Results and Outlook

Development of a Friction Approach for the FE Method of

Sheet Metal Forming Based on Multi-Scale Modeling

Motivation

Prof. Dr.-Ing. B.-A. Behrens

Prof. Dr. P.-A. Guidault

Goals

Methods

Dipl.-Math. B. Homann

ViVaCE „Virtual Materials and their

Validation: German-French School of

Computational Engineering” – IRTG 1627

• Correlations between occurring normal force, effective plastic strain,

direction of motion, and resulting roughness

𝑅𝑎𝛽 = 𝑓1 𝑓n, 𝑒𝑝𝑠max, α

• Function for friction coefficient of change in roughness, sliding

velocity, and direction of motion

𝜇 = 𝑓2 𝑣, ∆𝑅𝑎, 𝛼

𝛼 Angle between direction of motion and rolling direction

𝛽 Angle between direction of measurement and rolling direction

𝑅𝑎𝛽 Arithm. mean surface roughness measured in 𝛽 to rolling direction

𝑓n Maximal occurring normal pressure

𝑒𝑝𝑠max Maximal occurring effective plastic strain

𝜇 Friction coefficient

𝑣 Current sliding velocity

∆𝑅𝑎 Change in roughness

• Strong influence of

friction on the part

quality

• Existing laws for friction

are not adequate for the

realistic description of

local contact conditions.

Investigation of surface topography evolution

• Material: aluminum alloy AlMg3 (EN AW-5754)

• Basic experiments:

Pressure test (PT)

Tensile test (TT)

Strip drawing test (SD)

• Roughness measurement before and after the tests

• Measurements in and to rolling direction

Main influences on deep drawing processes

Focus of study: Friction modeling in FE simulation

Setup to apply contact pressure

Setup for tensile test

Setup for strip drawing test

Strong influence of friction coefficient µ on the result, e.g. sheet thickness

Friction modeling

• Mathematical description of

the friction coefficient

• Depending on

Roughness evolution

Forming parameters

Implementation

• In FE software LS-DYNA

• User subroutine usrfrc in

dyn21.F Algorithm of

the new friction law

Specimens of different rolling directions

Longitudinal 0°

Transversal 90°

Diagonal 45°

59 mm 730 mm

20 mm 9 mm

Simulation of basic experiments

• To analyze the forming parameters

• With respect to rolling direction

x y

z

Sheet thickness [mm]

1.10

1.08

1.06

1.04

1.02

1.00

0.99

0.97

0.95

0.93

0.91

initial

Numerical models of tensile test (upper) and strip drawing test (lower)

with evaluated element for roughness calculation

Further investigations

• Further parameter studies to extend the

model

• Adoption/adjustment of the model to

different materials

ViVaCE-Projects with strong Interaction

• Multiscale FEM for Rubber Friction on

Rough Surfaces (P. Wagner)

• Multiphysics Homogenization Schemes for

Microstructured Interfaces (N. Noii)

y x

z

Initial state

Stretched state

Evaluated element

Specimen

Force

Chafe body of the machine

z x

y

Initial state Drawn state

Evaluated element

epsmax [−]

𝑅𝑎

0 [

µm

]

Example of roughness-strain dependence

of tensile test for -specimen 0°

0° -specimen

0° 90°