a comparison of shear characterization of pinus pinaster ait., with the iosipescu and off-axis shear...

A comparison of shear characterization of Pinus Pinaster Ait., with the Iosipescu and off-axis shear test methodsJ. Xaviera, N. Garridob, M. Oliveirab,

J. Moraisa,P.Camanhoc, F. Pierrond

(a) CETAV/UTAD, Vila Real, PT

(b) ESTV, Viseu, PT

(c) DEMEGI/FEUP, Porto, PT

(d) LMPF/ENSAM, Châlons-en-Champagne, FR

Composites Testing and Model Identification28-30 January 2003 – ENSAM, Châlons-en-Champagne, France

Table of contents

Introduction

Data reduction

Experimental work

Finite element analyses

Results and discussion

Conclusions

L

RT

LR

LT

RT

Introductions Wood as an orthotropic material:

Stress-strain functions in the LRT coordinate system:

LL RR TT RT LT LR

LL f11 f12 f13

RR f12 f22 f23

TT f13 f23 f33

RT f44

LT f55

LR f66 - Iosipescu shear test

- Off-axis tensile test

Identification of the shear behaviour of Pinus Pinaster Ait.:

Data reduction Iosipescu shear test:

45º 45º, , P

45º

P

O x

y

612

6

av

aav

G 6

failureideal PX

A

6av P A

6 45º 45ºav

12 12 aG CSG

Shear modulus correction:

6 6O avC 6 6

av OS

Assumption: exists a uniform distribution of shear stress and strain

through the thickness of the specimen;

The strains measured on both faces of the specimen

can be quite different due to boundary conditions

effects (Pierron (1998))

Averaging the shear strains on the two faces of the specimen

eliminates that effect.

Off-axis tensile test:

6 sin cosa P

A

6 2 sin 2 cos 2ava b c a c

612

6

av

aav

G

22 2

61 1 2 2

1 1 2 2 6

1rr r r r

X X X X X

Tsai-Hill strength criterion:

12 12aG CSG

y

, , ,a b c P PPx

a

b

c

12

Experimental work Material

Wood of maritime pine (Pinus Pinaster Ait.), of about 74 years old, from Viseu (Portugal).

Specimens:

Iosipescu specimen:

(Dimensions based on ASTM D 5379-93 Standard)

9, 10 and 8 specimens in the LR, LT and RT planes, respectively;

0/90 rosettes (CEA-06-125WT-350);

Moisture content: 10% - 12%;

Oven-dry density: 0.616 – 0,655 (g/cm3);

24

2

2 0 0

20

2 7

36°

R (T )L

16 °

Off-axis specimens:

Oblique end tabs were bounded for specimens in the

LR and LT planes:

16

66

SCotg

S

Kambala

1 2 0

20

RT

2 5

1 8°2 0

16, 14 and 14 specimens in the LR, LT and RT planes, respectively;

60-ded-delta rosettes (CEA-06-125UR-350);

Tabless specimens were used in the RT plane:

Moisture content: 10% - 12%;

Oven-dry density: 0.616 – 0,655 (g/cm3);

Mechanical testing:

INSTRON 1125 universal machine of 100 KN of capacity

Data acquisition system HBM SPIDER 8

Temperature of 23ºC (1ºC) e relative humidity of 40% (5%)

Controlled displacement rate of 1 mm/mn

Iosipescu tests:

Stationary part of fixture

Movable part of the fixture Parte móvel da amarra

Specimen

Adjustable wedges to tighten the specimen

Wedge adjusting

screw

Fixture linear guide rod

Attachement to test machine

EMSE Iosipescu Fixture

Off-axis tests:

Specimen

Gripping

arrangement

Finite element analyses Objectives of the analyses:

to acess to the stress and strain fields at the test section of the specimens;

to determine the numerical corrections factors C and S.

Wood was modeled as an linear elastic, orthotropic and homogeneous material.

Elastic properties of wood Pinus Pinaster Ait.:

EL

(GPa)ER

(GPa)ET

(GPa)LR TL RT

GLR

(GPa)GLT

(GPa)GRT

(GPa)

15.133 1.912 1.010 0.471 0.051 0.586 1.262 1.100 0.221

Numerical analysis of the Iosipescu and off-axis shear test were developed in ANSYS 6.0®.

Mesh and boundary conditions:

2-D finite element models were developed;

Quadrilateral isoparametric element PLANE82, with 8 nodes;

1800 elements and 5577 nodes.

0yu

0xu

0yu yu

yu

L

R

L

T

R

T

planeLR

planeLT

planeRT

x

y

0.1mm

Iosipescu shear test models and results:

Normalizes stress components along the vertical line, between the V-notches:

-1 ,0

-0 ,8

-0 ,6

-0 ,4

-0 ,2

0 ,0

0 ,2

0 ,4

0 ,6

0 ,8

1 ,0

-0 ,1 0 ,0 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7 0 ,8 0 ,9 1 ,0 1 ,1 1 ,2

LR Plane

XY XY Y XY

X

XY

Normalizes stress components along the vertical line, between the V-notches:

LT Plane

-1 ,0

-0 ,8

-0 ,6

-0 ,4

-0 ,2

0 ,0

0 ,2

0 ,4

0 ,6

0 ,8

1 ,0

-0 ,1 0 ,0 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7 0 ,8 0 ,9 1 ,0 1 ,1 1 ,2 1 ,3 1 ,4

No

rma

lize

d s

tre

ss

co

mp

on

en

ts XY XY Y XY

X

XY

Normalizes stress components along the vertical line, between the V-notches:

RT Plane

-1 ,0

-0 ,8

-0 ,6

-0 ,4

-0 ,2

0 ,0

0 ,2

0 ,4

0 ,6

0 ,8

1 ,0

-0 ,1 0 ,0 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7 0 ,8 0 ,9 1 ,0 1 ,1 1 ,2

XY XY Y XY

X

XY

Normalizes shear strain under an area circumscribed by the strain-gage grid:

XY XY

LR Plane

Normalizes shear strain under an area circunscribed by the strain-gage grid:

LT Plane

XY XY

Normalizes shear strain under an area circunscribed by the strain-gage grid:

RT Plane

XY XY

Numerical corrections factors C and S:

Principalmaterialplanes

C S CS

LR 0.967 0.988 0.955 (4.5%)

LT 0.919 0.995 0.914 (8.6%)

RT 1.050 0.972 1.021 (2.1%)

xu

0zu 0yu

0 xy uu

0zu

L

TR RT

x

)(zy)(yz

xu

0 xy uu0zu

0zu

0yu

R

T L

y

z x

LRand LT plane

19089 elements

16000 nodes.

RT plane

3159 elements

1920 nodes.

Mesh and boundary conditions:

3-D finite element models

were developed;

Solid isoparametric element

SOLID64, with 24 DOF;

Off-axis tensile test models and results:

Uniformity of stress components in the LR plane:

:XY

:X

Uniformity of stress components in the LT plane:

:XZ

:X

Uniformity of stress components in the RT plane:

:Y

:YZ

Numerical corrections factors C and S:

Principal material planes

C S CS

LR 0.997 1.001 0.998 (0.2%)

LT 0.978 0.961 0.940 (6.0%)

RT 0.876 1.039 0.910 (9.0%)

Results and discussion Iosipescu tests:

Experimental data obtained for a specimen in the LR plane:

0

4

8

1 2

1 6

-1 0 0 0 0 -8 0 0 0 -6 0 0 0 -4 0 0 0 -2 0 0 0 0 2 0 0 0 4 0 0 0 6 0 0 0

N orm a l s tra in g a g e rea d in g s ()

(fro n t)

(fro n t)

(b ack )

(b ack )

45º

45º

45º

45º

Initial zone of the shear stress-strain curves, in the LR plane:

0 ,0

0 ,4

0 ,8

1 ,2

1 ,6

2 ,0

2 ,4

2 ,8

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0

E n g in ee rin g sh ea r s tra in (e )

She

ar s

tres

s (M

Pa)

F ron t fac e (A ) B ack face (A ) F ron t fac e (B ) B ack face (B )

The apparent shear modulus definition:

2

2 1

a b c

r

ijG b

ij

ijO

1 ,0

1 ,1

1 ,2

1 ,3

1 ,4

1 ,5

1 ,6

1 ,7

1 ,8

1 ,9

2 ,0

0 1 2 3 4 5 6 7 8 9 1 0

S p ec im en s

Shea

r m

odul

us in

the

LR

pla

ne (

GP

a) Shear modulus, in the LR plane:

Specimen

1 1,274

2 1,516

3 1,500

4 1,543

5 1,415

6 1,258

7 1,164

8 1,457

9 1,577

MEAN 1,411

CV (%) 10,31

LRG

2%

18%

Complete shear stress-strain curves, in the LR plane:

0 ,0

2 ,0

4 ,0

6 ,0

8 ,0

1 0 ,0

1 2 ,0

1 4 ,0

1 6 ,0

1 8 ,0

2 0 ,0

2 2 ,0

0 4 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 0 2 4 0 0 0 2 8 0 0 0

A verage en g in eerin g sh ea r s tra in (e)

She

ar s

tres

s (M

Pa)

0 ,0

2 ,0

4 ,0

6 ,0

8 ,0

1 0 ,0

1 2 ,0

1 4 ,0

1 6 ,0

1 8 ,0

2 0 ,0

2 2 ,0

0 4 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 0 2 4 0 0 0 2 8 0 0 0

A verage en g in eerin g sh ea r s tra in (e)

She

ar s

tres

s (M

Pa)

Typical failure for LR principal material plane:

Local crushing

Large displacement and deformations

Cracks

1 ,1

1 ,2

1 ,3

1 ,4

1 ,5

1 ,6

1 ,7

0 1 2 3 4 5 6 7 8 9 1 0 11

S p ec im en s

Sh

ear

mod

ulu

s in

th

e L

T p

lan

e (G

Pa)

Specimen

1 1,258

2 1,287

3 1,303

4 1,420

5 1,168

6 1,091

7 1,262

8 1,160

9 1,112

10 1,144

MEAN 1,220

CV (%) 8,42

Shear modulus, in the LT plane:

LTG

0,4%

16%

0

2

4

6

8

10

12

14

16

18

0 4000 8000 12000 16000 20000 24000 28000 32000

Average engineering shear strain (e)

Shea

r st

ress

(M

Pa)

Complete shear stress-strain curves, in the LT plane:

0

2

4

6

8

10

12

14

16

18

0 4000 8000 12000 16000 20000 24000 28000 32000

Average engineering shear strain (e)

Shea

r st

ress

(M

Pa)

Typical failure for LT principal material plane:

Local crushing

Large displacement and deformations

Cracks

Shear modulus, in the RT plane:

0 ,1 8

0 ,2 0

0 ,2 2

0 ,2 4

0 ,2 6

0 ,2 8

0 ,3 0

0 ,3 2

0 ,3 4

0 ,3 6

0 ,3 8

0 ,4 0

0 ,4 2

0 1 2 3 4 5 6 7 8 9

S p ec im en

Shea

r m

odul

us in

the

RT

pla

ne (

GP

a)

19%

5%

Specimen

1 0,216

2 0,258

3 0,348

4 0,273

5 0,255

6 0,339

7 0,315

8 0,283

MEAN 0,286

CV (%) 15,85

RTG

Complete shear stress-strain curves, in the RT plane:

0 ,0

1 ,0

2 ,0

3 ,0

4 ,0

5 ,0

6 ,0

0 4 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 0 2 4 0 0 0 2 8 0 0 0 3 2 0 0 0

A verage en g in eerin g sh ea r s tra in (e)

She

ar s

tres

s (M

Pa)

1F

2F

0 ,0

1 ,0

2 ,0

3 ,0

4 ,0

5 ,0

6 ,0

0 4 0 0 0 8 0 0 0 1 2 0 0 0 1 6 0 0 0 2 0 0 0 0 2 4 0 0 0 2 8 0 0 0 3 2 0 0 0

A verage en g in eerin g sh ea r s tra in (e)

She

ar s

tres

s (M

Pa)

Two typical failure for RT principal material plane:

1F

2F

Off-axis tests:

Experimental data obtained for a specimen in the LR plane:

0

6

1 2

1 8

2 4

3 0

3 6

4 2

4 8

-2 4 0 0 -1 4 0 0 -4 0 0 6 0 0 1 6 0 0 2 6 0 0 3 6 0 0 4 6 0 0 5 6 0 0

G a g e n o rm a l stra in ()

L o a d (N )

abc

Complete shear stress-strain curves, in the LR plane:

0

2

4

6

8

1 0

1 2

1 4

1 6

1 8

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0

E n g in eer in g sh ear stra in ()

Sh

ear

stre

ss (

MP

a)

Typical failure for a specimen in the LR plane:

0

2

4

6

8

1 0

1 2

1 4

1 6

1 8

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0

E n g in eer in g sh ear stra in ()

Sh

ear

stre

ss (

MP

a)

Shear properties in the LR plane:

Specimens

1 1,228 3,613

2 1,316 3,360

3 1,164 3,435

4 1,111 2,903

5 1,142 4,621

6 1,031 3,583

7 1,150 3,923

8 1,104 4,637

9 1,129 4,121

10 1,050 4,064

11 1,095 3,404

12 1,089 3,725

13 1,093 3,907

14 1,031 4,802

15 1,054 3,142

16 1,017 4,604

MEAN 1,113 3,865

CV (%) 7,00 14,88

LRG LRX

0

2

4

6

8

1 0

1 2

1 4

1 6

1 8

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0 2 2 0 0 0

E n gin eerin g sh ea r s tra in ()

Shea

r st

ress

(M

Pa)

Complete shear stress-strain curves, in the LT plane:

0

2

4

6

8

1 0

1 2

1 4

1 6

1 8

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0 2 2 0 0 0

E n gin eerin g sh ea r s tra in ()

Shea

r st

ress

(M

Pa)

Typical failure for a specimen in the LT plane:

Shear properties in the LT plane:

Specimens

1 0,980 2,875

2 0,942 4,205

3 0,951 3,659

4 0,922 3,934

5 1,108 3,883

6 1,037 3,461

7 1,161 3,565

8 0,891 4,151

9 0,916 4,596

10 1,032 4,038

11 0,955 3,953

12 0,943 4,220

13 0,977 3,338

14 0,893 3,874

MEAN 0,979 3,839

CV (%) 8,12 11,30

LTG LTX

Complete shear stress-strain curves, in the RT plane:

0 ,0

1 ,0

2 ,0

3 ,0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0 2 2 0 0 0 2 4 0 0 0

E n g in ee rin g sh ea r s tra in ()

She

ar s

tres

s (M

Pa)

0 ,0

1 ,0

2 ,0

3 ,0

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0 1 6 0 0 0 1 8 0 0 0 2 0 0 0 0 2 2 0 0 0 2 4 0 0 0

E n g in ee rin g sh ea r s tra in ()

She

ar s

tres

s (M

Pa)

Typical failure for a specimen in the RT plane:

Shear properties in the RT plane:

Specimens

1 0,157 0,755

2 0,133 0,790

3 0,144 0,938

4 0,149 0,834

5 0,153 0,603

6 0,157 0,584

7 0,328 0,784

8 0,142 0,779

9 0,127 0,693

10 0,140 0,565

11 0,152 0,746

12 0,124 0,750

13 0,142 0,685

14 0,126 0,675

MEAN 0,155 0,727

CV (%) 32,75 14,03

RTG RTX

Comparison of the shear properties obtained from both Iosipescu and off-axis shear test methods:

Shear modulus Shear strength

Iosipescu test 1.411 1,220 0,286 - - -

Off-axis test 1,113 0,979 0,155 3,865 3,839 0,727

Difference (%) 21,12 19,75 45,80 - - -

LRG RTGLTG LTXLRX RTX

Conclusions

The Iosipescu and off-axis shear test methods are suitable for measuring the shear moduli in all principal material planes of Pinus Pinaster Ait.;

The complete shear behaviour of Pinus Pinaster Ait., including the shear strength, can not be properly determined by the Iosipescu sheat test;

The off-axis tensile test is suitable for the complete identification of the shear stress-strain functions of Pinus Pinaster Ait.;