Porosity Distribution Research Articles

Effect of Porosity on the Free Vibration Analysis of a Rotating Pretwisted Sandwich Blade with a Functionally Graded Core in the Thermal Environment

This work deals with the investigation of the effect of porosity on the natural frequencies of the rotating pretwisted sandwich blade with a functionally graded core in the thermal environment. The top metallic and the bottom ceramic surfaces are exposed to ambient temperature and high inlet temperature, respectively. A finite element approach using a layerwise theory is developed. Two different porosity distributions are assumed here. The effect of the volume fraction index, rotational velocity, porosity model and temperature gradient on the natural frequencies of the pretwisted sandwich blade is studied.

3D printed multifunctional hierarchical structured cellular silicones with ultraelasticity, extreme load-bearing capacity, shape morphing and sensing properties

Multifunctional lightweight cellular silicone with adjustable properties has aroused great interests in many fields. However, it remains a challenge to facilely prepare multifunctional lightweight porous silicones with high load-bearing capacity. Herein, this work developed a 3D printing technique to prepare lightweight hierarchical structured cellular silicones with macroscale lattice structure and microscale intra-strand close-cell porosities, which was achieved by the expansion of thermally expandable microspheres (TEM) with plastic shells dispersed in formulated silicones. The obtained silicone foam with hierarchical porosity distributions shows excellent mechanical properties, including extreme load-bearing capacity (load is more than 165000 times its weight), high elasticity (negligible stress and strain loss under 80% compression), and high cycle durability (less than 4% strain loss under 1000 compression cycles). Besides, the incorporation of conductive fillers of MWCNTs endowed the foam with multifunctional piezoresistive and temperature-sensing properties. Furthermore, by printing multiple mixture inks of varying expansion ratios, shape morphing ability was endowed to the printed foam, to achieve complex curvature geometry facilely, demonstrating excellent versatility and potential applications in manufacturing flexible and conformal electronics of this method.

Beyond Scanning Electron Microscopy: Comprehensive Pore Analysis in Transparent Ceramics Using Optical Microscopy

Developing an effective method of quantifying defects in the bulk of transparent ceramics is a challenging task that could facilitate their widespread use as a substitute for single crystals. Conventionally, SEM analysis is used to examine the microstructure but it is limited to the material surface. On the other hand, optical transmittance assesses material quality, but does not provide information on the size and concentration of defects. In this study, we illustrate the use of a digital optical microscope for the non-destructive, precise, and rapid analysis of residual porosity in transparent ceramics. YAG-based ceramics doped with Yb have been selected for this study because they are used as laser gain media, an application that requires virtually defect-free components. Different production processes were used to produce YAG samples, and the digital optical microscope analysis was used to compare them. This analysis was shown to be effective and precise to measure the size and concentration of the residual pores. In addition, the comparison of samples obtained with different production processes showed that the size and distribution of the residual porosity is affected by the drying step of the powders before shaping by pressing, as well as by the sintering aids used to ease the densification. It also showed that the transmittance is influenced by both the total volume and the concentration of the pores.

Numerical investigation of effect of mechanical compression on the transport properties of fuel cell microporous layer using a pore-scale model

The microporous layer (MPL) plays an important role in water and thermal management of proton exchange membrane fuel cells (PEMFCs). An in-depth investigation of the mechanical compression effect on transport properties in the MPL can help optimize cell performance. In this work, the microstructure of the MPL is numerically reconstructed and the finite element method is applied to simulate mechanical behavior. Besides, the distribution of stress-strain, porosity, and pore size in the MPL under ten different levels of mechanical compression strains are studied. Lastly, the pore-scale model is employed to investigate the effective transport properties of the MPL as a function of compression strain. The analysis reveals that as the MPL strain increases from 0% to 40%, there is a 29% decrease in porosity, a 50% reduction in average pore diameter, a 60% decrease in effective gas diffusivity, a 100% increase in tortuosity, and an 80% increase in electrical and thermal conductivity. With the escalation of mechanical compression, both the magnitude and uniformity of stress-strain-displacement concurrently rise. Mechanical compression strains below 20% exhibit a lesser impact on transport properties. Beyond this threshold, exceeding the 20% compression strain point, mechanical stress assumes a critical role in influencing MPL transport properties.

Evaluation of Grain Size Effects on Porosity, Permeability, and Pore Size Distribution of Carbonate Rocks Using Nuclear Magnetic Resonance Technology

Evaluation of Grain Size Effects on Porosity, Permeability, and Pore Size Distribution of Carbonate Rocks Using Nuclear Magnetic Resonance Technology

Nonlinear deformations of size-dependent porous functionally graded plates in a temperature field

In this paper, the Variational Iteration Method (VIM) or Extended Kantorovich Method (EKM) is formulated for the first time for flexible porous functionally graded (PFGM) plates with different boundary conditions and geometric nonlinearity according to the theory of Theodore von Karman. Its accuracy and efficiency are demonstrated. The plate is subjected to a uniform transversal load and temperature field. The displacement field of the plate is approximated based on the classical plate theory (CTP) or Kirchhoff's plate theory. The governing equations are derived using Hamilton's principle. Modified Coupled Stress Theory (MCST) is used to account for size-dependent effects. The material properties vary with thickness and are temperature dependent. Four porosity distribution patterns are considered in this study. Several examples are solved to demonstrate the proposed algorithm. The results obtained are compared with solutions obtained by the Bubnov-Galerkin Method (BGM) in higher approximations, the Finite Difference Method (FDM) of second order accuracy, as well as with results obtained by the Finite Element Method (FEM) of other authors. The results include an analysis of the effect of size dependent parameters, porosity type pattern, porosity index, functionally graded index, temperature field and different types of boundary conditions on the stress–strain state and bending deflection of plates.

Multi-objective optimization of transpiration cooling for high pressure turbine vane

Transpiration cooling is a promising cooling measure for high-temperature components in gas turbines. Although the flow and heat transfer characteristics of transpiration cooling have been investigated in several experimental and numerical researches, the design optimization of transpiration cooling is less studied until now. In this paper, a multi-objective optimization framework based on the ANN surrogate model and the NSGA-Ⅱ is built to optimize the transpiration cooling of C3X turbine vane. The transpiration cooled C3X vane consists of multiple porous zones whose porosities could be different and are treated as the design parameters. The optimization objectives are minimum area-averaged vane surface temperature and minimum aerodynamic loss. A total of 960 CFD simulations are conducted to prepare the sample dataset. After the validation of the surrogate-based optimization framework, the Pareto front is obtained as an output. Three representative Pareto-optimal points are chosen from the Pareto front, considering the best cooling performance, the lowest aerodynamic loss, and a balance between them. The porosity distributions and coolant allocations, the cooling performances, and the aerodynamic losses for the three Pareto points are discussed, and the involved flow and heat transfer characteristics are analyzed. The results reveal that to reach a balance between the cooling efficiency and the aerodynamic loss for an optimal transpiration cooled C3X vane, coolant should be appropriately distributed to the leading edge, as well as zones immediately downstream of the leading edge.

A Four-Variable Shear Deformation Theory for the Static Analysis of FG Sandwich Plates with Different Porosity Models

This study is centered on examining the static bending behavior of sandwich plates featuring functionally graded materials, specifically addressing distinct representations of porosity distribution across their thickness. The composition of the sandwich plate involves a ceramic core and two face sheets with functionally graded properties. Mechanical loads with a sinusoidal distribution are applied to the sandwich plate, and a four-variable shear deformation theory is employed to establish the displacement field. Notably, this theory involves only four unknowns, distinguishing it from alternative shear deformation theories. Equilibrium equations are derived using the virtual work concept, and Navier’s method is applied to obtain the solution. The study addresses the impact of varying porosities, inhomogeneity parameters, aspect ratios, and side-to-thickness ratios on the static bending behavior of the sandwich plates. The influence of various porosities, inhomogeneity parameter, aspect ratio, and side-to-thickness ratio of the sandwich plates are explored and compared in the context of static bending behavior. The three porosity distributions are compared in terms of their influence on the bending behavior of the sandwich plate. The findings indicate that a higher porosity causes larger deflections and Model A has the highest central deflection. Adopting the four-variable shear deformation theory demonstrated its validity since the results were similar to those obtained in the literature. Several important findings have been found, which could be useful in the construction and application of FG sandwich structures. Examples of comparison will be discussed to support the existing theory’s accuracy. Further findings are presented to serve as benchmarks for comparison.

Spatial 3D correlation of flux pinning with porosity distribution in YBa2Cu3O7−δ using tensorial neutron tomography

Engineering devices from High Temperature Superconductors (HTS) for practical applications such as in transport and medical imaging requires an understanding of their critical current density (JC) distribution and how the material properties affect this. JC describes the maximum gradient of flux that can be found in a superconductor sustained by vortex pinning which is the preferential positioning of vortex in defective regions of weaker superconductivity. Local correlation of imperfections with high pinning has required destructive methods such as slicing then scanning with local magnetic probes. We describe the first case of non-destructive spatial correlation of flux pinning and consequently JC with bulk imperfections at different temperatures in top-seeded melt grown (TSMG) YBa2Cu3O7−δ chosen for its high pinning in addition to a rich structure of pores, twins and grain boundaries. This is facilitated by a combination of polarized neutron tomography to image trapped magnetic fields in a range around the material critical temperature and conventional neutron tomography to characterize potential pinning objects. The results indicate that there is indeed preferential trapping in the porous regions independent of the resolvable pore size. Polarized optical microscopy data suggests that the observed phenomenon is attributable to twin boundaries and crack defects located at the pore interface.

Static analysis of functionally graded porous beam-column frames by the complementary functions method

In this paper, an efficient and accurate numerical approach is implemented to examine the static behavior of Functionally Graded Porous (FGP) planar frames for the first time. The symmetric material constitutive relationship (SMCR), monotonic material constitutive relationships (MMCR), and uniform material constitutive relationship (UMCR) models are used to define the gradation of porosity along the thickness direction. The effects of porosity coefficient and material porosity distribution type on the static behavior of the FGP frames are investigated in detail. A direct relation between porosity coefficient and nodal deformations is observed.The effect of shear deformation is considered in the governing equations based on the Timoshenko Beam Theory (TBT). Within the scope of the presented procedure, fifth-order Runge-Kutta (RK5) algorithm is applied in the solution of the initial value problems. Imposing the rigidity matrix-based Complementary Functions Method (CFM) on the static analysis of the FGP planar frames is the novelty of this research. The results of the suggested approach are verified with the those of the finite element method (FEM), and those of the available literature. It has been carried out that type of the porosity distribution and porosity gradient index have an important impact on the response of FGP planar frames. By increasing the porosity coefficient, the displacement values of the frames made of UMCR and MMCR porosity distribution are affected more than those of the UMCR distributions. It can be noted that the SMCR can be preferred for designing the FGP beam-column structure as the minimum deformation values are obtained.

Nonlinear vibrations analysis of two-directional functionally graded porous cylindrical shells resting on elastic substrates in a thermal environment based on Donnell nonlinear shell theory

The primary objective of this study is to investigate the nonlinear free vibrational characteristics of temperature-dependent two-directional functionally graded porous (TDFGP) cylindrical shells resting on elastic substrates in a thermal environment. To accomplish this, the thermomechanical equations are derived based on the Donnell nonlinear shell theory framework in conjunction with the von Kármán assumption. Two-directional functionally graded porous cylindrical shell models have mechanical properties that can change smoothly and continuously across the length and thickness of the shell. Additionally, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The nonlinearity in free vibration assessed via the nonlinear-to-linear frequency ratio concerning the central deflection amplitude can be gained employing the Galerkin discretization approach and modified Poincare–Lindstedt (P-L) method. The accuracy and effectiveness of the present analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear free vibration characteristics of structures under different conditions. The results of this article demonstrate that parameters such as gradient indices, volume fraction, distribution pattern of porosity, geometric parameters, and ambient temperature rise significantly influence the structure’s nonlinear frequency and free vibration response.

Modelling diagenetic reactions and secondary porosity generation in sandstones controlled by the advection of low‐molecular‐weight organic acids

AbstractHigher secondary porosity was observed in the centre of a sandstone unit in the Eocene Shahejie Formation fan delta front sandstones from the Bozhong Depression, Bohai Bay Basin. This differs from past studies showing secondary porosity mainly in the marginal parts of sandstones adjacent to shales. This study utilized reactive transport models involving low‐molecular‐weight organic acids (LMWOA) to discuss potential processes resulting in the contrary distribution of secondary porosity. An interface model simulating LMWOA diffusion from adjacent shales to the sandstone resulted in secondary porosity in sandstones adjacent to shales. In contrast, an advection model simulating advective transport of LMWOA parallel to the sandstone bedding successfully generated higher secondary porosity in the central part. The central part of the sandstone exhibited better grain sorting (greater depositional porosity) and significantly less early carbonate cements compared to the marginal sandstone parts. Consequently, the central part had greater porosity prior to the dissolution through LMWOA. The initially higher porosity in the central part allowed for a higher advective flux of LMWOA‐rich water and associated lower pH, resulting in decreased oligoclase saturation, higher oligoclase dissolution rates and ultimately higher secondary porosity. This study indicates that grain sorting during sediment deposition, early carbonate cementation, LMWOA production in adjacent shales, and advection processes collectively control the diagenetic reactions and the distribution of secondary porosity in sandstones.

Free vibration analysis of functionally graded graphene platelet-reinforced metal foam doubly curved panel

In this research, free vibration characteristics of functionally graded metal foam doubly curved panels reinforced with graphene platelets and with porosities have been surveyed. Halpin Tsai's approach is utilized for extracting the effective Young modulus of porous metal foam nanocomposite and also the effective density of nanocomposite porous doubly curved shell panel is estimated by using an extended rule of mixture. The FSDT hypothesis is utilized for determining the displacement field and the Finite element and Hamilton principle are utilized for deriving the mass and stiffness matrices of the structure. Finally, the influences of several variables such as porosity distribution, porosity coefficient, GPL dispersion pattern, the weight fraction of Nanofillers, and span angles on the free vibrations characteristics of doubly curved shell panels with FG porosities and reinforced by graphene platelet have been reported in detail.

Effect of ultrasonic vibration on microstructural evolution, clad defects, and surface properties in laser direct energy deposition of Inconel 625

Laser direct energy deposition (DED) has some accompanying issues, such as existence of micropores, elemental segregation at grain boundaries, intergranular corrosion, etc. Therefore, the current work aims for a reduction in clad defects and enhancement in surface properties for laser direct deposition of Inconel 625 by implementing ultrasonic vibration. The acoustic streaming and cavitation effect induced by ultrasonic vibration results in the breaking of columnar grains, along with grain refinement and better elemental distribution in the matrix during the solidification process. The investigation is carried out for deposition using a 240 W Yb-fiber laser under the application of ultrasonic vibration with a variable amplitude of 6–13 μm (frequency: 33–28 kHz). A relatively higher vibration amplitude was found more efficient in converting long columnar grains into finer and uniformly distributed equiaxed grains, with a significant reduction in micropores. Further, it resulted in a shorter molten pool lifetime because of the generation of more nucleation centers, leading to better cooling. The above effects resulted in higher microhardness of the deposited layer. Further, the wear and corrosion resistance showed an improvement with the application of vibration, which may be due to the finer equiaxed grains, less porosity, and better elemental distribution at a higher vibration amplitude.

The effect of phenolics from bergamot juice powder extracted with different solvents on the physicochemical and antibacterial properties of chitosan films

Due to its bitterness, bergamot juice has no practical use, but it is a rich source of phenolic compounds, which provide significant antibacterial and antioxidant activity. In this study, extracts were prepared from spray-dried bergamot juice powder using acetone, dimethylsulfoxide, ethanol, and distilled water. These extracts were then incorporated into chitosan film matrices at 1%, 2%, and 3% (v/v) ratios. The analysis revealed that adding extracts generally created a barrier against light in the chitosan films, improved color, increased moisture content and water solubility, and caused significant enhancements in antioxidant activity, total phenolic content, thickness, mechanical strength, and provided substantial antibacterial activity against both Gram(+) and Gram(-) bacteria. The most effective modification of film properties was achieved by adding 3% acetone extract, while the 1% distilled water extract resulted in the least improvement. Specifically, the transparency, opacity, chroma, moisture, solubility, antioxidant activity, total phenolic content, thickness, puncture strength, and elasticity of pure chitosan film were 4.3–73.8%, 1.13 abs/mm, 15.61, 25.35%, 41.28%, 20.66%, 919.53 ppm, 1.09 N/mm2, 132.44%, and 0.07 mm, respectively. Meanwhile, those of the film with 3% acetone extract were 0.2–70.10%, 2.07 abs/mm, 36.34, 42.33%, 54.64%, 46.13%, 2915.72 ppm, 3.34 N/mm2, 142.68%, and 0.15 mm, respectively. The pure chitosan film exhibited no antibacterial effect against Gram(+) and Gram(-) bacteria, but adding extract enhanced antibacterial activity. Moreover, SEM analysis revealed distinct structural differences in the films, including varying porosity and phenolic distribution. At the same time, FTIR spectra demonstrated shifts in chemical composition and bonding within the films.

Nonlinear thermal buckling analysis of temperature-dependent porous annular and circular microplates reinforced by graphene platelets by using isogeometric analysis method

In this research, by using isogeometric analysis (IGA) method, nonlinear thermal buckling analysis of porous circular and annular microplates reinforced by graphene platelets (GPLs) under uniform temperature rise is performed by taking both the temperature dependence of the material properties and the size effects into account. The closed-cell metal foam scheme combined with the Halpin-Tsai micromechanics model and the rule of mixture is utilized to identify the effective material properties of the porous nanocomposites for three GPL dispersion patterns and three porosity distributions. With the aid of the virtual work principle, the classical and the non-classical motion equilibrium formulation based on the higher-order shear deformation theory in conjunction with the modified strain gradient (MSG) theory for the nonlinear temperature-dependent buckling behaviour are established. The higher-order NURBS basis functions capable of accomplishing easily the smoothness of arbitrary continuity order are successfully utilized to solve the nonlinear governing equations by satisfying the C2-continuity of the displacement field required by the MSG theory. The thermal buckling behaviour is assessed in detail by using various parameters such as the thickness-to-radius ratio, the porosity coefficient, the GPL weight fraction and the material length scale as well as the porosity distribution scheme and the GPL dispersion pattern. The results show the significance of incorporating the temperature dependency of the material properties when analyzing the thermal buckling behaviour and present the combination scheme of porosity and GPL distributions for enhancing the thermal buckling resistance.

Effect of porosity on the nonlinear free vibrational behavior of two-directional functionally graded porous cone-shaped shells resting on elastic substrates

The present article describes an analytical approach to investigate the nonlinear free vibrational behavior of a two-directional functionally graded porous (TDFGP) cone-shaped shell resting on elastic substrates. A mixture model with the power-law distribution functions is utilized to obtain the TDFGP shell’s mechanical properties. In addition, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The field displacement in the TDFGP shell is approximated using first-order shear deformation theory. Hamilton’s principle and von Karman’s large deformation assumptions give a dynamic model for the TDFGP shell. The Galerkin decomposition method is employed to discretize the governing partial differential equations into time-dependent ordinary differential equations. The harmonic balance method is used to analytically solve the final time-dependent equations and acquire the nonlinear frequency response of the TDFGP shell. Research has been conducted on porosity, gradient indexes, elastic substrates, boundary conditions, and geometric ratios through parametric studies to investigate the outcomes and their applicability to real-world issues.

Effect of CVI-induced porosity on elastic properties and mechanical behaviour of 2.5D and 3D Cf/SiC composites with multilayered interphase

The effect of CVI-induced porosity on mechanical behaviour of Cf/SiC composites possessing 2.5D (woven) and 3D (NOOBed) architectures with multilayered (PyC/SiC)n=4 interphase has been investigated. X-ray computed micro-tomography has shown that inter-bundle and inter-fibre pore distribution is influenced by fibre architecture. Elastic constants measured by ultrasound phase spectroscopy have revealed greater anisotropy in 2.5D Cf/SiC composite than 3D Cf/SiC composite. Owing to negligible Cf fraction and flattened inter-bundle pores distributed in thickness direction of 2.5D Cf/SiC composite, the elastic constant, C11 (∼15±0.03 GPa) is <1/6th of C22 and C33 obtained along fibre directions. Despite the flexural strength of 2.5D Cf/SiC composite (∼335±8 MPa) being ∼24% higher than 3D Cf/SiC composite, a more equitable distribution of Cf along three mutually orthogonal directions leads to higher fracture toughness of 3D Cf/SiC composites (∼19±1 MPa-m1/2) and greater damage tolerance. Porosity distributions having influence on crack paths, also affect both strength and fracture behaviour.

Enhancing Electrode Performance through Triple Distribution Modulation of Active Material, Conductive Agent, and Porosity.

The increasing demand for large-scale energy storage propels the development of lithium-ion batteries with high energy and high power density. Low tortuosity electrodes with aligned straight channels have proved to be effective in building such batteries. However, manufacturing such low tortuosity electrodes in large scale remains extremely challenging. In contrast, high-performance electrodes with customized gradients of materials and porosity are possible to be made by industrial roll-to-roll coating process. Yet, the desired design of gradients combining materials and porosity is unclear for high-performance gradient electrodes. Here, triple gradient LiFePO4 electrodes (TGE) are fabricated featuring distribution modulation of active material, conductive agent, and porosity by combining suction filtration with the phase inversion method. The effects and mechanism of active material, conductive agent, and porosity distribution on electrode performance are analyzed by experiments. It is found that the electrode with a gradual increase of active material content from current collector to separator coupled with the distribution of conductive agent and porosity in the opposite direction, demonstrates the best rate capability, the fastest electrochemical reaction kinetics, and the highest utilization of active material. This work provides valuable insights into the design of gradient electrodes with high performance and high potential in application.

Numerical analysis on the effect of graded porosity in closed-cell metal foams/PCM composites

The porous metal foams are potential to integrate phase change materials (PCMs) to form the shape-stabilized composited PCMs for the applications of thermal energy management and temperature regulation. However, the effect of porosity distribution of foam keeps challenging in designing such PCM-based composites. In this work, the closed-cell graded porosity foams (GPFs) involving various gradient directions and gradient differences of porosity are engineered by shrinking Voronoi tessellations to achieve precisely tunable microstructure. Then the GPF/PW composite is formed by integrating paraffin wax (PW) in each pore and its melting performance is investigated by the computational model, which is validated by the melting experiment of a specific sample. The investigations on the gradient configurations of foams reveal that the gradient direction and gradient difference of porosity have significant influences on the pore-scale melting behavior, liquid fraction variation in time and overall energy storage efficiency of PW. The positive gradient variation along the direction of heating source and the moderate gradient difference, i.e. 20% or 30%, are beneficial to improve the melting behavior of graded models. In contrast to the uniform model, the complete melting time of the graded models can maximum shorten by 5.6%, 3.8% and 3.7% for the bottom, lateral and top heating modes, respectively.