Nonhomogeneous Materials Research Articles

Torsional wave propagation on a penny-shaped crack in an orthotopic layer sandwiched between two rigid discs bonded by an orthotropic elastic half-space

The mechanical stability of the interface of two materials determines the stress behavior of the interface. So, observation of failure analysis in orthotropic composites with penny-shaped crack and circular disc in orthotropic materials due to the presence of torsional waves play a major role in structural design. The present article concerns the study of the torsional wave propagation of a penny-shaped crack in an orthotropic layer and two circular discs bonded between the layer and half-spaces. A general solution for the system is presented as a set of dual integral equations using the Hankel transform technique. Using Abel's transform method, the equations have been transformed into Fredholm integral equations of the second kind, which have been solved numerically to compute the stress intensity factors (SIFs) near the rims of crack and discs. Numerical results are obtained using material constants of two orthotropic mediums to demonstrate the impact of material non-homogeneity, normalized disc radius, and layer depth on SIFs and portrayed by virtue of graphs. The analysis of the physical quantity SIF in the present model leads to speculation about the stability of composites against the propagation of cracks in layered engineering solids by surveilling geometric parameters of orthotropic materials and layer depth.

Influence of low-temperature heat treatment on microstructure and mechanical properties of hydrostatically extruded titanium

• Titanium processed by hydroextrusion is a highly nonhomogeneous material. • Continuous dynamic recrystallization operates during the later stages of processing. • Low-temperature heat treatment increases ductility significantly. Subjecting a material processed by a Severe Plastic Deformation method to low-temperature heat treatment has not been the subject of any study so far. Therefore, hydrostatically extruded titanium has been examined within the present work with respect to its mechanical properties and microstructure upon heat treatment at 200 °C. Static tensile tests as well as microstructural analyses with the use of electron backscatter diffraction and transmission electron microscopy have been realized. Even though the material has been annealed, deformation-induced defects were still present within the microstructure what proves that continuous dynamic recrystallization dominates at the later stages of the processing. A significant increase in ductility of a heat-treated material compensates the drop in its tensile properties. Low-temperature annealing might provide an initial solution for resolving the strength-ductility paradox in materials processed by Severe Plastic Deformation techniques.

Deep learning in frequency domain for inverse identification of nonhomogeneous material properties

The inverse identification of nonhomogeneous material properties from measured displacement/strain fields, especially when noise exists, is crucial for both engineering and material science. The conventional physics-based solutions either require time-consuming iterative calculations, or are sensitive to noise. While the new machine learning methods either need excess data for high-dimensional matchups, or mainly apply to case-by-case analyses with informed physics. In this paper, to solve the complex matchup between the measured displacement/strain fields and the randomly distributed modulus field rapidly and robustly, a novel method of deep learning in frequency domain is proposed, with discrete cosine transform (DCT) to achieve frequency domain transformation as well as dimensionality reduction and convolutional neural network (CNN) to implement learning in frequency domain. Results show that our method not only has high prediction accuracy on zero-noise samples (with L1-error of 4.249%) but also presents great robustness to noise (with L1-error of 5.085% on large-noise samples). Besides, by our method, only one-time training on a dataset with mixed noise is basically enough to deal with arbitrary levels of noise (with L1-errors below 5.202%), improving the efficiency significantly in practical applications. Moreover, our method can be directly transferred to neighbor sampling spaces with different sampling points, showing a great generalization. The study provides a powerful approach for inverse identification of material properties and promises for wide applications such as real-time elastography and high-throughput non-destructive evaluation techniques.

Investigation of the thermomechanical behavior of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading

For mixed-mode, thermal shock crack problems with thermal lagging behaviors, it is difficult to obtain the transient thermal stress intensity factors (TSIFs). This paper aims to develop a method combining the Newmark method and the transient interaction energy integral method (IEIM) to extract the transient, mixed-mode TSIFs of nonhomogeneous, layered materials with mixed-mode cracks. The transient temperature field obtained by non-Fourier heat conduction theory is discretized in the spatial and temporal domains through the finite element method (FEM) and Newmark method, respectively. The effect of the continuity of thermomechanical parameters at the dual interface on the transient, mixed-mode TSIFs of nonhomogeneous, layered materials is discussed, then the fracture resistance of nonhomogeneous, layered materials is evaluated. Moreover, the maximum hoop stress criterion is utilized to obtain the crack growth angle and the equivalent, transient TSIFs of nonhomogeneous, layered materials. The influences of the interface on crack growth angle and equivalent transient TSIFs of nonhomogeneous layered materials are also studied. The present work is beneficial for the thermal design of nonhomogeneous, layered materials with mixed-mode cracks subjected to rapid thermal shock loading.

Concurrent topology optimization of coated structure for non-homogeneous materials under buckling criteria

Concurrent topology optimization of coated structure for non-homogeneous materials under buckling criteria

General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term

This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. Such model describes wave traveling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Moreover, we also obtain the instability of the solutions at the infinity in the presence of the nonlinear damping.

An RVE recognition method for non-homogeneous materials based on two-point correlation function

An RVE recognition method for non-homogeneous materials based on two-point correlation function

Obtaining thermal images of creole corn by means of photoacoustic microscopy

The use of non-destructive techniques, such as photothermal techniques, can be used for characterization of non-homogeneous materials with different components and thermophysical properties. Among the photothermal techniques, the photoacoustic microscopy (PAM) has been used to obtain thermal images of different samples, ranging from semiconductors to biological materials. In the present study, the thermal imaging of six different creole corn varieties was obtained by using PAM. According to the color, these varieties were nominated as M1 (orange–yellow), M2 (blue), M3 (blue), M4 (light yellow), M5 (yellow), and M6 (red). Thermal images allowed us visualize corn characteristic features and structures, with higher values of photoacoustic signal amplitude in floury regions and pedicel. The highest values of photoacoustic signal amplitude corresponded to M1 (0.39), M6 (0.35), and M5 (0.34) corn samples, followed by M4 sample. Also, colorimetric parameters L*a* and b* of the creole corn samples were evaluated, and they showed significant statistical differences (p < 0.5). The colorimetric results were analyzed by the statistical method of Kernel density estimation, showing a higher density of data in the B component, followed by R and G. The non-destructive techniques allow characterizing non-homogeneous materials with different components. Thermal images, obtained by using PAM, can be analyzed by several statistical methods.

Study on the formation mechanism of cutting surface of carbon fiber-reinforced composites

Carbon fiber-reinforced plastic (CFRP) is used widely in aerospace. The cutting mechanism of CFRP is markedly different from that of metals due to anisotropic and non-homogeneous material structure. The cutting mechanisms are highly dependent on the fiber orientation. The quality of the machined surface can be affected by the fiber fracture models. In this paper, based on the elastic foundation beam theory and the Hertzian contact theory, the cutting mechanics are established. And the cutting model is simulated by the three-dimensional micro-scale numerical model. Then, the continuous varying cutting mechanism and the sub-damage are deeply studied in detail by combining the cutting mechanics model and the simulation model. The results indicate that the fiber orientation θ = 80° and θ = 150° is the transition critical point of the fracture form. When θ = 0°, the fiber failure mode is buckling dominated. When 0° < θ < 80° and 150° < θ < 180°, the fiber failure mode is dominated by contact fracture. When 80° < θ < 150°, the fiber failure mode is bending-dominated. The cutting mechanics model and finite element model can effectively reflect the evolution law of CFRP-machined surface.

Analysis of Thermal Fracture for Nonhomogeneous Materials Plate with Multiple Cracks

In this paper, the transient interaction integral method (IEIM) is established to obtain the transient thermal stress intensity factors (TSIFs) in order to study the fracture problems of nonhomogeneous materials under thermal shock loading. The transient temperature field is evaluated by using the finite difference method and the finite element method. The TSIFs of nonhomogeneous materials with multiple cracks are analysed, then the mixed-mode TSIFs of nonhomogeneous materials with different positions are discussed. The results of this study have shown that the current approach is applicable to obtain fracture parameters of nonhomogeneous materials with multiple cracks efficiently, which can be used as a significant reference for the engineering application of nonhomogeneous materials.

Numerical Analysis of the Calcaneal Nail C-NAIL

The presented article investigates the biomechanics of the calcaneal nail C-NAILTM by numerical calculations and, partially, experimentally. This nail is widely used in trauma and orthopaedics. A numerical model of implants directly interacting with the bone tissue model obtained from CT scans was calculated. The material properties of the bone tissue can be described by several models; in this work, a non-homogeneous material model with isotropic elements and prescribed elastic modulus was used to provide a more accurate model of the applied force distribution on the individual parts of the implants. The critical areas of the nail and its fixtures were investigated using finite element strength calculations to verify their strength and reliability, contributing to the safety and faster and easier treatment of patients. These analyses suggest that the strength of the calcaneal nail C-NAIL, as well as the stabilization of bone fragments resulting from its use, are sufficient for clinical practice.

A new path-independent interaction integral for the SIFs of interfacial crack

A new path-independent interaction integral, which is derived from the dynamic Ĵ integral, is developed to compute the stress intensity factors (SIFs) of interfacial crack and the path-independence of the new interaction integral is theoretically proven. In the calculation, the second derivative of the displacement is avoided since the explicit analytical expressions of the auxiliary stress fields near an interfacial crack tip are utilized. In addition, for non-homogenous materials the computation of the derivatives of material properties is not required by introducing the appropriate incompatibility auxiliary fields. This study significantly enhances the application of the interaction integration technique since the determination of SIFs of interfacial crack between two homogeneous or non-homogeneous materials under static or dynamic loadings can be conducted efficiently by the new interaction integral. For more efficient crack modeling, a local refinement technique using the variable-node element (VNE) is implemented into the framework of the extended finite element method (XFEM). The efficiency and accuracy of the proposed new interaction integral are demonstrated by numerical examples.

Thermoelastic damping analysis model of transversely isotropic micro/nano-resonators based on dual-phase-lag heat conduction model and surface effect

Thermoelastic damping (TED) is one of the key factors for lowering the quality factor (Q-factor) of micro/nano-resonators. However, due to a complex small-scale effect and governing equations of non-homogeneous isotropic materials, the existing TED models usually focus on homogeneous isotropic micro/nano-resonators. In this paper, a closed-form TED model is derived to estimate the influence of the small-scale effect on TED of transversely isotropic micro/nano-resonators. The surface effect and the dual-phase-lag model are included to distinguish the influence of mechanical and thermal small-scale effects on TED, respectively. The obtained TED model is theoretically verified. The results indicate that TED values are underestimated if the classical TED model is employed. Moreover, a critical thickness can be determined by the frequency shift curve is proposed. The small-scale effect results in higher TED values within the critical thickness. However, since the small-scale effect has a weak influence on TED, it can be neglected when the resonator thickness is higher than the critical thickness. Additionally, the surface effect plays a dominant role in improving the TED of nano-resonators. In this paper, a more reasonable theoretical approach for estimating TED in transversely isotropic micro/nano-resonators is provided.

Pressure-resistant cylindrical shell structures comprising graded hybrid zero Poisson's ratio metamaterials with designated band gap characteristics

Deep submersible technology is currently an important part of oceanic advanced technologies while developing new pressure-resistant materials has become its inevitable trend. Mechanical metamaterials can be flexibly designed to exhibit a unique range of mechanical properties, among which zero Poisson's ratio (ZPR) metamaterials can yield no transverse displacements under in-plane unidirectional tensile or compressive loadings. Thus, it is projected to be applied to the pressure-resistant cylindrical shell structures to avoid circumferential extrusion stress when subjected to radial forced compression due to underwater distributed pressure. Inspired by nonhomogeneous or graded composite materials and structures, this work proposes a novel pressure-resistant cylindrical shell cover comprising graded ZPR metamaterials with vibroacoustic attenuation capabilities. The periodic boundary condition (PBC) and Bloch's Theorem are implemented with the finite element method (FEM) to optimally design the ZPR metamaterials with specified load-bearing properties and band gap characteristics. The mechanical and vibroacoustic performance of the corresponding homogeneous and graded metamaterial structures is finally discussed. The results indicate that the designed structure made of titanium alloy can safely bear the hydrostatic distributed pressure of 10 MPa with a weight-bulk ratio of 0.540 g/cm3 and also yield higher STL within specified frequency regions corresponding to the designable band gaps, which strongly demonstrates the effectiveness of the optimal design for multi-functional ZPR functional elements. Moreover, both acoustic mediums and preloads affect its underwater vibroacoustic performance. Therefore, this work offers an innovative design idea of pressure-resistant protective covers for marine structures and also extends the route to enhance their underwater vibroacoustic behavior via designing the band gap characteristics of the graded metamaterials.

Photometric and spectroscopic evolution of the interacting transient AT 2016jbu(Gaia16cfr)

ABSTRACT We present the results from a high-cadence, multiwavelength observation campaign of AT 2016jbu (aka Gaia16cfr), an interacting transient. This data set complements the current literature by adding higher cadence as well as extended coverage of the light-curve evolution and late-time spectroscopic evolution. Photometric coverage reveals that AT 2016jbu underwent significant photometric variability followed by two luminous events, the latter of which reached an absolute magnitude of MV ∼ −18.5 mag. This is similar to the transient SN 2009ip whose nature is still debated. Spectra are dominated by narrow emission lines and show a blue continuum during the peak of the second event. AT 2016jbu shows signatures of a complex, non-homogeneous circumstellar material (CSM). We see slowly evolving asymmetric hydrogen line profiles, with velocities of 500 km s−1 seen in narrow emission features from a slow-moving CSM, and up to 10 000 km s−1 seen in broad absorption from some high-velocity material. Late-time spectra (∼+1 yr) show a lack of forbidden emission lines expected from a core-collapse supernova and are dominated by strong emission from H, He i, and Ca ii. Strong asymmetric emission features, a bumpy light curve, and continually evolving spectra suggest an inhibit nebular phase. We compare the evolution of H α among SN 2009ip-like transients and find possible evidence for orientation angle effects. The light-curve evolution of AT 2016jbu suggests similar, but not identical, circumstellar environments to other SN 2009ip-like transients.

Study of fracture processes in sandstone subjected to four-point bending by means of 4D X-ray computed micro-tomography

&lt;p class="Abstract"&gt;High-resolution X-ray computed micro-tomography (CT) is a powerful technique for studying the processes of crack propagation in non-homogenous quasi-brittle materials such as rocks. To obtain all the significant information about the deformation behaviour and fracture characteristics of the studied rocks, the use of a highly specialised loading device suitable for the integration into existing tomographic setups is crucial. Since no adequate commercial solution is currently available, a completely newly-designed loading device with a four-point bending setup and vertically-oriented scanned samples was used. This design of the loading procedure, coupled with the high stiffness of the loading frame, allows the loading process to be interrupted at any time and for CT scanning to be performed without the risk of the sudden destruction of the scanned sample.&lt;/p&gt;This article deals with the use of the 4D CT for the visualisation of crack initiation and propagation in clastic sedimentary rocks. Two types of quartz-rich sandstones of Czech provenance were used for tomographic observations during the four-point bending loading performed on chevron notched test specimens. It was found that the crack begins to propagate from the moment that ca. 80 % of the maximum loading force is applied.

Fully Coupled Vibrations of Cable-Harnessed Beams with a Non-Periodic Wrapping Pattern

Power- and signal- cable attachments have a significant impact on the vibrations of space structures. Recent works show the importance of having an analytical model to gain physical insight into the influence of cabling on the dynamics of host structures. The models in the literature focus mainly on pure bending vibrations and ignore the effect of coupling between different coordinates. Recently, the authors demonstrated the importance of modeling the coupling effects in cable-harnessed (CH) beams with straight and periodic wrapping patterns. In real-life situations, the cable attachment patterns are mostly non-periodic, and the cables are also attached to host structures that consist of a combination of several harness elements of same (homogenous) or different (non-homogenous) material properties. Hence, the fully coupled vibration model developed in this article is the first to analyze the vibrations of homogenous and non-homogenous CH beams with non-periodic wrapping patterns. The Frequency Response Functions (FRFs) of the developed model are compared with experiment FRFs in the case of the homogenous non-periodic wrapping pattern. The study shows that the coupling effects are pronounced in non-periodic wrapped CH beams, and the advantage of developing the coupled model over the decoupled model is shown through experimental validation.

Multiple elastic or rigid line inclusions in a multilayered orthotropic solid

This paper studies the problem of multiple line inclusions in a non-homogeneous medium. The formulation and solutions for rigid line inclusions and homogeneous medium are special cases when the stiffness values of the inclusions are infinite and the non-homogeneity of the material vanishes. The model built in this study is capable of dealing with any material non-homogeneity (material properties vary continuously or in step-wise form), orthotropic mechanical properties, isotropic mechanical properties, and any number of parallel or collinear inclusions. More importantly, the inclusions are not limited to rigid (they can be elastic). Dependence of the inclusion tip fields on the strain intensity factor is given in closed form. Numerical results are given for the situations of mechanical load as well as thermal load applied in the medium.

An Alternative Digital Image Correlation-Based Experimental Approach to Estimate Fracture Parameters in Fibrous Soft Materials.

One of the main challenges in experimental fracture mechanics is to correctly estimate fracture parameters of a nonhomogeneous and nonlinear material under large deformation. The crack tip detection is strongly affected by fibers at crack tip, leading to inaccurate measures. To overcome this limitation, a novel methodology based on the Digital Image Correlation (DIC) method for crack tip detection of fibrous soft composites is proposed in this work. The unidirectional composite was manufactured using a matrix of polydimethylsiloxane reinforced with a single layer of extensible cotton knit fabric. For two different fiber orientations, the crack growth (), Crack Tip Opening Displacement (CTOD) and Crack Tip Opening Angle (CTOA) were determined using pure shear specimens under mode I fracture. A consistent estimation of fracture parameters was obtained. The location of the crack tip position during the fracture test using the DIC-based methodology was validated against a visual inspection approach. Results indicated that the DIC-based methodology is easily replicable, precise and robust.

Time Period of Thermal-Induced Vibration of Skew Plate with Two-Dimensional Circular Thickness

In this study, two-dimensional circular thickness effects on time period of skew plate made with nonhomogeneous material properties are computed in variable temperature environment. Clamped C , simply supported S , and free-edge F conditions are the various combinations considered in this work. One-dimensional circular density and two-dimensional parabolic temperature variation on the plate are considered due to the nonhomogeneous nature of the material and variable temperature environment. Rayleigh–Ritz method is used to compute the time period for the first two modes of vibration. A convergence study of frequency modes of skew plate on various edge conditions has also been performed. The present work has been compared with the frequency modes of parallelogram and rectangle plate on various edge conditions. The objective of the study is to present a numerical data of time period as well as to show how one can control the frequencies of plate by taking an appropriate variation in plate parameters.