Relative Density Distribution Research Articles

Comparative Study on Seismic Response of Pile Group Foundation in Coral Sand and Fujian Sand

The physical and mechanical properties of coral sand are quite different from those of common terrestrial sands due to the special marine biogenesis. Shaking table tests of three-story structures with nine-pile foundation in coral sand and Fujian sand were carried out in order to study the dynamic response characteristics of pile-soil-structure system in coral sand under earthquake. The influence of shaking intensity on the dynamic response of the system was taken into consideration. The results indicated that the peak value of the excess pore pressure ratio of coral sand was smaller than that of Fujian sand under two kinds of shaking intensities; moreover, the development speed of excess pore pressure ratio of coral sand was smaller than that of Fujian sand. The liquefaction of coral sand was more difficult than Fujian sand under the same relative density and similar grain-size distribution. The horizontal displacement, settlement, column bending moment, and pile bending moment of coral sand were smaller than those of Fujian sand, respectively. The magnification effect of column bending moment of buildings in coral sand was less than that in Fujian sand with increasing shaking intensity. This study can provide some supports for the seismic design of coral reef projects.

Effect of clay minerals on the suction stress of unsaturated soils

The primary objective of this study is to investigate the characteristics of suction stress in two types of unsaturated weathered soils with different clay minerals. To obtain the mineralogical properties of the two samples, X-ray diffraction and scanning electron microscope analyses were conducted, and a large amount of kaolinite and montmorillonite was subsequently contained in the granite soil and mudstone soil, respectively. The granite soil was first remolded to obtain the same relative density and particle size distribution as the mudstone soil, and an automated soil-water characteristic curve (SWCC) apparatus was used to measure the water content and matric suction. The weathered granite soil had a higher air-entry value, and the volumetric water content was significantly changed by small changes in matric suction. The weathered mudstone soil showed a large hysteresis in the SWCCs between drying and wetting processes because of the ink-bottle effect, contact angle effect, and trapped air. The suction stress characteristic curve (SSCC) demonstrates that weathered mudstone soil had a larger magnitude of suction stress. The SSCCs of the weathered granite and mudstone soils display similar tendencies to the SSCCs of silt and clay, respectively. Therefore, the unsaturated characteristics considerably depend on the clay mineral composition and particle size distribution.

In situ fabrication of a titanium-niobium alloy with tailored microstructures, enhanced mechanical properties and biocompatibility by using selective laser melting.

A titanium-niobium (Ti-Nb) alloy with tailored microstructures, enhanced mechanical properties and biocompatibility was in situ fabricated by selective laser melting (SLM) using a blended powder with 25wt.% Nb content. The effect of laser energy density from 70J/mm3 to 110J/mm3 on the phase transformation, microstructure, and mechanical properties of the SLM-printed Ti-25Nb alloy was investigated. The results indicate that the energy density of 110J/mm3 results in the highest relative density and homogeneous element distributions in the alloy. The α' and β phases with an orientation relationship of [023]β//[-12-16]α' were identified through X-ray diffraction and transmission electron microscopy, and their proportions are crucially determined by the laser energy density. With an increase in the energy density, the microstructure of the Ti-25Nb alloy varies from acicular-shaped grains to coarsened lath-shaped grains and to lath-shaped grain+cellular-shaped subgrains, due to the decrease in cooling rate and the rise in temperature gradient. The yield strength and microhardness of the printed Ti-25Nb alloy decrease with the increase in energy density from 70J/mm3 to 100J/mm3, and then increase to the highest values of 645MPa and 264HV at 110J/mm3, respectively. This variation of mechanical properties is dependent on both the coarsening of α' phase and the formation of β (Ti, Nb) solid solution. Besides, the SLM-printed Ti-25Nb alloy exhibits both the excellent in vitro apatite-forming capability and better cell spread and proliferation compared to pure Ti.

Comparative analysis of the hot-isostatic-pressing densification behavior of atomized and milled Ti6Al4V powders

A numerical model is established based on the plasticity theory and a thermomechanical coupled finite element method (FEM) to simulate the hot isostatic pressing (HIP) process of atomized and milled Ti6Al4V powders and is then experimentally verified. Key material parameters related to the simulation are obtained by experimental and calculation methods. The HIP densification mechanism for two types of Ti6Al4V powders are clarified through the analysis of the powder flow and relative density distribution of compacts using the proposed model. The results indicate that the densification trends of the two powders are not much different under the same working conditions and that milled powder with a higher energy is more conducive to densification and can better overcome the “corner effect” compared to atomized powder. The equiaxed microstructure of the milled powder sintered body contributes to increasing its strength, whereas the lamellar microstructure of the atomized powder sintered body contributes to increasing its plasticity.

X-ray computed tomography investigation of dilation of mineral-filled PVC under monotonic loading

The deformation-induced dilation of mineral-filled polyvinyl chloride (PVC) is investigated by means of polychromatic X-ray absorption tomography (XCT). Axisymmetric notched tensile specimens are strained to prescribed elongations using a tensile test apparatus and subsequently scanned by XCT after relaxation. During straining, surface deformations are quantified by digital image correlation (DIC) and contour tracking. The influence of stress triaxiality and strain rate on dilation is investigated by using tensile specimens with three different notch radii, all strained to three deformation levels at two different nominal strain rates. Pronounced reduction of density, corresponding to an increase of volume, is observed for all specimens in the XCT scans, but markedly different relative density distributions are measured for the three geometries. The accuracy of the polychromatic XCT density estimates is evaluated against data obtained with monochromatic synchrotron radiation computed tomography (sr-XCT), and a comparison to surface deformation-based dilation estimates is presented.

Comprehensive numerical modelling of the hot isostatic pressing of Ti-6Al-4V powder: From filling to consolidation

Hot Isostatic Pressing (HIP) is a manufacturing process for production of near-net-shape components, where models based on Finite Element Method (FEM) are generally used for reducing the expensive experimental trials for canister design. Researches up to date implement in the simulation a uniform powder relative density distribution prior HIPping. However, it has been experimentally observed that the powder distribution is inhomogeneous after filling, leading to a non-uniform tool shrinkage. In this study a comprehensive numerical model for HIPping of Ti-6Al-4V powder is developed to improve model prediction by simulating powder filling and pre-consolidation by means of a two-dimensional Discrete Element Method (DEM). Particles’ dimension has been scaled up in order to reduce the computational cost of the analysis. An analytical model has been developed to calculate the relative density distribution from powder particle distribution provided by DEM, which is then passed in information to a three-dimensional FEM implementing the Abouaf and co-workers model for simulating powder densification during HIPping. Results obtained implementing the initial relative density distribution calculated from DEM are compared with those obtained considering a uniform relative density distribution over the powder domain (classic approach) at the beginning of the analysis. Experimental work has been carried out for validating the DEM (filling) and FEM (HIP) model. Comparison between experimental and numerical results shows the ability of the DEM model to represent the powder flow during filling and pre-consolidation, providing also a reliable values of the relative density distribution. It also highlights that taking into account the non-uniform powder distribution inside the canister prior HIP is vital to improve numerical results and produce near-net-shape components.

Multi-lattice inner structures for high-strength and light-weight in metal selective laser melting process

Due to the development of additive manufacturing (AM), lattice structure which cannot be fabricated by the conventional manufacturing process or have shape restriction has attracted much attention. We propose a new lightweight design method using two types of lattice structures considering the manufacturability in the metal selective laser melting (SLM) and structural characteristics. Firstly, the specific procedure for the proposed design method is presented. In order to apply the two lattice structures, relative density criterion is derived by fabricating experiments using metal SLM process and analyzing geometry according to relative density. The optimal relative density distribution is calculated by performing the topology optimization with minimum relative density using a commercial software package. This proposed method is computationally and experimentally validated by a three-point bending test. Simultaneously, the same procedure is applied to uniform lattice for comparison with the proposed method. This proposed design has a 46% increase in stiffness, a relative flexural rigidity of 35% compared to the solid material, and has a deformation mode different from the uniform lattice. This design sets the standard for using two lattice structures and gives a new perspective on lightweight design with lattice structures.

Design and Optimization of Graded Cellular Structures With Triply Periodic Level Surface-Based Topological Shapes

Periodic cellular structures with excellent mechanical properties widely exist in nature. A generative design and optimization method for triply periodic level surface (TPLS)-based functionally graded cellular structures is developed in this work. In the proposed method, by controlling the density distribution, the designed TPLS-based cellular structures can achieve better structural or thermal performances without increasing its weight. The proposed technique can be divided into four steps. First, the modified 3D implicit functions of the triply periodic minimal surfaces are developed to design different types of cellular structures parametrically and generate spatially graded cellular structures. Second, the numerical homogenization method is employed to calculate the elastic tensor and the thermal conductivity tensor of the cellular structures with different densities. Third, the optimal relative density distribution of the object is computed by the scaling laws of the TPLS-based cellular structures added optimization algorithm. Finally, the relative density of the numerical results of structure optimization is mapped into the modified parametric 3D implicit functions, which generates an optimum lightweight cellular structure. The optimized results are validated subjected to different design specifications. The effectiveness and robustness of the obtained structures is analyzed through finite element analysis and experiments. The results show that the functional gradient cellular structure is much stiffer and has better heat conductivity than the uniform cellular structure.

Parameters prediction of hot-pressing sintering of high entropy alloys using numerical modeling and simulation

In this work, numerical modeling and simulation method was firstly used to obtain the hot-pressing sintering parameter of high entropy alloy (HEA). The finite element model was built to describe the consolidation process. Constitutive relation of powder material was applied assuming that metal powder is a kind of elasto-plastic material with an elliptical yield criterion. The change law of relative density for sintered bulk varying with pressure, time and temperature were obtained. Besides, the flow stress as well as relative density distributions were acknowledged with different sintering time. The simulation results indicate that the HEA would achieve a relative density of more than 95 % if the pressure above 45 MPa at 1150 ℃. The relative density from experiment is well agreement with that of simulation results when the sintering parameter are within the predicted range. This work is of great importance to the study of hot-press sintering of HEA.

Numerical simulation and optimization of the hot isostatic pressure process of a part of aircraft structure

Hot isostatic pressure process (HIP) has been widely used in aviation and aerospace fields to produce high-performance components with requirements of lightweight, high-reliability, and high-load requirement. During the HIP process, components are produced by powders arrangement, deformation, and bound diffusion. However, the limitation of the HIP process is the non-uniform density distribution of the product, which should be eliminated by appropriate design of the process. In this study, the HIP process of a part of aircraft structure is numerically studied. An improved Shima model for the HIP is introduced to investigate the deformation and densification process of the component. Two schemes of the HIP process are designed and compared by analyzing the relative density distribution at the selected sections of the component. Based on the optimized scheme, the component with uniform density distribution and high density is produced. The results indicated that the proposed model can predict the density distribution of the component produced by the HIP process and is helpful for process optimization.

Study into the rolling of a double-layered powdered core in a metallic sheath

We have developed an analytical model of the stressed-strained state of the two-layered powdered core in a metal sheath in the deformation zone when fabricating a composite material by rolling. Based on the constructed mathematical model, we performed a theoretical analysis of the influence of starting parameters on the course of the process of rolling a composite material. By using a finite element method, we simulated the process of rolling diverse powders in a metal sheath. The result of the theoretical research is the established effect of a material and the thickness of a sheath on the geometrical characteristics of a deformation site, as well as the influence of an asymmetry factor on a change in the zone of plastic shape alteration and the density of a powdered material. We have determined the distributions of normal contact stresses and relative density over a deformation site under different clamping. We calculated the components of rolling forces under deformation of a powdered core and a metal sheath. It was established that an increase in the thickness of a sheath leads to an increase in energy-force parameters of the process. In this case, the component of a rolling force due the sheath deformation can be both comparable to the component from the deformation of a powdered core, and exceed it by several times. The undertaken experimental study into the process has confirmed the validity of the constructed mathematical model that could be applied for determining the optimal technological regimes for rolling a 2-layer powdered core in a metal sheath. A technology for rolling a 2-layer powdered core in a metal sheath has been proposed, which includes rolling in two runs, filling the metal sheath consistently with components. It was established that at rolling based on the proposed technology the core’s relative density increases under the same rolling modes. In this case, the size of a powder’s fraction is retained, which is a prerequisite for a given production technology

Measuring bulk density variations in a moving powder bed via terahertz in-line sensing

Monitoring the relative density of static or moving powder inside a process line is essential for manufacturing high-quality products. The aim of this study was to predict density variations in a moving powder bed using terahertz reflection technology. We systematically investigated three grades (varying true density and particle size) of two materials: lactose and silicified microcrystalline cellulose (SMCC). These six powders specifically differ in their compressibility, which can be applied to assess the sensitivity and applicability of our method. The powders were filled into a round container, and terahertz reflection measurements were acquired continuously during the container’s rotation. The setup allowed to adjust the relative density by compacting the powders into specific powder bed heights. Each powder was compacted to various relative densities (compression pressures up to 100 kPa). We calculated the surface refractive index based on the in-line terahertz measurements acquired during rotation, which has a linear dependence on the relative density of the powder. This was confirmed by correlating the refractive index values with the theoretical relative densities based on the bulk and true densities of the powder. The coefficient of determination (R2) was larger than 0.962 (Lactohale 100) for all six powders, with the highest coefficients for Lactohale 220 (R2 = 0.996) and SMCC 50 LD (R2 = 0.995). The results suggest that the proposed method can resolve relative densities averaged across the powder bed that are as small as 0.3% (Lactohale 100). The high acquisition rate of the terahertz system (15 Hz) made it possible to determine the powder density in 230 positions uniformly distributed throughout the container, facilitating the investigation of the relative density uniformity in the container as a function of the powder bed height. It was observed that SMCC powders undergo a smaller change in the relative density variations upon compaction than the lactose powders. Moreover, the relative density maps clearly indicate local density differences in the powder bed for all powders. The relative density variations that were introduced by packing of the container prevailed throughout the compaction process for all samples with the exception of Lactohale 220. The presented approach allows a precise resolution of the spatial distribution of relative density, which facilitates an in-depth analysis of powder behavior upon compaction.

Morphometric Analysis of One-Component Polyurethane Foams Applicable in the Building Sector via X-ray Computed Microtomography.

A detailed morphometric analysis of one-component polyurethane (PU) expanding foams, with densities of 26 and 28 kg/m3 (‘SUMMER’ and ‘WINTER’ product versions), was conducted to evaluate the topology of the foam cells and to discover processing-to-structure relationships. The microstructural analysis of the heterogeneously distributed pores revealed tight relationships between the foam morphology and the cell topology, depending on the growth rate and local environmental conditions, governed by the properties of the blowing gas used. The most significant morphometric output included the following: open/closed porosity and (heterogeneous) pore distribution, relative density and (homogeneous) strut distribution, and total solid matrix surface and closed pore surface area—at the macroscopic level of the foam. While, at the microscopic level of the cells, the results embraced the following: the size of every detected strut and pore, identified two-dimensional (2D) shapes of the cell faces, and proposed three-dimensional (3D) topologies modelling the PU foam cells. The foam microstructure could be then related with macroscopic features, significant in building applications. Our protocol outlines the common procedures that are currently used for the sample preparation, X-ray scanning, 3D image reconstruction and dataset analysis in the frame of the X-ray computed microtomography (µ-CT) testing of the one-component PU foams, followed by a statistical (multiple Gaussian) analysis and conceptual considerations of the results in comparison with thematic literature.

Hip Implant Design With Three-Dimensional Porous Architecture of Optimized Graded Density

Even in a well-functioning total hip replacement, significant peri-implant bone resorption can occur secondary to stress shielding. Stress shielding is caused by an undesired mismatch of elastic modulus between the stiffer implant and the adjacent bone tissue. To address this problem, we present here a microarchitected hip implant that consists of a three-dimensional (3D) graded lattice material with properties that are mechanically biocompatible with those of the femoral bone. Asymptotic homogenization (AH) is used to numerically determine the mechanical and fatigue properties of the implant, and a gradient-free scheme of topology optimization is used to find the optimized relative density distribution of the porous implant under multiple constraints dictated by implant micromotion, pore size, porosity, and minimum manufacturable thickness of the cell elements. Obtained for a 38-year-old patient femur, bone resorption is assessed by the difference in strain energy between the implanted bone and the intact bone in the postoperative conditions. The numerical results suggest that bone loss for the optimized porous implant is only 42% of that of a fully solid implant, here taken as benchmark, and 79% of that of a porous implant with uniform density. The architected hip implant presented in this work shows clinical promise in reducing bone loss while preventing implant micromotion, thereby contributing to reduce the risk of periprosthetic fracture and the probability of revision surgery.

Experimental analysis and numerical simulation of sintered micro-fluidic devices using powder hot embossing process

For the past 2 years, interest in manufacturing technologies based on micro-fluidic systems has been continuously increasing. Today, micro-fluidic systems are used in numerous biomedical and pharmaceutical applications. Micro-fluidics cannot be thought about separately without advances in micro- and nano-fabrication. Investigations based on experiments, finite element modelling and simulations of powder hot embossing process (PHE) were performed to optimise the sintering step and processing parameters of micro-fluidic components. The model pertaining to thermo-elasto-viscoplastic behaviour was identified for 316L stainless steel powders. In this regard, different material properties such as sintering stress, bulk, and shearing viscosities were identified by inverse analysis from present dilatometer measurements using beam-bending and free sintering tests. The identification of materials was performed for various powder volume loadings and kinetic rates for different 316L elaborated feedstock, and the parameters were obtained as functions of relative density. The initial inhomogeneity due to the PHE process has been taken into account in the sintering simulation, as it affects the final shrinkage of the sintered components. The solid-state sintering simulations were investigated for various final sintering temperatures and kinetic rates to obtain high and homogeneous relative density distributions, achieve isotropic shrinkage and optimise the sintering process parameters. The numerical simulations were realised based on the identified parameters on a 3D micro-structured specimen with an associated rectangular plate support elaborated by PHE; this allowed a comparison between the numerical predictions and the experimental results for the sintering stage. The finite element simulation results of the sintering stage with a micro-fluidic structured component at a high final temperature (1360 °C) are in excellent agreement with the results of the experiments. The comparison of the simulation and experimental results validated the identified and implemented physical model and proposed methodologies.

Numerical Simulation of Densification of Cu–Al Mixed Metal Powder during Axial Compaction

The densification mechanism of Cu–Al mixed metal powder during a double-action die compaction was investigated by numerical simulation. The finite element method and experiment were performed to compare the effect of the forming method, such as single-action die compaction and double-action die compaction, on the properties of compact. The results showed that the latter could significantly raise the densification rate and were in good agreement with Van Der Zwan–Siskens compaction equation. The effects of the different initial packing structures on the properties of the compact were studied. The results showed that a high-performance compact could be obtained using a dense initial packing structure at a given compaction pressure. Additionally, the effects of the Al content and compaction pressure on the relative density and stress distribution were analyzed. It was observed that, with an increase in the Al content at a given compaction pressure, the relative density of the compact increased, whereas the stress decreased. Furthermore, when the Al content was fixed, the relative density and stress increased with increasing compaction pressure. The relationship between the relative density and the compaction pressure under different friction conditions was characterized and fitted according to the Van Der Zwan–Siskens compaction equation. The influence mechanisms of die wall friction on the compaction behavior were investigated. It was revealed that friction is a key factor that causes the inhomogeneity of the powder flow and stress distribution. Finally, the effects of the dwell time and height–diameter ratio on the densification behavior were analyzed, and it was found that an increase in the dwell time promoted the densification process, whereas an increase of the height–diameter ratio could hinder the process.

Two-Dimensional Multiparticle Finite Element Modeling on the Cold Isostatic Pressing of Al Powder

In this article, the cold isostatic pressing (CIP) of Al powders with different initial packing structures was numerically simulated in two dimensions using the multiparticle finite element method from particulate scale. The effects of external pressure and initial packing structures on the packing densification and performance of the compacts were systematically studied. Various macro/micro properties (such as relative density and distribution, local stress and distribution, and particle deformation behavior) and the densification dynamics/mechanisms were characterized and analyzed. Corresponding modeling on die compaction was also conducted for comparison. The results show that the relative displacement of particles is much less and the particle shape is more regular for CIP of ordered initial packing structure than those for CIP of random initial packing structure, and the distributions of relative density and local stress in the compact for the former case are more homogeneous. Compared with die compaction, the formability of CIP is much better; also, the compact has higher relative density and more uniform density and stress distributions. The normal stresses are transmitted in all directions in the compact during CIP because the external load is applied uniformly to the outer surface of the rubber mold from all directions in the entire process, while the normal stresses are directional along the loading path during die compaction.

Sinter structure analysis of titanium structures fabricated via binder jetting additive manufacturing

To facilitate functional part production in metal binder jetting additive manufacturing, the relationship between materials, process and sintering needs to be understood. This work relates sintering theory with process outcomes. For this, commercially pure titanium was deployed to study the effect of powder size distributions on green and sintered part qualities (bulk density, relative density, particle size, pore size, sinter neck size). The powders were uni- and bi-modal blends of 0–45 μm, 45–106 μm, and 106–150 μm. Computed tomography analysis was used to evaluate non-densifying (1000 °C) and densifying (1400 °C) sintering regimes. For green parts, the relative density and powder size distribution along the build direction followed a periodic fluctuation equivalent to the 150 μm layer thickness. The relative density fluctuation range was higher (±20%) for bi-modal blends with 0–45 μm, compared to all other blends (±8%) due to powder segregation. For non-densifying sintering, parts with 0–45 μm blends displayed both densifying and non-densifying behavior. For densifying sintering, powders containing 0–45 μm blends surpassed the 70% density threshold expected for this sintering regime. Overall, the finer particles improved bulk density of sintered parts, at the expense of higher levels of shrinkage and density anisotropy along the build direction.

Compaction and solid-state sintering of tungsten powders: MPFEM simulation and experimental verification

The uniaxial die compaction and solid-state sintering of different sized tungsten powders in powder metallurgy (PM) process was numerically reproduced in multi-particle FEM (MPFEM) modeling from particulate scale. The effects of particle size, initial packing structure, compaction pressure and sintering temperature on the relative density of the tungsten powder component were systematically studied and discussed. Various macroscopic and microscopic properties of the powder mass with different initial packing structures during compaction and sintering were characterized and analyzed. These properties include the overall relative density, local stress distributions, force structure and transmission, particle rearrangement and deformation, void filling behavior, as well as the densification dynamics and mechanism. The results show that by properly controlling the operating conditions such as initial packing structure, compaction pressure and sintering temperature, high performance PM component with high relative density, uniform density, stress, and void distributions can be obtained. Meanwhile, physical experiments were implemented to verify the simulation results. It is indicated that MPFEM modeling used in current work can provide the researchers with an effective method to simulate the whole PM process for refractory tungsten powders from particulate scale, especially the coupling of different stages can reduce the assumptions in the modeling and make the simulation results more accurate and much closer to the actual process.

Multifunctional design of heterogeneous cellular structures

Mesoscale cellular structures with different desired physical properties are promising for a broad spectrum of applications. The availability of Additive Manufacturing (AM) technology has significantly relaxed the fabricating limitation of cellular structures. It enables the design of cellular structure with complex cell topologies and relative density distribution. In this paper, a multifunctional design method for heterogeneous cellular structures is proposed. To introduce this method, Function-Performance-Property-Design parameter model is proposed at first. This proposed model can help designers to analyze the complex relations between focused functions and their related design parameters. Based on the proposed F-P-P-D model, the template of compromise Decision Support Problem (DSP) is applied to generate the optimization formulation which can generally consider the performances defined for several different functions. To solve the defined optimization problem, a multifunctional design simulation infrastructure is proposed for the designed heterogeneous cellular structures. Based on this simulation infrastructure, both the value of the objective function and its gradients can be evaluated. Then, Sequential Quadratic Programming (SQP) solver can be applied to solve the defined optimization formulation. The optimal relative density of cellular structures can be achieved and converted to the heterogeneous cellular structures at the end. A case study is provided at the end of this paper. For this case study, two different cell topologies and several different combinations of optimization parameters are used. A brief discussion is made to conclude the effects of cell topologies and other optimization parameters on the optimization results. Generally, the result of this design case validates the efficiency of the proposed design method. This method provides a useful design tool for users to take advantage of heterogeneous cellular structures for multifunctional purposes.