Applicability of Engineering Models in Multiscale Modeling of Natural Fiber Hygro- Elastic Properties

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1 Applicability of Engineering Models in Multiscale Modeling of Natural Fiber Hygro- Elastic Properties Janis Varna and Eri Marlund Department of Applied Physics and Mechanical Engineering

2 Where is Luleå?

3 Outline Multiple length scales in natural fibers Suitable models for each scale Homogenized properties (stiffness and moisture expansion) on each scale Effect of different parameters Composite properties (stiffness and moisture expansion) Conclusions

4 Multiple length scales Composite or mat with fiber orientation Elastic properties Moisture expansion Aligned fiber composite (wood) Fiber wall S,S etc layers Lignin, Hemicellulose, Cellulose

5 Objective To analyze stiffness and moisture expansion of natural fibers and their composites Approach Analyze suitable models for lining different scales Perform multiscale analysis

6 Composite with fiber orientation Laminate analogy Suitable models Fibers and aligned composite (wood) CCA= concentric cylinder assembly 3... N Orthotropic materials in local axes CCA Fiber wall Laminate theory S,S etc layers Elastic properties Moisture expansion CCA, rule of mixtures Lignin, Hemicellulose Cellulose

7 Softwood fiber Ultrastructure of the fiber wall Lumen S3 S S P (L/d ) Long cylinder structures

8 Layer properties: unit cell Constituent E (GPa) E (GPa) G (GPa) 3 Cellulose Hemicellulose Lignin Model B r 3 r r Lignin Hemicellulose + Cellulose Volume fractions are different in different cell wall layers

9 The Concentric Cylinder Assembly An N-phase cylinder assembly with orthotropic constituents 3... N Calculates all engineering constants of the homogenized assembly Suitable for natural fibers (having layered structure) Modulus in axial direction 3 C H L E V E VC E VH E VLE Rule of mixtures models Transverse modulus and shear modulus ( Halpin-Tsai with two step homogenization) Poisson s ratio 3 C H L V VC VH VL C+H model: cellulose in hemicellulose matrix (C+H)+L model: C+H in lignin matrix

10 Moisture swelling in natural fiber composites Definition H H M i C ij j H j H is free swelling strain in direction due to moisture weight content change by M Average moisture content CCA model has been applied on cell wall layer and also on fiber scale M assembly M assembly V Input: moisture contents, assembly V expansion coefficients in constituents

11 S Layer properties Property Model B ROM models Model B r 3 r r Lignin Hemicellulose + Cellulose E (GPa) E (GPa) G (GPa).. G 3 (GPa) According to CCA the parameter in H-T relationships for transverse modulus is different.

12 Fiber wall=laminate (symmetric!!!) Lumen S3 S S P Lumen S3 S S P Matrix Stiffness in local axes In global axes m cos E 4 4 m n m n 664m n Laminate stiffness matrix Earlywood Latewood Thicness Angle Thicness Angle P. Random. Random S S S E z A ij ij Laminate compliance matrix S h A Cell wall elastic constants S E h S

13 Influence of Helical Fiber Structure The axial deformation is coupled with torsion z a) r L T b) z r z r r zr z z r r zr z Using orthotropic fiber wall models: True modulus or in situ modulus?

14 Fiber or aligned fiber assembly: Fiber with homogenized fiber wall CCA models Fiber with all fiber wall layers Lumen r 3 matrix S3 r r cell wall + wood fiber S S lumen Matrix Volume fraction of the lumen in fiber V lumen.36 Resin Properties E m 3.GPa m.35

15 Hygroexpansion coefficient Example : hygroexpansion of a fiber T.5.5 L MFA (deg) Solid line = individually included layers Dashed line = homogenized layers (CLT) + CC

16 E z (GPa) zr Fiber with Helical Structure (composites) Two extreme cases: (i) No rotation and (ii) free rotation Layers E (GPa) E (GPa) G (GPa) G 3 (GPa) 3 S and S S Free rotation.6 No rotation 5 No rotation Free rotation MFA (deg) MFA (deg) V f = 5 % ; dashed line = empty lumen ; solid line = filled lumen

17 Hygroexpansion coefficient Aligned composite: hygroexpansion T.3.. L V f Solid line = filled lumen Dashed line = empty lumen

18 Axial Modulus (GPa) Shear Modulus (GPa) Aligned composite: effect of microfibril angle in S V lumen V f Earlyw ood Com posite, Vf=.4 filled empty 3 4 Microfibril Angle,4,,,8,6,4,,,8 Earlyw ood Com posite, Vf=.4 G-filled G-empty G3-filled G3-empty 3 4 Microfibril Angle

19 Real Composite f n a n cos n Relative frequency i comp ij ij f d y z x Use the UD layer properties!

20 Elastic Modulus (GPa) Poisson's ratio Random composites comp ij f ij f d comp comp 8 comp a 8 3 a a 6 3 a a 4 a 66 a 4 Effect of fiber content a 66 comp comp G 66 comp comp comp comp comp comp E G Random Com posite Random com posite,3,3 8,8 6,6 4 filled empty,4, filled empty V lumen.36,,3,4,5,6 Vf,,,3,4,5,6 Vf

21 Conclusions The hierarchical structure of the natural fiber composite with large differences in scales justifies the use of the multiscale approach Models covering the scales from chemical constituents to macrocomposite with a given fiber orientation distribution are applied Simple rule of mixtures models may be successfully used in many cases