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Fracture characteristics of different wood species under mode I loading perpendicular to the grain
Materials Science and Engineering A332 (2002) 29 – 36 www.elsevier.com/locate/msea
Fracture characteristics of different wood species under mode I loading perpendicular to the grain A. Reiterer *, G. Sinn, S.E. Stanzl-Tschegg Institute of Meteorology and Physics and Christian Doppler Laboratory for Fundamentals of Wood Machining, Uni6ersity of Agricultural Sciences Vienna, Tu¨rkenschanzstraße 18, A-1180 Vienna, Austria Received 28 November 2000; received in revised form 10 May 2001
Abstract Mode I fracture characteristics of different wood species (one softwood and three hardwoods) in two crack propagation systems were investigated using the wedge splitting test under loading perpendicular to the grain. From the obtained load– displacement curves the initial slope, the critical stress intensity factor and the specific fracture energy were determined. The initial slope and the critical stress intensity factor were shown to depend strongly on density within all species whereas for the specific fracture energy differences between the softwood and the hardwoods were found. Differences between the crack propagation systems could be explained by the higher volume fraction of radial oriented tissue (rays) of the hardwoods. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Wood; Fracture toughness; Specific fracture energy; Microstructure of wood; Heterogeneity of wood
1. Introduction Wood is an inhomogeneous, cellular and widely used engineering material with excellent mechanical properties in spite of its low density. These properties are achieved through an optimized hierarchical structure. Concerning its fracture properties there is still a great need for investigations as most studies in the literature focused on softwoods and on linear elastic and isotropic concepts. Due to its orthotropic nature with three main directions, a longitudinal direction (L) parallel to the stem axis, a transverse direction (R) perpendicular to the tree rings and a transverse direction (T) parallel to the tree rings, six crack propagation systems exist for characterizing the fracture behavior. The crack propagation systems are usually indicated using two letters, the first letter indicates the direction perpendicular to the crack plane and the second one serves for the direction of the crack propagation [1]. * Corresponding author. Present address: Austrian Industrial Research Promotion Fund, Ka¨rtner Straße 21-23, A-1015 Vienna, Austria. Tel.: + 43-1-512458464; fax: +43-1-512458441. E-mail address: [email protected] (A. Reiterer).
Moreover, softwoods and hardwoods are different in their microstructure. Softwoods like spruce consist of up to 95% tracheids oriented in the longitudinal direction parallel to the stem axis. Only approximately 5% of the tissue is oriented in the radial direction, the uniseriate rays. Hardwoods are more specialized in their structure consisting of different tissue types like vessels, fiber tracheids, libriform fibers and rays. Hardwoods can have bigger rays (multiseriate rays) and a higher relative volume fraction of this radially oriented tissue. The basic structure of softwoods and hardwoods is shown in Fig. 1. In this paper we apply the wedge splitting method [2] and finite element simulations considering the orthotropic material behavior for the investigation of the Mode I fracture characteristics of wood in the crack propagation systems RL and TL. Results from four wood species, one softwood spruce (Picea abies [L] Karst.) and three hardwoods alder (Alnus glutinosa Gaertn.), oak (Quercus robur L.) and ash (Fraxinus excelsior L.) are presented. Differences between the softwood and the hardwoods are shown and discussed. Moreover, differences between the two crack propagation systems were analyzed and discussed in terms of structural features. The results are supported by scan-
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A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
proximately 12% was reached. Notched specimens as shown in Fig. 2 were prepared in the RL as well as in the TL system. The dimensions were the following: W= 0.10 m; H=0.13 m; T= 0.04 m; a= 0.045 m; L=0.085 m. The starter notch was sharpened using a razor blade. All specimens were stored in the climate chamber prior to testing. Six samples were investigated for each crack propagation system and wood species. The densities of the samples were in the following ranges: spruce (479940) kg m − 3; alder (510935) kg m − 3; oak (5539 37) kg m − 3; and ash (7019 55) kg m − 3.
2.2. Methods
Fig. 1. Principle structure of wood. (a) Structure of softwood consisting of earlywood tracheids, latewood tracheids and uniseriate rays (adapted from [22]). (b) Structure of hardwood consisting of vessels, libriform fibers and multiseriate rays.
ning electron microscope (SEM) pictures of the fracture surfaces and acoustic emission measurements.
In order to characterize the Mode I fracture behavior of the different wood species the wedge splitting technique according to Tschegg [2] was used. This method has several advantages like a favorable ratio of specimen weight to ligament area and a simple and stiff loading equipment [3]. The method has been used for fracture characterization of inhomogeneous materials like concrete [3,4], wood [5] or wood composites [6] as well as for brittle materials like ceramic refractory material [7]. The principle of the method is shown in Fig. 3. A wedge is pressed against load transmission pieces in a standard material testing machine, the friction being minimized by the use of roll bodies. From the measurement of the force of the testing machine FM the horizontal splitting force FH can be determined according to FH = FM/2 tan(h/2)
2. Materials and methods
2.1. Material One softwood, spruce, one diffuse porous hardwood, alder and two ring porous hardwoods, oak and ash were chosen for this study. Beams were stored in a climate chamber at 20 °C temperature and 66% relative humidity until an equilibrium moisture content of ap-
(1)
where a is the wedge angle. A wedge angle of 18° was used in this study. The crack mouth opening displacement d is measured by inductive displacement gauges mounted directly on the specimens on both sides of the starter notch. The measured load–displacement curve characterizes the fracture process. The initial slope of the load–displacement curves in the linear elastic region kinit is
Fig. 2. Specimen geometry and orientations.
A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
Gf =
1 A
&
31
lmax
FH(l)dl.
(2)
0
This quantity is a ‘toughness’ quantity characterizing the whole Mode I fracture process until the specimen is split into two halves and does not depend on specimen size and shape if the specimen size is not too small. The used size is large enough to obtain size independent values [5]. In order to characterize the maximum stress state the critical stress intensity factor KIc was determined. In the literature the critical stress intensity factor of wood is often determined according to a formula of the form (3)
KIc = FcY(a/W,B,H)
Fig. 3. Testing arrangement of the wedge splitting test.
where Fc is the force necessary for crack initiation and Y is a factor depending on the geometry, in particular the length of the starter notch a, the sample thickness B and the sample height W (see for example [8–10]). Strictly speaking this formula is for isotropic materials only. In order to determine the critical stress intensity factor considering the orthotropic nature of wood the maximum horizontal splitting forces were taken as input data for a two-dimensional finite element simulation using the ANSYS© software package. The stresses at the crack tip were modeled using quarter point elements as suggested in Stanzl-Tschegg et al. [5] and Schachner et al. [11] (see Fig. 4). The stress intensity factors were calculated from the node displacements according to
' KI = KII
Fig. 4. Arrangement of the quarter point elements at the crack tip used in the finite element simulation. Table 1 Elastic parameters (elastic moduli Ei, shear moduli Gij and Poisson ratios nij) of the different wood species used for the finite element simulations
EL (GPa) ER (GPa) ET (GPa) GLT (GPa) GLR (GPa) nLT [1] nLR [1]
Spruce
Alder
Oak
Ash
10 0.8 0.45 0.65 0.6 0.4 0.4
11.7 1.1 0.6 0.7 0.8 0.3 0.3
13 1.6 0.9 0.8 1.2 0.3 0.3
15.8 1.5 0.8 0.6 0.9 0.3 0.3
Values taken from Niemz [12] and modified such that the initial slope was predicted correctly.
determined in order to characterize the elastic behavior. The area under the load– displacement curve divided by the fracture area A yields the specific fracture energy Gf according to
y − 1 4(uB − uB%)− (uC − uC%) B 8L 4(6B − 6B%)− (6C − 6C%)
(4)
where uB, uB%, uC, uC% are node displacements in the x direction and 6B, 6B%, 6C, 6C% node displacements in the y-direction (see Fig. 4) and L is the element length. The matrix B depends on the stiffness matrices of the wood species (for details see [11]). The elastic parameters used for the stiffness matrices are shown in Table 1. They were taken from the literature [12] and were modified in such a way that the initial slope of the load displacement curves was predicted correctly.
3. Results The load–displacement curves for the different crack propagation systems are shown in Fig. 5a (RL-System) and b (TL-System). For both systems spruce showed stable crack propagation until complete separation of the specimens. The hardwoods behaved differently. After macrocrack initiation at the maximum horizontal splitting force a sudden drop in the load–displacement curve occurred indicating unstable crack propagation.
A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
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Fig. 5. Typical load – displacement curves obtained by the wedge splitting test in the RL (a) and TL (b) system.
This drop was followed by crack arresting leading to another maximum. This behavior was repeated several times in most cases. In Table 2 the results for the initial slope kinit, the critical Mode I stress intensity factor KIc and the specific fracture energy Gf are shown. The initial slope kinit is characteristic for the elastic properties and proportional to an effective modulus of elasticity [7]. As specimen geometry and size was the same for all wood
species and orientations the initial slopes can be compared. The stiffness in the RL system is higher than in the TL system. The hardwoods show higher initial slopes than spruce in both systems except for alder where the initial slope is nearly the same. For the TL system the differences between the wood species are lower. In general, the initial slopes vary from 1.4 to 3.5 N m − 1 in the RL system and from 0.9 to 1.6 N m− in the TL system. This agrees well with the known fact that conventional moduli of elasticity are higher under loading in the radial direction than in the tangential direction [12]. From the maximum splitting forces the critical stress intensity factor KIc was determined considering the orthotropic nature of wood. The finite element simulation yielded the results shown in Table 2. In both systems spruce has the lowest fracture toughness whereas within the hardwoods ash has always the highest one. The values range from 0.49 to 1.16 MPam1/2 in the RL and from 0.31 to 0.65 MPam1/2 in the TL system. The results for the specific fracture energy, characterizing the whole fracture process until complete separation of the specimen into two halves and therefore including crack initiation and propagation yield that in the RL system ash has the highest specific fracture energy and spruce and oak show almost equal values. In the TL system the situation is quite similar. In both systems alder reaches the lowest specific fracture energies. The values vary from 244 to 550 J m − 2 in the RL system and from 155 to 350 J m − 2 in the TL system.
4. Discussion The shape of the load–displacement curves of spruce and the hardwoods is different (see Fig. 5). All spruce specimens show completely stable load–displacement curves whereas the hardwood specimens show unstable parts after crack initiation accompanied by crack ar-
Table 2 Mean values and standard deviations (S.D.) for the initial slope kinit, the critical stress intensity factor KIc and the specific fracture energy Gf Spruce
kinit (N m−1) S.D. KIc (MPam1/2) S.D. Gf (J m−2) S.D.
Alder
Oak
Ash
RL
TL
RL
TL
RL
TL
RL
TL
1.44 0.17 0.49 0.01 337 47
1.01 0.10 0.31 0.03 213 16
2.33 0.15 0.67 0.07 244 41
0.95 0.08 0.33 0.03 155 39
2.58 0.12 0.83 0.03 348 38
1.31 0.12 0.41 0.06 271 44
3.57 0.22 1.16 0.06 551 38
1.60 0.09 0.65 0.03 345 57
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Table 3 Mean values and standard deviations (S.D.) for the acoustic emission counts AE (only for the RL system, from [14]) and the brittleness number B Spruce
AE [1] S.D. B (mm)
Alder
Oak
Ash
RL
TL
RL
TL
RL
TL
RL
TL
9567 1300 1.1
– – 0.9
1367 120 2.1
– – 1.8
867 176 2.0
– – 1.2
433 33 2.1
– – 1.9
resting. In principle the wedge splitting test is favorable in achieving stable crack propagation as the method reduces the compliance of the testing system by the factor tan2(a/2) as discussed in Harmuth [13]. Moreover, a rising crack growth resistance curve and a low critical stress intensity factor increase the stability of crack propagation [7,13]. As can be seen in Table 2 the critical stress intensity factors are generally higher for the hardwoods. A rising crack growth resistance curve can only occur with non-linear material behavior. Regarding the load–displacement curves of the hardwoods the maximum load is visible as sharp peaks which is typical for linear elastic brittle materials. Quite in contrast the load– displacement curves of spruce show a round maximum load peak and clear deviation from linear elastic behavior. Therefore one can conclude that spruce displays more ductile and the hardwoods more linear elastic and brittle behavior. The interpretation is supported by recently obtained acoustic emission measurements during Mode I fracture of RL specimens [14]. These measurements showed much less acoustic emission counts until the maximum splitting force is reached for spruce compared to the three hardwoods (see Table 3). As the crack initiation phase is characterized by the formation of a process zone around the crack tip consisting of microcracks the lower amount of acoustic emission events indicates a much smaller amount of microcracks during process zone formation and therefore less energy dissipating processes in the crack initiation phase. Due to the simpler structure of softwood the a crack can take rather straight paths whereas the more complex hardwood structure could force the crack to take a more circuitous path. Moreover, in the crack propagation phase fiber bridging might play an important role in dissipating energy. Tracheids of spruce are much longer [15] than the fibers of the hardwoods (fiber tacheids, libriform fibers). The dimensions of the spruce tracheids are in the range of 3– 4 mm whereas the fibers of the hardwoods typically reach a length of less than 1 mm. Therefore fiber bridging effects due to the longitudinally oriented fiber types might be considered to be not so effective in hardwoods than in spruce. In the future
a more in-depth analysis should be used to identify the onset of unstable fracture. In order to characterize whether the behavior is more ductile or brittle the maximum forces, the initial slopes and the specific fracture energy were combined to obtain a brittleness parameter according to B=
1 F 2H,max . L kinitGf
(5)
FH,max is the maximum horizontal splitting force and L is the ligament length. Lower values of B indicate a more ductile behavior whereas higher values indicate a more brittle behavior. This parameter is proportional to the reciprocal of the characteristic length according to Hillerborg [16] and is similar to conventional brittleness quantities (see for example [7]) except that the initial slope was used to consider the stiffness. The obtained values for B (see Table 3) indicate clearly that this brittleness parameter is higher for the hardwoods being in the range of approximately 2 mm except for oak in the TL system. The values for spruce are in the range of 1 mm. As all mechanical parameters of wood are related to density it is not surprising that the fracture mechanical quantities do so also. The initial slope in both crack propagation systems had a strong correlation to the measured density at 12% moisture content of the different wood species (Fig. 6a). A linear regression showed a high significance with correlation coefficients of R= 0.93 for the RL and R= 0.94 for the TL system. The regression lines showed clearly different slopes for the two systems. The greater differences for the RL system lead to a higher slope compared to the TL system. Quite similar the critical stress intensity factors were also strongly influenced by density (see Fig. 6b). In both systems linear regressions showed excellent fits with regression coefficients of R =0.98 for the RL and R= 0.99 for the TL system. The differences between the differently dense species were higher for the RL system leading to a higher slope of the regression line. The influence of density on the critical stress intensity factors is in accordance with investigations in the literature (see for example [17–19]). However, a distinction between the two systems with crack propagation along
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A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
the grain has not been made up to now and investigations on hardwoods are still quite seldom. Here, it should be pointed out that models for cellular materials developed by Gibson and Ashby [19], predict a relationship between density and critical stress intensity
Table 4 Ratio of initial slope kinit, critical stress intensity factor KIc and specific fracture energy Gf between the RL and TL crack propagation system
Ratio kinit Ratio KIc Ratio Gf
Fig. 6. Initial slope Kinit (a), critical stress intensity factor KIc (b) and specific fracture energy Gf (c) for the RL (squares) and TL system (triangles) versus density. For the Kinit and KIc values linear regression lines are shown. The regression coefficients for the Kinit values were R= 0.93 for the RL and R= 0.94 for the TL system. The regression coefficients for the KIc values were R= 0.98 for the RL and R =0.99 for the TL system.
Spruce
Alder
Oak
Ash
1.4 1.5 1.6
2.4 2.2 1.6
2.0 2.2 1.3
2.2 1.8 1.6
factor of the form KIc 8 r3/2 and it was shown that this holds for wood quite well. For the results presented in this paper a relationship of this form gave fits almost as well as the linear ones. Therefore, the results do not contradict the foam model. Nevertheless, in the foam model a distinction between the RL and TL system for wood is not included and it was one intention of this paper to show this difference. Both for the initial slope and the critical stress intensity factor the dependence on density is represented better by the measured density values in the TL system. The reason is that in this crack propagation system the crack plane is oriented perpendicular to the annual rings. The crack separates both earlywood and latewood of the annual rings and the sample density is therefore quite representative. In the RL system the crack plane is oriented parallel to the annual rings giving the crack the opportunity to run in weaker earlywood zones of an annual ring. The influence of density is also obvious for the specific fracture energy but only within the hardwoods (see Fig. 6c). This is due to the different crack propagation phase of spruce compared to the hardwoods. The different slope of the dependence on density is reflected in the ratio for the determined values. For the initial slopes the ratio between the RL and TL systems was 1.4 for spruce and 2.4 for alder, 2.0 for oak and 2.2 for ash. For the critical stress intensity factor the ratios were 1.5 for spruce, 2.2 for alder and oak and 1.8 for ash. The differences were higher for the hardwoods. For the specific fracture energy such a clear trend could not be found although the fracture energies were always higher in the RL system. The ratios for all three parameters are shown in Table 4. This behavior could be explained considering the differences in structural features between spruce and the hardwoods. Spruce consists of approximately 95% of axial oriented fibers, the tracheids. Only approximately 5% are radially oriented rays. Hardwoods consist of a much higher volume fraction of rays. Typical mean values are 12% for alder, 20% for oak and 16% for ash [20]. There is little knowledge about the properties of the rays in comparison to the axial oriented cells. Recently finished investigations on separated rays of beech points to a clearly higher strength of the rays compared to the strength of the axial cells under radial loading [21]. Therefore we concluded that the rays can be considered as reinforcements in the radial direction
A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
Fig. 7. Fracture surface of spruce. (a) RL system, the softwood fibers (tracheids) and the radially oriented tissue (rays) are visible; (b) fracture surface in the TL system, zones where the rays were separated from the axial tissues are visible; (c) an uniseriate ray cut by the crack front (RL system) is shown in higher magnification. The black arrows indicate the longitudinal direction.
Fig. 8. Fracture surface of ash. (a) RL system, a multiserate ray cut by the propagating crack is visible. (b) TL system, a multiseriate ray separated and cut is shown The black arrows indicate the longitudinal direction.
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leading to a higher ratio between the RL system and TL system for the hardwoods with a higher percentage of rays. This holds for the stiffness as well as for the critical stress intensity factors. The specific fracture energy in the RL system is higher than in the TL system but a trend like mentioned above was not found. Therefore the influence of rays may be more important in the crack initiation phase compared to the propagation phase. Other effects, like different cell geometry or different properties of rays of different species could also play a role but have not been investigated yet. The structural features are clearly visible on the fracture surfaces which were investigated in the high vacuum mode of a Philips XL 30 ESEM. In Fig. 7a the fracture surface of spruce in the RL system is shown. The axial running cut and partially pulled out tracheids are visible as well as the uniseriate radially oriented rays cut by the propagating crack. In Fig. 7b the fracture surface of spruce in the TL system is depicted. Areas with rays separated from the axial tissue are visible. In Fig. 7c a uniseriate ray on the RL fracture surface is shown in higher magnification. Ash serves as a good example for the fracture surface of a hardwood. In Fig. 8a the RL fracture surface of ash can be seen. A multiserate rays cut by the propagating crack is visible. The TL fracture surface of ash is shown in Fig. 8b. A multiseriate ray, separated and cut, is visible. 5. Conclusions The Mode I fracture behavior of spruce, alder, oak and ash was investigated in the crack propagation systems RL and TL using the wedge splitting test. The load–displacement curves were used to determine the initial slope and the specific fracture energy. The maximum load was used to calculate the critical stress intensity factor by a finite element simulation considering the orthotropic nature of wood. The following conclusions can be made. Spruce shows complete stable crack propagation whereas the hardwoods show unstable crack propagation followed by crack arresting. This is explained by the more linear elastic behavior of the hardwoods and the fact that hardwood fibers are shorter than spruce fibers and therefore energy dissipating processes like fiber bridging are less effective. Moreover, less microcracks are formed during the crack initiation phase for the hardwoods which has been shown using acoustic emission measurements. The initial slope indicating the stiffness of the species and the critical stress intensity factor indicating the resistance against crack initiation are higher in the RL system and show a pronounced dependence on density in both systems. However, the differences between differently dense species are higher in the RL system than in the TL system.
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A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
The specific fracture energy shows a dependence on density within the hardwoods but not within all four species due to the different crack propagation behavior of spruce and the hardwoods. The differences of the RL and the TL system are explained considering the different anatomical features, especially the higher volume fraction of radially oriented rays of the hardwoods leading to a reinforcement in the radial direction. This has a strong influence on the ratio of the initial slope and ratio of the stress intensity factor of the RL and TL system. The specific fracture energy is less influenced by the volume fraction of rays.
References [1] J. Bodig, B.A. Jayne, Mechanics of Wood and Wood Composites, Krieger Publishing Company, Malabar, Florida, 1993, p. 322. [2] E.K. Tschegg, Equipment and Appropriate Specimen Shape for Tests to Measure Fracture Values (in German), Patent AT390328, 1986. [3] E.K. Tschegg, M. Elser, H. Kreuzer, J. Mater. Sci. 30 (1995) 235. [4] E.K. Tschegg, D.M. Tan, H.O.K. Kirchner, S.E. Stanzl, Acta Metall. Mater. 41 (1993) 569.
[5] S.E. Stanzl-Tschegg, D.M. Tan, E.K. Tschegg, Wood Sci. Technol. 29 (1995) 31. [6] R.J.A. Ehart, S.E. Stanzl-Tschegg, E.K. Tschegg, Wood Sci. Technol. 32 (1998) 43. [7] H. Harmuth, K. Rieder, M. Krobath, E.K. Tschegg, Mater. Sci. Eng A 214 (1996) 53. [8] G. Prokopski, J. Mater. Sci. 28 (1993) 5995. [9] G. Prokopski, Int. J. Fract 79 (1996) R73. [10] M.J. King, I.J. Sutherland, L. Le-Ngoc, Holz Roh-Werkstoff 57 (1999) 235. [11] H. Schachner, A. Reiterer, S.E. Stanzl-Tschegg, J. Mater. Sci. Lett 19 (2000) 1783. [12] P. Niemz, Physik des Holzes und der Holzwerkstoffe, DRWVerlag, Leinenfelden-Echterdingen, 1993, p. 153. [13] H. Harmuth, Theor. Appl. Fract Mech 23 (1995) 103. [14] A. Reiterer, S.E. Stanzl-Tschegg, E.K. Tschegg, Wood Sci. Technol. 34 (2000) 417. [15] D. Fengel, G. Wegener, Wood — Chemistry, Ultrastructure, Reactions, De Gruyter, Berlin, New York, 1989. [16] A. Hillerborg, RILEM Techn. Com 8 (1985) 292. [17] A.P. Schniewind, T. Ohgama, T. Aoki, T. Yamada, Wood Sci. 15 (1982) 101. [18] R.W. Petterson, J. Bodig, Wood Fiber Sci. 15 (1983) 302. [19] L.J. Gibson, M.F. Ashby, Cellular Solids, Cambridge University Press, Cambridge, 1997. [20] R. Wagenfu¨ hr, C. Scheiber, Holzatlas, VEB Fachbuchverlag, Leipzig, 1989. [21] I. Burgert, A. Bernasconi, D. Eckstein, in: H.-C. Spatz, T. Speck (Eds.), Plant Biomechanics, Thieme Verlag, Stuttgart, New York, 2000, p. 413. [22] J.S. Poulsen, P.M. Moran, C.F. Shih, E. Byskov, Mech. Mater. 25 (1997) 67.
Fracture characteristics of different wood species under mode I loading perpendicular to the grain A. Reiterer *, G. Sinn, S.E. Stanzl-Tschegg Institute of Meteorology and Physics and Christian Doppler Laboratory for Fundamentals of Wood Machining, Uni6ersity of Agricultural Sciences Vienna, Tu¨rkenschanzstraße 18, A-1180 Vienna, Austria Received 28 November 2000; received in revised form 10 May 2001
Abstract Mode I fracture characteristics of different wood species (one softwood and three hardwoods) in two crack propagation systems were investigated using the wedge splitting test under loading perpendicular to the grain. From the obtained load– displacement curves the initial slope, the critical stress intensity factor and the specific fracture energy were determined. The initial slope and the critical stress intensity factor were shown to depend strongly on density within all species whereas for the specific fracture energy differences between the softwood and the hardwoods were found. Differences between the crack propagation systems could be explained by the higher volume fraction of radial oriented tissue (rays) of the hardwoods. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Wood; Fracture toughness; Specific fracture energy; Microstructure of wood; Heterogeneity of wood
1. Introduction Wood is an inhomogeneous, cellular and widely used engineering material with excellent mechanical properties in spite of its low density. These properties are achieved through an optimized hierarchical structure. Concerning its fracture properties there is still a great need for investigations as most studies in the literature focused on softwoods and on linear elastic and isotropic concepts. Due to its orthotropic nature with three main directions, a longitudinal direction (L) parallel to the stem axis, a transverse direction (R) perpendicular to the tree rings and a transverse direction (T) parallel to the tree rings, six crack propagation systems exist for characterizing the fracture behavior. The crack propagation systems are usually indicated using two letters, the first letter indicates the direction perpendicular to the crack plane and the second one serves for the direction of the crack propagation [1]. * Corresponding author. Present address: Austrian Industrial Research Promotion Fund, Ka¨rtner Straße 21-23, A-1015 Vienna, Austria. Tel.: + 43-1-512458464; fax: +43-1-512458441. E-mail address: [email protected] (A. Reiterer).
Moreover, softwoods and hardwoods are different in their microstructure. Softwoods like spruce consist of up to 95% tracheids oriented in the longitudinal direction parallel to the stem axis. Only approximately 5% of the tissue is oriented in the radial direction, the uniseriate rays. Hardwoods are more specialized in their structure consisting of different tissue types like vessels, fiber tracheids, libriform fibers and rays. Hardwoods can have bigger rays (multiseriate rays) and a higher relative volume fraction of this radially oriented tissue. The basic structure of softwoods and hardwoods is shown in Fig. 1. In this paper we apply the wedge splitting method [2] and finite element simulations considering the orthotropic material behavior for the investigation of the Mode I fracture characteristics of wood in the crack propagation systems RL and TL. Results from four wood species, one softwood spruce (Picea abies [L] Karst.) and three hardwoods alder (Alnus glutinosa Gaertn.), oak (Quercus robur L.) and ash (Fraxinus excelsior L.) are presented. Differences between the softwood and the hardwoods are shown and discussed. Moreover, differences between the two crack propagation systems were analyzed and discussed in terms of structural features. The results are supported by scan-
0921-5093/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 7 2 1 - X
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A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
proximately 12% was reached. Notched specimens as shown in Fig. 2 were prepared in the RL as well as in the TL system. The dimensions were the following: W= 0.10 m; H=0.13 m; T= 0.04 m; a= 0.045 m; L=0.085 m. The starter notch was sharpened using a razor blade. All specimens were stored in the climate chamber prior to testing. Six samples were investigated for each crack propagation system and wood species. The densities of the samples were in the following ranges: spruce (479940) kg m − 3; alder (510935) kg m − 3; oak (5539 37) kg m − 3; and ash (7019 55) kg m − 3.
2.2. Methods
Fig. 1. Principle structure of wood. (a) Structure of softwood consisting of earlywood tracheids, latewood tracheids and uniseriate rays (adapted from [22]). (b) Structure of hardwood consisting of vessels, libriform fibers and multiseriate rays.
ning electron microscope (SEM) pictures of the fracture surfaces and acoustic emission measurements.
In order to characterize the Mode I fracture behavior of the different wood species the wedge splitting technique according to Tschegg [2] was used. This method has several advantages like a favorable ratio of specimen weight to ligament area and a simple and stiff loading equipment [3]. The method has been used for fracture characterization of inhomogeneous materials like concrete [3,4], wood [5] or wood composites [6] as well as for brittle materials like ceramic refractory material [7]. The principle of the method is shown in Fig. 3. A wedge is pressed against load transmission pieces in a standard material testing machine, the friction being minimized by the use of roll bodies. From the measurement of the force of the testing machine FM the horizontal splitting force FH can be determined according to FH = FM/2 tan(h/2)
2. Materials and methods
2.1. Material One softwood, spruce, one diffuse porous hardwood, alder and two ring porous hardwoods, oak and ash were chosen for this study. Beams were stored in a climate chamber at 20 °C temperature and 66% relative humidity until an equilibrium moisture content of ap-
(1)
where a is the wedge angle. A wedge angle of 18° was used in this study. The crack mouth opening displacement d is measured by inductive displacement gauges mounted directly on the specimens on both sides of the starter notch. The measured load–displacement curve characterizes the fracture process. The initial slope of the load–displacement curves in the linear elastic region kinit is
Fig. 2. Specimen geometry and orientations.
A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
Gf =
1 A
&
31
lmax
FH(l)dl.
(2)
0
This quantity is a ‘toughness’ quantity characterizing the whole Mode I fracture process until the specimen is split into two halves and does not depend on specimen size and shape if the specimen size is not too small. The used size is large enough to obtain size independent values [5]. In order to characterize the maximum stress state the critical stress intensity factor KIc was determined. In the literature the critical stress intensity factor of wood is often determined according to a formula of the form (3)
KIc = FcY(a/W,B,H)
Fig. 3. Testing arrangement of the wedge splitting test.
where Fc is the force necessary for crack initiation and Y is a factor depending on the geometry, in particular the length of the starter notch a, the sample thickness B and the sample height W (see for example [8–10]). Strictly speaking this formula is for isotropic materials only. In order to determine the critical stress intensity factor considering the orthotropic nature of wood the maximum horizontal splitting forces were taken as input data for a two-dimensional finite element simulation using the ANSYS© software package. The stresses at the crack tip were modeled using quarter point elements as suggested in Stanzl-Tschegg et al. [5] and Schachner et al. [11] (see Fig. 4). The stress intensity factors were calculated from the node displacements according to
' KI = KII
Fig. 4. Arrangement of the quarter point elements at the crack tip used in the finite element simulation. Table 1 Elastic parameters (elastic moduli Ei, shear moduli Gij and Poisson ratios nij) of the different wood species used for the finite element simulations
EL (GPa) ER (GPa) ET (GPa) GLT (GPa) GLR (GPa) nLT [1] nLR [1]
Spruce
Alder
Oak
Ash
10 0.8 0.45 0.65 0.6 0.4 0.4
11.7 1.1 0.6 0.7 0.8 0.3 0.3
13 1.6 0.9 0.8 1.2 0.3 0.3
15.8 1.5 0.8 0.6 0.9 0.3 0.3
Values taken from Niemz [12] and modified such that the initial slope was predicted correctly.
determined in order to characterize the elastic behavior. The area under the load– displacement curve divided by the fracture area A yields the specific fracture energy Gf according to
y − 1 4(uB − uB%)− (uC − uC%) B 8L 4(6B − 6B%)− (6C − 6C%)
(4)
where uB, uB%, uC, uC% are node displacements in the x direction and 6B, 6B%, 6C, 6C% node displacements in the y-direction (see Fig. 4) and L is the element length. The matrix B depends on the stiffness matrices of the wood species (for details see [11]). The elastic parameters used for the stiffness matrices are shown in Table 1. They were taken from the literature [12] and were modified in such a way that the initial slope of the load displacement curves was predicted correctly.
3. Results The load–displacement curves for the different crack propagation systems are shown in Fig. 5a (RL-System) and b (TL-System). For both systems spruce showed stable crack propagation until complete separation of the specimens. The hardwoods behaved differently. After macrocrack initiation at the maximum horizontal splitting force a sudden drop in the load–displacement curve occurred indicating unstable crack propagation.
A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
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Fig. 5. Typical load – displacement curves obtained by the wedge splitting test in the RL (a) and TL (b) system.
This drop was followed by crack arresting leading to another maximum. This behavior was repeated several times in most cases. In Table 2 the results for the initial slope kinit, the critical Mode I stress intensity factor KIc and the specific fracture energy Gf are shown. The initial slope kinit is characteristic for the elastic properties and proportional to an effective modulus of elasticity [7]. As specimen geometry and size was the same for all wood
species and orientations the initial slopes can be compared. The stiffness in the RL system is higher than in the TL system. The hardwoods show higher initial slopes than spruce in both systems except for alder where the initial slope is nearly the same. For the TL system the differences between the wood species are lower. In general, the initial slopes vary from 1.4 to 3.5 N m − 1 in the RL system and from 0.9 to 1.6 N m− in the TL system. This agrees well with the known fact that conventional moduli of elasticity are higher under loading in the radial direction than in the tangential direction [12]. From the maximum splitting forces the critical stress intensity factor KIc was determined considering the orthotropic nature of wood. The finite element simulation yielded the results shown in Table 2. In both systems spruce has the lowest fracture toughness whereas within the hardwoods ash has always the highest one. The values range from 0.49 to 1.16 MPam1/2 in the RL and from 0.31 to 0.65 MPam1/2 in the TL system. The results for the specific fracture energy, characterizing the whole fracture process until complete separation of the specimen into two halves and therefore including crack initiation and propagation yield that in the RL system ash has the highest specific fracture energy and spruce and oak show almost equal values. In the TL system the situation is quite similar. In both systems alder reaches the lowest specific fracture energies. The values vary from 244 to 550 J m − 2 in the RL system and from 155 to 350 J m − 2 in the TL system.
4. Discussion The shape of the load–displacement curves of spruce and the hardwoods is different (see Fig. 5). All spruce specimens show completely stable load–displacement curves whereas the hardwood specimens show unstable parts after crack initiation accompanied by crack ar-
Table 2 Mean values and standard deviations (S.D.) for the initial slope kinit, the critical stress intensity factor KIc and the specific fracture energy Gf Spruce
kinit (N m−1) S.D. KIc (MPam1/2) S.D. Gf (J m−2) S.D.
Alder
Oak
Ash
RL
TL
RL
TL
RL
TL
RL
TL
1.44 0.17 0.49 0.01 337 47
1.01 0.10 0.31 0.03 213 16
2.33 0.15 0.67 0.07 244 41
0.95 0.08 0.33 0.03 155 39
2.58 0.12 0.83 0.03 348 38
1.31 0.12 0.41 0.06 271 44
3.57 0.22 1.16 0.06 551 38
1.60 0.09 0.65 0.03 345 57
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Table 3 Mean values and standard deviations (S.D.) for the acoustic emission counts AE (only for the RL system, from [14]) and the brittleness number B Spruce
AE [1] S.D. B (mm)
Alder
Oak
Ash
RL
TL
RL
TL
RL
TL
RL
TL
9567 1300 1.1
– – 0.9
1367 120 2.1
– – 1.8
867 176 2.0
– – 1.2
433 33 2.1
– – 1.9
resting. In principle the wedge splitting test is favorable in achieving stable crack propagation as the method reduces the compliance of the testing system by the factor tan2(a/2) as discussed in Harmuth [13]. Moreover, a rising crack growth resistance curve and a low critical stress intensity factor increase the stability of crack propagation [7,13]. As can be seen in Table 2 the critical stress intensity factors are generally higher for the hardwoods. A rising crack growth resistance curve can only occur with non-linear material behavior. Regarding the load–displacement curves of the hardwoods the maximum load is visible as sharp peaks which is typical for linear elastic brittle materials. Quite in contrast the load– displacement curves of spruce show a round maximum load peak and clear deviation from linear elastic behavior. Therefore one can conclude that spruce displays more ductile and the hardwoods more linear elastic and brittle behavior. The interpretation is supported by recently obtained acoustic emission measurements during Mode I fracture of RL specimens [14]. These measurements showed much less acoustic emission counts until the maximum splitting force is reached for spruce compared to the three hardwoods (see Table 3). As the crack initiation phase is characterized by the formation of a process zone around the crack tip consisting of microcracks the lower amount of acoustic emission events indicates a much smaller amount of microcracks during process zone formation and therefore less energy dissipating processes in the crack initiation phase. Due to the simpler structure of softwood the a crack can take rather straight paths whereas the more complex hardwood structure could force the crack to take a more circuitous path. Moreover, in the crack propagation phase fiber bridging might play an important role in dissipating energy. Tracheids of spruce are much longer [15] than the fibers of the hardwoods (fiber tacheids, libriform fibers). The dimensions of the spruce tracheids are in the range of 3– 4 mm whereas the fibers of the hardwoods typically reach a length of less than 1 mm. Therefore fiber bridging effects due to the longitudinally oriented fiber types might be considered to be not so effective in hardwoods than in spruce. In the future
a more in-depth analysis should be used to identify the onset of unstable fracture. In order to characterize whether the behavior is more ductile or brittle the maximum forces, the initial slopes and the specific fracture energy were combined to obtain a brittleness parameter according to B=
1 F 2H,max . L kinitGf
(5)
FH,max is the maximum horizontal splitting force and L is the ligament length. Lower values of B indicate a more ductile behavior whereas higher values indicate a more brittle behavior. This parameter is proportional to the reciprocal of the characteristic length according to Hillerborg [16] and is similar to conventional brittleness quantities (see for example [7]) except that the initial slope was used to consider the stiffness. The obtained values for B (see Table 3) indicate clearly that this brittleness parameter is higher for the hardwoods being in the range of approximately 2 mm except for oak in the TL system. The values for spruce are in the range of 1 mm. As all mechanical parameters of wood are related to density it is not surprising that the fracture mechanical quantities do so also. The initial slope in both crack propagation systems had a strong correlation to the measured density at 12% moisture content of the different wood species (Fig. 6a). A linear regression showed a high significance with correlation coefficients of R= 0.93 for the RL and R= 0.94 for the TL system. The regression lines showed clearly different slopes for the two systems. The greater differences for the RL system lead to a higher slope compared to the TL system. Quite similar the critical stress intensity factors were also strongly influenced by density (see Fig. 6b). In both systems linear regressions showed excellent fits with regression coefficients of R =0.98 for the RL and R= 0.99 for the TL system. The differences between the differently dense species were higher for the RL system leading to a higher slope of the regression line. The influence of density on the critical stress intensity factors is in accordance with investigations in the literature (see for example [17–19]). However, a distinction between the two systems with crack propagation along
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A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
the grain has not been made up to now and investigations on hardwoods are still quite seldom. Here, it should be pointed out that models for cellular materials developed by Gibson and Ashby [19], predict a relationship between density and critical stress intensity
Table 4 Ratio of initial slope kinit, critical stress intensity factor KIc and specific fracture energy Gf between the RL and TL crack propagation system
Ratio kinit Ratio KIc Ratio Gf
Fig. 6. Initial slope Kinit (a), critical stress intensity factor KIc (b) and specific fracture energy Gf (c) for the RL (squares) and TL system (triangles) versus density. For the Kinit and KIc values linear regression lines are shown. The regression coefficients for the Kinit values were R= 0.93 for the RL and R= 0.94 for the TL system. The regression coefficients for the KIc values were R= 0.98 for the RL and R =0.99 for the TL system.
Spruce
Alder
Oak
Ash
1.4 1.5 1.6
2.4 2.2 1.6
2.0 2.2 1.3
2.2 1.8 1.6
factor of the form KIc 8 r3/2 and it was shown that this holds for wood quite well. For the results presented in this paper a relationship of this form gave fits almost as well as the linear ones. Therefore, the results do not contradict the foam model. Nevertheless, in the foam model a distinction between the RL and TL system for wood is not included and it was one intention of this paper to show this difference. Both for the initial slope and the critical stress intensity factor the dependence on density is represented better by the measured density values in the TL system. The reason is that in this crack propagation system the crack plane is oriented perpendicular to the annual rings. The crack separates both earlywood and latewood of the annual rings and the sample density is therefore quite representative. In the RL system the crack plane is oriented parallel to the annual rings giving the crack the opportunity to run in weaker earlywood zones of an annual ring. The influence of density is also obvious for the specific fracture energy but only within the hardwoods (see Fig. 6c). This is due to the different crack propagation phase of spruce compared to the hardwoods. The different slope of the dependence on density is reflected in the ratio for the determined values. For the initial slopes the ratio between the RL and TL systems was 1.4 for spruce and 2.4 for alder, 2.0 for oak and 2.2 for ash. For the critical stress intensity factor the ratios were 1.5 for spruce, 2.2 for alder and oak and 1.8 for ash. The differences were higher for the hardwoods. For the specific fracture energy such a clear trend could not be found although the fracture energies were always higher in the RL system. The ratios for all three parameters are shown in Table 4. This behavior could be explained considering the differences in structural features between spruce and the hardwoods. Spruce consists of approximately 95% of axial oriented fibers, the tracheids. Only approximately 5% are radially oriented rays. Hardwoods consist of a much higher volume fraction of rays. Typical mean values are 12% for alder, 20% for oak and 16% for ash [20]. There is little knowledge about the properties of the rays in comparison to the axial oriented cells. Recently finished investigations on separated rays of beech points to a clearly higher strength of the rays compared to the strength of the axial cells under radial loading [21]. Therefore we concluded that the rays can be considered as reinforcements in the radial direction
A. Reiterer et al. / Materials Science and Engineering A332 (2002) 29–36
Fig. 7. Fracture surface of spruce. (a) RL system, the softwood fibers (tracheids) and the radially oriented tissue (rays) are visible; (b) fracture surface in the TL system, zones where the rays were separated from the axial tissues are visible; (c) an uniseriate ray cut by the crack front (RL system) is shown in higher magnification. The black arrows indicate the longitudinal direction.
Fig. 8. Fracture surface of ash. (a) RL system, a multiserate ray cut by the propagating crack is visible. (b) TL system, a multiseriate ray separated and cut is shown The black arrows indicate the longitudinal direction.
35
leading to a higher ratio between the RL system and TL system for the hardwoods with a higher percentage of rays. This holds for the stiffness as well as for the critical stress intensity factors. The specific fracture energy in the RL system is higher than in the TL system but a trend like mentioned above was not found. Therefore the influence of rays may be more important in the crack initiation phase compared to the propagation phase. Other effects, like different cell geometry or different properties of rays of different species could also play a role but have not been investigated yet. The structural features are clearly visible on the fracture surfaces which were investigated in the high vacuum mode of a Philips XL 30 ESEM. In Fig. 7a the fracture surface of spruce in the RL system is shown. The axial running cut and partially pulled out tracheids are visible as well as the uniseriate radially oriented rays cut by the propagating crack. In Fig. 7b the fracture surface of spruce in the TL system is depicted. Areas with rays separated from the axial tissue are visible. In Fig. 7c a uniseriate ray on the RL fracture surface is shown in higher magnification. Ash serves as a good example for the fracture surface of a hardwood. In Fig. 8a the RL fracture surface of ash can be seen. A multiserate rays cut by the propagating crack is visible. The TL fracture surface of ash is shown in Fig. 8b. A multiseriate ray, separated and cut, is visible. 5. Conclusions The Mode I fracture behavior of spruce, alder, oak and ash was investigated in the crack propagation systems RL and TL using the wedge splitting test. The load–displacement curves were used to determine the initial slope and the specific fracture energy. The maximum load was used to calculate the critical stress intensity factor by a finite element simulation considering the orthotropic nature of wood. The following conclusions can be made. Spruce shows complete stable crack propagation whereas the hardwoods show unstable crack propagation followed by crack arresting. This is explained by the more linear elastic behavior of the hardwoods and the fact that hardwood fibers are shorter than spruce fibers and therefore energy dissipating processes like fiber bridging are less effective. Moreover, less microcracks are formed during the crack initiation phase for the hardwoods which has been shown using acoustic emission measurements. The initial slope indicating the stiffness of the species and the critical stress intensity factor indicating the resistance against crack initiation are higher in the RL system and show a pronounced dependence on density in both systems. However, the differences between differently dense species are higher in the RL system than in the TL system.
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The specific fracture energy shows a dependence on density within the hardwoods but not within all four species due to the different crack propagation behavior of spruce and the hardwoods. The differences of the RL and the TL system are explained considering the different anatomical features, especially the higher volume fraction of radially oriented rays of the hardwoods leading to a reinforcement in the radial direction. This has a strong influence on the ratio of the initial slope and ratio of the stress intensity factor of the RL and TL system. The specific fracture energy is less influenced by the volume fraction of rays.
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