Knots in trees: strain distribution in a naturally optimised structure

Electronic speckle pattern interferometry was applied to directly measure the distribution of longitudinal, tangential, and shear strains in small boards of Norway spruce (Picea abies (L.) Karst.) exposed to tensile load in longitudinal direction. A sample with a central intergrown knot and one with an equivalent loose knot were compared with reference samples made of clear wood with an artificial central circular or square hole, respectively. The observed measurements were compared with a finite element (FE) simulation. The FE model was based on a geometric model to quantify the local fibre orientation and a micromechanical model to estimate elastic constants of clear wood and knot tissue. Both the measurements and simulation clearly illustrate a rather homogenous strain distribution around the intergrown knot. In comparison, the natural optimisation of dispersing strain peaks is less efficient in the case of loose knots. The artificial circular and square holes in samples with parallel fibre orientation lead to high gradients in the strain field and peak values in vicinity of the disturbance.     

Modeling wood pole failure

Summary In part 1 of this series, a three-dimensional, structural analysis, finite element program has been developed to predict the stress distribution in wood poles with and without spiral grain and variable material properties. This program serves as a basis for a model to predict the strength and failure location in full-size wood poles. Fundamental to this model is the ability to quantify the effects of key material and geometric properties of the pole. This paper deals with the enhancement of the program to quantify the effect of knots and their associated cross grain on the stress distribution of wood poles. The technique is based on the theoretical behavior of laminar fluid flow around an elliptical obstruction. The flow-grain analogy was employed to develop empirical relationships between knot diameter and pertinent variables (grain deviation angle near the knot and area of influence of the knot). Prior to the development of the empirical relationships, a study was conducted to determine the size and distribution of knots in Douglas-fir and western redcedar poles.The validity of the technique to describe knot behavior is reflected in the ability of the finite element model to predict the strength and failure location of wood poles. The results suggested that the flow-grain analogy is a rational mechanism to quantify the fiber orientation near a knot. Furthermore, this technique could have meaningful implication in improving visual grading methods for wood poles.The authors would like to recognize the contributions of Engineering Data Management, Inc. of Ft. Collins, Colorado for their contribution of test materials and facilities for this study.     

Location of the neutral axis in wood beams: A preliminary study

Abstract

It is commonly accepted in the analysis of wood beams that the neutral axis coincides with the beam's centroid. However, wood is not an isotropic material, has different elastic properties in the tangential, radial and longitudinal directions, and is non-homogeneous, as it contains characteristics such as knots. Therefore, there is need for an analysis of the neutral axis for anisotropic, non-homogeneous materials, such as wood, to predict deformations and strains. Specifically, digital imaging correlation, a non-contact technique to measure deformation of an object's surface, is used to examine how knots influence neutral axis location. Output from digital imaging correlation software provides a clear image of the location of the neutral axis. The neutral axis in a clear wood beam remains close to the centroidal axis throughout loading, while the location of a knot determines the size of the compression and tension zones as well as the location of the neutral axis.     

J-integral evaluation in cracked wood specimen using the mark tracking method

In this paper, an experimental analysis of the fracture parameters via the invariant J-integral for a cracked specimen made of wood is presented. The experimental test is realized using a sample made of Douglas fir loaded in opening mode. The sample geometry is a mix between the single edge notch and wedge splitting specimens, and the crack advances in the radial-longitudinal system, parallel to the wood rings. By using the optical mark tracking method, the displacement field evolution close to the crack tip is recorded during the test. The stress and strain fields are calculated using a finite element model generated from the experimental displacement fields. Further, the energy release rate is evaluated for different circular paths or crowns defined around the crack tip and for different loading values.     

Differences of tensile strength distribution between mechanically high-grade and low-grade Japanese larch lumber 11: Effect of knots on tensile strength distribution

The tensile strength (TS) test results of Japanese larch (Larix kaempferi, Carriere) lumber of varying length have shown that the length effects on TS were different between high-grade (H) and low-grade (L) lumber. In this paper, we examined the effect of knots on the TS distribution by measuring the number of knots and the knot area ratio of each specimen. There were more knots in L than in H; and the knot area ratio in L distinctly increased as the length increased compared to that in H. The correlation coefficients between physical properties and TS indicated that knots were the most influencial factor for TS among several physical properties: annual ring width, distance from pith, density, dynamic Young's modulus, and knots. We attempted to estimate the length effect parameters by introducing the concept of assumed knot strength. We thought that the length effect parameters for 50th percentiles of TS could be estimated well with fitted 3P-Weibull, and that the parameters for 5th-percentiles could be estimated well with 2P-Weibull fitted to lower-tail 10% data by the likelihood method. The differences of length effect on TS between H and L should be governed by the presence of knots. The independent model based on the concept of assumed knot strength may express the TS of structural lumber of various lengths.     

Relationship between branch-scar parameters and knot features of oriental beech (Fagus orientalis Libsky)

The classification of roundwood is inextricably linked to the measurement of a particular single wood defect. The appearance, location, and number of defects are important in the quality evaluation of logs and sawn timber, and the most important defects are knots. The purpose of this study was to investigate the relationship between the appearance of branch scars and features of the related knot inside oriental beech logs, and to model the relationship between well-defined branch-scar and knot parameters. One hundred and fifty knots in 15 stems of oriental beech trees were studied. Image analysis software was used to measure the branch-scar and knot features. The results showed a significant positive correlation between the branch-scar parameter “moustache length” and the knot length. The ratio of branch-seal length to width was found to be a good estimator of the stem diameter at the time of knot occlusion and the amount of clear wood between the knot occlusion and the bark. The relationship obtained for the oriental beech stem radius at time of knot occlusion confirms relationship reported for European beech (Fagus sylvatica L.).     

Fatigue of structural plywood under cyclic shear through thickness II: a new method for fatigue life prediction

For plywood specimens under shear through the thickness, a fatigue life prediction method based on strain energy has been newly developed with the fatigue process and failure criterion applicable to various loading conditions. Once the fatigue process and failure criterion of the plywood specimen were determined by the fatigue data measured under a loading condition other than the square loading waveform, the fatigue life of a specimen under various loading conditions could be predicted easily and accurately by the first cycle loading test. The relationship between stress level and the predicted fatigue life was also similar to that between stress level and the experimentally determined fatigue life. The fatigue life prediction method proposed may be widely applicable to the prediction of the fatigue life of solid wood and wood composites.     

Modeling wood pole failure

Summary This is the first of two papers designed to describe the most recent efforts in using contemporary technology to predict strength and failure location in wood poles. In this report, a three-dimensional finite element model is presented which was developed to provide a rational stress analysis tool for wood poles. Due to practical considerations, only critical pole segments were subjected to stress analyses. Twelve-inch (30.5 cm) segments were selected for analysis which contained knots or knot clusters deemed consequential.The linear elastic model assumes small-deflection theory, and exploits linear strain, 15-node wedge and 20-node parallelepiped, isoparametric finite elements. Element geometry was selected to reflect knot size distribution found in full-size wood poles used in North America. Boundary conditions represented both applied loading and support considerations.Model verification studies were conducted on poles with isotropic (steel) and anisotropic (wood) material properties with and without spiral grain and variable longitudinal elastic properties along the pole radius. The results showed excellent agreement between theoretical and numerically-predicted pole stresses. The effect of boundary conditions on predicted stress distribution was defined, and the element geometry was appropriately modified. The developed model proved to be a rational basis for a more enhanced version to predict the mechanical behavior of wood poles with several inherent growth characteristics.     

Strain analysis of lumber containing a knot during tensile failure

We analyzed the strain distribution of lumber containing a knot under a tensile load. The local tensile strain near the knot was measured using the digital image correlation method. Fracture often initiated near the knot where the fiber orientation changed in a three-dimensional manner. The fiber direction in this zone was different from that in the clear part, coinciding with the thickness direction and not with the longitudinal direction of the specimen. Our results disagree with those of previous models that assumed the longitudinal direction of lumber as the direction of crack propagation. Strain analysis showed that a nonlinear region existed around the knot just before ultimate fracture occurred. The results indicated that nonlinear characterization is necessary to determine the failure mechanism of lumber containing a knot, despite the brittleness fracture at the macroscopic scale.     

A three-dimensional paradigm of fiber orientation in timber

Knowledge of the three-dimensional orthogonal directions of wood material at any position within a tree is necessary for the understanding of strength reducing effects of knots and essential for the continuation of research in areas which relate small clear wood specimen behavior to the behavior of full size structural timber. A complete three-dimensional paradigm describing the geometry of knots and related fiber distortion, initially derived to predict the strength-reducing behavior of knots in structural timber of Norway Spruce with the finite element method, is presented in this article. Besides strength prediction analyses, it is believed that the paradigm may be useful in other areas of research on structural timber that are effected by fiber orientation, such as drying and form change of structural timber. The paradigm generates fiber orientation in any position within a log or lumber from assumed fiber patterns in planes parallel to the longitudinal direction of the original tree. Fiber patterns in the radial and tangential directions are derived from physical restraints related to fiber production within the annual increase surfaces of the tree and from theories of knot formation. The adaptability of the paradigm allows practically any softwood knot to be modeled with an accuracy that is limited only by input-data. The knot-axis may be non-linear, and the knot cross-section oval with its vertical and horizontal axis increasing from the pith of the stem at chosen rates. Spiral grain may also be included in the paradigm and vary with the annual growth layers. Investigations presented in this article showed that generated fiber orientations for Picea abies complied well with measured fiber distortions, and that the general trends of fiber orientation, explained by the applied knot formation theory, is reflected in the measured specimens. Received 12 May 1999     

Acoustoelastic birefringence effect in wood III: ultrasonic stress determination of wood by acoustoelastic birefringence method

Stress conditions produced in wood were analyzed by means of the acoustoelastic birefringence method. Bending load was applied against a wood beam specimen. Under loading, ultrasonic shear waves were propagated through the breadth direction of the wood beam specimen. The velocities of shear waves polarized in the longitudinal or tangential direction of the wood beam specimen were measured with the sing-around method. Bending stresses were determined by dividing the difference between the acoustic anisotropy and the texture anisotropy by the acoustoelastic birefringence coefficient. Shear stresses were also determined. These stress distributions of the beam specimen were in good agreement with those obtained by the strain gauge method and mechanical calculation.     

Creep and stress relaxation behavior for natural cellulose crystal of wood cell wall under uniaxial tensile stress in the fiber direction

We investigated the temporal changes in creep and stress relaxation behavior in both microscopic crystalline cellulose and macroscopic strain of wood specimen using Japanese cypress (Chamaecyparis obtusa Endl.) to understand the viscoelastic properties of wood cell walls. Specimens 600 µm in thickness were observed by the X-ray diffraction and submitted to tensile load. The crystal lattice strain of (004) plane and macroscopic strain of specimen were continuously detected during creep and stress relaxation tests. It was found that the creep compliance based on macroscopic strain showed a gradual increase after instantaneous deformation due to loading and then the parts of creep deformation remained as permanent strain after unloading. On the other hand, crystal lattice strain showed a different behavior for macroscopic strain; it kept a constant value after instantaneous deformation due to loading and then increased gradually after a certain period of time. These differences between macroscopic and microscopic levels were never found in the stress relaxation tests in this study. Relaxation modulus at the macroscopic level only showed a decreasing trend throughout the relaxation process. However crystal lattice strain kept a constant value during the macroscopic relaxation process. In addition, the microfibril angle (MFA) of wood cell wall has a role of mechanical behavior at microscopic level; crystal lattice strains were smaller with increasing MFA at both creep and relaxation processes. Creep compliance and stress relaxation modulus at the macroscopic level decreased and increased with increasing MFA, respectively. Our results on the viscoelastic behavior at microscopic level evidenced its dependency on MFA.     

Mechanical behavior of the crystal lattice of natural cellulose in wood under repeated uniaxial tension stress in the fiber direction

This study investigated the relationship between the cellulose crystal lattice strain (crystalline region) and the macroscopic surface strain in specimens of Chamaecyparis obtusa wood under repeated uniaxial tension stress in the fiber direction. Changes in the strain of the crystal lattice were measured from the peak of (004) reflection using the transit X-ray method. The macroscopic surface strain of each specimen was measured with a strain gauge. In both loading and unloading, the surface strain changed linearly with changes in stress. However, crystal lattice strain was not linear but exhibited changes along a curve with changing stress. Under stressed conditions, the crystal lattice strain was always less than the surface strain, regardless of the frequency of repetition in the loading and unloading cycle. The ratio of the crystal lattice strain to the surface strain showed a negative correlation for stress in both loading and unloading. That is, the ratio decreased with increasing stress, and finally tend to converge to a specific value. The ratio (I/I ₀) between the diffracted intensity (I ₀) in the (004) plane in the unloaded condition and the diffracted intensity (I) in the (004) plane in the loaded condition tend to converge on a specific value with increasing frequency of repetition. When the substantial tension Young’s modulus of the wood in the longitudinal direction decreased, the ratio of the strain of the crystal lattice to the surface strain also decreased. Moreover, the ratio decreased with increasing microfibril angle of the specimen.     

Feasibility of automatic detection of knots in maritime pine timber by acousto-ultrasonic scanning

In order to assess the lengthwise variation of mechanical properties of maritime pine (Pinus pinaster Ait.) a study on the possibility of automatically detecting knots by ultrasonic readings across the grain was carried out. A through-transmission acousto-ultrasonic (AU) setup was implemented allowing acquisition of AU profiles along the central mid-third of each specimen. An algorithm was proposed and successfully implemented for enhancing variations on the AU profiles due to knot presence. Discriminant analysis was applied to the AU profiles. The results show the possibility of automatically differentiating clear wood zones from zones with a knot area ratio value above 20% or 30%, with a success rate of 75% to 83% depending on the dimension of the specimens tested.This research project was supported by the Foundation for Science and Technology (FCT) under contract Nos. PBIC/C/AGR/2296/95 and POCTI/33967/AGR/2000     

世界节子研究进展

通过对大量文献的整理分类,从节子自身研究状况、对木材加工利用的影响和节子的无损检测技术几个方面,对截至目前世界上对节子研究的进展状况进行了综述,并提出了今后的一些研究发展方向。     

Strain-softening behavior of wood under tension perpendicular to the grain

Three softwood samples and one hardwood sample were tested under a tension load applied along the radial direction using small clear specimens and the local tension strain was measured using the digital image correlation method. We successfully obtained a stress-strain curve with a strain-softening branch by calculating the stress using the strain distributions in the vicinity where the specimen ruptured. The continuous digital imaging of the specimen proved to be very effective for measuring the strain in quasi-brittle materials such as wood under tension. The nonlinearity of the stress-strain curve was quantified using two parameters representing the deviation from linear elasticity, and the formula of the stress-strain curve was deduced from the interrelation between these parameters. This formula is expressed quite simply by using the modulus of elasticity along the radial direction and another constant that is unique to the material. Part of this article was presented at the 56th Annual Meeting of the Japan Wood Research Society, Akita, Japan, August 2006     

扭叶松实木板材三种动态弹性模量和静态弹性模量比较研究(英文)

采用Pundit、Metriguard、FFT等三种无损检测方法和常规弯曲法对加拿大扭叶松(lodgepole pine)蓝变与非蓝变实木板材的动态及静态弹性模量进行检测和比较研究。结果表明,蓝变材三种动态弹性模量及静态弹性模量均高于非蓝变材;对比分析表明,蓝变材和非蓝变材的动态及静态弹性模量存在差异,其中动态弹性模量差异均达到0.01显著性水平,静态弹性模量差异达到0.05显著性水平,并且心、边材及密度值不同是导致以上差异的主要原因。相关性分析表明,动态与静态弹性模量间相关性达到0.01显著性水平;尽管三种无损检测方法测量结果存在差异,但它们之间仍存在密切相关性,FFT 技术测量的准确性高于Pundit和Metriguard;板材中结子数影响木材动态和静态弹性模量,随着板材结子数增加弹性模量相应地降低。     

A stress transformation approach to predicting the failure mode of wood

Summary A simple model, based on the use of transformations of second-order tensors, is presented in this paper to predict the failure mode of wood members stressed in various degrees of parallel-and perpendicular-to-grain tension and parallel-to-grain shear. This type of loading is indicative of structural wood members with cross grain or grain deviations in the vicinity of knots subjected to bending or tension. The model is based on the assumptions that failure is dictated by the presence of any of the aforementioned stresses that exceed the clear wood strength in that mode and that failure does not result from stress interactions. The magnitudes of the applied stresses are normalized relative to the wood strength in that mode. The ratio of applied stress to material strength that is greatest at any particular angle of load to grain is presumed to be the failure mode at that angle. To verify model predictions, optical and microscopic analyses of surfaces of failed specimens loaded in uniaxial tension at angles between 0° and 90° to grain were compared to previously obtained, or otherwise known, surfaces of specimens tested in tension and shear. Specimens tested at various angles to grain demonstrated failed surfaces very much like those associated with specimens loaded in the modes predicted by the model.