Micromechanics of wood Fiber under axial tension; experiment …cost-fp0802.tuwien.ac.at/fileadmin/mediapool-cost/... · 2018-06-05 · Micromechanics of wood Fiber under axial tension;

Paper Mechanics Workshop on “Single Fiber Testing and Modeling”COST Action FP0802, Innventia: November 4-5, 2009 / Stockholm

Micromechanics of wood Fiber under axial tension; experiment and modeling

Parviz NAVI*Marjan SEDIGHI-GILANI

Institute of Materials Science, Swiss Federal Institute of Technology, Switzerland*Bern University of Applied Sciences, Biel, Switzerland

1

Paper Mechanics Workshop on “Single Fiber Testing and Modeling”

Introduction3- Study of the

tensile behavior of fsingle wood fibers

4- Results interpretation

2- Morphological study of wood 1-Tensile behavior ofinterpretation,

Micromechanical approach

yfiber

microstructure, CLSM

1 Tensile behavior of thin wood specimens

2


1. Tensile behavior of thin wood specimens ~100m

A thin wood specimen

Experimental apparatus

3


Failure mode of longitudinal specimens under tensile forces

4


Force-displacement curve, sampledi i 160 20 4 3 b ittl

Force-displacement curve in thin tissu, di i 28 2 74 19 3 d tildimensions 160x20x4 mm3 ,brittle dimensions 28x2.74x.19 mm3 , ductile

5


ce(N

)Fo

rc

Displacement(μm)

• Force-extension behavior of a thin wood (30 mm x 3 mm x 0.14 mm) under controlled cyclic tensile test

Navi et al (1995), Wood science and technology

6

• Hypothesis• Fibers are considered non-uniform• Wood tissue with thin thickness

becomes non-uniform• Thicker elements represent more

uniformity

C• Consequences:• Under tensile forces the thick elements

(uniform) illustrates strain localization with a brittle failure

Schematically representation of a thin wood section with a brittle failure

• Non-uniform thin elements undergo elasto-plastic behavior with ductile failure


Latewood

2. Study the morphology and variation of MFAs of the spruce fibers

Latewood Ray cell

EarlywoodSingle fiber Fiber ultra structure

Thi ti t tThin tissu structure

8


110

120

y

80

90

100

Pixe

l int

ensi

ty

I=33.92 cos 2 (P-24)+70.78 Fluorescent intensity curve measured CLSM

60

70

-90 -70 -50 -30 -10 10 30 50 70 90

Angle of incident polarization, P (degree)

by CLSM for the marked area, MFA=24º.The Method first was developed by

JANG (1998) equation : I=A cos2(P- )+I

9

Angle of incident polarization, P (degree) I=A cos (P- )+I min

Confocal laser scanning microscopy CLSM


Confocal laser scanning microscopy, CLSMRadial face of an earlywood fiber

Bordered pit

Bordered pit

Sedighi-Gilani ,et al. (2005), wood and fiber scienceSedighi-Gilani ,et. al. (2005), , Holz Roh-Werk

10

Bergander , et al. (2002), J. Wood Science


Inside the border of a pit in an earlywood fiber

Measured data show the pattern of MFA

Schematic sketch (a proposition)

11


Reduction of MFA between bordered pits

60

70

80

90

sity

I=42.02 cos2(P-(0))+35.04

30

40

50

Pixe

l int

en

I=25.26 cos2(P-(16))+14.31I=25.26 cos2(P-(-16))+14.31

10

20

-90 -70 -50 -30 -10 10 30 50 70 90

Angle of incident polarization, P (degree)

Two proposed patterns

MFA of an area with two crossed planes of microfibrils (MFA=16º, -16º) is the resultant of the

two directions (MFA=0º)

12

( )


Latewood fiber

itpit

MFA uniformity in Latewood fiber

13

MFA uniformity in Latewood fiber


Cross-field zone in earlywood fibers

-Microfibril angles in S2 are not uniform-Microfibril angles in S2 are not uniform-Fiber can be considered inhomogeneous

14


3. Tensile behavior of Wood fiber

•Sample preparation for test, Kersavage (1973)

15


micro-band with two screws for

Sample

micro band with two screws for adjusting the fiber alignment

a) Displacement screws, b) force transducer, c) circular steel piece, d) micro-band

Perez et al (2000),wood and wood fiber composites conference Semi-circular steel piece with

16

pconical hole


4 E i t ti R lt I t t ti d M d li

1

4. Experimentation, Results, Interpretations and Modeling

0.7

0.8

0.9

)MFAs=20.5, 21, 35 º

MFAs=19,14,24,20 ºMFAs=23, 24.5, 24.5 º

0.4

0.5

0.6

Stre

ss(G

pa)

MFAs=24, 26 º

0.1

0.2

0.3MFAs=60.5, 59.5, 60º

00.0 2.0 4.0 6.0 8.0 10.0 12.0

Strain (%)

Stress-strain curves of dry wood fibers under tensile test, measured local MFAs in some points along fiber have been mentioned

17


0.35 Stress-strain curve of two earlywood fiber (32° d 37°) d li t il l di

0.20

0.25

0.30

s(G

pa)

(32° and 37°) under cyclic tensile loading-unloading test

0.05

0.10

0.15

Str

ess

Observation

1 The results show plastic deformation

32°0.00

0.0 5.0 10.0 15.0 20.0

Strain (%)

0.25

0.30

0.35

pa)

1- The results show plastic deformation2- History dependent behaviour3- Increasing the Young’s modulus with increasing applied force4 Elasticity domain increases

37°

0 05

0.10

0.15

0.20

Stre

ss(G

p 4- Elasticity domain increases

180.00

0.05

0.0 5.0 10.0 15.0 20.0

Strain (%)

Fig 2 Under tensile forceFig 1 Under controlled cyclic tensile force

4.1 Modeling and micromechanical approach

Fig. 2 Under tensile force

0 35

Fig. 1 Under controlled cyclic tensile force

1

MFA 19 14 24 20 ºMFA 23 24 5 24 5 º

0 15

0.20

0.25

0.30

0.35

0.5

0.6

0.7

0.8

0.9

ess(

Gpa

)

MFAs=20.5, 21, 35 º

MFAs=24, 26 º

MFAs=19,14,24,20 ºMFAs=23, 24.5, 24.5 º

0.00

0.05

0.10

0.15

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

S i (%0

0.1

0.2

0.3

0.4Stre

MFAs=60.5, 59.5, 60º

Observation:1- Fig. 2 shows non-linear behaviour of single fibres2- Fig. 1 shows increasing the Young’s modulus and increasing the elasticity

Strain (% 0.0 2.0 4.0 6.0 8.0 10.0 12.0

Strain (%)

domain after yield point 2- Fig. 1, indicates history dependent behaviour3.- Fig. 1 illustrate elastic-plastic behaviour.Consequences:1- Local damaging of matrix with local large deformation make MFA decrease locallylocally2- Increasing of tension force might produces redistribution of the strain along the fibre.

19


Hypothesis for modeling:

• Wood fiber is considered as a long hollow cylinder of length L

•Cell was is made of only S2 layer which is composed of three constituents,cellulose hemicelluloses and lignin with known characteristicscellulose, hemicelluloses and lignin with known characteristics.

•MFA is non-uniform along the fiber;bordered pits, cross-field zones and all natural defect like dislocation or micro-pcompression which add to the fiber heterogeneities along the fiber, all arereplaced by MFA non-uniformities

20


•MFA is non-uniform

Effective Young’s modulus of a fiber

•A set (α α αn) is assumed to represent the local MFAs of differentsegments along the fiber

n 21

LLLL n 21

n21

1 21 1 ( )nLL L

nEEE 21

MFA is constant along 1 2

1 2

( ..... )n

eff nE L E E E MFA is constant along

each segment

21 (1 )E 1 E 1' = (1 )E 1 E 1

' < E 1

Fiber property after yielding (only matrix damages but not fibers


Fiber property after yielding (only matrix damages but not fibers, isotopic damage theory of Kachanof 1984 is applied)

EEE 21

Damage first will happen in part L1Persson (2000)

E)1( nEEE 21

is damage parameter

Constituent CoefficientMean

engineering constant value

Volume fraction for 12% M.C.

E1(GPa) 150 Mean engineering Volume

g pLets take = 0.9

Cellulose 44.5

E2(GPa) 17.5

G12(GPa) 4.5

21 .01

32 .5

Constituent Coefficient constant value are 90% reduced

fraction for 12% M.C.

E1 (GPa) 1.6

E2 (GPa) .35

Hemicellulose

E1 (GPa) 16

31.6

E2 (GPa) 3.5

G12 (GPa) 1.5

21 .1

Hemicellulose 31.6G12 (GPa) .15

ν21 .1

ν32 .4

LigninE (GPa) .275

23 921

3 .4

LigninE (GPa) 2.75

23.9ν .33

Lignin 23.9ν .33

22


Local wood fiber Young’s modulus after isotropic matrix degradation

60.0

40 0

50.0du

lus(

Gpa

)

E L intact material

30.0

40.0

You

ng's

Mod

E L1 matrix rigidity is reduced 50%

E t i i idit i d d 70%

10.0

20.0

ongi

tudi

nal Y E L2 matrix rigidity is reduced 70%

E L3 matrix rigidity is reduced 90%

0.00.0 10.0 20.0 30.0 40.0 50.0

Microfibril angle(Deg)

L

o

•Local longitudinal Young’s modulus of a fiber segment as a function of microfibril angle , for virgin fiber (EL) and for the same fiber with reduced matrix constants (EL1 ,EL2 ,EL3)

g ( g)

23

El i b h i i h


RDifferent possible scenarios after damage initiation in a fiber segment and its progress

Elastic behavior with brittle failure

AA1

50.0

60.0

s(G

pa)

P Perfect plasticity

AA1

30.0

40.0

oung

's M

odul

u

p y

AA2

P

10.0

20.0

ongi

tudi

nal Y

o

A

B2B

A4

Localization and strain softening damage

AA30.0

0.0 10.0 20.0 30.0 40.0 50.0

Microfibril angle(Deg)

L A2

A1

B1 A3

R

elasto-plasticity with positive strain hardening

AA3

P

R

AA4Sedighi-Gilani & Navi (2007), Wood Science and TechnologyKeckes and Burget et al. (2003), Nature Materials

24


Experimental observations

1 Positive slope of the stress-strain curve after the yield point indicates that no strain1. Positive slope of the stress-strain curve after the yield point indicates that no strainsoftening happens

2. Slight increase of the Young’s modulus (see the slopes of unloading-loading cycles intensile test) indicates positive strain hardening behaviour

RB

S t i fib il l P ASegment microfibril angle

Segment young’s modulusLine AA4

elasto-plasticity with positive strain hardening

Y ’ d l i

Potential of large tensile strain = e + irr

Young’s modulus increaseNon-localized damage

25

e irr

Observation by light microscopy the process of fiber damaging and failure

26


27


Conclusion and remarks

• MFA of an individual wood fiber is non-uniform.• Fiber tensile behavior is not a simple function of average MFA.Non-uniformities of MFA and other natural heterogeneities have dominantNon uniformities of MFA and other natural heterogeneities have dominanteffect on the fiber stress-strain curve.• Under tensile force non-uniform wood fiber seems to behave as an elasto-plasticity with positive strain hardening. This might be the consequence ofp y p g g qnon-localized damage with re-strain distribution along the fiber

•Micromechanical Approaches (Modeling of heterogeneity effects andpp ( g g yexperiments) can provide more possibility to understand the mechanismsinvolved in wood cell behavior before and after damage

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Micromechanics of wood Fiber under axial tension; experiment …cost-fp0802.tuwien.ac.at/fileadmin/mediapool-cost/... · 2018-06-05 · Micromechanics of wood Fiber under axial tension;