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At least 19 records

Thermal modulation of nonlinear ultrasonic waves for nondestructive evaluation of elastic materials

Temperature variation is often considered an undesirable factor in ultrasonic testing, as wave velocity is highly sensitive to thermal fluctuations. However, completely eliminating the temperature effect is difficult, particularly in tests requiring precise velocity measurements. Recently, a method called Thermal Modulation of Nonlinear Ultrasonics (TMNL) has been developed. Instead of eliminating the thermal effect, the TMNL method leverages the temperature variation as a driving force to stimulate the nonlinear response of the medium and modulate the ultrasonic waves propagating in it. These modulated waves can then be used to evaluate the nonlinear behaviours of the test medium. This paper presents a focused review of the TMNL technique, including its theoretical foundations, particularly the conceptual challenges in integrating thermal effects into classical acoustoelastic theory, and recent applications in non-destructive evaluation (NDE). Three case studies are presented to demonstrate TMNL’s application in detecting microcracking in concrete, assessing ageing in polymer materials, and enabling temperature compensation in acoustoelastic tests. In conclusion, the review also summarises related studies, including photothermal crack modulation, and discusses current limitations and future directions of TMNL in elastic media.

NDE↗

Kinetics of Failure in an Elastic Peridynamic Material

The dynamic behavior of an elastic peridynamic material with a nonconvex bond potential is studied. In spite of the material’s inherently unstable nature, initial value problems can be solved using essentially the same techniques as with conventional materials, both analytically and numerically. In a suitably constructed material model, small perturbations grow exponentially over time until the material fails. Additionally, the time for this growth is computed explicitly for a stretching bar that passes from the stable to the unstable phase of the material model. This time to failure represents an incubation time for the nucleation of a crack. The finiteness of the failure time in effect creates a rate dependence in the failure properties of the material. Thus, the unstable nature of the elastic material leads to a rate effect even though it does not contain any terms that explicitly include a strain rate dependence.

36 MATERIALS SCIENCE↗

Interface gasket for building envelope

A gasket assembly for attaching a window to a panel opening includes an inner frame, an outer frame, and an elastic material connecting the inner frame to the outer frame. The elastic material extends contiguously and circumferentially to couple the outer frame to the inner frame. The outer frame and inner frame can include gap flanges and the elastic material can include opposing lateral side portions. The gap flanges are embedded in the lateral side portions of the elastic material. The outer frame includes connecting structure for coupling of the outer frame to the panel opening. The inner frame includes a connecting structure for coupling of the gasket assembly to the window. The gasket assembly is configured to support the window in the panel opening and form a seal between the panel opening and the window. A method of making a gasket assembly is also disclosed.

Aaron, Adam M.↗

Lagrange-Remap strategy for multi-material fluid-solid simulations using compressive limiters

In the present work, the Lagrange-Remap strategy proposed in [1] is extended to multi-material fluid-solid simulations. Both hypo-elastic and hyper-elastic material models are considered to describe the mechanical behavior of the solids. In practice, the deviatoric stress tensor (for hypo-elastic materials) and the left Cauchy-Green tensor (for isotropic hyper-elastic materials) are remapped, while the use of compressive limiters effectively reduces numerical diffusion during the remapping step. The simplicity of this diffuse interface approach is emphasized in the context of multi-material fluid-solid simulations. A series of Lagrange-Remap test cases, involving both solids and fluids, are conducted and compared with reference Lagrangian simulations, demonstrating the robustness and accuracy of the overall numerical strategy.

Compressive limiters↗

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗

Evaluating Novel Polymer-Composite Resins for the Ability to Derive Elastic Properties for Explicit Formulations, or to Develop Nonlinear Models Thereof

This project evaluates the ability to derive elastic material properties for novel additively manufactured carbon-polymer matrix materials. Initially stress-strain equilibrium equations were thought to be sufficient to characterize the elastic region of material performance. However, initial test data shows the cured material behaves nonlinearly in the elastic region. To properly determine the elastic performance, additional strain data must be collected in future testing. This paper discusses the initial test data, methods and models used to describe nonlinear elasticity, and the determination of mean elastic material properties, such as Lame’s constants, using the stress-strain equilibrium equations.

36 MATERIALS SCIENCE↗

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗

From force chains to nonclassical nonlinear dynamics in cemented granular materials

In this letter, we present evidence for a mechanism responsible for the nonclassical nonlinear dynamics observed in many cemented granular materials that are generally classified as mesoscopic nonlinear elastic materials. We demonstrate numerically that force chains are created within the complex grain-pore network of these materials when subjected to dynamic loading. The interface properties between grains along with the sharp and localized increase of the stress occurring at the grain-grain contacts leads to a reversible decrease of the elastic properties at macroscopic scale and peculiar effects on the propagation of elastic waves when grain boundary properties are appropriately considered. These effects are observed for relatively small amplitudes of the elastic waves, i.e., within tens of microstrain, and relatively large wavelengths, i.e., orders of magnitude larger than the material constituents. The mechanics are investigated numerically using the hybrid finite-discrete-element method and match those observed experimentally using nonlinear resonant ultrasound spectroscopy.

36 MATERIALS SCIENCE↗

Sound Speeds of Solids from Ultrasonic Pulse Receiver Measurements

A common method of determining elastic material properties is utilizing an ultrasonic pulse receiver. This is a non-destructive test (NDT) causing no plastic deformation of the material. It requires a pulse generator, oscilloscope, and two transducers to measure the sound velocity of a material. Both longitudinal and shear sound velocities may be obtained by utilizing the appropriate transducer. Acoustic nondestructive testing methods are often used in manufacturing certification processes and for material defect detection in industry. These methods can also be utilized to directly measure the elastic moduli of a material without damaging the material. Overall, it is a low-cost experiment with minimal preparation, and is easy to use.

36 MATERIALS SCIENCE↗

Effect of plasticity on the experimental characterization of the creep property of a cement paste: Spherical vs. conical microindentation

Microindentation is today a powerful tool for rapidly characterizing the elastic modulus and the logarithmic basic creep of a cement paste. However, a theoretical work proved that a microindentation test with a sharp indenter shape involves stress concentration and delayed plasticity which can cause an overestimation of the estimated creep property. This work aims at experimentally investigating the effect of the shape indenter on the identification of the visco-elastic property of a cement paste by microindentation. First, several microindentation grids were carried out on a cement paste with both a Berkovich indenter and a spherical indenter at different penetration depths or load levels for load control (creep) tests or displacement control (relaxation) tests, respectively. As for a visco-elastic material the duality principle between creep and relaxation holds, a numerical method was developed for predicting the relaxation response from the assumed logarithmic creep compliance. The present results show that only spherical microindentation satisfy the duality principle for which creep and relaxation response can be predicted by a unique logarithmic creep compliance function. Finally, spherical microindentation creep tests at low load as well as spherical microindentation relaxation tests provide a greater indentation modulus M and contact creep modulus C{sub v} as likely less affected by possible plasticity effects.

36 MATERIALS SCIENCE↗

Planar, longitudinal, compressive waves in solids: Thermodynamics and uniaxial strain restrictions

A new tri-axial pressure-based constitutive expression has been found using Cauchy's stress tensor. This stress state emphasizes pressure and shear stress. The description is a pressure plus an effective shear stress allowing for a constitutive law based on atomic solid-state phase changes in crystalline cells due to pressure plus shear-based dislocation motion commonly associated with plasticity. Pressure has a new role in the material's constitutive response as it is separated from plasticity. The thermo-mechanical system describes third-order Gibbs’ expressions without specific volume restrictions placed upon the material. Isothermally, the ratio of heat to shear work in elastic copper is shown to approach zero at a very low temperature and become larger than one as temperature approaches melting. Wave compression models investigated are elastic and plastic: in fully elastic materials, the planar wave is restricted by Poisson's effect although plastic shear changes this constraint. Plastic deformation, dominated by dissipative shear stresses in uniaxial strain, heats the material while excluding phase changes from hydrostatic pressures. The material properties per se across Hugoniot shocks are described with entropy concepts. Shock waves are exceedingly complex since the constitutive laws are linked at extreme temperatures, pressures, and shear stresses. Isothermal, isentropic, isochoric, and iso-shear conditions are used throughout with Jacobian algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering

The surface roughness of a thin film at a liquid interface exhibits contributions of thermally excited fluctuations. This thermal roughness depends on temperature (𝑇), surface tension (𝛾), and elastic material properties, specifically the bending modulus (𝜅) of the film. A nonzero 𝜅 suppresses the thermal roughness at small length scales compared to an interface with zero 𝜅, as expressed by the power spectral density of the thermal roughness. The description of the x-ray scattering of the standard capillary wave model (CWM), which is valid for zero 𝜅, is extended to include the effect of 𝜅. The extended CWM (eCWM) provides a single analytical form for both the specular x-ray reflectivity (XRR) and the diffuse scattering around the specular reflection, and recovers the expression of the CWM at its zero 𝜅 limit. This theoretical approach enables the use of single-shot grazing incidence x-ray off-specular scattering (GIXOS) measurements for characterizing the structure of thin films on a liquid surface. The eCWM analysis approach decouples the thermal roughness factor from the surface scattering signal, providing direct access to the intrinsic surface-normal structure of the film and its bending modulus. Moreover, the eCWM facilitates the calculation of reflectivity at any desired resolution (pseudo-XRR approach). The transformation into pseudo-XRR provides the benefit of using widely available XRR software to perform GIXOS analysis. The extended range of the vertical scattering vector (𝑄 𝑧 ) available with the GIXOS pseudo-XRR approach allows for a higher spatial resolution than with conventional XRR. Experimental results are presented for various lipid systems, showing strong agreement between conventional specular XRR and pseudo-XRR methods. This agreement validates the proposed approach and highlights its utility for analyzing soft, thin films.

36 MATERIALS SCIENCE↗

Competition between roughness and strength for scale-dependent surfaces

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

elasticity↗

Optimal local truncation error method for 3-D elasticity interface problems

The paper deals with a new effective numerical technique on unfitted Cartesian meshes for simulations of heterogeneous elastic materials. Here, we develop the optimal local truncation error method (OLTEM) with 27- point stencils (similar to those for linear finite elements) for the 3-D time-independent elasticity equations with irregular interfaces. Only displacement unknowns at each internal Cartesian grid point are used. The interface conditions are added to the expression for the local truncation error and do not change the width of the stencils. The unknown stencil coefficients are calculated by the minimization of the local truncation error of the stencil equations and yield the optimal second order of accuracy for OLTEM with the 27-point stencils on unfitted Cartesian meshes. A new post-processing procedure for accurate stress calculations has been developed. Similar to basic computations it uses OLTEM with the 27-point stencils and the elasticity equations. The post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing numerical techniques (e.g., with finite elements). Numerical experiments show that at an accuracy of 0.1% for stresses, OLTEM with the new post-processing procedure significantly (by 10 5 -10 9 times) reduces the number of degrees of freedom compared to linear finite elements. OLTEM with the 27-point stencils yields even more accurate results than high-order finite elements with wider stencils.

42 ENGINEERING↗

Analyzing the Validity of Brazilian Testing Using Digital Image Correlation and Numerical Simulation Techniques

Characterizing the mechanical behavior of rocks plays a crucial role to optimize the fracturing process in unconventional reservoirs. However, due to the intrinsic anisotropy and heterogeneity in unconventional resources, fracture process prediction remains the most significant challenge for sustainable and economic hydrocarbon production. During the deformation tracking under compression, deploying conventional methods (strain gauge, extensometer, etc.) is insufficient to measure the deformation since the physical attachment of the device is restricted to the size of the sample, monitoring limited point-wise deformation, producing difficulties in data retrieval, and a tendency to lose track in failure points, etc. Where conventional methods are limited, the application of digital image correlation (DIC) provides detailed and additional information of strain evolution and fracture patterns under loading. DIC is an image-based optical method that records an object with a camera and monitors the random contrast speckle pattern painted on the facing surface of the specimen. To overcome the existing limitations, this paper presents numerical modeling of Brazilian disc tests under quasi-static conditions to understand the full-field deformation behaviors and finally, it is validated by DIC. As the direct tensile test has limitations in sample preparation and test execution, the Brazilian testing principle is commonly used to evaluate indirectly the tensile strength of rocks. The two-dimensional numerical model was built to predict the stress distribution and full-field deformation on Brazilian disc under compression based on the assumptions of a homogenous, isotropic and linear elastic material. The uniaxial compression test was conducted using the DIC technique to determine the elastic properties of Spider Berea sandstone, which were used as inputs for the simulation model. The model was verified by the analytical solution and compared with the digital image correlation. The numerical simulation results showed that the solutions matched reasonably with the analytical solutions where the maximum deviation of stress distribution was obtained as 14.59%. The strain evolution (normal and shear strains) and displacements along the central horizontal and vertical planes were investigated in three distinguishable percentages of peak loads (20%, 40%, and 90%) to understand the deformation behaviors in rock. The simulation results demonstrated that the strain evolution contours consistently matched with DIC generated contours with a reasonable agreement. The changes in displacement along the central horizontal and vertical planes showed that numerical simulation and DIC generated experimental results were repeatable and matched closely. In terms of validation, Brazilian testing to measure the indirect tensile strength of rocks is still an issue of debate. The numerical model of fracture propagation supported by digital image correlation from this study can be used to explain the fracturing process in the homogeneous material and can be extended to non-homogeneous cases by incorporating heterogeneity, which is essential for rock mechanics field applications.

58 GEOSCIENCES↗

Predicting Elastic Properties of Materials from Electronic Charge Density Using 3D Deep Convolutional Neural Networks

Materials representation plays a key role in machine learning-based prediction of materials properties and new materials discovery. Currently both graph and three-dimensional (3D) voxel representation methods are based on the heterogeneous elements of the crystal structures. Here, we propose to use electronic charge density (ECD) as a generic unified 3D descriptor for materials property prediction with the advantage of possessing close relation with the physical and chemical properties of materials. We developed an ECD-based 3D convolutional neural networks (CNNs) for predicting the elastic properties of materials, in which CNNs can learn effective hierarchical features with multiple convolving and pooling operations. Extensive benchmark experiments over 2170 $Fm\bar3m$ face-centered-cubic materials show that our ECD-based CNNs can achieve good performance for elasticity prediction. Especially, our CNN models based on the fusion of elemental Materials-Agnostic Platform for Informatics and Exploration features and ECD descriptors achieved the best fivefold cross-validation performance. More importantly, we showed that our ECD-based CNN models can achieve significantly better extrapolation performance when evaluated over nonredundant data sets, where there are few neighbor-training samples around test samples. As an additional validation, we evaluated the predictive performance of our models on 329 materials of space group $Fm\bar3m$ by comparing to density functional theory calculated values, which shows a better prediction power of our model for bulk modulus than shear modulus. Because of the unified representation power of ECD, it is expected that our ECD-based CNN approach can also be applied to predict other physical and chemical properties of crystalline materials.

36 MATERIALS SCIENCE↗