8 finite element modelling

8/3/2019 8 Finite Element Modelling

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FE-MODELING

Bertil Jonsson

Expert weld strength

Nov 2011

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Content General

Program overview

Boundary conditions

Accuracy

Non linearity

Sub modeling

3D-models

Some notes about software

Summary

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General


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Method used determines often the tool

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6


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Program overview


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Some software tools

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Boundary conditions

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A HAULER AT WORK


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Boggi beam

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GEOMETRY REAR FRAME

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GEOMETRY BOGGI BEAM


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Example bearing in boggi

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Example bearing in boggi

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Project LOST example of HSS Light Optimized STructures

Duration 2006-2009

Budget appr 18 mSek

End-conference 24-25 march 2010 in Sweden

13 Work-packages, 3 of them are

New weld class system

Analysis course on local based methods

Demonstrator boggi beam

Education &

seminars planned

Continuation

project: WIQ


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LOST Workpackage no 10GOAL : decrease weight by at least 20%

Demonstrator boggi beam

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Old BB compare to the new

Old New

t = 15 / 8 mm t = 12 / 6 mm

183 kg 143 kg (-22%)

Mtrl grade: 350 Mpa Usage of high strength steel (HSS)

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Max static load material grade

Yield 350 Mpa at bearing

Yield 460 Mpa in flanges

Yield 600 Mpa in webs

Control of buckling


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Fatigue analysis using local based methods

Equivalent load from test track

Main principal stress range + FAT 225 Mpa

Fatigue life > 1000 hours on test track

allowed stress level 370 Mpa

Radius = 1 mm

Notch method

Loads on global model Transferring displacements

local sub models and study

the stresses

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Test set up

Rig setup Spectrum load (range pair)

Range Pai r

0

100

200

300

400

500

600

10 10 0 10 00 10 00 0 100 00 0

Antal ranger

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Test of boggi no 1, failure after 120 h

Expected > 1000 h

Failure after 120 hours Lack of fusion

(demand penetration i = 2 mm)

However :

Chocking !!! this could not be the only reason


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Multi axial stresses !

Normally This case is in shear loading

max Principal Stress range use von Mises (diff signs !) & FAT 200

PS = 516 Mpa vM = 745 Mpa

N = 420 hours N = 100 h [agrees well with test 120 !]

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Test of boggi no 3 failure after 920 h

Fully penetrated on root side

Now failure from toside !

Same cause: Multiaxial stress state with different signs

in principal stresses

PS = 241 Mpa vM = 393 Mpa

N = 4100 hours N = 660 h (appr in agree with test 920 h)

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Multi axial proportional cases

- effective notch method -

Use Mises stress range & FAT 200 Mpa

in cases when Mises > Max principal stress range

Comparison of life calculation in notch method

( multi axial cases with diff. signs in principal stresses, proportional loads )

10

100

1000

10000

10 100 1000 10000

Tested life (hours BII)

Calculatedlife(hoursBII)

Mises

Princ stress

Equality

Non c

onser

vative

Conse

rvative


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Cost estimations

Lowered weight & production cost

win-win situation for customer & producer

COST ESTIMATION (% of total) OF NEW BOGGI BEAM

-10

-8

-6

-4

-2

0

2

4

6

slit r emo ved mtrl+cut plate a way fixture

improved

extra weld weld

prearation

TIG

treatment

Totally

Percentage

(%)

-8%

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Demonstrator Boggi Beam results:

Lowered weight 22%

Using HSS & improved weld quality

Life target almost reached

Lower production cost 8 %

Lessons learned:

Multiaxial problem found and verified

Use Mises when > principal stresses

A high production quality is needed !

Process variation & control

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Accuracy & non linearities


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A-stay

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Assembly of an A-stay

with studied welds

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FE-models

SimplifiedSimplified linearlinear

elasticelastic modelmodel

ComplexComplex modelmodel

includingincluding screwsscrews,,

axleaxle casingcasing,,

contactcontact elementselements


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Global model

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Sub model

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Example of the NOTCH-method

Rear frame of a loader

(without a weld prepared plate)


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GEOMETRY OF REAR FRAME

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Section through the sub model

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Result symetric load

Global model w/o notch


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Zoomed picture

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Submodell incl notch


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Sectio through the sub model

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Zoom around the weld / notch

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Result w/o deformation


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Result w deformation

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Max principal stress in the notch

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Zoom, max stress = 1932 MPa


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Hand calculation on white board !

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Brottmekanisk ansats

Global modell

Submodell 1

Submodell 2

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Fracture mechanicsFracture mechanics

> @)4()4(21

21122

CBCBI vvvvl

GK

S

N

mKCdN

da)(* '

)/( WafaK SV''

'

fa

a

mda

KCN

0

1

ParisParis lawlaw DDisplacementisplacementcorrelation techniquecorrelation technique


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Automatic crack propagation in

3D

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Tvrsnitt genom submodellen

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XCRACK

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Submodel 2Section through weld with crack

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Submodel 2 swept to 3D


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Submod 2 merged into submod 1

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Result in section

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Zoom at the root crack

Opening of the crack determinesthe stress intensity


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Stress intensity along the sub model

Bakrams-spricka

SPG-INT lngs axelgenomfringen

0,0

2,0

4,0

6,0

8,0

10,0

12,0

14,0

0 200 400 600 800 1000

s (mm)

dK[(MPa_

rot(m)

]

Chan

TH=2

TH=5

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3 sub models are analysed:

Spricklngd Spg-intensitet Lutning

a=8 mm K = 12 MPam (16-12)/(12-8) = 1

a=12 K = 16 (40-16)/(16-12) = 6

a=16 K = 40

Approx. bi-linjr fkn : K = 1*a+4 resp 6*a-56

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Stress-intensity as fcn of crack growth

Antag linjr fkn : K = a+4 resp 6a-56

Spnnings-intensitet sfa sprickvg

0

5

10

15

20

25

30

35

40

45

5 7 9 11 13 15 17

Sprickstorlek (mm)

Spg.int(Mparot(m))


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Hand calculation on white board !

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Comparison of calculated lifes

Konservativ berkning kan vara fr skert

Notchmetod stmmer bra med brottmekanik

Livslngd med olika metoder

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

1 rt linje 2 rta linjer krkt linje notch-metoden

Livslngd(cykler)

N

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More about accuracy


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Use the right stiffness in the

FE-model...

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Arm to excevator

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B/BRG

Initial root

crack

4mm~6mm

Field Crack Section View

CRACK PATTEN

Section view


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LEFM Analysis of arm

[Case A]

16t

2mm

2mm

2.8mm

5.6mm

4mm

Sub1

Sub2

Sub3

Sub4

Model Cases

Digging Force Side Force

Load Cases

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Definition of Crack Direction in Sub1 Model

- Principal Max Stress Direction Check

Crack Growth Direction

Principal Max Drection

2mm

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L

Sub2 Model Analysis Result

- Sub2 Model

2.8mm

Principal Max Directio

Crack Growth

Direction

Keff = 28.75

Digging Force

Keff = 1.57

Side Force


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LEFM Analysis of arm

2mm

2.8mm

5.6mm

4mm

Sub1

Sub2

Sub3

Sub4

Model Cases

Digging Force Side Force

Load Cases

[Case B]

18t

2mm

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Arm FE Model ( Case B )

[ Analysis Result ] [ Coupled Model ]

[ Sub Model ]

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Conclusion

Bench Test Loading

Failure Life=99677(Cycle)

Failure Life=79095(Cycle)

Initial Crack length : 2mm

Failure Crack length : 25mm

(Median 50%)


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Cold lap

Spatter induced cold lap

Compared with

line cold lap

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What is the difference between a line

cold lap and a spatter induced cold lap

?

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Geometry spatter induced cold lap


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Cold lap 2D vs 3D

Question: what is the expected increase in life for a spatter induced

cold lap compared to a line cold lap ?

Spatter induced: has a/c=1 at start, this requires a 3D-model &

analysis.

Line cold lap: has a/c=0 at start, can be calculated in a 2D-

model.

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Studied case

Korsprovstav:

t = 12 mm

= 100 MPa

a = 5 mm = 70 grader

R = 0

i = 2 mm

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2D analysis in FRANC2D

of

a line cold lap


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2D-modellen (a/c=0)

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3D analysis in FRANC3D

of

a spatter induced cold lap

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Initial flaw: cold lap of crack size a=0.2 [mm] and a/c=1

(fringe values are crack opening displacement in [mm])

(deformation magnified 5)


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Crack trajectory at step 3(fringe values are crack opening displacement in [mm])


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Crack trajectory at step 8(fringe values are crack opening displacement in [mm])


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Crack trajectory at step 13(fringe values are crack opening displacement in [mm])(deformation magnified 5)


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Resultat 3D

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Resultat 3D

a/c goes to 0 relatively slow Is appr 0,1-0,2 at full life (N=2,7E6 cycles)

N is calculated along the edge with K=K(c) (not area) and

with extrapolated.

Mixed mode in the beginning, there after mode I KI+KII at bottom gives a great kink-angle KI+KIII at edge gives a small kink-angle

Crack grows deepest at bottom (comp kink) Similar conditions as in the 2D-analysis

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Result in lifeLife for cold lap = 0,2 mm - comparison 2D (a/c=0) with 3D (a/c=1)

( crusiform joint, t12, a5, 70 deg, R0, 100 MPa )

0

1

2

3

4

5

6

0,0E+00 5,0E+05 1,0E+06 1,5E+06 2,0E+06 2,5E+06 3,0E+06

LIFE (cycles)

Crac

kgrowth(mm)

3D (a/c=1)

2D (a/c=0)


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Comparison line CL vs spatter CL

Life N cold lap from spatter = 2,7E6

Life N lilne cold lap = 1,0E6

Thus is N appr 3 times bigger

Edge crack has K(a/c=1) 0,63*K(a/c=0)

Theoretical longer N is then (0,63) -3 4

Fits well with 3 above

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Some notes on softwares

Ansys Classic fracture mechanics 2D

Ansys WorkBench notch method 3D

Afgrow fracture mechanics 2D

(load plane)

Franc2D fracture mechanics 2D

(load//plane)

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Ansys Classic

fracture mechanics, 2D


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Ansys Classic

fracture mechanics, 2D

Result:

KI, KII, KIII for a point

Repeat of growth points

Integration gives life

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Ansys WorkBench (+DesignModeler)

notchmetoden 3D

Result:

Stresses in the notch

SN-curve gives life

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A new layout is seen in WB.12


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Afgrow

fracture mechanics in 2D

Result

Cycles = life

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Afgrow, result

Result

Cycles = life

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Franc2D

Automatic crack growth in 2D

Result

KI, KII, KIII as fcn

of crack path.

(Integration of

Paris law

gives life)


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Summary

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Some short conclusions

Daily work: Use notch-method

Failure analysis: Use linear fracture mechanics

Free of charge ! 2D: Agfrow (?) and Franc2D

Be careful with: Contacts, stiffnes

Do not forget: Root side of welds

Useful technique: Sub-modeling

8 finite element modelling

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