Modeling of contact interactions of micrometer- sized ......Modeling of contact interactions of micrometer-sized particles under compression ... have irregular shapes behave elastic-plastically

1 Siegen 2012, October 1th-2th

Modeling of contact interactions of micrometer-

sized particles under compression

Hamburg University of Technology

Institute of Solids Process Engineering and Particle

Technology

S. Kozhar, S. Antonyuk, S. Heinrich


Introduction Research objectives

Birkenfeld

Setting up the measurement

system

Measurements of particle-particle

and particle-wall contact

interactions

Capturing of the 3D shape

of particles

Hamburg

Determination of materials

parameters from experiments

Selection and calibration of

appropriate contact models for each

material

DEM/FEM-simulations of single

particle and bulk material

PiKo B4 project

The aim of the project is to describe the mechanical interactions of finely

dispersed particles with diameter of 20…100 µm by using experimentally

calibrated contact models


Piezo drive Particle

Experimental part Experimental set-up

Current set-up

allows to carry out tests of

particles at compressive

and tensile loading with

adjustable relative humidity

and temperature in climate

box

Device Minimum

value

Maximum

value

Resolution

Piezo drive 0 µm 250 µm 0.2 nm

Laser vibrometer -∞ ∞ 0.2 nm

Force sensor - 200 mN + 200 mN 40 µN

Box (Temperature) 15 °C 35 °C 1 °C

Box (Relative humidity) 10 % 90 % 2 %

20 mm

Microscope Force sensor


Experimental part Tested materials

Maltodextrin particles elastic-(visco)plastic

2 µm

Hollow glass particle pure elastic

Titan dioxide particles elastic-plastic


Parameter Unit Value

Diameter [µm] 39.1 ± 9.5

Displacement

at breakage [µm] 6.7 ± 3.7

Breakage force [mN] 98 ± 53

Breakage strain [%] 18.3 ± 12.3

Compressive strength [MPa] 92.6 ± 67.8

E-Modulus [GPa] 3.3 ± 1.7

Mean values of mechanical characteristics of titan dioxide

under compression

Experimental part Titan dioxide



Cyclic compression test of titan dioxide

particle with constant maximum force



Cyclic compression test of titan dioxide

particle with increasing maximum force


Modulus of elasticity of titan dioxide particles

determined from cyclic compression tests


E-Modulus [GPa]

Loading part of cycle 18.2 ± 6.9

Unloading part of cycle 37.8 ± 19.2

Titan dioxide particles:

have irregular shapes

behave elastic-plastically

demonstrate cyclic hardening behavior


Experimental part Maltodextrin

25°C 28% r.h.

Cyclic compression test of maltodextrin

particle with constant maximum force



Cyclic compression test of maltodextrin

particle with increasing maximum force

25°C 31% r.h.



Loading type E-Modulus

[GPa]

Loading Increasing of maximum force in cycle

at 115 mN/s

5,4 ± 2.9

Unloading 6.8 ± 4.9

Loading Increasing of maximum force in cycle

at 460 mN/s

4.6 ± 2.9


Loading Constant maximum force at higher

loading rate

2.2 ± 0.2


Modulus of elasticity of maltodextrin particles

determined from cyclic compression tests

Maltodextrin particles:

have irregular shapes

behave elastic-viscoplastically

demonstrate cyclic hardening behavior


Experimental part Hollow glass particles

Cyclic compression tests of hollow

glass particles

Glass particles:

have spherical shapes

behave elastically

Stiffness

[N/mm]

Loading 1.47 ± 0.16



Modeling Contact models

Contact models for normal load

Linear and nonlinear

(visco)elastic models

Elastic-plastic models

with hysteresis

Hertz

Sadd

Schäffer

Tsuji

Kuwabara & Kono

…

Walton & Braun

Thornton & Ning

Tomas

Vu-Quoc & Zhang

Mangwandi

…

Tomas, J. Mechanics of Particle Adhesion. Manuscript, Magdeburg (2008)

Kruggel-Emden,H, et al. Review and extension of normal force models for

Discrete Element Method. Powder Technology. 171, 157-173 (2006)


Aims of modeling by contact models


Contact models must

be simple in order to be implemented into DEM code

good reproduce the real particle behavior at mechanical

contacts

Two proposed ways to represent cyclic behavior of tested

particles

use of the averaged loading-unloading curve for fitting by

contact models with following conditions

𝑠0 =1

𝑁 𝑠0,𝑗 =

𝑁

𝑗=1

s0,ave

use the saturation function to reproduce the decrease of

residual displacement in loading cycle

𝑠𝑚𝑎𝑥 =1

𝑁 𝑠𝑚𝑎𝑥,𝑗

𝑁

𝑗=1

= 𝑠𝑚𝑎𝑥,𝑎𝑣𝑒 𝑒𝑒𝑞 =1

𝑁 𝑒𝑒𝑞,𝑗

𝑁

𝑗=1


Fo

rce

Displacement

Equivalent restitution coefficient


WL – total energy during loading

WUN – energy released at unloading

Wdiss– dissipated energy 𝑒𝑒𝑞 =

𝑊𝑈𝑁𝑊𝐿=

= 1 −𝑊𝑑𝑖𝑠𝑠𝑊𝐿

smax s0

Fmax


Modeling Fitting of average loading-unloading curve

Model of Walton & Braun

𝑾𝒅𝒊𝒔𝒔,𝑚𝑾𝒅𝒊𝒔𝒔,𝑎𝑣𝑒

= 1.21

𝑒𝑒𝑞,𝑚𝑒𝑒𝑞,𝑎𝑣𝑒

= 1.16

𝑠0,𝑚𝑠0,𝑎𝑣𝑒= 1.0

Titan dioxide



Model of Tomas


= 1.25


= 1.11

𝑠0,𝑚𝑠0,𝑎𝑣𝑒= 0.89

Titan dioxide



Model of Thornton & Ning


= 1.50


= 1.10

𝑠0,𝑚𝑠0,𝑎𝑣𝑒= 0.91

Titan dioxide


Aims of modeling by contact models


Contact models must

be simple in order to be implemented into DEM code

good reproduce the real particle behavior at mechanical

contacts

Two proposed ways to represent cyclic behavior of tested

of particles

use of the averaged loading-unloading curve for fitting by

contact models with following conditions

𝑠0 =1

𝑁 𝑠0,𝑗 =

𝑁

𝑗=1

s0,ave

use the saturation function to reproduce the decrease of

residual displacement in loading cycle

𝑠𝑚𝑎𝑥 =1

𝑁 𝑠𝑚𝑎𝑥,𝑗

𝑁

𝑗=1

= 𝑠𝑚𝑎𝑥,𝑎𝑣𝑒 𝑒𝑒𝑞 =1

𝑁 𝑒𝑒𝑞,𝑗

𝑁

𝑗=1


Modeling Modeling by using the saturation function

Equivalent restitution coefficient as

function of number of cycles Walton & Braun model

𝐹𝑛 = 𝑘𝐿𝑠, 𝑠 ∈ [0; 𝑠max]

𝑘𝑈𝑁 𝑠 − 𝑠0 , 𝑠 ∈ [𝑠0; 𝑠max]

Residual displacement

𝑠𝑜 = 𝑠𝑚𝑎𝑥 1 −𝑘𝐿𝑘𝑈𝑁

Proposed saturation function

𝑘𝑈𝑁 = 𝑐𝑜𝑛𝑠𝑡

𝑁 - number of cycles

𝐴, 𝑏 - parameters

𝑒𝑒𝑞 = 𝑓(𝑘𝐿) = 𝐴(1 − 𝑒−𝑏∙𝑁)

Titan dioxide



𝐹𝑛 = 𝑘𝐿𝑠, 𝑠 ∈ [0; 𝑠max]

𝑘𝑈𝑁 𝑠 − 𝑠0 , 𝑠 ∈ [𝑠0; 𝑠max]

Walton & Braun model

Residual displacement

𝑠𝑜 = 𝑠𝑚𝑎𝑥 1 −𝑘𝐿𝑘𝑈𝑁

Proposed saturation function

𝑒𝑒𝑞 = 𝑓(𝑘𝐿) = 𝐴(1 − 𝑒−𝑏∙𝑁)


𝑁 - number of cycles

𝐴, 𝑏 - parameters

Residual displacement as function of

number of cycles

Titan dioxide



Comparison

𝑠0,𝑒𝑥𝑝 = 2.28 µ𝑚

𝑠0,𝑚𝑜𝑑𝑒𝑙 = 2.09 µ𝑚

Titan dioxide


Modeling Test with increasing maximum force in cycle

Walton & Braun model for cyclic

compression with increasing force

𝑒𝑛 =𝑘𝐿𝑘𝑈𝑁 ,


𝑘𝐿 = 𝑐𝑜𝑛𝑠𝑡,

𝑠0,𝑒𝑥𝑝 = 0.87 µ𝑚

𝑠0,𝑒𝑥𝑝 = 0.85 µ𝑚

𝑒𝑒𝑥𝑝 = 𝑒𝑚 =0.76

Titan dioxide

Fo

rce

[m

N]

Fo

rce

[m

N]


Elastic properties of spherical maltodextrin particles

Modeling Spherical maltodextrin

0

1000

2000

3000

4000

5000

6000

20% r.h. 30% r.h. 40% r.h. 60% r.h. 70% r.h.

Mo

du

lus

of

ela

sti

cit

y [M

Pa]


FEM simulation of contact FEM as additional tool

3D particle shape from CLSM FEM meshing

Import into FEM software FEM calculus

IA-MESH

ANSYS

ABAQUS


Preliminary FEM simulation Hollow glass particle under compression

891 elements of CAX4R type

Particle elastic properties (fused silica)

E = 73 GPa ν = 0.17

Determination of wall thickness

with the help of FEM model

Wall: rigid body


Preliminary FEM simulation Hollow glass particle under compression

Wall thickness [µm]

measured values 0.6…0.8

determined by FEM 0.81

10 µm

Outer diameter [µm]

mean value 83.5 ± 3.1

value of FEM model 82

Loading stiffness [N/mm]

mean value 1.41 ± 0.15

FEM-model 1.41


Preliminary FEM simulation Spherical particle under compression

Simulation of compression test – 2D case

Wall: rigid body Particle elastic properties

E = 70 GPa ν = 0.17

ANSYS ABAQUS

Hertz

Contact force [N] 0.274 0.294 0.275

Maximum contact

pressure [MPa] 6891 7188 7624

Determination of normal contact parameters

at interference of s = 1,38 µm


Simulation of compression test – 3D case


E = 70 GPa ν = 0.17

ANSYS ABAQUS

Hertz

Contact force [N] 0.268 0.293 0.275

Maximum contact

pressure [MPa] 7141 7512 7624

Determination of normal contact parameters

at interference of s = 1,38 µm



Simulation of compression test - 2D case



E = 70 GPa ν = 0.17

Frictionless contact

of „nodes to surface“ type



strain hardening



E = 70 GPa ν = 0.17

Particle plastic properties

sy = 500 MPa

𝑠𝑌 = 0,028 µm

𝑃𝑌 = 0,02 mN

𝑝𝐹 = 733 MPa

𝐸𝑇/𝐸 = 0; 0,23; 0,33; 0,5

Frictionless contact of

„node-to-surface“ type

s/𝑠𝐹 = 13,5 s/𝑠𝐹 = 1,2 s/𝑠𝐹 = 108,1



strain hardening



E = 70 GPa ν = 0.17

Particle plastic properties

sy = 500 MPa

𝑠𝑌 = 0,028 µm

𝑃𝑌 = 0,02 mN

𝑝𝑌 = 733 MPa


Future work

Planned Measurements

Adhesion of particle-particle and particle-wall systems

Tests under shear loading and torsional loading

Influence of climatic condition on material response

Modeling

Allowance for adhesion forces

Choice of theoretical contact model for each

material and loading type

Further determination of material parameters

Simulations

Implementation of contact models into simulation

software

Reproducing of irregular particle shapes in

simulation

DEM simulation of powder behavior


Documents

Modeling of contact interactions of micrometer- sized ......Modeling of contact interactions of micrometer-sized particles under compression ... have irregular shapes behave elastic-plastically