Principal Axes Of Anisotropy Research Articles

Micro-mechanical numerical analysis on ductile damage in multiaxially loaded anisotropic metals

The paper deals with numerical analysis of the effect of stress state and loading direction with respect to the rolling direction on damage and fracture behavior of anisotropic metals. The continuum damage model has been enhanced to take into account the influence of production-induced anisotropies and loading direction on damage criteria and on evolution equations of damage strains. Constitutive parameters are determined using experimental results taken from tests with uni- and biaxially loaded specimens. The focus of the paper is on three-dimensional micro-mechanical numerical analyses of micro-defect-containing representative volume elements covering a wide range of stress states. These calculations lead to more insight in the different damage and failure processes on the micro-scale and their influence on the macroscopic damage laws. With the obtained numerical results it is possible to detect general trends, to propose governing equations for the damage criteria, to develop evolution equations for the damage strains, and to identify constitutive parameters of the anisotropic material model. It is shown that the anisotropic behavior and the loading direction with respect to the principal axes of anisotropy affect the evolution of damage mechanisms on the micro-level as well as the corresponding damage strains.

Review of Selected Issues in Anisotropic Plasticity under Axial Symmetry

The present review paper consists of two main parts, which are not connected. The first part is devoted to a general axisymmetric elastic–plastic plane stress solution, assuming polar anisotropy. Strains are infinitesimal. The principal stress trajectories coincide with the principal axes of anisotropy. No restrictions are imposed on the yield criterion other than the conventional restrictions imposed on the yield criteria in plasticity. The plastic portion of the strain rate tensor is determined from the associated flow rule. A simple example illustrates the general solution. The second part is devoted to the stationary ideal flow theory for anisotropic materials under axial symmetry. The elastic portion of the strain tensor is neglected. A piece-wise linear yield criterion is adopted. This criterion generalizes Tresca’s yield criterion. The existence of ideal flow is proven. It is also shown that the available solutions for Tresca’s yield criterion can be used for deriving solutions for the yield criterion under consideration. Miscellaneous topics are shortly discussed in the third part of the paper.

Analysis of Damage and Failure in Anisotropic Ductile Metals Based on Biaxial Experiments with the H-Specimen

BackgroundDependence of strength and failure behavior of anisotropic ductile metals on loading direction and on stress state has been indicated by many experiments. To realistically predict safety and lifetime of structures these effects must be taken into account in material models and numerical analysis.ObjectiveThe influence of stress state and loading direction on damage and failure behavior of the anisotropic aluminum alloy EN AW-2017A is investigated.MethodsNew biaxial experiments and numerical simulations have been performed with the H-specimen under different load ratios. Digital image correlation shows evolution of strain fields and scanning electron microscopy is used to visualize failure modes on fracture surfaces. Corresponding numerical studies predict stress states to explain damage and fracture processes on the micro-scale.ResultsThe stress state, the load ratio and the loading direction with respect to the principal axes of anisotropy affect the width and orientation of localized strain fields and the formation of damage mechanisms and fracture modes at the micro-level.ConclusionsThe enhanced experimental program with biaxial tests considering different loading directions and load ratios is suggested for characterization of anisotropic metals.

Darcy–Brinkman Flow Over a Screen Embedded in an Anisotropic Porous Medium

A screen composed of in-plane thin strips is embedded in a porous medium. The screen is either normal or parallel to the applied pressure gradient which forces a flow through the anisotropic porous medium. The principal axes of anisotropy are assumed to be aligned with that of the screen. The governing equation is fourth order and cannot be factored as in the isotropic case. The solutions are found by eigenfunction superposition (with complex eigenvalues) and point match. Anisotropy has first-order effects on the flow and the drag on the screen. Extrapolation yields fundamental results for the drag of a single slat in an anisotropic porous medium.

Effects of intrinsic anisotropy on the dynamic behaviour of undisturbed loess

To investigate the effects of the relative orientation between a sample's principal axes of anisotropy and the principal stress axes on the dynamic behaviour of undisturbed loess, samples with axial inclinations 30° and 90° relative to the horizontal were prepared. The effects of confining pressure and depth of soil also were examined to investigate variations in the dynamic behaviour of loess. The results showed an obvious effect of intrinsic anisotropy on the dynamic behaviour of loess. With all other conditions constant, the higher the confining pressure, the greater the dynamic stress to generate the same dynamic strain. The dynamic stresses of the 90° samples were always greater than those of the 30° samples. The effect of intrinsic anisotropy on the backbone curves was more obvious for the 2 m depth samples than for the 6 m depth samples. The damping ratio was within a certain range and initially increased as the dynamic strain increased and then gradually levelled off. The 2 m samples exhibited higher damping ratios than the 6 m samples. Finally it was found that the intrinsic anisotropy of loess might weaken the sample during the loading process and a confining pressure of 300 kPa was sufficient to nearly eliminate the effects of intrinsic anisotropy.

Determining the type of initial anisotropy of elastic material from a series of experiments

An experimental program has been developed to identify the type of initial elastic anisotropy of the material. The program includes a series of compression experiments to determine the orientation of the principal axes of anisotropy of the material and additional experiments to find the orientation of the canonical axes of anisotropy. In order to distinguish isotropic and cubic materials, it is necessary to fulfill an experiment on biaxial tension-compression in the direction of two canonical axes of anisotropy, and a shear experiment in the same plane. Similar experiments make it possible to identify trigonal, tetragonal and hexagonal materials. To identify triclinic, monoclinic, and rhombic materials, three shear experiments in planes determined by the canonical axes of anisotropy are required.

Non-linear anisotropic hyperelasticity for granular materials

We describe a non-linear anisotropic hyperelastic model appropriate for geomaterials, deriving the full stress-strain response from strain energy or complementary energy functions. Specific forms of the functions are chosen so that the stiffness and compliance matrices have the appropriate minor symmetries. The model employs two material parameters to describe basic volumetric and shear response, one to express nonlinearity of stiffness as a function of mean stress, and two more (together with the directions of the principal axes of anisotropy) to express the degree of anisotropy. The model is modular, so that non-linearity and anisotropy can be included separately or in combination. For specific parameter settings it reduces to simpler cases such as linear isotropic elasticity. Because the model employs hyperelasticity, thermodynamic acceptability is ensured and all appropriate cross-coupling terms are included between the shear and volumetric behaviour.

Orthotropic mechano-sorptive creep behavior of Chinese fir during moisture desorption process determined in tensile mode

Time-dependent creep behavior is one of the most important material characteristics in wood products exposed to various environmental conditions. The creep behaviors, including the general viscoelastic creep (VEC) at constant moisture content and the mechano-sorptive creep (MSC) during moisture content variations, are, however, not sufficiently described. Given the anisotropy of wood, comprehensive data on the creep behavior will require knowledge of its moisture-dependent properties in relation to the three principal axes of anisotropy. The present study examined the tensile orthotropic creep behaviors of Chinese fir (Cunninghamia lanceolata): VEC at constant moisture content and MSC during desorption process, at 0, 20, 40, and 60% relative humidity (30 °C). The creep anisotropy of MSC was more pronounced than that of VEC. The free shrinkage caused the specimens to deform in the opposite direction to load in MSC tests. Based on the databases of free shrinkage, VEC, and MSC, it is obvious that the mechanical stress has a positive effect on MSC, which is presumed to be a result of the double effect composed of the rearrangement of hydrogen bonds and unstable state. The unstable state could be evaluated quantitatively by the mechano-sorptive strain. The mechano-sorptive strain of radial and tangential specimens is affected by the relative humidity to a higher degree than that of longitudinal specimens. Further, the unstable state exerted more influence on tangential specimens and less on longitudinal specimens.

Effects of anisotropic composite skin on electrothermal anti-icing system

To study the effects of anisotropic thermal conductivity of composite aircraft skin on the heat transfer characteristics of electrothermal anti-icing system, the differential equation of anisotropic heat conduction was established using coordinate transformation of principal anisotropy axis. In addition, it was coupled with the heat and mass transfer model of the runback water film on the anti-icing surface to perform numerical simulation of the electrothermal anti-icing system. The temperature results of the vertical and cylindrical orthotropic thermal conduction in the rectangular and semi-cylindrical composite skin were consistent with those obtained by the traditional orthotropic model, which verified the anisotropic heat conduction model. The temperature distribution of anti-icing surface agreed well with the literature data, which validated the coupled heat and mass model of the runback water flow and the anisotropic skin. The anisotropic thermal conductivity of composite skin would make temperature change more gradual, and the effect was more significant where the curvature of the temperature curve was greater. However, the anti-icing surface of the electrothermal anti-icing system was slightly affected by the anisotropic heat conduction of the multilayered composite skin.

What do variable magnetic fabrics in gabbros of the Oman ophiolite reveal about lower oceanic crustal magmatism at fast spreading ridges?

The magmatic processes responsible for accretion of the lower oceanic crust remain one of the least-constrained components of the global seafloor spreading system. Samples of gabbroic rocks recovered by scientific ocean drilling are too limited to allow effective assessment of spatial variations in magmatic flow within in situ lower crust. Extensive exposures of gabbros in ophiolites, on the other hand, provide opportunities to study accretion processes in three dimensions across wide areas and at a resolution that allows variations in magmatic fabrics through the crust to be quantified. Here, we show that magnetic anisotropy provides a reliable proxy for lower-crustal magmatic fabrics in the world’s largest ophiolite in Oman. Important differences in magnetic fabrics are detected that reflect variations in magmatic processes on a range of scales. Fabrics in layered gabbros are aligned with modal layering and display a consistency in the orientation of maximum principal axes of anisotropy between localities at a regional scale. These fabrics are compatible with subhorizontal preferred alignment of crystals orthogonal to the inferred orientation of the Oman spreading axis, resulting from magmatic flow or deformation of melt-rich crystal mushes during spreading. In contrast, magnetic anisotropy in foliated gabbros at the top of the lower crust reveals for the first time distinctly different linear and anastomosing fabric styles between localities sampled at the same pseudostratigraphic level. These differences reflect spatial variations in the style and trajectory of flow in the crystal mush beneath the axial melt lens during upward melt migration at the spreading axis.

Coring induced sediment fabrics at IODP Expedition 347 Sites M0061 and M0062 identified by anisotropy of magnetic susceptibility (AMS): criteria for accepting palaeomagnetic data

SUMMARY Anisotropy of magnetic susceptibility data obtained from discrete subsamples recovered from two Integrated Ocean Drilling Program sites (Expedition 347 sites M0061 and M0062 in the Baltic Sea) by an Advanced Piston Corer are compared to results obtained on subsamples recovered by replicate 6-m-long Kullenberg piston cores. Characteristic natural remanence directions were obtained from the total of 1097 subsamples using principal component analyses. The three principal anisotropy axes of subsamples taken from Advanced Piston Core liners align to the subsample axes, with the maximum axis (K1) parallel to the split core surfaces, possibly caused by outwards relaxation of the core-liners after splitting. A second anomalous anisotropy fabric is characterized by steep values of the angular difference between the inclination of the minimum anisotropy axes (K3) and that expected for horizontal bedding (90°). This fabric is confined to the upper 1–2 m of the Kullenberg cores and specific sections of the advanced piston cores, and we attribute it to conical deformation caused by either excessive penetration speeds and downwards dragging of sediment along the edge of the liner or stretching caused by undersampling. By using our data in an example, we present a protocol to accept palaeomagnetic secular variation data that uses (i) a threshold 90-K3 value of 15°, combined with a modelled, locally applicable minimum inclination of 65° and (ii) an A95 cone of confidence based on Fisher statistics applied to virtual geomagnetic pole distributions.

Numerical analysis and experimental observation of ultrasonic wave propagation in CFRP with curved fibers

The relationship between the propagation directions of ultrasonic wave and the direction of the principal axis of anisotropy in uni-directional CFRP with straight fiber is well known. However, the behavior of ultrasonic wave in CFRP with curved fibers is not clarified in details. In this paper, numerical analyses using the finite difference method were conducted to visualize the behavior of ultrasonic waves in CFRP with concentrically curved fibers. Numerical simulation results showed the energy of quasi-longitudinal ultrasonic wave curved along the fiber direction. In order to confirm the analytical result, CFRP specimen with curved fibers were prepared by utilizing 3D-printer and the behavior of ultrasonic propagation was observed by using Laser ultrasonic system. The observed results confirmed the analytical results that the ultrasonic wave curved along carbon fibers.

Construction of combined models of the properties of bulk high-temperature superconducting materials

The article contains the results of research that was aimed at improving the models of properties of bulk high-temperature superconducting (HTS) materials, which are necessary for numerical analysis of electromagnetic fields in electrical devices containing elements of high-temperature superconductors. Approximating combined models for a set of transport and bound currents are considered, which are determined, respectively, by the resistive model for currents and the nonlinear hysteresis model for the magnetization. The model of transport currents is based on the known types of the critical-state model. The material-magnetization model is composed for a set of magnetic moments of elementary superconducting cylinders with diameters that are much smaller than their length, which are oriented in the direction of the principal anisotropy axis of the material. The approximation to the actual conditions is realized by the statistical characteristics that specify the possible changes in the critical current density, the critical field strength, and the spatial orientation of the basic axes of the elementary cylinders. The results of studies of a laboratory model, which consists of a cylindrical HTS element and an annular permanent magnet, are presented and compared with the results of electromagnetic-field calculations according to the proposed models of properties.

Moisture-dependent orthotropic elasticity and strength properties of Chinese fir wood

Elastic and strength properties are very important material characteristics in mechanical modelling. Due to the anisotropic and hygroscopic nature of wood, a characterization of wood mechanical behavior will require knowledge of its moisture-dependent properties in relation to the three principal axes of anisotropy. The influence of moisture content (MC) on the elastic and strength anisotropy of Chinese fir (Cunninghamia lanceolata [Lamb.] Hook) wood was examined in the present study. Selected parameters, including the anisotropic Young’s moduli, shear moduli, Poisson’s ratios, yield and ultimate stress values in the longitudinal, radial and tangential directions, were determined in compression and tension tests at different moisture conditions. The results indicated that a distinct moisture dependency is exhibited for the elastic and strength behavior of Chinese fir wood. With the exception of some Poisson’s ratios, all investigated elastic and strength parameters were shown to decrease with increasing MC, whereby individual moduli and strength values were affected by the MC to different degrees. The two- and three-dimensional representation of the compliance matrix and the two-dimensional visualization of a yield surface give a valuable overview on the moisture-dependent elastic and strength anisotropy of Chinese fir wood.

Magnetic Anisotropy in Pentacoordinate NiII and CoII Complexes: Unraveling Electronic and Geometrical Contributions.

The magnetic properties of the pentacoordinate [MII (Me4 cyclam)N3 ]+ (Me4 cyclam=tetramethylcyclam; N3 =azido; M=Ni, Co) complexes were investigated. Magnetization and EPR studies indicate that they have an easy plane of magnetization with axial anisotropy parameters D close to 22 and greater than 30 cm-1 for the Ni and Co complexes, respectively. Ab initio calculations reproduced the experimental values of the zero-field splitting parameters and allowed the orientation of the anisotropy tensor axes with respect to the molecular frame to be determined. For M=Ni, the principal anisotropy axis lies along the Ni-Nazido direction perpendicular to the Ni(Me4 cyclam) mean plane, whereas for M=Co it lies in the Co(Me4 cyclam) mean plane and thus perpendicular to the Co-Nazido direction. These orientations match one of the possible solutions experimentally provided by single-crystal cantilever torque magnetometry. To rationalize the geometry and its impact on the orientation of the anisotropy tensor axis, calculations were carried out on model complexes [NiII (NCH)5 ]2+ and [CoII (NCH)5 ]2+ by varying the geometry between square pyramidal and trigonal bipyramidal. The geometry of the complexes was found to be the result of a compromise between the electronic configuration of the metal ion and the structure-orienting effect of the Me4 cyclam macrocycle. Moreover, the orientation of the anisotropy axes is mainly dependent on the geometry of the complexes.

Extreme conditions of elastic constants and principal axes of anisotropy

This paper describes the derivation of extreme conditions of each elasticity coefficient (Young’s modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the principal axes of anisotropy, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. The example of a material with cubic symmetry is given.

Residual Stress Determination in Orthotropic Composites by Displacement Measurements Near Through Hole

Novel method for a determination of residual stresses in orthotropic composite plates based on local displacement measurements by electronic speckle-pattern interferometry is developed and verified. The values of hole diameter increments in principal residual stress directions serve as initial experimental deformation. The technique is based on analytical solution of S.G. Lekhnitsky, which describes a stress concentration along the edge of central open hole in rectangular orthotropic plate under one-axis tension in arbitrary direction. A situation when principal directions of residual stresses coincide with principal axes of anisotropy is considered. The relations, which connect initial experimental data with residual stress components, are unequivocally solution of the properly posed inverse problem. An availability of interference fringe patterns, a quality of which is high enough for reliable recognizing of fringe orders at the hole edge immediately, is the essential experimental foundation of the approach developed. The accuracy of the proposed method has been assessed by two different ways. The results of residual stresses determination in rectangular composite plate are presented.

Full decoherence induced by local fields in open spin chains with strong boundary couplings

We investigate an open XYZ spin- chain driven out of equilibrium by boundary reservoirs targeting different spin orientations, aligned along the principal axes of anisotropy. We show that by tuning local magnetic fields, applied to spins at sites near the boundaries, one can change any nonequilibrium steady state to a fully uncorrelated Gibbsian state at infinite temperature. This phenomenon occurs for strong boundary coupling and on a critical manifold in the space of the fields amplitudes. The structure of this manifold depends on the anisotropy degree of the model and on the parity of the chain size.

Generalized method for retrieving effective parameters of anisotropic metamaterials.

Electromagnetic or acoustic metamaterials can be described in terms of equivalent effective, in general anisotropic, media and several techniques exist to determine the effective permeability and permittivity (or effective mass density and bulk modulus in the context of acoustics). Among these techniques, retrieval methods use the measured reflection and transmission coefficients (or scattering coefficients) for waves incident on a metamaterial slab containing few unit cells. Until now, anisotropic effective slabs have been considered in the literature but they are limited to the case where one of the axes of anisotropy is aligned with the slab interface. We propose an extension to arbitrary orientations of the principal axes of anisotropy and oblique incidence. The retrieval method is illustrated in the electromagnetic case for layered media, and in the acoustic case for array of tilted elliptical particles.

Derivation of Green's Functions for Paraxial Fields of a Wedge with Particular Anisotropic Impedance Faces

A dyadic Green's function of a wedge with anisotropic impedance faces, excited by an electric dipole source, is derived for the paraxial region where the source and observation points are in proximity to the apex but widely separated. The principal anisotropy axis is the edge axis, and surface impedances parallel and transverse to this axis are considered. Following a “separation of variables” derivation, final dyadics involve eigenfunction solutions over an angular wave number and a longitudinal spectral integral, which is evaluated asymptotically assuming that k|z – z′| is large. It is observed that derived forms reveal three distinct scattering mechanisms: edge-guided waves, surface waves, and guided waves in the classical sense. Numerical simulations limited to paraxial region show that edge-guided and guided-wave terms are dominant at points away from the wedge surface, whereas surface waves are dominant near impedance surfaces. Both capacitive, inductive, and mixed (one face capacitive and the other inductive) reactive surface impedances are numerically analyzed. The resulting expressions can be used in the analysis of antennas located near the apex of a wedge and electromagnetic scattering from artificially hard and soft surfaces.