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FE Simulation of Die Compaction of FE Simulation of Die Compaction of Cylindrical Sample and Subsequent Cylindrical Sample and Subsequent
Diametrical Compression TestDiametrical Compression Test
Wenhai Wang and Antonios Zavaliangos
Drexel University, Department of Materials Science and Engineering, Philadelphia, PA 19104
Funding provided by NSF –CMS 0100063
NoComposition effect
Starting to understandFatigue
Starting to understandStrength
In simple cases onlyFracture location/direction
HeuristicallyFracture tendencies
ApproximatelyDimensions after compactionReasonableLoad on tools
GoodDensity distributionIn compact
PREDICTION QUALITY
Modeling Prediction CapabilityModeling Prediction Capability
(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
I. C. Sinka, J. C. Cunningham, and A. Zavaliangos, Powder Technology, 2003, vol. 133, pp. 33-43.I. C. Sinka, J. C. Cunningham, and A. Zavaliangos, Journal of Pharmaceutical Science, 2004,vol.93,pp.2040-2053.J. C. Cunningham, I. C. Sinka and A. Zavaliangos, Journal of Pharmaceutical Science, 2004,vol.93,pp.2022-2039
•The radial distribution of porosity is completely inverted simply bychanging the wall friction conditions (lubricated V.S. unlubricated die).•Simulation prediction by Drucker-Prager model (phenomenological model) is in good agreement with experimental observation.
Unlubricated Lubricated (magnesiumstearate)
Previous WorkPrevious WorkThe effect of wall friction in the compaction of
pharmaceutical tablets with curved faces
Diametrical Compression Test
ba
020406080
100120140160180200
0 0.2 0.4 0.6 0.8 1 1.2
Distance, mm
Forc
e, N
lubricated die unlubricated die
0.3740.3800.416
0.464
0.505
0.560
0.590
0.422
0.433
0.472
0.510
0.5590.612
•Diametrical compression (side compression) is a common test in pharmaceutical industry, rocks, soils etc. (brittle materials in general)- If the material is uniform and brittle – Hertz solution applies - If the material is non-uniform or plasticity occurs – numerical solution is needed to understand results like those above.•Tablets made under different lubrication conditions shows different strength and fracture modes during diametrical compression test.
Unlubricated Lubricated
Previous WorkPrevious Work
Understand the limitations of the DruckerPrager/Cap model in predicting failure.
–Implement a more efficient form of the model in ABAQUS/EXPLICIT: VUMAT Subroutine–Verify the VUMAT–Use the VUMAT to “predict” fracture load and mode in diametrical compression of non-uniform density compacts NOTE: The work presented here was validated with pharmaceutical powders. The key principles are identical in P/M and the conclusions derived are of general validity.
Main GoalsMain Goals
σ
p
Shear failure Region
CapRegion
Non-associated plasticity
Associated plasticity
Failure+Dilation Densification
DruckerDrucker-- PragerPrager Cap ModelCap Model
Has its roots in civil engineering and soils, adapted & modified by P/M in the 90’s then 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 are described 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.
VUMAT VUMAT –– Implementation of DPC ModelImplementation of DPC Model
• Prior work was done with the ABAQUS/Standard library version of the model
• ABAQUS/Standard may have convergence problems with friction or contact
• ABAQUS/Explicit library version of Drucker-Prager/Cap is not general enough
• A VUMAT (user material subroutine) was implemented and tested.
Final Relative density distribution (2-D)
Initial Relative density distribution (3-D)
Die Compaction
Diametrical Compression
Mapping
Unlubricated Lubricated
Simulation ProcedureSimulation Procedure
2D Die Compaction2D Die CompactionSimulation Simulation ResultsResults
Comparison with prior experiments and simulations for validation of the VUMAT subroutine
Validation of VUMAT subroutine (implementation of the Drucker-Prager model).
Good agreement with experimental results and previous simulation results.
Porosity DistributionPorosity Distribution
a
c d
b
0.0125 mm
Center axis
A A’
Center axis
0.0125 mm
a
c d
b
0.0125 mm
Center axis
0.0125 mm
Center axis
0.0125 mm
Center axis
A A’
Center axis
0.0125 mm
A A’
Center axis
0.0125 mm0.0125 mm0.0125 mm0.0125 mm
Unlubricated Lubricated
Unlubricated Lubricated
The unlubricated tablet required a slightly larger load to achieve the same overall density.
The different slopes (triaxiality) of the stress paths indicate corresponding differences in the densification mode.
Loading PathsLoading Paths
a
A B
Center axis
c d
ba
A B
Center axis
c d
b
3D Diametrical Compression 3D Diametrical Compression SimulationSimulation ResultsResults
a bUnlubricated Lubricated
Force displacement ComparisonForce displacement Comparison
•Peak indicates the failure;•The predictions for the lubricated tablets are quite reasonable;•Machine compliance effect.
a bExperimentSimulation
The fracture load increases with relative density.
Break ForcesBreak Forces
Unlubricated
Lubricated
Porosity EvolutionPorosity Evolution
Failure is relate to the porosity increasing;Same failure mode in both cases.
Rankine criterionFailure occurs when the maximum (normal) Principal stress reaches either the uniaxial tensionstrength, or the uniaxialcompression strength .
2.5E5 9.0E3
-5.8E5
3.0E5 8.3E4
-7.5E5
2.8E5 9.2E3
-6.2E5
3.3E5 9.2e4
2.9E50.8E4
3.1E50.8E4
-6.3E5
-7.5E5
-6.5E5
2.5E5 9.0E3
-5.8E5
3.0E5 8.3E4
-7.5E5
2.8E5 9.2E3
-6.2E5
3.3E5 9.2e4
2.9E50.8E4
3.1E50.8E4
-6.3E5
-7.5E5
-6.5E5
Fracture mode ProbingFracture mode Probing
Principle Stresses for Unlubricated Die
Principle Stresses for Lubricated Die
Fracture mode ProbingFracture mode Probing
A significant tensile stress along the direction of prior compaction
1.58E4
-8.63E5
3.91E5 1.29E5
-1.24E6
3.88E5 1.53E4
-9.75E5
1.99E5
-1.17E5
-1.8E6
4.95E5 2.21E5
-1.18E6
4.93E5 1.63E4
-1.12E6
3.0E51.58E4
-8.63E5
3.91E5 1.29E5
-1.24E6
3.88E5 1.53E4
-9.75E5
1.99E5
-1.17E5
-1.8E6
4.95E5 2.21E5
-1.18E6
4.93E5 1.63E4
-1.12E6
3.0E5
• Drucker-Prager/Cap (DPC) model has been successfully implemented into ABAQUS/Explicit via a versatile user material subroutine
• It offers good predictions on relative density distribution at the end of compaction – validated through experiments
• DPC has limitations on predicting fracture of green compacts– The overall load displacement in diametrical compression
is reasonably predicted– The mode of failure is not captured by DPC
• A Rankine model for failure (max principle tensile stress) gives better insight into failure.
• An anisotropic model is needed, in which the consolidation path effect should be taken into account. (future work)
Conclusions and Future WorkConclusions and Future Work