Quasi-non-linear fracture mechanics analysis of splitting failure in simply supported beams loaded perpendicular to grain by dowel joints

A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied for analysis of the splitting failure of dowel joints loaded perpendicular to grain. Simply supported beams symmetrically loaded by two dowels are considered, and the effects of edge distance, dowel spacing, and distance between dowels and supports are accounted for. The foundation modulus used in the beam on elastic foundation model is chosen so that the perpendicular-to-grain tensile strength and fracture energy properties of the wood are correctly represented. This ensures that a conventional stress analysis and failure criterion lead to the same solution as the compliance method of fracture mechanics. A semiempirical efficiency factor is proposed to account for the influence of the total beam depth, which does not enter the beam on elastic foundation model, but the effect of which is evident from tests. It is shown that the so-called Van der Put/Leijten model, which recently has been adopted in Eurocode 5, appears as a special case of the model presented. Tests on simply supported beams with a single dowel joint at midspan are compared with the theoretical predictions. Various edge distances, beam depths, and spans were tested.     

Quasi-non-linear fracture mechanics analysis of the double cantilever beam specimen

A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied for analysis of the double cantilever beam (DCB) specimen for determination of fracture energy of wood. The properties of the elastic foundation are chosen so that the perpendicular-to-grain tensile strength and fracture energy properties of the wood are correctly represented. It is shown that this particular choice of foundation stiffness makes a conventional maximum stress failure criterion lead to the same solution as the fracture mechanics compliance method. Results of linear elastic fracture mechanics are obtained as a special case by assuming an infinitely large value of the perpendicular-to-grain tensile strength. The quasi-non-linear fracture mechanics model is compared with other models and with results of tests conducted to reveal the influence of the geometrical properties of the DCB specimen. In addition, the appropriateness of choice of the foundation stiffness is investigated.     

Quasi-non-linear fracture mechanics analysis of splitting failure in moment-resisting dowel joints

This article addresses the splitting failure of moment-resisting dowel-type fastener joints, in which the failure may be attributed to the perpendicular-to-grain loading of one single dowel located close to the end of a beam. A quasi-non-linear fracture mechanics model based on beam on elastic foundation theory is applied. A simple approximation suitable for practical design is also proposed. Model predictions of the influence of edge distances and end distances are compared with test results.     

Axially loaded glued-in hardwood dowels

The failure load of axially loaded hardwood dowels glued-in parallel to the grain direction of the jointed timber parts is considered. Two simple theoretical solutions using linear elastic fracture mechanics/ideal plasticity and linear elastic stress analysis, taking into account the finite shear stiffness of the bond line are, presented and compared with experimental results. Theory shows that bond line shear strength is the governing strength property for ductile joints and fracture energy is the governing strength property for brittle joints. Bond line shear strength and fracture energy are determined by means of curve-fitting. Received 24 April 1997     

Prediction of the load carrying capacity of bolted timber joints

Failure of bolted timber joints is analyzed experimentally and numerically. In this study, the prediction of the load-carrying capacity of dowel-type joints with one dowel under static loading is based on the analysis of fracture in wood contrarily to most engineering methods that are based on the yield theory. Mechanical joints consist of glued laminated spruce members and steel dowels. In the different analyzed tests, the bolt loads the wood parallel or perpendicular to the grain. The wood member thickness is chosen sufficiently thin to avoid the fastener from presenting plastic hinges. The influences of different structural parameters such as the dowel diameter, the edge- and end-distances are investigated. The fracture propagation analysis is carried out with the Finite Element (FE) method in the framework of Linear Elastic Fracture Mechanics (LEFM). The only identified parameter is the critical energy release rate in mode I (G_Ic). The comparison between experimental and numerical results shows that the fracture must be considered for a correct prediction of the ultimate load and that LEFM can help to improve design codes. Received 11 August 1997     

Splitting strength of beams loaded perpendicular to grain by dowel joints

A linear elastic fracture mechanics model for calculation of the splitting strength of dowel-type fastener joints loaded perpendicular to grain (Van der Put/Leijten model) has previously been presented, and now forms the basis for design in Eurocode 5. The original Van der Put/Leijten model was derived using a number of simplifying assumptions, e.g., that the normal forces in the cracked parts of the beam can be ignored, leading to a solution that does not involve the effect of an initial crack. In the present article an extended version of the Van der Put/Leijten model is derived without any simplifying assumptions, and it is shown that the original Van der Put/Leijten model appears as a special case, namely by assuming that only contributions from shear deformations are significant. The model presented here involves the effect of an initial crack and may be characterized as a generalized linear elastic fracture mechanics model. Results of tests showing the influence of initial cracks of various lengths are presented and compared with the predictions.     

Elastic layer model for application to crack propagation problems in timber engineering

A fracture mechanics model for analysis of crack initiation and propagation in wood is defined and applied. The model has the advantage of being simple, yet it enables reasonably general and accurate analysis commonly associated with more complex models. The present applied calculations are made by means of the finite element method and relate to progressive cleavage fracture along grain. The calculations concern a tapered double cantilever beam specimen and an end-notched beam. Comparisons are made of experimental test results. The fracture properties of the wood are modelled by means of a very thin linear elastic layer located along the crack propagation path. The properties of the layer are such that the strength and fracture energy of the wood are represented correctly. This makes a single linear elastic calculation sufficient for strength prediction. Both crack development and pre-existing cracks can be analyzed. Both material strength and fracture energy and stiffness are taken into account, their relative influence on structural strength being different for different elements. The fracture layer is in the finite element context represented by joint elements. Propagation of a crack can be analyzed either by a series of elastic calculations corresponding to different crack lengths or by use of a finite element code for non-linear analysis. The computational results include sensitivity analysis with respect to the influence of the various material parameters on structural strength.     

Effect of decay on shear performance of dowel-type timber joints

Monotonic and reversed cyclic loading tests were conducted on dowel-type timber joints with varying degrees of wood decay due to Fomitopsis palustris (Berk. et Curt.), a brown rot fungus, and the effect of decay on various shear performances of dowel-type joints was investigated. For joints affected by the brown rot fungus, the initial stiffness, yield load, and maximum load of dowel-type joints were significantly decreased, even with a small mass loss of wood. The reductions in shear performance were the largest for initial stiffness, followed by yield load and maximum load, in that order. For a 1% reduction of the yield load, initial stiffness and maximum load showed reductions of 1.15% and 0.77%, respectively. When dowel-type joints that had been exposed to the brown rot fungus were subjected to reversed cyclic loading, the gap between the dowel and the lead hole of the wood was increased and equivalent viscous damping was decreased. These results indicate that decay around the dowel lead hole especially affects the load-displacement behavior at small displacement level, and dowel-type joints under cyclic loading have very low resistance to forces acting on the wooden structure. Part of this report was presented at the 5th Symposium on Timber Bridges of the Japan Society of Civil Engineers, Tokyo, July 2006; the 56th Annual Meeting of the Japan Wood Research Society, Akita, August 2006; and the Annual Meeting of the Architectural Institute of Japan, Fukuoka, August 2007     

Shear strength of beam splice joints with glued-in rods

Splitting failure in beam splice joints with glued-in rods parallel to grain in endwood subjected to pure shear is considered. A simple theoretical expression based on beam-on-elastic-foundation theory and quasi-non-linear fracture mechanics is presented for calculation of the joint strength. Tests were conducted on jointed beams in a four-point bending test setup in which the joints were located at the point of pure shear force. Hardwood dowels with a diameter of 12mm and a glued-in length of 120mm were used as rods, and various beam cross sections and dowel configurations were tested. The theory presented is found to agree well with test results in all cases in which the edge distance of the glued-in rods is relatively small. Some test results indicate that the theory may be conservative in case of large edge distances.     

Fracture analysis of perpendicular to grain loaded dowel-type connections using a 3D cohesive zone model

The strength and fracture behavior of dowel-type connections with stiff dowels loaded perpendicular to grain was studied by nonlinear 3D finite element (FE)-analysis. A cohesive zone model was used to model the perpendicular to grain fracture of the wood, i.e., failure by wood splitting along the grain. The influence of load eccentricity and dowel-to-loaded-edge distance was studied for a plate type of geometry loaded in tension and for a simply supported beam loaded in bending. The strength found from the FE-analysis is compared to strength from experimental tests with centric loading, showing overall good agreement. Numerical results for centric loading are further compared to strength predictions according to the linear elastic fracture mechanics (LEFM)-based design criterion present in Eurocode 5 (EN 1995-1-1:2004). The comparison showed good agreement regarding the relative influence of connection geometry, but the design criterion appears, however, to yield unconservative strength predictions. The results of the FE-analyses regarding dowel load eccentricity showed that such loading conditions may yield significantly lower strengths compared to centric loading. An approximate engineering method to account for the strength reduction due to load eccentricity is, furthermore, presented.     

Fracture mechanics analysis of row shear failure in dowelled timber connections

A quasi-nonlinear fracture mechanics model is presented for the analysis of row shear failure in timber connections with multiple fasteners in a row. A prerequisite for use of the model is a known distribution on the fasteners of the total applied load. It is shown that the ideal plastic and linear elastic fracture mechanics solutions appear as special cases of the quasi-nonlinear model. The model offers strength predictions that include the effect of among others the number of fasteners in a row, fastener spacing, row spacing, end-distance, edge-distance, fastener diameter, and material properties, such as shear strength, fracture energy, and modulus of elasticity. Simple explicit expressions are obtained from the analysis for any known fastener load distribution. For bolted connections, where bolt-hole gaps cause high loads on certain bolts at random, the model may be used in simulation procedures or in probabilistic models.     

Fracture of multiply-bolted joints under lateral force perpendicular to wood grain

The crack initiation and propagation of multiplybolted joints subjected to lateral forces perpendicular to the grain were analyzed. Two types of bolted joint were subjected to lateral loads perpendicular to the grain. One had joints of two bolts aligned with the wood grain (type H), and the other had joints of two or three bolts aligned perpendicular to the grain (type V). The crack initiation and propagation were analyzed by means of the average stress method (ASM) and linear elastic fracture mechanics (LEFM), respectively. The maximum loads calculated by LEFM agreed comparatively well with the experimental results, and it was proved that the LEFM was an appropriate tool to analyze the fracture of multiply-bolted joints subjected to a force perpendicular to the grain. It was also found that the multiply-bolted joints failed with the fracture of the wood before the joints yielded, and that it caused a considerable decrease of the maximum loads. The reduction of strength should be considered in the design of multiply-bolted joints subjected to lateral forces perpendicular to the grain.Part of this work was presented at the annual meeting of the Architectural Institute of Japan, Hikone, September 1996     

Estimation of stiffness and strength in timber knee joints with adhesive and verification by experiment

The use of adhesive joints is gradually increasing, especially those with glued-in steel rods (GIRs). There are, however, some problems with the design methods when used for moment-transmitting applications. In this article, design methods for GIRs and cross-lapped glued joints (CLJs) are proposed. For CLJs, we made a hypothesis that both rotational deformation of CLJ and stress of the glue line occurred with bending and shearing deformation of the timber. Using this hypothesis and Kelvin’s theorem, a mechanical model of CLJ is proposed. For GIRs, the axial stress component of the rod and the lateral stress component of the rod were taken into account using the theory of a beam on an elastic foundation. From the comparisons between calculations and experimental results, it was recognized that the stiffness and strength of CLJs and GIRs could be predicted precisely using our proposed models.     

Ultrastructural features affecting mechanical properties of wood fibres

Abstract

The purpose of this review is to re-examine some of the existing knowledge on the ultrastructure of softwood fibres and modelling of the hygroelastic properties of these fibres. The motivation is that the ultrastructure of wood fibres has a strong influence on fibre properties such as stiffness and hygroexpansion. This structure–property relationship can be modelled with, for instance, composite mechanics to assess the influence of ultrastructure on the fibre properties that in turn control the engineering properties of wood fibre composites and other wood-based materials. Comprehensive information about the ultrastructure is presented that can be useful in modelling the hygroelastic behaviour of wood fibres. Many attempts to model ultrastructure–property relationships that have been carried out over the years are reviewed. Even though models suffer from limiting approximations at some level, they have been useful in revealing valuable insights that can help to clarify experimentally determined behaviour of wood fibres. Still, many modelling approaches in the literature are of limited applicability, not the least when it comes to geometry of the fibre structure. Therefore, an example of finite element modelling of geometrically well-characterized fibres is given. This approach is shown to be useful to asses the influence of the commonly neglected irregular shape on elastic behaviour and stress state in wood fibres. Comparison is also made with an analytical model which assumes cylindrical fibre shape. Predictions of the elastic properties made with analytical modelling of cylindrical fibres and with finite element modelling of geometrically characterized fibres are in concert, but the stress state and failure predictions only show qualitative similarity. It can be concluded that calculations on fibres with the irregular and more realistic geometry combined with experiments on single fibres are necessary for a better and more quantitative understanding of the hygroelastic behaviour and particularly failure of wood fibres. It is hoped that this paper can provide a foundation and an inspiration for modelling, in combination with experiments and microscopy, for better predictions of the mechanical behaviour of wood fibres and wood fibre composites.     

Ultrastructural features affecting mechanical properties of wood fibres

The purpose of this review is to re-examine some of the existing knowledge on the ultrastructure of softwood fibres and modelling of the hygroelastic properties of these fibres. The motivation is that the ultrastructure of wood fibres has a strong influence on fibre properties such as stiffness and hygroexpansion. This structure-property relationship can be modelled with, for instance, composite mechanics to assess the influence of ultrastructure on the fibre properties that in turn control the engineering properties of wood fibre composites and other wood-based materials. Comprehensive information about the ultrastructure is presented that can be useful in modelling the hygroelastic behaviour of wood fibres. Many attempts to model ultrastructure-property relationships that have been carried out over the years are reviewed. Even though models suffer from limiting approximations at some level, they have been useful in revealing valuable insights that can help to clarify experimentally determined behaviour of wood fibres. Still, many modelling approaches in the literature are of limited applicability, not the least when it comes to geometry of the fibre structure. Therefore, an example of finite element modelling of geometrically well-characterized fibres is given. This approach is shown to be useful to asses the influence of the commonly neglected irregular shape on elastic behaviour and stress state in wood fibres. Comparison is also made with an analytical model which assumes cylindrical fibre shape. Predictions of the elastic properties made with analytical modelling of cylindrical fibres and with finite element modelling of geometrically characterized fibres are in concert, but the stress state and failure predictions only show qualitative similarity. It can be concluded that calculations on fibres with the irregular and more realistic geometry combined with experiments on single fibres are necessary for a better and more quantitative understanding of the hygroelastic behaviour and particularly failure of wood fibres. It is hoped that this paper can provide a foundation and an inspiration for modelling, in combination with experiments and microscopy, for better predictions of the mechanical behaviour of wood fibres and wood fibre composites.     

Lateral resistance of anchor-bolt joints between timber sills and foundations III: numerical simulations of the effect of sill thickness on the effective lateral resistance of multiple anchor-bolt joints

Effective lateral resistance of multiple anchorbolt joints was estimated by considering sill thickness or length/diameter ratios of anchor bolts. Load-slip relationships of single anchor bolt joints were analyzed by the stepwise linear approximation based on the generalized theory of a beam on an elastic foundation and the criterion of “fracture bearing displacement” for several sill thicknesses or length/diameter ratios of anchor bolts. Monte Carlo simulations of the effective lateral resistance of multiple anchor-bolt joints were conducted using the analyzed load-slip curves of single anchor-bolt joints. Effective resistance ratios of multiple anchor-bolt joints were simulated for some combinations of length/diameter ratios of anchor bolts, lead-hole clearances, and number of anchor bolts. The simulated results are: (1) the influence of lead-hole clearance becomes more apparent as length/diameter ratios of single anchor-bolt joints decrease; (2) there is no obvious effect of number of anchor-bolts over the range of 5 to 15; (3) average effective resistance ratios can be adopted for allowable stress design; and (4) reduction of effective resistance ratios should be considered particularly for small length/diameter ratios of anchor-bolt joints.     

Sensitivity study of the finite element model for wood-framed shear walls

A sensitivity study was performed with a nonlinear elastic finite element model for monotonie analyses of wood-framed shear walls. The objective was to provide information about simplifying a model of wood-framed shear walls with no significant loss in accuracy. The simplifications concern features such as slips in joints between frame members, slips in hold-down connections, and bearing between adjacent sheathing panels. The results from analyses of a shear wall with an opening of window shape show that the effect of constraint by the bearing between sheathing panels and slips in frame joints on the overall stiffness of the wall is limited. Thus, there are great possibilities for reducing the calculation time by not taking these phenomena into account, avoiding an excessive number of degrees of freedom and iterations. The influence of the simplifications on the distribution of vertical reaction forces along the wall is more significant. Furthermore, if each simplification is introduced separately, the effect on the overall stiffness is greater. The difference, however, is less than 10%. The failing pattern of the nail connections is also clearly influenced by the simplifications when they are introduced separately. The results from the analyses show that slips in frame joints can be sufficiently represented by those in connection with the opening.     

线弹性断裂力学原理在木材中应用的特殊性与木材顺纹理断裂

阐述了线弹性断裂力学 (LEFM)的原理以及在木材中应用的特殊性 ,并以杉木和马尾松为研究对象 ,采用不同试样和方法测定了木材的顺纹断裂韧性KTLIC 。研究表明 ,建立在各向同性体之上的LEFM原理对木材裂纹顺纹扩张是适用的 ,其顺纹断裂韧性是木材的固有属性     

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.     

Numerical analysis on tensile performance of bolted glulam joints with initial local cracks

Under varying climate conditions, cracks are commonly observed in bolted joints, owing to the shrinkage of wood and confinement from slotted-in steel plates and bolts. A three-dimensional finite element model was developed to investigate the mechanical behavior of bolted glulam joints with initial cracks. Wood foundation was prescribed in the model to simulate the local crushing behavior of wood surrounding the bolts. The behavior of wood in compression and the foundation were defined as transversely isotropic plastic in the software package ANSYS. Cohesive zone model was applied in the numerical analysis to consider the propagation of initial cracks and brittle failure of wood in the bolted joints under tension load. The numerical model was validated by the experiments conducted on full-scale specimens and it is indicated that the numerical model has good ability in predicting the failure modes and capacity of tension joints with local cracks. To further investigate the influence of crack number, length and locations, a parametric study was conducted with the verified model. Moreover, to study the effects of cracks on the behavior of bolted joints with different failure modes, another bolted joint including bolts with different strength grades and diameters was designed and analyzed in the parametric study, which was expected to have bolt yielding failure mode. It was found that the initial cracks can decrease the capacity and initial stiffness of tension joints by up to 16.5 and 34.8%, respectively.