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Constitutive Modeling of Shape Memory Polymers

Constitutive Modeling of Shape Memory Polymers

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  • 1. Constitutive Modeling and Simulation of Shape Memory Polymers Defense Proposal ADVISOR: DR I.J. RAO DATE : 11/17/2008 MAHESH KHANOLKAR
  • 2. Outline
    • Introduction
      • What are shape memory materials.
      • Different types of shape memory materials
      • How shape memory polymers work
    • Modeling
      • Natural Configurations
      • Thermo-mechanical Framework
      • Model development
          • Glassy SMP Model
          • Application of Crystallizable SMP Model
    • Simulations and Results
    • Conclusions
  • 3. What Are Shape Memory Materials?
    • “ Remember” the original shape even after undergoing significant deformation
    • Revert back to original shape by a suitable trigger
      • Most common trigger: heating above a recovery temperature, TR
      • Other triggers: Magnetic fields, electromagnetic radiation etc.
    Trigger
  • 4. Overview of SMP’s
    • Mechanism for “remembering” original shape and transient shape.
      • Common mechanisms: Entanglements, Crosslinks and hard-domains.
      • Transient shape fixed usually with crystalline phase or the glassy state.
    • Revert back to original shape by heating.
      • Heating above Tm (if the crystalline phase is used to fix the transient shape)
      • Heating above Tg (if the glassy phase is used to fix the transient shape)
  • 5. How Shape Memory Polymers Work Original: Chemical Cross-Links Temporary: Glassy Phase Lendlein et al. Original: Crystalline Hard domains (Physical cross-links) Temporary: Crystallites Original: Chemical Cross-Links Temporary: Crystallites
  • 6.
      • Shape Memory Alloys (SMA)
      • - Extensive work has been carried out in the last 10 years.
      • - Constitutive equations and modeling fairly well developed.
      • Shape Memory Polymers (SMP)
      • - Advantages
      • - SM effect can be seen for large deformation
      • - Manufacturing methods are conventional and cheap
      • - Bio-compatible
      • - Recovery temperature can be adjusted
    • - Disadvantage
      • - Actuation force (SMP) << Actuation force (SMA)
    Types of Shape Memory Materials
  • 7. Shape Memory Polymers Representative Application Biodegradable Shape Memory Polymer for Suturing wounds. (Langer 2002)
  • 8. Shape Memory Polymers Representative Application   Time series photographs that show the recovery of a shape-memory tube. (a)- (f) Start to finish of the process takes a total of 10 s at 50°C (Marc Behl et al 2007).
  • 9. Shape Memory Polymers
    • Applications
      • SMP fibers for comfort wear
      • MEMS devices, temperature sensors
      • Damping elements
      • Intravenous needles and implantable
      • Medical device
      • Films and fibers used in insulation applications
      • Rewritable digital storage devices
      • Morphing Aircraft Wings
      • many more…
  • 10. Shape Memory Mechanism in CSMP’s Deform Cool Unload Heat Amorphous polymer Cross-link Crystallite Legend Melting Crystallization T > T r T < T r State 1 State 4 State 2 State 3 Stretch Nominal Stress 1 2 3 4
  • 11. Shape Memory Mechanism in GSMP’s Deform Cool Unload Heat Amorphous polymer Cross-link Glassy polymer Legend Glass Transition T > T r T < T r State 1 State 4 State 2 State 3 Stretch Nominal Stress 1 2 3 4
  • 12. Modeling (Salient Features) ‏
    • Constitutive Modeling – Mathematical description of how a material responds to deformations.
    • It is a relation between two physical quantities (often described by tensors).
    • Modeling of polymers– Write equations for stress tensor in terms of deformation gradient.
    • Change in Entropy and internal energy is macroscopic manifestation of changes in microstructure.
    • Non-linear response.
  • 13. Modeling (Salient Features) ‏
    • Above Tr the material behavior is rubber like
      • Hard domains act as cross-links in thermoplastic SMP’s
      • Chemical cross-links in the case of thermoset SMP’s
    • Cooling in deformed shape causes partial
    • crystallization / glass transition
      • Crystallization – drop in stress
      • Glass-Transition- stress remains constant or increases
      • Semi-crystalline polymer is anisotropic
    • Unloading the the specimen below Tr, a small recovery strain observed.
    • Heating above Tr, return to original shape
  • 14. Modeling Framework
    • Need to account for the influence of each phase
      • Amorphous rubbery phase above the recovery temperature.
      • Semi-crystalline polymers: amorphous and crystalline phases
      • Glassy polymers: amorphous and glassy phases (mixture region)
      • Each phase can have its own stress free state
  • 15. Modeling - Natural Configurations
    • In most traditional approaches the response of the material is assumed to be known from a single configuration.
    • Well known that a body can be stress-free in more than one configuration
      • Solid which can exist in two different phases (e.g. Austenite and Martensite) with different symmetries.
      • Polymers, which can exist in the amorphous and crystalline phase
    Deform Unload
  • 16. Modeling - Natural Configurations Natural configurations associate with a viscoelastic melt
  • 17. Modeling - Glassy SMP (Amorphous Rubbery Phase)
    • Model as an incompressible hyperelastic material
    • Stress is given by:
    • Based on Rubber elasticity: entropic in origin.
  • 18. Modeling – Glassy SMP
    • 100 % conversion into glass during vitrification
    • Glassy phase is viscoelastic
    • Glassy phase is formed in stressed state
    Little Change in length on cooling, iso-stress, Mather(2006)
  • 19. Modeling – Glassy SMP (Mixture of rubbery and glassy phase)
    • Stress in nascent glass = stress in rubbery phase
    • Stress is given by:
    Current configuration of glassy phase Current configuration of amorphous phase Natural configuration of amorphous phase
  • 20. Modeling – Glassy SMP (Mixture of rubbery and glassy phase)
    • Constrained Cooling below the glass transition temperature.
    • Increase in thermal stress.
    • Natural configurations evolve as the material is cooled/deformed.
    • Natural configuration associated with the previously formed material shifts to a new position.
    • Increase in mechanical deformation gradient, decrease in thermal deformation gradient, so that the total deformation gradient remains constant (constrained cooling).
  • 21. Modeling – Glassy SMP (Mixture of rubbery and glassy phase) Natural Configurations associated with the glassy-rubbery phase solid phase mixture
  • 22. Modeling – Glassy SMP Cycle - Equations
    • Loading:
    • where T is the stress in the rubbery part of the polymer and µ a is the modulus
    • Cooling:
  • 23. Modeling – Glassy SMP Cycle - Equations
    • Unloading
    • Melting
  • 24. Modeling – Glassy SMP Cycle Stress–strain–temperature diagram illustrating the thermo mechanical behavior of a shape memory polymer under different strain/stress constraint conditions
  • 25. Simulation and Results (Uniaxial Deformation Cycle GSMP) Stress vs Strain for the complete SMP Cycle T L (K) 273 T g (K) 343 T H (K) 358 (Mpa) 8.8 MPa (Mpa) 750 MPa
  • 26. Simulation and Results (Uniaxial Deformation Cycle GSMP) Stress vs Temperature
  • 27. Simulation and Results (Uniaxial Deformation Cycle GSMP) Stress vs Strain plot (Yiping Liu et al, 2005)
  • 28. Nanoparticle Reinforced Glassy SMP
    • Reinforcing Glassy SMP with nanoparticles increases its stiffness.
    • Rubbery Phase:
    • Glassy phase:
    • where
    • K is the concentration of nanoparticles
  • 29. Simulation and Results (Uniaxial Deformation Cycle GSMP) Effect of Nanoreinforcemnts Elastic moduli of the SMP and SMP composite at 26 and 118°C (Yiping Liu et al 2003) .
  • 30. Simulation and Results (Uniaxial Deformation Cycle GSMP) Effect of Nanoreinforcemnts Stress vs Strain Above the glass transition
  • 31. Torsion of a Cylinder Undeformed Cylinder Deformation after applying Torsion Motion: Deformation gradient: M (in sec -2 ) (MPa) (MPa) 0.33 120 1200 0.00007 0.256 50
  • 32. Simulation and Results: Torsion of a Cylinder Moment vs Time (Torsion of a cylinder)
  • 33. Simulation and Results: Torsion of a Cylinder Moment vs Shear (Torsion of a cylinder)
  • 34. Simulation and Results: Torsion of a Cylinder Shear vs Time (Torsion of a cylinder)
  • 35. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS)
    • Shape memory cycle on a single element using an UMAT (User Defined Material)
    • A strain of 100% (large deformation) has been applied to the element and the resulting deformation is seen
    • Steps involved in the shape memory cycle.
      • Large Deformation on the single element
      • Constraining the element to retain its temporary shape
      • Removing load – Small amount of strain recovery
      • Return to Original Shape
  • 36. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Applied load to the Element
  • 37. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 1 Large Deformation on the single element
  • 38. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 2 Constraining the element to retain its temporary shape
  • 39. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 3 Removing load – Small amount of strain recovery
  • 40. Simulation and Results: Large Deformation on a single cubic element using UMAT (ABAQUS) Step 4 Back to Original Shape
  • 41. Conclusion and Future Work
    • Developed a model for SMP’s undergoing glass transition using the notion of natural configurations.
    • Developed model takes in to account the thermal expansion of polymers.
    • Reinforcements have a impact (increased modulus) on SMP’s.
    • Illustrated application of a CSMP Model for a non-homogenous deformation (Torsion of a cylinder).
    • Illustrated application of CSMP Model using ABAQUS.
    • Further develop GSMP model within a full thermodynamic framework.
    • Solve inhomogeneous boundary value problems of importance.
  • 42.
    • THANK YOU