Void Volume Fraction Research Articles

MODELING OF POROUS DRY MATERIALS USING RHEOLOGICALDYNAMICAL ANALOGY

<p class="ABSTRACT">A theoretical model for porous viscoelastoplastic (VEP) materials under dry conditions is examined based on the principles of mass and energy conservation using rheological-dynamical analogy (RDA). The model provides the expressions for the creep coefficient, Poisson's ratio, modulus of elasticity, damage variable and strength in the function of porosity and/or void volume fraction (VVF). Compared with numerous versions of acoustic emission monitoring developed to analyze the behavior of the total wave propagation in inhomogeneous media with density variation, the RDA model is found to be comprehensive in interpretation and consistent with physical understanding. The reliability of the proposed model is confirmed by the comparison of numerical results with experimental ones on hardened concrete and rocks.</p>

Plastic deformation and fracture of AlMg6/CNT composite: A damage evolution model coupled with a dislocation-based deformation model

Understanding the plastic deformation and fracture behavior of Carbon nanotube (CNT)-reinforced aluminum composites is crucial for determining the factors controlling their strength and ductility. This article presents a novel approach by proposing a coupled micromechanical dislocation-based constitutive model combined with the Gurson-Tvergaard-Needleman (GTN) damage evolution model. The objective of this research is to accurately predict the load-displacement behavior of an AlMg6/CNT composite, which is manufactured through accumulative roll bonding (ARB), from yield to fracture. The study investigates the correlations between the number of ARB passes, which affects the dislocation density of the matrix, and the distribution of CNTs in the composite, with the GTN parameters. The analysis reveals that the volume fraction of void nucleating particles (fN) is a critical parameter influencing the ductility of the composite ductility. Initially, due to CNT agglomeration, they act as nucleation sites for damage, resulting in an increase in fN and a decrease in ductility. However, as the number of ARB passes increases, leading to a homogeneous CNT distribution, fN decreases, and CNTs contribute to improved strength and ductility of the composite. The proposed model accurately predicts the load-displacement curve of the composite during uniaxial tensile testing, taking into account the effect of ARB passes. The research findings provide insights for future extensions of the GTN model, aimed at enhancing its theoretical framework and applicability in the field.

Onset of dynamic void coalescence in porous ductile solids

This paper investigates void growth and coalescence in porous ductile solids under dynamic loading condition. A physical definition for the onset of void coalescence in porous ductile solids under dynamic loading is proposed. The onset is deemed to occur when the third invariant of the tensorial form of the Hill–Mandel condition attains a zero value. The definition allows for systematic investigations on the effects of dimensionless stress rate κ and stress state, defined by the stress triaxiality T and Lode parameter L, on the onset of void coalescence via micromechanical analyses. The analyses reveal that the critical macroscopic effective strain for the onset of void coalescence displays an increasing–decreasing transition trend as the dimensionless stress rate increases, for all levels of T and L considered. The macroscopic effective strain at the transition is identified as the “ductile–brittle” transition strain. The dimensionless stress rate at which the transition strain occurs is found to be relatively constant. A mapping in the κ−T space for L=−1, representative of a generalized uniaxial tension typical in spall fracture experiments, is established which depicts regions where coalescence and non-coalescence can take place, as well as the ductile–brittle regions demarcated by a ductile–brittle transition curve. The results also show that the critical void volume fraction and macroscopic effective strain at the onset of void coalescence are insensitive to inertia at high stress triaxialities at L=−1.

Exploring the Effect of Specimen Size on Elastic Properties of Fused-Filament-Fabrication-Printed Polycarbonate and Thermoplastic Polyurethane.

Additive manufacturing (AM) is often used to create designs inspired by topology optimization and biological structures, yielding unique cross-sectional geometries spanning across scales. However, manufacturing defects intrinsic to AM can affect material properties, limiting the applicability of a uniform material model across diverse cross-sections. To examine this phenomenon, this paper explores the influence of specimen size and layer height on the compressive modulus of polycarbonate (PC) and thermoplastic polyurethane (TPU) specimens fabricated using fused filament fabrication (FFF). Micro-computed tomography imaging and compression testing were conducted on the printed samples. The results indicate that while variations in the modulus were statistically significant due to both layer height and size of the specimen in TPU, variations in PC were only statistically significant due to layer height. The highest elastic modulus was observed at a 0.2 mm layer height for both materials across different sizes. These findings offer valuable insights into design components for FFF, emphasizing the importance of considering mechanical property variations due to feature size, especially in TPU. Furthermore, locations with a higher probability of failure are recommended to be printed closer to the print bed, especially for TPU, because of the lower void volume fraction observed near the heated print bed.

The cyclic GTN model for ULCF fracture analysis of Q355 steel

The cyclic GTN (C-GTN) model, built upon the GTN model, considers the influence of cyclic loadings on the evolution of microvoids, enabling the prediction of ULCF fracture in materials. In this study, the C-GTN model was calibrated for Q355 steel based on tests on notched round bar specimens reported in the literature. Following existing four tests on single-edge notched plate (SENP) specimens subjected symmetric cyclic loadings, additional four ULCF tests were conducted on SENP specimens with asymmetric cyclic loadings. ULCF fracture was observed in these tests and ULCF lives of these SENP specimens were obtained. Mesh sensitivity was investigated for the ULCF fracture analysis of the SENP specimens with the C-GTN model. After balancing the computational accuracy and cost, the ULCF fracture analysis of the SENP specimens were conducted using finite element models with a mesh size of 0.2 mm at the notch tip. ULCF lives predicted by the C-GTN model agree very well with test results for all SENP specimens. The agreement validated the applicability of the C-GTN model for the ULCF fracture analysis of Q355 steel. The increase of the void volume fraction and the degradation of its critical value played dominant roles in the ULCF fracture of V-notched and U-notched SENP specimens respectively.

Ductile crack growth of high-graded pipeline steels in the presence of Lüders plateau

Strain-based engineering critical assessment methods allows certain amount of plastic strain during installation and in service, for pipelines crossing seismically-active areas. Most strain-based engineering critical assessment methods are established for materials with smooth stress-strain relationship, leaving the so-called Lüders plateau influence on ductile fracture response seldomly explored. This work studied the effect of the Lüders plateau on mode I ductile crack growth with the modified boundary layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model was implemented and the Gurson damage model was selected to simulate crack propagation. Factors including the plateau length and softening modulus in the “up-down-up” constitutive model, strain hardening of the matrix material and the initial void volume fraction parameter were analyzed. Numerical results show that the Lüders plateau modifies the crack tip constraint and the damage evolution, and the plateau length plays the dominant role on ductile crack growth behaviour in the presence of Lüders plateau.

On elastoplastic behavior of porous enamel–An indentation and numerical study

The micro/nano pores in natural mineralized tissues can, to a certain extent, affect their responses to mechanical loading but are generally ignored in existing indentation analysis. In this study, we first examined the void volume fraction of sound and caries lesion enamels through micro-computed tomography (micro-CT). A Berkovich indentation study was then carried out to characterize the effect of porous microstructure on the mechanical behavior of the human enamels. The indentation tests were also modeled using the nonlinear finite element analysis technique to simulate indentation load-displacement curves, which showed reasonable agreement with the experimental measurements. From the simulation results, the extent of densification in the plastic zone was identified and the corresponding stress and contact pressure evolutions were quantified. Further, a conventional elastic-perfectly plastic material model without considering micropores was also developed to investigate the compaction effect of the porous structure. The simulation results reveal that conventional elastic perfect-plastic constitutive models become less reliable to model the mechanical behavior of carious lesion enamel with increasing loss of mineral content as it underestimates the yield stress and plastic energy dissipation. This study divulges the importance of compaction of porous enamel structure beneath the indented area. Note that understanding the effect of porous microstructures on plastic behavior is vital as the involved inelastic deformation mechanism associated with irreversible processes, such as wear and localized microcracking, has a significant bearing on wear and fatigue behavior of enamel. Statement of significanceBased on micro-CT and nano-indentation characterization, a numerical model was developed aiming to precisely describe the deformation behavior of naturally porous enamel. Inelastic properties and energy dissipation characteristics of porous enamel were investigated in detail. This work demonstrated that the existence of micro-pores in White Spot Lesions (WSLs) contributes to mechanical stability, which can mitigate the reduction in Young's modulus and fracture toughness resulting from loss of mineral components. The knowledge gained from this study can be used to explain the mechanisms related to irreversible processes, such as contact induced cracking and wear, and strengthen understanding of the mechanical behavior of porous mineralized tissues.

Retracted: Micromechanical properties characterization of 4H–SiC single crystal by indentation and scratch methods

Growth and micromachining of single crystal silicon carbide (SiC) have drawn extensive attention in wide bandgap semiconductors and remained challenging. The micromechanical properties (i.e., hardness, elastic modulus, fracture toughness), which are the key to machinability and machining quality (and therefore the yield of the grown SiC), of 4H–SiC were assessed by nanoindentation, microhardness, and microscratch tests. Consistent values of true indentation hardness of 4H–SiC can be obtained by different approaches without the need for the area function of the indenter. Accurate determination of elastic modulus (i.e., 583.5 GPa) and indentation hardness (i.e., 38 GPa) of 4H–SiC by the instrumented indentation technique requires low loads with slight indentation-induced damage. Consistent values of fracture toughness Kc of 4H–SiC were obtained by different methods such as the Vickers/Berkovich indenter-induced cracking method (2.1 MPa·m1/2), energy-based nanoindentation approaches (the critical void volume fraction of 0.062 should be used for 4H–SiC when the deterioration of indentation hardness is used), and linear elastic fracture mechanics (LEFM)-based scratch approach with a spherical indenter (2.6 MPa·m1/2). This work provides the guidance for the mechanical machining of 4H–SiC wafers and the paradigm of micromechanical characterization of brittle solids by indentation and scratch technologies.

Thermo‐mechanical properties of epoxy composites filled with inorganic particulate fillers for robust solder mask application

AbstractFiller components play a crucial role as thermo‐mechanical reinforcement to the epoxy‐based solder mask, ensuring effective insulation and passivation. This study investigates the impact of different inorganic filler types (talc, silica (SiO2), boron nitride (BN) and barium sulfate (BaSO4)) and loadings (5 and 15 wt%) on the tensile and thermal properties of the epoxy composites. The composites were blended, cast and thermally cured. Of these composites, only 15 wt% SiO2/epoxy composite exhibits notable increments in both tensile strength and modulus, surpassing unfilled epoxy by 11.65% and 31.9%, respectively. It also displays the highest elongation at break, supported by small particle size, high specific surface area and minimal void volume fraction. For thermal tests, the addition of all fillers increases the storage modulus in both glassy and rubbery regions, especially 15 wt% talc/epoxy composite with 30.09% increment at 25 °C. Additionally, all fillers raise the glass transition temperature (Tg), notably improving it by 9 °C in the 15 wt% BN/epoxy composite. Moreover, their inclusion generally enhances the onset decomposition temperature (Tonset) and reduces weight loss during decomposition. © 2024 Society of Chemical Industry.

Leakage characteristics of plug flow in the case of pipe leakage

AbstractIn order to study the changes in two‐phase flow parameters after pipeline damage and the impact of gas injection on water leakage from damaged pipelines, experimental and simulation studies were conducted on the damaged pipelines. The main objective is to compare the void fraction in intact and damaged states and to investigate the factors influencing and variations in gas–liquid leakage flow rates. The results show that increasing the liquid superficial velocity can reduce the difference in void fraction distribution caused by different damage directions. The leakage flow rate is affected by the direction of damage and the superficial velocity of the respective phase. It has been discovered that gas injection in the pipeline can make it easier to find small‐area pipeline damage. The change rate of the volume void fraction shows different changes with the increase in gas proportion in different directions; the shape of the bubble has no bearing on this change.

Effect of processing temperature on interface microstructure of diffusion welded joint of super-duplex stainless steel and zirconium alloy with nickel alloy interlayer

In the present study, super-duplex stainless steel (SDSS) and zirconium alloy (ZrA) was vacuum welded using nickel alloy (NiA) interlayer by the diffusion welding process. The welded joints were processed from 800 to 950 °C in steps of 50 °C using 4-MPa compressive load for 75 min. The joints were characterised using optical microscopy, scanning electron microscopy, electron probe micro-analyser, and x-ray diffractometer. The SDSS│NiA interface is planar in nature for all welding temperatures; however, layer-wise Ni5Zr, Ni10Zr7, NiZr, and NiZr2 reaction products were observed at the NiA│ZrA interfaces. The reaction products and width of these products increase with welding temperature. At both the interfaces, hardness values gradually increase with an increase in welding temperature. NiA│ZrA interface exhibited higher hardness as compared to the SDSS│NiA interface due to the presence of layer wise intermetallics. Joints reached a maximum tensile strength of ∼370 MPa (with an elongation of ∼7.9 %) when the joints were processed at 900 °C due to optimal reaction zone width and the least embrittling effect of the respective intermetallics. At lower temperatures, fracture surfaces of welded assemblies showed featureless morphology and voids present due to the poor coalescence of mating surfaces. At higher welding temperatures, the fracture surface of the transition joint preferred brittle fracture mode due to the cleavage planes with different alignments with insignificant volume fraction of voids on the fractography.

Physicomechanical, water absorption and thermal properties and morphology of Paederia foetida fiber–Al2O3 powder hybrid‐reinforced epoxy composites

AbstractHybridization of natural fibers with ceramic materials for reinforcing composites allows the optimization of the properties of these materials. For this reason, the present study aims to investigate physical, mechanical, water absorption, swelling and thermal properties as well as morphological characteristics of a hybrid Paederia foetida fibers–alumina powder (PFs–Al2O3)‐reinforced epoxy composite. Epoxy resin served as the matrix, while PFs and Al2O3 were employed as reinforcement. Five types of composites were fabricated using the hot‐pressing technique. The corresponding ratios of PFs:Al2O3 volume fractions (%) considered here were 0:40 (SFA), 10:30 (SFB), 20:20 (SFC), 30:10 (SFD) and 40:0 (SFE). The results reveal that the density of the hybrid PFs–Al2O3 composites decreased for increasing volume fractions of PFs: from 2.173 g cm−3 of SFA to 1.042 g cm−3 of SFE. The highest values of tensile strength (i.e. 49.085 MPa), tensile elastic modulus (i.e. 1.431 GPa) and impact strength (24 kJ m−2) were obtained for the SFD composite material with 30% volume fraction of PFs and 10% volume fraction of Al2O3: this happened because interface bonds between PFs, Al2O3 and epoxy phases achieved their optimal configuration. Overall, mechanical properties of the hybrid PFs–Al2O3‐reinforced epoxy composites were superior to those of composites reinforced only by PF fibers or only by Al2O3. Water absorption and swellability reached their maximum values at the steady state occurring after tested samples remained immersed in water for 820 h. The SFE composite reinforced only by PFs presented the highest water absorption and swelling (i.e. 6.034% and 5.81%, respectively) while for all other hybrid composites (SFD, SFC and SFB) these two quantities remained below 5%. Density and volume fraction of voids of hybrid PFs–Al2O3‐reinforced composites were consistent with the corresponding properties of the composites reinforced only by Al2O3 or PFs. SFD was also the most thermally stable material. Scanning electron microscopy observations of fractured surfaces indicated that the microstructure of the PFs–Al2O3‐reinforced epoxy composites presents several voids, fiber pullouts and transverse fibers, which together optimize the mechanical response of the composite material. Remarkably, the SFD composite material was highly competitive with the most recently developed hybrid composites employing natural reinforcements. © 2024 Society of Industrial Chemistry.

Micromechanical characterization of zirconia and silicon nitride ceramics using indentation and scratch methods

Micromechanical characterization of brittle ceramics remains challenging due to the difficulty in sample preparation required by conventional tests. The micromechanical properties (e.g., elastic modulus EIT, indentation hardness HIT, and fracture toughness KIC) of ZrO2 and Si3N4 were investigated by indentation and scratch tests with different indenters (e.g., Vickers, Knoop, and Berkovich indenters) under various loads. The ratio of the true hardness by the Vickers indenter over that by the Knoop indenter is approximately a constant of 1.13 and independent of material. Elastic recovery of residual imprint by the Knoop indenter was also used to assess elastic modulus of ZrO2 and Si3N4, and modified equations were proposed. The length of Vickers indenter-induced cracking was found to be proportional to the applied load under large loads, and a modified formula for calculating fracture toughness was proposed for ZrO2 and Si3N4, which have relatively large fracture toughness of about 9 MPa⋅m1/2. The critical void volume fraction f* in the nanoindentation energy-based methods was found to linearly decrease with the exponent mf of the power-law equation used for curve fitting of the degradation of HIT or EIT with hmax. The determination of fracture toughness by scratch methodology was found to be affected by mechanical properties of material, indenter geometry, and data range.

Predictive Modeling of Fracture Behavior in Ti6Al4V Alloys Manufactured by SLM Process

This study focuses on ductile fracture behavior prediction for Ti6Al4V alloys fabricated via Selective Laser Melting (SLM). A modified Gurson-Tvergaard-Needleman (GTN) model characterizes void growth and shear mechanisms under uniaxial stress. The research explores the impact of Artificial Neural Network (ANN) architecture, specifically hidden layers and neurons, on predicting fracture parameters. Results reveal that increasing hidden layers substantially enhances accuracy, particularly for fracture displacement. Notably, predicting maximum force requires fewer layers than fracture displacement. Using selected layers and neurons, the system consistently achieved R2-values exceeding 0.99 for both maximum force and fracture displacement. The study identifies the initial void volume fraction (f0) parameter as having the most significant influence on both properties.

Numerical simulation of void elimination in the billet during hot shape rolling processes based on the Gurson–Tvergaard–Needleman model

The presence of voids can compromise the strength and continuity of downstream products. The Gurson–Tvergaard–Needleman model was utilized to obtain the relevant parameters. A 3D finite element model was then employed to investigate the elimination of voids in a porous free-cutting steel 1215MS during the hot shape rolling process. The center distribution of voids in the billet was considered in the finite element model, and the relationships between the void elimination and the pressure stress in the billet were analyzed. The influences of rolling reduction, rotation speed, and friction between the work roller and billet on the void elimination were also discussed. The results revealed that the pass reduction has a significant influence on the ultimate value of void volume fraction, which is beneficial for better material self-healing during the shape-rolling process. These findings suggest that accurate predictions of void elimination in the workpiece can be achieved using the finite element method for successful simulation of the hot shape rolling process.

Numerical simulation of gas-liquid two-phase flow in a disc pump under different inlet bubble diameters

Visual investigation and numerical simulation were utilized to analyze the internal flow pattern transformation and bubble diameter variation of a gas-liquid two-phase flow disc pump. The results reveal that increasing the intake volume fraction (IGVF) from 1.12% to 27.67% changes the flow pattern in the suction chamber from bubbly to agglomerate bubbly, slug flow, and separated flow. Due to the particularity of the impeller structure of the disc pump, the blades in the leaf area of the front and rear cover plates play a barrier role. The gas phase gathers most violently at the edge of the blade in the leaf area, while the flow channel in the middle leafless area is wider and has higher permeability. At 1500r/min and 7.11% inlet volume void fraction, the local void fraction extreme value of the front edge of the blade in the blade area of the front cover plate increases to three times the initial void fraction, while the void fraction extreme value of the middle section of the bladeless area decreases to two-thirds of the initial void fraction. This research can be used to analyze the gas phase distribution and migration law in the disc pump impeller.

Automated Manufacturing of Grid Stiffened Panels with Radically Reduced Tooling

Grid stiffened continuous fiber reinforced composite panels are an attractive option for creating lightweight structures due to the tailorability for various applications and the resulting high specific properties. However, the panel stiffeners and stiffener intersections result in high tooling complexity and correspondingly high cost of implementation. These factors have limited the impact of such structures in the composites industry. Previous research has demonstrated the ability to produce high quality, high aspect ratio beams, representative of individual grid stiffeners, using E-glass/PET comingled tow via direct digital manufacturing. Further, prior preliminary efforts have demonstrated the potential to use the same approach to manufacture grid intersections that have continuous fiber in both directions. To expand on the previous efforts in grid stiffeners produced by direct digital manufacture with radically reduced tooling requirements, this effort compares two methods of providing positioning and consolidation, nozzle vs. roller. Both processes are based on a commingled yarn feedstock. The extrusion through a nozzle has been shown to enable grid intersection control through local variations in applied consolidation and serves as the baseline process. However, this approach requires a continuous placement path to create the complete grid stiffened panel as no mechanism for cutting and restarting has been implemented. Alternatively, a newly developed placement head incorporating cut and refeed, mounted to a 6-axis robot, offers the potential of improved path placement efficiency. The two techniques are used to produce similar grid composite stiffeners to evaluate the effectiveness of producing the grid intersections. Rate of deposition of the two end effectors are compared and the quality of the associated grid stiffeners, and intersections, are determined through measurement of geometry, fiber volume fraction and void fraction.

Study on the damage behaviour of titanium alloy laser-welded blank during hot gas pressure forming

The damage behaviour of titanium alloy laser-welded seam during hot gas pressure forming was studied by experiment and simulation. The GTN damage model was used to simulate the hot gas pressure forming process of the welded blank. The evolution of the void volume fraction during the forming process was obtained. Hot gas pressure forming experiments of cup-shaped parts were carried out. The microstructure at different positions of the cup-shaped part was observed by scanning electron microscope. Results show that the damage to the weld seam during hot gas pressure forming was mainly related to the strain. The damage of the inside fillet near the flange develops most rapidly, and it easily cracks due to the large deformation during the free bulging stage. The damage on the bottom centre develops slowly at the free bulging stage. After the bottom of the cup-shaped part contacted the die, the volume fraction of damage on the bottom center continued to increase firstly and then reached to a stable value gradually. Various micro cracks were observed during the hot gas pressure forming. The volume fraction of cracks increased with the increasing strain, and the small cracks gradually grew, expanded, and merged to form larger cracks. It is important to control the maximum strain of the weld seam during the forming to avoid possible harmful damage.

Microstructural evolution during superplastic deformation of commercial Al5083 alloy

The aluminum alloy SPF process has found extensive application in the aviation and rail transportation industries. The commercial Al5083 alloy presents the advantages of low density, high specific strength, a simplified manufacturing technique, and low cost, thus making it an appealing option for producing components with minor strain and complex configurations. This study focused on examining the mechanical properties of the commercially available Al5083 alloy. Different temperatures (450 °C, 480 °C, 510 °C) and strain rates (0.01 s−1, 0.005 s−1, 0.001 s−1, 0.0005 s−1) were employed to investigate the behavior of the material. Furthermore, a constitutive equation was developed to describe the alloy's response under superplastic conditions. The utilization of EBSD allowed for the investigation of the evolution of grain and dislocation density, while XRD was employed to determine the development of macroscopic texture strength and texture type. The dominant mechanism of superplastic deformation in the commercial Al5083 alloy was identified as dynamic recrystallization and intra-crystalline slip, which distinguishes it from conventional fine-grained aluminum alloys. SEM was used to establish the exponential relationship between void volume fraction and true strain. The results provide valuable insights into the evolution of the macro-mechanical properties and microstructure of commercial Al5083 alloy during superplastic forming.

Novel Design Charts for Anisotropic Effective Elastic Properties of Pyramidal Lattice Materials

Novel design charts for predicting the anisotropic effective elastic properties of pyramidal lattices are proposed for a wide range of relative density and various struts shape through finite element (FE) simulations. Pyramidal lattices are 3D printed using digital light processing (DLP) and are subsequently subjected to uniaxial compression tests to provide a partial experimental validation for the presented design charts. Regarding strut shape, the presented results uncover that using hollow-tapered instead of solid-uniform struts leads significant improvements for effective Young's and shear moduli. In addition, this study has paved the way towards enhancing our understanding of how the anisotropy of pyramidal lattices can be tailored by tuning the relative density and strut architecture. Resorting to an analytical framework, results indicate that controlling the void volume fraction of struts can lead the same effective Young's modulus for all three principal directions of pyramidal lattices with low relative densities.