Modelling of PM Processing

Didier BOUVARD

Powder Metallurgy School, 2016, Valencia, Spain

Outline

Introduction : interest of modelling and pertinent scales

Discrete element modelling at particle assembly scalemethodexamples

Finite element analysis at component scalemethodexamplesfocus on multimaterials and field assisted sintering

Summary

Support for understanding• Analysing observed phenomena

• Validating assumptions drawn from experiments

• Guiding novel experiments

• Anticipating the effect of material and process parameters, etc.

Tool for virtual processing• Prediction of material behaviour during an industrial process for

reducing trial and error procedure

For each problem, the most relevant scale should be identified.

Interest of modelling

Relevant scales in PM

Particle assemblyParticleAtoms Component

At each scale, specific issues can be investigated and various modelling techniques are available.

This lecture focuses on two scales, particle assembly and component, and two techniques, discrete element method and finite element analysis

Process

Related issues :• Volume changes• Grain growth• Cracking• Properties

(conductivity, permeability, …)

Induced by individual and collective behaviour of particles in thermo-mechanical conditions

Modelling techniques :• Discrete Element Method• Monte Carlo models• Finite elements analysis

Particle assembly scale

Principle :

Simulating an assembly of particles (typically thousands) in a box, assuming an interparticle contact law, imposing force or displacement at the boundaries of the box and solving the equations of motion for every particle

Discrete Element Modelling (DEM)

DEM codes :

PFC (commercial), EDEM (commercial), SimPARTIX (Fraunhofer Freiburg), dp3D (SIMAP/Univ. Grenoble Alpes), etc.

• Contact detection + calculation of contact forces (Normal + Tangential)with a prescribed contact law

• Calculation of the total force applied to each particle

• Calculation of accelerations due to applied forces(same procedure for rotations)

• New positions of particles, quasi-static simulations

Typical process of a DEM simulation

Fx x xm

final position after rearrangement

N

N

TF

T

Example of DEM simulation (1)

Die filling

Bierwisch et al., Powder Tech. 196 (2009) 169

Relative density at various step of the filling process

Contact law : Elasticity and adhesion (JKR model)Aggregates cannot break.

aggregate mimicking a Distaloy AE particle

Example of DEM simulation (2)

No aggregate breaking

Realistic aggregatebreaking

0

50

100

150

200

250

300

350

400

450

500

0.30 0.40 0.50 0.60

Densité relative

Con

trai

nte

axia

le (M

Pa)

Axi

al s

tres

s (M

Pa)

Relative density

Experiments

Martin et al., J. Amer. Ceram. Soc. 89 (2006) 3379

Contact laws :Intraaggregate : elasticity and breaking Interaggregate : adhesion (JKR model)

Pressing of particle aggregates

Martin et al., Scripta Mater. 55 (2006) 425

Example of DEM simulation (3)

0.70 0.75 0.80 0.85 0.90Relative density

Den

sific

atio

n ra

te, 1

/s

1. 10-5

1. 10-4

5. 10-5

5. 10-6

2. 10-6

2. 10-5 T = 850°C

T = 950°C

Experimental data

DEM with constant particle size

DEM with coarsening

Contact law : Two-sphere sintering equation with overlapping volume redistribution

Sintering of copper powder with grain growth

T = 950°C

T = 850°C

substrate

Martin and Bordia, Acta Mater. 57 (2009) 549

Example of DEM simulation (4)

Sintering of a ceramic powder upon a rigid substrate Constraint sintering

Contact law : Two-sphere sintering equation

Formation of defects close to the substrate

substrate

Martin and Bordia, Acta Mater. 57 (2009) 549

Example of DEM simulation (4)

Sintering of a ceramic powder upon a rigid substrate

Pertinent issues :

• Shape changes• Heterogeneities in density,

microstructure or composition• Cracking

Due to powder-die friction, component geometry, gravity, thermal gradients, etc.

Modelling technique :

• Finite element analysis

The material is considered as a continuum.

Component scale

Constitutive equation

Experimental data Assembly-scale modelling

Finite element simulation

Finite element analysis

Initial state: dimensions, density distribution residual stresses

Process conditions : pressure, temperature, boundary conditions …

Deformation, density distribution, stresses, etc., all over the process

Relation describing the deformation of an elementary volume of material under « any » temperature and stress conditions met during processing :

= F ( , , T, internal variables)

: strain rate tensor

: stress and stress rate tensors

T : temperature (if required)

internal variables : relative density D, grain size G, etc.

,

Constitutive equation

Constitutive equations for powders

Sintering Atom diffusion Viscous, with a term accounting for free sintering

Pressing RearrangementPlastic deformation Elasto-plastic, granular-type

Mechanisms Class of equationProcess

Several commercial FEA codes integrate constitutive equations for powder pressing but none for sintering.

Example of FEA simulation (1)

Densité relative

Geometry and relative density after sintering

Relative density after simple action pressing

Friction Green density gradients Conical shape

Compression force

Pow

der-

die

fric

tion

Powder/punch friction

Pressing and sintering of a WC-Co cylinder

Example of FEA simulation (2)

1: 0.5602: 0.5753: 0.5904: 0.6055: 0.6206: 0.6357: 0.6508: 0.6659: 0.680

10: 0.69511: 0.710

Relative Density1: 0.5602: 0.5753: 0.5904: 0.6055: 0.6206: 0.6357: 0.6508: 0.6659: 0.680

10: 0.69511: 0.710

Relative Density

1110

5 4

2

1

1 1~2

2~3

3

2

2~3

5~6

92

1~282

7

32

6 2

1~2

2

2

6

1110

5 4

2

1

1 1~2

2~3

3

2

2~3

5~6

92

1~282

7

32

6 2

1~2

2

2

6Densité relative

Relative density after pressing

Pressing

SinteredGreen

Shape changes after sintering

Kim et al., Int. J. Mech. Sci. 14 (2002) 2523

Pressing and sintering of an alumina part

O. Gillia, PhD. Thesis, Grenoble, 2000

0.61

0.5850.585 0.595

Green density distribution after die pressing

Bending during sintering

0

50

100

150

200

0 5000 10000 15000 20000

Length co-ordinate (µm)

Def

orm

atio

n (µ

m)

.

Simulation with gravity

Simulation without gravity

Example of FEA simulation (3)

Sintering of a WC-Co rail

“Metcer”Metallic phase is preponderant“Cermet”Ceramic phase is preponderant

Different sintering behaviours

What about co-sintering ?

e

Stra

in

Sintering of a two-material part

Multimaterials (1)

Crack formation during heating

1 cm

Cermet

Metal

In situ observation of shape changes

Finite element simulation

Vertical tensile stress distribution

Largiller et al., Mech. Mater. 53 (2012) 132

Multimaterials (2)

Field assisted sintering (1)

Phenomena :

Interaction between an electric field and the material

Internal heating source

Temperature increase

Sintering

FEA procedure :

Iterative simulation coupling electrical, thermal and mechanical phenomena

Spark Plasma Sintering Microwave Sintering

Bouvard et al., Adv. Sinter. Sci. Tech. 209 (2010) 173

Field assisted sintering (2)

Vanmeensel et al. Acta Mater. 53 (2005) 4379

Temperature

Current

Electrical field

Temperature

Summary

Modelling can bring relevant information for better understanding and prediction of PM processes.

Various techniques and tools are available for this purpose ; the choice depends on the scale of interest and on the issue to be investigated.

Discrete element modelling is particularly relevant for particle assembly scale and finite element analysis for component scale.

Modelling is especially helpful for the investigation of complex processes, as for example multimaterials fabrication, constraint sintering and field assisted sintering.