Modeling the hygroexpansion of aligned wood fiber composites

The effect of wood fiber ultrastructure and cell wall hygroelastic properties on wood fiber composite hygroexpansion has been analyzed. An analytical concentric cylinder model extended to include also free hygroexpansion of orthotropic phase materials has been used on several length scales. Using properties of the three main wood polymers, cellulose, hemicellulose and lignin the longitudinal and transverse hygroexpansion coefficients for the microfibril unit cell were obtained and the volume fraction change of the wood polymers in the microfibril unit cell depending on relative humidity was calculated. The fiber cell wall was modeled regarding each individual S1, S2 and S3 layer and the cell wall longitudinal hygroexpansion coefficient was determined depending on microfibril angle in the S2 layer. A homogenization procedure replacing the S1, S2 and S3 layers with one single layer was found not to influence the results significantly for low microfibril angles. Finally the hygroexpansion coefficients of an aligned softwood fiber composite were calculated.     

Damage analysis of pseudo-ductile thin-ply UD hybrid composites – A new analytical method

A new simple analytical approach for predicting all possible damage modes of Uni-Directional (UD) hybrid composites and their stress–strain response in tensile loading is proposed. To do so, the required stress level for the damage modes (fragmentation, delamination and final failure) are assessed separately. The damage process of the UD hybrid can then be predicted based on the order of the required stress for each damage mode. Using the developed analytical method, a new series of standard-thickness glass/thin-ply carbon hybrid composites was tested and a very good pseudo-ductile tensile response with 1.0% pseudo-ductile strain and no load drop until final failure was achieved. The yield stress value for the best tested layup was more than 1130 MPa. The proposed analytical method is simple, very fast to run and it gives accurate results that can be used for designing thin-ply UD hybrid laminates with the desired tensile response and for conducting further parametric studies.     

Design of Cellular Composite Sandwich Panels for Maximum Blast Resistance Via Energy Absorption

This paper presents a design methodology for optimizing the energy absorption under blast loads of cellular composite sandwich panels. A combination of dynamic finite element analysis (FEA) and simplified analytical modeling techniques are used. The analytical modeling calculates both the loading effects and structural response resulting from user-input charge sizes and standoff distances and offers the advantage of expediting iterative design processes. The FEA and the analytical model results are compared and contrasted then used to compare the energy response of various cellular composite sandwich panels under blast loads, where various core shapes and dimensions are the focus. As a result, it is concluded that the optimum shape consists of vertically-oriented webs while the optimum dimensions can be generally described as those which cause the most inelasticity without failure of the webs. These dimensions are also specifically quantified for select situations. This guidance is employed, along with the analytical method developed by the authors and considerations of the influences of material properties, to suggest a general design procedure that is a simple yet sufficiently accurate method for design. The suggested design approach is also demonstrated through a design example.     

Dynamically loaded light-frame wood stud walls: experimental verification of an analytical model

Light-frame wood structures may deform well beyond the elastic limit when loaded by dynamic forces such as earthquakes and sea wave impacts. This paper reports the results of an investigation into the response effects of structural modeling assumptions typically made in the design of light-frame wood structures. Two dimensional and three dimensional models based on previous research were developed to simulate such responses and examine the validity of such models. The models utilize the finite-element method and include options of nonlinear connection properties, elastic constitutive laws of wood material, large deformations, contact forces, and inertial forces. The models were subjected to an estimate of the impact load imparted by a rapidly moving sea wave. To validate the models, the results of a wave-channel experiment of a full-scale wall were used wherein the wall was instrumented with reaction load cells, displacement transducers, and strain gauges on plywood sheathing and wood framing. A closed-loop hydraulic system utilizing a time varying loading function generated the wave trains. The resulting reactions, deformations, and strains were recorded as functions of time while high-speed cameras visually recorded the failure modes and wall behavior. Material tests were conducted before and after testing to record both the observed member properties and the localized section properties. Connection tests were conducted to provide the ultimate strengths for input in the finite element model. Reasonable agreement between the experimental and analytical results over the duration of the analysis depended on the model and model assumptions as well as the result of interest. The three dimensional model captured observed failure modes including rigid-body motions after connection failures and may reliably be used to analyze similar nonlinear systems loaded well beyond the elastic limit.     

General analytical solution for elastic radial wave propagation and dynamic analysis of functionally graded thick hollow cylinders subjected to impact loading

An analytical method is proposed for the dynamic response analysis of functionally graded thick hollow cylinders under impact loading. The wave motion equation is solved using an analytical method that is based on the composition of Bessel functions. The mechanical properties are considered as power functions of the radius across the thickness of FG cylinder. The FG cylinder is excited by an impact loading at the inner surface of the cylinder, and the plane strain and axisymmetry conditions are assumed for the problem. The time histories of radial displacement and radial and hoop stresses are presented. Also the dynamic response of the FG cylinder is obtained and discussed for various kinds of power function exponents.     

Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical method

Transient stress field and thermo-elastic stress wave propagation are studied in functionally graded thick hollow cylinder under arbitrary thermo-mechanical shock loading, in this article. Thermo-mechanical properties of functionally graded (FG) cylinder are assumed to be temperature independent and vary continuously and smoothly in the radial direction. The governing dynamic equations are analytically solved in temperature and elastic fields. To solve the problem, Laplace transform is used respect to time in all constitutive equations and boundary conditions. At first, temperature field equation analytically solved using Laplace transform and series method. The dynamic behaviors of thermo-elastic stresses are illustrated and discussed for various grading patterns of thermo-mechanical properties in several points across the thickness of FG cylinder. Time history of temperature field and thermal stresses are obtained using the residual theorem and the fast Laplace inverse transform method (FLIT), respectively. Also, the effects of the cylinder thickness and convection heat transfer coefficient on dynamic response of FG cylinder are revealed and discussed. The presented analytical method provides a ground to study the time histories of radial and hoop stresses in FG cylinders with different thickness and various volume fraction exponents. The advantage of this method is its mathematical ability to support simple and complicated mathematical function for the thermo-mechanical boundary conditions. A reasonable agreement can be seen in comparison of obtained results based on the presented analytical method with published data.     

Modeling the Effect of Helical Fiber Structure on Wood Fiber Composite Elastic Properties

The effect of the helical wood fiber structure on in-plane composite properties has been analyzed. The used analytical concentric cylinder model is valid for an arbitrary number of phases with monoclinic material properties in a global coordinate system. The wood fiber was modeled as a three concentric cylinder assembly with lumen in the middle followed by the S3, S2 and S1 layers. Due to its helical structure the fiber tends to rotate upon loading in axial direction. In most studies on the mechanical behavior of wood fiber composites this extension-twist coupling is overlooked since it is assumed that the fiber will be restricted from rotation within the composite. Therefore, two extreme cases, first modeling fiber then modeling composite were examined: (i) free rotation and (ii) no rotation of the cylinder assembly. It was found that longitudinal fiber modulus depending on the microfibril angle in S2 layer is very sensitive with respect to restrictions for fiber rotation. In-plane Poisson’s ratio was also shown to be greatly influenced. The results were compared to a model representing the fiber by its cell wall and using classical laminate theory to model the fiber. It was found that longitudinal fiber modulus correlates quite well with results obtained with the concentric cylinder model, whereas Poisson’s ratio gave unsatisfactory matching. Finally using typical thermoset resin properties the longitudinal modulus and Poisson’s ratio of an aligned softwood fiber composite with varying fiber content were calculated for various microfibril angles in the S2 layer.     

Two-dimensional dynamic analysis of thermal stresses in a finite-length FG thick hollow cylinder subjected to thermal shock loading using an analytical method

This work is aiming to present an analytical method to study the dynamic behavior of thermoelastic stresses in a finite-length functionally graded (FG) thick hollow cylinder under thermal shock loading. The thermo-mechanical properties are assumed to vary continuously through the radial direction as a nonlinear power function. Using Laplace transform and series solution, the thermoelastic Navier equations in displacement form are solved analytically. The solution of the displacement field in the FG cylinder is obtained in the Laplace domain. Also, the fast Laplace inverse transform method (FLIT) is employed to transfer the results from Laplace domain to time domain. The effects of thermal shock loading on the dynamic characteristics of the FG thick hollow cylinder are studied in various points across the thickness of cylinder for various grading patterns of FGMs. A good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data.     

Finite element analysis of deformation and fracture of an exploded gas cylinder

This paper presents the finite element simulations of deformation and fracture of a gas cylinder which catastrophically failed as a result of an accidental explosion. The results of a previous detailed investigation of this incident indicated that detonation of a low-pressure oxygen-rich mixture of hydrogen and oxygen was the cause of the cylinder failure. In the current study, the finite element method was used to provide a more realistic modeling of geometry, material behavior, and boundary conditions of the cylinder. The overall transient dynamic response of the cylinder to gaseous detonation loading was studied using the ANSYS/LS-DYNA V10 package and the crack growth simulations were performed using the WARP3D-R15 research code. The crack growth analyses were performed using interface cohesive elements. The finite element results were validated using analytical solutions and data collected from the remains of the cylinder. The simulations clearly showed that the stresses caused by the assumed loading profile were indeed capable of creating local ruptures at the actual crack initiation sites. It was also shown that the self-similar growth of the initial axial crack in the main body of the cylinder was a fatigue-type incremental growth governed by the structural waves. The subsequent cyclic bulging of the crack flaps and the resultant crack curving and branching were also simulated.     

Evaluation of wood-thermoplastic-interphase shear strengths

A macroscopic pull-out technique has been developed to determine the interphase properties in wood/low-molecular-weight-thermoplastic systems. Experimental variables affecting the shear properties of these types of composites were first identified so that the test could be used to compare the effect of different surface treatments on the interfacial properties. The relationship between the debonded force,F, and embedded length,L, was not linear, suggesting a failure mechanism that was different from interfacial yielding. Low embedded lengths provide useful comparative data on the maximum interfacial-shear strength of the system. The test is also useful for evaluating the quality of the fibre-matrix bond after exposure to water, since dimensional stability is an important consideration for wood-fibre-based composites. The test can be used to screen the effects of modifications on the lignocellulosic and/or the thermoplastic matrix on adhesive bonding for the development of composites. The use of lignocellulosic fibres (recycled wood fibres and natural fibres such as jute) in combination with recycled plastics could find applications in the automotive, furniture and building-materials industry.     

An attempt to model the influence of gradual transition between cell wall layers on cell wall hygroelastic properties

To better understand the hygroelastic property of wood cell wall, the transition of materials in the area between the S1 and S2 layers is considered in the modeling of cell wall hygroelastic properties. The concentric cylinder model is modified and employed for its compatibility with arbitrary additional layers in different scales. In order to explain the results of the cell wall model, the polymer contribution to the cell wall hygroexpansion is investigated first. Although the amorphous cellulose slightly affects the cell wall hygroexpansion, its influence on the softening of cell wall moduli is not significant. The contributions of hemicellulose and lignin to the hygroexpansion vary as the microfibril angle in the S2 layer changes. The results of the polymer analysis help to explain the effect of the interlayer. Compared to the model without the S1–S2 interlayer, the cell wall swells more in the transverse direction if the transition in the inner S1 layer (S1-part) is considered. For the case of transition in the outer S2 layer (S2-part), the effect reverses. Whilst, in the longitudinal direction, the S1-part amplifies the shrinkage and the S2-part suppresses it. The interlayer affects the cell wall moduli under moisture condition in the same way as under the dry condition. The modeled softening effects can be managed to approach the measurements by adjusting the thickness of the interlayer. We believe that paying more attention to the materials transition between cell wall layers can certainly help us to better understand the cell wall behaviors.     

Prediction of reliability analysis of composite tubular structure under hygro-thermo-mechanical loading

The present paper focuses on reliability prediction of composite structure under hygro-thermo-mechanical loading, conditioned by Tsai-Wu failure criterion, where the Monte–Carlo method is used to estimate the failure probability(Pf). This model was developed in two steps: first, the development of a deterministic model, based on an analytical and numerical approach, and then, a probabilistic computation. Using the hoop stress for each ply, a sensitivity analysis was performed for random design variables, such as materials properties, geometry, manufacturing, and loading, on composite cylindrical structure reliability. The probabilistic results show the very high increase of failure probability when all parameters are considered.     

Inducing large deformation in wood cell walls by enzymatic modification

It has been shown recently that wood with a high cellulose microfibril angle in the S2-layer, e.g. compression wood, shows permanent plastic deformation without significant mechanical damage to the matrix. This molecular stick-slip mechanism was explained by a gliding of the cellulose fibrils, after a certain shear stress in the matrix was exceeded [1]. Such a material behaviour would be desirable for various applications, for instance, to cover complex geometries with highly deformable veneers as needed in the automotive industry. However, veneers that are typically used for these purposes have a rather brittle failure behaviour, which leads to breakage, and drastic quality and productivity losses. A better deformability of such veneers might be achieved when the underlying deformation principles are conferred by modifying the wood cell wall components, in particular the cellulose fibrils and their matrix coupling. Enzyme treatments were performed on mechanically isolated wood fibres to plastify the entire lignified secondary cell wall. Cellulase Onozuka R-10 from Trichoderma viride (E.C.3.2.1.4) with activity on cellulose and xylan was utilized. Micromechanical tests and FT-IR microscopy studies revealed the change of mechanical properties and nanostructural features of the cell wall. An extended deformability was achieved for two of ten of the modified fibres.     

Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures

Abstract: The response of three different cellular core types, suitable for manufacturing crashworthiness sandwich cellular structures, is investigated in this paper. A methodology is developed, comprising linear static and eigenvalue buckling analysis, as well as nonlinear material elastoplastic analysis. The methodology is used to study the structural response and failure process of open lattice metallic cellular cores and derive the most important structural properties of the cellular core, i.e. elasticity modulus, plateau stress and compaction strain. The critical elastoplastic buckling stress of the metallic struts is approximated by analytical solutions, while a simple engineering approach is applied for the estimation of the compaction strain. The influence of core basic design parameters, i.e. strut aspect ratio (radius/length), unit‐cell spatial configuration and unit‐cell size on the structural behaviour is assessed.     

Analytical assessment of the load-carrying capacity of axially loaded wooden reinforced tubes

As a natural resource, an efficient use of wood should be also a requirement for structural timber design, but the usual structural solid sections do not achieve the required optimal behaviour. The performance of the structural elements (serviceability and strength) depends not only on the material properties, but mainly on the moment of inertia of the cross section. The Timber Construction Institute of Technische Universität Dresden has developed a process for the manufacture of structural wood profiles. The resulting profiles combine economy, an efficient use of the material and optimal structural performance. They are externally reinforced with composite fibres, which improve the mechanical characteristics of the wood and protect it from weathering. The available experimental tests to axial loading show the outstanding properties of this new technology. Herein, the preliminary model developed to obtain the axial strength of longitudinally compressed tubes is presented. Two different analytical algorithms are discussed and applied. The model adequately predicts the axial strength of fibre reinforced wood profiles. The analytical results are within an error less than 10% to the available experimental results, with a mean error ratio less than 3%.     

Nonlinear inelastic buckling of rigid-jointed frames under finite displacements

Summary A nonlinear analytical approach for establishing the precise load-carrying capacity of imperfection-sensitive frames, made from ideal elastic-plastic material, is presented. The imperfection sensitivity is due to support eccentricities of columns. Stability criteria for both modes of failure, due to elastic and inelastic buckling, are established. The failure through inelastic buckling occurs for frames exhibiting postbuckling strength or monotonically rising equilibrium paths. The inelastic analysis is approximate with a basic assumption that the overall response of the frame can be predicted by considering the elastoplastic stress distribution at only one single (the most unfavorable) cross-section. Plastic buckling is associated with a limit point instability. Simple formulas for evaluating the stress distribution at the critical sections in both the elastic and inelastic range are assessed. The proposed method is demonstrated by means of a simple two-bar frame for which the overall response from the onset of loading up to failure is determined.With 5 Figures     

Matrix dominated time dependent failure predictions in polymer matrix composites

Various types of matrix dominated failures in polymer matrix composites (PMC) are reviewed. Current methods to evaluate the modulus degradation of PMC materials are discussed including viscoelastic/plastic and continuum damage models. It is pointed out that in each case the approach is based upon developing an analytical constitutive relation for the material in order to represent a measured stress–strain response. The suggestion is made that care must be used in the measurement of stress–strain behavior such that the modeling represents the true material behavior. New digital imaging methods are suggested as a means to determine in situ properties at a local scale commensurate with the continuum modeling procedure. A little used method to model viscoelastic/plastic (linear and non-linear) effects is discussed and modified to obtain a simple and easy to use time dependent failure law. Also, a little used energy based time dependent failure criterion is presented which can be combined with a non-linear viscoelastic integral approach to provide a prediction method for the time for creep rupture under simple stress states. Each is validated with experimental data for simple stress states but their generality is such that they could be used for complex (3-D) stress states. Advantages and limitations of both are addressed. Finally, a discussion of possible fruitful research areas are presented with the view of providing engineers in industry with an easy to use accelerated life prediction procedure.     

Assessment of interfacial bonding between polymer threads and epoxy resin by transverse fibre bundle (TFB) tests

Two experimental approaches were employed to assess the fibre/matrix adhesion between polymer threads and epoxy resin by transverse fibre bundle (TFB) tests. The first approach was to measure interfacial bonding strength of the fibre/matrix interface in dog-bone-shaped tensile specimens by applying normal stress until failure, simulating the Mode I failure mode. The second approach was to determine the fibre/epoxy interfacial bonding strength in shear (simulating the Mode II failure mode) by means of a V-notched beam shear testing method, i.e. a modified Iosipescu test. In both methods, polymer threads were transversely incorporated in the middle section of the specimens. It was found that both methods were simple, reliable, and sensitive to changes in the fibre/matrix adhesion conditions, though interpretation of the test results was somewhat complex. The two experimental approaches were able to produce consistent results and can thus be adopted as alternative methods for determining the interfacial bonding properties between fibres and matrix in composite systems where conventional micro-mechanical or macro-mechanical testing methods cannot be used.     

A PROBABILISTIC APPROACH TO FAILURE PREDICTION OF FRP LAMINATED COMPOSITES

The failure of fiber-reinforced plastic (FRP) laminated composites is examined, taking into account statistical aspects of the basic strength properties of the material The purpose of the analysis is to establish simple rules and methodologies for failure prediction under specific reliability requirements. An analytical approach is developed for the prediction of failure under general in-plane loading, consisting of a functional expansion technique for the derivation of the cumulative distribution Junction of the failure condition. A semideterministic method is also examined, according to which the failure criterion is used in the usual deterministic way but with the basic strength values at a certain reliability level. The two methods are gradually built up by first examining their effectiveness on the failure prediction of unidirectional laminae. Results for the case of a unidirectional laminate are presented for the case of off-axis layers, and both methods are shown to yield results in fair agreement with Monte Carlo simulated ones and experimental data. For the more general case of multilayered composites, comparison of theoretical results with numerical simulated data and experimental ones reveals that both methods hold their effectiveness.     

Circumferential stiffness tailoring of general cross section cylinders for maximum buckling load with strength constraints

Stiffness tailoring of laminated composite structures using steered fibre tows is a design method that maximally uses the directional properties of composite materials. Cylindrical structures usually have circular cross sections while some application, geometric or aerodynamic requirements can necessitate other cross sections, e.g. elliptical. Circumferential tailoring can increase the buckling load of thin cylinders by compensating for non-uniform sectional loading such as bending and/or varying radius of curvature in general cylinders. Here, strength constraints are considered in maximum buckling load design, to ensure that the failure load is greater than the buckling load. A two-step optimisation framework is used to separate the theoretical and manufacturing issues in design. A computationally cheap semi-analytical finite difference method is used to solve the linear static and buckling problems. Conservative failure envelopes based on Tsai-Wu failure criterion are used for strength evaluation. To avoid repetitive analyses, successive convex approximation method is used. For demonstration, circumferential tailoring framework is applied to a circular cylinder under bending and an elliptical cylinder under axial compression. The improvements in buckling capacity of variable over constant stiffness designs are shown and verified using nonlinear buckling analysis in the commercial FEM software Abaqus^TM, and the mechanisms of improvements are investigated.