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CHARACTERIZATION OF THE SHEAR BEHAVIOUR OF WOOD USING THE
IOSIPESCU TEST
J. C. Xavier
Master of Science Thesis
LMPF seminary - 11/12/2003
University of Trás-os-Montes e Alto DouroVila Real, Portugal
Plan
Introduction
The Iosipescu test
Numerical simulation of the Variable Span Method
Numerical simulation of the Iosipescu test
Experimental work
Presentation and discussion of the experimental results
General conclusions and future work
Introduction Wood modelling at the macroscopic level:
Shear properties:
─ Shear moduli : GLR , GLT , GRT .
─ Shear strengths : SLR , SLT , SRT .
fff
f
f
f
fff
fff
fff
ffff
66
55
44
333231
232221
131211L
R
T
RT
LT
LR
L
R
T
RT
LT
LR
f11 f12 f13
f21 f22 f23
f31 f32 f33
f44
f55
f66
[5] prEN 408. European Committee for Standardization, 2000.[6] ASTM D198-94. American Society for Testing and Materials, 1994.
[7] ASTM D143-94. American Society for Testing and Materials, 1994.[8] NP 623. Portuguese Standard, 1973.
Drawbacks of the standardized tests for the identification of the shear properties of wood [3,4]:
(i) Give only the shear properties parallel to the fibres
(shear moduli : GLR, GLT and shear strengths : SLR e SLT).
(ii) The variable span method [5,6] proposed for the determination of EL and GLR (or GLT), is not a
fundamental test.
(iii) The failure of the specimen of the shear block test [7,8] proposed for the identification of SLR and SLT,
occurs under stress concentrations.
[3] Yoshihara et all.. Journal of Wood Science, 44:15-20, 1998.[4] Rammer D.R. e L.A. Soltis. Res. Pap. FPL-RP-527, FPL, 1994.
L [0,0025; 0,035] cL
F/2
F
h
b
F/2
Nominal distribution of the shear stress Real distribution
of the shear stress
Increase of the shear stress
Aim of this work:
Investigation of the applicability of the Iosipescu shear test for characterizing the shear behaviour of wood Pinus Pinaster Ait.
(i) simultaneous identification of the shear modulus and the shear strength, in a particular symmetry plane.
Justifications for the choice of the Iosipescu test:
(ii) possible application of this test method for all the symmetry planes of wood thanks to the small size of the specimen.
Among different shear tests for orthotropic materials : Iosipescu test
(standard test for synthetic composite materials [9]).
[9] ASTM D 5379-93. American Society for Testing and Materials, 1993.
The Iosipescu test Iosipescu specimen [9]:
[9] ASTM D 5379-93. American Society for Testing and Materials, 1993.
General view of the Iosipescu fixture [9]:
[9] ASTM D 5379-93. American Society for Testing and Materials, 1993.
Wedge adjusting screw
Specimen
Stationary part of fixture
Movable part
of the fixture
Fixture linear guide rod
Base
Adjustable wedges to tighten the specimen
Attachment to the test machine
Data processing [9]:
Experimental information:
+45º , –45º , P
Engineering shear strain:
Nominal shear stress:
6=P/A
Apparent shear modulus:
Apparent shear strength:
G12= 6 / 6
a
S12= P / Aa ult
[9] ASTM D 5379-93. American Society for Testing and Materials, 1993.
6=+45º – – 45º
For an orthotropic material the distributions of 6 and 6
are not homogeneous [10,11].
The correction factors C e S are calculated through finite element analyses.
G12 = CSG12
a
[10] Pierron F. e A. Vautrin. Composite Science and Technology, 5:61-72, 1994.[11] Pierron F. Journal of Composite Materials, 32(22):1986-2015, 1998.
where C = 6 / (P/A) and S = 6 / 6oo ros
G12
a
Aspects about the identification of G12:
[10] Pierron F. e A. Vautrin. Composite Science and Technology, 5:61-72, 1994.[11] Pierron F. Journal of Composite Materials, 32(22):1986-2015, 1998.
The distribution of 6 through
the thickness of the specimen
can be heterogeneous due to
geometrical imperfections of its
loading surfaces [10,11].
This effect is eliminated by considering 6 as the average of the shear
strains measured over both lateral faces of the specimen [10,11].
Grandes deformaçõesPequenos módulos
Pequenas deformaçõesGrandes módulos
Face frontal do provete
Indeformado
Deformado
P
Large deformationsSmall modulus
Small deformationsLarge modulus
Front face of the specimen
Undeformed
Deformed
Aspects about the identification of S12:
[12] Pierron F. e A. Vautrin. Composite Science and Technology, 57(12):1653-1660, 1997.[13] Pierron F. e A. Vautrin. Journal of Composite Materials, 31(9):889-895, 1997.[14] Odegard G. e M. Kumosa. Journal of Composite Materials, 33(21):1981-2001, 1999.
The failure of the specimens occurs under a homogeneous stress state
although both 6 and 2 components exist [12-14].
S12 should be determined through a failure criterion.
S12 = P / A represents an overestimated value.a ult
2 component should be calculated from finite element analysis,
introducing in the model an suitable shear constitutive law.
Numerical simulation of the variable span method
Aim:
Investigating the applicability of the variable span method [5,6] for validating the Iosipescu test.
3D models of the three-point-bending test developed in ABAQUS 6.2-1®.
Finite element models:
Wood was modelled as:
– continuous;
– homogeneous;
– orthotropic;
– linear elastic.
[5] prEN 408. European Committee for Standardization, 2000.[6] ASTM D198-94. American Society for Testing and Materials, 1994.
F
F/2F/2L
500
20
20R
L
L = 120, 135, 160, 200 and 400 mm
Configuration of the specimens in the three-point-bending tests:
Geometrical model used in the finite element analyses:
20
L/2
D E,I
F,J
B
C,H
A,G
10
x,L
y,R
A,E,D
B
C,F
G,I
H,J
Elastic properties used in the numerical models:
EL(1) ER
(1) ET(1) LR
(1) LT(1) RT
(1) GLR(2) GLT
(2) GRT(2)
(GPa) (GPa) (GPa) (GPa) (GPa) (GPa)
15,13 1,91 1,01 0,47 0,05 0,59 1,11 1,10 0,18(1) Pinus Pinaster Ait. [15].(2) Pinus Tarda L. [16].
Calibration of the friction coefficient:
Element C3D8
Mesh and boundary
conditions of the model :
[15] Pereira J.L. MSc Thesis, UTAD (in progress).[16] FPL. FPL-GTR-113, 1999.
Euler-Bernoulli beam theory:
EL =L3 F
4h4 f
a f1 = uy
f2 = uy
f3 = uy
f4 = uy – uy
A
B
C
C D
D A
B
C x,L
y,RA
B
C
Numerical results:
Timoshenko beam theory:
f1 f2 f3 f4
EL (GPa) 16,63 (9,9%) 16,05 (6,1%) 16,01 (5,8%) 15,57 (2,9%)
GLR (GPa) k = 1,2 0,74 (33,6%) 1,12 (0,6%) 1,22 (9,6%) 1,94 (74,6%)
k = 1,5 0,92 (17,0%) 1,39 (25,8%) 1,52 (37,0%) 2,42 (118,3%)
Lh
EL a
1 =
EL
2 1
+GLR
k
This assumption is not verified at midspan (AC ):
Kinematical assumption of the Timoshenko beam theory :
─ The deflection is the same for each point belonging to the same
vertical cross section, initially perpendicular to the neutral axis.
A
C
B
Numerical simulation of the Iosipescu test
Aims:
Determination of the stress and strain fields in the central region of the Iosipescu
specimen of Pinus Pinaster Ait.
Computation of the correction factors C and S.
Finite element models:
2D models developed in ANSYS 7.0® and ABAQUS 6.2-1®.
The hypothesis and elastic properties are the same as the ones used
in the numerical simulation of the variable span method.
Nominal dimensions of the Iosipescu specimen:
Mesh of the finite elements models:
5577 nodes and 1800 elements.
Elements: PLANE82 (ANSYS)CPS8 (ABAQUS)
L
R
L
T
R
T
Boundary conditions [17-19]:
Flexão no plano
i.base:
ii.iterative(LR plane):
iii. with contact:
AN
SYS
AB
AQ
US
[17] Pierron F. PhD, University of Lyon I, 1994.[18] Ho H. et al. Composite Science and Technology, 46:115-128, 1993.[19] Ho H. et al. Composite Science and Technology, 50:355-365, 1994.
Average engineering shear strain ()
Ave
rage
she
ar s
tres
s (M
Pa)
Base BC
Iterative BC
Contact BC
Reference
Average engineering shear strain ()
Ave
rage
she
ar s
tres
s (M
Pa)
Base BC
Iterative BC
Contact BC
Reference
Comparaison and validation of the boundary conditions:
Numerical results:
(LR plane)
Stress and strain fields for the LR specimen:
LR/|P/A|
─ Stress field in the central region of the specimen:
─ Stress distribution along the vertical line between notches:
RR/|P/A|LR/|P/A|
RR/|P/A|R
L
─ Strain field over the strain gauge area :
LR/|LR| RR/|LR|
Stress and strain fields for the LT specimen:
LT/|P/A|
─ Stress field in the central region of the specimen:
─ Stress distribution along the vertical line between notches:
TT/|P/A|
LT/|P/A|
TT/|P/A|T
L
─ Strain field over the strain gauge area :
LT/|LT| TT/|LT|
Stress and strain fields for the RT specimen:
RT/|P/A|
─ Stress field in the central region of the specimen: ─ Stress distribution along the vertical line between notches :
TT/|P/A|
RT/|P/A|
TT/|P/A|
T
R
RR/|P/A|
─ Strain field over the strain gauge area :
RT/|RT| TT/|RT|
Calculation of the correction factors C and S:
AC =6O
FYi=1
m
S=+45º – –45º)i=1
n
ii
n6
1
Symmetry planes
Correction factors
for wood C S CS
LR 0,97 0,99 0,95 (4,8%)
LT 0,92 0,99 0,91 (8,6%)
RT 1,04 0,97 1,01 (0,6%)
Experimental work Preparation of the specimens:
Material: wood of Pinus Pinaster
Ait. (maritime pine), 74-year-old, from Viseu (Portugal).
Iosipescu specimen:
RT specimen
LT specimen
LR specimen
─ Moisture content: 9,5% – 12,1%;
─ Density: 0,537 – 0,623;
─ 0/90 strain gauge (CEA-06-125WT-350), bonded on both faces of the
specimens, with the M-Bond AE-10 adhesive.
EMSE fixture [20]:
[20] Pierron F. Ecole des Mines de Saint-Etienne, No. 940125, 1994.
Tightness of the wedges with a dynamometrical key : 1 Nm
Experimental procedure:
INSTRON 1125 Universal test machine with the capacity of 100 kN
Data acquisition system : HBM SPIDER 8
Temperature of 23ºC (1ºC) and relative humidity of 45% (5%)
Controlled displacement rate
of 1 mm/min
Experimental equipment :
5 kN Load cell
Presentation and discussion of the experimental results
LR specimens:
Typical experimental data measured for the LR specimens:
(A)
(A)
(B)
(B)
Linear deformation measured with strain gauges ()
Load (N)
Front face (A)
Front face (A)
Back face (B)
Back face (B)
Apparent average LR – LR curves :
─ The response of the specimens contain some variability.
─ The curves are nonlinear; the source of such nonlinearity can be attributed to [19,21]:
(1) the nonlinear behaviour of the material;
(2) the geometric nonlinearity;
(3) the nonlinearity due to the contact conditions specimen/fixture.
[21] Kumosa M. e Y. Han. Composite Science and Technology, 59:561-573, 1999.
Average engineering shear strain ()
Ave
rage
she
ar s
tres
s (M
Pa)
Dispersion of the shear moduli values (GLR , GLR and GLR ):a, A a, B a
GLR GLR GLR
Mean (GPa) 1,41 ± 0,151 1,54 ± 0,181 1,48 ± 0,121
C.V.2 (%) 14,1 15,0 10,3
a, A a, B a
─ Reduction of the dispersion of GLR when the average of 6 , between the
measurements on both faces of the specimen, is considered.
a
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
Specimens
She
ar m
odul
i (G
Pa)
Moisture content (u), density (d) and shear moduli (GLR, GLR) :c
Specimens u (%) d GLR (GPa) GLR (GPa)
1 11,9 0,561 1,33 1,27
2 11,8 0,607 1,59 1,52
3 12,1 0,612 1,57 1,50
4 11,8 0,605 1,62 1,54
5 12,1 0,615 1,48 1,42
6 10,3 0,538 1,32 1,23
7 10,0 0,537 1,22 1,16
8 10,4 0,609 1,53 1,46
9 9,4 0,614 1,65 1,58
Mean 11,1 0,589 1,48 ± 0,121 1,41 ± 0,111
C.V.2 (%) 9,1 5,6 10,3 10,3
ca
a
─ Applying the t test for equality of means between two samples it is concluded
that GLR and GLR belongs to the same population, at a 95% confidence level.a c
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
GLR shear modulus identified by the Iosipescu and off–axis [22] tests:
Test method
Iosipescu Off-axis
d GLR (GPa) d GLR (GPa)
Mean 0,589 1,41 ± 0,111 0,582 1,11 ± 0,041
C.V.2 (%) 5,6 10,3 4,0 7,0
─ The dispersion of the GLR values are of the same order of magnitude.
─ Applying the t test of equality of means, it is concluded that the GLR values
from both tests lead to different proprieties, at 95% confidence level.
[22] Garrido N. MSc thesis, UTAD (in progress).
─ The average of GLR is great than GLR in 26%.
Iosipescu Off-axis
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
LR – time curves :
Initial cracks
Geometric nonlinearity due to the rotation of the fibres
Nonlinearity due to the specimen/fixture contact
Crushing of the loading surfaces of the specimen
Time (s)
She
ar s
tres
s (M
Pa)
Shear stresses identified in the LR specimens :
Specimens LR LR
1 14,4 14,9
2 12,6 16,3
3 17,2 18,6
4 16,2 17,9
5 19,1 19,1
6 13,2 13,8
7 14,9 15,0
8 15,9 16,8
9 19,5 19,5
Mean (MPa) 15,9 ± 1,91 16,9 ± 1,61
C.V.2 (%) 15,2 12,1
1f ult
─ It is not possible to identify SLR using a suitable failure criterion, since the nonlinear shear constitutive law of
wood Pinus Pinaster Ait. is not known.
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
Shear stresses identified by the Iosipescu and off–axis [22] tests :
Test method
Iosipescu Off-axis
LR LR LR SLR1
Mean (MPa) 15,9 ± 1,91 16,9 ± 1,61 14,1 ± 0,91 16,5 ± 1,51
C.V.3 (%) 15,2 12,1 12,1 16,7
1f ult ult
(1) Shear strength determined using the Tsai – Hill failure criterion;(2) Confidence intervals at 95% confidence level;(3) Coefficient of variation (C.V.).
─ The Iosipescu test gives a good estimation of SLR for wood Pinus Pinaster Ait.:
LR < sLR < LR
1f ult
[22] Garrido N. MSc thesis, UTAD (in progress).
LT specimen:
Typical experimental data measured for the LT specimens:
Linear deformation measured with strain gauges ()
Load (N)
Front face (A)
Front face (A)
Back face (B)
Back face (B)
Apparent average LT – LT curves :
─ The response of the specimens contain same variability.
─ The curves are nonlinear; the source of the nonlinearity can be attributed to [19,21]:
(1) the nonlinear behaviour of the material;
(2) the geometric nonlinearity;
(3) the nonlinearity due to the contact conditions specimen/fixture.
Average engineering shear strain ()
Ave
rage
she
ar s
tres
s (M
Pa)
Dispersion of the shear moduli values (GLT , GLT and GLT ):a, A a, B a
GLT GLT GLT
Mean (GPa) 1,33 ± 0,121 1,34 ± 0,101 1,34 ± 0,081
C.V.2 (%) 12,2 10,3 8,5
a, A a, B a
─ Reduction of the dispersion of GLT when the average of 6 , between the
measurements on both faces of the specimen, is considered.
a
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
Specimens
She
ar m
odul
i (G
Pa)
─ Applying the t test for equality of means between two samples it is concluded
that GLT e GLT belongs to the same population, at a 99% confidence level.
Moisture content (u), density (d) and shear moduli (GLT, GLT) :c
Provetes u (%) d GLT (GPa) GLT (GPa)
1 11,7 0,603 1,38 1,26
2 11,7 0,595 1,41 1,29
3 11,7 0,590 1,43 1,31
4 11,5 0,599 1,55 1,42
5 11,4 0,592 1,29 1,17
6 10,8 0,581 1,19 1,09
7 10,6 0,606 1,38 1,26
8 11,3 0,556 1,27 1,16
9 10,8 0,574 1,21 1,11
10 10,5 0,593 1,25 1,15
Média 11,2 0,589 1,34 ± 0,081 1,22 ± 0,071
C.V.2 (%) 4,5 2,6 8,5 8,5
ca
a
a c
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
GLT shear modulus identified in the Iosipescu and off–axis [22] tests :
Test method
Iosipescu Off-axis
d GLT (GPa) d GLT (GPa)
Mean 0,589 1,22 ± 0,071 0,538 1,04 ± 0,051
C.V.2 (%) 2,6 8,5 4,0 8,1
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
─ The dispersion of the GLT values are of the same order of magnitude.
─ Applying the t test of equality of means, it is concluded that the GLT values
from both tests lead to different proprieties, at 95% confidence level.
─ The average of GLT is great than GLT in 17%.
Iosipescu Off-axis
[22] Garrido N. MSc thesis, UTAD (in progress).
LT – time curves :
Initial cracks
Geometric nonlinearity due to the rotation of the fibres
Nonlinearity due to the specimen/fixture contact
Crushing of the loading surfaces of the specimen
Time (s)
She
ar s
tres
s (M
Pa)
Shear stresses identified in the LT specimens :
(1) These values does not follow a Normal distribution (Shapiro-Wilk test);
(2) Confidence intervals at 95% confidence level;
(3) Coefficient of variation (C.V.).
Specimens LT LT
1 15,4 16,6
2 14,7 19,0
3 15,5 17,3
4 14,5 18,6
5 16,1 17,3
6 16,5 18,1
7 19,1 20,6
8 16,0 17,5
9 14,7 18,1
10 16,1 18,1
Média (MPa) 15,9 1 18,1 ± 0,82
C.V.3 (%) 8,4 6,1
1f ult
─ It is not possible to identify SLT using a suitable failure criterion, since the nonlinear shear constitutive law of
wood Pinus Pinaster Ait. is not known.
Shear stresses identified in the Iosipescu and off–axis [22] tests :
Test method
Iosipescu Off-axis
LT LT LT SLT1
Mean (MPa) 15,9 18,1 ± 0,81 14,0 ± 0,81 16,6 ± 1,01
C.V.3 (%) 8,4 6,1 9,5 10,9
[22] Garrido N. MSc Thesis, UTAD (in progress).
1f ult ult
(1) Shear strength determined using the Tsai – Hill failure criterion;(2) Confidence intervals at 95% confidence level;(3) Coefficient of variation (C.V.).
LT < sLT < LT
1f ult
─ The Iosipescu test gives a good estimation of SLT for wood Pinus Pinaster Ait.:
RT specimen:
Typical experimental data measured for the RT specimens:
Linear deformation measured with strain gauges ()
Load (N)
Front face (A)
Front face (A)
Back face (B)
Back face (B)
─ The response of the specimens contains some variability.
─ The curves are nonlinear.
Apparent average RT – RT curves :
Average engineering shear strain ()
Ave
rage
she
ar s
tres
s (M
Pa)
Dispersion of the shear moduli values (GRT , GRT and GRT ):a, A a, B a
GRT GRT GRT
Mean (GPa) 0,278 ± 0,0631 0,286 ± 0,0301 0,282 ± 0,0381
C.V.2 (%) 27,2 12,4 16,2
a, A a, B a
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
─ Reduction of the dispersion of GRT when the average of 6 , between the
measurements on both faces of the specimen, is considered.
a
Specimens
She
ar m
odul
i (G
Pa)
─ Applying the t test for equality of means between two samples it is concluded
that GRT e GRT belongs to the same population, at a 95% confidence level.
Moisture content (u), density (d) and shear moduli (GRT, GRT) :c
Specimens u (%) d GRT (GPa) GRT (GPa)
1 11,3 0,542 0,221 0,216
2 11,6 0,551 0,254 0,259
3 11,7 0,559 0,341 0,348
4 11,7 0,556 0,271 0,276
5 12,1 0,548 0,249 0,254
6 10,2 0,622 0,338 0,345
7 9,8 0,622 0,311 0,318
8 11,4 0,623 0,280 0,285
Média 11,2 0,578 0,282 ± 0,0381 0,288 ± 0,0391
C.V.2 (%) 7,2 6,5 16,2 16,2
ca
a
a c
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
GRT shear modulus identified by the Iosipescu and Arcan [23] tests:
Ensaio de corte
Iosipescu Arcan
d GRT (GPa) d GRT (GPa)
Média 0,578 0,288 ± 0,0391 0,650 0,229 ± 0,0351
C.V.2 (%) 6,5 16,2 5,9 24,0
[23] Oliveira M. MSc thesis, UTAD (in progress).
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
─ The dispersion of the GRT values is slightly greater in the Arcan tests.
─ Applying the t test of equality of means, it is concluded that the GRT values
from both tests lead to different proprieties, at 95% confidence level.
─ The average of GRT is great than GRT in 20%.
Iosipescu Arcan
RT – time curves :
Cracks Cracks
Time (s)
She
ar s
tres
s (M
Pa)
Shear stresses identified in the RT specimens :
Specimens RT RT
1 2,38 3,29
2 2,76 3,88
3 0,97 4,16
4 2,86 3,36
5 4,65 4,65
6 1,01 4,62
7 1,16 5,63
8 3,27 5,18
Mean (MPa) 2,38 ± 1,08 2 4,35 ± 0,702
C.V.2 (%) 54,3 19,2
1f ult
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
Shear stresses identified by the Iosipescu and Arcan [23] tests :
Test method
Iosipescu Arcan
RT RT
Mean (MPa) 4,35 ± 0,701 4,54 ± 0,311
C.V.2 (%) 19,2 12,1
ult ult
[23] Oliveira M. MSc Thesis, UTAD (in progress).
─ It was found a good agreement between RT values identified in both tests.
However, as the failure of the Iosipescu RT specimens does not correspond to
shear, it is not possible to say that the Iosipescu test gives a good estimation
for sRT to wood Pinus Pinaster Ait.
ult
(1) Confidence intervals at 95% confidence level;(2) Coefficient of variation (C.V.).
Comparison between the LR and LT specimens:
─ Applying the t test of equality of means between two
samples it is concluded, for a 95% confidence level, that :
(1) GLR and GLT are different properties, with GLR > GLT .
(2) LR and LT are equal properties, suggesting that for
wood Pinus Pinaster Ait.: SLR = SLT .
ult ult
General conclusions and future work
The GLR, GLT and GRT shear moduli identified by the Iosipescu test are
greater than the ones obtained by the off-axis and Arcan tests by
26%, 17% e 20%, respectively, leading to different properties at a
95% confidence level.
Although it is not possible to directly identify the shear strengths SLR,
SLT and SRT using the Iosipescu test, it was proved that this test gives a
good estimation of these properties, at least for the LR and LT planes.
Perpectives :
─ The use of identification technics, based on optical measurements
and heterogenous fields, in order to identify several mechanical
properties from only one test method.
─ The use of a micro/macro approach that allows the estimation of
the macroscopic behaviour of wood through the characterization
of its micro-structure.