Effects Of Material Anisotropy Research Articles

A transient simulation of thermomechanical instability in metal-free friction materials with anisotropic properties

A two-dimensional non-linear transient thermomechanical model is developed to incorporate the anisotropic properties of a metal-free friction material sliding against a steel disc using a finite element approach. The main focus of the study is the effect of material anisotropy on thermomechanical instability (TMI) of friction linings used in automotive disc clutches or brakes. The model is validated by comparing the result to an existing eigenvalue solution. A parametric study on the material anisotropy revealed that for contact with the separation effect, an increase in elastic modulus E11 in the sliding direction and thermal conductivity K22 in the thickness direction discourage TMI formation. Conversely, a higher thermal conductivity K11 in the sliding direction and elastic modulus E22 in the thickness direction make the friction material more susceptible to TMI formation for a full-contact regime and contact with the separation effect. In addition, the effect of the thermal expansion coefficient was considered in this work.

Dynamic response of a transversely isotropic and multilayered poroelastic medium subjected to a moving load

The dynamic response of a transversely isotropic and multilayered poroelastic medium over an impermeable rigid base due to a surface moving strip load with constant speed is investigated. First, the moving load and induced response of any field quantity are expanded in the form of Fourier series. Then, based on the Biot's poroelastodynamic theory, the governing equations in terms of the displacement and pore pressure components are decoupled via a potential-function method, and the corresponding general solutions in each layer are derived. A recursive relation for the field quantities is established by utilizing the powerful dual variable and position method along with the continuity conditions on the layer interface. By virtue of the boundary conditions, semi-analytical solutions for the transversely isotropic and multilayered poroelastic medium with different surface hydraulic conditions are finally derived. After verifying the accuracy of the developed solutions by comparison with existing solutions, the effects of surface hydraulic condition, material anisotropy, layer thickness, material layering and load speed on the dynamic response are analyzed in detail. Results show that the effects of material anisotropy and layering are significant for the accurate assessment of the dynamic response induced by the moving strip load over a transversely isotropic and poroelastic medium. • Analytical method for anisotropic layered poroelastic media under moving load. • Governing equations in terms of Fourier expansion and potential-function method. • Layered poroelastic media via the stable dual variable and position method. • Effect of anisotropy, layering, and loading speed on the dynamic response.

Research on guided wave propagation characteristics of C/C thermal protection structures

Abstract Thermal protection structures (TPS) are the key component in the design and manufacture of the reusable launch vehicle. The probability of failure of TPS in an aerodynamic thermal environment during reentry is much higher than that of ordinary structures. There is an urgent need to develop a structural health monitoring (SHM) method that can achieve rapid diagnostic for TPS to realize the high reliability and maintainability of the reusable launch vehicle. Hence, this paper aims at the typical TPS made of C/C composite material, the feasibility of SHM methods based on the active piezoelectric guided wave was studied and verified. And the propagation characteristics of guided wave in the TPS such as the multi-mode, the signal frequencies of monitoring and the effects of material anisotropy on the propagation characteristics of the guided wave were analyzed. Then, a guided wave monitoring experiment of C/C TPS with simulation damage was carried out, and the variation of a guided wave under different damage levels was analyzed from the aspects of amplitude, phase, damage scattering and damage index. The results show that the SHM methods based on active piezoelectric guided wave can effectively monitor the damage and damage expansion on the surface of C/C TPS.

Investigation on the Influencing Factors of K0 of Granular Materials Using Discrete Element Modelling

Earth pressure coefficient at rest K0 is commonly estimated by empirical equations, which to date has had insufficient accuracy and universality. For better prediction, the investigation on the factors influencing K0 is required. A series of discrete element method (DEM) simulations of oedometer tests are conducted to verify the key factors influencing K0 of granular materials. The influences of initial fabric anisotropy, particle shape, initial void ratio, inter-particle friction angle is investigated. The evolution of microstructure is monitored during the tests to reveal the relationship between the microstructure evolution and K0 values. The results show that the effect of fabric anisotropy exists but is limited. Particle shape, initial void ratio, and inter-particle friction angle all significantly affect the K0 values alone. According to the DEM results, an attempt is made to propose a more reasonable empirical equation in which K0 is a function of relative density, critical state friction angle, and “shape factor”. This new empirical equation has higher accuracy and can consider the effect of particle shape, inspiring the determination of K0 values in practical engineering.

Effect of Material Anisotropy on the Mechanical Response of Automotive Steel under High Strain Rates.

A constitutive model for automobile steel with high elongation needs to be established to predict the dynamic deformation behavior under hydroforming applications. In order to clarify the confusing discrepancy in the essential parameters of the classical Cowper-Symonds (C-S) model, a series of automobile structural steels have been employed to investigate the strain rate response by conducting tensile dynamic deformation. Metallographic microscopy and orientation distribution functions were used to characterize the microstructure and texture components of the steels. The microstructure observation discloses that the matrix of all steels is mainly of ferrite and the texture constituent provides a framework for steel to withstand external deformation. The C-S model can be applied to simulate the dynamic deformation with satisfied expectations. It is concluded that the essential parameters D and p in the model show a specific relationship with the steel grade, and the parameter D is proportional to the steel grade and related to material anisotropy, while the parameter p is inversely proportional to the steel grade and has close links with the grain boundary characteristics.

3D topology optimization of sandwich structures with anisotropic shells

The development of a density-based 3D minimum compliance topology optimization approach for sandwich structures with anisotropic shells is presented. A constant thickness shell is enforced at the interface of a base structure through a two-step filtering approach. Homogenous effective properties of a cellular material are assigned to the base structure while the shell is treated as a constant stiffness laminate with anisotropic properties. Local shell normal vectors are obtained from the density gradient introduced in the second filtering step and local material orientations in the shell’s tangent plane are approximated based on the fabrication process of the structure. Simple approximating strategies using the Gauss map are presented for a fabric draping process and the fused filament fabrication additive manufacturing process. The effect of material anisotropy on the optimal topology is studied on the Messerschmitt Bölkow Blohm beam benchmark problem. An application to composite structures is then presented where a square, simply supported laminate is reinforced on one face by a topology optimized sandwich structure. Though manufacturability cannot be ensured in the current implementation, careful consideration of the optimization parameters allow to constrain the problem towards manufacturable solutions using additively manufactured cores.

Time-domain elasto-dynamic model of a transversely isotropic, layered road structure system with rigid substratum under a FWD load

In this paper, the time-domain elasto-dynamic model of a transversely isotropic, layered road structure system resting on rigid bedrock under a falling weight deflectometer (FWD) load is proposed by using the Laplace-Hankel transformation, and developing an improved propagator matrix method (PMM) with less calculation cost, higher calculation accuracy and better numerical stability. The improved model greatly avoids the problem of data overflow and maintains the computational efficiency of PMM. The present model is then verified by comparing with the corresponding FEM results. A parametric analysis is finally performed to discuss the effects of material anisotropy and rigid substratum on dynamic response of a road system, which is meaningful for design and practice of road engineering with modulus back-calculation.

3D asymmetric dynamic Green’s functions of a thermoelastic transversely isotropic solid by a method of potentials

A theoretical formulation is presented for the displacements, temperature and stresses in a 3 D transversely isotropic thermoelastic solid under arbitrary mechanical loads and heat flux. By using two scalar potential functions, 3 D patch-load, patch-heat source, point-load and point-heat source Green’s functions are given for the displacements, temperature and stresses. Basic governing equations of coupled thermoelasticity in transversely isotropic solids are presented in the cylindrical coordinates system. By means of two scalar potential functions, the four coupled governing equations for this class of problems are uncoupled into a 6th order and a 2nd order partial differential equations. Applying the Fourier expansions and Hankel transforms, the angular and radial variables are suppressed and 6th and 2nd order ordinary differential equations are obtained. By solving the ordinary differential equations, the potential functions, displacements, temperature and stresses are obtained in the Fourier-Hankel transformed space. By applying the Hankel inversion theorem, all responses are presented in the physical time-spatial space. To prove the validity of the analytical and numerical solutions, our results are compared with existing solutions reported in the literature. Numerical results are also included to show the effects of material anisotropy, elastic and thermal properties; and frequency of excitation on the responses.

Effect of fabric anisotropy on bearing capacity and failure mode of strip footing on sand: An anisotropic model perspective

Soils are inherently anisotropic, which may significantly influence their mechanical behavior and the performance of related geostructures. In this study, the response of strip footing on anisotropic sand was investigated using a J2-type deformation model coupled with state-dependent dilatancy and fabric evolution. The capability of the model was validated by simulating several element tests and a centrifuge test of strip footing. Footing tests with varying fabric orientations and relative densities were numerically simulated, revealing the influence of fabric anisotropy on the bearing capacity and its mobilization mechanism. Additionally, the effect of fabric on the failure mode of strip footing, including the pattern of the shear band, displacement field within the sand mass, and progressive failure characteristics, was also investigated. The simulation results obtained using an isotropic model indicate that neglecting the fabric anisotropy may cause severe overestimation of the bearing capacity of the strip footing.

A new analytical solution for elastic flexure of thick multi-layered composite hybrid plates resting on Winkler elastic foundation in air and water

A new analytical flexural solution based on double finite integral Fourier transform and trigonometric series differentiation procedures was developed for thick multi-layered composite hybrid rectangular plates resting on Winkler elastic foundation in air and water. The effect of material anisotropy, coupled hydro-mechanical loads, and underwater floor inclination angle,which were overlooked in the literature, is considered in this study. Furthermore, the predetermination of the shape deformation function is not required in our proposed analytical solution, which offers more accurate results. For the particular cases where the plate made of isotropic material is in air, the analytical results are compared with, and verified by the literature. Literature is lacking to investigate thick multi-layered composite hybrid rectangular plates with free edges and under hydro-mechanical load; hence our analytical results are compared with, and verified by,numerical analysis employing finite element method (FEM). The analytical results provide excellent agreement with both literature and the proposed FEM. FEM is shown to be time-intensive since the results converge after 60 seconds runtime with definition of 12159 elements during mesh refinement, yet the proposed analytical method demonstrates that the convergence can easily be achieved after 5 seconds runtime through selecting small values for Fourier terms.

The effect of material anisotropy on the mechanics of a thin-film/substrate system under mechanical and thermal loads

In this study, the stress analysis for an orthotropic thin film bonded to an orthotropic elastic substrate is addressed using both the analytical and finite element methods. The analytical method employs the integrodifferential formulation with the aid of membrane assumption. Utilizing the finite element method, the effect of orientation of the material principal directions are studied. The loading scenarios include a temperature gradient imposed on the film and a far-field uniaxial tension on the substrate. The results of current study indicate that the ratio of the film to the substrate stiffness plays a leading role in the film stress distribution. For the mechanical loading applied to the substrate, a soft thin film attached to a relatively stiffer substrate is preferred. The film can tolerate the induced thermal stresses as it is bonded to a softer host structure. The rotation angle of material orthotropy directions significantly affects the stress singularity near the film edges up to a certain extent.

Modeling and analysis of material anisotropy-topology effects of 3D cellular structures fabricated by powder bed fusion additive manufacturing

For lightweight cellular structures fabricated via powder bed fusion additive manufacturing (PBF-AM), both the material anisotropy and the cellular topology design are both important design factors. In this work, a direct stiffness matrix-based analytical modeling approach was employed for the evaluation of material anisotropy-topology effects on three representative 3D cellular structures (auxetic, BCC and octahedral). The established models were verified via experimentation with samples fabricated by EB-PBF using Ti6Al4V as material, using the material anisotropy information established experimentally using single struts with different build orientations (0°, 15°, 30°, 45°, 60°, 75° and 90°). The predicted mechanical properties of the Ti6Al4V cellular structures showed good agreement with experimental results. It was shown that both the strength and elastic modulus anisotropy of the materials affect the strength of the cellular structures, which must be determined based on the topology design. In addition, the material anisotropy-topology effects on cellular structures of varying cellular pattern sizes were also investigated in order to quantify the pattern size effects. It was found that the pattern size effects and the material anisotropy effects can be decoupled during the design of the mechanical properties of these cellular structures.

A generalized criterion for fatigue crack growth in additively manufactured materials – Build orientation and geometry effects

The effect of material anisotropy on the fatigue crack growth (FCG) behavior in additively manufactured materials is investigated by developing an energy-based criterion. The criterion is developed based on the strain energy density concept in an anisotropic domain and considers the effects of specimen geometry by introducing the T-stress in the solution. The proposed criterion is examined by predicting the FCG experimental results available in the literature for 3D-printed Inconel 718 and 17-4PH stainless steel components built in different orientations. It is found that both material anisotropies resulting from build orientation and the T-stress play remarkable roles in FCG behavior of 3D-printed components.

An exact closed-form solution of three-dimensional transient Green's functions in a constrained transversely isotropic half-space

In this paper, we derive an exact closed-form solution of three-dimensional transient Green's functions (GFs) at the free surface of a constrained transversely isotropic (TI) half-space due to an arbitrarily oriented surface point force of Heaviside time variation. The solution clearly delineates the distinct features of body waves (P-, SV- and SH- waves) as well as Rayleigh surface wave in displacement components and demonstrates the travel time of each wave amplitude in terms of inequalities among elastic coefficients. It is further shown that owing to material anisotropy, the radial and angular displacements due to horizontal point force may contain a special disturbance, which attenuates proportionally to the inverse square of epicentral distance from the source whilst varies linearly with time. This novel feature is attributed to the peculiarities of shear wave splitting, a consequence of polarization, with different velocities, of the SV- and SH- waves in TI materials, and as such, does not exist in isotropic materials. It is also worthwhile to mention that for this constrained anisotropy, the Rayleigh wave function is degenerated into a new elegant formulation whose real root specifies the Rayleigh wave velocity in terms of elastic coefficients. Moreover, the transient GFs are computed for the entire range of the elastic coefficients including also the case when the Rayleigh function has complex conjugate roots. For validation, the new GFs derived in this paper are suitably degenerated into the corresponding solutions for the isotropic (Poisson's) material and are compared with the existing solutions. The effect of Poisson's ratio on the isotropic response functions is graphically illustrated and so is the effect of material anisotropy for different synthetic TI materials.

Microstructure effects on the material behaviour of magnesium sheet in bending dominated forming

Abstract Predicting springback in the bending of magnesium sheet is difficult because it has high mechanical anisotropy leading to significant differences in the material behaviour in tension and compression. The tension/compression yield mismatch in magnesium is affected by the twinning behaviour which depends on the grain size and the direction of loading in regard to the crystal (C-axis) orientation. In this study the C-axis orientation of magnesium sheet was controlled by cutting sheets from a hot rolled block. Combined with heat treatment to produce different conditions for grain size and material strength this enabled for the first time to separately analyse the effect of material strength, grain size and C-axis orientation on the springback of AZ31 sheet metal. Pure and V-bending tests were performed and combined with advanced Digital Image Correlation (DIC) to experimentally determine the neutral layer shift for different levels of outer fibre bending strain before and after springback. Our study shows that springback in AZ31 reduces with increasing grain size but that it does not change with the C-axis orientation despite a reversal in the neutral layer position. The variation of springback shows more correlation with the bending yield strength measured directly from the pure bend test rather than the tensile yield strength and strongly correlates with the change in neutral layer shift in relation to grain size. Based on the experimental results analytical equations were developed to account for the effect of grain size on springback in magnesium. The model assumes the fully plastic, plane strain bending of strip and takes into account the effect of the tension/compression yield mismatch on the neutral layer position to determine the resulting bending moment. The developed equations provide, for the first time, a simple and clear mathematical explanation for the effect of material anisotropy (Yield strength mismatch) on the bending behaviour and springback of magnesium. If tuned with experiments, the model enables the estimation of springback as a function of the microstructure (grain size) in industrial practice.

Acoustic Vibration of Hexagonal Nanoparticles With Damping and Imperfect Interface Effects

Abstract In this paper, acoustic vibration of hexagonal nanoparticles is investigated. In terms of the spherical system of vector functions, the first-order differential equation with constant coefficients for a layered sphere is obtained via variable transformation and mass conservation. The propagation matrix method is then used to obtain the vibration equation in the multilayered system. Further utilizing a new root-searching algorithm, the present solution is first compared to the existing solution for a uniform and isotropic sphere. It is shown that, by increasing the sublayer number, the present solution approaches the exact one. After validating the formulation and program, we investigate the acoustic vibration characteristics in nanoparticles. These include the effects of material anisotropy, damping, and core–shell imperfect interface on the vibration frequency and modal shapes of the displacements and tractions.

Partial slip contact analysis for a monoclinic half plane

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

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.