Elastic Field Research Articles

Thermo-mechanical behavior of 2D functionally graded porous-auxetic metamaterial rotating disk with an auxetic foundation

In the present study, the thermo-mechanical behavior of two-directional functionally graded porous-auxetic metamaterial rotating disk (2D-FGPAMRD) has been analyzed. The rotating disk subjected to combination of transient thermal and steady mechanical loads and supported by an auxetic foundation. Haber-Schaim (H-S) frictionless elastic foundation model is considered to drive the structure-structure interaction. The governing equations are obtained based on the thermoelasticity theory. The response of disk to mechanical and thermal loads has been obtained by solving nonhomogeneous governing equations. To this end, the alternating direction implicit (ADI) finite difference scheme and combination of state-space and differential quadrature (DQ) methods have applied to solve the Fourier heat conduction and thermoelasticity equations, respectively. In the numerical examples, the effects of porosity and auxeticity, as well as inhomogeneity indices of the disk on its thermo-mechanical behavior have been investigated for the first time. The results reveal that, the elastic field components of rapid heating disk are significantly affected by the nature of temperature diffusion, inhomogeneity indices and the auxeticity of the disk material. Besides, the changes of thermal expansion gradient indices provide a relaxation in the normal transverse stress.

Determination of the Strain Tensor and the Elastic Stress Fields in a Diamond Plate with a High Bending Curvature Using Local Laue Diffraction Data

Cylindrically bent diamond single-crystal plates have a great potential for creating energy dispersive spectrometers and focusing crystal monochromators. When they are designed, it is necessary to take into account the significant stresses that appear on bending the plates. The strain tensor and the elastic stress fields in a cylindrically bent single-crystal (110) diamond plate are calculated. The calculations are based on experimental data obtained by local Laue diffraction. The calculation results can be used to design new X-ray optical devices with the ability to control their parameters.

Elastic crack-tip field in hydride forming metals under hydrogen chemical equilibrium

Elastic crack-tip field in hydride forming metals under hydrogen chemical equilibrium

Thermomechanical modeling of dissimilar-material interfaces in composite structures

Due to the heterogeneities in material properties of strongly-bonded multi-material composite structures, there exist singularities of the stress fields at the material interface as well as the interface corners on the bounding surfaces. The finite-element method is probably the only plausible option to analyze the stress around such interfaces between dissimilar materials subjected to combined thermo-mechanical loading. In this article, we propose a novel mathematical model for the computational analysis of coupled thermo-elastic fields with perfectly bonded interfaces of dissimilar isotropic/orthotropic composite-material structures. A scalar function of the spatial variables, namely, the displacement function, is used to integrate the temperature field and the associated displacement-function field to obtain two nonhomogeneous partial-differential equations of equilibrium that govern two thermo-mechanical sub-problems defined in terms of the appropriate conditions of orthogonal temperature gradients. For a specific temperature field, obtained as a steady-state solution of the given thermal problem, the two thermo-mechanical sub-problems are solved independently to obtain the full-field solution of the thermo-elastic problem using the method of superposition. As an alternative to the conventional computational approach, we employed a single variable semi-analytical method of solution to determine the thermo-mechanical response of the multi-material composite structures. The continuity of the temperature and the heat flux in the thermal field problem and the continuity of the displacement and the traction vectors are utilized in the elastic field problem to determine the appropriate algebraic equations suitable for nodal application at the interfaces as well as interface corners on the boundaries of the respective problems. The quantitative comparison of the present displacement-function solutions to several mixed-boundary-value problems with those obtained by the conventional finite-element method verifies the high accuracy and effectiveness of the present method. This computational model has potential applications in identifying near-interface high-stress locations as well as possible critical regions of the physical boundary of composite structures subjected to mixed modes of thermal and mechanical loadings.

Formula omitted]-TFA based multiscale analysis of failure in elasto-plastic composites

This paper describes a novel homogenization methodology for analyzing the failure of elastoplastic composite materials based on elastic and eigen influence tensors-driven transformation field analysis (E2-TFA). The proposed technique considers the microscopic eigenstrain field accounting for intra-phase damage and inelastic strains. This results in realistic computations by alleviating the post-damage stiffness response, which is a drawback of TFA-based methods. We attain computational efficiency by identifying the preprocessing data solely from the elastic and eigen transformation functions and adopting a reduced order modeling technique with a piecewise constant eigenstrain field throughout the subdomains. The performance of the model is assessed by simulating the response for (a) the representative volume element (RVE) as a homogenized continuum and (b) the various composites under complex load histories with intricate macroscale morphologies. Furthermore, the nonlinear shear stress–strain response of a glass fiber composite is calculated and compared to experimentally measured fracture initiation parameters, failure plane orientation, and strain histories. Finally, we show that E2-TFA can accurately and efficiently capture damage and inelastic deformations in order to estimate the mechanical response of composite materials in a better way.

Designing L21-Co2TiAl precipitate-strengthened ferritic alloys with excellent high-temperature mechanical properties

Recently, Fe–Cr–Ni–Al–Ti ferritic alloys strengthened by L21-type Ni2TiAl precipitates have demonstrated superior high-temperature strength compared to conventional ferritic steels. However, it still shows a lower high-temperature strength than that of Ni-based superalloys. Therefore, in the current study, we designed new ferritic alloys to improve the high-temperature strength by introducing L21-Co2TiAl precipitates, known as having better high-temperature properties than the Ni2TiAl structure. Specifically, the Ni element has been replaced with the Co element. In addition, the Ti element has been adjusted because the structural evolutions of precipitates, such as composition, lattice misfit and size rely on the Ti content. For instance, the addition of 2 wt% Ti forms a semi-coherent Co2TiAl precipitate with a relatively low density of misfit dislocations. More Ti addition up to 6 wt % leads to an increase in the lattice parameter of the precipitate, while that of the Fe matrix remains unchanged, which results in an increased lattice misfit. The increased lattice misfit causes a higher amount of misfit dislocations, which leads to a reduction of the elastic strain field around the precipitates. It was found that the semi-coherent interface with a high level of the elastic strain field (2 wt % Ti), as compared to the precipitates with a high amount of misfit dislocations (4 and 6 wt % Ti), plays a crucial role in enhancing the mechanical properties at 973 K. In addition, the designed ferritic alloys show superior strength, compared to the previously-reported ferritic alloys.

Determination of the Strain Tensor and the Elastic Stress Fields in a Diamond Plate with a High Bending Curvature Using Local Laue Diffraction Data

Determination of the Strain Tensor and the Elastic Stress Fields in a Diamond Plate with a High Bending Curvature Using Local Laue Diffraction Data

A hybrid dislocation deforming two welded anisotropic crystals

ABSTRACT The elastic field of an angular dislocation line that has a branch placed in a crystal of a bi-material while the other branch is along a strongly bound or welded interface, is found when the two crystals have anisotropic properties. Since the field of this angular dislocation depends on the elastic constants of the two crystals, it can be called hybrid dislocation (HD). To face this problem already treated using isotropic elasticity, the analysis first formulates the elastic field of a closed dislocation loop whose surface S is that of a circular sector centred in a point O of the interface. By virtue of the Saint Venant principle, when the circular segment moves far away from O, the field induced by the loop near O tends towards that of a HD. The calculation is possible thanks to the knowledge of the Green’s tensor of the bi-material which has already been the subject of several works. Thanks to the use of polar coordinates, the solution is reduced to convenient line-integral expressions which make the calculation faster. This work complements a previous approach to the HD problem based on the integral formalism. By combining two HD’s, it also gives the solution to the problem of an interfacial angular dislocation. Some applications illustrate anisotropy effects and highlight an inability of integral formalism to deal with a interfacial branch strictly in the interface.

Two-dimensional problem of an infinite matrix reinforced with a Steigmann–Ogden cylindrical surface of circular arc cross-section

The plane strain problem of an elastic matrix subjected to uniform far-field load and containing a Steigmann–Ogden material surface with circular arc cross-section is considered. The governing equations and the boundary conditions for the problem are reviewed. Exact complex integral representations for the elastic fields everywhere in the material are provided. The problem is further reduced to the system of real variables hypersingular boundary integral equations in terms of the first component of the surface stress tensor (surface stress) and the remaining component of that tensor and its second derivative, along with various problem parameters. The two unknowns are then approximated by the series of trigonometric functions that are multiplied by the square root weight functions to allow for automatic incorporation of the tip conditions. The unknown coefficients in series are found from the system of linear algebraic equations that is solved using standard collocation method. The numerical examples are presented to illustrate the influence of dimensionless parameters. The connection of the problem with that of rigid circular arc is discussed.

Analysis of three-dimensional cracks horizontally placed in transversely isotropic FGMs under interior compressive stresses

This paper develops the dual boundary element method (DBEM) using a new fundamental singular solution. This new solution is the elastic fields of transversely isotropic multilayered materials of infinite extent under point concentrated loads. The discretization technique is utilized to approximate arbitrary variations of functionally graded materials (FGMs) with transverse isotropy in a graded direction. The proposed DBEM is used to analyze the three-dimensional crack problems in FGM halfspaces. The penny-shaped and elliptical cracks are horizontally placed on the interface between the FGM layer and homogeneous halfspace and are subjected to uniform compressive stresses on crack surfaces. The stress intensity factors are provided to understand the fracture behaviors of transversely isotropic FGMs. An influential factor is defined to describe the influence of the anisotropy of the FGMs on stress intensity factors. Results show that the anisotropy and heterogeneity of materials exert an obvious influence on the fracture properties of crack problems.

A continuous leakage real-time localization method based on space phase image of elastic wave field with improved CNN

To satisfy the requirement of real-time monitoring and locating of the leakage in large pressure vessels, a method of leakage source location based on improved convolutional neural network (CNN) is proposed in this paper. In this method, the polar coordinate model of elastic wave propagation excited by continues leakage is established, and the improved CNN is constructed according to its spatial field distribution, and the training set of the network is obtained by finite element simulation. The experimental results show that this method can be applied to locate the leak at any time after it occurs, and only a single sensor array is used. In the experiment of 1 m2 stiffened test plate, the absolute distance error was less than 0.1 m and the absolute angle error was less than 0.1 rad in 90.2 % of all samples.

Diffusion of hydrogen in the Volterra elastic fields around dislocations in α-Ti: Coupling DFT calculations and elasticity method

Hydrogen around dislocation has a great influence on the mechanical properties of Titanium (Ti) alloys. In this study, the diffusion of hydrogen around dislocations in α-Ti alloys is investigated by coupling density functional theory (DFT) calculations and the elasticity method. Initially, the attempt frequency and hopping activation energy of hydrogen atom in the α-Ti lattice are calculated using the DFT method under various simple strain fields, including volume strain, biaxial strain, and shear strains, within a strain range of −2%–2 %. It is observed that both volume strain and biaxial strain have the most pronounced effects on the hopping activation energy of hydrogen atom, while the attempt frequency remains relatively unaffected across different strain conditions. Subsequently, the hopping activation energy in the elastic strain field has been parameterized using an elasticity method based on elastic dipole and diaelastic polarizability. Using the elasticity method, an analysis is conducted on the effective activation energy of hydrogen atoms and their hopping tendencies in the Volterra elastic strain fields around the perfect edge and screw dislocations. The elastic strain field around screw dislocation enhances the diffusion of hydrogen atoms and simultaneously promotes their migration toward the dislocation core. In the vicinity of edge dislocation, the tensile elastic strain field enhances the diffusion of hydrogen atoms and facilitates their migration toward the dislocation core. Conversely, the compressive strain field retards the diffusion of hydrogen atoms and promotes their migration away from the dislocation core or towards regions with tensile strain.

Lead-free Zr-doped ceria ceramics with low permittivity displaying giant electrostriction

Electrostrictors, materials developing mechanical strain proportional to the square of the applied electric field, present many advantages for mechanical actuation as they convert electrical energy into mechanical, but not vice versa. Both high relative permittivity and reliance on Pb as the key component in commercial electrostrictors pose serious practical and health problems. Here we describe a low relative permittivity (<250) ceramic, ZrxCe1-xO2 (x < 0.2), that displays electromechanical properties rivaling those of the best performing electrostrictors: longitudinal electrostriction strain coefficient ~10−16 m2/V2; relaxation frequency ≈ a few kHz; and strain ≥0.02%. Combining X-ray absorption spectroscopy, atomic-level modeling and electromechanical measurements, here we show that electrostriction in ZrxCe1-xO2 is enabled by elastic dipoles produced by anharmonic motion of the smaller isovalent dopant (Zr). Unlike the elastic dipoles in aliovalent doped ceria, which are present even in the absence of an applied elastic or electric field, the elastic dipoles in ZrxCe1-xO2 are formed only under applied anisotropic field. The local descriptors of electrostrictive strain, namely, the cation size mismatch and dynamic anharmonicity, are sufficiently versatile to guide future searches in other polycrystalline solids.

Scratch-induced surface formation mechanism in C/SiC composites

Due to the extremely complex composition of C/SiC composites, their material removal mechanisms are significantly different from those of conventional single-phase ceramic materials. Therefore, the grinding removal mechanism of C/SiC composites must be investigated so that the components based on these composites can be machined efficiently and with low damage. In this paper, nano-scratch experiments with various cutting depths are carried out along different fiber orientations to simulate the material removal process in grinding and theoretically clarify the damage failure mechanism based on different cutting thicknesses. According to the assessment of surface and subsurface morphology of the various constituents in the scratch grooves regarding different fiber orientations, the multiple brittle breakage modes and surface integrity of carbon fiber are revealed. Green’s function is applied to establish a half-space anisotropic analytic elastic stress field considering the microstructural characteristics of material, and the crack nucleation and propagation principles during micro brittle fracture regime for nano-scratch experiment are elucidated based on the fracture mechanics and the maximum principal stress criterion. The formation mechanism of machined surface morphology in macro brittle removal process is investigated under the crack deflection effect at the weak interface and based on the elastic foundation beam theory. The related findings can provide a reasonable reference framework for optimizing the grinding technology, material and tool design regarding C/SiC composites.

Piezoresistive Theory and Numerical Calculation for Carbon Nanotube Polymer Composite.

A three-dimensional theory has been established for the piezoresistivity of carbon nanotube (CNT) polymer composites. Based on the Mori-Tanaka method in meso-mechanics theory and considering quantum tunneling effect between CNTs, an approach to calculate equivalent electrical conductivity of composites was proposed. On this basis, a piezoresistive theory, which incorporates the effect of composites' geometric nonlinearity, was developed for CNT polymer composites. The theory is dependent only on some basic physical parameters of the materials. A finite element formula of the theory for the numerical calculation of piezoresistivity was presented from the analysis of both elastic and electric fields. Numerical simulations demonstrated that the results predicted by the theory were in good agreement with those of the experimental tests. Parameter sensitivity analysis revealed that when both the potential barrier height of the matrix and the initial average separation distance between CNTs increased, the piezoresistivity obviously increased. However, with the increase in aspect ratio and CNT conductivity, the piezoresistivity decreased gradually. A practical engineering application of this theory is also provided.

A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials

In this paper, we propose and analyse a numerical method to solve 2D Dirichlet time-harmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure (P-) and Shear (S-) waves via a suitable Helmholtz–Hodge decomposition. For the approximation of the two scalar potentials we apply a virtual element method associated with different mesh sizes and degrees of accuracy. We provide for the stability of the method and a convergence error estimate in the L2-norm for the displacement field, in which the contributions to the error associated with the P- and S- waves are separated. In contrast to standard approaches that are directly applied to the vector formulation, this procedure allows for keeping track of the two different wave numbers, that depend on the P- and S- speeds of propagation and, therefore, for using a high-order method for the approximation of the wave associated with the higher wave number. Some numerical tests, validating the theoretical results and showing the good performance of the proposed approach, are presented.

Analysis of Stress Concentration in Functionally Graded Plates with Linearly Increasing Young’s Modulus

In this article, the strain and stress analyses of functionally graded plates with circular holes that are subject to a uniaxial far-field traction load are analytically considered. The Young’s modulus is assumed to vary linearly along the radial direction around the hole. The adoption of such a type of inhomogeneity variation can be justified as follows. Firstly, and among all the possible variations of stiffness, the linear one is indeed the simplest inhomogeneity distribution. Surprisingly however, according to our knowledge extent, the associated elastic fields were not yet addressed in the literature. Secondly, a linearly varying stiffness could reasonably imply a remarkable advantage from a technological point of view. In fact, unlike nonlinearly varying stiffness plates, manufacturing routes are only required to handle constant variations throughout the radial domain. After recalling the basic equations for plane stress elasticity, the displacement, strain, and stress fields around the hole were numerically tackled and discussed for different stiffness ratios. A comparison was also carried out with other Young’s modulus distributions that have been commonly employed in the literature.

Numerical simulations of pure quasi-P-waves in orthorhombic anisotropic media

The accurate simulation of anisotropic media is critical in seismic imaging and inversion. In recent years, some scholars have dedicated efforts to the study of precise elastic waves in anisotropic media; however, it is easy to separate P-wave and S-wave from elastic wave fields in isotropic media but difficult to separate them in anisotropic media. To address this issue, others have proposed pseudo-pure-wave equations based on the theory of wave-mode separation, but shear wave interference still exists. Therefore, we derived the first-order pure quasi-P-wave equation with no shear wave component in orthorhombic anisotropic media (ORT) which is common in the Earth’s crust and has very important research value. The presence of a pseudodifferential operator in the equation poses a challenge for solving. In order to solve the pure wave equation, we decomposed the original pseudodifferential operator into an elliptic differential operator and a scalar operator, both of which are easily solvable. In addition, we extended the equation from ORT media to tilted ORT (TORT) media. The example results indicate that our pure quasi-P-wave equation can yield a more stable and accurate P-wave field. The pure wave equation we propose can be applied in reverse time migration (RTM), the least squares RTM (LSRTM), and even the full waveform inversion (FWI).

Generalized strain-based finite element for non-linear stability analysis of beams with thin-walled open cross-section

Based on the generalized strain theory a shear-deformable finite element is developed for nonlinear stability analysis of thin-walled open-section beams in multibody systems. In this formulation a finite number of deformations, characterized as generalized strains, is defined which are related to dual stress resultants in a co-rotational frame. The stiffness formulation is based on a second-order approximation of the local elastic displacement field. Timoshenko’s beam theory and Vlasov’s modified thin-walled beam theory are used to include the shear strain effects due to non-uniform bending and restrained warping torsion and their mutual coupling effects. Axial shortening associated with the Wagner Hypothesis is taken into account such that the nonlinear behaviour of the beam is predicted accurately, especially under large torsion. Coupling between bending and torsional deformation due to non-coincident centroid and shear centre is modelled using a second-order cross-section transformation matrix. Cubic Hermitian polynomials are used as shape functions for the lateral displacements and twist rotation to derive the elastic and geometric stiffness matrices. Geometric nonlinearities associated with axial elongation and bending curvatures are described by additional torsion, bending and warping-related quadratic deformation terms yielding a set of modified deformations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. The accuracy and the computational efficiency of the new beam element is demonstrated in several static and dynamic examples.

Statistical analysis of fracture of silica glass using molecular dynamics

AbstractDisordered solids exhibit intermittent avalanches when slowly driven by an external load. These avalanches are associated with plastic rearrangements of the atoms at the nanoscale that manifest as stress and energy drops in the loading curve. The complexity arising from their interactions through long‐range elastic fields and the disorder makes statistical approaches suitable for studying their behavior by considering yielding and fracture as a phase transition. To investigate the avalanche statistics, we perform nanoscale simulations using the athermal quasistatic deformation protocol to induce fracture to silica glass samples, which were simulated using the melting‐quenching technique. We identify and measure the avalanches and voids and investigate their evolution in the process of fracture. Our results confirm that the avalanches exhibit scale‐free power law statistics, indicative of a critical phenomenon.