Presence Of Material Anisotropy Research Articles

A ray tracing approach to focusing ultrasonic beams in isotropic and anisotropic solids

Focal depths in solid materials are generally calculated using analytical expressions that rely on the paraxial approximation (i.e., small angles related to shallow focusing). However, with increasing use of highly focused probes for acoustic microscopy and backscattering studies, these assumptions are often challenged. Additional challenges are posed by the presence of material anisotropy within the solid. In this presentation, we present a ray tracing based approach to characterize ultrasonic beam focusing when using highly focused ultrasonic transducers. The results are compared to traditional methods to calculate focal regions to evaluate the range of applicability for isotropic and anisotropic materials. For isotropic solids, a non-paraxial focusing equation is derived and compared to the conventional focusing equation for both normal incidence and oblique incidence immersion setups. Both focusing equations are compared through ray diagrams where the proximity to the true geometric focus is explored. The proposed focusing equation results in a closer approximation to the geometric focus, a smaller beam cross-section, and a greater time convergence compared to the conventional focusing equation. Lastly, the results are expanded to anisotropic media where potential for multiple foci and complex beam behavior arise.

On ultrasound propagation in composite laminates: advances in numerical simulation

The growing use of composite materials for aerospace applications has resulted in the need for quantitative methods to analyze composite components. Ultrasonic guided waves constitute the physical approach for nondestructive evaluation (NDE) and structural health monitoring (SHM) of solid composite materials, such as carbon fiber reinforced polymer (CFRP) laminates. Ultrasound based NDE methods are commonly used in the aerospace field, but ultrasonic wave behavior can be complicated by the presence of material anisotropy, complex geometries (e.g., highly curved parts, stiffeners, and joints) and complex geometry defects. Common defects occurring in aerospace composites include delaminations, porosity, and microcracking. Computational models of ultrasonic wave propagation in CFRP composites can be extremely valuable in designing practical NDE and SHM hardware, software, and methodologies that accomplish the desired accuracy, reliability, efficiency, and coverage. Physics based simulation tools that model ultrasonic wave propagation can aid in the development of optimized inspection methods and in the interpretation of NDE data. This paper presents a review of numerical methodologies for ultrasound and guided wave simulation in fiber reinforced composite laminates summarizing the relevant works to date, different methods, and their respective applications.

Modal properties of elastic surface waves in the presence of material anisotropy and prestress

Elastic surface waves have been widely applied across many disciplines such as crystallography, seismology, non-destructive evaluation (NDE) and microfluidics. Thorough understanding and accurate prediction of modal properties of surface waves is essential for successful practical applications. However, computations of surface waves could be challenging due to two frequently encountered complications: material anisotropy and acoustoelasticity induced by prestress. Although a lot of approaches, such as solving secular equations, matrix method and perturbation method, have been developed to deal with these complications, some of them may suffer from mathematically algebraic complexity, tedious numerical coding and limited applicability. A method, combining the semi-analytical finite element (SAFE) method and perfectly matched layers (PMLs), is proposed in this paper for computation of the modal properties of surface waves. As the governing equations of the model are formulated based on acoustoelasticity, the model can simulate surface waves in materials with anisotropic properties and prestress. The governing equations of the model are reorganized in a standard finite element eigenvalue formalism which can be implemented into a commercial software, enabling easy access of the method. Therefore, the method provides a powerful forward modelling to understand the response of surface waves to material anisotropy and prestress. The method is firstly validated by analytical solutions as well as perturbation solutions available in the literature and then applied to two challenging cases to demonstrate its capability.

Axial–torsional vibrations of rotating pretwisted thin walled composite beams

Axial–torsional vibrations of rotating pretwisted thin-walled composite box beams exhibiting primary and secondary warping are investigated. Considering the nonlinear strain–displacement relations, the coupled nonlinear axial–torsional equations of motion are derived using Hamilton's principle. Ignoring the axial inertia term leads to differential equation of motion in terms of elastic torsion in the case of axially immovable beams. Centrifugal load in the presence of material anisotropy and pretwist angle leads to an induced static torque. The nonlinear equation should be linearized about the corresponding equilibrium state to obtain the linear differential equation of motion. Extended Galerkin's method is utilized to achieve the proper eigenvalue problem. The results obtained in this paper seek to clarify the individual and collective effects of axial loading, pretwist, stagger and fiber angles on the torsional behavior of the non-uniform thin-walled composite blades. The results are compared to available analytical and experimental results in the literature which reveals excellent agreements. The outcomes of this study are expected to offer better predictions of the dynamic behavior of this kind of structures in general, and in design of rotor blades of turbo-machinery, in particular.

Polarization state and level repulsion in two-dimensional phononic crystals and waveguides in the presence of material anisotropy

We investigate the polarization of Bloch waves in two-dimensional piezoelectric phononic crystals and phononic crystal waveguides managed therein. It is found that in addition to the strong coupling induced for waves polarized in the plane of the periodic structuration, a weaker but non-negligible coupling of polarization components originates from material anisotropy. Numerical illustrations are given for an array of air holes in lithium niobate arranged according to a square lattice. It is observed that when a band mostly polarized in-plane gets close to a band mostly polarized out-of-plane, a phenomenon of repelling can occur, that in some instances introduces a local band gap. This interaction is accompanied by a transfer of the polarization state from one band to the other.

Full-vectorial analysis of optical vortex propagation in anisotropic cubic-quintic non-linear optical medium

This paper presents for the first time a full-vectorial analysis of optical vortex propagation in anisotropic cubic-quintic (CQ) non-linear medium. The purpose is to investigate the energy transfer mechanism and stability between orthogonal field components and how they are affected by the presence of material anisotropy in CQ materials. The numerical simulations were carried out via a three-dimensional finite difference based beam propagation method (3D-FD-BPM) which is capable of handling variations in any of the permittivity tensor components. Therefore, in this work we allowed all tensor components to vary independently and simulate vortex propagation for distances several times longer than the diffraction length. We expect that this work can provide new and important information regarding the behavior of these objects that may become valuable for the design of new photonic devices.

Polarization and dispersive properties of elliptical-hole photonic crystal fibers

We survey the properties of photonic crystal fibers with elliptical air holes, examining mode shapes, birefringence, group velocity walkoff and dispersion, and cutoff conditions. We find new types of behavior for each quantity and demonstrate the possibility achieving large birefringence with zero walkoff in the single-mode regime. We show that the dispersive properties of the vector modes are closely tied to those of the so-called fundamental space filling modes, and that at long wavelengths, the fibers exhibit a single-polarization single-mode regime of propagation without the presence of material anisotropy.

On the implementation of anisotropic yield functions into finite strain problems of sheet metal forming

Abstract In this article the implementation of anisotropic yield functions into finite element investigations of orthotropic sheets with planar anisotropy is discussed within a plane-stress context. Special attention is focused on the proper treatment of the orientation of the anisotropic axes during deformation into the finite-strain range. As an example problem the hydrostatic bulging of a membrane is considered in conjunction with a recently proposed anisotropic yield function. It is shown that the aspects of the plane-stress assumption, which do not come into consideration in isotropic analyses, can play an important role on the accuracy of the solution when the rotation of the orthotropic axes enters the computation directly due to the presence of material anisotropy. When the material anisotropy is considered and when the deformation of the workpiece is not limited to the plane of the undeformed sheet (such as cup drawing, hydrostatic bulging, etc.), the numerical experiments indicate that the only correct formulation is the one based on numerically imposing the requirement that for the plane-stress application, the in-plane material axes have to remain in the plane of the sheet during the deformation.

Experimental measurement of the near tip strain field in an iron-silicon single crystal

Experimental results are presented for the plastic deformation field near a crack (200 μm wide notch) tip in an iron-3% silicon single crystal. The specimen was loaded in four point bending and the measurements were made at zero load after extensive plastic deformation had occurred. Results are given for a crack on the (011) plane with its tip along the [01|T] direction. The surface deformation field was measured using moire microscopy and a grating on the specimen surface. The in-plane Almansi strain components have been obtained by digitally processing the moire fringes. A well-structured asymptotic field has been found at a distance of 350–500 μm from the notch tip, where the maximum plastic strain is about 9%. The asymptotic field is observed to be composed of many distinct angular sectors. Three (six symmetric) of these sectors are found to have approximately constant strains. In a fourth (two symmetric) sector, the surface strains are approximately 1/ r singular. Between these sectors there are interconnecting transition sectors. The location of the stress state on the yield surface and the active slip systems in each sector are identified by assuming that the plastic strain rates are normal to a Schmid law yield surface. The slip systems identified in this manner show excellent agreement with direct observations of the slip texture on the surface and dislocation etch pits in the interior of the specimen. The experimental strain measurements also show that the constant strain sectors are regions in which unloading occurs. Because of this unloading, the crack tip stress and deformation state is substantially different from an HRR type field which assumes proportional loading. This strong nonproportional loading is thought to be caused by the presence of material anisotropy. The nonproportional loading also provides a large amount of crack tip shielding that is evidence of a toughening mechanism that results from the presence of material anisotropy.

Finite deformation analysis of restrictions on moving strong discontinuity surfaces in elastic-plastic materials : Quasi-static and dynamic deformations

This paper reports the results of a finite deformation study of the conditions under which propagating surfaces of strong discontinuity (across which components of stress, strain or material velocity jump) can exist in a general class of purely mechanical elastic-plastic solids. By enforcing the standard weak continuum-mechanical requirements of momentum conservation and geometrical compatibility, together with skeletal constitutive assumptions that are in broad agreement with experimental results and that subsume many specific material models, we derive explicit jump conditions that must be satisfied by such moving surfaces (and which in many cases rule out their existence). Our results confirm many of the restrictions derived previously via a small-displacement-gradient formulation, showing how those must be interpreted in a finite deformation situation. But they also demonstrate that certain conditions adopt a more complex form. especially in the presence of material anisotropy. The cases of quasi-static and dynamic deformations are considered separately, and it is shown how the results are related. Finally, we derive a thermodynamically motivated jump dissipation inequality that is sensibly applied to an extremely broad class of elastic-plastic materials ; the quasi-static version of this is identical in form to a dissipation inequality derived in a different manner by knowles ( J. Elasticity 9, 131. 1979) for propagating equilibrium shocks in purely hyperelastic materials.

Residual stress determination in aluminium using electromagnetic acoustic transducers

The residual stresses in a shrink-fit specimen were measured ultrasonically, using shear-horizonal (SH) waves transmitted and received by noncontacting electromagnetic acoustic transducers. The presence of stress induces a small change in the velocity of the SH-waves. The difference in velocities of orthogonally polarized SH-waves (acoustic birefringence) was measured with a simple time-interval averaging system; this velocity difference can be related to the difference of principal stresses. The presence of material anisotropy (texture) in the specimen also causes relative velocity changes comparable to stress-induced changes. A simple method was used to remove the anisotropy-dependent component of the total relative velocity change, thereby allowing a determination of residual stress. This method consisted of measuring the birefringence in unstressed reference specimens and subtracting it from the birefringence measured at stressed locations. For the specimen used here, good agreement between theoretical and experimental values of stress was obtained.