Three-dimensional modelling of wood fracture in mode I,perpendicular to the grain direction at fibre level

Abstract

A coupled experimental and numerical modelling approach was used to investigate the mechanism of softwood fracture at the fibre level. First, a three-dimensional mixed lattice–continuum fracture model was developed to investigate the mechanism of wood fracture, taking into account the porosity of its structure and its heterogeneities at the fibre level. The critical volumes in the specimen where crack propagation was more probable were modelled by a lattice that could show the alternation of earlywood and latewood fibres, and the other regions were considered as the continuum medium. The proposed model was used to investigate the mode I fracture of a small softwood sample in RL orientation. Secondly, a method was developed for microscopic observation of the crack trajectory and investigating the mechanism of initiation and propagation of cracks. This approach was used for microscopic investigation of the fracture behaviour of spruce specimens in mode I and RL orientation. The results of the numerical study were compared with the experimental results. The prepeak and postpeak behaviour of the obtained stress–displacement curve and also the crack opening trajectory in cross-section and longitudinal section in the model and experiments were in good agreement. Both the model and the microscopic observation showed that in mode I fracture and RL orientation, the main trajectory of the crack propagates in the earlywood ring.     

Micromechanical approach to wood fracture by three-dimensional mixed lattice-continuum model at fiber level

To investigate the fracture behavior of wood, the porosity and heterogeneities of its microstructure should be taken into account. Considering these features of wood microstructure in a continuum-based model is still a difficult problem and the lattice model might be an alternative. In the developed mixed lattice-continuum model, the probable crack propagation volume was modeled by defining a three-dimensional lattice of different beam elements and the other regions were considered as continuum medium. Different beam elements of lattice represented the earlywood fibers, latewood fibers, ray cells and bonding medium between the fibers. The proposed model was used to investigate the mechanism of mode I fracture in a small notched wood specimen in RL orientation. The resulting pre-peak and softening curve and also the crack opening trajectory in both cross-section and longitudinal-section in model were in good agreement with the experimental observations. This model shows the importance of considering the three-dimensional and distributed propagation of microcracks and main cracks in fracture stability. It was also shown that in mode I fracture, RL orientation, the main crack propagates in the earlywood ring.     

Fracture behaviour of laminated veneer lumber under Mode I and III loading

Mode I and Mode III loading experiments were performed on side grooved CT specimens of two types of Laminated Veneer Lumber (LVL). Steady state crack propagation was maintained in order to detect complete load displacement diagrams. Fracture behaviour and influence of fiber orientation were studied and all important fracture mechanical values (stiffness/compliance, microstructural damage, crack initiation energy, specific fracture energy etc) were determined. Much higher crack initiation energies and specific fracture energies resulted in mode III loading than in mode I loading for both material types. Under external mode III loading, crack initiation occurs in mode III and crack propagation however takes place under mode I owing to crack surface interference. The influence of fiber orientation on fracture mechanical properties of LVL was discussed. Received 15 September 1999     

The fracture behaviour of single wood fibres is governed by geometrical constraints: in situ ESEM studies on three fibre types

In situ tensile tests were performed in an environmental scanning electron microscope (ESEM) on earlywood, transition wood and latewood cells of Norway spruce (Picea abies [L.] Karst.). In order to examine the single wood fibres in a wet state, a specially designed tensile testing stage with a cooling device was built. The fracture behaviour of the cell types was studied at high resolution while straining. Different failure mechanisms were observed for the three tissue types. The thin-walled earlywood fibres showed tension buckling which gave rise to crack initiation and resulted in low tensile strength, whereas thick-walled latewood fibres predominately failed by transverse crack propagation without fibre folding.     

Microfracture in wood monitored by confocal laser scanning microscopy

The paper deals with the experimental characterisation of damage evolution within the radial (R)–tangential (T) growth plane of softwood loaded in tension perpendicular to the grain. The reported investigations comprise in-situ monitoring of crack propagation by means of Confocal Laser Scanning Microscopy (CLSM) and evaluations of crack patterns of broken specimens. Three types of notched specimens, representing different crack propagation systems, were tested; for all configurations, both, loading and crack propagation direction were located within the RT plane of wood. The CLSM pictures of broken specimens show distinct differences among the regarded configurations with respect to crack paths. Two different damage mechanisms were identified being rupture of earlywood cell walls in the case of crack propagation in tangential direction and debonding of wood fibers, i.e. rupture of the interface zone between adjacent tracheids, in case of crack progression in radial direction. In the case of an intermediate crack system with an angle of 45° between initial notch direction and radial direction the crack evolution was monitored in-situ during the tension test, whereby the combined action of both basic fracture mechanisms was observed.     

Mode I fracture and acoustic emission of softwood and hardwood

 The Mode I fracture behaviour of two softwoods (spruce and pine) and three hardwoods (alder, oak and ash) was studied in the RL crack propagation system using the splitting test in combination with monitoring acoustic emission (AE) activity. Test parameters measured included notch tensile strength, specific fracture energy, characteristic length and AE cumulative counts, AE amplitudes as well as parameters characterizing the frequency spectra of the emitted acoustic emission events. The notch tensile strength was found to correlate with density. The specific fracture energy and characteristic length showed the different crack propagation process between the softwoods and hardwoods. The softwoods fractured in a more ductile way and the hardwoods showed a more linear elastic behaviour. This finding was supported by the AE measurements showing much less cumulative counts for the hardwoods indicating that less microcracks were formed and that processes like fiber bridging were not so effective. Differences in the frequency domain of the AE signals between softwoods and hardwoods could not be detected. Received 13 January 1999     

Modelling longitudinal elastic an shrinkage properties of wood

Summary A model was developed for estimating elastic and shrinkage properties of a softwood cell wall from the properties of its polymeric constituents: cellulose, hemicellulose and lignin. The theory of composite materials was used. Based on a literature survey, models of latewood, earlywood and compressionwood of a softwood cell wall structure were made. The model takes into account the helical winding of the microfibrils in the cell wall and it estimates the behaviour of a balanced laminated double-cell wall in which rotation is restrained by adjacent cells. The calculated elastic and shrinkage properties were compared with earlier test results and good agreement was found.     

Mode III fracture energy of wood composites in comparison to solid wood

A simple experimental setup for mode III and mixed mode (I?+?III) fracture tests with anisotropic materials under steady state crack propagation has been developed. Load-displacement curves can be recorded up to the complete separation of the specimen. From the load-displacement curves several mechanical material parameters can be derived. The tests have been performed for solid wood and different wood composites, being PARALLAM^® PSL in different orientations, particleboard and INTRALLAM^® LSL, and the fracture behaviour is characterised by the specific fracture energy.     

Relationship between crack propagation and the stress intensity factor in cutting parallel to the grain of hinoki (<Emphasis Type="Italic">Chamaecyparis obtusa</Emphasis>)

The method of digital image correlation (DIC) was applied to the digital image of orthogonal cutting parallel to the grain of hinoki, and the strain distribution near the cutting edge was evaluated. The wood fracture associated with chip generation was considered as mode I fracture, and the stress intensity factor K_I for fracture mode I was calculated from the strain distribution according to the theory of linear elastic fracture mechanics for the anisotropic material. The calculated K_I increased prior to crack propagation and decreased just after the crack propagation. The change in K_I before and after crack propagation, ΔK_I, decreased in accordance with the crack propagation length, although the variance in ΔK_I should depend on the relationships between the resolution of DIC method and the dimensions of cellular structure. The calculated K_I in this study was almost on the same order as reported in the literatures. It was also revealed, for the case of chip generation Type 0 or I, the stress intensity factor for fracture mode II could be negligible due to the higher longitudinal elastic properties of wood in the tool feed direction than the one radial ones, and the mode I fracture was dominant.     

The fracture toughness and properties of thermally modified beech and ash at different moisture contents

The fracture toughness of thermally modified beech (Fagus sylvatica L) and ash (Fraxinus excelsior L) wood under Mode I loading was quantified using Compact Tension (CT) specimens, loaded under steady-state crack propagation conditions. The influence of three heat-treatment levels and three moisture contents, as well as two crack propagation systems (RL and TL) was studied. Complete load–displacement records were analysed, and the initial slope, k _init, critical stress intensity factor, K _Ic, and specific fracture energy, G _f, evaluated. In the case of both species, thermal modification was found to be significantly affect the material behaviour; the more severe the thermal treatment, the lower the values of K _Ic and G _f, with less difference being observed between the most severe treatments. Moisture content was also found to influence fracture toughness, but had a much less significant effect than the heat treatment.     

Fracture in Norway spruce wood treated with <Emphasis Type="Italic">Physisporinus vitreus</Emphasis>

Changes in the fracture behaviour of Norway spruce tonewood after fungal treatment were studied. Specimens were incubated for 6, 9 and 12 months with Physisporinus (P.) vitreus. Fracture tests were performed in a compact-tension fracture experiment set-up, and the results were compared with the morphological analysis of the degraded wood structure and transverse sections of the crack tip viewed under light and fluorescence microscopy. It was evident that both the failure load and critical stress intensity factors were reduced in wood after prolonged incubation periods. Weight losses were significantly higher in sapwood than in heartwood. With prolonged incubation periods, the frequency of unstable fracture and brittle behaviour of the wood increased. In untreated wood, cracks were initiated in the earlywood. The process involved both delamination of the cells within the middle lamellae and rupture of the cell walls, inducing a zigzag crack tip pattern. In fungally treated wood, cracks often commenced from the intersection between late- and earlywood, resulting in a straight tangential crack line. Micrographic images showed that P. vitreus was more active in the secondary walls of latewood tracheids. In this region of the wood, the cell walls were strongly degraded after 9–12 months of incubation, resulting in a reduction in tensile strength, even though the wood did not show strong features of decay at the macroscopic level.     

Mode I interlaminar fracture property of moso bamboo (Phyllostachys pubescens)

Bamboo is a unidirectional fiber-reinforced bio-composite. Once having cracks, the delaminating propagation is not controlled by the strength but by the interlaminar fracture toughness. In this paper, the behaviors of Mode I (crack opening mode) interlaminar fracture parallel to grain of moso bamboo (Phyllostachys pubescens) were studied. Based on energy theory, the Mode I interlaminar fracture toughness, G _IC, was measured using the double cantilever beam specimens, and the fracture surfaces were examined under scanning electron microscope. The results show that: (1) the interlaminar fracture toughness of Mode I is the basic characteristic of bamboo material. The mean value of G _IC = 358 J/m² (coefficient of variation = 16.88%) represents the resistance arresting crack propagation. No significant difference was found for G _IC among the specimens located at different heights of the bamboo. (2) Due to the low G _IC of bamboo, the crack propagation parallel to grain developed easily. The crack was a self-similar fracture without fiber-bridging. On the fracture surfaces, smooth fibers and plane ground tissue were found at the extended area of Mode I fracture along the longitudinal direction. Under scanning electron microscope, it could be seen that the crack propagation developed along the longitudinal interface between fibers or ground tissue. It indicates that the longitudinal interface strength was weak among bamboo cells.     

Fracturing of wood under superimposed tension and torsion

A testing method using circumferentially notched round bars for investigating mixed mode behaviour under loading in tension and torsion is applied to wood. The applicability of the method to anisotropic materials is investigated for two types of wood, beech and spruce, considering the longitudinal and radial orientation with respect to the stem axis of the tree. The strong anisotropy of wood requires different evaluation procedures for radial and longitudinal sample orientation. The K-concept of linear elastic fracture mechanics (LEFM) and concepts of non-linear elastic fracture mechanics (NLEFM) were used for the evaluation of radial and longitudinal samples, respectively. Differences between the investigated wood types under radial orientation, in their durability to withstand torsional loads, could be observed by examining ratios of the values of the fracture toughness in mode III against mode I. Micrographs of the fracture surfaces support the assumption that the higher amount of wood rays in beech is responsible for the higher toughness under torsion. In case of longitudinal specimen geometry it was found that at very high levels of torsional deformation beech and spruce reach similar values in their specific fracture energy in mode I.     

Resistance curve for the mode II fracture toughness of wood obtained by the end-notched flexure test under the constant loading point displacement condition

 The measurement method of mode II fracture toughness-crack propagation length relation (i.e., the resistance curve, or R-curve) was examined by end-notched flexure tests on sitka spruce (Picea sitchensis Carr.). The tests were conducted by varying the span/depth ratios under the constant loading point displacement condition. The fracture toughness was measured from the load-crack shear displacement (CSD) and load-longitudinal strain relations. The crack length was determined by a combination of load-CSD and load-strain compliances and Williams's end correction theory, as well as the observation of crack propagation. When the specimen had an appropriate span/depth ratio, the fracture toughness and crack propagation length were measured from the load-CSD compliance and combined load-CSD and load-strain compliances, respectively, and the R-curve could be determined properly under the constant loading point displacement condition. Received: March 15, 2002 / Accepted: July 25, 2002     

Modelling elastic and shrinkage properties of wood based on cell structure

Summary In a previous article of the authors a model was developed for estimating elastic and shrinkage properties of a softwood cell-wall. In the present article this model is enlarged to simulate the elastic properties of defect-free softwoods. The wood model consists of earlywood, latewood and ray cells, each of which have a different cell-wall structure. In the model the ratio of earlywood to latewood is defined by a given wood density. The calculated elastic properties are in good agreement with test results.     

The fibrillar orientation in the S2-layer of wood fibres as determined by X-ray diffraction analysis

Summary It is the fibrillar orientation in the S2-layer which to a great extent determines the mechanical properties of the wood fibre, with regard both to strength and stiffness and to swelling properties. Measurements of the average fibril angle of fibres are not however easy and the results differ between the methods used. In order to evaluate in more detail how the fibril angle varies in spruce wood, an X-ray method based on diffraction from the 040-plane was developed. By comparison with microscopic examination it is concluded that reliable results relating to the fibrillar orientation in the S2-layer are obtained with the X-ray technique. It is shown that the fibril angle of mature wood is rather constant with regard to both age of the annual ring and its position in the height of the tree. The fibril angle of the earlywood is found to be only slightly higher than that of latewood fibres. It is also shown that compression wood may be easily identified by virtue of the fact that its fibril angle is much higher than that of normal mature wood.The authors thank Ms Ulla Jonsson for the microscopic measurements and Dr Anthony Bristow for the linguistic revision     

Evaluation of end-check propagation based on mode I fracture toughness of sugi (<Emphasis Type="Italic">Cryptomeria japonica</Emphasis>)

The relation between crack propagation based on fracture mechanics and end-check propagation during drying was evaluated in this study. Corresponding to the direction of end-check propagation, the mode I fracture toughness of air-dried sugi specimens in TR, TL, and intermediate systems was examined by single-edge-notched bending tests. The occurrence and propagation of end checks on sugi (Cryptomeria japonica D. Don) blocks during drying were observed at the scale of the annual rings. It was found that the critical stress intensity factor (K _IC) decreased as the crack propagation changed from TL to TR. The value of K _IC in the TR system was significantly lower than that in the TL system. As a measure of fracture energy, the area under the load-crack opening displacement curve in the TR system was more than twice that in the TL and intermediate systems. These results indicate that cracks perpendicular to the tangential direction initiate radially with ease, and then crack arrest occurs to prevent growing. This finding provides a consistent interpretation of the end-check propagation observed during drying as follows: tiny end checks, as an analog of TR cracks, occur easily and selectively in latewood or transition wood and propagate toward the pith during drying. When there is no corresponding secondary check in the forward latewood, the checks are arrested and do not propagate further.     

Fibril angle variability in earlywood of Norway spruce using soft rot cavities and polarization confocal microscopy

The main purpose of this study was to investigate the variability of the fibril angle of tracheids in earlywood of Norway spruce (Picea abies L. Karst.). Polarization confocal microscopy was chosen and compared with the method utilizing the orientation of soft rot cavities. There was a significant correlation between the soft rot and polarization confocal microscopy methods, which showed the same trend of high fibril angles in the first part of the earlywood followed by a decrease toward the end of earlywood. This declining trend was less pronounced in annual rings containing compression wood. Moreover, large variations in fibril angle occurred between neighboring tracheids. The investigation also emphasized the differences between X-ray diffraction and microscopic methods, as the large variation seen by the latter methods is not seen by the X-ray diffraction approach because of its large area of measurement. No correlation was found between fiber morphology (i.e., average length, width, density) and the average fibril angle in the investigated annual rings.     

Crack formation due to weathering of radial and tangential sections of pine and spruce

The development of cracks and changes in appearance have been investigated on radial and tangential sections of pine (Pinus sylvestris L.) and spruce (Picea abies Karst.) after exposure outdoors for 61 months. The degradation of the sections has also been studied at the micro-level. The annual ring orientation was the most important factor affecting crack development on weathering. After 61 months of outdoor exposure, the tangential sections of spruce had 1.7-2.2 times greater mean total crack length per area unit than the corresponding radial sections. In pine, the total crack length per area unit on the tangential sections was 2.2-2.6 times greater than that on the radial sections. Tangential and radial sections show the same colour change as a result of weathering. Tangential sections have more and deeper cracks than radial surfaces. The cracks on the tangential sections occur frequently in both earlywood and latewood. On radial sections, cracks occur primarily at the annual ring borders, but to a certain extent also in the earlywood. Decomposition of the cell wall takes place in both radial and tangential cell walls, and cracks tend to follow the fibril orientation in the S2-layer of the cell wall. The radial cell wall of the earlywood has a large number of pits which are degraded at an early stage.     

Crack propagation in notched wood specimens with different grain orientations

Summary The cracking patterns of load induced cracks were studied by in-situ testing of compact tension specimens within the specimen chamber of a scanning electron microscrope. The cracks propagated in a generally straight path parallel to the grain, regardless of the orientation of the notch. On a microscopic scale, the crack could not be described as an ideal parallel-walled crack as assumed in fracture mechanics models. Many irregularities such as tortuosities, branching, discontinuities and bridging between the crack walls could be seen. Observations were carried out at the tip of the stable crack and at the same zone after the crack was induced to propagate beyond it. The processes taking place in this zone are discussed. The implication of these observations on the applicability of linear elastic fracture mechanics to wood are also discussed.When this work was carried out, Dr. Bentur was on leave at Purdue University, West Lafayette, Indiana