Large Residual Stresses Research Articles

Fracture Analysis and Working Stress Calculation of Bearing Cage Used in Charging Pump in a Nuclear Power Plant

This paper presents an analysis of the fracture accident of a cylindrical roller bearing cage used in a charging pump in a nuclear power plant. The causes and mechanisms of bearing cage breakage were investigated by material failure analysis and simulation calculations. Macroscopic observation results confirmed that the cage fracture occurred at the stress concentration position. The microfracture morphology of the cage obtained from scanning electron microscopy showed a fatigue feature. The analysis of residual stress indicated large residual stress perpendicular to the fracture surface. The finite element calculation showed that when the bearing was moving in and out of the working area during operation, large working stress appeared at the stress concentration position. Working stress and residual stress acted together, approaching the fatigue limit of materials, and finally led to the cage fatigue fracture. The stress of the other two structural cages of the same type of bearing was also calculated, and no such large stress concentration was identified; thus, one plastic cage was temporarily used.

Wire ARC Additive Manufacturing of Functional Metals - A Review

The need for wire arc additive manufacturing (WAAM) has substantially expanded in recent years, and it has emerged as a possible alternative to subtractive production. According to research, the mechanical qualities of wire arc additively manufactured materials are comparable to cast material. When compared to other fusion sources, WAAM provides considerable cost savings as well as a higher deposition rate. However, WAAM presents considerable problems, including undesired microstructures and mechanical characteristics, large residual stresses, and deformation. As a result, more study is required to address the aforementioned problems by optimizing process parameters and post-deposition heat treatment. In accordance with the foregoing, this paper attempts to fill the gap by presenting a comprehensive review of WAAM literature, which includes stage-wise development of WAAM, metals, and alloys used, effects of process parameters, and methodologies used by various researchers to improve the quality of WAAM components. Furthermore, this work suggests topics that could be explored further in the future. Keywords: Wire Arc Additive Manufacturing, Subtractive production, cost saving, optimizing parameters, stage wise development.

Numerical Simulation and Experiment of Stress Relief and Processing Deformation of 2219 Aluminum Alloy Ring

Large aluminum alloy ring forgings are the core components of heavy-duty rocket fuel storage tanks, and the large residual stress inside the rings leads to poor shape accuracy of large thin-walled parts. The initial stress of the 2219 aluminum alloy ring blank was tested using the drilling method, and the creep constitutive coefficient of the 2219 aluminum alloy was determined through stress relaxation tests. The numerical simulation processes of thermal stress relief (TSR), vibration stress relief (VSR), and thermal–vibration stress relief (TVSR) were compared and established. Through the correlation analysis between the actual measurement results of residual stress and the simulation results, it can be seen that the strong correlation in three directions at each measurement point accounts for over 37.5%, and the moderate correlation accounts for over 62.5%. This indicates that the numerical simulation model of 2219 aluminum alloy ring containing initial residual stress can accurately reflect the size and distribution of residual stress inside the actual ring. The simulation results show that the derived constitutive model can describe the stress relaxation process of TVSR by combining a single thermal time effect stress relaxation constitutive theory with a VSR plastic deformation material model. The simulation models established above were used to calculate the residual stress homogenization ability of three types of aging. The results showed that VSR, TSR, and TVSR can homogenize and reduce the residual stress field inside the ring, improve the distribution of residual stress inside the ring, and have a better overall homogenization ability of TVSR. The VSR control has a certain effect on reducing and homogenizing residual stress, but compared with TSR and TVSR, the reduction and homogenization ability of residual stress control is limited. The homogenization control effect TVSR > TSR > VSR, and the maximum equivalent stress homogenization rates of VSR, TSR, and TVSR are 52.8%, 80.6%, and 82.2%, respectively. Then, numerical simulation technology was used to study how the initial residual stress in the blank causes the deformation of the ring during the thin-walled machining process. The roundness error theory of the minimum containment area method was applied to evaluate the deformation degree during the thin-walled numerical machining process, and the TVSR method was used for stress regulation. The deformation law of the thin-walled machining of the ring under different aging parameters was studied.

Selective laser melting of 316L–CuCrZr bimetallic structure via IN718 transition layer

Steel/copper bimetallic structural materials combine the good strength and corrosion resistance of steel with the high thermal and wear resistance of copper and have been widely used in fusion reactors, conformal cooling channels, and heat transfer devices. Due to the large difference in thermal and physical properties of steel and copper, and the immiscibility of steel and copper, the bonding interface usually produces a large residual stress during the forming process, which leads to the formation of interface cracks. In order to combine CuCrZr with 316L stainless steel by using selective laser melting technology, IN718 was deposited on 316L stainless steel as a transition layer. The effects of the IN718 alloy transition layer on the microstructure, phase composition, and mechanical properties of the interface of 316L–CuCrZr were studied. IN718–316L had no defects such as pores and cracks at the interface and achieved good metallurgical bonding. The IN718–CuCrZr interface area and copper side had round key holes and relatively small pores. In the solidification process, IN718 preferentially solidified in the shape of fine particles, providing a nucleation point for the copper grain, thus forming equiaxed grains because of the high cooling rate of the interface. No macroscopic defects were observed at the bonding position of the 316L–IN718–CuCrZr samples, and the elements at the interface were fully diffused by each other. The tensile strength of the 316L–IN718–CuCrZr samples reached 403 MPa, and the interface strength was significantly improved upon the addition of the transition layer.

Analysis of spring-back deformation of CF/PEEK thin angled laminates by laser-assisted forming

Laser-assisted forming is an advanced manufacturing method for thermoplastic composites, which has attracted much attention in recent years. Angled structure is the basic element of complex components. In this paper, the influence of forming characteristics and process parameters of laser-assisted forming on the angle deviation of angled thermoplastic laminates is studied. The results show that thin angled laminates with no more than 7 layers of thermoplastic tapes manufactured by laser-assisted forming have angles larger than that of the mold, that is, the spring-back deformation. Laser power, consolidation force and the number of layers have significant effects on the spring-back deformation. The local heating and pressing, and the fast cooling rate during laser-assisted forming cause large residual stress in the samples, which is the main reason for the spring-back deformation. In addition, the effect of repass treatment on spring-back deformation is studied. It turns out that the repass treatment can significantly reduce the spring-back deformation. This is due to the prolonged time of samples at high temperature, which could relax the molecular chain and reduces the residual stress.

Growth mode and characterizations of electrodeposited Re thick films from aqueous solutions with additives on Cu (110) + (311) substrates

Rhenium (Re) thick films were electrodeposited on copper (Cu) substrates with (110) + (311) texture from aqueous solutions with additives of 2 g l−1 gelatin, 1 mM sodium lauryl sulfate, and 1 mM vanillin. The microstructure and morphology of the films with different thickness values were characterized by scanning electron microscopy and atomic force microcopy. The chemical composition and the crystallographic structure of the films were identified by energy dispersive spectroscopy and x-ray diffraction, respectively. Re thick films were obtained due to the synergistic effect of additives. The additives had a significant influence on electrodeposition of the films. The microstructure and growth mode of Re films were influenced by surface topography and orientation texture of the substrate. The deposition rate was about 0.064 mg min−1. Re thin films adhered well to the substrate with no evidence of delamination and cracking. However, the Re thick film was not stable, fine microcracks were present, and even delamination occurred in vacuum condition due to large residual stress in the deposits or the shrinkage from decomposition of Re hydrides in the vacuum environment. Re films consisted of an amorphous phase structure. The Re film had a high hardness of 349 ± 15 VHN and exhibited a Stranski–Krastanov growth mode.

Preliminary tests on additive-manufactured Al-Sc specimens for the setup of a numerical model for Laser Shock Peening

Aluminum-Scandium alloys offer a great potential in aerospace applications due their high corrosion resistance and improved strength properties. Furthermore, these alloys have been qualified for laser additive manufacturing (AM), producing parts with static strengths rivalling their conventionally manufactured counterparts. However, laser processing also results in large residual stresses that can severely affect fatigue properties and result in geometric distortion. A proven method for reducing the fatigue-related problems in metallic structures is to drive compressive residual stresses into the affected area by means of Laser Shock Peening (LSP). This surface treatment is very effective in bulk structures, improving life performances of fatigue-sensitive aeronautical components, such as jet engines turbine blades or helicopter gearboxes. On the other hand, quite a limited number of studies has been presented on the effect of LSP on fatigue crack growth in thin components and laser AM structures. This work presents first the results of preliminary tensile tests on additive manufactured Al-Sc specimens. The tensile strengths of as-built and heat-treated samples are compared. Then, a reliable and computationally time-effective numerical model of laser peening is reviewed, referring to case studies investigated earlier. In view of applying LSP to additive manufactured Al-Sc components, the effects of different laser parameters and geometries are discussed. Finally, the possible drawbacks of the LSP treatment are addressed, in order to exploit its full potential in increasing the fatigue life of AM components.

Electrochemical-mechanical coupling failure mechanism of composite cathode in all-solid-state batteries

Composite cathode composed of active particles and solid electrolytes (SEs) can considerably enlarge the particle-SE contact areas and achieve high areal loadings in all-solid-state batteries (ASSBs). However, the challenging interfacial instability and particle damage problems remain unsolved. Herein, we establish a 3D electrochemical-mechanical coupled model to investigate the underlying failure mechanism by considering the governing electrochemical and physics processes. Micro-scale heterogeneous primary particles with random crystallographic orientation and size inside the LiNi1/3Co1/3Mn1/3O2 (NCM111) secondary particle of the model result in the anisotropic Li diffusion and volume variation within the secondary particle, leading to significant nonuniformity of the Li concentration, and GPa-level stress distributions at primary particle boundaries, and finally causing the particle internal cracks. The particle volume shrinkage under the constraint of stiff Li7La3Zr2O12 (LLZO) SE triggers the interface debonding (gap>50 nm) with increased interfacial impedance to degrade cell capacity. Higher C-rates result in larger residual stress (∼100 MPa)/strain/debonding gap at discharging end, more likely to deteriorate the cell performance. Increasing the interfacial strength between the particle and SE can suppress the interface debonding but induces high stress (up to 10 GPa). Results reveal the underlying mechanism of the electrochemical-mechanical coupling failure mechanism for composite cathode and provide promising guidance on the further improvement of a more robust composite cathode for ASSBs.

Thermoelastoplastic Finite Element Analysis of TiAl6V4 Thin-walled Ring Parts Based on Laser Metal Deposition Processing

Based on the simulation theory of stress field and temperature field in additive manufacturing, this paper numerically simulates and analyzes the laser metal deposition process of thin-walled ring, optimizes the simulation results by setting different process parameters, and analyzes the possible problems in the process of laser metal deposition and the corresponding optimization scheme. The comparison results of temperature field simulation results show that the phenomenon of temperature superposition and slow heat dissipation will occur in the printing process. Set a certain cooling time between the two adjacent layers, the temperature will gradually increase from layer by layer, and the heat dissipation will also improve, which plays an optimization role in preventing excessive temperature and remelting to a certain extent. The results of stress field analysis show that under the influence of temperature change, the upper material has a certain stress release effect on the lower material during welding, which makes the stress change between the middle layers in the printing process show a wavy trend, and large residual stress will be generated in the cooling process of the formed parts after printing. Through the deformation analysis results of the formed parts, it is concluded that the deformation of the formed parts increases gradually from bottom to top, and with the increase of printing speed, the maximum deformation caused by welding decreases gradually, but the area of high deformation area on the formed parts increases gradually.

The effect of rescanning strategy on residual stress and deformation of laser-based powder bed fusion of 316L stainless steel thin-walled parts

Purpose Laser-based powder bed fusion (LPBF) is a new method for forming thin-walled parts, but large cooling rates and temperature gradients can lead to large residual stresses and deformations in the part. This study aims to reduce the residual stress and deformation of thin-walled parts by a specific laser rescanning strategy. Design/methodology/approach A three-dimensional transient finite element model is established to numerically simulate the LPBF forming process of multilayer and multitrack thin-walled parts. By changing the defocus amount, the laser in situ annealing process is designed, and the optimal rescanning parameters are obtained, which are verified by experiments. Findings The results show that the annealing effect is related to the average surface temperature and scan time. When the laser power is 30 W and the scanning speed is 20 mm/s, the overall residual stress and deformation of the thin-walled parts are the smallest, and the in situ annealing effect is the best. When the annealing frequency is reduced to once every three layers, the total annealing time can be reduced by more than 60%. Originality/value The research results can help better understand the influence mechanism of laser in situ annealing process on residual stress and deformation in LPBF and provide guidance for reducing residual stress and deformation of LPBF thin-walled parts.

Recoater-Induced Distortions and Build Failures in Selective Laser Melting of Thin-Walled Ti6Al4V Parts

Additively manufactured thin-walled structures through selective laser melting (SLM) are of great interest in achieving carbon-neutral industrial manufacturing. However, residual stresses and warpages as well as recoater crashes often occur in SLM, leading to the build failure of parts, especially for large-scale and lightweight geometries. The challenge in this work consists of investigating how the recoater affects the warpage and (sometimes) causes the failure of different thin-walled Ti6Al4V parts (wall thickness of 1.0 mm). All these parts are printed on the same platform using a commercial SLM machine. After the loose powder removal and before the cutting operation, a 3D-scanner is used to obtain the actual warpage of each component. Next, an in-house coupled thermo-mechanical finite element model suitable for the numerical simulation of the SLM process is enhanced to consider the recoater effects. This numerical framework is calibrated to predict the thin-walled warpage as measured by the 3D-scanner. The combination of numerical predictions with experimental observations facilitates a comprehensive understanding of the mechanical behavior of different thin-walled components as well as the failure mechanism due to the recoater. The findings show that the use of a higher laser energy input causes larger residual stresses and warpage responsible for the recoater crashes. Finally, potential solutions to mitigate the warpage and the recoater crashes in the SLM of lightweight structures are assessed using the validated model.

Experimental research and numerical analysis of welding residual stress of butt welded joint of thick steel plate

The thickness of steel plates used in the member has gradually increased to meet the load-bearing capacity requirements of long-span steel bridges. As the primary connection method of thick steel plate, welding will result in considerable welding residual stress with complex distribution. Large welding residual stress will significantly impact the performance of steel bridges. In this paper, the distribution of residual stress in welded thick steel plate is systematically studied, a specimen with a thickness of 80 mm was designed and fabricated, and the welding residual stress was measured by X-ray diffraction. The finite element model was established and verified by test results. Subsequently, the finite element calculation of the welding residual stress of steel plates with thicknesses of 20, 40, 60, 80, and 100 mm was carried out, and the distribution of surface residual stress and the influence of plate thickness on residual surface stress were studied; then the spatial evolution mechanism of welding residual stress was studied, and the distribution of residual stress inside steel plate and the influence of plate thickness on the distribution of residual stress were revealed. The results show that the surface and internal residual stresses of 20–100 mm thick plates have good symmetry on the paths perpendicular to the weld seam, and asymmetry only occurs in the weld seam and heat-affected zone where the stress fluctuates. On the paths perpendicular to the weld seam, the stress in the X direction transitions from the “M” shape distribution on the surface to the “Π” shape distribution inside for 20–40 mm thick plates, and the residual stress near the weld seam gradually changes from compressive to tensile; The distribution of stress in the X direction in the 80–100 mm thick plate has experienced the transition from “M” shape to “Π” shape to “M” shape, and the stress near the weld seam has experienced the transition from compressive to tensile to compressive. The stress change in the X direction of the 60 mm thick plate is between the above two cases. On the path of internal stress along the thickness, the maximum stress in the X direction is 310–400 MPa for 20–40 mm thick plates, which appears at about 1/2 plate thickness. The maximum stress in the X direction for 60–100 mm thick plates is 400–480 MPa, which appears at 0.2–0.3 times the thickness of the plate from the upper surface. The results could serve as a reference for welding residual stress analysis and guide optimization design of steel bridges made of thick steel plate.

Research on the Warping and Dross Formation of an Overhang Structure Manufactured by Laser Powder Bed Fusion

Warping and dross formation are the main defects of an overhang structure formed by laser powder bed fusion. In order to study these defects, a seven−shaped overhang structure with different lengths and heights of the overhang was printed. The influence of the temperature and stress field on the overhang structure was investigated using a 3D finite element (FE) model. The results of the simulation showed that the molten pool in the powder support zone was much larger than the molten pool in the solid support zone. The molten pool sank due to the actions of gravity and the capillary force. This led to the powder melting, which then formed a droplet−like dross formation on the lower surface. The temperature difference between the regions led to a large residual stress. When the residual stress exceeded the material strength, warping deformation occurred in the top area, affecting the subsequent powder−laying process. The warping zone was remelted when the next layer was processed. As the number of forming layers increased, the thermal conductivity and stiffness increased continuously, and the deformation of the top area gradually decreased. The experiment results showed that the longer the overhanging length was, the more serious the warpage was. When the overhanging length was below 3 mm, the warping of the top area continued to decrease to zero as the building process proceeded. Meanwhile, the dross formation appeared at the bottom of the overhanging area in all experimental groups. Studying the process of warping and dross formation was helpful to understand the defect change process in the manufacturing process of an overhang structure.

Methods for Non-destructive Testing of Welding Residual Stresses in Aluminum Alloys

There will be large residual stress after welding, and the residual stress will affect the service life of the aluminum alloy welding structure. Therefore, aluminum alloy welding residual stress needs to be accurately detected. Compared with the lossy method, the nondestructive testing method can produce negligible damage to aluminum alloy, which will not affect the reuse of aluminum alloy and can detect the residual stress. This paper summarizes the nondestructive testing methods of welding residual stress in aluminum alloy and their advantages, disadvantages, and applicability, which lay a foundation for rapid nondestructive testing of welding residual stress in aluminum alloy.

Modeling of welding residual stress in a dissimilar metal butt-welded joint between P92 ferritic steel and SUS304 austenitic stainless steel

In this study, a butt-welded joint between P92 ferritic steel and SUS304 austenitic stainless steel was fabricated with a nickel-based filler material. Based on Sysweld software, three-dimensional thermal-metallurgical-mechanical coupled finite element analyses were performed to investigate the hardness and welding residual stress in the welded joint. In the material behavior model, various factors influencing the formation and distribution of hardness and welding residual stress were carefully considered, including the austenitic transformation, martensitic transformation, and the tempering of martensite in P92 steel; the isotropic strain hardening, annealing effect, and melting effect of all materials; and the differential thermal expansion between dissimilar metals. The neutron diffraction method and hole-drilling strain gauge method were applied to measure the profiles of residual stress of the welded joint, respectively. Hardness mapping was performed on a weld cross-section specimen. The predicted results of welding residual stress and hardness are in good agreement with the measurements, respectively. The peak residual stresses in longitudinal and transverse directions are above 600 MPa in P92 steel. There are high tensile residual stress and significant cold work near the weld root in SUS304 stainless steel. The solid-state phase transformation induces compressive longitudinal residual stress in the heat-affected zone, high tensile transverse residual stress near the weld toe in P92 steel, and a significant stress gradient. The tempering effect can reduce the hardness and tensile residual stress in the heat-affected zone of P92 steel. The formation mechanism of welding-induced residual stress was illustrated based on the Satoh test. The effects of peak temperature, internal restraint, and differential thermal expansion are found to be decisive for the formation of residual stress. Large tensile residual stress can be generated with internal restraints, which promote the stress increase and lead to material yielding. A restraint factor was proposed for the quantitative assessment of stress evolution.

Probing the composition dependence of residual stress distribution in tungsten-titanium nanocrystalline thin films

Nanocrystalline alloy thin films offer a variety of attractive properties, such as high hardness, strength and wear resistance. A disadvantage is the large residual stresses that result from their fabrication by deposition, and subsequent susceptibility to defects. Here, we use experimental and modelling methods to understand the impact of minority element concentration on residual stresses that emerge after deposition in a tungsten-titanium film with different titanium concentrations. We perform local residual stress measurements using micro-cantilever samples and employ machine learning for data extraction and stress prediction. The results are correlated with accompanying microstructure and elemental analysis as well as atomistic modelling. We discuss how titanium enrichment significantly affects the stress stored in the nanocrystalline thin film. These findings may be useful for designing stable nanocrystalline thin films.

Interlayer Investigations of GaN Heterostructures Integrated into Silicon Substrates by Surface Activated Bonding

Thinning the buffer layer thickness between the GaN epilayer and Si substrate without introducing large residual stress is persistently desired for GaN-on-Si devices to promote their thermal budgets and low-cost, multifunctional applications. In this work, the GaN-on-Si heterostructures were directly bonded at room temperature by surface activated bonding (SAB) and the therein residual stress states were investigated by confocal micro-Raman. The effects of thermal annealing process on the residual stress and interfacial microstructure in SAB fabricated GaN-on-Si heterostructures were also systematically investigated by in situ micro-Raman and transmission electron microscopy. It was found that a significant relaxation and a more uniform stress distribution was obtained in SAB bonded GaN-on-Si heterostructure in comparison with that of MOCVD grown sample; however, with increasing annealing temperature, the residual stresses at the SAB bonded GaN layer and Si layer evolute monotonically in different trends. The main reason can be ascribed to the amorphous layer formed at the bonding interface, which played a critical stress relaxation role and transformed into a much thinner crystallized interlayer without any observable structural defects after 1000 °C annealing.

Experimental Research of Welding Residual Stress of Butt Welded Joint of Thick Steel Plate

The thickness of steel plates used in the structure has gradually increased to meet the load-bearing capacity requirements of long-span steel bridges. Thick steel plate welded by arc welding process will result in considerable welding residual stress with complex distribution. Large welding residual stress will significantly impact the performance of steel bridges. At present; residual welding stress of thick steel plates is not considered enough in bridge engineering; which could lead to potential dangers in safety. In this paper; a butt welded joint with a thickness of 80 mm was designed; the residual welding stress was measured by X-ray diffraction method; and the distribution of residual stress in the direction perpendicular to the weld seam and along the direction of the weld seam is analyzed; and the distribution pattern of welding residual stress in thick steel plate is systematically studied. It is found that in the area near the weld; the stress in the direction along the weld seam is more significant than that in the perpendicular direction; the peak stress in the direction perpendicular to the weld seam usually appears in the weld seam and the heat-affected zone; and the maximum value tends to appear close to the last weld bead on the surface; on the path perpendicular to the weld seam; the stress in the direction perpendicular to the weld seam is distributed in a “Π” shape; the stress in the direction along the weld seam is distributed in an “M” shape; and the stresses in the direction along and perpendicular to the weld seam are symmetrically distributed; however the axis of symmetry may appear anywhere in and around the weld seam. The results could serve as a reference for welding residual stress analysis and guide optimization design of steel bridges made of thick steel plates.

Effect of quenching residual stress on precipitation behaviour of 7085 aluminium alloy

The quenching-induced residual stress in ultrahigh strength Al-Zn-Mg-Cu alloys has a great influence on their precipitation behaviour in subsequent heat treatment and the properties of the final products. In the present work, the cladding quenching method was employed for 7085 Al alloy slabs to tailor different quenching residual stresses. Then the effects of quenching residual stress on the precipitation behaviour of the 7085 Al alloy were investigated through finite element analysis, residual stress and hardness distribution measurements and microstructural examinations. The results indicate that the reduction in residual stress increases with increasing cladding layer thickness. For a cladding layer thickness in the range of 1-1.4 mm, the residual stress is almost eliminated. The hardness at the surface of the aged sample with a large compressive residual stress is decreased, while the hardness at the centre of the sample with a large tensile residual stress is increased. The hardness is approximately identical between the aged samples with little or no residual stress. The elastic lattice distortion caused by residual stress is found to promote the nucleation of precipitates during the artificial ageing process. The in-depth mechanisms for the effect of quenching residual stress on the precipitation of 7085 Al alloy are also discussed.

Necking and failure of a particulate gel strand: signatures of yielding on different length scales.

"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.