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Turkish J. Eng. Env. Sci.31 (2007) , 89 118.c TUBITAK
Experimental Investigation of the Mechanical Behavior of Solid
andTubular Wood Species under Torsional Loading
Ezgi GUNAY
Gazi University, Department of Mechanical Engineering, 06570,
Ankara-TURKEY
e-mail: [email protected]
Yusuf ORCAN
Middle East Technical University, Department of Engineering
Sciences, 06531, Ankara-TURKEY
Received 27.09.2006
Abstract
Torsion experiments are performed in order to examine the
mechanical behavior of Turkish beech, pine,hornbeam, and chestnut
wood specimens. Solid and tubular bars of different geometries are
tested undertorsional loading. The results are compared for
different species and geometries of wood specimens. Theshear
stress-strain curves are obtained in order to show their
characteristic behavior in detail. The dataobtained from torsional
loading experiments are used to estimate the modulus of rigidity of
different woodspecimens. The factors affecting the slopes of the
characteristic shear stress-strain curves of different woodspecies
under forward/backward and cyclic loading are discussed. Stress
relaxation tests are performed onboth pine and beech for torsional
loading.
Key words: Wood, Torsion tests, Shear modulus, Solid and tubular
bars, Cyclic loading, Size effect.
Introduction
Interest in the determination of mechanical proper-ties of wood
under the action of different types ofloading has never ceased.
Wood fibers from a mi-cromechanical point of view and wood
materials atmacro level have been examined under different
as-sumptions. Mack (1940) studied small-scale, circularspecimens
under torsion in order to obtain the shear
strength of wood. Mack (1979) introduced the Aus-tralian
standard test methods among the other com-mon test methods (BSI-The
British Method, 1957;ASTM method of testing, 1972) for small clear
spec-imens of timber. Pagano and Kim (1988) consid-ered
graphite-fiber carbon-matrix composite mate-rial tube specimens
subjected to torsional loadingand studied the interlaminate shear
stresses. Wood-ward and Minor (1988) examined Douglas fir tim-bers
for the determination and comparison of thefailure formulas for 6
different grain angles. Tsai andDaniel (1990) studied prismatic
composite specimens
for the determination of the 3 principle shear moduli:G12, G23
and G13. The chosen graphite/epoxy andsilicon carbide/glass ceramic
type specimens weretested under torsional loading. They obtained
aclosed form relationship between the angle of twistand the applied
torque. Tsai et al. (1990) includedthe shear properties of the
composite specimen foreach layer. The chosen composite material was
uni-directional composite graphite/epoxy, and 3 princi-
pal shear modulus values,G12, G23 and G13, wereused in their
expressions. Hayashi et al. (1993) stud-ied the response of wood
specimens to tensile load-ing and obtained viscoelastic compliance
terms for12% equilibrium moisture content. It was observedthat the
time-dependent strain reduced the ultimatestrength by 58%. The
compliances were representedby time power functions. Hayashi et al.
(1993) stud-ied wood for the determination of 4 compliance
termsunder a tensile test. Govic et al. (1994) explainedthe main
methods for tensile and compression testson Okoume poplar, maritime
pine, plywood, and
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particle board. Ifju (1994) introduced a shear gaugefor reliable
shear modulus measurements. Park andBalatinecz (1997) investigated
the mechanical prop-
erties of wood-fiber/toughened polypropylene com-posites.
Wood-fiber thermoplastic composites wereprepared with isotactic
polypropylene. They showedthat the fibers of wood increased the
stiffness andthe percentage elongation at break and decreasedthe
impact strength. Rezai and Warner (1997) in-vestigated the water
absorbance of wood fibers. Di-nus and Welt (1997) gave a review of
fiber proper-ties with the help of biological methods. Liu
(1997)performed a viscoelastic 2-dimensional finite elementanalysis
of vacuum forming of wood fiber filled withisotactic polypropylene.
The analysis showed that
the viscoelastic effect of the polymer should not beneglected in
the modeling of a vacuum-forming prob-lem. Liu and Ross (1998)
investigated the mechani-cal property variations in wood with grain
slope.
Experimental studies using nondestructive eval-uation (NDE) and
nondestructive test (NDT) meth-ods showed that the properties of
wood are affectedby the growth rate, internal decay, defect
distribu-tion, and density variation separately. The ultra-sonic
stress wave method for the detection of deflec-tion was proposed by
Mal et al. (1988) and Beall(1987) for nondestructive testing of
wood. Bodig
(2001) explained the pseudo-NDE techniques such asdeflection
method, electrical properties, gamma radi-ation, penetrating radar
method, and X-ray method.
Rammer et al. (1996) described experimentalstudies for the
determination of shear strength, sizeeffect, and fracture of
Engelmann spruce, Douglasfir, and southernwood type beams. They
pointedout that the shear strength of wood varies with size,shear
surface area, and volumetric change. Shearstrength of wood (Forest
Products Laboratory, 1999)was based on the shear block test (ASTM,
1978).March et al. (1942) introduced a method called
the plate twist test (ASTM, 1976) to measure theshear modulus of
wood. This test did not considerthe effect of grain slope;
nevertheless, the test find-ings were compared with shear text
fixture and an-alytical equations by Liu (2000). Here, the usedwood
specimens were Sitka spruce (Picea sitchensis)(E1 = 11.8 MPa,E2 =
2.216 MPa,G12 = 910 MPa,12 = 0.37). The shear strain s values were
mea-sured with 45 strain rosette and shear gauge (seeAppendix). Liu
(2000) studied the effects of shearcoupling on the shear properties
of wood. Liu etal. (1999) presented a shear test fixture using
the
Iosipescu specimen. Yoshihara et al. (2001) studiedrectangular
wood specimens to determine the shearstress-strain equations. The
research included the
experimental results obtained by the Iosipescu sheartest and
torsion test with their comparisons. The as-sumed approximated
equation for shear modulus byLekhnitskii (1963) and Yoshihara et
al. (1993) (seeAppendix) was used and the numerical results
werediscussed. The specimens used were Sitka spruce(Picea
sitchensis Sarr.) and Shioji (Japanese ash,Faxinus
spaethianaLingelsh).
Yamasaki and Sasaki (2000a, 2000b) studied thefailure behavior
of Japanese beech wood under com-bined axial force and torque in
order to check the fail-ure behavior of wood for grain angles90
90.
Zidi (2000) studied the finite torsion problem ofanisotropic
solid and tubular bars numerically.
Ors et al. (2001) studied the layered wood shellstructures under
shear, tensile, and bending tests.The timber used was poplar
(Populus xeureameri-cana I 45/51). The results obtained show that
themechanical properties of plywood can be improvedby changing the
pressure, press time, and thicknessof veneer parameters during the
preparation of thelayers. Groom et al. (2002) determined the
Youngsmodulus and ultimate tensile stress of pine singlewood fiber
within the ranges 6.55-27.5 GPa and 410-
1422 MPa for different tree heights and juvenilities.Bucur and
Rasolofosaon (1998) used ultrasonic
wave propagation techniques in order to explain theanisotropic
and nonlinear elastic behavior of woodand rock. Bucur (2003)
assumed that wood has atriclinic symmetry and obtained the elastic
materialconstants matrix [Cij] using ultrasonic methods. Ina review
article by Bucur (2003), the main measure-ment techniques on
material properties of wood werediscussed. They were grouped as
ionizing radiation,microwaves, ultrasonic, nuclear magnetic
resonance,and X-ray methods. In a related study, Bucur et al.(2002)
presented the related equations for the an-alytical propagation of
ultrasonic waves. Winandy(1994), and Winandy and Rowell (2005)
explainedthe micro- and macrostructural concepts of wood ina
general view.
Gunay and Sonmez (2003) investigated experi-mentally the
mechanical behavior of Turkish beech,pine and oak wood using solid
round specimens sub-jected to torsional and tensile loadings.
Nafa and Araar (2003) presented some applieddata concerning the
torsional behavior of glued-laminated wood beams under several
loading pro-
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grams. They have shown the failure characteristicsof the studied
beams in monotonous torsion and theinfluence of the loading
amplitude in cyclic torsion.
Chen et al. (2006) presented the results of aseries of
experiments on hardwood (red lauan) andsoftwood (Sitka spruce) test
pieces under static andcyclic torsional loading. It was noted that
most re-search has focused on wood laminates and for ap-plications
such as wind turbine blades, since woodhas several advantages over
other materials for bladeconstruction. They have shown that the
strengthof both hardwood and softwood decreased as thegrain
orientation of the sample to the axis of twistincreased from 0 to
90 with a corresponding de-crease in elastic modulus under static
torsional load-
ing. The authors noted that hardwood shows a smalldecrease in
stiffness with each loading cycle prior tofailure, whereas the
stiffness of the softwood onlychanges slightly before failure.
Results of the hys-teresis loop for a hardwood show that before
crack-ing occurs the hysteresis loop area and maximumshear stress
at each cycle decrease with an increasein cyclic loading. This is a
relaxation behavior thathas been reported by Bodig and Jayne (1982)
andKollmann and Cote (1968).
The aim of this article is to examine the mechan-ical response
of Turkish pine, beech, hornbeam, andchestnut under torsional
loading for solid and tubu-lar type specimens with different radial
dimensions.With the help of a series of experiments, the
general
behavior characteristics of the stress-strain responseof wood
specimens are obtained comparatively.
Experimental
Solid and tubular test specimens
The geometries of solid and tubular specimens in tor-sion
experiments were chosen from 4 different outerdiameters:d1 = 12.50
mm,d2= 12.0 mm,d3 = 10.00mm and d4 = 7.0 mm. The tubular specimens
wereproduced using a drilling process and the exact in-ner
diameters were measured and found to be 6.0,6.3, 6.4, 6.5, 6.6,
6.8, 7.6 and 9.2 mm, while theouter diameters were chosen the same
as the outer
diameters of the solid specimens mentioned above.A fixed gauge
length Lg = 90 mm was used in thetorsion experiments, whereas the
total length L ofthe specimen was taken as 150 mm. A and H arethe
dimensions of the grip section (Figure 1). Thevalue ofHwas taken as
25, 21 and 13.5 mm and thesizeAwas taken as 30 mm.
Experimental Method
Torsion tests were performed at a room tempera-ture of 15-17 C
in winter. The average moisture
content of the test specimens was measured using aDelmhorst
Instrument BD-10 moisture meter for
L
Lg
A
d
H
Do
Lo
Di
Lo
Do
Figure 1. Geometries of solid and tubular specimens used in
torsion tests.
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wood and found to be 6%. The longitudinal axesof the wood
specimens were chosen parallel to thegrain directions. However,
each wood specimen had
different grain angles, , which vary between 0 and+35.
The main groups of the research are as follows:
Torsion tests on beech, pine, hornbeam andchestnut specimens
(Figure 1) that have solidcircular cross sections with 3 different
radii,
Torsion tests on pine, chestnut and steel spec-imens that have
tubular circular cross sectionshaving the same outer but different
inner radii,
Cyclic torsion tests on solid circular wood spec-imens having
the same outer radii (Figure 3).
Torsion tests were performed starting from zerotorque value
until the failure torque values werereached at constant strain
rates in different phasesof the loading procedure. The tests were
performedat slow strain rates until the specimen yielded.
Afterthat, the motor speed was increased until the failurestage of
the test was reached. The torsion testingmachine SM21 (TecQuipment,
1982) has a digitalcounter, each data-counter increment of which
cor-responds to a 0.3 angle of twist. Each value of theangle of
twist was transformed to m12, the maxi-mum shear strain at the
cross section for both solidand tubular bars. Indices 1, 2, and 3
represent theprincipal directions of the corresponding
orthogonalcoordinate system, which is attached at an edge ofthe
cross section (Figures 2 and 3). Axes 2 and 3 liein the cross
section whereas axis 1 is parallel to thelongitudinal twist axis.
Wood is assumed to be antransversely isotropic composite material.
The inde-pendent elastic constants for orthotropic and for
thespecial case of the transversely isotropic materialsare given in
the Appendix.
2-Tangentialaxis
1- Longitudinal axis (along the grains)
3-Radial axis
Figure 2. General specification of orthotropic materialwith the
principal directions.
The stress-strain relationships in torsional load-ing can be
written as m12 =
m12/G12 = ro
m/Lgand m12 = T ro/J = 2 T r3o . Here, ro is the outerradius,
m12 is the maximum shear stress developingat each cross section,
G12 is the shear modulus, Tis the instantaneously applied torque by
the torque-machine, andJis the polar moment of inertia of thecross
section of solid or tubular bars.
Results and Discussion
In Tables 1 and 2, the available elastic mechanicalconstants of
typical wood specimens from the liter-ature are listed. As can be
seen, there are still un-
known material specifications for some wood species.In Tables
3-6, the shear modulus values of pine,beech, chestnut, and hornbeam
wood obtained fromthe present study are listed both for the solid
andtubular circular cross-sectional bars. Statistical val-ues
showing the central tendency and the spread ofdata for all
experimental results are listed in Table7 comparatively.
Static torsion tests without unloading
Figure 4 shows the stress-strain graphs for differ-
ent r/L parametric ratios of pine and beech solidtest specimens.
Note that shear stresses take nega-tive values when the test
specimens are subjected tobackward directional torsional loading.
The stressincreases sharply in thin bars with r/L= 0.07 com-pared
to the thick ones with r/L= 0.13 at the sameangle of twist in the
range of 0.0075 0.015. It isnoted from Figure 4 that thin solid
bars yield at12 = 0.016 and 12 = 46 MPa, while the thicksolid
specimens continue to deform at a compara-tively small rate up to
12 = 0.05.
Figures 5 and 6 show that tubular pine wood
bars break at a smaller angle of twist compared totubular
hornbeam bars, while the shear stress lev-els at cracking are
slightly higher. It is noted thatthe stress-strain curves are
parallel to each other andtheir slopes are approximately the same.
Sometimes,due to undetected production damage, specimens ex-hibit
stress-strain curves with extraordinary slopes.Figure 6 displays
the stress-strain behavior of tubu-lar hornbeam. The 2 tubular
hornbeam bars failed atrelatively large strain values compared to
the other6 species (Figure 1).
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(a) (c)
(d) (e)
(b)
Figure 3. (a) TQ-SM21 torsion test fixture and (b) chestnut, (c)
pine, (d) beech, (e) hornbeam tubular and solid woodtest
species.
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Table 1. Mechanical properties of different types of wood
(Hibbeler, 1991; Chandrupatla, 1997).
WoodSpecies
1E
GPa 2
1
E
E
13
G MPa
32
1
G
E
T
(Elastic
Tensile
Strength)MPa
C
(Elastic
Comp.
Strength)MPa
uT
(Ultimate
Tensile
Strength)MPa
uC
(Ultimate
Comp.
Strength)MPa
13 MPa
Balsa wood 0.83 20.0 0.30 - 29.0 - - - - -
Pine wood 9.81 23.8 0.24 - 13.3 - - - - -
Plywood 11.7 2.00 0.07 - 17.1 - - - - -
Douglas fir,
green 11.0 - - - - 33 23 - 27 6.2
Douglas fir23.5-24.5
- - - - - - 853 - 912 - -
Douglas fir,
air dry
13.00-
13.01- 2.10 - - 56 44 - 26-51 6.2-7.6
Red oak,
green10.00 - - - - 30 18 - 24 8.3
Red oak, air
dry12.00 - - - - 58 32 - 48 12.4
White
spruce9.65 - 0.31 - - - - 2.5 36 6.7
Loblollypine
latewood
6.55 -
27.5- - - - - - 410 -1422 - -
Table 2. Typical elastic constants of some wood material
(Chandrupatla, 1997).
Wood Types 1E
GPa
2E
GPa
3E
GPa
21G
GPa
32G
GPa
31G
GPa21 32 31
Douglas fir 14.8 0.6 1.0 0.7 0.1 0.8 0.017 0.432 0.0216
SpruceHexagonal
Model
0.0143 1.120 0.556 0.605 0.035 0.594 0.049 0.11 0.022
Spruce
measurement6.0-25. 0.7-1.2 0.4-0.9 0.6-.07 0.02-0.7 0.5-0.6
0.02-0.05 0.2-0.35 0.01-0.025
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Table
3.
Shearmodulusvaluesofcircularcross-sectionalpinewoodspecimensundertorsionalloading.
Test
No
Woodspecimenandloadin
g
types:
Forwardloading-F
Backwardloading-B
Solidspecimen-S
Tubularspecimen-T
Radius(mm)
ri:inner
ro:outer
G12(G
Pa)
1
WhitePine-T-F
ri=4.6,ro=6.0
3.01
2
WhitePine-T-B
ri=4.6,ro=6.0
9.03
3
WhitePine-T-F
ri=3.4,ro=6.0
7.34
4
WhitePine-T-F
ri=3.2,ro=6.0
3.77
5
WhitePine-T-B
ri=4.6,ro=6.0
9.03
6
WhitePine-T-B
ri=4.6,ro=6.0
11.4
7
Pine-T-F
ri=3.2,ro=6.0
5.51
8
Pine-T-F
ri=3.2,ro=6.0
5.88
9
Pine-T-F
ri=4.6,ro=6.0
7.48
10
Pine-T-F
ri=4.6,ro=6.0
2.84
11
Pine-T-F
ri=4.6,ro=6.0
8.26
12
Pine-T-F
ri=4.5,ro=6.0
7.88
13
Pine-T-F
ri=4.6,ro=6.0
6.69
14
Pine-T-F
ri=4.5,ro=6.0
1.30
15
Pine-T-F
ri=4.6,ro=6.0
2.19
16
Pine-T-F
ri=3.0,ro=6.0
2.18
17
Pine-T-F
ri=3.0,ro=6.0
3.53
Test
No
Woodspecimenandloading
types:
Forwardloading-F
Backwardloading
-B
Solidspecimen-
S
Tubularspecimen
-T
Radius(mm)
ri:inner
ro:outer
G
12
(GPa)
18
Pine-T-F
ri=3.0,ro=6.0
3.45
19
Pine-S-F
ro=6.25
1.44
20
Pine-S-B
ro=6.25
2.09
21
Pine-S-B
ro=3.5
2.19
22
Pine-S-B
ro=5.00
1.57
23
Pine-S-B
ro=5.00
5.98
24
Pine-S-B
ro=5.00
2.82
25
Pine-S-B
ro=6.00
5.24
26
Pine-S-F
ro=6.00
4.25
27
Pine-S-F
ro=6.00
1.11
28
Pine-S-F
ro=6.00
1.92
29
Pine-T-B/F(avg-forward-
backward)
ri=4.5,ro=6.1
3.25
30a
Pine-S-F-1stcy
cle
ro=10.0
0.18
30b
Pine-S-B-2nd cy
cle
ro=10.0
0.35
30c
Pine-S-F-3rdcy
cle
ro=10.0
0.40
30d
Pine-S-B-4th cycle
ro=10.0
0.33
30e
Pine-S-F-5th cy
cle
ro=10.0
0.35
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Table4.Shearmodulusvaluesofcircularcross-sectionalhornbeam
woodspecimensundertorsionalloading.
Test
No
Woodspecimenandloading
types:
Forwardloading-F
Backwardloading-B
Solidspecimen-S
Tubularspecimen-T
Radius(mm)
ri:inner
ro:outer
G12
(GPa)
1
Hornbeam-T-F
ri=3.0,ro=5.8
1.36
2
Hornbeam-T-F
ri=3.2,ro=6.0
2.62
3
Hornbeam-T-F
ri=3.3,ro=6.0
7.72
4
Hornbeam-T-F
ri=3.2,ro=6.0
7.40
5
Hornbeam-T-F
ri=3.2,ro=6.0
7.50
6
Hornbeam-T-F
ri=3.2,ro=6.0
2.02
7
Hornbeam-T-F
ri=3.2,ro=5.9
2.90
8
Hornbeam-T-B
ri=3.15,ro=6.0
7.31
9
Hornbeam-T-F
ri=3.3,ro=5.7
1.45
10
Hornbeam-T-F
ri=3.8,ro=6.0
2.41
11
Hornbeam-T-F
ri=3.2,ro=6.0
3.12
12
Hornbeam-T-F
ri=3.2,ro=6.0
2.76
13
Hornbeam-T-F
ri=3.0,ro=6.0
3.78
Test
No
Woodspecimenandloading
types:
Forwardloading
-F
Backwardloading
-B
Solidspecimen-S
Tubularspecimen
-T
Radius(mm)
ri:inner
ro:outer
G
12
(GPa)
15
Hornbeam-S-F
ro=6.0
2.53
16
Hornbeam-S-F
ro=6.0
4.39
17
Hornbeam-S-F
ro=6.1
1.34
18
Hornbeam-S-F
ro=6.1
3.64
19
Hornbeam-S-F
ro=6.1
3.80
20
Hornbeam-S-F
ro=6.0
3.06
21
Hornbeam-S-B
ro=6.1
0.83
22
Hornbeam-T-B/F(avg-
forward-backward)
ri=3.25,ro=6.0
3.40
23
Chestnut-T-F
ri=3.25,ro=6.0
7.33
24
Chestnut-T-F
ri=3.30,ro=6.0
7.18
25
Chestnut-T-F
ri=3.25,ro=6.0
1.48
14
Hornbeam-T-F
ri=3.3,ro=6.0
1.30
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Table
5.
Shearmodulusvaluesofcircularcross-sectionalchestnutwoodsp
eci-
mensundertorsionalloading.
Table6.
Shearmodulusvalues
ofcircularcross-sectionalbeechwoods
pecimens
undertorsionalloading.
Test
No
Woodspecimenandloading
types:
Forwardloading-F
Backwardloading-B
Solidspecimen-S
Tubularspecimen-T
Radius(mm)
ri:inner
ro:outer
G12
(GPa
)
1
Chestnut-T-F
ri=3.25,ro=6.0
7.33
2
Chestnut-T-F
ri=3.30,ro=6.0
7.18
3
Chestnut-T-F
ri=3.25,ro=6.0
1.48
4
Chestnut-T-F
ri=3.10,ro=5.9
3.55
5
Chestnut-T-F
ri=3.30,ro=6.0
5.97
6
Chestnut-T-F
ri=3.00,ro=6.0
1.82
7
Chestnut-T-F
ri=3.25,ro=6.0
6.62
8
Chestnut-T-F
ri=3.00,ro=6.0
6.12
9
Chestnut-T-F
ri=3.20,ro=5.9
5.57
10
Chestnut-T-F
ri=3.10,ro=6.0
7.53
11
Chestnut-T-F
ri=3.0,ro=6.00
7.75
12
Chestnut-T-F
ri=3.0,ro=6.0
5.22
13
Chestnut-T-F
ri=3.25,ro=6.0
0.65
14
Chestnut-T-B
ri=3.0,ro=6.0
1.98
15
Chestnut-T-B
ri=3.15,ro=6.0
7.01
16
Chestnut-T-B
ri=3.15,ro=6.0
0.98
17
Chestnut-T-F
ri=3.0,ro=6.0
3.21
18
Chestnut-T-F
ri=3.0,ro=6.0
3.61
19
Chestnut-S-F
ro=6.0
2.07
20
Chestnut-S-B
ro=6.01
0.17
21
Chestnut-S-F
ro=6.01
0.40
Test
No
Woodspecimenandlo
ading
types:
Forwardloading-
F
Backwardloading-B
Solidspecimen-S
Tubularspecimen-T
Radius(mm)
ri:inner
ro:outer
G
12
(GPa)
23
Beech-S-B
ro=6.25
2.15
24
Beech-S-B
ro=5.00
2.80
25
Beech-S-B
ro=6.25
1.72
26
Beech-S-B
ro=3.50
5.60
27
Beech-S-B
ro=3.50
7.66
28
Beech-S-B
ro=3.50
1.00
29
Beech-S-B
ro=5.00
0.53
30a
Beech-S-1stcycle
ro=6.25
8.62
30b
Beech-S-6thcycle
ro=6.25
9.48
30c
Beech-S-9thcyc
le
ro=6.25
10.8
31a
Beech-S-1stcycle
ro=6.25
6.48
31b
Beech-S-7thcycle
ro=6.25
10.14
31c
Beech-S-7thcycle
ro=6.25
5.75
31d
Beech-S-9thcycle
ro=6.25
9.06
32
Beech-T-B/F(avg-forward-
backward)
ro=6.25
7.42
33a
Beech-S-2ndcycle
ro=6.25
4.73
33b
Beech-S-4thcycle
ro=6.25
6.32
33c
Beech-S-5thcycle
ro=6.25
9.48
22
Beech-S-B
ro=6.25
0.93
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Table7.
StatisticalvaluesofshearmodulusforTurkishwoodspecies.
Typeofwood
(numberofspecies)
Average
Shear
M
odulus
G12(GPa)
Standard
Deviation
(GPa)
Coefficien
tof
variation
c.v.(%)
Pine(solid+tube)(24)
3.72
3.64
97.67
Pine(solid+tube)-withoutcyclic
load(22)
3.90
-
95.24
Whitepine(6)
7.26
5.77
79.44
Tubularpine(13)
4.65
3.87
83.21
Solidpine(11)
2.63
2.69
102.54
Solidpine-withoutcyclicload
(10)
2.86
2.85
99.44
Hornbeam(solid+tube)(22)
3.48
3.37
96.76
Hornbeam(solid+tube)without
cyclicload(21)
3.48
3.37
96.59
Tubularhornbeam(14)
3.83
3.46
90.41
Solidhornbeam(7)
2.80
1.66
59.25
Chestnut(solid+tube)(21)
4.11
4.32
105.10
Solidchestnut(3)
0.88
1.04
117.84
Tubechestnut(18)
4.64
4.63
99.66
Pine(solid+tube)-forwardload
(15)
2.69
3.75
119.67
Tubularpine-forwardload(12)
4.77
3.90
81.89
Typeofwood
(numberofspecies)
Average
Shear
Modulus
G12(GPa)
Standard
Deviation
(GPa)
Coef
ficientof
va
riation
c.v.(%)
Tubularhornbeam-forward
load(13)
3.56
2.99
83.75
Tubularhornbeam-backward
load(1)
7.31
-
-
Solidhornbeam-forwardload
(6)
3.13
1.74
55.81
Solidhornbeam-forwardload
(1)
0.83
-
-
Chestnut(solid+tube)forward
load(17)
4.48
4.44
99.20
Tubularchestnutbackward
load(3)
3.32
3.23
97.24
Solidchestnutbackwardload
(1)
0.17
-
-
Tubularchestnutforwardload
(15)
4.91
4.70
95.76
Solidchestnutforwardload(2)
1.24
2.44
1
97.84
Beech(solid+tube)forward
load(12)
4.51
5.61
1
24.42
Solidbeech-backward
directionandwithoutcyclic
load(8)
1.87
3.22
1
40.65
Solidpine-backwardload(6)
3.32
2.85
85.98
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Wood solid bars under torsion
-6,E+07
-5,E+07
-4,E+07
-3,E+07
-2,E+07
-1,E+07
0,E+00
1,E+07
2,E+07
3,E+07
0,
000
0,
005
0,
010
0,
015
0,
020
0,
025
0,
030
0,
035
0,
040
0,
045
0,
050
0,
055
0,
060
0,
065
Shear strain (rad)
Shearstress
(Pa)
Beech d=0.007 Beech d=0.0125 Pine d=0.0125 Beech d=0.0125
Pine d=0.0125 Beech d=0.007 Beech d=0.007 Beech d=0.007
Pine d=0.01 Beech d=0.01 Pine d=0.01 Beech d=0.01
Pine d=0.01 Pine d=0.01
Figure 4. Curves for Turkish pine and beech wood solid specimens
under 1 forward and 13 backward torsional loadingfor do(m).
Figures 7-9 represent the tubular hornbeam,pine, and chestnut
wood specimens under back-ward and forward torsional loading. These
seriesof experiments have been carried out with vari-able inner
radial dimensions of specimens. t/roratios of these specimens lie
in the ranges of0.5 (t/ro)hornbeam2.6, 0.23 (t/ro)pine 0.25,
and0.45 (t/ro)chestnut 0.5. In Figures 7-9, when we
compare the shear stress values at the same shearstrain = 0.015
(rad), it is seen that the aver-age torsional shear stresses of the
samples satisfythe inequality pine chestnuthornbeam. The min-imum
torsional shear stress at the same shear strain = 0.015(rad) occurs
for pine tubular specimensthat have relatively small wall
thicknesses.
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Tubular pine under torsion
r outer= 6.0 mm
-3,E+07
-2,E+07
-1,E+07
0,E+00
1,E+07
2,E+07
3,E+07
4,E+07
0,000 0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040 0,045
Shear Strain (rad)
S
hearstress
(Pa)
r- inner =4.6 mm r- inner= 4.6 mm r- inner =3.2 mm
r- inner =3.2 mm r- inner =3.4 mm r- inner =3.2 mm
Pine-8 solid
1.51E+07
Figure 5. Curves for 7 tubular and 1 solid pine wood specimens
under forward/backward torsional loading.
Tubular hornbeam wood
router
= 6.0 mm
-1.E+07
0.E+00
1.E+07
2.E+07
3.E+07
0 0.01 0.02 0.03 0.04 0.05 0.06
Shear str ain(rad)
Shearstress(Pa)
r- inner= 3.2 mm r- inner =3.2 mm r- inner =3.3 mm r -inner= 3.2
mm
r- inner =3.8 mm r- inner =3.3 mm r- inner= 0.0 mm r- inner= 0.0
mm
Figure 6. Curves for tubular hornbeam wood specimens under
forward torsional loading.
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Tube hornbeam wood
0.5< t/r0
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Tube chestnut wood
0.45
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Tubular chestnut under torque
0.475
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Tubular white-pine under torque
r outer: 6.0 mm
-2.16E+07
-3.E+07
-3.E+07
-2.E+07
-2.E+07
-1.E+07
-5.E+06
0.E+00
0.00 0.01 0.01 0.02 0.02 0.03
Strain(rad)
Shearstress
(Pa)
r- inner= 4.6 mm
r- inner =4.6 mm
Figure 11. Curves for tubular white-pine wood specimens under
backward loading for ro = 6mm.
White tubular pine under torque
r outer= 6.0 mm
r inner = 4.6 mm
9.46E+06
1.92E-02;
1.22E+07
1.05E-02;
9.01E+06
7.33E-03;
5.85E+06
6.28E-03;
2.70E+06
0.E+00
2.E+06
4.E+06
6.E+06
8.E+06
1.E+07
1.E+07
1.E+07
0.00 0.01 0.01 0.02 0.02 0.03
Strain(rad)
S
hearstress
(Pa)
Slope-3= 0.72E+09
Slope-2= 3.0E+09
Slope-1= 0.52E+09
Figure 12. Curve for tubular white pine specimen and three-slope
representation under forward torsional loading.
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Tubular steel bar torque loading
ST-1010 G2 rockwell
0.E+00
2.E+07
4.E+07
6.E+07
8.E+07
1.E+08
1.E+08
1.E+08
2.E+08
2.E+08
2.E+08
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Shear strain (rad)
Shearstress
(Pa)
Test-1
Test-2
Figure 13. Curves for tubular steel specimens under torsion
loading.
Solid hornbeam wood specimens under torque
-3.E+07
-2.E+07
-1.E+07
0.E+00
1.E+07
2.E+07
3.E+07
0.00 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04
Shear strain (rad)
She
arstress
(Pa)
r=6.16 mm
r=6.13 mm
r=6.13 mm
r=6.025 mm
Figure 14. Hornbeam solid specimens under 3 different forward
and 1 backward torsion loading.
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Solid chestnut wood specimens under torque
-2.E+07
-2.E+07
-1.E+07
-5.E+06
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
3.E+07
3.E+07
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Shear strain(rad)
S
hearstress
(Pa)
r=5.99mm
r=6.005mm
Figure 15. Chestnut solid specimens under 1 forward and 1
backward torsion loading.
Solid pine wood specimens under torque
r = 6.0 mm
-5.E+06
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
3.E+07
3.E+07
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Shear strain(rad)
She
arstress
(Pa)
test-1
test-2
Figure 16. Pine solid specimens under forward torsion
loading.
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Tube pine-hornbeam-chestnut wood
r i=3 mm-ro=6 mm
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
3.E+07
3.E+07
0.002 0.010 0.018 0.026 0.033 0.041 0.049 0.057
Shear strain (rad)
Shearstress
(Pa)
Pine-1 Pine-2 Pine-3 Hornbeam-1 Chestnut-1 Chestnut-2
Slope-1(Pine-1)=1.12E+09
Slope-2(Pine-1)=5.27E+09
Slope-3(Pine-1)=0.16E+09
Figure 17. Curves for tubular pine, hornbeam and chestnut
specimens and three-slope representation of specimen (Pine-
1) under forward loading.
From all of the shear stress-strain curves forwood under
torsional loading we observe segmentsof slightly parabolic curves
with different slopes. Ingeneral, 3 slightly linear regions of the
shear stress-strain curve can be distinguished. Sample
represen-tations are presented in Figures 12 and 17. Threeslopes
are shown in these graphs with their values.The second region
always has a sharp stress incre-ment with a few data points while
the first and thirdregions have relatively small inclinations that
includeconsiderably large amount of data. The shear mod-
ulus G12 values are calculated and tabulated fromthe second
region. The results of the torsional testscarried out on various
wood species are also given inTables 3-6 and the related
statistical data are tab-ulated in Table 7 in detail. As seen from
Table 7,quite large values of coefficients of variation (c.v.)were
obtained. This variation may be affected tosome extent by the data
taken from the second linearelastic region, which have a sharp
stress incrementas mentioned above, rather than considering an
av-erage value of the entire response having less vari-
ation. Although there is less variation in the firstand third
linear regions, the calculations were notbased on these regions
because the complete graspof the specimen occurred during the
development ofthe first region and in the third region in
generalthe elastic limit was exceeded. In an
experimentalinvestigation, Bektas et al. (2002) carried out
com-pression, static bending, impact bending, and shearstrength
tests on prismatic beech wood specimens inwhich the coefficient of
variation was as high as 35%.All the shear tests were carried out
parallel to the
grains. However, in the torsion tests performed onround
specimens in the present study it was not pos-sible to measure
shear strength perfectly parallel tograins. The structural
complexity of wood dependsmainly on the unidirectional grain angles
through thethickness of the specimens. The specimens used
havevariable grain angles, which are measured with re-spect to the
twist axis within the range 0 to +35.As expected, the variable
grain angles affect signifi-cantly the stress-strain distributions
under torsionalloadings. Furthermore, during the preparation of
the
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round specimens the occurrence of undetected cracksor defects at
the inner or outer surfaces could causethe stress concentration at
those points. This prob-
lem does not exist in pure shear tests since the aver-age shear
stress calculations are based on an internalplane area that is not
affected by stress concentra-tions to the same extent. It should
also be notedthat although the moisture contents were the samethe
specimens were extracted from different portionsof different trees
of the same wood species. This con-stitutes another factor
affecting the large variationsin the test results.
From the results obtained, it is also found thatthe torsional
response of wood depends on the ge-ometry (solid or tubular
specimens) and on the ap-
plication direction of the torque relative to the
fiberdirections as well. It can also noted that, when theYoungs
modulus E11 (Gunay and Sonmez, 2003)and the shear modulusG12 for
wood are compared,Youngs modulus is found to be approximately
10times larger than the shear modulus.
Hysteresis tests of solid and tubular speci-
mens
The hysteresis curves are obtained for the nonlin-ear permanent
deformation analysis under torsionalloading with unloading and
reloading steps. To the
best of our knowledge, there are few published datapresenting
the hysteresis behavior of solid and tubu-lar wooden bars under
torsional loading.
In Figure 18 the results for a hornbeam solid spec-imen under 2
cyclic forward and backward loadingshow clearly the permanent
deformations occurringin the wood specimens. Except for the initial
for-ward loading, there are no differences in the slopesof the
shear stress-strain curves. This shows that noadditional strain
energy is lost during the repeatedhysteresis cycles within the
tested ranges. Fig-ures 19 represents one forward and one
backwardcyclic loading of the solid hornbeam specimen. Theshear
stress and shear strain values reached = 25.6MPa and = 0.036 rad in
forward loading, which
caused a sudden drop in the shear stress value with-out
resulting in an open crack. The specimen wasthen unloaded
completely and the loading was re-versed, decreasing the stress to
= 21 MPa with= 0.080 rad where the gross failure of the speci-men
occurred.
In Figure 20, the pine specimen was loaded untilthe shear stress
reached approximately 30 MPa. Theunloading process after this
stress level caused per-manent shear strain remaining in the wood
specimen.Application of 2-cycles causes additional strain en-ergy
lost during the repeated hysteresis cycles withinthe variable
ranges.
Solid hornbeam wood specimen
-2.E+07
-1.E+07
0.E+00
1.E+07
2.E+07
3.E+07
4.E+07
-0.04 -0.02 0.00 0.02 0.04 0.06 0.08
Shear strain (rad)
Shears
tress
(Pa)
r=6.13 mm
Figure 18. Hornbeam solid specimen under 2-cycle
forward/backward loading.
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Solid hornbe am wood specimen
r= 6.25 mm
-3.E+07
-2.E+07
-1.E+07
0.E+00
1.E+07
2.E+07
3.E+07
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Shear strain(rad)
Shearstress
(Pa)
Figure 19. Hornbeam solid specimen under 1-cycle
forward/backward torsion loading.
Solid pine wood specimen
r=5.0 mm
-3.E+07
-2.E+07
-2.E+07
-1.E+07
-5.E+06
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
3.E+07
3.E+07
0.000 0.010 0.020 0.030 0.040 0.050
Shear Strain (rad)
S
hearStress
(Pa)
Figure 20. Pine solid specimen under 2-cycle forward / backward
loading.
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Figure 21 represents the solid beech specimen un-der 9 cyclic
loading and unloading steps. A series offorward loading and
unloading paths follow almost
linear stress-strain curves. It is noted that there isno
reduction in the stress level in the hysteresis be-havior. The peak
of each loading cycle reaches thesame stress value and follows its
characteristic linearpath when the loading is further
increased.
In Figure 22 cyclic loading and unloading stepswere carried out
on pine specimens. For 3 load-ing steps, the shear stress was
increased up to 13 MPa,and then the specimens were subjected
toreversed loading until zero shear strain was reached.It is noted
that no permanent deformation remainedin the specimen after the
first 3 unloading cycles be-
cause of the low shear stress level in each case. Thefirst 3
curves show small amounts of strain energylost during the repeated
forward/backward cycleswithin ranges. The curves become
parabolicduring the third cycle. After this step, backward
andforward loading steps follow linear paths.
Figure 23 represents one reverse cyclic and oneforward loading
of tubular pine specimen. Both re-sponses are slightly parabolic
and there is a signif-icant difference in the slopes of
stress-strain curvesfor reverse loading/unloading and forward
loading.
Figures 24-26 show the hysteresis loops of thesolid beech
specimen for 3 different test specimenradii: r = 3.25 mm, r = 5 mm,
r = 6.25 mm.Since unloading is done from a sufficiently high
stressvalue, permanent strain remained in the test speci-
mens upon complete unloading. It is interesting tonote that, in
each experiment, the stress level reachesthe same stress value or
its characteristic curve path
at the end of the hysteresis loop.
Shear stress relaxation tests of solid speci-
mens
Stress relaxation is defined as the behavior of stressreaching a
peak and then decreasing or relaxing overa time under a fixed level
of shear strain in a statictorsion test. The specimens are loaded
to a certaintorque load below the fracture load and the angle
oftwist is held at a fixed position. The relaxation of the
torque within the time scale is recorded for a long pe-riod, and
the results are plotted for hornbeam, beech,and pine specimens in
Figure 27. Hornbeam speci-men had been relaxed from 7.2 to 23 N.m.
in the firsthour. For the beech specimen, which has the
samegeometrical values as the pine, the torque decreasedfrom 7.75
to 2.3 N.m. within 11,000 min. The torquein the pine specimen
decreased exponentially from3.4 to 1.9 N.m within 10,000 min. It is
noted thatbeech and hornbeam are relaxing 2 times faster thanpine.
The torque relaxation curves indicate that, forall wood species,
the shear stress decays exponen-tially with time. Therefore, wood
can be considered
a viscoelastic material that obeys the Maxwell modelof stress
relaxation. According to this model, thestress relaxes completely
as time goes to infinity.
Solid beech wood specimen
r = 6.25 mm
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
2.5E+07
3.0E+07
3.5E+07
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035
Shear strain (rad)
Shearstre
ss
(Pa)
Figure 21. Beech solid specimen under 9-cycle forward
loading.
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Solid pine wood specimen under torque
r = 6.25 mm
-1.0E+07
-5.0E+06
0.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
2.5E+07
3.0E+07
-0.010 0.000 0.010 0.020 0.030 0.040
Shear strain (rad)
Shearstress
(Pa)
Figure 22. Pine solid specimen under 3-cycle forward 1-cycle
backward loading.
Tubular pine wood
r o= 6.0 mm - ri= 4.65 mm
-2.E+07
-1.E+07
0.E+00
1.E+07
2.E+07
3.E+07
4.E+07
5.E+07
-0.040 -0.020 0.000 0.020 0.040 0.060 0.080
Shear strain (rad)
Shearstress
(Pa)
cycle-1
loading-2
Figure 23. Pine specimen under 1-cycle backward and then
continuous forward loading.
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Solid bee ch wood
r=3.25 mm
-1.E+08
-8.E+07
-6.E+07
-4.E+07
-2.E+07
0.E+00
2.E+07
4.E+07
6.E+07
- 3.E-02 -2.E- 02 - 1.E- 02 0.E+00 1.E- 02 2.E- 02 3.E- 02 4.E-
02 5.E- 02
Shear strain(rad)
Shearstress
(Pa)
loading-1
loading-2
Figure 24. Curves for solid beech under 1 forward loading and 1
complete cycle.
Solid beech wood
r= 5.0 mm
-4.E+07
-3.E+07
-2.E+07
-1.E+07
0.E+00
1.E+07
2.E+07
3.E+07
4.E+07
0.00 0.01 0.02 0.03 0.04 0.05 0.06
Shear strain (rad)
Shearstress
(Pa)
loading-1
loading-2
Figure 25. Curves for solid beech under 1 forward loading and 1
complete cycle.
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Solid beech wood
r= 6.25 mm
-2.E+07
-2.E+07
-1.E+07
-5.E+06
0.E+00
5.E+06
1.E+07
2.E+07
2.E+07
-0.07 -0.02 0.03
Shear strain (rad)
Shearstress
(Pa)
Figure 26. Curves for solid beech wood under 1 forward loading
and 1 complete cycle.
Solid wood relaxation experiments
Beech (r=3.25 mm) - pine (r=6.25 mm)- hornbeam (r=6.21 mm)
0.1
1.1
2.1
3.1
4.1
5.1
6.1
7.1
8.1
0.1 1 10 100 1000 10000 100000 1000000
Time (min)
Torq
ue(Nm)
Beech-relaxation
Pine-relaxation
Hornbeam-relaxation
Figure 27. Stress relaxation curves of the beech, pine and
hornbeam solid specimens.
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Conclusions
Wood is a good example of an orthotropic fiber com-
posite material with its organic structure. Becauseof the
complexity in the cellulosic structure at microlevel, the general
mechanical behavior is not knownclearly. Furthermore, the behavior
of wood mate-rial changes with the type of loading,
temperature,moisture content, grain angles, material density,
thegrowth condition, and the age of the tree from whichthe specimen
is taken.
From the results of the torsion tests performed inthe present
study, the following conclusions can bedrawn:
1. In general, the response of wood to torsionalloading exhibits
a flexible character that is af-fected by specific alignments of
the grains andtype. The presence of possible defects in microlevels
produced during the preparation of thespecimens is also
important.
2. Failures occurred due to a longitudinal crackthat propagated
along the grain directions. Ifthe grain angles are parallel to the
longitudinalaxis the crack propagates along the twist axismore
slowly since the ends of the test speci-men act as a sort of
reinforcement against ax-
ial crack propagation. Therefore, for 0o grainangles, the
failures of the specimens are incom-plete.
3. Failure characteristics of the test specimens instatic
loading depend on the sense of the ap-plied torque, and the type
and geometry of thewood species.
4. In cyclic torsional loading, if the amplitude ofthe applied
torque is within the elastic range,the specimens are resistant to
alternating loadswithout having any residual distortion. How-
ever, if a specimen is loaded beyond the pro-portional limit, a
hysteresis loop is observed,which repeats itself in successive
cycles. Insamples with 0ograin angles, the hysteresisloops exhibit
similar stress-strain gradients inforward and backward loading.
Shear and nor-mal stresses are distributed equally throughoutthe
fiber and matrix combination.
5. Pine is more flexible compared to chestnut,hornbeam, and
beech. It can undergo largertwist angles before the nucleation of
any cracks.
6. Tubular specimens exhibit a sudden rise instress-strain
curves before transition to a per-manent deformation zone.
7. In general, shear stress-strain curves consist of3 slightly
linear portions with different slopes.The second region has the
steepest slope, whilethe third region is much wider than the
oth-ers and corresponds to permanent deformationzone of the
specimens.
8. Displacement controlled relaxation static testsof wood
species show that wood is a viscoelas-tic material that obeys the
Maxwell model dur-ing relaxation.
Based on the various experiments performed inthe present study,
it is concluded that much exper-imental and theoretical
investigation remains to bedone to understand the mechanical
behavior of woodin torsion.
Acknowledgments
All the experiments were performed at the MechanicsLaboratory of
Gazi University Mechanical Engineer-ing Department. The authors
would like to acknowl-edge the help of Asst. Prof. Dr. Rahmi Aras
andG.U. Graduation Project course students for supply-ing the wood
material, and technician Kadir Ylmazfor the preparation of solid
and thin tubular woodspecimens in this research.
Nomenclature
A grip dimension (mm)a, b Iosipescu shear test fixture con-
stantsc.v. coefficient of variationDi, Do inner and outer
diameters (m)E1, E2, E3, G12,G23, G13
Youngs and shear moduli of theorthotropic material in
principaldirections
N
m2
Ex, Ey, Ez, Gxy,Gxz, Gyz
Youngs and shear moduli of theorthotropic material through x,y,
z axes of the cartesian coordi-nate system
N
m2
J polar moment of inertia
m4
H grip dimension (mm)
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k constant number (Lekhnitskii)which is obtained from series
ex-pansion
kzx , kyz instantaneous shear modulus val-ues
Lg , L gauge and total length of speci-men (mm)
ri, ro inner and outer radii (m)st.d. standard deviationT torque
(N.m)
Greek symbols
x, y , z normal strain components of theorthotropic material
(rad)
angle of twist (rad)13, 23, 12 shear strain components of
the
orthotropic material in principaldirections (rad)
xs Lekhnitskii elastic constantxy, xz, yz Poissons ratios of the
or-
thotropic material
grain angle measured from thetwist axis (degree)
x, y, z normal stress components of theorthotropic material
N
m2
1, 2, 3 normal stress components of theorthotropic material in
principaldirections
N
m2
t, c, ut,uc
elastic tensile, compressive, ulti-mate tensile and ultimate
com-pressive stress
N
m2
13, 23, 12 shear stress components of theorthotropic material
Nm
2
s, s average shear stress andstrain
N
m2
,(rad)
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Appendix
Plane stress state, strain-stress relations of an orthotropic
material used in experimental studies.
xy
s
=
1/Ex yx/Ey sx/Gxyyx/Ex 1/Ey sy/Gxy
xs/Ex ys/Ey 1/Gxy
xy
s
(A1)
Lekhnitskii (1963) and Yoshihara et al. (2001) gave the shear
modulus formulations of orthotropic materialwith the following
series expansions:
Gzx = kzxa2 b k
8
2
GzxGyz
j=1
(1)j1
(2j 1)2
tanh (2j1) b
2a
GzxGyz
(A2)
Gyz = kyza2 b k
12 2
2 j=1
1
(2j1)2
cosh
(2j 1) b
2a
GzxGyz
1 (A3)
Here kzx , kyz are initially assumed slopes of the torsional
moment-shear strain curve or the instantaneousshear modulus values.
The geometric constants are: a = 22 mm, b = 12 mm defined on the
Iosipescu sheartest fixture. k is calculated by series expansion as
(Lekhnitskii, 1963);
k=1
3
2 a
b
GyzGzx
2
5 j=1
1
(2j 1)5 tanh
(2j 1) b
2 a
GzxGyz
(A4)
Transversely isotropic elastic materials have 5 independent
elastic constants and strain-stress relation canbe expressed in the
following form in combined loading:
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1
2
3
23
31
12
=
1
E1
21E2
31E3
0 0 0
12E1
1
E2
32E3
0 0 0
13E1
23E2
1
E30 0 0
0 0 0 1
G230 0
0 0 0 0 1
G310
0 0 0 0 0 2 1
E1 +21E2
1
2
3
23
31
12
(A5)
118
