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Effective Inelastic Response of Polymer Composites by Direct Numerical Simulations

Effective Inelastic Response of Polymer Composites by Direct Numerical Simulations. A. Amine Benzerga Aerospace Engineering, Texas A&M University. With: R. Talreja , K. Chowdhury , X. Poulain , A. DeCastro and B. Burgess. Background/ Motivation. Experiments. Polymer Model.

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Effective Inelastic Response of Polymer Composites by Direct Numerical Simulations

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  1. Effective Inelastic Response of Polymer Composites by Direct Numerical Simulations A. Amine Benzerga Aerospace Engineering, Texas A&M University With: R. Talreja, K. Chowdhury, X. Poulain, A. DeCastroand B. Burgess

  2. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Li et al. (JAE, July 2009) Background & Motivation • Goal: Develop a strategy aimed at predicting durability of structural components • Basic ingredient: Reliable physics-based inelastic constitutive models • Example: Composite blade containment casing for jet engines • Wide range of temperatures (service conditions) • Wide range of strain-rates (design for impact applications) • Ideal for implementing a multiscale modeling strategy: • the material is heterogeneous at various scales; • the physical processes of damage occur at various scales July 23rd2009 2

  3. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Background & Motivation July 23rd2009 3

  4. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression softening hardening rehardening elastic Typical Response of a Polymer T=298K Compression Epon862 Littel et al (2008) July 23rd2009 4

  5. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Temperature & Rate sensitivity Effect of Temperature (Epon 862) Strain-rate effects (Epon 862) 298K 323K 353K Tension Compression Littel et al (2008) Littel et al (2008) The behavior of polymers is temperature and strain-rate dependent July 23rd2009 5

  6. Polymer model Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Modified Macromolecular Model (Chowdhury et al. CMAME 2008) Specification of plastic flow: Pointwise tensor of elastic moduli Jaumann rate of Cauchy stress Assume additive decomposition where and Effective strain rate: Flow rule: (define direction of plastic flow) Effective stress: Deviatoric part of driving stress: Back stress tensor Strain rate effects Describe pressure sensitivity Material parameters Internal variable July 2009 6

  7. Evolution of back stress: • Evolution of athermal shear strength s : Nota Bene: Original law (Boyce et al. 1988 ) Polymer Model Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression July 2009 7

  8. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Temperature sensitivity Pressure sensitivity Small strain softening • Material parameters : • Elastic constants : Large strain hardening, cyclic response Pre-peak hardening Strain-rate sensitivity • Related to inelasticity : Forward flow stress s A, h0 h3 s1 f Reverse flow stress s2 s0 Littell et al. (2008) s N CR e E, n Material parameteridentification e July 18th 2009 8

  9. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Material parameteridentification 1- Uniaxial tension, compression and torsion tests at fixed strain-rate : 2- Tensile data at various temperatures and strain-rates : 3- s0 is determined from : 4- s1 is determined from : (at lowest temperature at given strain-rate) 5- s2 is determined from : (at lowest temperature at given strain-rate) 6- Large strain compressive response and/or unloading response at fixed strain-rate and temperature : 7- Specific shape of stress-strain curve around peak : July 18th 2009 9

  10. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Model validation 620/s 10-1/s 10-3/s Tension at T=323K July 18th 2009 10

  11. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Model validation T=298K T=323K T=353K Tension at 10-1/s July 18th 2009 11

  12. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Model validation 1600/s 700/s 10-1/s 10-3/s 10-5/s Compression at T=298K July 18th 2009 12

  13. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Numerical Homogenization • Principles of Numerical Simulations : • Unit cell composed of Epon 862 matrix (not optimized set), interface of fixed thickness and carbon fiber • Plane strain conditions • Damage not included • Objectives : • Investigate evolution of mechanical fields (strains, stresses) in unit-cells • Relate micro/macroscopic behaviors • Input for understanding of onset/propagation of fracture x2 Epon 862 b interface C fiber x1 a July 18th 2009 13

  14. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Numerical Homogenization • Geometries : • Height: b= 100 • Cell aspect ratio: Ac= 2 • Fiber volume ratio: Vw =0.1 • Fiber aspect ratio: Aw=variable July 18th 2009 14

  15. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Numerical Homogenization • Numerical implementation : • Convective representation of finite deformations (Needleman, 1989) • Dynamic principle of Virtual Work: • FEM : Linear displacement triangular elts arranged in quadrilaterals of 4 crossed triangles. • Equations of Motions : They are integrated numerically by Newmark-B method (Belytshko,1976) in an explicit FE code. • Constitutive updating is based on the rate tangent modulus method of Pierce et al (1984) Surface traction Kirchhoff stress Green-Lagrange strain July 18th 2009 15

  16. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Numerical Homogenization • Calculations at E22=0.10: • Tension • Fiber : AS4 (sim. To T700) • Et= 14 GPa • ut=0.25 • Geometries : • Height: b= 100 • Cell aspect ratio: Ac= 2 • Fiber volume ratio: Vw =0.2 • Fiber aspect ratio: Aw=1 (cyl.) • Dramatic effect of fiber volume ratio on strengthening at all fiber aspect ratios July 18th 2009 16

  17. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Numerical Homogenization • Calculations at E22=0.10: • Compression • Fiber : AS4 (sim. To T700) • Et= 14 GPa • ut=0.25 • Geometries : • Height: b= 100 • Cell aspect ratio: Ac= 2 • Fiber volume ratio: Vw =0.2 • Fiber aspect ratio: Aw=1 (cyl.) • Plastic strains: • Localization and maxima : same as in tension • Hydrostatic stresses : • Building-up in thin ligament between fiber and edge • Aw=6 : proximity of fiber to top surface where stresses are computed may explain strengthening? July 18th 2009 17

  18. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Damage Progression Objective: Develop an experimentally-valided matrix cracking model for use in mesoscale analyses July 18th 2009 18

  19. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Damage Progression Finding: Irrespective of the microscopic damage mechanisms, the fracture locus of the polymer matrix is pressure dependent and is temperature-dependent July 18th 2009 19

  20. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Asp et al., 1996 Benzerga et al.(JAE, 2009) Damage Progression TENSION (PMMA) DEBONDING : July 18th 2009 20

  21. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression Damage Progression COMPRESSION (PMMA) DEBONDING : Asp et al., 1996 July 18th 2009 21

  22. Background/ Motivation Experiments Polymer Model Material Parameter Identification Model Validation Numerical Homogenization Damage Progression • Initiation: micro-void nucleation • Propagation: Drawing of new polymer from active zone Sternstein et al, 1979 Gearing et Anand, 2004 • Breakdown: Chain scission and disentanglement Element Vanish Tech. of Tvergaard, 1981 Gearing et Anand, 2004 Polymer Fracture Model July 18th 2009 22

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