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Finite Element Modeling of Thermoplastics at Different
Temperatures
J.S. Bergström, Ph.D.Veryst Engineering, LLC
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Outline of Presentation
‣ Experimental Data for Polycarbonate (Lexan)
‣ Calibration of Plasticity and Creep Models
‣ Parallel Network Model:
– Theory
– Calibration
– FE Simulation
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Problem Statement
‣ Limited experimental data available from the raw material manufacturer (non-linear viscoplastic material)
‣What material model to select?
Goals:• Demonstrate how to effectively use both creep and uniaxial tension data• Demonstrate the material model calibration procedure• Demonstrate the use of an advanced user-material model in Abaqus
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Experimental Data
•Uniaxial tension at different temperatures
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Experimental Data
-60 -40 -20 0 20 40 60 80 100 120 140
0
500
1000
1500
2000
2500
3000
f(x) = -3.39x + 2439.93R² = 0.97
Temperature (deg C)
Yo
un
g's
Mo
du
lus
(M
Pa
)
• Young's modulus as a function of temperature
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Experimental Data
•Uniaxial creep experiments were performed at stresses between 15 MPa and 40 MPa
Region for creep experiments
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Experimental Data
•Creep strain as a function of time for different stress values
27 days
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Experimental Data
•Creep compliance as a function of time and stress
• The material is NOT linear viscoelastic
27 days
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Experimental Data
•Uniaxial fatigue data
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Material Model Selection• Linear viscoelasticity
–not-sufficient since the material is non-linear viscoelastic
• Elastic-Plastic with rate-dependence• Elastic-Plastic with creep• Viscoplastic user-material model
–Parallel Network Model from the Veryst Engineering PolyUMod library
What material model works best?
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Metal Plasticity Model – Calibration
*Elastic*Plastic*Rate Dependent, type=power law
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Metal Plasticity Model
The rate-dependent plasticity model does not capture the non-linear creep response very well
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Metal Creep Model – Calibration
*Elastic*Plastic*Creep, law=strain
The material model calibration was performed using the MCalibration software from Veryst Engineering. This software can calibrate any material model in Abaqus.
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Metal Creep Model
The plasticity-based creep model does not capture the non-linear creep response at high stresses
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Parallel Network Model (PNM)*
Neo-Hookean with piecewise linear temperature dependence
Neo-Hookean with piecewise linear temperature dependence
Power-law flow with exponential yield evolution and piecewise linear temperature dependence
*The PNM is commercially available for Abaqus/Standard and Abaqus/Explicit from Veryst Engineering
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Viscoplastic Flow Behavior
Power-law flow rate:
Exponential yield evolution:
γp = viscoplastic flow rateτ = driving shear stressτhat = flow resistancem = flow activation exponentialfp = 1
fe = yield evolution factor
fθ = piecewise linear temp factor
ff = final yield evolution factor
εpmax = max plastic strain
εhat = characteristic transition strain
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Damage Model
Rate of damage accumulation:
No damage (D=0) at time t=0
Element failure when D > 1
σe = Mises stress
[t0, σref , m] = material parameters
This damage model enables fatigue predictions
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Material Model Calibration
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Material Model ParametersNetwork A Neo-Hookean hyperelastic: [µ,κ] [174 MPa, 2000 MPa]
Network A temperature dependence: 5 pairs of [T, f] values
[(243 K, 0.64), (273 K, 0.53), (296 K, 0.76), (333 K, 0.67), (363 K, 0.60)]
Network B: Neo-Hookean hyperelastic: [µ,κ] [601 MPa, 2000 MPa]
Network B hyperelastic temperature dependence: 5 pairs of [T, f] values
[(243 K, 1.11), (273 K, 1.24), (296 K, 1.28), (333 K, 1.12), (363 K, 1.30)]
Network B flow: [tauHat, m] [14.2 MPa, 33]
Network B flow evolution: [ff, epsHat] [3.2, 0.0037]
Network B flow temperature dependence: 5 pairs of [T,f] values
[(243 K, 0.006), (273 K, 0.023), (296 K, 18.1), (333 K, 4243), (363 K, 12784)]
Damage accumulation model: [t0, σref, m] [5e-6 s, 50 MPa, 1]
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Model Predictions
The PNM captures the strain-strain response in monotonic loading at different temperatures.
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Creep Predictions
The PNM captures the non-linear creep response.
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Creep Predictions
Comparison between experimental and predicted creep behavior
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Damage Model Predictions
Predicted damage accumulation during a monotonic uniaxial tension simulation
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Damage Model Predictions
Predicted fatigue behavior from the damage model
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Exemplar FE Study‣ PC hook loaded with an
increasing force
‣ The top of the hook was fixed
‣ Abaqus/Explicit with 27k C3D8R elements
‣ Failure at a critical damage level
‣ Room temperature
Fixedend
Force
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Exemplar FE Study
Large pre-existing notch
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Damage Model Predictions
Configuration just before final failure
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Summary
‣Thermoplastic materials are non-linear materials: viscoplasticity, creep, failure
‣Abaqus built-in plasticity models with strain rate dependence and creep can capture some of the experimental data
‣Advanced user-material models (UMAT/VUMAT) can be used to accurately predict almost any aspect of isotropic and anisotropic polymers
