Forming Simulation using Rigid-Plastic Material Model in...

MSC Software Confidential MSC Software Confidential

Forming Simulation using Rigid-Plastic

Material Model in Marc 2013 America User Conference

Gary Huang – Simufact-Americas LLC

May 7, 2013

Hendrik Schafstall – Simufact, Germany

MSC Software Confidential

• Simufact – company introduction

• What is rigid-plastic material model?

• Why and how do we use the rigid-plastic material model?

• Examples

• Conclusions

Contents

2


Simufact: Company and Products

3

Hamburg

Balv

e Kassel

Marbur

g

• The company:

– Simufact Engineering GmbH, Hamburg, Germany

– MSC partner for 18 years

• The products:

– The three products are interconnected

– Simulation of process chain possible

– Using MSC Marc and Dytran as FEM and FVM

solvers

– Using JMatPro to compute material properties and

phase transformation data



4

• The applications:

– Cold and hot forging

– Bulk sheet forming

– Rolling, extrusion and cogging

– Welding

– Mechanical joining – riveting

– Heat treatment

– more

• The users:

– Many hundreds of companies

worldwide

– Including Daimler, Airbus, SMS

meer, GKN, Honda, Toyota,

Schuler …



5

• Simulation of process chain – from welding to sheet forming (using Marc)

Simufact.welding Simufact.forming

welding drawing



6

• Simulation of process chain – from sheet forming to welding (using Marc)

Simufact.forming Simufact.welding

drawing trimming welding



7

• Simulation of process chain – predicting material properties (using Marc and JMatPro)

Martensite built-up after welding Flow stress comparison



8

• Simulation of process chain – predicting material properties

Bending test comparison after welding –

with phase transformation and without



9

• Forming Application – Roll forming (using Marc) with 89 rollers



10

• Welding Application (Marc) – Transportation Part from Alstorm

– 582 weld paths

– 202 cooling steps

– 300,000+ elements

– Parallel simulation with 9 domains

– More than 2 weeks of simulation time


Using Rigid-plastic Material Model

11

• Why?

– Possibility to speed up simulation

– Allow larger model size

– A complement to Finite volume method and

Elastic-plastic FEM

Two side-by-side connecting

rods simulated by rigid-plastic

material model in Marc


Understand rigid-plastic material model

• Elastic-plastic (EP) material

– Elastic effect cannot be ignored

– Young’s modulus plays an important role

– Poisson ratio < 0.5

– Material is compressible in the elastic

region

• Rigid-plastic (RP) material

– Elastic effect can be ignored

– Young’s modulus (infinity) is not

important

– Poisson ratio = 0.5

– Material is incompressible

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EP

RP

σ

σ

ε

ε

ε= 𝜀𝑒 + 𝜀𝑝

ε= 𝜀𝑝



• Elastic-plastic (EP) material

– Yield surface exists

– Stress state is on yield surface when

material deforms plastically

– Complex constitutive equation

• Rigid-plastic (RP) material

– No yield surface

– Material deforms when effective plastic

strain-rate exceeds a cut-off value 𝜀 0

– Simple constitutive equation (Levy-

Mises)

13

RP

σ

ε



• Elastic-plastic (EP) material based FEM

– Iterations required at the integration

points for radial return mapping

– Storage needed for elastic data

– Extra operations to compute constitutive

matrix

• Rigid-plastic (RP) material based FEM

– No iterations required at the integration

points

– Simple operations to compute stress

tensor

– Less storage required

14

𝑅𝑎𝑑𝑖𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 𝑀𝑎𝑝𝑝𝑖𝑛𝑔 𝑓𝑜𝑟 𝐸𝑃



• Applications based RP FEM

– Metal Forming with large deformation

– Closed-die hot forging

– Glass forming

– Superplastic forming

• Applications not suitable for RP FEM

– Spring-back analysis - bending

– Residual stress

– Loading and unloading analysis

– Cold metal forming

15

𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑟𝑜𝑑 𝑓𝑜𝑟𝑚𝑖𝑛𝑔 𝑢𝑠𝑖𝑛𝑔 𝑅𝑃


Rigid-plastic material model in Marc

• Model section - ISOTROPIC

– Use RIGID

– No Young’s modulus and Poisson ratio

– Flow stress curve required

• Model and History - PARAMETER

– Incompressibility penalty number

– Initial strain rate

– Cut-off strain rate

– Proper setting of these parameters are

important for convergence

The cut-off value 𝜀 0 is used so that when

𝜀 < 𝜀 0, Marc program sets 𝜀 = 𝜀 0 to avoid

numerical difficulties.

16

Mentat menu to support 𝑅𝑃



• Simple uniaxial compression with thermal coupling

– Fixed time steps

– Temperature difference: RP(152-154), EP(150-152)

– Eff. Plastic strain: RP(0.70), EP(0.69)

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• RP model

• Wall Time: 34 sec.

• Elements: 3824

• Element storage: 21 Mb

• EP model


• Elements: 3824

• Element storage: 29 Mb



• Simple cylinder compression with friction

– 100 fixed increments

– Thermal-mechanical coupling

– Global remeshing

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• RP model

• Elements: 6570-10828


• Eff. Plastic strain: 0.03-1.23

• Temperature: 646-1016

• Punch force: 3.349E5

• EP model

• Elements: 6570-9333


• Eff. Plastic strain: 0.04-1.02

• Temperature: 646-1013

• Punch force: 3.353E5

2.6 times

faster



• Simple cylinder compression with friction

– Itemized CPU time comparison (RP vs EP)

– Itemized memory allocation comparison

– Most of time saving is at the element level during the stiffness

assembly and stress recovery

– RP uses less element storage even with 1000 more elements

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2.6 times

faster


Improving rigid-plastic FEM in Marc

• Difficulties in RP analysis in Marc

– What is the correct plastic strain rate cut-off value?

• Plastic strain rate cut-off value is used to decide if the material point is plastic

• Pre-selecting the correct cut-off value is tricky

• If the cut-off value is too large, we force most of the forming body to be plastic

• If the cut-off value is too small, we have ill-conditioned stiffness matrix and

difficulty in convergence

• Often analysis will not converge or results are incorrect

– Should cut-off value be used to compute total plastic strain?

• Initial plastic strain depends on the cut-off value?

• This is incorrect for some forming processes where the workpiece positions

itself before the large deformation happens

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• Improving RP analysis in Marc

– Compute cut-off value based on average plastic strain rate

• After 1st iteration compute average plastic strain rate over all RP elements

• Select cut-off value to be 1.0e-4*(average plastic strain rate)

• Compare with previous cut-off value

• If the difference is greater than 10 times, use the new cut-off value

– Do not compute total plastic strain based on cut-off value

• Plastic strain is computed based on the solution

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Incorrect plastic strain correct plastic strain



• Improving RP analysis in Marc

– Average plastic strain changes in heading example

• Cut-off value is adjusted over the whole simulation

• In the beginning, cut-off value is very small when workpiece is mostly rigid

• Cut-off value is increased when more and more material becomes plastic

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Examples using rigid-plastic FEM in Marc

• Forming Examples – Gear Forging (3 domains parallel )

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• RP effective plastic strain

• Wall time 2545 seconds

• Elements 10,000 – 27,000

• EP effective plastic strain

• Wall time 4285 seconds

• Elements 10,000 – 29,000

• Domain Re-decomposition

after remeshing



• Metal Forming Examples

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Wall time: 2662s Wall time: 1351s Wall time: 3041s





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Wall time: 719s Wall time: 25143s


Forming Simulation with RPFEM in Marc

• Conclusions

– Rigid-Plastic model in Marc helps speed up

simulation

– Allows more elements in the simulation

– The automatic computation of cut-off value

improves RP analysis

27

MSC Software Confidential 28

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