piam winter school - tu/epeters/inj_mould_lectures/gregnier_anisotropy.pdf · piam winter school...

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Shrinkage and Warpage

of Injection Molded

Thermoplastic Parts:

Physical Mechanisms and Anisotropy

Gilles Régnier

PIAM Winter School

January 15th - 19th, 2007

Aussois

2 / 40

The industrialproblem

Volumic shrinkageprediction

Linear shrinkagesdetermination

Mold design

Mass = 20 000 kgCost = 500 k€

Industrial aim:

To decreasetime and costof mold design

3 / 40

Full process simulation …

Optical lens(ISOFOTON®)




Filling predictionRheological analysis

Prediction of part deformationThermomechanical calculation

… not so easy

4 / 40

flowtransverse

normal

Sv ≈ Sp + Sn + Sz

VVmold VpartS

Vmold−

=3 ?v lS S=

Warpage

Causes- Non uniform volumic shrinkages- Shrinkage anisotropy

Post-filling modelingPrediction of the amount of material, which enters the cavity

Cooling modeling

Shrinkages

From the courtesyof

Solvay




5 / 40

PS (Atochem 1540)

Température (°C)

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

0 50 100 150 200 250

20

40

80

120

160

Vs (cm3/g) 0,1 Mpa

1.07 0.97 9 %1.07

Sv −= ≈

Two phases :• the filling phase• the cooling phase with a post-filling

piloted by holding pressure

1.01 0.97 4 %1.01

Sv −= ≈

Pressure records

0

100

200

300

400

500

0 5 10 15 20 25

P cavityP HydraulicP nozzle

p (b

ar)

t (s)

Frozen gate

Volumicshinkage

Post-filling andsolidification

Injection processprinciple

PvTdata

Molddeformation

PP Solvay ELTEX HV212

1

1.1

1.2

1.3

1.4

20 60 100 140 180 220 260Température (°C)

Vol

ume

spéc

ifiq

ue

(cm

3/g)

Données brutesModèle

0 MPa

20 60

100 160

1.34 1.1 18%1.34

Sv −= ≈

1.22 1.1 9 %1.22

Sv −= ≈

Crystallisation shrinkage ≈ Thermal shrinkage

Case of semi-crystalline polymers

Volumicshinkage



PvTdata

Molddeformation

7 / 40

Volumicshinkage



PvTdata

Molddeformation

Pressure history varies a lot in parts (even during holding phase)

Shrinkages increase with flow length

Influence of flow length

-500

50100150200250300350400450

0 1 3 4 6 7 9 10 12 13 15 16 17 19 20 22

Ps bar

Pf bar

PHyd bar

Flow

Time (s)

Pressure(bar)

Pressure records in 1mm-thick PP plates

PP: MFI = 11 g/10 minPlate length = 125 mm

8 / 40

Leo V, Cuvelliez CH, Polym. Eng. Sci., 36,15 (1996).

More uniform pressure ⇒ more homogeneous shrinkages

⇒ Step profiled packing pressure

Volumicshinkage



PvTdata

Molddeformation

Influence of flow length

9 / 40

Volumicshinkage



PvTdata

Molddeformation

Amorphous polymers

PS (Atochem 1540)

Température (°C)

0.92

0.94

0.96

0.98

1

1.02

1.04

1.06

1.08

0 50 100 150 200 250

20

40

80

120

160

Vs (cm3/g) 0,1 Mpa( ) (0) .Tg p Tg pα= +

Tg = f(p)

Tg

30 /100K MPaα ≈

No-flow temperature = Glass transition Tg

Low influence of cooling rate on Tg

10 / 40

Viscosity PS (BASF 456 F)

10

100

1000

10000

100000

0.1 1 10 100 1000 10000Shear Rate (s-1) / Frequency (rd/s)

η /

η*

(Pa.

s)

Capillary Rh. 202°CCapillary Rh. 230°CCapillary Rh. 260°C


10

100

1000

10000

0.1 1 10 100 1000 10000Shear Rate (s-1) / Frequency (rd/s)

/ * (

Pa.s

)

Cone-plate 200°CCone-plate 230°CCapillary Rh. 202°CCapillary Rh. 230°CCapillary Rh. 260°C


10

100

1000

10000

100000

1000000

10000000

0.01 0.1 1 10 100 1000 10000Shear Rate (s-1) / Frequency (rd/s)

η /

η*

(Pa.

s)

Cone-plate 120°CCone-plate 130°CCone-plate 140°CCone-plate 155°CCone-plate 170°CCone-plate 200°CCone-plate 230°CCapillary Rh. 202°CCapillary Rh. 230°CCapillary Rh. 260°CWLF 120°CWLF 130°CWLF 140°CWLF 155°CWLF 170°CWLF 200°CWLF 230°CWLF 260°C

Tréf = 373 KC1 = 25.5C2 = 36.3 K

10

2

( )exp

( )ref

refref

C T TC T T

η η⎡ ⎤−

= −⎢ ⎥+ −⎢ ⎥⎣ ⎦

Accurate viscosity model at low temperatures and shear rates

Volumicshinkage

Solidification and post-filling


PvTdata

Molddeformation

'1'2

( )( , ) exp( )

g

g g

C T T pT pT C T T p

αηη α

⎛ ⎞− −= −⎜ ⎟⎜ ⎟+ − −⎝ ⎠

WLF viscosity equation

Amorphous polymers

11 / 40

Semicrystalline polymersHigh influence of cooling rate and pressure on crystallization temperature

More complex phenomenon ⇒ need of crystallization kinetics

Onset ofsolidification

Volumicshinkage



PvTdata

Molddeformation

PP

12 / 40

Crystallization under deformation

Tc = 140°C / γ. = 0.5 s-1 / ts = 10s

Tc = 140°C / γ. = 5 s-1 / ts = 10s

Tc = 140°C / without shear :

t = 0 t = 60 min t = 120 min t = 180 min t = 240 min

t = 180 mint = 120 mint = 60 mint = 0

Experimental observations – PP

t = 0 t = 60 min

Volumicshinkage



PvTdata

Molddeformation

Crystallisation kinetics induced by deformationMany research works

Doufas A.K et al., J Rheol., 43(1), 85-109 (1999) Koscher E, Fulchiron R, Polymer, 43, 6931 (2002)Haudin JM, Chenot JL, Int. Poly. Processing, 19, 267 (2004)

Very difficult scientific problem …

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Fast cooling PvT data ?

CONTROLLEDTEMPERATURE

MEASUREDLENGTH

SAMPLESEALINGS

CONTROLLEDPRESSURE

2

specimenR LVm

π=

SWO PVT apparatus

Problem: a sufficient quantity of polymer is needed to measure precisely the volume⇒ significant thermal gradient in the sample

Volumicshinkage

Solidification andpost-filling


PvTdata

Molddeformation

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PvT experiment modeling

t1

ti

Time t0

ti+1

Radiusr0 r1 rj rj+1 rN

Thermal gradient equal to 0 ∀ t

Temperature equal to the control temperature ∀ t at r=R

tVHX

rT

rrT

rtT

VCP

∂∂α

∂∂

λ∂∂

∂∂λ

∂∂

spsp

∞∞∆+⎟

⎠⎞

⎜⎝⎛=− Heat due to Crystallization

• Crank-Nicholson finite difference Scheme

• Pressure dependent crystallisation kinetics identified by DSC

•

as λα−+αλ=λ )1(papsp CCC )1( α−+α=

Volumicshinkage



PvTdata

Molddeformation

15 / 40

Specific volume modeling(1 )crsp amV X VX Vα α∞ ∞= + − X∞: final crystallinity obtained

from density measurements or DSC

Fitted linear variations of Vcr with P and T

Vcr for Patm and 25°C consistent with the literature (ρ=0.936 g/cm3)

1°C/min

Tait Equation fitted on the liquid part of PVT diagram obtained with a low cooling rate (1°C/min)

1°C/min

Volumicshinkage



PvTdata

Molddeformation

16 / 40

PvT experiment modeling

Rapid cooling PvT tests have to be corrected from thermal gradient samplePvT tests to identify crystallinity kinetics ?

⇒ PvT data for injection simulation: low cooling rate for different pressures(The work is referenced in PvT ISO standard)

Predicted meanspecific volume

true specificvolume of PP

J.L Luyé et al., Journal of Applied Polymer Science,79, 302 (2001)

Volumicshinkage



PvTdata

Molddeformation

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0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10Time (s)

Pre

ssu

re (

MP

a)

RecordedSimulated

Nozzle

A

B

Hold pressure = 40 MPa

0

20

40

60

80

100

0 5 10 15 20Time (s)

Pre

ssu

re (

Mp

a)

SimulatedRecorded

Nozzle

A

B

Hold pressure = 80 Mpa

Effect of mold deformation

1: mold opening2: steel compressibility3: flexion of mold plate element.

PP - 1 mm

PP - 1 mm

Volumicshinkage



PvTdata

Molddeformation

18 / 40

-6

-4

-2

0

2

4

6

30 40 50 60 70 80 90Hold Pressure (Mpa)

Vol

um

ic S

hri

nk

age

(%)

Original mouldSv/deformed cavity

Original mouldSv/empty cavityMoldflow simulation

Effect of mold deformation

Over-packingPressure record3D Shrinkage measurementCavity thickness

⇒ Mold deflection = f(p)

Significant effect of mold deformation on pressure history and volumic shrinkage⇒ Coupling between rheology and elastic mold calculation.

D. Delaunay, et al., Part 2, Polymer Engineering & Science, 40 (7), 1682-1691 (2000)

PP - 1mm

Volumicshinkage



PvTdata

Molddeformation

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( )l lR Ts Taα= −

No residual stresses After ejectionCompression

Blocked shrinkage

Tensile

Homogenenousshrinkage after

ejection

In the mold

T∞ Thicknessshrinkage

T > Tsolidification Viscous behavior - T < Tsolidification Elastic behaviorEjection after core solidification

(Agassant et al., Polymer processing: principles and modeling, Hanser, 1996)

Restrained in-plane shrinkages

Linearshinkages

PhysicalRestraint effect

Solidification mechanisms

Cornereffect

In-plane shrinkageanisotropy

Thermal contact resistance

Viscoelastic behavior

20 / 40

Titomanlio G, Jansen K.M.B.,Polym. Eng. Sci., 36, 2041(1996)

Viscous behavior T > TsolidificationElastic behavior T < TsolidificationEjection after core solidification

1( )3l l s o l id i f i c a t io nR T s T a P

Bα= − −

If the layers wereindependent

Relevés de pression

0

100

200

300

400

500

0 5 10 15 20 25

P cavitéP HydrauliqueP buse

p (b

ar)

t (s)

Frozen gate

Pressure effect during solidification

Linearshinkages



Cornereffect



PSTmoule = 25°CTmoule = 55°C

21 / 40

Restrained shrinkage ⇒ Stress relaxation ↑ ⇒ in-plane shrinkage ↓

Effect of physical restraints

00.5

11.5

22.5

33.5

4

0 20 40 60 80Cavity pressure

Shrin

kage

s (%

)

SzS parallelS transverse

PP 3mm

Linearshinkages



Cornereffect



22 / 40

Polymer sliding

Linearshinkages



Cornereffect



Injection on strain gages (Pantani et al., Int. Pol. Proc., 12, 396; 1997)

PP - 3mm

1.00

1.10

1.20

1.30

1.40

1.50

Free Constrained

Shrin

kage

(%)

Parallel shrinkage

Perpendicularshrinkage

At low hold pressure, if no physical restraints, polymer slidingObviousness of stress relaxation

23 / 40

PP 3mm - freeParallel shrinkage

1.4

1.6

1.8

2

2.2

18s 35s 55sCooling time (s)

Sp (

%)

PolieGde Rugo

Ra = 0.1 µmRa = 10 µm

Prediction of linear shrinkage: ⇒ a viscoelastic behavior in the solid state is needed

Pressure records

0

100

200

300

400

500

0 5 10 15 20 25

P cavityP HydraulicP nozzle

p (b

ar)

t (s)

Effect of roughness

PP 3mm - t cooling = 35 sParallel shrinkage

1.4

1.6

1.8

2

2.2

free constrained

Sp (%

)

Ra = 0.1 µm

Ra = 10 µm

Mold

Polymer

Linearshinkages



Cornereffect


Thermal contactresistance

24 / 40

Phenomenology

40°C

40°C

60°C

20°C

60°C

20°CPP Thermal effect

( )XZ SS −α≈α∆

Spring forwardeffect

Linearshinkages





Cornereffect

25 / 40

Ammar A, Leo V, Régnier GInternational Journal of Forming Processes,6, 1-18, 2003

Spring forward effect

-1

0

1

2

3

4

5

6

7

0 5 10 15 20Opening time of the nozzle (s)

Mol

d An

gle

- Par

t Ang

le (°

) Angle A1Angle B1Sz-Sx (Side A)Sz-Sx (Side B)

-0.5

0

0.5

1

1.5

2

0 5 10 15 20

Opening nozzle time (s)

Pred

icte

d m

old

Ang

le -

part

ang

le (°

) 40°C20°C inner - 60°C outer

60°C inner - 20°C outer

Angle A2Thermal effect

Viscoelastic calculations⇒ low influence of thermal effect

3D simulation and thermo-viscoelastic calculation during the cooling

Linearshinkages





Cornereffect

26 / 40

Π 2

Π 1

0

Middle 1

T 20

T 10

∆T

Middle 2

Disturbed zone

T x 2 ( )

T x 1( )

Thermal contact resistance phenomenon

Gap (high variation) of temperature at the interface

( )2 /TTCRTherma

ml flux

K W∆=

Linearshinkages



Cornereffect



27 / 40

D. Delaunay, et al., Part 1, Polymer Engineering & Science, 40 (7), 1682-1691 (2000)

Influence of non perfect polymer-mold contact

0

10

20

30

40

50

-5 0 5 10 15 20 25Time (s)

Pres

sure

(MPa

)

Nozzle

Cavity

Fixed moldside

Mobile moldside

Polymerunsticking

Temperatures in thethermal sensor

Linearshinkages



Cornereffect



P > 0 ⇒ RTC ≈ 5 10-4 m2K/WP = 0 ⇒ air gap

coupling with polymer part thermo-mechanical calculation

28 / 40

SHEAR INDUCEDCRYSTALLIZATION Skin Core

ANISOTROPIC MECHANICAL

PROPERTIES

0

1000

2000

3000

-0.50 -0.30 -0.10 0.10 0.30 0.50Depth (mm)

Youn

g M

odul

us (M

Pa)

E // - 1 mm

En - 1 mm

ANISOTROPY OF SHRINKAGE

0.60.8

1

1.21.4

1.6

1.8

20 30 40 50 60 70 80Cavity pressure (MPa)

In-p

lane

shr

inka

ge (

%)

PP - 1 mm

Parallel

Normal

Why is it important to get induced microstructure?

Microstructure characterizationSpatial distribution of molecular orientation

Linearshinkages




Cornereffect


29 / 40

MaterialiPP Solvay ELTEX PP HV 252MFI = 11 g/min for 2.16 kg at 230° CMw = 180.8 g/molMw/Mn = 7.3

Processing parameters• Thickness 1mm and 3 mm• Injection times 0.7s and 1.6s

Sprue

Pressure sensorHeat flux sensor

Zone A Zone B

GateØ6

60

Ø4

6047

17

Feed geometry

Material and injection conditions

Linearshinkages




Cornereffect


30 / 40

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5Depth (mm)

Cry

stal

linity

(%)

PP 1 mm

PP 3mm

Crystallinity measurement of the microtomed slicesby means of a density gradient column

α phase

Crystallinity and microstructure

Linearshinkages




Cornereffect


31 / 40

Linearshinkages




Cornereffect


1mm thick / 0.2 mm deep

0

0.2

0.4

0.6

0.8

1

8009001000110012001300140015001600

cm-1Ab

sorb

ance pll polarization

P//

1mm thick / 0.2 mm deep

0

0.2

0.4

0.6

0.8

1

8009001000110012001300140015001600

cm-1Ab

sorb

ance pll polarization prp polarization

P⊥

( )2

2

+=α+θ

DDcos⊥

=h

//hD

Infrared dichroism principle

32 / 40

Linearshinkages




Cornereffect


2

2

1 2 22 2 1

D cotgfD cotg

αα

⎛ ⎞− +⎛ ⎞= ⎜ ⎟ ⎜ ⎟+ −⎝ ⎠ ⎝ ⎠

Uniaxial orientation 23 cos 12

f θ< > −=

Isotrope f = 0Orienté suivant z : f = 1Orienté ⊥ z : f = 0.5

Band (cm-1) Type Transition moment angle (°C)

998 C 181220 C 721256 A+C 02725 A 90

Choice of peaks for PP (Samuels, 1981) (Jasse et Koenig, 1979)

( ) amccrcav fVfVf −+= 1Vc : crystalline volumic fraction

Infrared dichroism principle

33 / 40

-0.10

0.10.20.30.40.50.60.70.80.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6

Depth (mm)

Orie

ntat

ion

func

tion

f crystalline - 988 cm-1f mean - 1256 cm-1fav Calculatedf amorphous - 2725 cm-1

Core Skin

Infrared dichroism on 35µm-thick microtomed slices

Molecular chain orientation – 1 mm plate

Linearshinkages




Cornereffect


Mendoza R, Régnier G, Seiler W, Lebrun JL,Polymer,, 44 (11),

3363-3370 (2003).

34 / 40

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Depth (mm)

f cry

stal

line

t = 1 mm - 'injection time = 1.6 st = 1 mm - injection time = 0.7 st = 3 mm - injection time = 1.6 st = 3 mm - injection time = 0.7 s

Crystalline orientation and injection time

Linearshinkages




Cornereffect


35 / 40

Morphology prediction

Zheng R, Kennedy, Journal of Rheology,48 (4), 823-842 (2004)

Kwon K, Isayev AI, Kim KH,Van Sweden C, Pol. Eng. Sci.,46, 712(2006)

Linearshinkages




Cornereffect


⇒ Possible to consider the mechanical properties prediction of semi-crystalline polymers according to micromechanics modeling

Mechanical properties prediction

Bedoui F, Diani J, Regnier G,Acta Materiala, 54, 1513 (2006)

Viscoelastic flow coupled withflow-induced crystallisation kinetics

36 / 40

NDz

MD

TDCylindrical sampleDiameter = 3mm

CCD camera

Synchrotron microbeam

y

x

DSAXS D = 1.3 mWAXS D = 0.14 m

300 µm100 µm

ESRFD2AM beamline

Coupled WAXS and SAXS microbeam technique

Linearshinkages




Cornereffect


37 / 40

Post-fillinglayer

Core

Fillinglayer

Plane 110 Plane 040

Specific bimodal orientationM

N

T

Daughterlamella

Mainlamella

-0.5

-0.25

0

0.25

0.5

0.75

1

0 0.2 0.4 0.6

Depth (mm)

f b

M - t =1.6s M - t =0.7s

T - t =1.6s T - t =0.7s

N - t =1.6s N - t =0.7s

b

WAXS Pole figures – 1mm-thick plate

Linearshinkages




Cornereffect


38 / 40

1 mmFilling layer

Post-fillinglayer

Core layer

3 mm

SAXS analysis

Linearshinkages




Cornereffect


39 / 40-0.5

-0.25

0

0.25

0.5

0 0.1 0.2 0.3 0.4 0.5Depth (mm)

Orie

ntat

ion

func

tion faM fbM fcM

≈ 2 µm 20 µm< 200 nm

10,5 nm

2,5 nm

? 9 nm

2 nm

M

1 mm-thick plate morphology

Linearshinkages




Cornereffect


Mendoza R, Morphologies induites dans les pièces injectées en polyoléfines, PhD thesis of ENSAM, mai 2005

40 / 40

ConclusionsPrediction of shrinkage and warpage : at the end of the simulation process

⇒ all the errors induced by the numerous hypothesis are piled up

Nevertheless, in-plane shrinkage anisotropy prediction ⇒ viscoelastic flow

Amorphous polymersPolymers reinforced by fillersSemi-crystalline polymers

Several big challenges are still remaining:

- Shear-induced crystallization prediction- Microstructure prediction- Thermomechanical properties (final properties and also during process)

Special thanks the SWIM, SCOOP and FISH partners

- Efficient polymer characterization methods- Flow-induced crystallisation kinetics- Viscoelastic law identification on a large range of temperature

Difficulties for shrinkage and warpage prediction

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