310

PP CC eCeC εεσσ −− −+−+= (7)

Were 0σ is the initial yield strength of the material and pε is the plastic strain. A methodfor determining the constants in Equation (7) has been developed by Dr Mats Sigvant [13].This method is based on using the Ag value and two points before to resolve the constantsK and n in a power law extrapolation such as:

npK )(εσ = (8)

Thereafter the stress at a fourth point is computed by adding a strain of four percent to thestrain that is found at the Ag and inserting this value into Equation (8). This set of points isthen used to compute the constants in Equation (7). The resulting curve increases almostlike a power law after the Ag value but as the strain increases the exponential termsvanishes and leaves only the initial yield stress and the constants C1 and C3 thus forming aplateau at higher strains. See Figure 3.1 for extrapolated yield curves concerning thedifferent materials used in this study.

30

Double Voce extrapolated yield curves

0.00200.00400.00600.00800.00

1000.001200.001400.001600.001800.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Plastic strain

Yiel

d st

ress

[MPa

]

Docol 800 DPDocol 1400 MDocol 350 YPDC04

Figure 3.1: Double Voce extrapolated yield data for the different materials.

4. ExperimentsTo generate data for validation of the simulations, punching tests with the beforementioned materials have been performed by Uddeholm Tooling AB. The experimentsgive information about the characteristic zones of the cut edges, forces used to penetratethe blank and the stroke required to complete the punching operation. For a summarisationof experimental data see Appendix 2.

4.1 Experimental setupThe machine used to produce the experimental data is an excenter driven press withsensors for measuring position and forces added to the main tripod. A piezoelectric loadcell is used for registering forces while an inductive position sensor is measuring theposition with a sampling frequency of 10kHz. The layout of the machine and position ofthe sensors can be seen in Figure 4.1-2.

Figure 4.1: A section view of the main tripod were: 1) Position of the load cell, 2) Punch, 3) Blankholder, 4) Die.

31

Figure 4.2: The main tripod with the position measuring sensor marked with a red arrow.

4.2 Data from experimentsIn order to be able to compare the load curves from the experimental punching machinewith simulations, some postprocessing had to be done. Because of the limited space in themachine, the load cell used to register the forces had to be placed in such a way that allforces used in the operation is registered see Figure 4.3 for an example of an experimentalload curve.

Punch forces DC350YP

6000

8000

10000

12000

14000

16000

18000

20000

22000

-0.2 0.8 1.8 2.8 3.8Distance between edges [mm]

Tota

l for

ce [N

]

Figure 4.3: Experimental load curve

To extract the data of interest from the experimental load curve a straight line was fitted tothe part of the force curve were the punch had not yet made contact with the blank andonly the force of the blank holder is being registered, see Figure 4.4. The equation of thisline gives the distance dependency of the holder force, which then can be withdrawn fromthe total force. The stroke is also corrected so the zero level is when the punch makes firstcontact with the blank.

32

Blank holder force vs stroke

0

2000

4000

6000

8000

10000

0 0.5 1 1.5 2 2.5 3 3.5 4

Distance between edges [mm]

Forc

e [N

]

Figure 4.4: Straight line fitted to the blank holder force

The above corrections have been made to all experimental load curves and the result ispresented in Figure 4.5

Experimental load curves

-50000

5000100001500020000250003000035000

0 0.2 0.4 0.6 0.8 1

Stroke [mm]

Forc

e [N

] DC04 ExperimentDC350YP ExperimentDC800DP ExperimentDC1400M Experiment

Figure 4.5: Corrected experimental load curves.

5. Simulation modelThe experimental data presented in Section 4.2 have been produced with different toolgeometry than were used during the parameter study in Section 2. A different materialmodel was also to be used for DC04. Therefore a new simulation model had to be made tosimulate the punching operation.

5.1 Geometry and mesh densityAn axisymmetric FE-model was used in all simulations with tool and blank dimensionsmatching those that were used in the experiments, see Figure 5.1 and Table 5.1. The meshdensity was 128 elements through thickness in the sheared zone and were chosen based onthe results from Section 2.

33

Figure 5.1: The axisymmetric FE-model.

Table 5.1: Tool and blank dimensions used with the different materials.Material r1 [mm] r2 [mm] r3 [mm] r4 [mm] c1 [mm] c2 [mm] t [mm]DC04 4.94 0.02 0.01 0.02 0.06 0.26 0.98DC350YP 4.94 0.02 0.01 0.02 0.06 0.26 1DC800DP 4.90 0.02 0.01 0.02 0.10 0.3 0.96DC1400M 4.90 0.02 0.01 0.02 0.10 0.3 0.97

5.2 Material modelThe isotropic von Mises material model described in Section 2.1.3 have been used for allmaterials except DC04 for which the model proposed by Hill in 1948 have been evaluated.Usage of this model is motivated by the high values of the plastic strain ratio shown byDC04. The yield criterion for this material model can be expressed in terms of stresscomponents as:

212

231

223

22211

21133

23322 222)()()()( σσσσσσσσσσ NMLHGFf +++−+−+−= (9)

Were the constants F, G, H, L, M and N are obtained by tests of the material in differentdirections. The definition of these constants is:

,2

3

,2

3

,2

3

),111(21

),111(21

),111(21

212

213

223

233

222

211

222

211

233

211

233

222

RN

RM

RL

RRRH

RRRG

RRRF

=

=

=

−+=

−+=

−+=

(10)

34

The parameters R11, R22, R33, R12, R13 and R23 are anisotropic yield stress ratios defined asfollows:

0

23

0

13

0

12

0

33

0

22

0

11 ,,,,,τσ

τσ

τσ

σσ

σσ

σσ

(11)

The type of anisotropy that will be modelled here is the normal anisotropy, whichdescribes the material as isotropic in the plane with increased yield strength in thethickness direction [11]. This kind of behaviour is modelled by setting (with the directions1 and 3 in the plane of the blank and 2 in the thickness direction):

R11=R33=1 (12)

21

22+= rR (13)

Were r is the normal anisotropy parameter given by Equation (6). The remainingparameters are set to a value of unity.

5.2.1 Strain rate dependencyThe material is modelled with a strain rate dependent function to account for the increasedyield strength during high strain rate deformation. This is implemented in ABAQUS byspecifying a yield stress ratio as a tabular function of the equivalent plastic strain rate:

0

)(σεσ pl

R�

= (14)

Were )( plεσ � is the yield stress at a specified plastic strain rate and 0σ is the referenceyield stress at a zero strain rate. The yield stress ratios used for the different materials andplastic strain rates can be found in Table 5.2.

Table 5.2: Yield stress ratios for the materials used in the simulations at different levels ofequivalent plastic strain rate

Yield stress ratio Equivalent plastic strain rateDC04 DC350YP DC800DP DC1400M1 1 1 1 01.064 1.069 1.04 1.054 101.145 1.126 1.072 1.078 1001.28 1.191 1.108 1.106 10001.28 1.191 1.145 1.127 100001.28 1.191 1.193 1.160 100000

5.3 Failure criterionThe shear failure model that is described in Section 2.1.5 has been used in all simulationsto predict the rupture behaviour.

35

5.4 Contact and boundary conditions

5.4.1 Contact conditionsAt first attempts were made using the pure master-slave kinematic contact definition as inSection 2. This proved to be insufficient when simulating materials that showed largeplastic deformation before rupture. When the mesh became distorted the distance betweenthe nodes in the blank became too great which caused penetration at the punch edge as canbee seen in Figure 5.2.

Figure 5.2: Penetration of the punch edge into the blank. The part of the punch that has penetratedthe blank is marked with red.

This effect altered the state of deformation around the punch edge, allowing high strains tobe generated in the elements thus triggering the failure criterion at an early stage of thesimulation. To prevent this phenomenon a new approach was made by defining a balancedpenalty contact condition between the edge and side of the punch and the top elements ofthe blank as shown in Figure 5.3. A similar definition was also added between the blankand die.

Figure 5.3: The penalty contact pair consisting of a) the discrete rigid punch and b) the topelement surface of the blank.

The penalty contact is a less stringent enforcement of contact than the kinematic contactcondition but allows for more general types of contact allowing rigid surfaces to act as

36

slave surfaces. With the penalty contact condition the algorithm searches for slave nodepenetrations and if penetration is found a force is applied to the slave nodes to oppose thepenetration while an force that is equal acts on the master surface on the penetration point.This is often referred to in the literature as adding a spring between the surfaces to preventpenetration [14]. When the balanced penalty contact algorithm is used the forces arecomputed in two steps were the master and slave designation is switched between thesurfaces. An average of the two forces is then applied [11]. When using this approach ofcontact modelling the penetration of the punch edge into the blank is eliminated, see

Figure 5.4: Deformation state around the punch edge with balanced penalty contact.

When the first element is removed from the top surface of the blank the penalty contact isno longer active. The contact between the blank and punch is then enforced by a kinematiccontact condition. The motivation for two different contact algorithms to handle the asingle contact between two surfaces is that ABAQUS does not allow using the samecontact algorithm to enforce contact with both the top elements of the blank and theinternal nodal surface that becomes exposed during the rupture.

37

5.4.2 Boundary conditionsAs the model is axisymmetric the only boundary condition that needs to be applied directlyto the blank is a locking of the nodes at the symmetry line in the radial direction. To holdthe blank in place during the punching operation a force of 10kN is applied in thedownward direction on the blank holder. This force is applied during the first step of thesolution with a ramp function during 0.001s and is then held at this level throughout thesimulation.

Friction between the blank and tools are of Coulomb type, which is described by Equation(2). A friction coefficient of 0.2 has been used throughout the simulations.

The punch is controlled by a prescribed velocity boundary condition were it is given avelocity of 70 mm/s. This velocity has been determined by a linear regression onexperimental data, see Figure 5.5. The velocity is then found by differentiating theequation of the regression line with respect to time.

Punch stroke vs time y = 70.144x + 0.0261

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Time [s]

Stro

ke [m

m]

Figure 5.5: A straight line fit to experimental data concerning the stroke as a function of time. Thezero level for both time and stroke is set at the position were the punch makes first contact with theblank.

38

6. Comparison with experimentsIt is necessary to compare the simulations with experimental results to evaluate the validityof the simulations. In this work comparisons to experiments will be made concerning theload curves, edge profiles, characteristic zones of the cut edges, maximum punch force,work done during the punching operation and stroke to failure. All simulations have beenperformed with the FE-Model described in Section 5.

6.1 Method of evaluating simulationsTo be able to extract the necessary data from the simulations in a reliable manner aframework for evaluating the simulations have been established.

6.1.1 Evaluation of simulated characteristic edge zonesThe rollover zone is generated by the initial plastic deformation of the blank. This has beentaken to be between the top of the blank and the first node that is found on the edge at thetransition point to the sheared zone, see Figure 6.1.

Figure 6.1: Measurement of the rollover zone.

As the punch continues to penetrate the blank the shear zone is formed. This zone isdefined to be between the rollover zone and the start of crack initiation leading to finalrupture of the blank. When simulating materials that experiences large deformation duringforming of the shear zone the mesh becomes distorted making the crack initiation hard todistinguish. Therefore two different measurement criteria have been evaluated: one werethe shear zone is measured to the point were the first element is deleted at the punch edgeand one where a crack of 0.05mm is to be initiated near the punch edge before themeasurement is taken. A graphical interpretation of the two criterions is shown in Figure6.2.

39

Figure 6.2: Two different criterions for determining the lower boundary of the shear zone: a) Acrack tip of 0.05mm at the edge of the punch b) The first element deletion at the edge of the punch.

The rupture zone is then evaluated from the lower boundary of the shear zone down to thelower edge of the blank.

6.1.2 Evaluation of workThe area under the graph of the load curve is used to evaluate the amount of work done bythe punch during the punching operation. A numerical integration method is used tocompute the area under the curve. The boundaries for integration are between the firstcontact of the punch and blank and until the load has dropped to 25% of the max levelbecause of some curves are lacking zero crossing.

6.1.3 Evaluation of stroke to failureThe stroke to failure is measured at the final load drop. If no zero crossing is observed atthe primary part of the load drop, a line will be drawn with the same slope and the strokewill be measured at that point see Figure 6.3.

Figure 6.3: A schematic description of how the stroke to failure are mesured when zero crossing isnot found in the primary part of the load drop.

40

6.1.4 Evaluation of maximum punch forceThe maximum force is taken as the first peak value registered in the load curve.

6.2 Load curves and edge profiles

6.2.1 DC04This steel quality has good deep drawing qualities and is highly ductile, resulting in a longstroke to failure. At the stroke that failure occurs the mesh is heavily distorted thuspreventing the crack tips originating from the punch and die to propagate through the meshand meet causing a delayed final rupture. When modelling the normal anisotropy using theHill 48 material model the maximum force is overpredicted but the force level duringforming of the shear zone is closer to experiment. The failure strain used when simulatingthis material was set to 3.5.

DC04

-2000

0

2000

4000

6000

8000

10000

12000

0.00 0.20 0.40 0.60 0.80 1.00

Stroke [mm]

Forc

e [N

]

ExperimentSimulation Hill 48Simulation von Mises

Figure 6.4: Comparison between simulated and experimental load curve for DC04. The failurestrain value was set to 3.5 in both simulations. When using the Hill 48 material model, normalanisotropy was assumed.

41

When comparing edge profiles the spatial orientation of the zones differs as an effect of thelarger rollover zone that was formed in experiments. The shorter rollover zone insimulations also causes a longer fracture zone than the one being measured in experiments.The simulated and experimental edge profiles are presented in Figure 6.5.

Figure 6.5: Experimental and simulated edge profiles. The profile to the left is simulated with Hill48 material model while the right profile has been simulated using an isotropic von Mises model.

6.2.2 Docol 350 YPWhen simulating this material the model was able to capture the stroke to failure andmaximum forces involved with reasonably good accuracy. The failure strain value was setto 3.5 for the simulation presented in Figure 6.6.

Docol 350 YP

02000400060008000

100001200014000

0.00 0.20 0.40 0.60 0.80 1.00Stroke [mm]

Forc

e [N

]

SimulationExperiment

Figure 6.6: Comparison between simulated and experimental load curves for Docol 350YP. Thefailure strain was set to 3.5 in the simulation.

42

The experimental and simulated edge profiles in Figure 6.7 shows good agreement whencompared to each other. It can bee seen from the picture of the experimental edge profilethat the shear zone has a slight variation along the edge which cannot be represented in thesimulations due to symmetry and thus adding a possible error source.

Figure 6.7: Experimental and simulated edge profiles.

6.2.3 Docol 800 DP

The simulation of Docol 800DP was able to capture the maximum force and the final loaddrop with good accuracy but underpredicted the stroke to failure. This could have beendone by increasing the failure strain value but then the work done (area under the graph)when simulating the process would be more than measured in experiments. Therefore thefailure strain value was set to 3 yielding a simulated load curve that can be seen in Figure6.8.

Docol 800DP

-5000

0

5000

10000

15000

20000

0.00 0.20 0.40 0.60 0.80 1.00

Stroke [mm]

Forc

e [N

]

SimulationExperiment

Figure 6.8: Comparison between simulated and experimental load curve. The failure strain was setto 3 in the simulation.

43

When comparing experimental and simulated edge profile a good agreement was found,see Figure 6.9.

Figure 6.9: Experimental and simulated edge profiles.

6.2.4 Docol 1400MSimulations of Docol 1400M captured the maximum force and final load drop with goodaccuracy. The stroke to failure was as in the case of Docol 800DP underpredicted becauseof the difference between simulations and experiments in the initial stage of the process.

Docol 1400M

-10000

-5000

0

5000

10000

15000

20000

25000

30000

35000

0.00 0.20 0.40 0.60 0.80 1.00

Stroke [mm]

Forc

e [N

]

ExperimentSimulation

Figure 6.10: Comparisons between simulated and experimental load curve. The failure strain wasset to 3 in the simulation.

44

When comparing experimental and simulated edge profiles the rollover was overpredictedin the simulations but the overall appearance of the edge were captured.

Figure 6.11: Experimental and simulated edge profile.

6.3 Characteristic zonesThe characteristic zones from simulations have been measured by the procedure outlinedabove and are here compared to experimental values in correlation diagrams. Numericalvalues concerning the different zones of the edge geometry are summarised in Table 6.1-3

6.3.1 RolloverThe rollover zone is predicted with good accuracy for DC350YP and DC800DP but thesimulation fails to capture the behaviour DC04 and DC1400M.

Rollover

0

0.05

0.1

0.15

0.2

0 0.05 0.1 0.15 0.2

Experiment [mm]

Sim

ulat

ion

[mm

]

Figure 6.12: Rollover measured from simulations plotted against experimental values.

Table 6.1: Numerical data concerning the rollover height measured in experiment and simulation.Material Experiment [mm] Simulation [mm]DC04 Hill 48 0.16 0.096DC04 v.Mises 0.16 0.1DC350YP 0.1 0.09DC800DP 0.1 0.082DC1400M 0.01 0.04

45

6.3.2 Shear zoneThe shear zone has been measured using two different criterions for evaluation. Resultscloser to experimental values are achieved when the shear zones are measured after a cracktip of 0.05 mm has initiated at the edge of the punch.

Shear zone

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Experiment [mm]

Sim

ulat

ion

[mm

]

0.05mm crackCrack initiation

Figure 6.13: Shear zone measured from simulations plotted against experimental values, measuredwith two different criterions for evaluation.

Table 6.2: Data concerning the dimensions of the sheared zones measured in experiments andsimulations. The simulated shear zone is measured with two different criterions for evaluation.

0.05 mm crack Crack initiationMaterial Experiment [mm] Simulation [mm] Simulation [mm]DC04 Hill 48 0.56 0.49 0.34DC04 v.Mises 0.56 0.47 0.36DC350YP 0.5 0.44 0.3DC800DP 0.25 0.25 0.194DC1400M 0.2 0.19 0.165

46

6.3.3 Fracture zoneThe length of the fracture zone is dependent on the measurement of the other zones. Theseries of data presented shows that variation of the fracture zone when the shear zone ismeasured by two different criteria of evaluation. The largest difference in fracture zone isalso shown by DC04 were the simulations did not capture the rollover zone.

Fracture zone

00.10.20.30.40.50.60.70.8

0 0.2 0.4 0.6 0.8

Experiment [mm]

Sim

ulat

ion

[mm

]

0.05 mm crackCrack initiation

Figure 6.14: Fracture zone measured from simulations plotted against experimental values.

Table 6.3: Data concerning the dimensions of the fracture zones measured in experimental andsimulations.

Material Experiment [mm] Simulation [mm]DC04 Hill 48 0.25 0.39DC04 v.Mises 0.25 0. 414DC350YP 0.4 0.47DC800DP 0.61 0.638DC1400M 0.75 0.61

47

6.4 Maximum punch forceThe simulations were able to capture the maximum punch force with good accuracy for allmaterials used in this study

Maximum force

0.005000.00

10000.0015000.0020000.0025000.0030000.0035000.00

0 5000 10000 15000 20000 25000 30000 35000

Experiment [N]

Sim

ulat

ion

[N]

Figure 6.15: Maximum punch force measured from simulations plotted against experimentalvalues.

Table 6.4: Numerical data concerning the maximum forces measured in experiment andsimulations.

Material Experiment [N] Simulation [N]DC04 Hill 48 8773 9166DC04 v.Mises 8773 8353DC350YP 11731 11704DC800DP 17990 17999DC1400M 30431 29542

48

6.5 WorkWhen comparing the work performed by the punch during the operation a good match wasfound between simulations and experiments. The work done during the simulations hasbeen used as an evaluation parameter for materials were experimental and simulated loadcurves differ at the initial stage of the simulation

Work

0

2

4

6

8

10

12

0 2 4 6 8 10 12

Experiment [Nm]

Sim

ulat

ion

[Nm

]

Figure 6.16: Work calculated from simulated load curves compared to experimental values.

Table 6.5: Data concerning work measured in experiments and simulations.Material Experiment [Nm] Simulation [Nm]DC04 Hill 48 5.68 5.79DC04 v.Mises 5.68 5.35DC350YP 6.76 6.10DC800DP 7.18 7.26DC1400M 9.66 9.80

49

6.6 Stroke to failureAs mentioned before the stroke to failure was underpredicted for Docol 800 and 1400while for DC04 and Docol 350 YP the mesh distortion cased a delay in fracture behaviour.

Stroke to failure

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Experimental stroke [mm]

Sim

ulat

ed s

trok

e [m

m]

Figure 6.17: The stroke to failure measured in simulations plotted against experimental values.

Table 6.6: Data concerning the length of the stroke to failure measured in experiments andsimulations.

Material Experiment [mm] Simulation [mm]DC04 Hill 48 0.84 0.92DC04 v.Mises 0.84 0.94DC350YP 0.71 0.75DC800DP 0.56 0.52DC1400M 0.47 0.39

50

7. DiscussionThe results from this study have shown that it is possible to simulate a punching processusing ABAQUS/Explicit and an axisymmetric model definition. Materials included in thestudy have yield strengths ranging from 184 to 1277 MPa, which gives a good indicationof the usefulness of the model. As the materials mechanical properties differ by farsimulation difficulties emerges at different areas. The softer material experiences a largedeformation before final rupture which causes mesh deformation resulting in a delayedfracture, a problem that most likely could have been solved with an adaptive meshrefinement function. For high strength qualities the initial response in the load curve showsdifferences between simulations and experiments. This have been observed in earlier workusing the DEFORM FE-code (Figure 2.18) which implies that the source of error could liein the material definition or the elastic response recorded in the experimental punchingmachine.

During the course of the work some problems were encountered when simulating materialsthat has a large amount of plastic deformation before crack initiation and rupture. Withthese materials penetrations of the punch radius into the blank caused a premature failureof the material or when the failure strain parameter was increased an abortion of thesimulation due to distorted elements. This could be avoided by adding a blended penaltycontact definition between the radius of the punch and top elements of the blank thuscapturing the state of deformation in the blank in a more realistic way.

When comparing experiments and simulations a set of evaluation a set of criterions had tobe adapted for evaluating the simulations. This was done because the transition pointsbetween the characteristic zones are diffuse when large deformations are present in theFE-mesh. Experiments also shows variations in the characteristic zones when measuring atdifferent positions on the blank edge which adds an element of insecurity to themeasurements as variations cannot be captured in the simulations due to symmetry.

51

8. Conclusions• Simulations using ABAQUS can give information regarding the maximum force and

characteristic zones with acceptable accuracy.

• Using a failure strain of 3.5 for DC04 and DC350 YP and 3 for DC800DP andDC1400M proved to be adequate as similar amount of work are measured inexperiments and simulations with these settings.

• For materials that show a large sheared zone the transition between the characteristiczones becomes diffuse making precise measurements hard to accomplish. Criterionsfor evaluation had to be adapted.

• The mesh density used is of great importance for capturing the rupture behaviour of theblank metal.

• Correct representation of the contact between tools and the blank is a key factor whensimulating a punching process.

52

9. Future work• Simulations of parameter variation with experimental verification.

• Implementing improved failure criterions in ABAQUS.

• Evaluation of tool stresses by using elastic tools in the simulations.

• Simulations of metal trimming.

• Making the experiments even more accurate by eliminating elastic response anddynamic effects.

53

10. AcknowledgementsThis project has been founded by SSAB Tunnplåt, TDI AB and Volvo Cars BodyComponents within the SIMR member program.

The author would like to express his gratitude to the following people for theircontributions to the project:

Berne Högman, Anders Thuvander and Ulrika Åhs, Uddeholm Tooling AB for producing

experimental data used to verify the simulations.

Daniel Eriksson, SSAB Tunnplåt, for supplying tensile test data.

Mats Sigvant, Volvo Cars Body Components, for extrapolating yield data and valuable

advice concerning FE-simulations.

Lars Gunnarson, Swedish Corrosion and Metals Research Institute, who has been my

supervisor during the course of this work and has given me great support and guidance.

Prof Arne Melander, Swedish Corrosion and Metals Research Institute, for help and good

advice during this work.

54

11. References1. “Tooling solutions for advanced high strength steels selection guidelines”, SSAB and

Uddeholm Tooling, 20042. D. Thunvik, FE-simulation of trimming, Swedish Institute for Metals Research, 2004.3. E.Taupin, J. Breitling, W-T. Wu, T. Altan, “Material fracture and burr formation in

blanking results of FEM simulations and comparison with experiments”, Journals ofMaterials Processing Technology, 1996

4. G. Fang, P. Zeng, L. Lou, “Finite element simulation of the effect of clearance on theforming quality in the blanking process”, Journals of Materials Processing Technology,2002.

5. R. Hambli, A. Potrion, “Finite element modelling of sheet metal blanking operationswith experimental verification”. Journals of Materials Processing Technology, 2000.

6. W. Klingenberg, U.P. Singh, “Finite element simulation of the punching/blankingprocess using in process characterisation of mild steel”, Journals of MaterialsProcessing Technology, 2002.

7. E.M. Mielnik, “Metalworking science and engineering”, McGraw-Hill, Inc, 1991.8. A. Elsner, “Advanced hot rolling strategies for IF and TRIP steels”, Delft University

Press, 2005.9. HKS-ABAQUS, “ABAQUS Theory manual”, Version 6.5-1.10. N. Ottosen, M. Ristinmaa, “The Mechanics of Constitutive Modelling”, Volume 1

Classical topics, Division of Solid Mechanics, Lund University, 1999.11. HKS-ABAQUS, “ABAQUS Analysis users manual”, Version 6.5-1.12. “Handbok och formelsamling i hållfasthetslära”, Instutionen för hållfasthetslära KTH,

1998.13. M. Sigvant, “The Hemming Process, A Numerical and Experimental Study, Chalmers

University of Technology, Göteborg, Sweden, 2003.14. J.O. Hallqvist, “LS-DYNA Theoretical manual”, LSTC, 1998.

55

Appendix 1 Mechanical properties

Figure 1: True stress versus true strain in the rolling direction for the materials included in thisstudy.

0

200

400

600

800

1000

1200

1400

1600

0 0.05 0.1 0.15 0.2 0.25True strain

True

str

ess

[MPa

]

DC04 (t=0.97 mm)

Docol 350YP (t=1 mm)

Docol 800DP (t=0.98 mm)

Docol 1400M (t=0.98)

Figure II: True stress versus true strain in the 45 degree direction for the materials included in thisstudy.

0

200

400

600

800

1000

1200

1400

1600

0 0.05 0.1 0.15 0.2 0.25

True strain

True

str

ess

[MPa

]

DC04 (t=0.97 mm)

Docol 350YP (t=1 mm)

Docol 800DP (t=0.98 mm)

Docol 1400M (t=1 mm)

56

0

200

400

600

800

1000

1200

1400

1600

0 0.05 0.1 0.15 0.2 0.25True strain

True

str

ess

[MPa

]

DC04 (t=0.97 mm)

Docol 350YP (t=1 mm)

Docol 800DP (t=0.98 mm)

Docol 1400M (t=0.98)

Figure III: True stress versus true strain in the transverse direction for the materials included inthis study.

57

Appendix 2 Data from punching experiments

Sheetmaterial

Sheetthickness[mm]

Punchmaterial

Punchhardness[HRC]

Punchdiameter[mm]

Rollover[mm]

Shearzone[mm]

Fracturezone[mm]

Burrheigh[µm]

Holediameteralong[mm]

Holediametertransverse[mm]

Maxforce[N]

DC04 0.97 Sverker21

60-62 9.88 0.16 0.56 0.25 11.25 9.88 9.88 8773

Docol350YP

1 Sleipner 60-62 9.88 0.1 0.5 0.4 15.25 9.88 9.88 11731

Docol800 DP

0.98 Notincluded

Notincluded

9.8 0.11 0.25 0.61 9.6 9.82 9.82 17990

Docol1400M

0.98 Notincluded

Notincluded

9.8 0.01 0.2 0.75 7 9.54 9.54 30431