Effects Of Material Anisotropy Research Articles

Electron paramagnetic resonance magnetic field sensors for particle accelerators.

We report on four electron paramagnetic resonance sensors for dynamic magnetic field measurements at 36 mT, 100 mT, 360 mT, and 710 mT. The sensors are based on grounded co-planar microwave resonators operating at about 1 GHz and 3 GHz, realized using printed circuit board technology, and on single-chip integrated microwave oscillators operating at about 10 GHz and 20 GHz, realized using complementary metal-oxide-semiconductor technology. The sensors are designed to mark precisely the moment when a time-dependent magnetic field attains a specific value. The trigger from the sensor can be used to preset the output of real-time magnetic field measurement systems, called "B-trains," which are in operation at several large synchrotron installations, including five of the CERN's particle accelerators. We discuss in detail the performance achieved, in particular, the magnetic field resolution that is in the range of 0.1 nT/Hz1/2-6 nT/Hz1/2. The effects of material anisotropy and temperature are also discussed. Finally, we present a detailed characterization of the sensors with field ramps as fast as 5 T/s and field gradients as strong as 12 T/m.

An efficient method for the elastic field in a transversely isotropic full space due to arbitrary inclusions

The present study is on the analytical solution for the elastic field due to a cuboidal inclusion of uniform eigenstrain within a transversely isotropic full-space material, and a numerical method to model inclusions of any arbitrary shapes and with any eigenstrain distributions as the integration of a set of such cuboidal inclusions. The fast Fourier transform (FFT) is applied for efficient computation. The developed method and results are implemented to analyze the elastic field in a transversely isotropic full-space material containing inclusions of different shapes, different eigenstrain distributions, and multiple cuboids of different densities. Furthermore, the effect of material anisotropy on the stress field subjected to a spherical inclusion with pure dilatant eigenstrains is explored by comparing the behavior of a transversely isotropic material with that of a corresponding isotropic one. The numerical results show that the induced stresses are drastically influenced by the Young’s moduli of transversely isotropic materials, and that material constant C33 has a large influence on normal stress σ33.

Effect of material anisotropy on ultra-precision machining of Ti-6Al-4V alloy fabricated by selective laser melting

Selective laser melting (SLM) is generally characterized by the brief laser-powder interaction time, highly localized heat intensity and input distributions, steep temperature gradients and high cooling rate. It was admitted that the mechanical properties of as-built SLMed components exhibit significantly anisotropic due to different heat history and microstructures in different directions. Post-processing of additively manufactured parts is generally considered an essential operation due to poor surface quality and dimensional accuracy. In this paper, comprehensive research is conducted about the influence of material anisotropy of additively manufactured Ti-6Al-4V alloys on machining performance in ultra-precision micromachining. The machining performance of SLMed Ti-6Al-4V alloys was derived from two cutting directions (parallel/perpendicular to the laser scanning direction), two machining surfaces (top/front surface) and three laser scanning strategies (0°-line scanning, 67.5°/90°- rotation scanning). Surface topography, roughness, microstructure and microhardness were assessed to characterize the material anisotropy of SLMed titanium alloy. The machining results showed that the anisotropic mechanical properties and microstructure feature of the Ti-6Al-4V alloys are the fundamental reasons for the anisotropic machining performance in terms of cutting force and surface roughness. The machining properties of SLMed Ti-6Al-4V alloys are affected by the microstructure, machining surfaces, cutting directions and cutting parameters. Both the magnitude and fluctuation of dynamic cutting force produced on the front surfaces are obviously larger than those generated on the top surfaces. Significant improvement in surface roughness ranging from Sa = 80–100 nm could be achieved along the laser scanning direction for 0°-line SLMed Ti-6Al-4V sample when cutting depth was from 1 to 15 μm at vc = 50 mm/min. In addition, some typical SLMed defects appear on the machined surface and produced chips. This research is applicable to assist manufacturers in choosing the appropriate machining method for SLMed components in ultra-precision machining.

Effect of material anisotropy on rolling contact fatigue life under dry and lubricated point contact conditions: A numerical study

Rolling bearings have to operate reliably and efficiently under increasingly severe conditions. Previously ignored effects of material inhomogeneity with varying crystallographic orientation may significantly affect rolling contact fatigue life. In this paper, it is demonstrated that Multigrid techniques allow the computational analysis of such effects in a full 3D setting. Using grain configurations created by Voronoi tessellation, the dependence of the maximum von Mises stress, and of a predicted fatigue life stress field integral with load, friction, mean grain size and crystallographic orientation distribution is shown. Crystallographic orientation variations are shown to potentially significantly reduce predicted rolling contact fatigue life relative to homogeneous isotropic material. The results contribute to material optimization and to computational diagnostics of criticality of material crystallographic (sub)structures.

Generalized solution to the anisotropic Mandel's problem

SummaryExisting solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel‐Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction.

Stress Analysis of a Flange Stiffened FRP Composite Panel with Varying Stacking Sequence

Large panel structures made of composites are common building units in aerospace industries. In order to increase the stiffness of such structures, the panel or skin is adhered to a flange and supported by a web. Such a stiffened panel is modeled as an arrangement of web, flange and panel with an interface between the flange and the panel. In this paper, three dimensional stress analysis of one such stiffened panel has been carried out using the finite element analysis. The geometric non-linearity has been assumed in the analysis. The effect of material anisotropy and the laminate stacking sequence on the stress components has been studied. Material Graphite Fiber Reinforced Polymeric (GFRP) composite has been used and, two different configurations were considered while the unidirectional prepregs were laid up in quasi-isotropic [0/0/0/0]2 and cross-ply [0/90/90/0]2. Subsequently, the coupled stress failure criterion has been used to predict the critical location of damage onset. When component damage indicator attained the value of 1.0, the component was considered to lose stiffness and structural integrity.

Stability of an anisotropic dielectric elastomer plate

A variety of methods have been proposed to improve the performance of dielectric elastomer transducers, which lead to the anisotropic electromechanical behavior of the material. This paper theoretically analyzes the effect of material anisotropy on the diffuse modes of instability in dielectric elastomer plates. As a first step, a transversely isotropic material is considered in the present study. The linearized incremental theory is used and the plate thickness is considered in the stability analysis. The bifurcation equations are solved with Wolfram Mathematica (Wolfram Research, Inc., 2019) [1] to obtain the critical stretches under different electric field. It is found that, compared to the isotropic material, material anisotropy results in larger unstable regions and higher critical stretches above which the plate is stable. It is also shown that material anisotropy has a stronger influence on a thinner plate. As the plate thickness increases, the influence decreases.

Evanescent waves in two-dimensional fluid-saturated porous metamaterials with a transversely isotropic matrix

Wave propagation in a two-dimensional periodic fluid-saturated porous metamaterial (FSPM) is investigated. The constitutive relation considered for fluid-saturated porous materials is based on Biot’s homogeneization theory. Such media generally support two shear and two longitudinal elastic waves. Anisotropic wave propagation results both from anisotropy of the solid matrix and from the periodic structure of the metamaterial. Special attention is devoted to the dispersion and attenuation of evanescent Bloch waves in a FSPM whose matrix is transversely isotropic in which case in-plane elastic waves are a superposition of one shear wave and of two longitudinal waves. Bloch waves, complex band structures, and transmission properties are obtained numerically using finite element analysis. The case of homogeneous fluid-saturated porous media is considered since numerical simulations can be compared directly with analytic results in this case. The effects of material anisotropy and of fluid viscosity on wave propagation in two-dimensional FSPM are then discussed. It is found that wave-number band gaps appear in the complex band structure of the lossless FSPM due to the interference of waves with different but nonorthogonal polarizations. Wave-number band gaps are connected continuously by complex-frequency bands, hence, defining stop bands in the time domain. No complete frequency band gaps are found in two-dimensional lossless FSPM, in contrast to the one-dimensional case [Y.-F. Wang et al. Phys. Rev. B 99, 134304 (2019)] due to the presence of the additional quasishear wave accompanying the two quasi-longitudinal waves. Both the complex band structure and the transmission properties are affected by the anisotropy of the solid matrix. Wide transmission dips come up when viscosity is introduced as a result of the strong attenuation and the coupling of all wave polarizations. Concurrently, wave-number band gaps are washed out by viscosity. This theoretical paper has relevance to practical applications of fluid-saturated porous metamaterials, e.g., in concrete structures and geological soils.

Ductile and brittle crack-tip response in equimolar refractory high-entropy alloys

Understanding the strengthening and deformation mechanisms in refractory high-entropy alloys (HEAs), proposed as new high-temperature material, is required for improving their typically insufficient room-temperature ductility. Here, density-functional theory simulations and a continuum mechanics analysis were conducted to systematically investigate the competition between cleavage decohesion and dislocation emission from a crack tip in the body-centered cubic refractory HEAs HfNbTiZr, MoNbTaVW, MoNbTaW, MoNbTiV, and NbTiVZr. This crack-tip competition is evaluated for tensile loading and a totality of 15 crack configurations and slip systems. Our results predict that dislocation plasticity at the crack tip is generally unfavorable – although the competition is close for some crack orientations, suggesting intrinsic brittleness and low crack-tip fracture toughness in these five HEAs at zero temperature. Fluctuations in local alloy composition, investigated for HfNbTiZr, can locally reduce the resistance to dislocation emission for a slip system relative to the configuration average of that slip system, but do not change the dominant crack-tip response. In the case of single-crystal MoNbTaW, where an experimental, room-temperature fracture-toughness value is available for a crack on a {100} plane, theoretical and experimental results agree favorably. Factors that may limit the agreement are discussed. We survey the effect of material anisotropy on preferred crack tip orientations, which are found to be alloy specific. Mixed-mode loadings are found to shift the competition in favor of cleavage or dislocation nucleation, depending on crack configuration and amplified by the effect of material anisotropy on crack tip stresses.

Free Vibration Analysis of Generally Layered Composite Beam with Various Lay-Up and Boundary Conditions

A mathematical formulation of the first order shear deformation theory to analyze free vibration of layered composite beam is discussed. The finite element model is prepared for the modal analysis by using 281 shell element which is having 8 nodes with six degrees of freedom at each node. The effect of material anisotropy, Poisson effect, slenderness ratio, lay-up angle and boundary conditions on the free vibration of the layered composite beams are studied by taking suitable example from various literatures. The modal analysis results obtained are tabulated and compared with the previously published analytical and experimental results to demonstrate the efficacy and accuracy of the model. AS4/3501-6 graphite-epoxy, glass-polyester and hydrothermally curvature stable composite are considered for this study. The prime focus of the work is to study the effect of multiple parameters on the natural frequency of four layered composite beam by using FE model since parametric study using analytical model would be highly complex. Natural frequency of all the modes is observed to be highly sensitive to a smaller layup angle than a higher lay up for all the boundary conditions. Poison effect cannot be neglected as it affects all the modes prominently.

Boundary element analysis of dynamic interaction of anisotropic elastic half-space and structure under impact load

In this paper, a direct boundary element formulation for numerical modelling of threedimensional dynamic soil-structure interaction is briefly described. Formulation is applicable to problems involving isotropic and anisotropic elastic materials. It is based on the Laplace domain regularized boundary integral equations for the displacements under assumption of vanishing initial conditions and zero body forces. Mixed boundary elements are employed for the spatial discretization of the boundary integral equations. Subdomain technique is used to tackle problems involving piecewise homogeneous material properties. The described formulation is employed for the boundary element analysis of dynamic soil-structure interaction problem involving a structure which contains a cavity with a complex geometrical form. Soil is represented by a transversely isotropic elastic half-space. Effect of material anisotropy of half-space on the transient response of the embedded structure is assessed. It is observed that the shear modulus anisotropy have substantial impact on the displacements response. Influence of the Young’s modulus in the plane of isotropy is lesser but still pronounced.

Time-harmonic response of transversely isotropic and layered poroelastic half-spaces under general buried loads

A semi-analytical method is developed for solving the dynamic response of transversely isotropic, multilayered, and poroelastic half-spaces with different surface hydraulic conditions and subjected to time-harmonic vertical and horizontal loads buried in the layered half-space. The coupled governing equations of motion are presented in details in terms of the Biot's poroelastodynamic theory via the (u,p) formulation. The cylindrical system of vector functions is introduced to express the unknown primary quantities so that the coupled governing partial differential equations can be reduced and separated into two sets of first-order ordinary differential equations (i.e., the LM- and N-types). A recursive relation for the expansion coefficients among different layers is established by virtue of the stable and efficient dual variable and position method. Making use of the boundary and interface conditions, the fundamental solutions are obtained in terms of the vector-function system. The corresponding physical-domain solutions are then derived via an accurate semi-infinite integral algorithm. The developed fundamental solutions are carefully checked with existing solutions, and numerical examples are further presented to demonstrate the effect of material anisotropy, loading depth, material layering, and surface hydraulic condition on the dynamic response, which should be useful to design engineers. These solutions could be further served as benchmarks for future numerical methods.

3D dynamic responses of a multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure

Dynamic Green's function plays an important role in the study of various wave radiation, scattering and soil-structure interaction problems. However, little research has been done on the response of transversely isotropic saturated layered media. In this paper, the 3D dynamic responses of a multi-layered transversely isotropic saturated half-space subjected to concentrated forces and pore pressure are investigated. First, utilizing Fourier expansion in circumferential direction accompanied by Hankel integral transform in radial direction, the wave equations for transversely isotropic saturated medium in cylindrical coordinate system are solved. Next, with the aid of the exact dynamic stiffness matrix for in-plane and out-of-plane motions, the solutions for multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure are obtained by direct stiffness method. A FORTRAN computer code is developed to achieve numerical evaluation of the proposed method, and its accuracy is validated through comparison with existing solutions that are special cases of the more general problems addressed. In addition, selected numerical results for a homogeneous and a layered material model are performed to illustrate the effects of material anisotropy, load frequency, drainage condition and layering on the dynamic responses. The presented solutions form a complete set of Green's functions for concentrated forces (including horizontal load in x(y)-direction, vertical load in z-direction) as well as pore pressure, which lays the foundation for further exploring wave propagation of complex local site in a layered transversely isotropic saturated half-space by using the BEMs.

Undrained Yielding of Black Cotton Soil Treated with Calcium Carbide Residue

This study focuses on the use of calcium carbide residue (CCR) together with black cotton soil (BCS) to produce a stabilised material. Undrained shear strength of the CCR-treated soil was measured in this work. Optimum CCR dosage was obtained from Atterberg limits, pH and unconfined compressive strength tests. Triaxial tests were then conducted on the treated samples to study the effect of confining pressure on the pore pressure response. The results showed that the treated samples started to destructure only upon reaching their primary yield stress. The primary yield stress was shown to increase with the increase in CCR content. The variation of the predicted and observed yield surface was then determined by directly fitting an intuitively acceptable curve to the effective stress paths with the help of a destructuring parameter. This parameter was shown to depend upon the CCR content and confining pressures. The gradient of the ultimate state increased with the increase in CCR content. All stress paths appeared to cross the state boundary surface of the original untreated clay to reach a new peak. These results are attributed to the development of additional shear resistance of the CCR-treated soil because of the cementation and the effect of fabric anisotropy.

The effects of material anisotropy on secondary processing of additively manufactured CoCrMo

Components produced by near net shape additive manufacturing processes often require subsequent subtractive finishing operations to satisfy requisite surface finish and geometric tolerances. It is well established that the microstructure and properties of the as-built component are sensitive to the additive processing history. Therefore, downstream secondary processes may be affected by the as-built components’ mechanical behavior. In this work we study the sensitivity of secondary machining operations on CoCrMo samples produced via laser powder bed fusion. Utilizing novel high-throughput mechanical testing, microstructure characterization, and a rigorous statistical analysis we investigate the degree of material anisotropy present in the as-built material. We then study the effects of this anisotropy on secondary processing via slot milling experiments. Our results indicate that mechanical anisotropy is driven by both the morphology of the microstructure as well as crystallographic texture. The machining force response is correspondingly sensitive to these sources of anisotropy, which has the potential to impact how manufacturers finish additively built parts.

Non-coaxial behavior modeling of sands subjected to principal stress rotation

This paper attempts to clarify the necessary elements for describing the non-coaxial behavior of sand in the plasticity framework based on the critical-state soil mechanics. Such sand response to two representative loading types, the monotonic loading with fixed principal stress direction and rotation of principal stress direction, is the main focus. The present constitutive model can be regarded as an extension of the existing platform model for sand considering the inherent anisotropy. A novel non-coaxial flow direction involved in the plastic flow rule is the crucial feature, which is defined as the part of stress increment perpendicular to a reference direction related to the current stress direction through the Gram–Schmidt orthogonalization process. Such incorporation of the effects of the stress increment on the plastic deformation makes the model capture the non-coaxiality for the monotonic loading with fixed principal stress direction. In order to describe the plastic response induced by the pure rotation of principal stress direction, a set of mapping rules included in the bounding surface plasticity are formulated to develop plastic flow mechanism in the general multi-axial stress space. Besides, the effects of fabric anisotropy on simulating the non-coaxial plastic behavior are discussed. The results show that the above-mentioned modifications on these model ingredients make the theoretical simulation fit well with test data for Toyoura sand under the foregoing two loading conditions.

Anisotropic Strength of Granular Material Considering Fabric Evolution

Abstract The effect of fabric anisotropy on strength has not been considered in most strength criterions for granular material. Some criterions can describe the variation of material strength with stress-induced anisotropy, but micro-mechanism and physical meanings are undefined. Some criterions consider the effect of fabric anisotropy, but the evolution of fabric is ignored during loading by assuming a constant fabric tensor. Based on strength mechanical characteristics of granular material, in this paper, the relationship between macro stress and micro contact force of granular material is derived by micromechanics. Then, the concept of true stress tensor is proposed. An anisotropic strength criterion of granular material considering fabric evolution is established and its applicability is validated by comparing with test results for different granular materials. The analysis results indicate that the proposed anisotropic criterion can be utilized to describe the strength feature of anisotropic granular materials, which gives a way for the cause analysis of the strength of granular materials from the perspective of Microscopic mechanism.

Effect of material anisotropy on buckling load for laminated composite decks plates

New numerical results are generated for in-plane compressive biaxial buckling which serves to quantify the effect of material anisotropy on buckling loading. The coupling effect on buckling loads is more pronounced with the increasing degree of anisotropy. It is observed that the variation of buckling load becomes almost constant for higher values of elastic modulus ratio.

Effects of material anisotropy on impact mitigation in single column woodpile structures

We studied effects of material anisotropy on impact mitigation in single column woodpile structures. Local vibrations and nonlinear contacts of cylindrical members are key mechanisms of wave modulation in woodpile structures. We numerically obtained wave propagations in single column woodpile structures by changing longitudinal and/or transverse stiffness different from stiffness along the stacking direction. We found that changes in longitudinal and/or transverse stiffness altered wave propagation tendency as well as impact mitigation rate. We observed compact and wide waves propagated through single column woodpile structures with small stiffness ratio, while disintegrated but narrow waves with large stiffness ratio. According to dynamic behavior under impact loadings and frequency responses of woodpiles, bending vibration changed from 3rd to 1st mode and low energy band moved to relatively low frequency region when the single column woodpile structures had small stiffness ratio. This leads to increase impact mitigation characteristics of single column woodpile structures.

Effect of anisotropy on the dynamic electromechanical instability of a dielectric elastomer actuator

Electrically driven dielectric elastomer actuators (DEAs) are susceptible to an electromechanical instability because of a positive feedback between the applied electric field and the concomitant reduction in thickness of the membrane. This paper investigates the effect of material anisotropy on the dynamic electromechanical instability of a dielectric elastomer actuator when subjected to DC and AC voltage signals. We use a computationally efficient energy based Hamiltonian approach, which relies on the energy balance at the position of maximum overshoot in an oscillation cycle, for extracting the DC dynamic instability parameters of a biaxially prestretched anisotropic DEA. Analytical solutions are obtained for static and DC dynamic instability parameters. The AC dynamic instability fields are extracted by numerically integrating the differential equations of motion devised using the Euler–Lagrange equation. The trends of variation of the thickness stretch and electric field on the onset of static and dynamic pull-in instability with the material anisotropy parameter are presented. The results demonstrate a significant enhancement in the deformation and electric field on the onset of electromechanical instability with increase in the anisotropy parameter. The results of the present investigation can find potential application in the development and design of the dielectric elastomer actuator subjected to transient loading.