Constitutive Behavior of Materials in Powder Compaction: Fundamental and Practical 

Aspects Related to Tableting and Compaction Simulation

Antonios ZavaliangosDepartment of Materials Science & Engineering 

Drexel University

Compaction Simulation Forum 2012

Also recent current support from Institute of Fine Powder Research and Abbot Laboratoriesas well as recent completedmini project with Bristol Myers Squibb

Relevant Projects and Collaborations

NSF GOALI 2001-05Experimental & Theoretical Studies on Compaction with Application on Pharmaceutical Powders

9/06-2/07 Sabbatical 3/06-6/07 Sabbatical

NSF GOALI 2009-12Optimization of Design and Processing of Bilayer tablets

Graduate Fellowship programDept. of Education at Drexel University“Engineering for Pharmaceutical Applications”

PhDGalen  (Merck Eng)  Merck  and now Covance PharmaceuticalsCunningham (Merck Eng) Merck and then Johnson and Johnson and now CentecorProcopio (Merck Eng)  Merck  Klinzing  Merck Wang Postdoc at Temple and then at Mount Sinai Hospital  Garner OngoingMSMillili PhD at U Del and then MerkRobinson (coop J&J) Merck  Snyder (coop J&J) US Navy (NAVSEA)  Panis CVM Engineers  Sexton  Peace Corps and then U Florida grad schoolTrivic Solar Atmospheres  Weber Ongoing Thomas (GSK ) Ongoing 

Senior DesignTJ US Navy (NAVSEA)Andrew (coop at Merck)  Merck Sean Grad School (Drexel)Gus (Colorcon Eng) ColorconDan Boeing HelicoptersBrandon (coop at Merck) PhD at Drexel then at Army Research Lab

PostdocSinka Merck and now U Leicester

External colleeaguesTracy Mascaro J& J and now ColorconDenita Williams J&JJames Michael Merck

Acknowledgments

• Harold Hindman & George Burr (MIT) during WWII were working on substitutes for silk that could be used parachutes.

• No commercial machine could deal with the accuracy and control needed for this project.

• They came up with 1) a unique cross-head drive system,

similar to the radar antenna positioning drive on naval warships.

2) a transducer for the load system based on the strain gauge, which had just been developed at MIT (and Caltech ).

• The machine they developed was so unique that they enabled them to form INSTRONestablished in 1946 which has become a familiar name to all those involved in mechanical testing

Journal of Pharmacy and Pharmacology, 1956, p. 745

To UNDERSTAND compaction

• We need :

1. Mechanics2. Mechanical behavior of materials3. Overall behavior of compaction equipment4. Characterization techniques

mechanical testing, micro CT,  Raman, IR, XPS 5. Computational modeling techniques

FEM, DEM, and more…

CAUSE EFFECT RELATIONS IN TABLETING

An example of the “complexity”...• In an effort to predict the compaction of an excipient in 

standard concave deep concave and oval geometries, the predictions of simulation were all over the place. 

SINGIFICANT DIFFERENCES IN INITIAL PACKING BASED ON THE TOOL GEOMETRY

Complexity of tableting is what makes simulators to be exactly what their name mean – they are “Simulators”

Examples of what is that simulators can not replicate accurately

1. Initial filling – depends on the feeding system 2. Temperature – function of history and system   

(feeder, table, atmosphere)3. System elastic compliance

Still we can get a lot out of compaction simulators 

• But we need to understand:

1. Mechanics of the problem

2. Mechanical behavior of materials

3. Overall simulator behavior

Mechanics and misconceptions 

From a brochure of an excipient manufacturer

Hardness vs. Diametrical Strength

0

1

2

3

4

5

6

7

8

9

0 0.2 0.4 0.6 0.8 1 1.2

Hardn

ess, N

Compaction Force (kN)

PS=4.5mm

PS=6.7mm

Avicel PH‐102

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10 20 30 40

Strength (M

pa)

Axial Pressure (MPa)

Avicel PH‐102

Outline

• Example 1: Tool‐tablet friction• Example 2: Temperature during compaction• Example 3: Using a simulator for in‐die 

mechanical spectroscopy• Example 4: 3 pictures related to microcrack

detection in compacts

• Example 5: Bilayer strength (at the Arden House Conference)

EXAMPLE 1: Tool‐Tablet Friction

• The effect of tools/tablet friction on the distribution of density of tablets and its implications for post compaction properties

Cunningham J., C. I. Sinka, and Zavaliangos A. “Analysis of Tablet Compaction. Part 1 – Characterization of Mechanical Behavior of Powder and Powder/Tooling Friction”, Journal of Pharmaceutical Sciences, Vol. 93, No 8, Date: August 2004, Pages: 2022‐2039

C. I. Sinka, Cunningham J., and Zavaliangos A. “Analysis of tablet compaction. Part 2 – Finite element analysis of density distributions in convex tablets”, Journal of Pharmaceutical Sciences, Vol. 93, No 8, Date: August 2004, Pages: 2040‐2053

Show the differences between two tablets of identical geometry and average densityunder two extreme conditions:1) High tool lubrication by precompacting a MgSt “tablet” 

before the actual compaction2) High friction – clean tools with solvent before compaction

• Using– simulator data for flat tablets – finite element modeling

• Predict – predict the behavior of the 

Phenomenological models

• Based on a few calibrating experiments

• Predict material behavior over a much broader set of conditions than the calibrating experiments

Antonios Zavaliangos

p

“Drucker‐Prager Cap” Model

Has its roots in civil engineering/soilsadapted & Modified by P/M in the 90’sthen by Pharmaceuticals in 2000’s

* Compact of a given density are weaker under tensile than compressive conditions

* The stresses required to cause permanent shape/volume change of a compact aredescribed by two parts

- half of an ellipse for heavily compressive states

- a Mohr-Coulomb model for shear(like rocks and other brittle materials)

* Increasing density causes an expansion of the yield locus.

Upper Punch Displacement

Lower Punch Displacement

Upper Punch Force

Lower Punch Force Ejection Force

Die Wall Force

Cunningham J., C. I. Sinka, and Zavaliangos A. “Analysis of TabletCompaction. Part 1 – Characterization of Mechanical Behavior ofPowder and Powder/Tooling Friction”, Journal of PharmaceuticalSciences, Volume 93, Issue 8, Date: August 2004, Pages: 2022‐2039

Experimental Calibration 

ONE test on a FLAT FACE tablet in an  INSTRUMENTED DIE

DIAMETRICAL and SIMPLE COMPRESSION on FLAT FACE tablets at 5‐6 DENSITY/LOADS tablets

(1) (2)

(3)(4)

Hydrostatic Stress

Effe

ctiv

e St

ress

FailureLine

Experimental resultsYoung's Modulus of Elasticity v RD for Avicel102/A-Tab Mixtures (wt%)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

13.00

14.00

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

Relative Density - RD (-)

Youn

g's

Mod

ulus

- E

(GPa

)

0% A-Tab20% A-Tab40% A-Tab60% A-Tab80% A-Tab100% A-Tab

Strong variation with porosity – usually non linearTends to fully dense material property as RD 1

Experimental resultsPoisson's Ratio v RD for Avicel 102/A-Tab Mixtures (Wt%)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

Relative Density - RD (-)

Pois

son'

s R

atio

- nu

(-)

0% A-Tab20% A-Tab40% A-Tab60% A-Tab80% A-Tab100% A-Tab

Poisson tends to zero towards packing limit…

Friction

00.10.20.30.40.50.60.70.80.9

1

0 15 30 45 60 75 90

Contact Pressure, MPa

Coe

ffici

ent o

f Fric

tion

lubricated die

clean die

Friction is one of the major origins of inhomogeneity in powder  compactionand is often associated with defects, and redundant energy

In general friction is function of density, pressure, velocity, temperature, etc.

Pressure and Velocity Effect on Friction

favivt7, run2,3,4

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150

Radial Stress at Sensor, MPa

Coe

ffici

ent o

f Fric

tion

1 mm/s

10 mm/s

100 mm/s

“High” frictiondie cleaned by alcohol before experiment

(a)

(c)

0.712

0.643

0.667

0.689

0.604

0.625

0.647

0.604

0.566

0.597

0.633

0.616

0.604

0.582

0.601

0.616

0.579

0.566

0.562

0.601

0.597

0.572

0.575

0.484?

0.556

0.575

0.575

0.572

0.569

0.515

0.556

0.562

0.579

0.572

0.556

0.569

0.472?

0.544

0.562

0.566

0.559

0.566

0.5470.474?

0.544

0.575

0.572

0.586

0.556

0.544

0.482?

0.539

0.575

0.562

0.579

0.569

0.530

0.559

0.593

0.597

0.597

0.575

0.556

0.589

0.586

0.608

0.612

0.586

0.647

0.643

0.620

0.620

0.657

0.662

0.662

0.689

0.6940.700

5 mm

0.70.66

0.640.62

0.6 0.550.57

0.712

0.643

0.667

0.689

0.604

0.625

0.647

0.604

0.566

0.597

0.633

0.616

0.604

0.582

0.601

0.616

0.579

0.566

0.562

0.601

0.597

0.572

0.575

0.484?

0.556

0.575

0.575

0.572

0.569

0.515

0.556

0.562

0.579

0.572

0.556

0.569

0.472?

0.544

0.562

0.566

0.559

0.566

0.5470.474?

0.544

0.575

0.572

0.586

0.556

0.544

0.482?

0.539

0.575

0.562

0.579

0.569

0.530

0.559

0.593

0.597

0.597

0.575

0.556

0.589

0.586

0.608

0.612

0.586

0.647

0.643

0.620

0.620

0.657

0.662

0.662

0.689

0.6940.7000.712

0.643

0.667

0.689

0.604

0.625

0.647

0.604

0.566

0.597

0.633

0.616

0.604

0.582

0.601

0.616

0.579

0.566

0.562

0.601

0.597

0.572

0.575

0.484?

0.556

0.575

0.575

0.572

0.569

0.515

0.556

0.562

0.579

0.572

0.556

0.569

0.472?

0.544

0.562

0.566

0.559

0.566

0.5470.474?

0.544

0.575

0.572

0.586

0.556

0.544

0.482?

0.539

0.575

0.562

0.579

0.569

0.530

0.559

0.593

0.597

0.597

0.575

0.556

0.589

0.586

0.608

0.612

0.586

0.647

0.643

0.620

0.620

0.657

0.662

0.662

0.689

0.6940.700

5 mm5 mm

0.70.66

0.640.62

0.6 0.550.57

0.70.66

0.640.62

0.6 0.550.57

5 mm5 mm

(b)

(d)

0.525

0.539

0.616

0.629

0.608

0.550

0.633

0.638

0.633

0.652

0.643

0.647

0.643

0.629

0.643

0.638

0.629

0.657

0.633

0.638

0.643

0.638

0.638

0.652

0.647

0.633

0.612

0.657

0.633

0.625

0.643

0.625

0.643

0.652

0.652

0.652

0.647

0.616

0.620

0.652

0.647

0.652

0.647

0.625

0.647

0.643

0.657

0.633

0.643

0.629

0.625

0.647

0.672

0.662

0.643

0.633

0.638

0.657

0.662

0.647

0.652

0.638

0.638

0.629

0.638

0.647

0.633

0.643

0.667

0.652

0.652

0.620

0.647

0.652

0.6430.547

0.643

0.530.61

0.63

0.640.650.64 0.66

0.660.65

0.640.6

0.530.525

0.539

0.616

0.629

0.608

0.550

0.633

0.638

0.633

0.652

0.643

0.647

0.643

0.629

0.643

0.638

0.629

0.657

0.633

0.638

0.643

0.638

0.638

0.652

0.647

0.633

0.612

0.657

0.633

0.625

0.643

0.625

0.643

0.652

0.652

0.652

0.647

0.616

0.620

0.652

0.647

0.652

0.647

0.625

0.647

0.643

0.657

0.633

0.643

0.629

0.625

0.647

0.672

0.662

0.643

0.633

0.638

0.657

0.662

0.647

0.652

0.638

0.638

0.629

0.638

0.647

0.633

0.643

0.667

0.652

0.652

0.620

0.647

0.652

0.6430.547

0.643

0.525

0.539

0.616

0.629

0.608

0.550

0.633

0.638

0.633

0.652

0.643

0.647

0.643

0.629

0.643

0.638

0.629

0.657

0.633

0.638

0.643

0.638

0.638

0.652

0.647

0.633

0.612

0.657

0.633

0.625

0.643

0.625

0.643

0.652

0.652

0.652

0.647

0.616

0.620

0.652

0.647

0.652

0.647

0.625

0.647

0.643

0.657

0.633

0.643

0.629

0.625

0.647

0.672

0.662

0.643

0.633

0.638

0.657

0.662

0.647

0.652

0.638

0.638

0.629

0.638

0.647

0.633

0.643

0.667

0.652

0.652

0.620

0.647

0.652

0.6430.547

0.643

0.530.61

0.63

0.640.650.64 0.66

0.660.65

0.640.6

0.530.53

0.610.63

0.640.650.64 0.66

0.660.65

0.640.6

0.53

“Low” frictionMgSt “tablet” compacted 

before experiment 

C. I. Sinka, Cunningham J., and Zavaliangos A. “Analysis of tablet compaction. Part 2 – Finite element analysis of density distributions in convex tablets”, Journal of Pharmaceutical Sciences, Volume 93, Issue 8, Date: August 2004, Pages: 2040‐2053

Radial distribution of porosity is completely inverted simply bychanging the wall friction conditions

Important implications for strength, dissolution and drug availability

VALIDATION

Friability and Abrasion test

1000 rev

2000 rev

Friability Abrasion

C. I. Sinka, Cunningham J., Zavaliangos A. “Analysis of tabletcompaction. Part 2 – Finite element analysis of densitydistributions in convex tablets”, Journal of PharmaceuticalSciences, 2004

While results cannot be quantitatively predicted, they can be rationalized by the model 

Unlubricated

Lubricated

EXAMPLE 2• Temperature increase during tableting

Klinzing G.R., Zavaliangos, A., Cunningham J. C.,   Mascaro T. and Winstead D. A.,  “Temperature and density evolution during compaction of a capsule shaped tablet”,  accepted for publication in Computers in Chemical Engineering, Volume 34, 2010, pp. 1082–1091 

Zavaliangos, A., Galen S., Cunningham J. C., and Winstead D. A., “Temperature Evolution During Compaction of Pharmaceutical Powders”, Journal of Pharmaceutical Science, Volume 97, Issue 8, 2008, pp. 3291‐3304

Tablets after compaction are “warm”.What is the maximum temperature thatthe tablet reaches during compaction?

Ejection

5 sec post ejection

30 sec post ejection

1 min post ejection

INTERESTINGLONG TERM,TRANSIENT

Measurements of temperature?

• IR at the exit• Thermochromic powders• Melting inclusions (?)• Thermocouples are too slow for ms level events

• This is a case that for all practical purposes it is impossible to measure the temperature duringcompaction

Temperature evolution in tableting

End of compaction

Beginning of ejection

0

10

20

30

40

50

60

2.5mm 120mm/s 3.0mm 120mm/s 2.5mm 960mm/s 3.0mm 960mm/s

Tem

pera

ture

at t

op-c

ente

r of t

able

t (o C

) ExperimentSimulation

1. Zavaliangos, A., Galen, S., Cunningham, J., and Winstead, D. 2008. Temperature Evolution during Compaction of Pharmaceutical Powders. J. Pharm. Sci. 97, 3291‐3304.

2. Klinzing, G., Zavaliangos, A., Cunningham, J., Mascaro, T., and Winstead, D. Temperature and density evolution during compaction of a capsule shaped tablet.  Computers in Chemical Engineering (2010)

More Details:

Diameter 3/8”, initial height=6mm final to RD~93%

0.1mm/s

10mm/s

1mm/s

100mm/s

EFFECT OF SPEED ON TEMPERATURE AT THE END OF COMPACTION

Temperature Results

IR image of capsule immediately after ejection from the die

L1 is line along flat edge from outer edge to center of tablet

L2 is line along flat edge from center to outer edge of tablet

Temperature (Celsius)L3 is line along height of tablet from top to bottom

If surface temperatures are predicted then internal temperatures can be predicted as well 

Importance of the max temperature in compaction

• Although such maxima are transient

there may be important effects on

• Active ingredients• Compressibility • Sticking and picking tendency (especially in the

presence of soft secondary phases)• Lubricant performance and thus on friction and

ejection

ΕΧΑΜPLE 3: Viscoelasticity

Excerpt from a textbook on formulation:

The “street definition” of rate dependence = Changes in tableting speed result in different hardness

RATE DEPEDENCE ≠

VISCOELASTICITY

Viscoelasticity is a time-dependent phenomenon butthere are many other phenomena that are time dependent,such as

• heat conduction, • air flow in a porous medium, • plastic deformation • friction

Viscoelastic Characterization

Based on frequency:1) Low:          Creep or relaxation test ( < 1Hz )2) Medium:   DMA  (0.1 – 100 Hz)3) High:          Wave propagation (Split Hopkinson Bar)     

(100 Hz and higher)

• IMPORTANT FREQUENCY/TIME IN TABLETING ▫ Compaction: 10‐200 ms or 5‐100 Hz▫ Ejection (same as compaction due to mechanism)▫ Post compaction > 1 seconds up to days  < 1Hz

• Dynamic Mechanical Analysis (DMA)▫ Applied strain:           = o cos(t)▫ Response with lag:    σ = σo cos(t + )

• Complex Modulus▫ Storage and Loss components

E*() = E() + iE()

• Dissipation (Loss) Factor     tan = E / E

Stress Relaxation Creep

DMA result for viscoelastic material

Literature: 

Hancock et al.• Simple dynamic tensile test and a

dynamic version of the three-point beam-bending test. (MCC)

• Out of die characterization

Beam-Bending Test Tensile Test

Literature

Rippie and Danielson et al.• Addressed directly the issue 

by studying unloading and postcompression periods of tableting on a rotary press

• Analyzed the data using basic viscoelastic models

• Results are fitted but some “strange” data parameters are extracted, e.g.,  negative “elastic modulus”

Welch et al.• Split Hopkinson Pressure Bar 

technique to identify the complex modulus for frequencies up to 20 kHz 

• Out of die characterization

Important range

Goals  (MS work of Barbara Robinson)

To evaluate the role of viscoelasticity on the powder compaction process, specifically bulk viscoelasticity, which is more relevant to compaction.

1. Perform viscoelastic characterization of powder compacts by use of in die Dynamic Mechanical Analysis (DMA) – sometimes called mechanical spectroscopy.  

2. To compare viscoelasticity of Young’s and bulk moduli.3. Contrast the viscoelasticity of two common excipients, MCC and Starch.

DMA Experimental Method• Huxley Bertram servo-hydraulic Compaction Simulator

(J&J PRD, Spring House)• Three Steps

– Lubrication – Compaction

• 3-4 Densities (0.6 – 0.9)

– DMA• 9 Frequencies (0.1 – 50 Hz)• 3 Strain Amplitudes

DMA WITH DUAL ACTION, I.E. BOTH PUNCHES MOVE SYMMETRICALLY TO MINIMIZE FRICTION

Experimental challenges faced

• Simulator behaved well up to 20Hz• Significant drop in strain amplitude compared to the 

specified input at 50 Hz and above• Assuming strains small enough to achieve linear 

viscoelasticity, this should not be a problem.

• Piezoelectric sensor drifts by 0.15 MPa over 1 minute.              Maximum DMA test duration was 30 seconds.

• Needs resetting after in die relaxation• Die stress in the subsequent experiment need to be 

corrected by an offset that corresponds to the relaxed wall stress. 

• DMA results are insensitive to the value because they only depend on the amplitude of the signal

Raw Data Output

• Raw data for single experiment.

• True viscoelastic relaxation has a time constant of seconds 

• Effective DMA requires additional relaxation.

• Relaxation extends into oscillations.

• Variation in relaxation is minimal compared to amplitude of oscillations.

Compaction DMA

Stress Output Signal

• Asymmetry of the output stress signal.• - Friction between sample and tooling.

unloading

loading

Reminder: Elastic behavior of powder compacts

K

G

EEE

EE

rrzzzz

rrzzzz

zzrrzzzz

zzrrzzrrrr

rr

22

1212

10

2

Shear modulus

Bulk modulus

IN DIE

OUT OF DIE zzzz E E G Κ

E (Young) andK = bulk modulus

Data Processing

Axial & Radial Loss Factor Deviatoric & Hydrostatic Loss Factor

• Considers axial and radial stress directly

• Axial Loss Factor▫ σzz versus zz

• Radial Loss Factor▫ σrr versus zz

• Analysis difficult due to mixture of moduli in the results.

• Considers mean pressure and volumetric strain

• Deviatoric Loss Factor▫ (σzz ‐ σrr) versus zz

• Hydrostatic Loss Factor▫ (σzz + 2σrr) versus zz

• Analysis simplified because one modulus at a time involved.

Effect of Friction

• One of major difficulties to overcome in terms of the in die DMA is the contribution of frictionBetween compact and die

• Investigations of energy lost due to friction rather than viscoelasticity– Mathematical Calculations– Additional Experimentation– Numerical Simulation

Friction Experiments ‐ Starch

• Tablet mass was reduced to decrease friction contribution

• Results show that decreased friction produces a decreased apparent viscoelastic effect.

• Extrapolation of loss factor to zero tablet height = frictionless loss factor.

• Additional experiments involved varying tablet height while keeping other variables constant.

• Contact area between tablet and die is varied which should have direct effect on friction.

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.1 1 10 100

tan

Frequency (Hz)

Starch Deviatoric Tan vs Frequency - 0.8RD 0.7% Strain

Full Height1/2 Height1/4 Height0 Height Ext.

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.1 1 10 100

tan

Frequency (Hz)

Starch Hydrostatic Tan vs Frequency - 0.8RD 0.7% Strain

Full Height1/2 Height1/4 Height0 Height Ext.

“Frictionless”estimate

“Frictionless”estimate

Friction Experiments ‐MCC

• Only difference is the original tablet height for MCC was already quite small.

• Therefore, the height could only be halved for experimental purposes.

• Similar experiments run for MCC –varying tablet height.

• Show similar correlation between friction and viscoelastic dissipation.

0.000

0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

MCC Deviatoric Tan vs Frequency - 0.8RD 0.7% Strain

Full Height1/2 Height

0.000

0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

MCC Hydrostatic Tan vs Frequency - 0.8RD 0.7% Strain

Full Height1/2 Height

“Frictionless”estimate

“Frictionless”estimate

Friction Numerical Simulation

• Varied the friction coefficient to observe the effect on the stress signal• Utilizes exact dimensions of experimental specimen and similar sinusoidal

DMA signal• Viscoelastic data taken from literature for Starch (Welch et al.)• Shows strong correlation between friction and distortion of signal

Friction Numerical Simulations• 1/2 , 1/4, and 1/8 heights tested at

constant friction coefficient of 0.2

• Plotted ratio of frictional energy dissipation to viscoelastic energy dissipation

• Results show slightly non-linear dependence of height on viscoelasticity

• Results suggest using linear fit to extrapolate “frictionless” loss factor will slightly undershoot actual value.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

01234

Wf

/ Wd

Tablet Height (mm)

Numeral Simulation Frictional Loss vs Height

DMA Experimental Results

Effect of Strain• Minor dependence of viscoelasticity on strain

• Slight deviation from linear viscoelastic behavior

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.1 1 10 100

tan

Frequency (Hz)

Starch Axial Tan -0.8 Relative Density

0.33%0.50%0.67%

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.1 1 10 100

tan

Frequency (Hz)

MCC Axial Tan - 0.8 Relative Density

0.70%1.06%1.41%

NOTE: Data are not friction corrected.

Out of Die DMA Experiments• Comparison of elastic and bulk 

components of viscoelasticity• Out of die has higher 

viscoelasticity than in die

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0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

Starch Tan versus Frequency - 0.8RD 0.7% Strain

In DieOut of Die

0.000

0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

MCC Tan versus Frequency - 0.8RD 0.7% Strain

In DieOut of Die

1%MgSt / MCC Blend• Often viscoelasticity is “blamed” on the 

presence of lubricants • Test the idea by comparing MCC vs MCC + 

1% MgSt

• Minimal dissipation due to particle surfaces• Dissipation from bulk of material instead

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0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

Axial MCC Tan versus Frequency - 0.8 RD - 0.7% Strain

Out of DieMgSt Blend Out of Die

Effect of Relative Density• Hydrostatic viscoelasticity  shows similar dependence.

• Dependence is more distinguished for MCC as compared to Starch.

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0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

MCC Hydrostatic Tan vs. Frequency 0.7% Strain

0.60.70.8

0.000

0.050

0.100

0.150

0.200

0.250

0.1 1 10 100

tan

Frequency (Hz)

Starch Hydrostatic Tan vs Frequency 0.7% Strain

0.60.70.8

Conclusions

• The simulator can do MUCH more than just simulate • Used it to get out of die and in‐die viscoelasticity

• Strong direct correlation between friction and “apparent” viscoelastic effect, requires correction – done.

• Minor dependence of viscoelasticity on strain• Lower relative densities produce higher viscoelastic effects, exaggerated in MCC (this implies high local stresses at contacts and is in line with the nonlinear effect).

• Definite contribution of bulk viscoelasticity which differs from young’s modulus viscoelasticity

• Out of die results clearly shows bulk contribution is significantly less than Young’s modulus contribution

• Out of die tanδ is higher than in die tanδ

Microcrystalline celluloseCompaction direction

62

Limits of Density Based ModelsIsostatic Compaction

Triaxial Compaction

85% 85%25 Ksi 55 Ksi

Die Compaction

RDf

85%20 Ksi

KOERNER ‐ 1973

Strength in Die  Isostatic  Triaxial Compaction

p

The concept of “excluded” porosityin hard+soft mixtures

EXCLUDED POROSITY

Porosity between the hard particles is not possible to close.

Soft

Hard

Soft particles can readily deform and easily produce a fully dense compact

SIZE EFFECTS"Breaking" the clusters of the hard particles

Deformation of hard particles

"Extrusion" of soft particles into excluded porosity

MECHANISMS OF REDUCTION OF EXCLUDED POROSITY

(a) (b)

(c)1

10

100

1/f V

, f

V=p

oros

ity

0 100 200 300 400Applied Stress, MPa

0%10%20%30%40%50%60%

Fraction of Hard Phase

S

Nor

mal

ized

slop

e S(

X%

)/S(0

%)

Percentage of Hard Phase

0.4

0.6

0.8

1

0% 20% 40% 60%

Small Hard-Large Soft

Small Soft-Large Hard

Equal size

(d)

(e)

Mixing quality

Percolation phenomena in binary mixtures

The importance of 1‐1 vs 2‐2 vs 1‐2 contacts (non unique for given volume fractions

MODEL

75

80

85

90

95

100

0 20 40 60 80 100

% Hard

Rel

ativ

e D

ensi

ty

X=1X=0.5

The effect of mixing quality on compressibility

EXPERIMENTS (Al-Ti)

75

80

85

90

95

100

0 20 40 60 80 100

% Hard

Rel

ativ

e D

ensi

ty

30 min5 min1 min

Models and experiments show that there is a reduction of compressibility with decreasing mixing quality

Using a geometric definition of mixing quality a model is formulated