Radial-tangential Plane Research Articles

On the inverse identification of wood elastic properties using a DIC-based FEMU approach

PurposeThis work aims to identify the linear elastic orthotropic material paramters of Pinus pinaster Ait. wood, using full-field measurements and an inverse identification strategy based on the finite element (FE) method updating technique.Design/methodology/approachCompression tests are carried out under uniaxial and quasi-static loading conditions on wood specimens oriented on the radial-tangential (RT) plane, with different grain orientations. Full-field displacements and strains are measured using digital image correlation (DIC), which are then used as a reference in the identification procedure. A FE model is implemented assuming plane stress conditions, where wood is modelled as an orthotropic homogeneous material. Based on the numerical results, a synthetic image reconstruction scheme is implemented to synthetically deform the reference experimental image, which is then processed by DIC and further compared to the experimental results.FindingsThe results for both approaches were similar when both specimen configurations were used in a single run. However, when using the DIC-based FEMU approach with the on-axis configuration, the identified modulus of elasticity in the tangential direction and shear modulus are closer to the reference values.Originality/valueThis approach ensures a fair comparison between both sets of data since the full-field strain maps are obtained through the same filter and therefore have the same strain formulation, spatial resolution and data filtering. Firstly, the identification is performed using a single configuration, either the on-axis or the off-axis specimen. Secondly, the identification is carried out by merging data from both on-axis and off-axis configurations.

Identification of Orthotropic Elastic Properties of Wood by a Synthetic Image Approach Based on Digital Image Correlation.

This work aims to determine the orthotropic linear elastic constitutive parameters of Pinus pinaster Ait. wood from a single uniaxial compressive experimental test, under quasi-static loading conditions, based on two different specimen configurations: (a) on-axis rectangular specimens oriented on the radial-tangential plane, (b) off-axis specimens with a grain angle of about 60° (radial-tangential plane). Using digital image correlation (DIC), full-field displacement and strain maps are obtained and used to identify the four orthotropic elastic parameters using the finite element model updating (FEMU) technique. Based on the FE data, a synthetic image reconstruction approach is proposed by coupling the inverse identification method with synthetically deformed images, which are then processed by DIC and compared with the experimental results. The proposed methodology is first validated by employing a DIC-levelled FEA reference in the identification procedure. The impact of the DIC setting parameters on the identification results is systematically investigated. This influence appears to be stronger when the parameter is less sensitive to the experimental setup used. When using on-axis specimen configuration, three orthotropic parameters of Pinus pinaster (, and ) are correctly identified, while the shear modulus () is robustly identified when using off-axis specimen configuration.

Identification of orthotropic elastic properties of wood by digital image correlation and finite element model updating techniques

Computer-aided engineering systems rely on constitutive models and their parameters to describe the material behaviour. The identification process, however, grows in complexity for more elaborated material models, increasing the number of experimental tests needed, therefore time and cost consuming. Recently, with the development of digital image technology, there has been a growing interest in the use of full-field deformation measurements. This advancement has highlighted a new methodology on inverse identification techniques such as the finite element model updating method. This work aims to identify orthotropic linear elastic constitutive parameters of Pinus pinaster Ait. wood based on a single uniaxial compressive experimental test. Clear wood specimens oriented in the radial-tangential plane were used and tested under quasi-static loading condition. Full-field displacement and strain maps were obtained using digital image correlation and used to simultaneously identify the whole set of elastic properties through finite element model updating methodology.

Numerical modelling of wood under combined loading of compression perpendicular to the grain and rolling shear

Numerical modeling is an efficient tool for experimental validation and for gaining a deeper understanding of complex material phenomena, especially when causal relationships are overlaid by material variability. Wood is such a highly orthotropic and complex material, which in engineering problems however is considered as macro-homogeneous. The aim of this study is to numerically investigate stress and strain states of wood in the radial-tangential plane and the influence of the orthotropic material behavior on the structural response. Model validation is based on experiments performed on clear wood of Norway spruce (Picea abies) by using a biaxial test setup. Three material models were used, namely Hill’s plasticity model, the Hoffman criterion and a novel quadratic multi-surface (QMS) criterion. After validation on the local material scale, the models were applied to the engineering problem of compression perpendicular to the grain for studying the effect of the unloaded length. As a novel part, the influence of the annual ring structure on the local material behavior and the global elasto-plastic force–displacement behavior of wood under compression perpendicular to the grain were numerically investigated. Hill’s failure criterion was found to be the least suitable at both length scales, local material behavior and global structural response. The Hoffman and the QMS criteria showed quite good agreement with the biaxial experiments in terms of force–displacement relations and strain distributions for different loading situations, especially for combinations with radial compression, while there was less agreement with experiments for the behavior of combinations with tangential compression. Application of these material models to compression perpendicular to the grain for studying the unloaded length effect yielded similar trends as observed in structural tests. A reasonable and similar force–displacement response by Hoffman and QMS criteria was observed, while Hill’s model yielded significantly overestimated force carrying capacity. Differences in force–displacement response for different loading situations were well in line with literature findings and the influence of the annual ring curvature on the overall force–displacement behavior could be quantified.

Influence of morphology on the effective hygro-elastic properties of softwood (spruce) and hardwood (balsa)

Wood materials are characterized by complex, hierarchical material structures spanning across various length scales. The present work aims at establishing a relation between the hygro-elastic properties at the mesoscopic cellular level and the effective material response at the macroscopic level, both for softwood (spruce) and hardwood (balsa). The particular aim is to explore the influence on the effective hygro-elastic properties under variations in the meso-scale morphology. The multi-scale framework applied for this purpose uses the method of asymptotic homogenization, which allows to accurately and efficiently obtain the effective response of heterogeneous materials characterized by complex meso-structural geometries. The meso-structural model considered for softwood is based on a periodic, two-dimensional statistically representative volume element that is generated by a spatial repetition of tracheid cells. The tracheid cells are modeled as hexagonal elements characterized by a certain geometrical irregularity. The hardwood meso-structure consists of a region composed of hexagonal cellular fibers with large vessels embedded, which is connected to a ray region that is constructed of ray cells. The hardwood fibers are modeled as hexagonal cellular elements, similar to softwood tracheids. The rays are represented by quadrilateral cells oriented along the radial direction, whereby different arrangements are considered, i.e., the ray cells are either regularly stacked or organized as a staggered configuration. The interface between the fiber and ray regions may also be characterized by a regular or a staggered arrangement. The meso-structural models for softwood and hardwood are discretized by means of plane-strain, finite element models, which describe the hygro-elastic response of the wood material in the radial–tangential plane. For softwood, the sensitivity of the effective elastic and hygro-expansive properties is explored as a function of the geometrical irregularity of the tracheids. For hardwood, the effective properties are studied under a variation of the ray cell arrangement, the type of interface between ray and fiber regions, and the vessel volume fraction. The modeling results agree well with results obtained from other numerical homogenization studies and show to be in reasonable agreement with experimental data taken from the literature.

Meso-modelling study of the mechanical response and texture evolution of magnesium alloy during hot compression

The mechanical response and texture evolution of magnesium alloy during hot deformation are closely related to the heterogeneous meso-deformation. The improved Voce hardening law was developed and introduced into the crystal plasticity (CP) theory, and a reconstruction method of textured representative polycrystal was proposed. Three-dimensional crystal plasticity finite element model (3D-CPFEM) was established to meso-simulate the hot compression deformation of ZK61 Mg alloy. The influence of the temperature and strain rate on mechanical response was investigated, and the corresponding texture evolution and the texture transformation mechanism was revealed through meso-simulation. The results show that the 3D-CPFEM with the improved Voce hardening law and the initial texture characteristic can well predict the mechanical response and texture evolution under different temperatures and strain rates during hot compression of ZK61 Mg alloy. The basal plane texture of the ZK61 tubular blank is transformed into the basal fiber texture after hot compression, where the basal plane of grains is deflected gradually from the radial-axial plane to the radial-tangential plane. The texture transformation is attributed to two reasons, i.e., the orientation deflection of the grains with larger basal slip systems Schmid factor (SF) and the orientation retention of the grains whose c-axis tends to be parallel to the axial direction (AD) of the tubular blank. The change of the grain orientation corresponding to the basal plane texture component of the tubular blank has little contribution to the formed basal fiber texture.

Mykhailo Dendiuk, Lyubomir Flud, Nazar Semenyshyn Software implementation of the construction of curves short-term strength of wood with biaxial stress state

This paper is devoted to implementing the algorithm for constructing short-term strength curves of wood with biaxial stress states in the radial-tangential plane of structural symmetry. To implement this algorithm was developed software based on the Qt cross-platform toolkit, which allows to build and analyze short-term strength curves in the cross section of wood. The created program has a possibility to choose one of three failure criteria, a kind of wood, temperature and humidity distribution of lumber. The C++ program code is designed so that you can easily add another type of wood as well as a failure criterion. To display the curves, you can select table or graph mode. Graphs can be fixed on a graphics widget, and new ones can be added to compare to previous ones. Based on the analysis of the constructed curves, the ultimate stress state of the material in partial cases is established. In conclusion about expedient using some criteria to describe the strength characteristics of wood with strong and weak asymmetry of strength limits.

Evaluating Timoshenko Method for Analyzing CLT under Out-of-Plane Loading

Cross-laminated timber (CLT) is an engineered wood product made up of layers of structurally graded timber, where subsequent layers are oriented orthogonally to each other. In CLT, the layers oriented in transverse direction, generally termed as cross-layer, are subjected to shear in radial–tangential plane, which is commonly known as rolling shear. As the shear modulus of cross-layers is significantly lower than that in other planes, CLT exhibits higher shear deformation under out-of-plane loading in contrast to other engineered wood products such as laminated veneer lumber (LVL) and glue laminated timber (GLT). Several analytical methods such as Timoshenko, modified gamma and shear analogy methods were proposed to account for this excessive shear deformation in CLT. This paper focuses on the effectiveness of Timoshenko method in hybrid CLT, in which hardwood cross-layers are used due to their higher rolling shear modulus. A comprehensive numerical study was conducted and obtained results were carefully analyzed for a range of hybrid combinations. It was observed that Timoshenko method could not accurately predict the shear response of CLTs with hardwood cross layers. Comprehensive parametric analysis was conducted to generate reliable numerical results, which were subsequently used to propose modified design equations for hybrid CLTs.

Effects of the crystallographic texture on the contractile strain ratio of Ti–3Al–2.5V tubing

The contractile strain ratio (CSR) is an important property and a quality control factor of cold-worked and stress-relieved Ti–3Al–2.5V tubing. In this work, the CSR values of three thin-walled Ti–3Al–2.5V tubing samples were obtained by uniaxial tensile tests, and the crystallographic textures of the tubing samples were characterized by orientation distribution functions (ODFs) which were determined on the basis of a series of pole figures obtained by X-ray diffraction. A quantitative method is proposed for exploring the correlation between the CSR values and the ODF data of the tubing samples, including the following steps: Firstly, taking advantage of the ODF data, the volume fraction (V%) of crystallites that lie within a certain range of Euler angles (φ1, Φ, φ2) can be calculated, and the calculation is performed on each set of Euler angles (φ1, Φ, φ2). Secondly, each V% is resolved into an effective fraction in the orientation of the ideal radial texture {0002}〈10\overline 10〉 corresponding to the Euler angles of (0, 0, 0), and the equivalent radial texture (ERT) is obtained as the sum of all such effective fractions. Thirdly, similarly to the previous step, the equivalent tangential texture (ETT) is calculated. The CSR will be related to the ratio of the ERT to the ETT, named the equivalent texture ratio (ETR). The CSR values of the tubing samples are 1.38, 1.96 and 2.19 and their ETR values are 1.33, 1.72 and 1.87, respectively. In particular, the CSR and the ETR of the tubing with a random distribution of the basal poles in the radial–tangential plane are both unity. It is found from the above data that the CSR increases approximately linearly with the ETR. Since the three-dimensional orientations of crystallites and the orientation distributions throughout the Euler space are taken into account in the calculations of the ETR, the proposed method can be used for predicting and explaining the mechanical anisotropy of Ti–3Al–2.5V tubing more accurately.

Synergetic Strengthening of Grain Refinement and Texture in Gradient Zircaloy-4 by Surface Mechanical Rolling Treatment

A Zircaloy-4 rod was subjected to surface mechanical rolling treatment (SMRT) to form a gradient structure, and the evolution of the resulting sub-grain-boundary property and texture across the gradient structure was characterized using electron backscattered diffraction. Dual-gradient structures in grain size and orientation were formed; the grain size was refined from several microns at the center to approximately 400 nm at the topmost surface. Texture analysis revealed that the c-axis gradually tilted from a random orientation toward the parallel-to-radial direction on the radial–tangential plane. The SMRT-induced formation of the dual-gradient microstructure is attributed to the formation of gradient distributions of stress and strain, which resulted in various deformation mechanisms (twinning and dislocation) being active at different depths. During the SMRT process, twinning and dislocations were activated to refine the grains. When the dual-gradient microstructure formed, twinning was mainly activated at the subsurface near the matrix, whereas dislocations were activated across the entire gradient. The geometrically necessary dislocation density increased with decreasing depth and then slightly decreased near the surface. The synergetic strengthening of the dual-gradient microstructure resulted in a gradient distribution of the microhardness near the surface. Thus, the Zircaloy-4 rod exhibited a good combination of strength and ductility.

Study on the ultrasonic wave convergence in the medium with bone

Low intensity pulsed ultrasound can shorten the healing time of a bone fracture; however, the present technique does not seem not to consider the complicated ultrasound propagation in the body with bone. In this study, the time reversal technique was used to effectively converge ultrasound in the bone part. A three-dimensional distal radius model was constructed by using a high resolution-peripheral quantitative CT data (spatial resolution; 61 μm). In the simulation using Finite Difference Time Domain method, one cycle of sinusoidal ultrasound wave (1 MHz) with Hanning window was transmitted from a virtual fracture point (1 mm3). The model was surrounded by water. The propagating ultrasound waves were observed by two ring shape array transducers, coaxially placed along the bone model at the distance of 30 mm from the fracture point. Then, time reversal waves were radiated from the array transducers, considering the phase shifts and amplitudes of the observed waves in the previous simulation. The time reversal waves successfully converged near the initial virtual fracture part, telling the usefulness of the technique. In the radial-tangential plane including the point, the converged area (−3dB of maximum stress value) was 42.8 mm2.

On the identification of earlywood and latewood radial elastic modulus ofPinus pinasterby digital image correlation: A parametric analysis

This work addresses the reconstruction of strain gradient fields at the wood growth ring scale from full-field deformation measurements provided by digital image correlation. Moreover, the spatial distribution of the earlywood and latewood radial modulus of elasticity is assessed. Meso-scale tensile tests are carried out on Pinus pinaster Ait. wooden specimens oriented in the radial–tangential plane under quasi-static loading conditions. A parametric analysis of the two-dimensional digital image correlation extrinsic and intrinsic setting parameters is performed, in a balance between spatial resolution and resolution. It is shown that the parametric module is an effective way to quantitatively support the choice of digital image correlation parameters in the presence of the high deformation gradient fields generated by the structure–property relationships at the scale of observation. Under the assumption of a uniaxial tensile stress state, the spatial distribution of the radial elastic modulus across the growth rings is obtained. It is observed that the ratio of the radial modulus of elasticity between latewood and earlywood tissues can vary significantly as a function of the digital image correlation parameters. It is pointed out, however, that a convergence value can be systematically established. Effectively, earlywood and latewood stress–strain curves are obtained and elastic properties are determined assuming the converged digital image correlation setting parameters.

Sensitivity of Ultrasonic Wave Velocity Estimation Using the Christoffel Equation for Wood Non-Destructive Characterization

To perform a non-destructive evaluation of wood, the Christoffel equation is frequently used to describe the relationship between the ultrasonic wave velocity and the mechanical parameters. In the context of acoustical tomography imaging of standing trees, the key contribution of this numerical study is to determine the influence of mechanical parameters of the wood radial-tangential plane on the wave velocity computation using the Christoffel equation. Mechanical parameters from six species were selected. A sensitivity analysis was carried out by increasing and decreasing every parameter by a given percentage, and then by computing the variation of velocity for a set of wave direction of propagations. The evolution of the wave velocity, according to the direction of propagation, depended on the considered species; there was a difference between the softwoods and the hardwoods. The sensitivity analysis showed a bigger influence of the Young’s moduli, followed by the Poisson’s ratio, and finally by the shear modulus. However, these last two parameters cannot be neglected when using the Christoffel equation to solve the inverse problem of standing tree tomography. A proposed solution involves determining the propagation paths using the Young’s moduli as variables and then inversing the set of equations in accordance with the overall parameters.

Shear stiffness and its relation to the microstructure of 10 European and tropical hardwood species

In this study, shear stiffness properties of 10 different hardwood species and their relation to the corresponding species-specific microstructure are investigated. For this purpose, shear stiffness of 10 different hardwood species is experimentally measured by means of ultrasonic testing. In addition, a micromechanical model for hardwood is applied in order to illustrate the influence of certain microstructural characteristics such as mass density and volume fractions of vessels and ray cells on the shear stiffness. Comprehensive microstructural and mechanical data from previous investigations of the same hardwood material support the interpretation of the microstructure–shear stiffness relationships. Mass density was confirmed to be the dominant microstructural characteristic for shear stiffness. Also, ultrasound shear wave propagation velocity increases with density, particularly in the radial-tangential (RT) plane. In addition to density, comparably higher shear stiffness GLR can be explained by comparably higher ray content and lower vessel content. As for GLT, a ring porous structure seems to lead to higher shear stiffness as compared to a diffuse porous structure. For this shear stiffness, vessel and ray content were found to have a less impact. Also, the rolling shear stiffness GRT was found to be higher for a diffuse porous structure than for a ring porous one. Moreover, the data supports that ray cells act as reinforcements in the RT plane and lead to higher GRT.

Anisotropic elastic properties of common ash (Fraxinus excelsior L.)

Abstract Hardwoods in principle show a similar orthotropic behavior as softwoods; however, the ratios of the mechanical parameters between the three anatomical directions and their magnitudes are different and depend strongly on the individual microstructure of the species. The aim of the current study was to characterize the 3-D elastic behavior of common ash (Fraxinus excelsior L.) by tensile, compression, and shear tests in the three anatomical directions and stepwise in between, by means of a universal testing machine in combination with a digital image correlation technique. Young’s moduli, shear moduli, and Poisson’s ratios have been determined for the different load directions. From studies on the radial-tangential plane of other wood species, it is known that the elastic moduli in the principal directions and the off-axis elastic moduli vary in a nonlinear correlation, depending on density gradients between earlywood and latewood. This angular dependency has been experimentally and theoretically proven for ash. Furthermore, the dependency of mechanical parameters on the fiber-load angle has been experimentally determined. The measurements for principal and off-axis load directions provide a sound basis for modeling of hardwood structures.

Experiments on the effective compliance in the radial–tangential plane of Norway spruce

Analysis and design of wood based composites and structures need reliable experimental compliance of their constituting materials. Therefore, an experimental method is presented to determine all of the effective in-plane elastic parameters and applied to Norway spruce specimens in the radial tangential RT plane due to the use of this species in wide variety of engineering applications. For the purpose, uni-axial compression experiments are conducted on the specimens for different material orientations under the assumptions of small strains and small rotations. Boundary extremes of the specimens are allowed to rotate for minimizing the boundary artifacts and providing near-ideal specimen deformation. During these experiments, digital image correlation is used to obtain the displacement and strain fields whilst the stress is computed through the applied load and specimen geometry. In addition to the common practice of tabulated parameters for each nominal material orientation, the experiment results are further processed through the transformation rule and least squares function. Consequently, the effective elastic parameters in the RT plane are obtained by taking general anisotropic linear elasticity into account and the material classification is performed. By means of the current method, it is expected to advance the effective in-plane compliance measurements of natural cellular materials.

Calculation of Iron Loss in Electrical Generators Using Finite-Element Analysis

The accurate calculation of iron loss from finite-element analysis in electrical machines is essential if optimal machines are to be designed. This paper conducts a holistic review of the extensive literature field before examining, in detail, several methods in order to recommend an optimum engineering solution. Both frequency domain and time domain methods are discussed including the use of different orthogonal components as well as the relative merits of using all, or some, of the eddy current, anomalous, and hysteresis loss components. A theoretical cubic meter of iron is simulated to quickly demonstrate the inaccuracies of Cartesian coordinate methods before calculations on several manufactured machines are undertaken showing the superior accuracies of major/minor loop calculation. Calculation undertaken using the radial tangential orthogonal plane is shown to have less than 1% average difference to that of the major/minor loop yet is over six times quicker. The peak percentage error in an individual element is shown to be less than 5%. Discussions are also made regarding the method of curve fitting to gain loss constants and any possible sources of inaccuracy particularly during manufacture.

Relationships between the anisotropy of longitudinal wave velocity and hydroxyapatite crystallite orientation in bovine cortical bone

Quantitative ultrasound (QUS) is now widely used for evaluating bone in vivo, because obtained ultrasonic wave properties directly reflect the visco-elasticity. Bone tissue is composed of minerals like hydroxyapatite (HAp) and a collagen matrix. HAp crystallites orientation is thus one parameter of bone elasticity. In this study, we experimentally investigated the anisotropy of ultrasonic wave velocity and the HAp crystallites orientation in the axial–radial and axial–tangential planes in detail, using cylindrical specimens obtained from the cortical bone of three bovine femurs. Longitudinal bulk wave propagation was investigated by using a conventional ultrasonic pulse system. We used the one cycle of sinusoidal pulse which was emitted from wide band transmitter. The nominal frequency of the pulse was 1 MHz. First, we investigated the anisotropy of longitudinal wave velocity, measuring the anisotropy of velocity in two planes using cylindrical specimens obtained from identical bone areas. The wave velocity changed due to the rotation angle, showing the maximum value in the direction a little off the bone axis. Moreover, X-ray pole figure measurements also indicated that there were small tilts in the HAp crystallites orientation from the bone axis. The tilt angles were similar to those of the highest velocity direction. There were good correlations between velocity and HAp crystallites orientation obtained in different directions. However, a comparatively low correlation was found in posterior bone areas, which shows the stronger effects of bone microstructure. In the radial–tangential plane, where the HAp crystallites hardly ever align, weak anisotropy of velocity was found which seemed to depend on the bone microstructure.

Characterization of viscoelastic, shrinkage and transverse anatomy properties of four Australian hardwood species

Several key wood properties of four Australian hardwood species: Corymbia citriodora, Eucalyptus pilularis, Eucalyptus marginata and Eucalyptus obliqua, were characterized using state-of-the-art equipment at AgroParisTech, ENGREF, France. The wood properties were measured for input into microscopic (cellular level) and macroscopic (board level) vacuum-drying models currently under development. Morphological characterization was completed using a combination of environmental scanning electron microscopy and image analysis software. A clear difference in fibre porosity, size, wall thickness and orientation was evident between species. Viscoelastic properties were measured in the tangential and radial directions using dynamic mechanical analysis instrumentation. The glass transition temperature was markedly different for each species owing to anatomical and chemical variations. The radial direction showed higher stiffness, internal friction and glass transition temperature than the tangential direction. A highly sensitive microbalance and laser technology were used to measure loss of moisture content in conjunction with directional shrinkage on microsamples. Collapse shrinkage was clearly evident with this method for E. obliqua, but not with other species, consistent with industrial seasoning experience. To characterize the wood–water relations of E. obliqua, free of collapse, thinner sample sections (in the radial–tangential plane) are recommended.

Measurement of standard and off-axis elastic moduli and Poisson’s ratios of spruce and yew wood in the transverse plane

It is well known that in the radial–tangential plane of softwoods, the elastic modulus in the principal directions is clearly higher than the off-axis elastic moduli, which decrease to a minimum at a growth ring angle α of about 45°. However, this angular dependency was experimentally proven by only a few early publications. The aims of this study were (1) to analyze this relationship with up-to-date equipment in compression tests on miniature softwood specimens with varying growth ring angles and (2) to compare the experimental results with those calculated by a tensor transformation to assess whether it is admissible to treat the investigated wood species as orthotropic materials. Two softwoods with distinctly different anatomic structures (Norway spruce and common yew) were chosen, and further properties such as Poisson’s ratios were determined. The results confirm the above-mentioned angle-dependent tendency for spruce elasticity, but also show that it is not valid for softwoods in general since the behavior of yew was completely different. The tissue textures of both species, particularly density and density distribution, were discussed as possible reason for these observed differences. The determined Poisson’s ratios for principal and off-axis load directions may be useful for modeling of material behavior.