FRACTURE of SOLID WOOD: a REVIEW of STRUCTURE and PROPERTIES at DIFFERENT LENGTH SCALES Michael P

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FRACTURE OF SOLID WOOD: A REVIEW OF STRUCTURE AND PROPERTIES AT DIFFERENT LENGTH SCALES Michael P. C. Conrad Graduate Research Assistant Metals and Materials Engineering Gregory D. Smith² Assistant Professor Wood Science

and GoÈran Fernlund Assistant Professor Metals and Materials Engineering University of British Columbia Vancouver, BC Canada V6T 1Z4 (Received February 2002)

ABSTRACT This paper presents a review of the fracture literature of solid wood. The review is not exhaustive and is focused on the structure and properties of wood at different length scales. Fracture of wood has been examined in all pure modes as well as mixed-Mode I and II and all directionsÐradial, tangential, and longitudinal. The literature has been studied at a variety of levels from molecular through cellular and growth ring to macroscopic. The major conclusions are that fracture toughness perpendicular to the grain is greater than that parallel to the grain and Mode II is greater than Mode I, within a given species. Also, fracture toughness increases with increasing density and strain rate. Defects typically reduce the strength and fracture toughness, with edge defects having a greater effect. Finally, the fracture toughness of solid wood reaches a maximum between 6 to 8% moisture content. The paper discusses how these macroscopic observations are related to the chemical composition and micro/meso-structure of wood. Keywords: Fracture mechanics, fracture morphology, solid wood, molecular structure, cellular structure.

INTRODUCTION Cramer (1987) and Barrett (1981). It is typically assumed that wood behaves as a brittle Fracture of solid wood can be examined on solid, which is valid if the moisture content of a variety of levels from molecular through cel- the sample is suf®ciently low. Wood is a nat- lular to macroscopic. An understanding of the ural material with inherent variability, and the mechanism of fracture at each level will give associated physical and mechanical properties greater insight into the fracture of solid wood have coef®cients of variation on the order of in general. Numerous authors have applied 20 to 25%. This variability leads to a wide fracture mechanics to solid wood as a means range of quoted fracture toughness values of understanding the failure and predicting the even within a given species, thus creating dif- strength of wooden structural members, with ®culties in using these values for design pur- review articles written by Patton-Mallory and poses. In practice, the modulus of elasticity and the compressive strength perpendicular to ² Member of SWST and corresponding author. the grain are based on average values, whereas

Wood and Fiber Science, 35(4), 2003, pp. 570±584 ᭧ 2003 by the Society of Wood Science and Technology Conrad et al.ÐFRACTURE OF SOLID WOOD 571

FIG. 1. Molecular components of wood: repeat unit of celluloseÐ(a) cellobiose molecule (Nikitin 1966); monomers of ligninÐ(b) coniferyl alcohol, (c) sinapyl alcohol, and (d) p-coumarly alcohol (Lin and Lebo 1995). all other properties use the values for the ®fth direction of crack growth. Fracture of wood percentile. The present review is focused on can be simpli®ed if the specimen is taken a the structure and fracture properties at differ- suf®cient distance from the tree center such ent length scales in an attempt to explain, or that the curvature of the growth rings can be at least indicate, the relationship between ignored. The specimen then behaves as an or- wood structure at different length scales and thotropic material. macroscopic fracture properties. In studying fracture mechanics of solids, MOLECULAR SCALE three pure modes of crack propagation are typically examined. In addition, mixed-mode At the molecular level, wood consists of fracture, which involves a combination of two cellulose and lignin and other organic mole- to three of the modes, is experienced. The cules such as hemicelluloses and uronic acids. three pure modes of fracture are described be- Cellulose is a semi-crystalline polysaccharide low. based on 1,4 linked ␤-D-glucose molecules (Fig. 1a). The molecular weight (both number- Mode I: Opening or tensile mode, where Å Å average, Mn, and weight-average, Mw) and de- the crack surfaces move directly gree of polymerization (DP) of cellulose are apart. dif®cult to obtain; however, evidence suggests Mode II: Sliding or in-plane shear mode, that in higher plants the DP is 3500 to 7000 where the crack surfaces slide or higher based on the cellobiose repeat unit across one another in the direc- (Richmond 1991). Higher plants are cellulose- tion perpendicular to the leading producing organisms that have conducting tis- edge of the crack. sues. This includes plants that ¯ower or pro- Mode III: Tearing or antiplane shear mode, duce cones, ferns, and others that are classi®ed where the crack surfaces move in the kingdom Plantae. The cellulose chains parallel to the leading edge of coalesce to form ordered, crystalline micro®- the crack. brils that have high strength and stiffness in Wood is a highly anisotropic material and the longitudinal direction. these fracture modes are further divided by the Lignin is considered an amorphous polymer three principal axes of anisotropy: radial (R), that is based on the following monomers: Figs. tangential (T), and longitudinal (L). A ®gure 1b, c, and d. Because of the dif®culty in iso- showing these directions is available from the lating lignin from wood without degradation, Forest Product Society (1999), but is not re- the actual molecular weight of lignin is un- Å produced here for brevity. The plane and di- known. However, the Mw of softwood milled rection of crack propagation are identi®ed by wood lignin is estimated at 20,000, with lower a pair of letters. The ®rst denotes the direction values reported for hardwoods. The polydis- Å Å ϭ normal to the crack surface and the second the persity of lignin is also high (Mw/Mn 2.5) 572 WOOD AND FIBER SCIENCE, OCTOBER 2003, V. 35(4)

FIG. 2. Organization of the cell-wall layers and middle lamella. Adapted from Nikitin (1966).

compared with cellulose, indicating that it is a mixture of long and short molecules. The low- FIG. 3. Schematic of various crack paths in wood: (a) crack advance by cell fracture (intracellular fracture), (b) er molecular weight and greater polydispersity crack advance by cell separation (intercellular fracture), of lignin lead to a lower fracture toughness and (c) crack arrest at a vessel showing a crack splitting than for cellulose. the wall of a vessel (crack de¯ection). Adapted from Gib- son and Ashby (1988). CELLULAR SCALE

At the cellular level, wood can be consid- is found in the S2 layer, the strength of wood ered a ®ber-reinforced polymer composite of is greater in the longitudinal direction com- cellulose micro®brils in a lignin matrix. The pared with the radial and tangential directions. cell wall consists of four discrete layers (Ni- Also, the secondary wall consists of approxi- kitin 1966) where the orientation of the cel- mately 80% of the total cellulose, and it has lulose micro®brils varies from 0Њ to 90Њ to the greater fracture toughness than the primary longitudinal axis of the ®ber; this is shown wall and middle lamella. schematically in Fig. 2. The primary wall, P, Moving towards the macroscopic scale, sol- is an irregular network of micro®brils with a id wood can be viewed as a honeycomb net- lignin content of less than 50%. In addition, work of cells cemented together by the middle the cellulose chains within the primary wall lamella. This leads to the two major fracture micro®brils have a low DP, approximately paths found in wood (Boatright and Garrett 250, as compared with a DP of 3500 to 7000 1983; Gibson and Ashby 1988), cell fracture for the cellulose found in the secondary wall. and cell separation (DeBaise 1972). The ®rst The micro®brils of the outer secondary wall, is through cell fracture or intracellular fracture

S1, form two overlapping spirals resulting in a as shown in Fig. 3a. The type of fracture that structure similar to a Ϯ45 layer in a polymer occurs is determined to a large extent by the

composite. The middle secondary wall, S2, wood density. For convenience, the density of forms the majority of the cell wall and consists a wood is often given as the ratio of wood ␳ ␳ of concentric layers of micro®brils oriented al- density, , to that of the cell-wall material, s, most parallel to the ®ber axis. Finally, the in- which is typically 1500 kg/m3. Cell fracture is ␳ ␳ Ͻ ner secondary wall, S3, consists of micro®brils generally found in low-density ( / s 0.2) that lie nearly perpendicular to the ®ber ori- woods and the earlywood of higher density entation. In total, the secondary wall of the woods and is the typical failure mode in the cell contains 10 to 12% lignin. The cells are RT, RL, LR, and LT directions. held together in a honeycomb fashion by the Cell separation or intercellular fracture is middle lamella, which consists of approxi- shown in Fig. 3b. During cell separation, the mately 70% lignin distributed isotropically. crack propagates through the middle lamella Since the majority of the cell-wall material and primary cell wall leaving the secondary Conrad et al.ÐFRACTURE OF SOLID WOOD 573 wall intact. This occurs in higher density ␳ ␳ Ͼ woods ( / s 0.2) along with some cell fracture. Gibson and Ashby (1988) found that propagation in the TR direction is through cell separation. In addition, a crack running at an angle between the RT and TR directions will tend to deviate toward the TR direction adopt- ing the cell separation mode of fracture. Cell fracture has higher fracture toughness than cell separation. This is shown by the greater fracture toughness of the RT, RL, LR, and LT directions over the TR and TL direc- FIG. 4. Schematic of crack propagating in the TR di- tions and the preference of the TR direction rection. E ϭ earlywood, L ϭ latewood. Adapted from for a crack running at an angle between the Thuvander and Berglund (2000). RT and TR directions. The difference can be explained by the relative proportions of cellulose and lignin as well as the type of cellu- ers. Earlywood, grown during the spring, con- lose found in the various cellular layers. Since sists of large-diameter, thin-walled cells. Late- cellulose has higher fracture toughness than wood, deposited later in the growing season, lignin and is predominantly found in the sec- consists of smaller diameter cells with thicker ondary cell wall, it is reasonable to assume cell walls. The repeated layering of the early that cell fracture, which occurs through frac- and latewood produces the pattern known as ture of the secondary cell wall, will have growth rings. The difference in cellular struc- greater fracture toughness than cell separation. ture of the earlywood and latewood leads to In addition, the cellulose in the primary cell variations in density and stiffness, which fur- wall has a signi®cantly lower DP as compared ther explain the difference in fracture tough- with the cellulose in the secondary cell wall ness for the various directions. Thuvander et and exhibits lower fracture toughness. al. (2000a, b; Thuvander and Berglund 2000) Vessels affect the fracture path by acting as demonstrate the increased fracture toughness crack arrestors as shown in Fig. 3c. The crack of the TR direction over the TL direction. The path tends to deviate towards a vessel and ei- crack propagates in the cell separation mode ther enter it or run partly around the edge of at the level of individual cells, and a stick-slip the channel and stop (Gibson and Ashby mechanism of crack growth was found at the 1988). These are examples of extrinsic tough- growth ring scale due to the alternating stiff ening mechanisms: crack-tip blunting and (latewood) and ¯exible (earlywood) layers. As crack de¯ection, respectively. well, crack propagation typically occurs With increasing temperature and moisture through the formation of secondary cracks that content, more viscoelastic deformation occurs, are displaced tangentially from the primary and there is a shift from cell fracture to cell crack where the latewood acts as a crack ar- separation. Also, this reduces the extent and restor, shown schematically in Fig. 4. Further frequency of unstable crack extension that typ- inactive secondary cracks are also found well ically occurs in the case of cell fracture as away from the primary crack. Since energy is compared with slow crack growth that occurs required to form the new surface area of the in the case of cell separation (DeBaise 1972). inactive secondary cracks, they contribute to the fracture toughness of wood. GROWTH RING SCALE The difference in stiffness between early As a tree grows over the course of a year, and latewood also causes inclined cracks to cells are added to the tree in two distinct lay- deviate to the TR direction (Thuvander and 574 WOOD AND FIBER SCIENCE, OCTOBER 2003, V. 35(4)

Berglund 2000). Inclined cracks are propagat- the crack propagating by cell fracture rather ed by both cell fracture and cell separation than cell separation. Cell fracture also leads to with the latter mechanism being dominant. the slightly higher value of fracture toughness Upon reaching the latewood, the crack is ar- for the RL direction over the TL direction. It rested, and a secondary crack is initiated in the should be noted that cracks tend to propagate radial direction at a weak point in the late- parallel to the grain even if the starter crack is wood. As above, this secondary crack is dis- originally in the LR or LT direction. placed tangentially from the original, i.e., hor- A variety of fracture toughness specimens izontally in Fig. 4. have been used to characterize the Mode I fracture toughness of wood. Wood properties are MACROSCOPIC SCALE inherently variable, and no major difference in Mode I fracture toughness due to specimen ge- While the knowledge gained in examining ometry has been reported. The ASTM Standard the fracture of wood at the molecular and cel- E399-90: Standard Test Methods for Plane- lular level is important, the majority of appli- Strain Fracture Toughness of Metallic Materials cations are on the macroscopic scale. Thus, the (1994) is typically applied to wood. However, majority of researchers concentrate on this Bostrom (1990) recommends against using the level. However, many of the effects seen at the CT specimen for measuring the Mode I fracture macroscopic scale can be explained by phe- toughness of solid wood due to dif®culties in nomena at the molecular and cellular level. determining when the crack begins propagat- The literature on the macroscopic fracture ing. toughness of wood can be divided into the The Mode I fracture toughness of solid three principal modes of crack propagation: wood is affected by strain rate, moisture con- Mode I, Mode II, and Mode III as well as tent, density, defects, and thickness. The effect mixed-mode fracture and studies on fracture of strain rate has been examined by various strength. authors (Blicblau and Cook 1986; Ewing and Williams 1979b; Johnson 1973; Mai 1975; Mode I fracture toughness Mindess et al. 1975a, b; Nadeau et al. 1982; Mode I, or the opening mode of fracture, is Schniewind and Pozniak 1971). With the ex- considered the most important mode in engi- ception of Mai (1975), they concluded that the neering failures. However, wood often exhibits fracture toughness of wood increases with a signi®cant component of Mode II fracture. strain rate. This is due to subcritical crack Mode I fracture toughness is the most easily growth that causes delayed failure of wood measured of the three modes; thus the majority (also known as the duration-of-load effect of the literature concentrates on this property. where the fracture toughness of wood speci- A summary of some of the work to date on mens decreases as a function of time). At low- the fracture of solid wood is listed in Table 1 er strain rates, there is suf®cient time for by fracture specimen geometry, direction of cracks to reach the critical size, at which point crack growth, species, and effect examined. the test specimen fails catastrophically. At The possible directions of a Mode I fracture higher strain rates, less time is available for toughness test can be grouped into those crack growth, and the fracture toughness of where the crack is propagating perpendicular these samples is higher than for specimens to the grain (LR and LT) and those parallel to strained more slowly. the grain (RL, TL, RT, TR). The Mode I frac- Studies on moisture content have examined ture toughness of wood perpendicular to the wood from oven-dry to green (Ewing and Wil- grain is approximately one order of magnitude liams 1979a; Johnson 1973; Kretschmann et greater than the fracture toughness in the other al. 1990; Mai 1975; Mindess 1977; Petterson directions as shown in Table 2. This is due to and Bodig 1983; Sobue et al. 1985), although Conrad et al.ÐFRACTURE OF SOLID WOOD 575 : (7) T Ewing and Wright and ϭ ϭ : (29, 30) ␳ unknown. Gibson and Ashby ϭ ϭ : (9) : (14) : (12) : (10) : (11) spruce, U Pearson 1974; 22 ␳ MC SR MC : (21) D ϭ D Schniewind and Centeno 1973; 15 ϭ ϭ HF, DF, U, AT, DF, P, Thuvander et al. 2000a; 7 pine, S ϭ ϭ : (9) Schachner et al. 2000; 29 ϭ : (14) oak, P : (10) ϭ ␳ D, MC MC : (21) Sobue et al. 1985; 21 D ϭ AT, DF, P, Mindess et al. 1975b; 14 maple, O ϭ ϭ Johnson 1973; 28 Thuvander et al. 2000b; 6 : (25) P: (21) P: (21) ϭ : (25) ϭ D SR : (14) lauan, M : (19) ϭ P: (4, 5, 6) P, S, DF: (14, 19) P: (19) B: (20) S: (18) MC SR DF, P: (19) DF, larch, La Blicblau and Cook 1986; 20 Nadeau et al. 1982; 13 Direction : (14) ϭ ϭ ϭ MC DF, S: (18) hem-®r, L Petterson and Bodig 1983; 27 ϭ ϭ Thuvander and Berglund 2000; 5 ϭ Atack et al., 1961; 19 ϭ hemlock, HF ϭ Boatright and Garrett 1979; 12 ϭ thickness. : (25) ϭ D : (14, 17) **: (2) : (26) : (27) T : (25, 27) : (15, 17) : (16) : (2) Douglas-®r, H B: (16) P: (17) MC D T ␳ S: (3) MC DF, B: (16, 26) P: (24) C, S, H, L:MC (26) P: (27) DF: (25, 27) P, C, M, Bi,SR O, La: (27) MC ϭ Schniewind and Ponziak, 1971; 26 Riipola and Fonselius 1992; 4 ϭ strain rate, ϭ Leicester 1947a; 11 ϭ cedar, DF Ewing and Williams 1979a; 18 ϭ : (27) SR ϭ ϭ : (23) RL TL RT TR LR LT N/A : (14) DF: (14, 15) density, : (8) HF, : (13) birch, C SR, MC : (22) SR SR MC ϭ ␳ϭ SR, MC SR La, Mindess 1977; 10 P: (24) ϭ beech, Bi Kretschmann et al. 1990; 3 Valentin and Morlier 1982; 25 ϭ ϭ Triboulot et al. 1984; 17 ϭ ϭ moisture content, ϭ MC Mai 1975; 24 Mindess et al. 1975; 9 ϭ Bostrom 1990; 2 ϭ defects, ϭ Australian Timber, B ϭ Mode I fracture toughness specimen geometries, directions, species, and effect examined. ϭ D Specimen geometry 1. Schniewind and Lyon 1973; 16 ABLE ** Effects: * Species: T *** Authors: 1 1988; 30 Leicester 1983. Notched Four Point Bend DF, T Compact Tension (CT) P*: (1)*** P: (2, 3, 4) ϭ Williams 1979b; 23 Fonselius 1986; 8 Double TorsionSingle Edge Notch (SEN) DF, DF, Tapered Cleavage P, Double Cantilever Beam (DCB) S, Double Edge Notch (DEN)Center Notch (CN) P, DF, C, M, Bi, O, DF: (25) DF: (19, 25) WedgeUnknown S: (28) S: (28) 576 WOOD AND FIBER SCIENCE, OCTOBER 2003, V. 35(4)

TABLE 2. Mode I fracture toughness of air-dry Douglas- ence in shrinkage rate of the radial, tangential, ®r. (Schniewind and Centeno 1973). and longitudinal directions. These lead to re- 1/2 Direction KIc (MPa´m ) sidual drying stresses (Ewing and Williams RL 0.41 1979a; Sobue et al. 1985) that produce radial TL 0.31 cracks and a subsequent reduction in fracture RT 0.35 toughness. Schniewind and Centeno (1973) TR 0.35 varied the relative humidity between 35 and LR 2.69 LT 2.42 87% with the humidity held at each value for 12 h and have shown that cyclic changes in humidity can signi®cantly decrease the time to failure of solid wood. the moisture content is typically between 10 The fracture toughness of wood increases to 15% (Boatright and Garrett 1979; Ewing with increasing density (Ashby et al. 1985; and Williams 1979b; Schniewind and Centeno Gibson and Ashby 1988; Kretschmann et al. 1973; Triboulot et al. 1984). Ewing and Wil- 1990; Leicester 1974a; Leicester 1983; Petter- liams (1979b) found that the fracture tough- son and Bodig 1983), as shown in Fig. 5. It ness of wood initially increases from an oven- should also be noted that this is true for green dry condition reaching a maximum between 6 wood (Petterson and Bodig 1983) where the to 8%, and then decreases monotonically validity of fracture mechanics is questionable. thereafter. This increase in Mode I fracture The following relationships between density toughness with moisture content is due to in- and K have been postulated: creased viscoelastic behavior of the wood Ic (Mindess 1977), leading to greater energy ab- ␳ 3/2 sorption through viscous deformation and an n ϭ 1/2 KIc 20΂΃␳ (MPa´m ) increased toughness. However, above the level s of 6 to 8%, it appears the Mode I fracture Ashby et al (1985), (1) toughness becomes constant or decreases ␳ 3/2 slightly (Kretschmann et al. 1990). More re- a ϭ 1/2 KIc 1.81΂΃␳ (MPa´m ) cently, Kretschmann and Green (1996) found s that the Mode I fracture toughness of Scots pine increased as the moisture content de- Ashby et al (1985), (2) n ϭ ␳ 1/2 creased from the green state to approximately KIc 0.0047 (MPa´m ) 8%, where it reached a maximum, and de- creased for lower moisture contents. The slight Leicester (1983), (3) a ϭ ␳ 1/2 decrease in Mode I fracture toughness for KIc 0.00063 (MPa´m ) moisture contents above 8% may be due to the ingress of water into the crystal structure of Leicester (1983), (4) the cellulose micro®brils. This leads to a re- ϭ ␳ 0.952 1/2 KIcg 0.00062( ) (MPa´m ) duction in crystallinity and a subsequent reduction in fracture toughness (Nikitin 1966). Petterson and Bodig (1983), (5) For higher moisture content values, the valid- n ϭ ity of fracture mechanics becomes question- where KIc Mode I fracture toughness able due to increased plasticity during crack normal to the grain (LR, propagation. Evidence of plastic work during LT direction), a ϭ the fracture event was observed by Atack et KIc Mode I fracture toughness al. (1961). along the grain (RL, TL, The reduction of Mode I fracture toughness RT, TR direction), ϭ at low moisture contents is due to the differ- KIcg Mode I fracture toughness Conrad et al.ÐFRACTURE OF SOLID WOOD 577

toughness decreases to a plateau when the thickness is increased. Wright and Fonselius found that for pine, spruce, and spruce-lami- nated veneer lumber (LVL), a specimen thickness of 20 mm was suf®cient to achieve plane strain conditions. Triboulot et al. (1984) also show that the necessary thickness for plane strain is on the order of 20 mm where 65% of the specimen is in a plane strain condition. The defects studied include notches (Ewing and Williams 1979a; Mindess 1977; Schnie- FIG. 5. Effect of density on Mode I fracture toughness. wind and Pozniak 1971), checks (Schniewind Data obtained from Ashby et al. 1985; Bostrom 1990; and Lyon 1973; Schniewind and Pozniak Johnson 1973; Kretschmann et al. 1990; Lei and Wilson 1971), and knots (Boatright and Garrett 1979; 1980; Mindess et al. 1975b; Nadeau et al. 1982; Patton- Mallory and Cramer 1987; Pearson 1974; Schniewind and Pearson 1974). Ewing and Williams (1979a) Centeno 1973; Schniewind and Lyon 1973; Schniewind states that the effect of changing notch depth and Pozniak 1971; White and Green 1980. (5 to 15 mm) and notch radius (from less than 5to300␮m) was inconclusive in the ranges studied. Schniewind and Pozniak (1971) found along the grain for green that Douglas-®r specimens with a notch length wood, of either 0.14 in. or 0.16 in. failed away from ␳ϭwood density (kg/m3, and the pre-existing notch tip. This con®rms the ␳ ϭ density of cell-wall mate- s existence of inherent ¯aws in Douglas-®r on rial (1500 kg/m3). the order of 0.15 in. Checks were found to It should be noted that all of the relationships reduce the fracture strength and toughness of between fracture toughness and density shown solid wood to a greater degree then other de- in Eqs. (1) to (5) are the result of a least fects when the wood is tested perpendicular to squares ®t to a log-log plot of the data and are the grain (Schniewind and Lyon 1973). neither average nor 5th percentile values. Checks are radial cracks formed due to differ- The model put forth by Leicester underes- ences in radial and longitudinal shrinkage timates the effect of density on Mode I frac- upon drying and terminate in a sharp crack tip, ture toughness normal to the grain, whereas whereas other defects studied such as resin the model by Ashby agrees better with exper- streaks, pitch pockets, and pith are blunt. This imental data. However, the Ashby, Leicester, difference in crack tip radius causes the great- and Petterson and Bodig models ®t well for er reduction in fracture toughness by checks fracture toughness along the grain. The in- over other wood defects. crease in fracture toughness with density is due to the increase in the amount of wood as Mode II fracture toughness compared to voids in a given cross-section and is comparable with the effect of latewood on While Mode I fracture is typically consid- the crack path as reported by Thuvander and ered the driving force behind engineering fail- Berglund (2000). ures in most materials, experience has shown Ewing and Williams (1979a), Wright and that wood failure often has a signi®cant Mode Fonselius (1986), and Triboulot et al. (1984) II component. Table 3 summarizes the litera- examined the effect of thickness on the Mode ture on Mode II fracture toughness for the I fracture toughness. Ewing demonstrates the specimen geometries, directions, species, and effect of moving from the plane stress regime effects that have been examined. The orthotro- to the plane strain regime as the fracture pic directions that have been studied are RL 578 WOOD AND FIBER SCIENCE, OCTOBER 2003, V. 35(4)

TABLE 3. Mode II fracture toughness specimen geometries, directions, species, and effect examined.

Direction Specimen geometry RL TL RT TR LR LT N/A End Notched Flexure (ENF) DF*, CL**: (1)*** DF, CL: (3) P, S: (4) H, CL: (2) H, CL: (2, 3) MC, ␳: (5) Center-Slit Beam (CSB) DF, CL, ␳: (6) Compact Shear (CS) P, DF, MC: (7) Compact Tension Shear (CTS) P: (8) Center Notch Under Shear Ba: (9) * Species: Ba ϭ balsa, DF ϭ Douglas-®r, H ϭ hemlock, P ϭ pine, S ϭ spruce. ** Effects: CL ϭ crack length, MC ϭ moisture content, ␳ϭdensity. *** Authors: 1 ϭ Murphy 1979a; 2 ϭ Barrett and Foschi 1977a; 3 ϭ Barrett and Foschi 1977b; 4 ϭ Wright and Fonselius 1986; 5 ϭ Fonselius and Riipola 1988; 6 ϭ Murphy 1989; 7 ϭ Cramer and Pugel 1987; 8 ϭ Valentin and Caumes 1989; 9 ϭ Wu 1967.

and TL. No literature on the other directions toughness of Scots pine and found that the has been foundÐlikely due to the dif®culty of Mode II fracture toughness increases steadily obtaining beams of signi®cant length where when drying from the green state, peaking at the length is not parallel to the longitudinal approximately 12% and decreasing for lower direction. moisture contents. Cramer and Pugel (1987) The majority of the researchers (Barrett and found that a harsher drying history, which pro- Foschi 1977a, b; Cramer and Pugel 1987; duces more and larger ¯aws within the sam-

Murphy 1989) have found that it is dif®cult to ple, led to a decrease in KIIc. obtain values for pure Mode II failure due to A similar relationship to that for Mode I the low Mode I fracture toughness parallel to exists between density and Mode II fracture the grain. Very little stress is required to pre- toughness, as KIIc also increases with increas- cipitate failure in this direction and therefore, ing density (Fonselius and Riipola 1988; Mode I failure may occur away from the de- Leicester 1974a, 1983; Murphy 1989). This sired location (Cramer and Pugel 1987) or the similarity between Modes I and II is also seen specimen may fail earlier than predicted (Bar- for varying crack lengths with an increase in rett and Foschi 1977b) for pure Mode II load- crack length leading to an increase in the ing. Closing friction and minor changes in Mode II fracture toughness for end-notched specimen geometry may also affect the cal- ¯exure and center-slit beam specimens (Bar- culated values for KII and KIIc leading to great- rett and Foschi 1977a, b; Murphy 1979b, er variability in these values compared with KI 1989). and KIc. However, the absolute values for KIIc Mixed-mode fracture toughness are consistently greater than KIc for the corresponding direction. For example, Douglas- Since pure Mode I or pure Mode II are rare-

®r in the TL direction has a KIc of 0.36 ly encountered in practice, a number of re- MPa´m1/2 (Schniewind and Centeno 1973) and searchers have examined mixed mode frac- 1/2 a KIIc of 1.56 MPa´m (Cramer and Pugel ture. Studies in mixed mode failure have given 1987). empirical mixed-mode failure criteria, based Varying the moisture content from 10 to on knowledge of pure Mode I and II values, 20% (Fonselius and Riipola 1988) appears to for use in design. The literature on mixed have little effect on Mode II fracture tough- mode fracture toughness is summarized in Ta- ness, which agrees with the results for Mode ble 4. I fracture toughness, although the range stud- The following empirical failure criterion ied was small. More recently, Kretschmann (Eqs. 6 to 13) have been proposed for the on- and Green (1996) studied the Mode II fracture set of mixed-mode fracture: Conrad et al.ÐFRACTURE OF SOLID WOOD 579

TABLE 4. Mixed Mode fracture toughness specimen geometries, directions, and species.

Direction Specimen geometry RL TL RT TR LR LT N/A Modi®ed End-Notched Flexure (mENF) BR*: (1)** H: (2) Compact Shear (CS) P: (3) P: (3) P: (3) S: (4) Compact Tension Shear (CTS) P: (3) P: (3) P: (3) End-Notched Flexure (ENF) DF, H: (5) Single Edge Notch (SEN) S: (4) Center Notch (CN) S: (4) Ba (6) * Species: Ba ϭ balsa, BR ϭ Baltic redwood, DF ϭ Douglas-®r, H ϭ hemlock, P ϭ pine, S ϭ spruce. ** Authors: 1 ϭ Hunt and Croager 1982; 2 ϭ Lum and Foschi 1988; 3 ϭ Valentin and Caumes 1989; 4 ϭ Mall et al. 1983; 5 ϭ Barrett and Foschi 1977b; 6 ϭ Wu 1967.

KI ϭ Ն sa and spruce may be coincidental; however, 1(KII 0) this failure criteria may describe the behavior KIc Mall et al. (1983) (6) of a wide variety of species. Further work is necessary to determine this. KK IIIϩϭ1 KKIc IIc Mode III fracture toughness Leicester (1974b) (7) The ®nal mode of fracture is Mode III: the ␤ tearing or antiplane shear mode. This has been KK IIIϩ␣΂΃ ϭ1 examined by Murphy (1980) using a side- KKIc IIc cracked cantilever beam of Sitka spruce in the 1/2 Hunt and Croager (1982) (8) RT direction obtaining a KIIIc of 0.66 MPa´m . This is comparable to Mode I or Mode II where ␣ϭ1.005 and ␤ϭ3.4, failure in the RL direction; however, due to 2 differences in species between Mode I and KKIII ϩϭ1 Mode III, this comparison cannot be made at KK΂΃ Ic IIc the present. For Mode II, the fracture tough- Leicester (1983) and Wu (1967) (9) ness for spruce in the RL direction is approximately twice that of Mode III in the RT di- KK2 ΂΃IIIϩϭ1 rection. Murphy found that for crack ratios KKIc IIc (crack length/specimen width) below 0.15, the Mall et al. (1983) and (10) beam behaves as if it were composed of clear wood. The shear span also affects the Mode KK2 ΂΃IIIϩϭ1 III fracture toughness; as the shear span KKIc IIc (length vs. width) and hence the crack width increases, KIIIc is reduced. It should be noted Mall et al. (1983). (11) that Murphy's work was validated using built- The criterion that best predicts the mixed- up I-beams rather than solid wood beams with mode failure is that postulated by Wu (1967), cracks or slits. Caution should be used when who studied balsa. The same failure criterion, extrapolating these experimental results to sol- Eq. (13), was also found to give the best cor- id wood specimens due to differences in the relation with experimental data in a later study stress ®elds. by Mall et al. (1983), who examined spruce. More recently, Erhart et al. (1999) devel- The fact that a single mixed-mode failure cri- oped a specimen and an experimental setup teria adequately describes the behavior of bal- that allows testing in Mode I, Mode III, and 580 WOOD AND FIBER SCIENCE, OCTOBER 2003, V. 35(4)

TABLE 5. Specimen geometries, directions, species, and effect examined in the study of fracture strength.

Direction Specimen geometry TL N/A Four Point Bend DF*: (1, 2)*** E: (3) H: (4, 5) Bm, C: (5) SR**: (2) D: (1, 2, 3) MC: (5) Three Point Bend DF: (1) Tension DF, D: (6) * Species: Bm ϭ balsam, C ϭ cedar, DF ϭ Douglas-®r, E ϭ eucalyptus. ** Effects: D ϭ defects, MC ϭ moisture content, SR ϭ strain rate. *** Authors: 1 ϭ Murphy 1979a; 2 ϭ Spencer 1979; 3 ϭ Leicester 1973; 4 ϭ Lum and Foschi 1988; 5 ϭ Steida 1966; 6 ϭ Cramer and Goodman 1983. FIG. 6. Diagram showing the values used in calculat- ing the knot ratio, KR. Adapted from Boatright and Garrett Mixed-mode I±III. They found that the frac- (1979). ture energy values were substantially greater for Mode III than for Mode I. of the ®gure has the contributions of both the Fracture strength vertical and horizontal length of the knot. The strength of the specimen decreases with in- Experiments on the fracture strength or fail- creasing knot ratio. ure load of wood, summarized in Table 5, ͸ ϩ demonstrate the applicability of fracture me- (xiiy ) KR ϭ , (12) chanics to the study of wood failure. Fracture 2(w ϩ t) mechanics predicts both the effect of defects ϭ such as notches and knots as well as the effect where xi the length of the knot ex- of moisture content. posed to the surface of the Knots in wood signi®cantly disturb the reg- board, ϭ ular grain structure of wood, which in turn yi the length of the vertical axis leads to changes in the fracture toughness. The of the knot, effect, however, is unclear since the knot may w ϭ the width of the board, and t ϭ the thickness of the board. increase KIc in some cases and decrease it in others. Boatright and Garrett (1979) found that Pearson (1974) modelled knots with equiv- the knot ratio, which is the ratio of the amount alent cracks and found that if the crack length of specimen perimeter that is covered by knots was taken to be the same as the knot dimen- to the entire specimen perimeter (Eq. 12) sions, the fracture toughness was underesti- shown in Fig. 6, was the best indicator of the mated. This suggests that a knot cannot be effect of knots on the fracture toughness of modelled by a crack. Fracture mechanics con- solid wood. The knot ratio, KR, depends on ®rms this as the maximum stress at the tip of the position of the knot within the board and an elliptical crack in an isotropic, elastic, in- takes into account the increased effect of edge ®nite body is given by: knots over face knots as well as its size. For ␴ max 2a example, the face knot shown on the left side ϭ 1 ϩ , (13) ␴ b of Fig. 6 only contributes the vertical length a ␴ ϭ of the knot to the numerator of the knot ratio, where max maximum applied stress at whereas the edge knot shown on the right side the end of the major axis, Conrad et al.ÐFRACTURE OF SOLID WOOD 581

␴ ϭ a applied stress applied nor- moisture content is increased to ®ber satura- mal to the major axis, tion, the material behavior shifts from brittle a ϭ half major axis, and to tough. This is similar to results for Mode I b ϭ half minor axis, and Mode II fracture. Initial failure at the and shows that as the minor axis is reduced, notch for dry material typically resulted in i.e., the crack tip becomes sharper, the maxi- complete failure of the beam, as is the case for mum stress at the end of the major axis in- brittle materials. In contrast, initial failure in creases. Since knots typically have a larger green material resulted in a small load drop minor axis than a crack, an equivalent crack followed by a subsequent increase in load, as will underestimate the fracture toughness of a the green specimens failed slowly by shear at knot. the notch tip rather than sudden cross-grain While the majority of researchers do not failure as is the case for dry beams. state the orthotropic direction studied, it is pre- The effect of strain rate was examined by sumably either the RL or TL direction. As Spencer (1979), who found that bending with Mode II fracture toughness, it is dif®cult strength increased with strain rate. The effect to obtain suf®ciently large specimens where was more pronounced for samples with a the length is not parallel to the longitudinal greater initial strength, which likely have a direction. smaller intrinsic ¯aw size. The mechanism for Several researchers (Leicester 1973; Leices- the increased bending strength at higher strain ter and Poynter 1979; Stieda 1966; Lum and rates is likely the same as that for Mode I frac- Foschi 1988) have studied the effect of notch- ture toughness. es on failure load, modulus of rupture (MOR), and stress intensity factor. Lum and Foschi Energy methods and nonlinear (1988) have shown that for a rectangular end- fracture mechanics notched ¯exure (rENF) specimen, the Mode I stress intensity factor increases with notch The literature discussed above has mainly depth and notch length. It should be noted that been using the concepts of linear elastic frac- this is not pure Mode I loading and therefore ture mechanics (LEFM) and in particular the must be categorized as mixed-mode. Leicester stress intensity factor (K) approach. LEFM re- (1973; Leicester and Poynter 1979) found that quires that the material be linear elastic, or at as the sharpness of the notch tip increases, the least that any material nonlinearity be restrict- MOR and failure load of the specimen are re- ed to a small region in the vicinity of the crack duced. This was also observed by Stieda tip (small scale yielding). If these conditions (1966), who reported a similar effect for notch are met, K is a measure of the intensity of the depth, which is an equivalent concept to crack stress and strain ®eld in the crack tip region. length. Energy methods do not explicitly consider the As with Mode I fracture, knots affect the local stresses and strains in the vicinity of the failure load. Using ®nite element analysis, crack tip and are based on the concept of an Cramer and Goodman (1983) show that edge energy balance between elastic energy in the knots lead to a greater stress concentration, de- system and the energy required to extend the ␴ ␴ ®ned as max/ a, than face knots. This con®rms crack. Energy methods can be used when the the effect found by Pearson (1974) where the material behavior is linear elastic (LEFM), and fracture strength of edge knots, modelled by they can be extended to cases when the ma- an equivalent crack, was between 30 to 62% terial behavior is nonlinear (NLEFM). Com- of the fracture strength for a similarly sized pared to the LEFM literature, the NLEFM lit- face knot. erature is limited. Although NLEFM is more Stieda (1966) examined the effect of mois- cumbersome to apply, Gustafsson (1988) ture content on the failure mechanism. As the pointed out the NLEFM is more appropriate 582 WOOD AND FIBER SCIENCE, OCTOBER 2003, V. 35(4) in many applications where the condition of lular level, as the crack must pass through a linearity is violated. Examples when NLEFM greater amount of cellulose, which has a high should be used are when there are creep ef- fracture toughness, to propagate. Finally, frac- fects, crack bridging behind the crack tip, and ture toughness increases with moisture con- when a fracture process zone with damage and tent, reaching a maximum between 6 to 8%, microcracks develops around the crack tip. and decreasing thereafter. This is due to a shift Some notable work in the area has been done in fracture behavior from brittle to ductile. At by Bostrom (1992) and Tan et al. (1995), who higher moisture contents, the crystal structure studied the softening of the process zone of the micro®brils is disturbed by the in- ahead of the crack tip, and Vasic and Smith creased water and hence fracture toughness is (2002), who developed a crack bridging model reduced. for fracture of spruce. NLEFM and the under- Other conclusions are based on an understanding of how the fracture process zone de- standing of fracture mechanics. Mode II frac- velops in different species, modes of loading, ture toughness is greater than Mode I for a and crack orientations are currently poorly un- given species as is the case with the majority derstood. However, nonlinear techniques are of materials. Fracture toughness increases with required to understand and predict creep, R- increasing strain rate since the internal ¯aws curve behavior, and damage tolerance of large do not have suf®cient time to reach the critical scale wood structures. length. Checks and other defects reduce the strength and fracture toughness of a specimen SUMMARY AND CONCLUSIONS as they introduce ¯aws greater than those inherently found in the material. However, in the Review of the literature on the fracture of case of knots, there is the possibility of an solid wood at different length scales shows increase in fracture toughness. Also, as with that its behavior is dependent on the mode of most materials, edge defects have a greater ef- loading (Mode I, Mode II, Mode III, and fect than face defects. mixed-modes) and the direction of crack prop- This review has shown that we can interpret agation (RL, TL, RT, TR, LR, and LT) because and to some extent explain the macroscopic of anisotropy of the structure and properties of fracture behavior based on an understanding wood. To understand and interpret the mac- of the structure and properties at smaller roscopic behavior of wood, fracture needs to length scales. However, currently we do not be examined at all scales: molecular, cellular, have suf®cient understanding to directly and growth ring, and macroscopic, with insight quantitatively relate chemical composition and into the behavior at each level provided from micro/meso-structure to the microscopic and the understanding of its behavior at the ®ner macroscopic fracture behavior of wood. scale. Thus, the major conclusions found on the ACKNOWLEDGMENTS macroscopic fracture of solid wood can be re- The authors would like to thank and ac- lated to the behavior of wood at the lower lev- knowledge Forintek Canada Corporation, the els. These major conclusions are that the frac- Structural Board Association, and the National ture toughness perpendicular to the grain is ap- Science and Engineering Research Council of proximately one order of magnitude greater Canada Collaborative Research and Develop- than that parallel to the grain. 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