Challenges in the Modeling of Plastics in Computer SimulationChallenges in the Modeling of Plastics...

strengthening the materials core of manufacturing enterprises

Challenges in the Modeling of

Plastics in Computer Simulation

Hubert Lobo President

DatapointLabs, Ithaca NY


Impact of Simulation

• Massive benefit to injection-molding process

– Great improvement in part quality

– Productivity increases

– Reduction in scrap

• Significant benefit to plastic part design

– Understand how to use these complex materials

– Create novel parts and products

– Prevent in-the-field part failure


Challenges

• Plastics are very complex

– Not all behavior is well understood

– Experimental artifacts accompany the data

– Mathematical material models have limitations

– Behavior is not correctly represented in simulation

• These limitations can cause errors

• With proper understanding, good design

decisions can be made


What Makes Plastics Complex

• Non-Newtonian, non-isothermal flow

• Cooling rate- and shear-dependent crystallization

• Viscoelastic (time-based behavior)

• Non-linear elasticity

• Complex plasticity (pre-yield, post-yield)

• Properties change over product operational

temperature and environmental exposure


Current Topics

• Injection-mold analysis

– Material model inconsistencies

– Fiber-orientation prediction

• Finite element analysis

– Non-linear elasto-plasticity (most plastics)

– Hyperelastic with plasticity (elastomers)

• Fiber orientation (fiber-filled plastics)

• The promise of validation


Data for Injection-mold Analysis

• Viscosity vs. shear rate and temperature

• Thermal conductivity vs. temperature

• Specific heat vs. temperature

• Transition temperature

• PVT

• Shrinkage data

– Mechanical properties

– CRIMS (Moldflow)

?

?

?


Transitions: No-flow Temperature

• When does the polymer

solidify in the mold?

• Different test methods

produce different transitions

• Transition inconsistency in

semi-crystalline polymers

– super-cooling

– cooling rate effect

– viscoelastic effects

• Impact on simulation unclear

1.E+3

1.E+4

1.E+5

100 120 140 160 180 200Temp (C)

Eta

(P

a.s

)

DMA cooling dynamic scan

(semi-crystalline polymer)


How to Measure PVT

0.90

0.95

1.00

1.05

1.10

1.15

100 150 200 250 300 350

Temperature °C

sp.v

ol (c

m3/g

)

PVT 10 MPa, Isobaric Heating

PVT 10 MPa, Isobaric Cooling

PVT 40 MPa, Isobaric Cool

PVT 40 MPa Isothermal Cool

Initial PVT data with injection-

molded sample has lower solid

density

Subsequent slow-cooled isobaric

sample has higher, incorrect

density

Shrinkage predictions can be affected


Accounting for Rate Effects in PVT

0.90

0.95

1.00

1.05

1.10

1.15

1.20

25 75 125 175 225 275 325

Temperature °C

sp.v

ol (c

m3/g

)

-10

0

10

20

30

40

50

60

100 C/min Kinetics

0 MPa

PVTmodel 0 MPa, 3°C/min

PVT 10 MPa, 3°C/min

DSC 0 Mpa, 100°C/min

• Possible to correct PVT data using DSC high-cooling-rate curves (H. Lobo, ANTEC 1999)

• Strategy is incorrect

– DSC is quiescent: high super-cooling effect

– Shear effects in molding mitigate super-cooling effect

(Kennedy, Janeshitz-Kriegl)


Solid State Behavior of Polymers

400%

Brittle plastic

(linear-elastic)

Ductile plastic

(elasto-plastic) Elastomer

(hyper-elastic)


Effect of Environment: Temperature

• Properties and dependencies

change with temperature

– Modulus

– Ductile-brittle

transitions

– Rate dependency


Effect of Environment: Moisture

Nylon

DAM vs. 50% RH


Effect of Environment: In-vivo

UHMWPE, 37C

(dry vs. saline soak, 30 days)


Models for Ductile Plastics

• True stress-strain curves – UTM with extensometers

– Testing to yield or break

• Material model: elasto-plasticity – Reduce to elasto-plasticity based on yield point

– Bilinear

– Multilinear

• Usage – Large deformation

– von Mises yield


Elasto-plasticity in Metals

• Evaluate a modulus

• Define elastic limit

• Calculate multi-point

plasticity

where,

E = elastic modulus (MPa)

σt = true stress (MPa)

pt E


Comparing Metal to Plastic

Aluminum

Polycarbonate


Polymer Elasto-plasticity

• Non-linear elasticity

• Elastic limit well below

classical yield point

• Significant plastic strains

prior to yield

• Post-yield with necking

behavior 0

5

10

15

20

25

30

35

0.0 5.0 10.0 15.0 20.0

Engineering Strain (%)

En

gin

ee

rin

g S

tre

ss (

MP

a)

data

Plastic Point


Modeling Options

Fidelity to plastic point Fidelity to curve shape


Applying Abaqus FeFp Model

• Non-linear hyper-

elasticity with pre-yield

plasticity

• Accurate representation

of elastic behavior

• Accurate representation

of plasticity

(Lobo & Hurtado, Abaqus 2006)


A True Representation of Plasticity

plas10

0

0.5

1

1.5

2

2.5

0 2000 4000 6000 8000

time, s

ex

ten

sio

n, m

m

0

200

400

600

800

0 200 400 600 800 1000

time (sec)

Lo

ad

(N

)

0

0.5

1

1.5

2

0 200 400 600 800 1000

time (sec)

exte

nsio

n (

mm

)


Post-yield Ductile Behavior

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Strain mm/mm

Str

ess

MP

a

UTM1-39.62-1

UTM1-39.62-2

Yield point

Necking starts

Necking propagation


Digital Image Correlation (DIC)

• Stereo camera system

(ARAMIS)

• Simultaneous XYZ

dimension change

• Complete surface is

measured

• Post-measurement

selection of region of

interest (Lobo et al., LS-DYNA 2013)


Measuring Post-yield Stress-Strain

0

20

40

60

80

100

120

140

160

180

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

True Strain (unitless)

Tru

e S

tre

ss (

MP

a)

1 mm GL

2 mm GL

4 mm GL

25 mm GL

50 mm GL

y x

z


Reasonable Post-yield Approximation


Fiber-filled Plastics

• Spatial orientation of fibers

– Properties vary spatially

• Can be approximated

– Worst case: use cross-flow data

• NEW: fiber-orientation material modeling

– Perform injection-molding simulation

– Obtain fiber orientations

– Calculate local orientation-based properties

– Send to FEA

Source:e-Xstream


Typical Test Protocol

• Mold long plaques

– Edge gated: short end

– Fully developed flow

– High fiber orientation

• Cut test specimens

– 0°, 90°, 45°, …

• Obtain true stress-strain data

• Calibrate material model


Example: Airbag Housing

Source:e-Xstream


Impact on Failure

Source:e-Xstream

With Fiber Orientation

Isotropic


The Promise of Validation

• Open loop validation

– Carefully designed benchmark models

– Not real-life component

– Multi-mode case

– Well-defined boundary conditions

– Load cases reproducible in virtual and real life


Dynamic FEA TestBench Model

• ASTM D3763 falling dart impact

• Multi-axial loading with well-defined boundary conditions

– Dart with a ½-inch rounded tip

– Dart weight of 22.68 kg

– Disk dimensions • Thickness = ~3 mm

• Diameter = 76 mm

– B.C.s: fixed edges

– I.C.s: initial velocity of 3.3m/s


Model Complexities

• Stress modes

– Biaxial

– Shear

– Bending

• Rate-dependent plasticity

• Complex failure


Simulation v. Test

• Percent error at peak force

• Time: -1.0%

• Distance: -0.52%

• Force: 1.3% Force vs Time

-500

0

500

1000

1500

2000

2500

3000

3500

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Time (s)

Fo

rce (

N)

Lab

LS-Dyna

Force vs Displacement

-500

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25

Displacement (mm)

Fo

rce (

N)

Lab

LS-Dyna


In Closing...

• Do not oversimplify

• Understand model limitations

• Use appropriate data

• Use self-consistent data

• Validate where possible


Acknowledgements

• J. Hurtado, Abaqus – FeFp model

• Sylvain Calmels – e-Xstream Engineering

• Brian Croop, DatapointLabs

• Dan Roy, DatapointLabs – DIC

• Megan Lobdell, DatapointLabs – Validation


Remembrance

• Dr. VW Wang (passed away Dec 10th 2014)

• Authored the first science-based injection-molding simulation code (Cornell University, PhD 1985)

• Founder of C-MOLD

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