Fracture behaviour of softwood

Fracture behaviour of softwood

Ian Smith a,*, Svetlana Vasic b

a University of New Brunswick, Bag Service #44555, Fredericton, NB, Canada E3B 6C2b Department of Wood Science, Universit�ee Laval, Pavillon Abitibi-Price, Sainte-Foy, QC, Canada G1K 7P4

Received 26 July 2001; received in revised form 11 April 2002

Abstract

In design wood is regarded as a brittle material, depending on the stress direction, duration of loading and moisture

content. The usual presumption is that wood is perfectly brittle–elastic (linear elastic fracture mechanics, LEFM), or

that its behaviour mimics other materials such as concrete. Attempts to verify modelling assumptions have been very

limited. To date the authors have focused on opening mode (mode I) behaviour of softwood. Real-time microscopic

observations have been made in the vicinity of crack tips. Small end-tapered �double cantilever beam� specimens were

loaded within a scanning electron microscope and direct measurement made of surface strain fields near cracks. This

revealed that a �bridged crack� model mimics behaviour best. Non-linear bridging stresses depend on the crack opening

displacement and fall to zero once crack faces are separated. Such precise modelling is necessary only for short cracks in

proximity to boundary conditions, e.g. in mechanical connections. Simplified fracture-based design methods can be

employed for certain common problems. For example, a closed-form LEFM design equation was developed to predict

critical load levels for notched bending members.

� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Notched beams; LEFM; Fracture mechanisms; NLFM; Bridged crack model

1. Introduction

Fracture being a process in which new sur-

faces are formed in a body is an essentially local

phenomenon promoted by stress concentration.

The process starts and propagates necessarily by

breakdown of internal bonds. It can be speculated

that no general fracture law exists and differentsolutions must be sought for each material, in ac-

cord with the apparent mechanisms and at scales

appropriate to problems at hand. Micro-mechan-

ics has to be embodied in any fundamental frac-

ture analysis and spans the gap between material

science and engineering applications.

Wood is a natural polymeric composite that is

heterogeneous, porous, hygroscopic and aniso-

tropic, with a microstructure that is reflected onthe macro-scale in its grain. Cell walls are layered

and composed of three organic components: cel-

lulose, hemicellulose and lignin. Cellulose is an

unbranched, long linear chain polymer of glucose

units and is physically arranged into slender

strands called microfibrils with periodic crystal-

line and non-crystalline regions along the length.

* Corresponding author. Tel.: +1-506-453-4944; fax: +1-506-

453-3538.

E-mail addresses: [email protected] (I. Smith), svetlana.vasic@

sbf.ulaval.ca (S. Vasic).

0167-6636/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S0167-6636(02)00208-9

Mechanics of Materials 35 (2003) 803–815

www.elsevier.com/locate/mechmat

mail to: [email protected]

Hemicellulose is somewhat similar to cellulose but

consists of chemically distinct compounds. Lignin

is natures adhesive. Wood is considered a two-

phase material with crystalline cellulose forming

the fibre and a combination of non-crystalline

cellulose, hemicellulose and lignin forming thematrix (Bodig and Jayne, 1982). There exist vari-

ous types of wood cells each with distinct features

and physiological and structural functions within a

tree. Which types of cells appear and how they are

arranged depends on the species of tree, but the

arrangement is always complex. Wood is sensibly

an elastic material in an undamaged state, and if

subjected to relatively low levels of stresses ofshort duration at room temperature. Both physical

and mechanical properties are non-linear with re-

gard to temporal history of the material. Wood is

often thought of as a cylindrically orthotropic

material (Fig. 1) or orthotropic at locations far

enough away from the pith (cylindrical origin)

that the effect of curvature in growth rings can

be neglected. Even neglecting local perturbationsin wood structure around features such as knots,

cylindrical orthotropy is a rather coarse concep-

tualization as it neglects effects such as radial

variation in the growth rings, and taper, crook and

sweep in logs. In fact, properties can vary signifi-

cantly along the L direction or along the R di-

rection. In engineering design it is assumed for

simplicity wood is transversally isotropic, i.e. ig-

nore directional dependence of properties in the

RT plane. That mechanical properties of wood are

highly variable with respect local direction �in the

parent tree� is no accident and reflects mechanicaland physiological needs when it was part of a

living organism (Mattheck and Breloer, 1994).

Although most cells are oriented essentially

parallel to the stem axis, others have different

alignment leading to interfacial coupling between

cells. Whatever level of representation is consid-

ered components of wood have been created in

order to inhibit fibres from sliding past oneanother and maintain integrity of the tree (Atkins

and Mai, 1985). Complex interactions at the mi-

croscopic scale at a multiplicity of interfaces play

a predominant role and should be reflected when

fracture mechanics is applied to wood. Presently

fracture of wood is relatively poorly understood

despite there being a significant number of papers

and reports in the literature. Fundamental studiesare limited (Porter, 1964; Perkins, 1967; Debaise

et al., 1966; Ashby et al., 1984; Smith and Chui,

1994). Valentin et al. (1991) produced their com-

prehensive state-of-the-art report, with an empha-

sis on engineering applications, almost one decade

ago but it remains an accurate reflection of current

practice.

When loaded in tension or unconfined shearwood exhibits quasi-brittle behaviour (Smith,

1982). Apparent strength decreases as volume is

increased. This volume (or size) effect is taken ac-

count of in a number of structural design codes but

the phenomena is not well understood and is

treated empirically. Structural situations where

brittle fracture via crack propagation is an issue

include flexure of shaped members, flexure ofbeams with holes or notches, and mechanical or

glued connections.

A comprehensive set of fracture concepts and

models for wood needs to recognise fracture

mechanisms at nano-, micro-, meso- and macro-

scales, as indicated in Fig. 2. This paper provides

insight into work over the last decade at the Uni-

versity of New Brunswick on fracture in wood, incontext of a brief commentary on the state-of-

knowledge.

Fig. 1. Wood stem represented as a cylindrically orthotropic

material: L––longitudinal or grain direction, R––radial direc-

tion, T––tangential direction.

804 I. Smith, S. Vasic / Mechanics of Materials 35 (2003) 803–815

2. Linear elastic fracture mechanics problems

To date the only well accepted application oflinear elastic fracture mechanics (LEFM) in

structural design in wood deals with situations

where bending members are notched on the ten-

sion side (Fig. 3). The re-entrant corners of not-

ches are loci for stress concentrations and wherecracking nucleates, and grows from once the

applied load reaches the critical level (Smith

Fig. 2. Levels of wood characterization.

I. Smith, S. Vasic / Mechanics of Materials 35 (2003) 803–815 805

and Springer, 1993). As members are inherently

strongly anisotropic crack growth occurs in thegrain direction whatever the notch geometry

(Ashby et al., 1984).

Extensive tests have been performed at the

University of New Brunswick on notched wood

members. Specimens were either solid sawn spruce

(lumber) joists or spruce glued-laminated-timber

(glulam) made with 38 mm thick laminates.

Lumber joists were 35 or 38 mm thick and between60 and 235 mm deep. Glulam members were 80

mm thick and 228 mm deep. Test spans were in the

order of 10 times the depth. Although both green

(saturated cell walls) and dry material has been

tested only results for dry material (9–12% mois-

ture content) are discussed here, as findings are

generally similar for either moisture condition

(Smith et al., 1996a). Test arrangement adoptedwere inclined members similar to that in Fig. 3(a),

and horizontal members similar to that in Fig.

3(b). Pin-support was provided at the un-notched

support and a horizontal roller at the notched

support, which made the system statically deter-

minate with only vertical reaction forces. Dis-

placement control was used and typically cracking

initiated in about 2 min with complete failure oc-curred in about 5 min. After the primary test,

compact tension (CT) specimens were cut out of a

member to enable the fracture toughness, KIC, to

be measured. The locations from which CT spec-

imens were cut are indicated in Fig. 3(a) and (b).

Further test details are given elsewhere (Smith

et al., 1996b). What is discussed here is how well

LEFM predicts the observed load capacities ofnotched members.

Stress intensity factors KI (opening mode) and

KII (forward shearing mode) were calculated by

finite element analysis assuming linear elastic or-

thotropic material response. Transverse isotropy

was assumed, with the member axis presumed to

be parallel to the grain of the wood. In analysis a

crack 0.1 mm in length parallel to grain was in-troduced at the notch corner to produce an ap-

propriate stress concentration at that location.

Fig. 4 shows a typical finite element mesh con-

structed using eight-noded quadrilateral plane

strain elements. For some elements one side of the

quadrilateral was collapsed to form a six-noded

triangular element. In the case of elements near

to the re-entrant notch corner this facilitated meshrefinement. For those element immediately adja-

cent to the corner, mid-side nodes were moved

to the quarter-point position to simulate an r�1=2

stress singularity. Remote from the notch, col-

lapsed elements simply facilitated meshing of the

geometry. Stress intensity factors were calculated

from the near tip displacement of the crack sur-

faces (Saouma and Sikiotis, 1986; Boone et al.,1987).

Crack initiation was detected experimentally by

surface gauges across the crack path adjacent to

the notch corner. In some instances the crack ini-

tiation resulted in an unstable crack and initiation

and ultimate (failure) loads coincided. However

Fig. 3. Typical notched members: (a) inclined bending member with bird-mouth notch, (b) horizontal member with a square end-

notch.


for most specimens crack growth was stable and

episodic and the failure load was markedly higher

than the crack initiation load. Cracks were often

arrested when they intersected gross irregular

features in the material such as knots, and finger

joints in the case of glulam. Fig. 5 shows the typ-ical level of agreement between predicted and ob-

served values of critical reaction force, Vf , while

Fig. 6 compares predicted crack initiation force

with observed failure force. For inclined members

the reaction force corresponds to the component

normal to the member axis, Vn in Fig. 3a.

Using various proposed mixed mode failure

criteria (Valentin et al., 1991) the mode II (forward

shearing mode) component makes a negligible

contribution to the estimation of Vf for notched

members of the types studied. Thus an appropriate

�strength� criterion is taking the mode I stress in-

tensity factor KI equals KIC. As illustrated in Fig. 5

in a global sense LEFM predicts behaviour ofnotched members well for geometry similar to

those tested. By contrast, as seen in Fig. 6 finite

element based LEFM analysis yields fairly con-

servative estimates of capacity compared with

observed ultimate capacities. This reflects thatFig. 5. Predicted versus observed crack initiation force (Smith

et al., 1996b).

Fig. 6. Predicted crack initiation forces versus observed failure

forces (Smith et al., 1996b).

Fig. 4. Typical finite element mesh: eight-node quadrilateral plane strain ANSYS elements.


analysis ignores toughening mechanisms associ-

ated with the anisotropy and gross inhomogeneity

allowed within commercially produced lumber and

glulam.

Because finite element analysis is not practical

for �everyday� design practice, closed-form LEFMmodels for notch wood members are widely ac-

cepted. Such models are based on a balance of the

elastic strain energy released during crack growth

with the critical elastic energy release rate, and

simple beam theory. In Canada the design ex-

pression used for wood members is (Smith and

Springer, 1993; Smith et al., 1996a,b):

Vf ¼bad

ffiffiffiffiffiffiffiffiffiffiffiGc=d

p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:6ða � a2Þ=Gxy þ 6g2ð1=a � a2Þ=Ex

p ð1Þ

where d, a and g are as defined in Fig. 3, b is

thickness of the member, Gc is mode I critical

elastic energy release rate, Gxy is shear modulus,

and Ex modulus of elasticity parallel the grain. It is

presumed that the grain direction is parallel to themember axis, which is always nominally the case

for straight members. Adoption of closed-form

solutions inevitably means some loss of precision

relative to analysis based on the finite element

method. Fig. 7 compares values of Vf calculated

using Eq. (1) with observed failure forces. As be-

fore, reaction force for an inclined member is the

component normal to the member axis. Overall the

closed-form model is reliable compared with test

data, however analysis errors can be significant

when the notch is very shallow or very short.

Unfortunately such cases are not uncommon in

practice when very deep glulam members are em-ployed.

LEFM analysis of wood only works well in

situations where the stress intensity region adja-

cent to the notch, or any other type of stress

raising feature, is small compared to general di-

mensions of the member. Crack tip strain fields

must be sensibly the same as in material tests used

to characterize fracture toughness, or LEFM willnot work well. If this is the case it does not actually

matter whether or not woods fracture behaviour is

truly linear or elastic. All that matters is that be-

haviour can be treated consistently when analysing

material property test data and when analysing

structural members. Apart from notched beams,

the other common situation that usually satisfies

requirements for successful application of LEFMis bending members with large holes (Aicher et al.,

1995). In that case however mode II rather than

mode I fracture behaviour is the dominant con-

sideration.

Although commonly encountered in practice

there has been little scientific study of problems for

which use of LEFM is an inadequate strategy. The

most common instance is glued or mechanical lapconnections (Fig. 8). What such problems have

in common is that crack tips and associated high

stress regions are not remote from boundary

conditions. As a guide, the inelastic process zone

must be confined to a sphere at a crack tip that has

a radius small enough to satisfy the condition

Fig. 7. Approximate predicted critical reaction forces (Eq. (1))

versus observed failure forces (Smith et al., 1996b). Fig. 8. Lap connection with laterally loaded bolts.


r=a < 0:02 (a is the crack length, or any dimension

of the cracked body) for LEFM to be valid.

3. How wood fractures: mode I

Recognising that wood fracture depends upon

behaviour within localised damage zones adjacent

to crack tips, attempts have been made to repre-

sent wood as non-linear fracturing material. Ex-

perience with other quasi-brittle materials, e.g.

concrete, ceramics and rocks, provides an under-

standing that the size of the process zone is a

‘‘. . .measure of the deviation from linear elasticbehaviour shown by the material’’ (Atkinson,

1987). The macroscopic inelastic behaviour is

completely controlled by heterogeneities on the

�grain scale� and their interaction under tri-axial

stress (or strain) induced at the major crack tip.

Based on the experience with other materials, ex-

perimental evidence for wood was initially inter-

preted as showing the existence of an inelasticprocess zone ahead of a crack. This led to adop-

tion of the fictitious crack model (FCM) origi-

nally developed for concrete by Hillerborg et al.

(1976). Its applicability to wood has been studied

thoroughly at the University of Lund, Sweden

(Bostrom, 1992; Wernersson, 1994). Despite vari-

ous attempts it has proved impossible to resolve a

number of discrepancies between FCM modelsand test data (Vasic et al., 2002). With this in mind

the authors decided to use real-time scanning

electron microscopy to elucidate the failure mech-

anism (Fig. 9). Although only opening mode type

fracture has been studied in any detail, it is ap-

parent as shown below that wood has fracture

behaviour that does not match that of other con-

struction materials, or models supposed valid(Vasic and Smith, 2002).

Work reported here was aimed at identifying

the crack evolution, including any restraining

mechanisms due to bridging and micro-cracking at

crack tips. This required a test arrangement and

specimen that favour sub-critical stable, steady-

state crack growth. Experimental evidence indi-

cates that sub-critical crack growth is a charac-teristic of wood fracture (Mai, 1975; Yeh and

Schniewind, 1992). As is well known, for quasi-

brittle materials the stability and rate of crack

velocity can be controlled through appropriate

choice of the rate of loading and experimentalarrangement. Thus an end-tapered double-canti-

lever beam (DCB) specimen (Fig. 10) and a dis-

placement controlled loading rate of 3 mm/min

were chosen. Size of the apparatus and specimens

were limited by the size of the SEM chamber and

available working space. Clear (defect free) spruce,

Picea mariana, at moisture content of 15% was

used. More limited tests were performed on otherspecies but that is not discussed here. A discrete

mesh deposited over the surface and oriented at

45� relative to the grain facilitated recognition and

measurements of the extent of damage and crack

profiles. Specimen thickness was in the order of 6

mm. Other dimensions are as implied in Fig. 10. In

most tests radial-longitudinal (RL) or tangential-

longitudinal (TL) orientations were studied, al-though some TR specimens were also investigated.

In this notation the first direction is the external

stress direction and the second the direction of

crack growth. A small specimen thickness insured

that surface observations were representative of

behaviour within the thickness. The starter notch,

0.5-mm-wide, was cut with a jewellery saw. The

process of crack evolution in real time was video-taped, which allowed measurements to be made

and crack profiles to be reconstructed. Time for

complete fracture of specimens was between 2 and

3 min. Because the SEM process causes specimens

Fig. 9. Fracture specimen and loading apparatus placed within

an SEM chamber.


to dry somewhat, matched tests were performed in

air. This confirmed that drying in the SEM does

not influence the nature of the mechanism, but it

does lower the load necessary to drive a crack

(Vasic, 2000).Tests were stable as intended (Fig. 11). As im-

plied by the figure, fracture properties for the RL

direction are higher than for the TL direction. This

reflects the reinforcing effect of radial ray cells

within the wood (Mattheck and Breloer, 1994).

Figs. 12–14 show typical micrographs taken dur-

ing SEM tests. These show the behaviour of anatural crack ahead of the starter notch. Although

there is some difficulty in correctly identifying the

Fig. 10. Aluminium loading apparatus with wedge shaped DCB test specimen.

Fig. 11. Typical load versus time (proportional to wedge movement) relationships.


crack tip, there was no evidence of a �large� damage

region ahead of the primary crack (Fig. 12). Once

initiated, the natural crack grows with a highly

localised fracture zone in both length (1–2 mm)and width. Damage was highly localised and ex-

tended two or three cells at most from the fracture

plane (Fig. 14). Pre-existing micro-cracks that

constitute inherent damage opened close to the

crack tip, growing to more than 100 lm in length.

The authors speculate that the inherent damage

develops at the sub-cellular level under combined

influences of stresses due to self-weight, growth

and environmental loads on the tree. Only those

micro-cracks of critical size joined the main crack.Most closed elastically once the crack tip passed,

but some did not close completely when the crack

advanced resulting in a finite residual strain behind

the crack tip. Behind the crack tip partially de-

laminated longitudinally oriented cells (tracheids)

bridged the crack (Fig. 13). This fibre bridging

Fig. 12. SEM Micrograph of crack tip region once a natural crack is established: RL orientation.

Fig. 13. SEM micrograph of partially peeled cells bridging the crack: RL orientation.


provided crack closure forces proportional to the

local crack opening displacement (Fig. 15). Bridg-

ing stresses were deduced via inverse application of

the bridged fibre model mentioned below. There

was self-arresting strain-energy-driven sub-criticalcrack propagation if a test was stopped tempo-

rarily to take pictures in the still mode. Previ-

ously mentioned radial cells contribute to bridging

forces in the RL fracture direction.

The contribution to toughness from opening

and extension of flaws, cell peeling and closure

forces due to bridging cells depends on the bridg-

ing configuration that is not strictly self-repeating.

Crack propagation in wood is locally episodic and

is itself a heterogeneous process, with continuous

re-initiation along the path of the crack. Macro-scopically it may appear like a quasi-static process,

but at the micro-scale crack growth is character-

ised by phases of stability and unstable micro-

failure. When examined microscopically fractured

surfaces are irregular and tortuous. Bridging is the

main mechanism of crack tip shielding in spruce,

Fig. 14. SEM micrograph of crack in radial-tangential plane.

Fig. 15. Influence of distance behind the crack tip and crack opening displacement on bridging stress.


and presumable other softwood species. There is

no evidence of a large damage zone ahead of the

crack tip as assumed to occur in materials such as

concrete, rock and ceramics.

Based on observations during the SEM study a

physically realistic bridging crack model (BCM)has been developed (Vasic, 2000; Vasic and Smith,

2002). Fig. 16 shows essential features of the model

in the context of an end-tapered DCB specimen.

The difference between the non-linear FCM and the

BCM is whether or not a stress singularity at the

crack tip is permitted. Analytically the BCM as-

sumes that the singularity at the sharp crack tip

coexists with the bridging zone behind the crack tip.

The bridging zone is not fictitious as in the cohesive

crack model (Ratanalert and Wecharatana, 1989).

In the BCM fracture occurs when critical fracture

toughness KIc is reached at the crack tip. Therefore,the fracture criterion is stress based and fracture

toughening during the crack growth is due to simple

summation of the bridging stress contribution and

the net crack tip stress intensity. Evaluation of the

inelastic (bridging) contribution Kb is crucial for

proper application of the model. Bridging stresses

in the SEM study were evaluated numerically based

on these concepts using a Green�s function typeapproach and results from non-linear finite element

analysis with the DIANA 7 finite element package

(Fig. 15; Vasic, 2000).

Fig. 17 shows typical results for fracture energy

release rate from application of the BCM. Obvi-

ously, there is no contribution to fracture energy

from the bridging stresses prior to crack initiation

and extension. Once established, the bridging zonecontributes about 10% to the total fracture energy

release rate even though its length is rather limited

(Fig. 15). Beyond a crack extension of about 4

mm, the drop off in energy release rate due to

elastic energy release, and the resultant drop in the

total release rate are due to large displacement

effects becoming dominant. Specimens behaved

almost as two separate halves that rotate as rigidFig. 16. Schematics of BCM.

Fig. 17. Energy release rate versus crack length for tapered DCB specimen: RL orientation.


bodies about a �hinge� located where the crack

eventually exits the base of the specimen. The point

of maximum energy release rate at 4 mm is related

to an intrinsic flaw size, which is equal to the

length of longitudinal cells (tracheids) in spruce.

Work is in progress to establish whether the BCMcan explain the size effect whereby apparent frac-

ture toughness in specimens depends upon the

width of the crack front (specimen thickness).

4. Conclusions

Work discussed here demonstrates the need fora range of fracture mechanics models for wood.

They can range from fairly simple LEFM models

that work when there are gross features such as

notches, to models that recognise the cellular na-

ture of the material. As observed in SEM studies,

at the fine scale wood has behaviour distinct from

that of other common structural materials. Re-

fined models are necessary only for short cracks inproximity to boundary conditions as occurs often

at structural connections. The BCM developed

by the authors is appropriate for representing near

tip fracture behaviour under mode I load condi-

tions.

Although there have been some significant ad-

vances in understanding wood fracture, much re-

mains undone. Future emphasis needs to be on theeffects of fracture under sustained or cyclic loads,

mechanosorptive effects, and fracture induced

other than by the opening mode with stress normal

to grain and crack growth along the grain.

Acknowledgements

This work was carried out with the aid of grants

to the first author from the Natural Sciences and

Engineering Research Council of Canada.

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Fracture behaviour of softwood

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