text
stringlengths 0
1.19M
|
|---|
= 0191., the macro module of volumetric strain K∼=K(q) is computed and compared with the lower boundary f(q) and the upper boundary g(q) when q |
∈ [0.15; 0.25]. represents the results of the comparison. Macro module is found within the described range: f(q) ⩽ |
K(q) ⩽ |
g(q).The mathematical model of micro-heterogeneous medium with voids and shrinkage porosity is proposed. Random properties of microstructure elements with discrete and continuous distributions are studied. The formulas for deformational properties of grain composites that take into account the microstructure damage are derived.Revalorization of sunflower stalks as novel sources of cellulose nanofibrils and nanocrystals and their effect on wheat gluten bionanocomposite propertiesNovel gluten based bionanocomposites reinforced with cellulose nanofibrils (CNF) and cellulose nanocrystals (CNC) extracted from sunflower stalks by respectively a steam explosion treatment and a hydrolysis procedure, were prepared by casting/evaporation. The extracted cellulose nanomaterials, both CNC and CNF, were embedded in gluten matrix and their effect was investigated. Morphological investigations highlighted that gluten based bionanocomposites showed a homogenous morphology, the absence of visible cellulose nanoreinforcements, and the presence of holes for Gluten_CNF nanocomposites. Gluten_CNF showed a reduction of water vapour permeability coefficients but the values are higher respect to gluten reinforced with CNC. This behaviour could be related to the ability of CNC to increase the tortuous path of gas molecules. Moreover, the results from thermal, mechanical and barrier properties confirmed the strong interactions obtained between CNC and gluten matrix during the process.The study suggested the possibility to re-valorise agricultural wastes with potential applications as reinforcement in polymer matrix bionanocomposites.The development and use of green resources represent new objectives for reducing gas emissions and consequent pollution while, in this context, lignocellulosic materials represent renewable resources for production of fuel ethanol from sugars. Among lignocellulosic materials, the use of agricultural residues is of particular interest because it has also the benefit of disposal of problematic solid wastes which usually do not have any economic alternative.Sunflowers have been considered as one of the major sustainable lignocellulosic materials used not only to extract oils but also for production of biofuels as an alternative to fossil fuels (). Sunflowers are renewable and are cultivated in large quantities (about 30–35 million metric tonnes) around the world; while sunflower seeds represent the fourth source of oil in the world, heads, stalks and leaves remain unutilized after harvesting (). These residues are not eco-friendly because after harvesting they are typically burnt under not well-controlled conditions, causing a negative environmental impact. Every year, the volume of sunflower residues produced in the world represents a huge environmental impact with 3-7 t of dry matter/ha (). For these reasons, the attention of the scientific community is now oriented to the revalorization of wastes after sunflower harvesting. Currently the most common use of residual stalks is for bioethanol production (). However, sunflower residues could be used also as precursors for the extraction of cellulose based materials. Cellulose nanocrystals (CNC) and cellulose nanofibrils (CNF) constitute the two main families of nanosized cellulose. The former is extracted from fibres after a complete dissolution of the non-crystalline fractions, while the latter results from the application of high shearing forces of disintegration leading to a high degree of fibrillation, which yields highly interconnected fibrils. Some different methods are known for the extraction of nanosized cellulosic materials, such as chemical, enzymatic, mechanical treatments, etc. Among the different existing pre-treatment methods, steam explosion is one of the most commonly used for fractionation of biomass components. In steam explosion pre-treatment, biomass is exposed to pressurized steam followed by rapid reduction in pressure. The treatment results in substantial breakdown of the lignocellulosic structure, hydrolysis of the hemicellulosic fraction, depolymerization of the lignin components and defibrillation. Compared with alternative pre-treatment methods, the advantages of steam explosion include a significantly lower environmental impact, lower capital investment and less hazardous process chemicals (Wheat gluten (WG) protein is an attractive material as agropolymer because of its high availability and it can be easily processed into films (). Besides the rapid biodegradability of wheat gluten films, such materials exhibit effective barrier properties against lipids and gases, such as oxygen, carbon dioxide and aroma compounds (). However, the poor mechanical properties and strong water absorption in humid environment of this material tremendously limit the applications in some industrial sectors as packaging. Solving these problems is a key research issue. Some actions have been taken to toughen the polymer matrix through using nanoparticles, for instance montmorillonite (), which are simple and represent an effective way to make a high-performance protein polymer composite.In the present research, we report the use of sunflower stalk wastes as precursors for the extraction of both cellulose nanofibrils (CNF) and cellulose nanocrystals (CNC) to be used as reinforcement phases in wheat gluten natural matrix. The effectiveness of an optimized alkaline pre-treatment followed by an acid hydrolysis was compared with a steam explosion assisted treatment that led the extraction of cellulose nanocrystals and cellulose nanofibrils, respectively. Then, gluten based bionanocomposites, reinforced with CNC or CNF, were produced by solvent casting in water. Finally, the dispersion of CNF or CNC in wheat gluten matrix, the mechanical response and the thermal and barrier properties of WG nanocomposites reinforced with cellulosic materials were deeply investigated.Sunflower stalks were collected in Umbria, Italy. The chemical composition of sunflower stalks, expressed in% with respect to dry weight of matter, has been analysed by many authors (quite wide range of identified values to the variability of growing and harvesting conditions): glucose 27.0–36.3%, xylose 16.7–22.4%, α-cellulose 40.3–45.7%; holocellulose 54.0–71.85%; lignin 19.5–28.1%, ethanol/benzene extractives 5.8–16.7%, ash 7.8–10.7% (). Glycerol, used as plasticizer, was purchased from Panreac Química (Castellar del Vallés, Barcelona, Spain). Wheat gluten (WG protein content; >80%, moisture content: 5.5–8.0%) and all chemical reagents were supplied by Sigma–Aldrich (Sigma–Aldrich Chemie GmbH, Steinheim, Germany).Sunflower stalks were chemically pre-treated before the cellulose nanocrystal (CNC) extraction. Before the chemical pre-treatment, the stalks were washed several times with water and the internal white pith was manually removed. The external fibrous structure was then treated with 5% wt/v NaOH solution at room temperature (RT) for 72 h (liquid/fibre ratio 30:1) and successively with 5% wt/v NaOH solution at 98 °C for 2 h (liquid/fibre ratio 10:1). The fibrous structure was also treated with 5% wt/v of sodium chlorite (bleaching fibre/liquid ratio 1:50), boiled for 2 h at pH = 4. A treatment with sodium bisulphate solution at 5% wt/v was then carried out (30 min at RT) and finally a 17.5% wt/v NaOH solution was applied (20 min at RT) (see Cellulose nanocrystal water suspensions were prepared from pre-treated fibres by sulphuric acid hydrolysis (). The hydrolysis was carried out with 64% wt/wt sulphuric acid at 45 °C for 30 min. After the hydrolysis, a centrifugation (4400 rpm 20 min) and a dialysis procedure (around 5–7 days) were applied in order to remove the excess of acid while a mixed bed ion exchange resin (Dowex Marathon MR-3 hydrogen and hydroxide form) was added to the cellulose suspension for 48 h and then removed by filtration in order to adjust the negative charges induced by the hydrolysis. The resultant cellulose nanocrystal aqueous suspension was ultrasonicated by means of a tip sonicator (Vibracell, 750) for 5 min (, Panel B). The final CNC water suspension was approximately 0.5% wt/wt and the final yield after the hydrolysis was calculated as% of initial weight of the used pre-treated sunflower fibres.The extraction procedure of cellulose nanofibrils (CNF) was done by a steam explosion treatment that involved (1) alkali treatment with steam explosion; (2) bleaching and (3) mild acid hydrolysis coupled with steam explosion (, Panel C). Initially the sunflower stalks were cut into small pieces with grinder. A laboratory autoclave, model no: KAUC-A1 which can work with 137 Pa was used for steam explosion treatment. 100 g of ground piece of stalks were treated with 5% wt NaOH solution and kept in an autoclave with the pressure of 137 Pa with the temperature of 180 °C in an autoclave for 1.5. After that, a bleaching of the resultant alkali treated stalk sample was done by treating with 5% wt sodium hypochlorite solution for 1.5. Bleaching was repeated six times until the residue become white in colour. After bleaching, the fibres were thoroughly washed, dried and subjected to mild acid hydrolysis using 5% oxalic acid under a pressure of 137 Pa in an autoclave for 20 min. The pressure was released immediately and the process was repeated six times. The fibres were taken out, washed and dispersed in water and homogenized under continuous stirring for 6 h and the resultant suspension became cellulose nanofiber aqueous suspension. The final product was washed with deionised water by successive centrifugations until neutralization.The microstructure of CNC was investigated by field emission scanning electron microscopy (FESEM, Supra 25-Zeiss) after gold sputtering, while the shear-induced birefringence of 0.6% wt CNC solution was analysed in a dark box. For comparison, the microstructure of the cross section and the surface of pristine sunflower stalks and the surface of chemically pre-treated fibres were also investigated by FESEM. The images of the pristine and pre-treated fibres were analysed with the NIS-Elements BR (Nikon) software in order to determine the fibre average diameters.Fourier infrared (FT-IR) spectra of pristine, chemically pre-treated fibres, and CNC were recorded using a Jasco FT-IR 615 spectrometer in transmission mode, while thermogravimetric measurements (TGA) were performed by using a Seiko Exstar 6300 analyser from 30 to 900 °C at 10 °C min−1 in nitrogen atmosphere.Transmission electron microscopy, (TEM, JEOL JEM 2100) was used to determine the dimensions of the extracted cellulose nanofibrils from the sunflower stalks. A drop of a diluted suspension (0.5 wt%) was deposited on the surface of a clean copper grid and coated with a thin carbon film. The sample was dried at room temperature before TEM analysis and the measurement was carried out with an accelerating voltage of 80 kV.X-ray equatorial diffraction profiles was used to determine the crystallinity of the sunflower stalks subjected to the different treatments. Each material in the respective treatment was milled into the powder and placed on the sample holder. The diffraction patterns of the raw, alkali treated, bleached and acid treated samples were obtained with an X-ray diffractometer (JEOL diffractometer, Model JDX 8P) using CuK radiation (λ_ = 0.1539 nm) at the operating voltage and current of 40 kV and 20 mA, respectively. The X-ray diffractograms were obtained at room temperature within a 2θ range from 5 to 80° and a scan rate of 2° min−1. The crystallinity index (Icr) of the material was determined by the Segal method as shown in the Eq. where Icr expresses the relative degree of crystallinity, I002 is the maximum intensity of the (0 0 2) lattice diffraction at 2θ = 22°, and Iam is the intensity of diffraction at 2θ = 18°. I002 represents both crystalline and amorphous regions, while Iam represents only the amorphous part.Fourier transform infrared spectra were recorded using a Shimadzu IR-470 IR spectrophotometer. Raw, alkali-treated, bleached, acid-treated fibres and nanocrystals of sunflower stalks samples were analysed. Prior to the experiment, the samples were dried in an air oven at 60 °C for 12 h. The FT-IR spectrum of each sample was obtained in the range of 400–4000 cm−1. The KBr disk (ultrathin pellets) method was used and the experiments were carried out with a resolution of 2 cm−1 and a total of 15 scans for each sample.The wheat gluten bionanocomposite films loaded with 1% wt. and 3% wt., respect to the matrix weight, of both CNC (density 1.3 g cm−3) () were prepared by using the method described by Kayseriliolu () with minor modification. The formulations are designed as Gluten_1CNC, Gluten_3CNC, Gluten_1CNF, Gluten_3CNF, respectively (volume fractions of cellulosic materials, CNC or CNF, respect to the gluten volume used for each samples are 0.47% v/v, 1.45% v/v, 0.41% v/v, 1.26% v/v, respectively). Deionized water was mixed with 2% wt of glycerol as plasticizer. Wheat gluten was dispersed in the prepared solution (10% wt) with magnetic stirring at high speed. Sodium hydroxide solution (0.5 M) was then carefully added to the solution with magnetic stirring at low speed at room temperature for 30 min, until pH = 10.8 was obtained, and a following heating in a water bath at 70 °C for 10 min under controlled pH, was applied. After cooling, specific amounts of both CNC and CNF aqueous dispersions were added and magnetically stirred for 30 min at RT. Finally, the solutions were casted on Teflon® sheet and the drying was performed at RT until films could be easily removed. Gluten based films 90–100 μm thick were obtained. The bionanocomposite films were conditioned before characterization at 20 °C and 53% relative humidity conditions in desiccators, by using a magnesium nitrate-6-hydrate saturated solution (Sigma–Aldrich) for at least one week. Neat gluten based films were also produced for comparison by using the same procedure and the excess of water used for CNC and CNF based formulations was here considered and added.The microstructure of the gluten based bionanocomposite fractured surfaces was investigated by scanning electron microscopy, FESEM, after gold sputtering of the surfaces. The surface properties of the produced formulations were investigated by both atomic force microscopy (AFM) and optical microscopy. The AFM analysis was performed by using a Nanoscope III.a Scanning Probe Microscope, (Multimode 8, Bruker AXS, Inc. Santa Barbara, California, USA), with a NanoScope® V controller electronics. Measurements were taken from several areas of the film surface (50 × 50 μm and 3 × 3 μm), using the phase imaging mode. Optical analysis was carried out by light microscopy using an optical microscopy (DM/LP Leica Microsystems, Wetziar GmbH) with a CCD camera incorporated, which allowed acquiring images from different samples. Images of films containing or not cellulose nanocrystals and nanofibrils were acquired by using ×200 magnification.The transparency of the films was determined from the surface reflectance spectra by using a spectrocolorimeter CM-3600d (Minolta Co, Tokyo, Japan) with a 30 mm illuminated sample area by applying the Kubelka–Munk theory for multiple scattering to the reflection spectra. This theory was based on that the light passes through the film, it is partially absorbed and scattered, which is quantified by the absorption (K) and the scattering (S) coefficients. Internal transmittance (Ti) of the films was quantified using Eq. . In this equation, R0 is the reflectance of the film on an ideal black background. Parameters a and b were calculated by Eqs. , where R is the reflectance of the sample layer backed by a known reflectance Rg. The reflection spectra on the white and black background were determined from 400 to 700 nm. Measurements were taken in triplicate for each formulation.Colour coordinates of the films, L*, C*ab (Eq. ) from the CIELAB colour space were determined using D65 illuminant and 10° observer and taking into account R∞ (Eq. ) which correspond with the reflectance of an infinitely thick layer of the material.Finally, colour differences between the different films and control film were evaluated by using, Eq. Thermal characterization was done by both differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). DSC measurements were carried out on a TA Instruments DSC Q200 in modulated mode (TA Instruments Inc., USA) equipped with Universal Analysis 2000 software. Film samples, weighing 8 ± 1 mg, were placed in a hermetically sealed sample pan and tested from −70 to 170 ∘C at a heating rate of 5 °C min−1. The period and the amplitude of modulation were respectively 60 s and 0.50 °C. The glass-rubber transition temperature (Tg) was determined from the temperature at the inflexion point, corresponding to the temperature at which the differential heat flow is maximum. TGA tests (Seiko Exstar 6300) from 30 to 600 °C at 10 °C min−1 under a nitrogen atmosphere were performed for each sample.X-ray diffraction was used to determine the crystallinity of the CNC and CNF gluten composite films with varying concentrations of CNC and CNF. Each film was placed on the sample holder to obtain total and uniform X-ray exposure. The X-ray diffraction patterns of neat gluten, Gluten_1CNC, Gluten_3CNC, Gluten_1CNF and Gluten_3CNF films were obtained with an X-ray diffractometer (SHIMADZU XRD-6000). The X-ray diffractograms were obtained at room temperature within a 2Θ range from 5 to 60° and a scan rate of 2° min−1.The mechanical behaviour of gluten based bionanocomposite films was evaluated by tensile tests, performed on rectangular probes (50 mm × 10 mm) on the basis of UNI ISO 527 standard with a crosshead speed of 50 mm min−1, a load cell of 500 N and an initial gauge length of 25 mm. The elastic modulus (E), the tensile strength (σb) and elongation at break (εb) were calculated from the resulting stress-strain curves. The measurements were done at room temperature and at least five samples were tested.The barrier properties of the gluten based formulations were evaluated by both water vapour permeability (WVP) test and oxygen transmission rate measurements. WVP was evaluated following the gravimetric method ASTM E96-95 (ASTM, 1995) by using Payne permeability cups (Payne, elcometer SPRL, Hermelle/sd Argenteau, Belgium) of 3.5 cm diameter. Deionised water or lithium chloride salt were used inside the testing cups to achieve 100 or 11% RH respectively, on one side of the film, meanwhile an oversaturated magnesium nitrate solution was used to control the RH (53% RH) on the other side of the film. The relative humidity of the tests was selected according to the final use of the flexible films as package material, thus simulating the contact with fresh food, such as meat or fresh cut fruit or very low water activity products, respectively. A fan placed on the top of the cup was used to reduce resistance to water vapour transport. Water vapour transmission rate measurements (WVTR) were performed at 25 °C. To calculate WVTR, the slopes in the steady state period of the weight loss vs. time curves were determined by linear regression. WVP was calculated according to ). For each type of film, WVP measurements were taken in quadruplicate.The oxygen barrier capacity of the gluten based bionanocomposite films was evaluated by measuring oxygen permeability (OP) by means of an Ox-Tran 1/50 system (Mocon, Minneapolis, USA) at 25 °C (ASTM Standard Method D3985-95, 2002). Measurements were taken at 53%RH in films previously equilibrated at the same RH. Films were exposed to pure nitrogen flow on one side and pure oxygen flow on the other side. The OP was calculated by dividing the oxygen transmission rate by the difference in the oxygen partial pressure on the two sides of the film, and multiplying by the average film thickness. At least three replicates per formulation were taken into account.Results were analysed by analysis of variance (ANOVA), using the Statgraphics Plus 5.1. Program (Manugistics Corp., Rockville, MD). To differentiate samples, Fisher’s least significant difference (LSD) was used at the 95% confidence level.Sunflower stalks present a heterogeneous structure characterized by an external lignocellulosic wall and an interior white core. In this research, we selected only the external fibrous part of the sunflower stalks for CNC extraction. shows the morphological appearance of the raw material ( a shows the porous honeycomb network that characterizes the cross section of sunflower stalks (), while the surface image confirms their heterogeneous, rough and pitted structure (The applied chemical treatment provoked an evident defibrillation process of the sunflower stalks as a consequence of hemicellulose and lignin removal (confirmed by the whitening, , Panel A) and the fibres appear well individualized, with a regular, smooth and clean surface ( c), while each elementary filament shows a compact structure and very long entangled cellulosic fibrils ( c-insert) with a diameter of pre-treated fibres of 12.3 ± 3.1 μm (calculated by FESEM images by the NIS-Elements BR-Nikon software).Concerning the hydrolysis procedure for the extraction of cellulose nanocrystals, the measured yield of the applied procedure was approximately 21% and this is an important result considering the low cellulose content that characterized the used raw material (about 40% for depithed stalks). The FESEM image (d) confirms that the aqueous suspensions containing cellulose nanocrystals consisted mostly of individual crystals with the previously reported acicular structure ranged from 150 to 200 nm in length and 5–10 nm in diameter (aspect ratio 26 ± 10) (), while a 69.8% of crystallinity index was calculated from XRD pattern. Finally, the aqueous suspension exhibited the typical shear-induced birefringence of CNC (d-insert), highlighting their ability to form a chiral nematic liquid crystalline phase in equilibrium with the isotropic phase and underlining the success and efficiency of the selective extraction procedure.The results of thermal and chemical investigations of raw material, pre-treated fibres and CNC are also summarized in e) suggest that the pyrolysis process of pristine fibres can be separated into three main stages: the first weight loss is due to moisture loss, the second is due to the main thermal decomposition of cellulose (centred at 304 °C with a shoulder peak at 225 °C due to hemicellulose and lignin components) () and the third step is related to the lignin and hemicelluloses decomposition. In the case of pre-treated fibres, the first weight loss was reduced, while the elimination of the shoulder in the second peak of the DTG profile confirmed the elimination of hemicellulose and lignin material by the treatment with sodium hydroxide. Moreover, the shift of the main peak related to cellulose decomposition to higher temperatures indicates an increase of the thermal stability of the pre-treated fibres, due to the reduced amount of non-cellulosic material of the fibre and the presence of high crystalline cellulosic components. In the case of CNC, two well-separated pyrolysis processes are observed in the DTG curves. The first one is likely due to the weaker interaction of single bond OH groups in cellulose that requires less energy to start the thermal degradation process, while the main DTG peak of the cellulose is shifted to higher temperature (353 °C) probably due to different ordered and packed cellulose regions, possibly higher crystallite size and therefore higher thermal stability (f shows the spectra fingerprint region of pristine, pre-treated fibres and CNC extracted from sunflower stalks. The interior part of the sunflower stem is extremely rich in polysaccharides, with OH hydroxyl group stretching leading to a large peak between 3000 and 3600 cm−1. The absorption peak around 2900 cm−1 indicates the stretching vibration of CH band of CH2 methylene group (2920 and 2850 cm−1), characteristic of waxes and fats (). In the case of pre-treated fibres, the signal at 1511 cm−1 assigned to the aromatic CO stretching mode for the guayacyl ring of lignin, disappeared as expected (). The spectrum of CNC reported identifiable bands as adsorbed water in cellulose (1641 cm−1) and bands at 1423, 1377, 1339 and 1311 cm−1 attributed respectively to CH2 symmetric bending, CH bending, in-plane OH bending and CH2 rocking vibration in cellulose. Furthermore, the signals at 1163, 1116, 1061, 1033, 897 cm−1 are assigned respectively to asymmetric CC stretching, anhydroglucose ring asymmetric stretching, CExtracted cellulose nanofibrils from sunflower stalks were examined by transmission electron microscopy to find the dimensions of the nanofibrils. From TEM image, a, it can be seen that fibres with average diameter in the range of 5–10 nm with a good network were obtained. In other words, a number of branches of small bundles or individualized nanofibrils were hooked up to larger aggregates. This TEM image concludes that steam explosion coupled with mild acid hydrolysis is an effective method to produce cellulose nanofibrils. The steam explosion treatment was expected to break down the lignocellulosic structure, hydrolyze the hemicellulose fraction and depolymerize lignin components (Crystallinity of cellulose in each nanofiber is an important factor for determining the mechanical and thermal properties. The ability of cellulose hydroxyl groups to bond each-other play a major role in directing the crystalline packing and also governing the physical properties of cellulose.Cellulose has a well prominent crystalline structure due to hydrogen bonding and van der Waals interactions existing between adjacent cellulose molecules compared to hemicellulose and lignin, which are amorphous in nature. The chemical treatment is one of the governing factors which deeply affect the crystallinity of the cellulose; hence, in order to evaluate the effectiveness of the chemical treatment, crystallinity of the treated fibres can be determined and compared with values for untreated fibre. b shows the diffraction patterns obtained for pristine, alkali treated, bleached and acid hydrolysed sunflower stalk samples. It is noticed that there is a gradual increase in crystallinity index at each stage of treatments and it is maximum for acid treated samples. The intense peak in the acid treated sample clearly indicates the efficient removal of non cellulosic polysaccharides and dissolution of amorphous zones (). The values of the crystallinity index obtained at different stages of isolation are shown in d. Crystallinity index showed a gradual increase in crystallinity from initial raw fibre to acid treated nanofiber. The high crystallinity of nanofibers will increase their stiffness and rigidity and it could be more effective in providing better reinforcement for composite materials.FT-IR analysis of the untreated, alkali treated, bleached and acid treated sunflower stalks samples are given in c. During isolation process, most of the lignin and hemicelluloses parts have been removed from the fibres. This could be understood from the IR studies. The peak at 3300 cm−1, which was observed in the spectra of all fibres, corresponds to the OH stretching vibrations of hydrogen bonded hydroxyl group and it shows the hydrophilic tendency of the fibre (). The peak at 1630 cm−1 is due to the bending mode vibration of the absorbed water with some contributions from carboxylate groups (). These results indicate that the cellulose component was not removed during the chemical treatment and hence we can conclude that the steam explosion coupled with the mild acid hydrolysis treatment effectively removed the lignin and hemicellulose portions from the fibre matrix.FT-IR studies have been done on the extracted cellulose nanofibrils and nanocrystals from sunflower stalks. FT-IR spectra of cellulose nanofibrils and cellulose nanocrystals are shown in a, it is observed that CNF show the band at 896 cm−1 which is assigned as β-glucosidic linkage for the cellulose I structure and cellulose nanocrystals shows the band at 894 cm−1 position which is due to the cellulose II structure (). The change occurred was due to the rotation of glucose residue around the glucosidic bond (). In addition, it can be seen that band of the CNF at 998 cm−1 was shifted to 996 cm−1 in the case of nanocrystals. This was also related to the transformation from cellulose I to cellulose II crystal structure (). This may be justified by transformation and regeneration of cellulose chains after prolonged chemical treatments. We can conclude that the cellulose nanocrystals and cellulose nanofibrils show the structure of cellulose II and cellulose I, respectively.XRD studies were done on both cellulose nanofibrils and nanocrystals from sunflower stalks to investigate the effect of chemical purification on crystallinity. b shows the X-ray diffraction peaks of both cellulose nanofibrils and nanocrystals. CNF shows diffraction peaks around 2θ = 16.3° and 2θ = 22.6° which typically represent cellulose type I. In the case of cellulose nanocrystals, the pattern was changed to Cellulose II, with a split peak around 2θ = 20° and 21.7° (). This may be justified by transformation and regeneration of cellulose chains after chemical treatments.The microstructure of the cross-section surfaces of gluten based bionanocomposites was qualitatively analysed by using FESEM, while the surface structure was analysed by AFM and optical microscope in order to evaluate the influence of cellulose nanoreinforcements and the modification on the neat gluten microstructure (FESEM images of fractured surfaces of gluten based nanocomposites show a homogenous aspect with the absence of visible cellulose nanoreinforcements; however, the presence of some holes was detected for Gluten_CNF nanocomposites. A high homogeneity was evidenced for gluten matrix based film that tended to decrease for the bionanocomposite systems; in fact, different phases can been seen by FESEM analysis (and then by AFM) both for Gluten_CNC and Gluten_CNF and this effect, more evident for CNF, can be related to the domains of gluten and cellulose nanoreinforcements that were formed during the processing. The production of the holes was, in fact, typically related to the incorporation of air and to the evaporation of the solvents during the casting of the materials, and it was here enhanced by the presence of CNF due to their different morphology and dimensions with respect to CNC (AFM images show the topographic analysis of gluten based bionanocomposites obtained by using Phase Imaging mode derived from Tapping Mode. Phase Imaging allows detecting variations in composition. In gluten and gluten based nanocomposites, heterogeneous response of different phase can be detected. In gluten film the different phases can be related to the presence of gluten and glycerol, while for nanocomposites the different areas can also be related to the presence of the nanoreinforcements. AFM images also underline a good distribution for the CNC into the matrix, whilst CNF agglomerates can be found in Gluten_1CNF; however, this effect is not evident for Gluten_3CNF because the analysed region does not allow identifying CNF agglomerates.Optical microscope images of film surfaces for the Gluten_CNF show a clear presence of heterogeneous materials due to the agglomeration of long nanofibrils created during the processing or cast phase identifiable as brown areas. The aggregation phenomenon is more evident for Gluten_3CNF. The presence of aggregates and holes negatively influences not only the morphology of the material but also its optical, barrier, and mechanical properties. shows the values of internal transmittance (Ti) at 450 nm, the gloss values at 60° and the values of the colorimetric analysis of gluten and gluten bionanocomposites. According to Kubelka–Munk theory, high values of Ti are associated to structural homogeneity and their degree of transparency, while low Ti values are related to a high structural heterogeneity and greater opacity.The highest Ti value was found for Gluten_3CNC and for the other gluten based bionanocomposites the values of transparency remain unchanged with respect to gluten film (). A significant difference (p < 0.05) was obtained between Gluten_3CNC and the other four formulations.The gloss of bionanocomposites was greatly affected by the presence of nanoreinforcements. In the case of bionanocomposites reinforced with CNC, the values of gloss increase as a function of filler percentage. The opposite behaviour was evidenced for the nanocomposites reinforced with CNF; in this case, the gloss decreases at the higher filler content. This result can be related to the presence of agglomerates on the surface of Gluten_CNF, as also evidenced by optical microscopy. In the case of Gluten_CNC, the nanoreinforcements are homogeneously distributed into the matrix while, as shown in , in the Gluten_CNF nanocomposites the surfaces show the presence of agglomerates related at the presence of CNF.The colour of the bionanocomposites is a consequence of the colour of gluten powder and it is expressed in term of lightness (L*), chroma (Cab*), hue (hab*). Incorporation of CNC or CNF in gluten films induced very small colour changes. CNC provoked a less saturated (lower chroma values) and less yellow (lower hue values) colour in gluten films, whereas CNF induce a more saturated and yellow colour. The total colour differences ΔE were estimated between the neat gluten and bionanocomposites. Since the ΔE values between the neat gluten and bionanocomposites were lower than 2, these are in the limit of the human eye perception (). To conclude, optical parameters are largely related to films microstructure, finishing degree, and degree of roughness.. During thermal degradation under nitrogen flow, the gluten based materials containing CNC and CNF have shown a four steps-decomposition pattern, which corresponds, respectively, to the elimination of moisture, glycerol evaporation, degradation of cellulosic nanoreinforcements and decomposition of wheat gluten. The first peak below 100 °C in DTG curves can be attributed to water evaporation, while the second step, in which there was a further weight loss, occurred after the elimination of moisture and corresponded to the evaporation of glycerol. As reported in , the DTG IIpeak moved to higher temperatures with increasing content of CNC from 0 to 3% wt. (from 248 to 251 and 252 °C, respectively for Gluten_1CNC and Gluten_3CNC). This was believed to be due to the preferable barrier property of CNC well dispersed in gluten matrix, which could efficiently delay the evaporation of glycerol or water vapour moisture. In the case of cellulose nanofibrils, we observed a shift towards lower temperatures (from 248 to 239 and 228 °C, respectively for Gluten_1CNF and Gluten_3CNF), indicating in this case a less stable structure. CNF consists of both individual and aggregated nanofibrils made of alternating crystalline and amorphous cellulose domains, with a different ordered and packed cellulose regions with respect of rigid CNC, that indeed present a higher crystallinity index than the others, due to the disruption of amorphous holocellulose surrounding and embedding the cellulose crystallites formed by well organized glucose chains (). The neat gluten maximum degradation was registered at 317 °C () and similar temperatures have been measured for DTGmax values (see ) in the case of films containing CNC (316 and 315 °C, respectively for Gluten_1CNC and Gluten_3CNC); a shift towards lower temperatures was registered for the Gluten_CNF at the two different weight percent (310 and 307 °C, respectively for Gluten_1CNF and Gluten_3CNF). A decrease of maximum degradation rate related to the main peak was observed in the case of CNC containing gluten (from 0.089 μg μgi−1 |
min−1 for neat gluten to 0.070 μg μgi−1 |
min−1 and 0.055 μg μgi−1 |
min−1, for Gluten_1CNC and Gluten_3CNC, respectively), indicating an effective action of CNC as barrier to diffusion of degradation products from the bulk of the gluten polymer to the gas phase. The same behaviour was not revealed in CNF containing gluten films, that nevertheless showed similar values for degradation rate peaks with increasing CNF content. The measured values of residual mass at the final temperature of the test (800 °C) (see ) showed that addition of CNC and CNF slightly influenced the measurement. The small increase in char formation for cellulose nanocrystals and cellulose nanofibrils could be due to two reasons: (1) the sulphate group acts as a dehydration catalyst and facilitates the char residue formation (), or (2) owing to their small particle size, a large number of free end chains is present which trigger decomposition at lower temperature, consequently increasing the yield of char (). The results of Tg measurements from modulated DSC heating scan (reversible heat flow) of wheat gluten bionanocomposites are also reported in . The registered high-temperature peak is associated with the glass transition of the plasticized gluten phase (high-Tg) (). The values for Tg increase from 107.9 °C to 111.8 °C with increase of CNC content from 0 to 3% wt. Even in the case of CNF reinforcement, we obtained a shift of the glass transition to higher temperature, but the increase was less evident in the case of gluten films containing cellulose nanofibrils at the two different weight percents, in particular no further increase was registered at 3% wt of CNF. This result suggests the strong increasing interactions between CNC and gluten matrix in the gluten rich phase, which restricts the mobility of the motion of gluten chain segments and elevates the glass transition temperature with increasing content of CNC and CNF (). In the case of wheat gluten bionanocomposites reinforced with CNF, the partial increase could be due to the limiting effect of CNF in restricting the mobility of the plasticized protein chain for a decreased plasticization effect of water due to a re-distribution of cellulose–water interactions within the matrix (X-ray diffraction patterns were obtained for the neat wheat gluten and gluten bionanocomposite films of various wt.% of CNC and CNF. b shows X-ray diffraction patterns of the neat gluten and that of bionanocomposite films. From the figure, it can be clearly shown that neat wheat gluten showed no crystallinity on its X-ray diffraction pattern due to its non-crystalline nature (Lim and Fujio 1989). In the case of Gluten_CNF composites films, the X-ray diffraction pattern showed a prominent peak around 2θ = 22.6°, indicating the presence of cellulose I CNF, whereas Gluten_CNC composite films showed two small peaks around 2θ = 20° and 21.7°, indicating the presence of cellulose II CNC. shows barrier and mechanical properties evaluated for gluten based nanocomposites (90–100 μm thick). The barrier characterization is one of the most important requirements for food packaging. The goal of food packaging is twofold: to contain the food and to decrease its contamination with the surrounding atmosphere, increasing its shelf-life (Incorporation of CNC and CNF slightly modify OP of gluten films, depending on their morphology and ratio. The lowest ratio of CNC reduced OP, whereas at the highest ratio reinforcements tend to increase OP, as for CNF. This effect can be attributed to the aggregation degree of the reinforcement material (depending on their ratio in the films), which was more intense in the case of CNF, as previously commented. The presence of particles increases the tortuosity factor for mass transfer through the polymer (), reducing permeability values, but the aggregation phenomenon and the induced morphology (presence of some holes) provoke a reduction of tortuosity factor, leading to OP values nearer to the gluten matrix.The water vapour permeability was evaluated at 25 °C and at two different conditions of relative humidity, the first one at 11–53% RH and the second one at 100-53%RH.The WVP analysis, at 11–53% RH gradient, show a significant reduction of the permeability coefficients for CNC composites, around 34 and 32% for Gluten_1CNC and Gluten_3CNC respectively, although no significant effect of CNF on WVP was observed. This behaviour can also be related to the ability of CNC to increase the tortuous path of water molecules through the nanocomposite structure (), while the greater aggregation degree of CNF reduced the capacity of reinforcement to limit permeation of water molecules. However, at 100–53% RH gradient, no significant differences among WVP values of gluten and bionanocomposite films were observed, probably due to the greater plasticization degree of the polymer matrix, which implied a sharp increase in the permeation capacity of water molecules. In this situation, the potential barrier effect of reinforcements was clearly inhibited, in line with the moisture gain of the hydrophilic gluten matrix and the subsequent increase in the molecular mobility and the rate of all diffusion dependent processes. Therefore, it is evident that gluten films should be only used as food packaging for dry foods because high humidity compromises the stability of films.Tensile tests of gluten and gluten based bionanocomposite films were performed at room temperature and the results are summarized in . All studied bionanocomposite formulations, both Gluten_CNC and Gluten_CNF based films, showed Young’s modulus higher than neat gluten (300 MPa), and significant increase was induced by the presence of both cellulosic nanostructures (CNC and CNF), highlighting their reinforcement effect. Moreover, the highest value of Young’s modulus was registered for Gluten_1CNC. Cellulose nanocrystals are known to form a percolating network within the polymer matrix in which the stress is assumed to be transferred through crystal/crystal interaction and crystal/polymer matrix interaction (). This result confirms again the strong interactions between CNC and gluten matrix. On the contrary, no particular changes were detected in tensile strength and elongation at break values with the presence of either CNC or CNF in gluten matrix.Gluten based bionanocomposites reinforced with cellulose based nanofillers extracted from sunflower stalks were prepared by solvent casting technique. Two types of nanostructured fillers were used: cellulose nanofibrils (CNF) and cellulose nanocrystals (CNC).Cellulose nanocrystals (150–200 nm in length and 10 nm in diameter) were successfully extracted from sunflower stalks by an acid hydrolysis with a relatively high yield (21%), while a steam explosion treatment that involved alkali treatment with steam explosion, bleaching and mild acid hydrolysis coupled with steam explosion, was successfully applied, allowing the CNF extraction. The chemical characterization of CNC and CNF underlined that cellulose nanocrystals and cellulose nanofibrils showed the structure of cellulose II and cellulose I, respectively.After the extraction procedures, the obtained cellulosic nanomaterials, both CNC and CNF, were embedded in gluten natural matrix by using a sustainable and low cost water casting procedure. FESEM investigations highlighted that gluten based bionanocomposites showed a homogenous morphology, with the absence of visible cellulose nanoreinforcements; the presence of some holes induced by the processing procedure and more evident for Gluten_CNF nanocomposites, was detected, affecting the optical properties and the gloss of the studied formulations. The different morphology and consequent dispersion of the cellulosic materials into the gluten matrix also affected the barrier properties of the produced bionanocomposite formulations. CNC were, in fact, more efficient in reducing the permeability to gases, due to their ability to increase the tortuous path of gas molecules. On the contrary, the presence of some CNF agglomerates, as shown by optical microscopic images of Gluten_CNF based systems, negatively affected the barrier properties of these formulations, especially with the oxygen and in the case of the highest content of cellulose nanofibrils. Finally, the results of mechanical investigations underlined that all the studied bionanocomposite formulations, both Gluten_CNC and Gluten_CNF films, showed Young’s modulus higher than neat gluten, highlighting the effect of reinforcement exerted by both CNC and CNF when embedded in gluten natural matrix, more evident for CNC.The proposed study suggested the possibility to re-valorise agricultural wastes, such as sunflower stalks, by the extraction of added value high-performance cellulosic materials with potential applications as reinforcement in natural polymer based bionanocomposites.Fabrication of dual-coated graphene oxide nanosheets by polypyrrole and poly(ionic liquid) and their enhanced electrorheological responsesA two-dimensional composite material, poly(ionic liquid)-modified graphene oxide/polypyrrole (GO/PPy/PIL) multilayered nanosheets, was fabricated and applied as a new electrorheological (ER) material. The morphological differences between the single- and dual-coated nanosheets were confirmed using scanning electron microscopy and transmission electron microscopy. Rheological properties measured using a rotational rheometer indicated that the GO/PPy/PIL composite nanosheets exhibited relatively high ER effect under a certain electric field strength than the GO/PPy nanosheets because of the universal PIL second coating. The dual-coated nanosheets also showed a higher applicable electric field strength due to the semiconductive properties of the thick PIL layer.Ionic liquids (ILs), having a melting point of generally less than 100 °C, are a subclass of molten salts and consist of many organic cations and weakly coordinated organic or inorganic anions ER materials are semiconducting or polarizable particles on the micron or nanometer size. They can undergo sensitive and reversible changes between the liquid-like and solid-like states via an applied external electric field when dispersed in an insulating liquid to form an ER fluid. This phenomenon is called the ER effect due to the formation and fracture of particulate chains or columnar structures. The formation of chain structures is accompanied by an increase in shear viscosity ER materials, such as silica and titania Here, we prepared dual-coated GO nanosheets. They were first coated with PPy and then by poly(1-vinyl-3-ethylimidazole bromide), an imidazolium-based PIL, to obtain a nanocomposite of GO with a lower electrical conductivity. The morphologies and structures of the single-coated GO and dual-coated GO nanosheets were analyzed and compared. Then, rheological properties of the multi-layered nanosheets in silicone oil were measured under different electric field strengths and compared with an ER fluid containing PPy-coated GO nanosheets. The multi-layered nanosheets combined the 2D anisotropic morphology of GO and the ER effects of each component showed relatively high yield stress and high available electric field strength.The 2,2′-azobis(isobutyronitrile) (AIBN) (>99.0%, TCI) was purified by recrystallization in methanol. Pyrrole (>99.0%, TCI), bromoethane (>99.0%, TCI), 1,4-dibromobutane (>98.0%, TCI), 1-vinylimidazole (>98.0%, Sigma-Aldrich), potassium hydroxide (KOH) (95%, Shanghai Macklin Biochemcial Co., Ltd., China), N,N-dimethylformamide (DMF) (TCI), silicone oil (viscosity: 50 cSt; density: 0.96 g/ml at 25 °C) (Beijing Hangping Guichuang Chemical Co., Ltd), ethanol, iron chloride hexahydrate (FeCl3·6H2O), acetonitrile, ethyl acetate and chloroform were purchased from Tianjin Kaitong Chemical Reagent Co., Ltd. and also used as received.The GO nanosheets were initially prepared using a modified Hummers method. The GO/PPy composites were then fabricated via an in situ polymerization method as described in the literature The 1-vinyl-3-ethylimidazole bromide (ViEtIm+Br−) was prepared according to the literature The GO/PPy/PIL nanosheets were fabricated according to the literature via a three-step process . GO/PPy-(CH2)4-Br: GO/PPy (0.12 g), 1,4-dibromobutan (0.58 g), and KOH (0.2 g) were dispersed in DMF (100 mL) by ultrasonication for 20 min. The reaction was then kept at 60 °C for 24 h under stirring. The products were dialyzed for 5 days and freeze–dried. GO/PPy/IL: The GO/PPy-(CH2)4-Br (0.0483 g) was dispersed in DMF (100 mL) by ultrasonication for 20 min followed by the addition of 1-vinylimidazole (0.432 g). The reaction was kept at 60 °C for 24 h under stirring. The products were dialyzed for 5 days and freeze–dried. GO/PPy/PIL: ViEtIm+Br− (0.15 g) and AIBN (0.025 g) were dissolved in chloroform (60 mL), and GO/PPy/IL (0.03 g) was added with ultrasonication for 5 min. The reaction was continued at 70 °C for 4 h with stirring under a nitrogen atmosphere. Finally, the products were dialyzed for 5 days and freeze-dried.The morphologies of GO/PPy and GO/PPy/PIL nanosheets were observed by scanning electron microscopy (SEM) (S4800, Hitachi, Japan) and transmission electron microscopy (TEM) (JEOL 2010, Japan). The chemical structures of the nanosheets were examined using Fourier transform infrared spectroscopy (FT-IR) (E55 + FRA106, Bruker, Germany). Thermogravimetric analysis (TGA) (STA4993, Netzsch, Germany) was applied at a heating rate of 10 °C/min from 25 to 800 °C in nitrogen atmosphere to detect the thermal properties and mass composition of the nanosheets. The crystal structures of the nanosheets were determined by the powder X-ray diffraction pattern (XRD) (MAX-2500PC, Rigaku, Japan) with a Cu-Kα radiation source.Two ER fluids at 8 wt% were prepared by dispersing the GO/PPy and GO/PPy/PIL nanosheets in silicone oil, respectively, with the help of sonication for 30 min. The silicone oil was dried at 120 °C for 2 h before use to avoid the influence of moisture. However, electrical breakdown occurred when an electric field was applied to the GO/PPy ER fluid because of the high conductivity of the as-prepared GO/PPy nanosheets. Therefore, the PPy/GO nanosheets were treated in a muffle furnace at 240 °C for 4 h in air atmosphere to destroy part of the PPy skeleton Dielectric properties of the ER fluids were measured using a Novocontrol broadband dielectric spectrometer (BDS) (Concept 80) in the frequency range of 0.03 − 107 |
Hz at 25 °C. The ER fluid was held between two brass electrodes of the BDS 1308 cell, which were separated by Teflon strips with thickness of 0.1 mm. A bias electric potential of 1 V was applied to the ER fluid in the measurement process.The morphologies of the GO/PPy and the GO/PPy/PIL composites with the nanoscale lamellar structure were confirmed via both SEM and TEM images in (a–c) presents SEM images of GO (a), GO/PPy (b), and GO/PPy/PIL (c) nanosheets. The differences in surface morphologies among the samples are obvious. The pristine GO nanosheets have a typical smooth layered structure with a neat, clear, and wrinkled form. The laminated structure remains in the GO/PPy nanosheets, and the surfaces of the nanosheets are rougher with distinct humps due to the adhesion of PPy nanoparticles. The multi-layered nanosheets of GO/PPy/PIL are significantly thicker than the GO/PPy nanosheets, indicating successful coating by the PIL layer on GO/PPy. In addition, small bumps are also observed on the surface of the nanosheets, which is caused by the second growth of PIL. (d–f) are the corresponding TEM images of the nanosheets. These data show that the GO nanosheets are highly transparent under the electron beam with folding at the edges confirming their thin nature. After PPy coating, the thickness increases and the transparency decreases. The GO/PPy/PIL nanosheets are very different from both the GO and GO/PPy nanosheets. These multi-layered samples are opaque and decorated with dark points, confirming the changes produced by the dual PPy and PIL coating. shows the FT-IR spectra of the GO, GO/PPy, and GO/PPy/PIL nanosheets. The broad band at 3427 cm−1 in the spectrum of GO is attributed to stretching vibration of OC is observed at 1575 cm−1. The bands at 1728 and 1080 cm−1 are due to stretching vibrations of CH. The bands at 1544 and 1471 cm−1 are attributed to the typical vibrations of the pyrrole ring. The in-plane vibrations of CH in the pyrrole ring are observed at 1298 and 1180 cm−1H are shifted to 1257 and 1159 cm−1. And the bands at 646 and 450 cm−1 become stronger due to the contribution of NC deformation vibrations. These data confirm that the GO/PPy nanosheets were modified by PIL.TGA and differential thermal analysis (DTA) curves of the GO, GO/PPy, and GO/PPy/PIL nanosheets are shown in a) is from 150 °C to 170 °C due to the removal of oxygen-containing groups on the GO surface or edges. A corresponding weight loss peak can be found in b. The gradual and steady weight loss might be due to the destruction of the GO carbon skeleton. Compared to GO, the GO/PPy nanosheets have similar decomposition temperature but more mass residue due to the larger residue of PPy as shown in Fig. S1. For a better understanding, the TGA and DTA curves the IL are shown in Fig. S1 as well. The main decomposition of PPy starts at 170 °C, then, a slower weight loss takes place in the range of 170–500 °C due to the degradation of PPy framework . It can be seen that the temperature required by GO/PPy/PIL is higher than GO/PPy when the maximum decomposition occurs. Over 380 °C, there is a slight mass loss on the TGA curve of GO/PPy/PIL, which is similar to the TGA curve of the IL monomer (ViEtIm+Br−) (Fig. S1). Therefore, this weight loss may be attributed to the decomposition of part of the ionic groups. Similar phenomena were observed in previous studies by other researchers shows the XRD patterns of GO, GO/PPy, and GO/PPy/PIL nanosheets. The GO diffraction peaks are observed at 2θ |
= 9.88° and 43°, corresponding to the reflection of (001) and (100) planes. The interlayer spacing of GO sheets depends on the number of water molecules in the graphite oxide corridor The microscopic structures formed by the nanosheets in the ER fluids were first observed using an optical microscope (OM). Two strips of conductive tape were adhered in parallel on a glass slide holding a narrow gap between which the ER fluid was dropped in and an electric field was applied. To clearly observe the structures, the ER fluids (8 wt%) were diluted by silicone oil. The particulate structures before and after the application of an electric field are presented in . In the absence of an electric field, the nanosheets are randomly dispersed in the liquid silicone oil, which is a liquid-like state. When an electric field is present (higher than a critical value), the nanosheets move rapidly and form chains or columnar structures due to interfacial polarization, and the sample then appears to be solid-like. shows the structural changes in the ER fluids of GO/PPy and GO/PPy/PIL nanosheets. They are similar in the off-field state, and both show freely dispersed particles. However, their on-field states are quite different. The chains formed by the GO/PPy/PIL nanosheets are thick and robust with almost no free particles, indicating good response of GO/PPy/PIL to the electric field. The GO/PPy nanosheets form thin networks rather than obvious chains. Rheological measurements were done next to analyze how the particulate structures influence the rheological properties of the ER fluids.The rheological properties of the two ER fluids (8 wt%) were measured at various electric field strengths using a rotational rheometer with a parallel plate geometry. A controlled shear rate (CSR) mode was first selected to observe the shear stress and shear viscosity curves of the ER fluids under steady flow. demonstrates shear stresses of the GO/PPy and GO/PPy/PIL ER fluids as a function of shear rate at an applied electric field. Both ER fluids show similar behaviors when the electric field is off, i.e., they act like a non-Newtonian fluid in the low shear rate region and more like a Newtonian fluid in the high shear rate region with a critical shear rate of about 10 1/s. This is attributed to the sheet-like morphologies of the GO/PPy and GO/PPy/PIL particles, which make the particles initially orientate in the shear flow. This results in a shear thinning effect. The shear stresses of the GO/PPy/PIL ER fluid are obviously higher than the GO/PPy ER fluid at low shear rates. This may be due to the enhanced thickness of the GO/PPy/PIL nanosheets that higher shear stresses are needed to rotate the nanosheets. When the electric field is applied, both the ER fluids show Bingham plastic behaviors with a certain yield stress at each electric field strength. The OM observations suggest that the dispersed nanosheets formed chain-like structures or particulate networks upon electric field stimuli. In other words, the field-induced phase transition from a liquid-like to a solid-like state occurs in the ER fluids. Therefore, yield stresses appear to deform the solid-like ER fluids. As the electric field strength becomes higher, the yield stress jumps to a higher level as well. This indicates that the particulate structures of ER fluids become stronger as the electric field strength increases. The flow curves of the GO/PPy ER fluid become unstable after a certain plateau area because of the weak interaction between the particles and slow reformation rate of particulate structures. The shear stress curves of the GO/PPy ER fluid exhibit a similar slope as the zero field curve when the shear rate is over ∼100 1/s. This suggests that the particulate structures could be totally destroyed if the shear rate is sufficiently high. In contrast, the GO/PPy/PIL ER fluid is more stable with higher shear stresses over the entire shear rate range. The different field-induced structures observed by OM predict that thick chains or columns need higher stresses to be destroyed than the thin networks. The extremely higher shear rate can destroy the GO/PPy/PIL structures.The available electric field strength is another significant difference between the two ER fluids. For the GO/PPy ER fluid, the highest electric field strength that could be applied is only 1 kV/mm. This is because of the high conductivity of PPy and GO even though thermal treatments were used before the preparation of the ER fluid. The available electric field strength is improved to 2 kV/mm and the corresponding yield stress is 280 Pa for the GO/PPy/PIL ER fluid. Comparing with GO based ER fluids reported by other researchers, the GO/PPy/PIL ER fluid shows a relatively high yield stress. For example, Mrlík et al. reported that the GO-grafted PGMA ER fluid had a yield stress of 100 Pa at 2.5 kV/mm presents the shear viscosity curves of the ER fluids obtained in the CSR measurement. It shows that when the electric field is not applied, the shear viscosity curves of the ER fluids exhibit similar behaviors as those shown in the shear stress curves. There is first shear thinning and then Newtonian behavior. In addition, the GO/PPy/PIL ER fluid shows higher zero shear viscosity than the GO/PPy ER fluid. When the electric field is applied, the zero shear viscosity first increases dramatically followed by obvious shear thinning across the entire shear rate range. The zero shear viscosity becomes higher as the electric field strength increases.Dynamic tests under oscillatory rotation are important tools to analyze the viscoelastic properties of ER fluids. First, amplitude sweeps were used to determine the linear viscoelastic (LVE) region of the solid-like ER fluids. The resulting storage modulus G′ (closed) and loss modulus G″ (open) are shown in as a function of strain. At zero electric field strength, both ER fluids are solid-like with a higher G′ than G″. This may be attributed to the sheet-like morphologies of the particles that are easier to form into three-dimensional frameworks than spherical particles at a certain particulate concentration. Under an applied electric field, both G′ and G″ are independent of strain, and G″ is always lower than G′ at a low strain range. This indicates a higher degree of solid-like behavior with ER fluids To effectively analyze the progressive structural breakdown in the ER fluids, the in-plate (elastic) stress component (τ′ = G′γ) of the total stress was calculated using the data in as a function of strain. The elastic stress increases linearly with increasing strain at low strain amplitudes within the LVE region. This means that the ER fluid responds elastically to the deformation. Without an electric field stimulus, the linearly increased elastic stress curves suddenly collapse at a critical point. This indicates the transition from viscoelastic to totally viscous state. Comparatively, the elastic stress reaches a maximum value at a critical strain when an electric field is applied. This is considered to be the elastic yield stress of the ER fluid. Afterwards, the elastic stress decreases slowly because the solid-like structures of the ER fluids begin to break down To compare the yield stresses of the two ER fluids, both the elastic yield stress and the dynamic yield stress are shown in as a function of electric field strength. In this case, the dynamic yield stress is obtained by extrapolating the shear stress to zero shear rate in . For conventional ER fluids, the correlation between yield stress (τy) and electric field (E) can be illustrated by a power law relationship as follows:Here, the slope m is 1.5 for the conducting model and 2.0 corresponds to the polarization model The dynamic yield stress was higher than the elastic yield stress because the static ER fluid contains more agglomerated particles than the fluid under dynamic conditions, thus, it is not controlled by the shear rate The frequency sweep indicates the inverse correlation of G′ and G″ of micron structures in an ER fluid. shows G′ and G″ of the GO/PPy and GO/PPy/PIL ER fluids measured in a frequency sweep ranging from 1 to 100 rad/s and at a strain amplitude of 0.003% in the LVE region. When the two ER fluids are in an electric field, the G′ curves are at a much higher level than G″ over the entire frequency range. The curves are also more stable, indicating that elasticity dominates in the ER fluids. Both the G′ and the G″ increase as the electric field strength increases. In addition, similar to the flow curves, the plateau value of G′ for the ER fluid of GO/PPy/PIL is significantly higher than that of GO/PPy ER fluid at the same electric field strength.To further verify the reliability and sensitivity of the GO/PPy and GO/PPy/PIL ER fluids, shear stress curves were measured at a constant shear rate (γ = 0.1 1/s) and a square-wave pulse voltage (time interval: 50 s). The results are shown in . Both of the ER fluids exhibit obvious switching effects under a square pulsed electric field. When an electric field is applied, the shear stresses of each ER fluid increase rapidly and then plateau. When the electric field is removed, the shear stress of each ER fluid decreases to a very low level. This suggests that the ER fluid can undergo rapid and reversible liquid–solid mutual transformation under the pulsed electric field. Stronger electric fields lead to a higher shear stress. Similar to the previous experimental results, the secondary coating with a PIL layer results in a stronger polarization of the multilayered nanosheets. This leads to stronger interactions between the nanosheets.In order to understand the polarization dynamics of the nanosheets further, dielectric spectra of the two ER fluids were measured by a broadband dielectric spectrometer in the frequency range of 0.03 to 107 |
Hz. shows the dielectric (a) and conductivity (b) spectra of the ER fluids in the measured frequency range. There is an obvious dielectric relaxation in the dielectric loss factor (ε²) curve of the GO/PPy/PIL ER fluid and the pre-increase in ε″ is caused by dc-conductivity. From the dielectric spectra of the GO/PPy ER fluid, dielectric relaxation is not observed due to the high conductivity of the GO/PPy particles. The high conductivity can be confirmed by the conductivity spectra of the ER fluid in b. The dielectric spectra of the GO/PPy/PIL ER fluid were analyzed by the Havriliak–Negami (HN) equation ε*(ω)=ε′+iε″=ε′∞+Δε′(1+(iωτ)α)γ+σdciε0ω+Aω−nwhere Δε′ = ε′∞-ε′0 is the dielectric strength, representing the polarizability of the dispersed phase, ε′0 and ε′∞ are the dielectric constant of low and high frequency, respectively, τ = 1/(2πfmax) represents the dielectric relaxation time, α and γ are the profile shape factors of relaxation dispersion, σdc represents the dc-conductivity at low frequency, and n is related to the slope at high frequency. Parameters obtained by fitting the modified HN equation are shown in In the conductivity spectra of the ER fluids, the conductivity (σ0) of each ER fluid is given by the plateau value of σ′ The GO/PPy/PIL multi-layered composite nanosheets were successfully synthesized via a chemical grafting polymerization process based on pre-synthesized GO/PPy nanosheets. It was interesting that the first coating by PPy exactly supported more reactive points with IL than pure GO that a nice PIL layer could formed on the nanosheets. SEM and TEM images of the dual-coated nanosheets showed a rough surface and an increase in sheet thickness. Both the GO/PPy and the GO/PPy/PIL nanosheet-based ER fluids exhibited typical ER performance and had recovery properties via steady shear under a square-wave pulse voltage. The steady and dynamic rheological measurements indicated that the GO/PPy/PIL nanosheets had a significantly higher ER effect and higher available electric field strength than the GO/PPy nanosheet, i.e., they had higher yield stress and modulus at the same electric field strength. This was attributed mostly to the nicely coated semiconducting PIL layer, which not only reduced the conductivity but also contributed to the nanosheets’ ER response.Supplementary data associated with this article can be found, in the online version, at The following is Supplementary data to this article:Experimental and numerical investigation of cross-shaped buckling-restrained SPSWs with composite structureThe square concrete-filled steel tube (CFST) column enjoys the advantages of high bearing capacity, a simple structure of beam-column joints, good ductility and seismic performance. Therefore, the square CFST columns are introduced as the boundary frame of buckling-restrained steel plate shear wall (SPSW). To investigate the cyclic behaviour of cross-shaped buckling-restrained SPSW with a composite frame consisting of H-shaped steel beams and square CFST columns, two specimens were prepared and tested under the cyclic quasi-static loading, and the failure modes and hysteretic curves of the specimens were discussed. Experimental results show that the cross-shaped buckling-restrained stiffeners can significantly reduce the out-of-plane deformation of the steel plate and improve the bearing capacity of SPSW structures. The finite element (FE) models of SPSWs with cross-shaped stiffeners were developed, and good agreement was observed between the FE analysis results and test results for the failure modes, skeleton curves and bearing capacity. Based on the parameter analysis results of the cross-shaped buckling-restrained SPSWs structures, it is assumed that the strength of the embedded steel plate can be fully exerted when the flexibility coefficient of square CFST columns is no greater than 2.5. In addition, the design rules of the flexibility coefficient of square CFST columns were proposed to promote the application of SPSW buckling-restrained by cross-shaped stiffeners in high-rise buildings.Steel plate shear wall (SPSW) structure is a new type of lateral load resisting structure developed in the 1970s. Due to the lack of in-depth research on the post-buckling mechanical behaviour of the thin SPSW in the early stage, only thick SPSW was used in the design of the actual project []. Thin SPSW is developed based on the theory of thin-belly girder and exhibits considerable post-buckling strength and ductility under the action of horizontal load, which is derived from the mechanism of tension field and can provide stable bearing capacity and lateral stiffness for the post-buckling SPSW. Compared with the thick SPSW, due to the low steel consumption and high bearing capacity of thin SPSW, a series of theoretical and experimental studies have been conducted on thin SPSWs []. The results show that although the SPSW still has certain stability bearing capacity and stiffness after yielding, there are some defects in the mechanical properties of SPSWs, such as: the steel plate has excessive out-of-plane buckling deformation, obvious “pinching” of the hysteretic curve, large noise in the process of loading, and considerable additional bending moment for columns. Therefore, to improve the mechanical properties of the thin SPSW mentioned above, suitable structural measures should be adopted to decrease the out-of-plane deformation of the steel plate. The common measures are to arrange stiffeners or anti-buckling covers for the steel plate [] were the first to conduct an experimental study on the seismic performance of stiffened SPSWs under horizontal cyclic loads. The experimental results show that the stiffened SPSW had better hysteretic and seismic performance than unstiffened SPSW, and the “pinching” phenomenon of hysteretic curve of stiffened SPSW was significantly improved. In 2007, Alinia et al. [] analysed the influence of stiffeners on the energy dissipation performance of SPSWs based on the ANSYS FE model. The results show that the unstiffened SPSW had good ductility but insufficient energy dissipation capacity, and the energy dissipation capacity of the unstiffened SPSW can be improved by the arrangement of appropriate stiffeners. In the following studies, Alavi et al. [] both proved that stiffeners can significantly improve the strength and stiffness of SPSWs through experiments. There are also some researchers [] devoted to using a concrete cover plate to restrain the buckling deformation of SPSW to improve the lateral bearing capacity of SPSW. Note that, no matter what measures are taken, the out-of-plane buckling deformation of the steel plate can be significantly reduced, and the bearing capacity and energy dissipation capacity of the steel plate can be improved.Cold-formed steel stiffener is a kind of assembly stiffener, which can effectively avoid the problems of residual stress, residual deformation and poor fatigue resistance caused by welding. In addition, the cold-formed steel composite wall enjoys excellent performance such as thermal insulation, seepage prevention and sound insulation. Therefore, the authors [] proposed a new type of cold-formed steel buckling-restrained SPSW that integrated architectural and structural function, as shown in , and the experimental and theoretical study of the SPSWs with the vertical arrangement of cold-formed steel stiffeners without considering the effect of the frame were carried out. There are also some research results [] that show that the cross-shaped stiffeners have a good buckling restraint effect on steel plates. Tan et al. [] conducted an experimental study on cyclic shear performance of SPSW with different buckling restraints, and the results showed that the cross-shaped cold-formed steel buckling restraints have the highest efficiency in improving the bearing capacity of SPSW. Meanwhile, the square concrete-filled steel tube (CFST) column enjoys the advantages of high bearing capacity, a simple structure of beam-column joints, good ductility and seismic performance. Besides, the outer steel tube can be used as concrete formwork and construction support, which improves the construction efficiency.Therefore, in order to further investigate the buckling restraint effect of cross-shaped cold-formed steel stiffeners on steel plates and the cyclic behaviour of cross-shaped buckling-restrained SPSW with composite frame consisting of square CFST columns and H-shaped steel beams, a series of studies were carried out on the proposed cold-formed steel buckling-restrained SPSWs with composite frame, as shown in . The failure mode, bearing capacity and seismic performance of the cross-shaped buckling-restrained SPSW with composite frame were studied, and some design methods were proposed to promote the application of SPSW buckling-restrained by cross-shaped stiffeners in high-rise buildings.A total of two 1/3 scaled single-bay two-story specimens of SPSW with composite frame were designed for the test programme, and the composite frame was composed of square CFST columns and H-shaped steel beams. The two specimens only vary in the embedded SPSWs, among which the unstiffened SPSWs were for specimen FSP0 and SPSWs with cross-shaped stiffeners were for specimen FSP1. The square steel tube was 200 × 200 × 6 mm. To prevent the column base from premature damage and buckling during the test, the section size of the square steel tube in the relevant area of the column base was selected as 200 × 200 × 10 mm for local strengthening. The beam was an H-shaped steel member, of which, the top beam and the bottom beam were HN300 × 150 × 6.5 × 9 mm, and the middle beam was HN200 × 100 × 5.5 × 8 mm. The total height of all the specimens was 3380 mm, the first and second stories of SPSWs of the specimens were identical. The cold-formed steel stiffeners on both sides of steel plate was connected by M12 high-strength bolts of grade 12.9. To improve the out-of-plane buckling restraint effect of the stiffeners, the section form suggested in literature [] was adopted. The four sides of the embedded SPSWs were connected to the fishplate by 10.9 M24 friction high-strength bolts. The details and dimensions of specimens are shown in The material grade of the square steel tube, H-shaped steel beam and steel plate of the specimens were all Q235B, and the cold-formed steel members was made of Q345B. The tensile coupon tests were carried out to determine the mechanical properties of steel materials, as illustrated in , and the average compressive strength of the concrete cube after 28 days was 31.1 MPa., the pseudo-static tests were applied by three 200-ton servo controlled electro-hydraulic actuators, and a total of 400 kN constant vertical load was applied to each of the CFST columns by the vertical hydraulic jacks. The out-of-plane restraining beam was arranged to prevent the specimens from out-of-plane instability during the loading process. The base beam was anchored to the rigid floor of the laboratory by 12 prestressed steel rods to ensure no relative slip between the base beam and the rigid floor of the laboratory. As shown in , the load-displacement hybrid control loading protocol was employed for the specimens []. At the beginning of the test, load control loading was adopted until the load was close to the yield bearing capacity of the specimens. Afterwards, the test was changed to displacement control. The test was terminated when the horizontal load dropped to 85% of the maximum load. shows the F-Δ hysteretic curves of the specimens FSP0 and FSP1, and the two curves have similar laws. It can be seen that the specimens were in the elastic stage at the beginning of the load. When the specimen entered the elastoplastic stage, and local buckling occurred. With the increase of the development of the tension field of the steel plate, the hysteretic loop gradually enlarged, and the energy dissipation capacity of the specimen gradually developed. The “breath effect” of the steel plates leads to the “pinching” phenomenon of the hysteresis curves. After the specimen reached the peak load, due to the accumulation of damage, the steel plates of specimens appeared obvious tearing failure, and the bearing capacity and stiffness decreased rapidly. It can also be found that the initial stiffness and bearing capacity of specimen FSP1 were greater than that of specimen FSP0, and the envelope area of the hysteresis curve was also larger than that of specimen FSP0, indicating that the cross-shaped stiffeners can effectively reduce the out-of-plane buckling deformation of steel plates and improve the shear capacity and seismic performance of steel plates.The relationships between the lateral displacement Δ and the equivalent viscous damping coefficient he of specimens are shown in . When the steel plate enters the yield stage and appeared out-of-plane buckling deformation, the equivalent viscous damping coefficient has entered into the phase of rapid growth, and the equivalent viscous damping coefficient of specimen FSP1 is higher than that of specimen FSP0. This indicates that the energy dissipation capacity of steel plates can be significantly improved by setting stiffeners. presents the stiffness degradation curves of specimens. Before yielding, the initial secant stiffness of specimen FSP1 was 75.40 kN/mm, which was larger than that of FSP0 (equal to 53.09 kN/mm). The results showed that the cross-shaped cold-formed steel stiffeners had an obvious effect on improving the initial secant stiffness of the SPSWs. With the increase of the load, the SPSW gradually yielded, and the secant stiffness degraded obviously. The secant stiffness of specimen FSP1 was basically the same as that of the specimen FSP0, which means that the stiffeners had a negligible contribution to the stiffness after the specimen entered the yield stage., in the load-controlled loading stage, the column almost has no lateral deflection, the tension field effect of the SPSW has not been formed, and the transverse force on the column is relatively small. In the displacement loading control stage, the SPSW buckled to form a tension field, and then produced a tension field force on the columns toward the center of the steel plate. As the displacement continued to increase, the horizontal displacement of each measuring point on the side of the columns also increased, indicating that the boundary condition of the embedded steel plate also changed correspondingly. When the top displacement of the column is the same, the horizontal displacement at the middle height of each column of the specimen FSP1 is larger than that of the specimen FSP0, and the corresponding deflection of the column is smaller. This means that the cold-formed steel stiffeners can reduce the tension field force of the steel plate on the columns.] was performed for the numerical study. The steel constitutive model of SPSW material was adopted according to reference []. The true stress-strain relationship determined by tensile coupon tests was considered in the FE model for the steel constitutive model of square steel tube, H-shaped steel beam and cold-formed steel members. The concrete damage plastic (CDP) model was employed for concrete. According to ACI 318M-05 [], the elastic modulus of concrete was 4730fc′ and the Poisson's ratio was 0.2. The constitutive relation recommended in the literature [] was adopted for the compressive behaviour of concrete. According to CEB-FIP MC90 [], the fracture energy was used to simulate the tensile behaviour of concrete.In the FE model, shell element (S4R) was employed for square steel tube, H-shaped steel beam and SPSW, and eight-node reduction integral solid element (C3D8R) was adopted for concrete. Based on analysis results of mesh size sensitivity, and considering the time consumption and calculation accuracy, the mesh sizes of square steel tube, concrete, steel beam and SPSW elements in the FE model were chosen as 30 mm × 30 mm, and the mesh sizes of cold-formed steel members were selected to be 15 mm × 15 mm. The FE model of the specimen is shown in The bottom end of columns was completely fixed in the FE model. Reference points RP1 and RP2 were introduced and coupled to the top end of the east and west columns, respectively. Vertical loads were applied to the CFST columns through the reference points RP1 and RP2, and the out-of-plane displacement of the two reference points was limited. The reference point RP3 was coupled with the outer steel plate of the column on the west side within the height range of the top beam, and the horizontal load was applied to the reference point RP3. The four sides of the SPSW were connected to the boundary frame members with “tie” constraints. The “surface-to-surface contact” with “Hard contact” was introduced to describe the normal direction of the interface between cold-formed steel stiffeners and SPSW and the interface between square steel tube and concrete, and the friction coefficients of the two interfaces were set as 0.15 and 0.6 respectively [According to the eigenvalue buckling analysis results of the FE model, the two reasonable orders buckling modes, as shown in , were selected to be superimposed as the initial geometrical imperfection of the specimen. According to Ref. [], two reasonable buckling modes were introduced based on the eigenvalue buckling analysis results of the FE models, the magnitude of the initial geometrical imperfection was introduced as 1/1000 of the height of the embedded steel plate.Failure modes of specimens obtained from FE analysis are shown in . It can be seen that good agreement are achieved between the FE model results and the test results in terms of the failure modes of steel plates, the torsional deformation of the cold-formed steel members and the local buckling deformation of columns. However, the FE model did not consider the damage and fracture of steel material, so the tear position of the embedded steel plate was not accurately simulated. are the comparison of the F-Δ skeleton curves and the bearing capacity of specimens between the test and FE model respectively. It can be seen that the FE results is in good agreement with the test results including the initial stiffness and bearing capacity, and the FE model has high accuracy in the calculation of the yield bearing capacity and peak bearing capacity of the specimens. Note that the FE model did not take into account the behaviours of steel plate cracking and beam-column joint weld tearing in the middle and late stages of the test, so the skeleton curves obtained from FE modelling did not show a declining segment. However, in general, the FE model established in this paper was accurate and reasonable in the simulation of failure modes, initial stiffness and bearing capacity of specimens.The stiffness of the boundary frame elements plays an important role in the strength of the embedded steel plate and affects the stress uniformity of the steel plate []. To investigate the interaction mechanism between the embedded steel plate and the boundary frame, the effects of the stiffness of the boundary frame on the stress uniformity of the embedded steel plate with cross-shaped stiffeners were studied. According to the analysis results, the stiffness limit requirements of the boundary frame which can give full play to the strength of the SPSW were proposed.. Among them, the SPSW can be regarded as the vertical cantilever beam, and the beam can be regarded as the transverse stiffener. If the boundary frame members have enough stiffness to provide anchorage for the steel plate and the tension field of the steel plate is assumed to be fully exerted, the vertical boundary members are not considered to carry the axial force and the influence of the deformation of the boundary members on the bearing capacity of the steel plate is considered, the expression of the flexibility coefficient is described as follows [where, h is the height of the column; Ec1 and Ec2 are the elastic modulus of the two side columns respectively; Ic1 and Ic2 are the moment of inertia of cross section of the two side columns respectively; L is the calculated length of the beam.When the cross sections of the two side columns are the same, and the elastic modulus of the side column is the same as that of the embedded steel plate, the flexibility coefficient of Eq. The stress uniformity coefficient σaverage/σmax was introduced to reflect the influence of the column flexibility coefficient on the tension field development degree of the embedded SPSW [σaverageσmax=2ωccosh(ωc)−cos(ωc)sinh(ωc)+sin(ωc)where, σaverage and σmax are the average stress and the maximum stress of the SPSW respectively; ωc is the side column flexibility, which can be obtained by integrating the stress of the tension field of each SPSW along the height direction.When the side column can provide sufficient anchorage constraint for the embedded steel plate, then the tension field of the steel plate is fully developed, and the maximum stress σmax is equal to the yield stress of steel plate fpy. Then Eq. σaverage=2fpyωc⋅[cosh(ωc)−cos(ωc)sinh(ωc)−sin(ωc)] shows the relationship curve between the flexibility coefficient and the stress uniformity coefficient when the tension field of SPSW is fully developed. When the column can provide sufficient anchorage constraint for the embedded steel plate, the full section of the steel plate material yields (i.e. σaverage=σmax), and the corresponding stress uniformity coefficient is equal to 1. When the column flexibility coefficient is 2.5, the corresponding stress uniformity coefficient of the steel plate is about 83%, indicating that most area of the steel plate has yielded. Therefore, Kuhn et al. [] suggested that the flexibility coefficient of the boundary members should not be greater than 2.5 to ensure the full strength of the steel plate. At this point, it is assumed that the boundary member has enough stiffness to anchor the steel plate and the steel plate strength can be fully exerted. The Canadian Code CAN/CSA-S16-09 [] refer to this recommendation and provide that the flexibility coefficient of the boundary frame for SPSWs using its post-buckled strength shall not be greater than 2.5. According to the Chinese Code JGJ 380–2015 [], the minimum stiffness requirement of the boundary column was calculated according to Eq. However, it should be noted that the stiffness limits of the boundary column mentioned above are determined according to the flexibility coefficient limits of the two boundary members with the same cross section and the same elastic modulus as the embedded steel plate. Therefore, Eq. is not applicable to CFST columns. To better reflect the relative section proportion between square steel tube and concrete, the design method of flexural stiffness of CFST members recommended by American Code ACI 318M-05 [] was adopted to determine the section stiffness of square steel tube columns, as follows:where, As is the sectional area of steel and Ac is the area of concrete.For the buckling-restrained SPSWs with composite frame, it is assumed that the square CFST columns on both sides of the embedded steel plate are the same, and the equivalent section stiffness of the square CFST column is calculated according to Eq. . Thus, the calculation method of the flexibility coefficient of the square CFST column can be expressed as Eq. ], the steel material of square steel tube reaching the yield stress was taken as the stress distribution state of the embedded steel plate. In the parameter analysis, the flexibility coefficients of CFST columns were selected as ω = 1.25, 2.0, 2.5, 3.75 (the corresponding the square steel tubes were: 100 × 100 × 4, 150 × 150 × 6, 200 × 200 × 5.6, 300 × 300 × 12, unit: mm), respectively. shows the influence of CFST columns with different flexibility on the horizontal load-displacement curve of the structure. As reported in a, when the column flexibility coefficient is small, the structure has greater rigidity, higher bearing capacity and better ductility. b shows the normalized load-displacement curves. It can be seen that the load-displacement curve when the column flexibility is 3.75 has different laws from the curves when the column flexibility is no more than 2.5, indicating that the column flexibility coefficient has a great influence on the performance of the structure and affects the strength of the embedded steel plate. When the flexibility of the column becomes smaller, the corresponding column section is larger, which is more conducive to the strength of the embedded steel plate, and the columns contributes more to the lateral stiffness and bearing capacity of the structure. shows the stress distribution of embedded steel plates of the different specimens. It can be seen that the buckling-restrained SPSW has better stress uniformity than that of the unstiffened SPSW, indicating that the cross-shaped cold-formed steel stiffeners can increase the area of the SPSWs to reach the maximum stress.To better evaluate the stress uniformity of the embedded steel plate, as reported in , the Mises stress of each node along the direction of tension field (path 1) and perpendicular to the direction of the tension field (path 2) of the first-story steel plate of each specimen was extracted according to the stress extraction path, and the relative path refers to the relative dimensions of the steel plate along different paths. As reported in a, the steel plate stress of specimen FSP1 at the beam-column connection joints was fully exerted, but the stress in the middle area of the steel plate did not reach the maximum. That is because the cross-shaped stiffeners can better prevent the out-of-plane deformation of the steel plate, and the tension field is discontinuous and cut off in the middle area of steel plate by the cold-formed steel stiffeners. illustrates the stress uniformity coefficient of the specimens along the direction of the tension band is all over 0.9. In the direction of the vertical tension field, the stress uniformity coefficient of unstiffened steel plate is 0.71, and the stress uniformity coefficient of FSP1 is greater than 0.8, indicating that the cold-formed steel members can improve the stress level and the bearing capacity of steel plate. shows the stress distribution of steel plates with different column flexibility. The flexibility coefficients of square CFST columns were considered as ω = 1.25, 2.0, 2.5 and 3.75, respectively, and the corresponding cross sections of square steel tubes are: 100 × 100 × 4, 150 × 150 × 6, 200 × 200 × 5.6 and 300 × 300 × 12 (unit: mm), respectively. It can be seen that the smaller flexibility of the square CFST column makes the steel material reach the larger yield area and the strength of the steel plate will be more fully exerted, which means that the column has a better anchoring effect on the steel plate., the stress uniformity of the steel plates is better when the flexibility coefficients of square CFST columns are no more than 2.5. When the column has a flexibility coefficient of 3.75, the strength of the steel plate has not been fully developed (see ), and the stress uniformity coefficient along the direction of the tension field is 0.83, while the stress uniformity coefficient perpendicular to the direction of the tension field is only 0.71 (), indicating that the stress uniformity of the steel plate is poor. Therefore, when the flexibility coefficient of the square CFST column is not greater than 2.5, it is assumed that the strength of the embedded steel plate can be fully exerted.To investigate the effect of the different width-height ratios of embedded steel plates on the stress uniformity of SPSW structures, the width-height ratio of steel plates B/H = 1.0, 2.0 and 3.0 was selected for FE parametric study. With the increase of the width-height ratio of the steel plate, as shown in , the proportion of the area in which the steel plate strength reaches the maximum value decreases, indicating that a large width-height ratio has a negative influence on the effect of stiffeners. shows Mises stress extracted along paths 3 and 4. As shown in a, with the increase of width-height ratio, the smaller the proportion of the stress reaching the maximum along the horizontal direction of the steel plate and the less the strength of the steel plate is fully developed. As can be seen from , the ratio of the average stress to the maximum stress extracted along the path is all greater than 80%, indicating that most of the strength of the embedded steel plate with cross-shaped cold-formed steel stiffeners can be fully exerted under different width-height ratios.According to the above analysis results, for the unstiffened SPSW structure with pure steel boundary frame members, when the flexibility coefficient of pure steel column is no more than 2.5, the stress uniformity coefficient of the embedded steel plate is greater than 83%. At this point, it can be assumed that the frame column can provide a better boundary constraint for the steel plate and the stress of the steel plate can be fully exerted []. However, the aforementioned assumption is not applicable to the square CFST columns. Because the stress uniformity coefficient of the unstiffened steel plate is less than 83% when the flexibility coefficient of the square CFST column is 2.5 (see Eq. ), which means the strength of the steel plate will not be fully exerted. But for SPSW with cross-shaped stiffeners, the stress uniformity coefficient of the steel plate can meet the limit condition of 83% when the flexibility coefficient of the square CFST column is 2.5. Therefore, when the CFST columns is adopted for the cross-shaped cold-formed steel stiffeners SPSWs structure, the CFST column can still be designed using the design rules proposed in the specification [] to ensure the full play of the strength of the embedded steel plate.Two 1/3 scaled single-bay two-story specimens of SPSW with composite frame consisting of square CFST columns and H-shaped steel beams were tested, and the cyclic shear performance of the specimens was reported including energy dissipation capacity, stiffness degradation and bearing capacity. The experimental results show that the cross-shaped buckling-restrained stiffeners can significantly reduce the out-of-plane buckling deformation of the steel plate and improve the bearing capacity of SPSW structures, decreasing the tension field force of the steel plate on the column, and ensure the strength of the embedded steel plate can be better exerted. Afterwards, the corresponding FE models were generated and validated against experimental results considering failure modes and bearing capacity. The interaction mechanism between the SPSW and the boundary frame and the effects of the flexibility coefficient of square CFST columns on the stress uniformity of the embedded steel plate with cross-shaped stiffeners were studied. The numerical results show that: (1) when the flexibility of the column becomes smaller, the strength of the embedded steel plate is more fully exerted; (2) with the increase of width-height ratio, the smaller the proportion of the stress reaching the maximum along the horizontal direction of the steel plate and the less the strength of the steel plate is fully developed; (3) when the flexibility coefficient of the CFST columns is no greater than 2.5, it is assumed that the strength of the embedded steel plate with cross-shaped cold-formed steel stiffeners can be fully exerted. Therefore, for the structure of SPSW with cross-shaped cold-formed steel stiffeners, the CFST columns can still be designed according to the design rules proposed in the specification for steel columns to ensure the full play of the strength of the embedded steel plate.Ji-Ke Tan: Investigation, Software, Writing - original draft, Visualization. Xu-Hong Zhou: Conceptualization, Supervision. Xin Nie: Writing - review and editing, Supervision. Yu-Hang Wang: Conceptualization, Supervision, Funding acquisition. Kang Wang: Software, Writing - original draft.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Bending mechanical properties of a single-grain Y123 bulk superconductor at liquid nitrogen temperatureIn order to investigate the mechanical properties of a single-grain Y123 bulk with 15 wt.% Ag at liquid nitrogen temperature (LNT), three-point bending tests of specimens cut from the bulk were carried out. The dimensions of the bending test specimens were 4 × 3 × 36 mm3. The loading was carried out in the c-axis or perpendicular to it such that the normal stress induced by loading was perpendicular to the c-axis. Young’s modulus at LNT by loading in the c-axis and perpendicular to it were 143 and 134 GPa and the bending strengths were 115 and 128 MPa, respectively. These bending strength values were higher than those at room temperature (RT) for this bulk. From the comparison with the other rare earth element based bulks, the smaller the ionic radius of Y or rare earth elements, the higher Young’s modulus and the bending strength of the bulks. This implies that the strength is basically controlled by the ideal crystal strength of bulks, irrespective of the crystal orientation and, further, defect induced during fabrication process, so long as the defect size is comparable. The step-wise undulation in the crack propagation direction on the fracture surfaces by loading in the c-axis was significant as compared with that by loading in perpendicular to it.Single-grain R123 (RBa2Cu3Ox, where R is Y or rare earth elements) bulks sometimes fracture due to thermal stress on cooling or electromagnetic force during magnetization process. Thus investigations of mechanical properties are important to their practical applications.In order to investigate the mechanical properties at cryogenic temperatures, bending tests of specimens cut from bulks have been carried out at liquid nitrogen temperature (LNT) such that the loading in the c-axis or perpendicular to it induces the normal stress perpendicular to the c-axis. Tomita et al. have reported the bending strength at LNT of the specimens cut from Y123 bulks along the growth sector boundary or the line tilted 45° from it by loading in the c-axis and perpendicular to it In this study, in order to investigate the mechanical properties at LNT of a single-grain Y123 bulk with Ag addition, three-point bending tests of specimens cut from the bulk were carried out and the effects of loading direction, testing temperature and Ag content on the mechanical properties were discussed.A commercial single-grain Y123 bulk (45 mm in diameter and 18 mm in thickness) with 15 wt.% Ag and 0.4 wt.% Pt fabricated by Dowa Mining Co., Ltd. was used. The molar ratio Y123:Y211 (Y2BaCuO5) of the precursor was 100−X:X (X |
= 28.6). This bulk sample is denoted as Y15. Four specimens with the dimensions of 4 × 3 × 36 mm3 were cut from the bulk using a slow-speed diamond wheel saw such that the longitudinal direction was perpendicular to the c-axis. The thickness (3 mm; loading) direction for two specimens was parallel to the c-axis and that for the other two specimens was perpendicular to it as schematically shown in . The pre-existing micro-cracks perpendicular to the c-axis inevitably formed in R123 bulks due to the phase transformation during the fabrication process are shown in the schematic figures. The specimen mounted on the three-point bending jig with 30 mm fulcrum span was immersed in a liquid nitrogen bath using two manual jacks. The temperature near the specimen was monitored using a thermo-couple such that the cooling rate was less than about 6 K/min. The loading was carried out at a displacement rate of 0.15 mm/min using the 2 kN Shimadzu Servopulser testing machine. The loadings in the c-axis and perpendicular to it are denoted as P |
∥ |
c and P |
⊥ |
c, respectively (see ). The applied load was measured using a 2 kN load cell. In order to measure the strain induced by the loading, a strain gage (gage length: 0.5 mm) was attached to the center of the 4 × 36 mm2 tensile side surface of the specimens. The load and the strain were recorded using a data logger at a sampling rate of 50 ms. Stress, σ, induced by the loading was calculated using Eq. where P is the applied load, L is the fulcrum span, w and t are the width and the thickness of the specimen, respectively. Fracture surfaces were observed using the KEYENCE VK-9500 violet laser color 3D profile microscope system.Stress–strain curves at LNT of Y15 for P |
∥ |
c and P |
⊥ |
c are shown in Young’s moduli were evaluated from the slope of the stress–strain curves (excepting the curve with ∗). The average Young’s modulus at LNT for P |
∥ |
c (143 GPa) was higher than that at RT (133 GPa) The average bending strengths at LNT of Y15 for P |
∥ |
c and P |
⊥ |
c, together with those at RT . Reported the average bending strengths for the other Y123 bulks Fujimoto reported the increase of the bending strength of the Y123 bulks at LNT for P |
∥ |
c with increase of the Ag content . Bending strength at LNT of Y15 for P |
∥ |
c was between the bending strength values of the bulks with 10 and 20 wt.% Ag.Scattering of the bending strength at LNT of Y15 was evaluated using the Weibull plot, although the number of the data points is small and the data for P |
∥ |
c and P |
⊥ |
c was not distinguished. The Weibull coefficient at LNT (4.7) was significantly smaller than that at RT (17.5). This temperature dependence coincides with that for the Y123 bulk without Ag; the Weibull coefficients at LNT and RT being 6.1 and 17.6, respectively The mechanical properties at LNT of Y15 were compared with those of the Dy123 with 10 wt.% Ag bulk (Dy10) shows the mechanical properties at LNT as a function of the ionic radius Since R123 bulks are brittle, it is expected that their fracture strengths depend on the initial crack propagation behaviors. To investigate the relationship between the bending strength and the initial crack propagation behavior, the fracture surface profiles in the direction from the outermost surface (where the tensile stress is the highest) to the interior were quantitatively observed using a violet laser color 3D profile microscope. (a) and (b) shows the fracture surfaces of Y15 for P |
∥ |
c and P |
⊥ |
c and shows the fracture surface profiles along the lines A and B in (a) and (b). It is notable that the step-wise undulation for P |
∥ |
c was significant as compared with that for P |
⊥ |
c. It is presumed that the pre-existing micro-cracks perpendicular to the c-axis, which are in perpendicular to the crack propagation direction, disturb the crack propagation. It may be associated with that the minimum strength value for P |
∥ |
c was higher than that for P |
⊥ |
c (see ). On the other hand, the difference in the altitude between the lines A and B for P |
⊥ |
c was significant as compared with that for P |
∥ |
c. It is presumed that the steps, plateaus and slopes are formed due to the pre-existing micro-cracks, which are in the crack propagation direction.The three-point bending tests of specimens cut from a single-grain Y123 bulk with 15 wt.% Ag were carried out at liquid nitrogen temperature such that the loading in the c-axis or perpendicular to it induces the normal stress perpendicular to the c-axis. The following conclusions were obtained.Young’s modulus at LNT for P |
∥ |
c (143 GPa) was higher than that at RT (133 GPa). On the other hand, the modulus at LNT for P |
⊥ |
c (134 GPa) was slightly lower than that at RT (139 GPa).Bending strengths at LNT for P |
∥ |
c and P |
⊥ |
c were 115 and 128 MPa, respectively. Both of the former and the latter were higher than those at RT (107 and 101 MPa, respectively). The former was between the bending strength values at LNT of the Y123 bulks with 10 and 20 wt.% Ag. Weibull coefficient of the bending strength at LNT (4.7) was slightly larger than that for the Y123 bulk with 10 wt.% Ag and almost equal to that with 20 wt.%.Both of Young’s modulus and the bending strength at LNT were higher than those of the other rare earth based bulks. The order of magnitude of Young’s modulus and that of the bending strength among these bulks were similar to each other; the smaller the ionic radius of Y or rare-earth elements, the higher Young’s modulus and the bending strength.The step-wise undulation in the crack propagation direction on the fracture surfaces for P |
∥ |
c was significant as compared with that for P |
⊥ |
c. It is presumed that the pre-existing micro-cracks perpendicular to the c-axis disturb the crack propagation in the former.Experimental study on seismic behavior of precast concrete circular section column with grouted sleeveThe seismic behavior of circular section precast concrete columns (PC) with grouted sleeves was experimentally studied. Six PC and three cast-in-situ concrete columns (CC) were designed, and their low cycle reciprocating loading tests were carried out. The differences of seismic performance between PC and CC under the same conditions were compared. The effects of longitudinal reinforcement ratio (LRR), stirrup volume ratio (SVR) and axial compression ratio (ACR) on hysteretic curve, energy dissipation performance and deformation capacity of PC were studied. The results show that: (1) the failure modes of PC and CC were similar, but there was a small amount of pull-out of the reinforcement in the sleeve; (2) compared with CC, the hysteretic curve of PC was fuller, the horizontal bearing capacity was reduced by about 10%, and the ductility was better; (3) with the increase of LRR, the bearing capacity of fabricated columns increases, the ultimate displacement remains basically unchanged, the ductility decreases and the energy dissipation performance increases; (4) with the increase of ACR, the bearing capacity of PC increases, the ductility decreases and the energy dissipation performance decreases; (5) the SVR has little effect on the seismic performance of PC.the axial pressure applied on the column topthe average value of prismatic compressive strength of concreterepresents the cross-sectional area of the column bodyPrefabricated concrete structure (PCS) is an important development of building industrialization and housing industrialization in China, which has been vigorously promoted by the state. PCS is connected by precast concrete components through reliable connection and forms an integral assembly with on-site post cast concrete and cement-based grout.Concrete column sections mainly include rectangular, circular, and anisotropic sections []. At present, there are many studies that have been performed on the most commonly used rectangular columns. For example, Zhang et al. [] analyzed the seismic characteristics of high-strength steel bar and high-strength concrete columns and compared them with ordinary reinforced concrete columns. In terms of circular section, Aboukifa and Moustafa [] conducted the experimental research on seismic characteristics of large-scale full UHPC concrete circular section columns. The results show that UHPC columns have reasonable ductility and anti-sliding ability. Khateeb et al. [] proposed two new types of circular section concrete-filled steel tube column foundation joints and performed experimental research. On the other hand, Zhang et al. [] tested and analyzed the seismic capacity of I-steel-circular concrete-filled steel tubular column with outer diaphragm. Zheng et al. [] presented a circular double-tube steel concrete composite column, and analyzed the seismic performance of it. Lv et al. [] proposed a PCS frame with some advantages like simple operation, economy and good fault tolerance.The most commonly used reinforcement connection method in PCS components is grouted sleeve connection (GSC) []. PCS frame structure is composed of all or part of frame beams and columns with prefabricated components. The seismic behavior of precast concrete column (PC) is very important to the seismic behavior of the whole structure. To improve poor seismic performance of GSC in PC, Guan et al. [] used UHPC to locally strengthen plastic hinge and made and carried out experimental research on two specimens. The results show that the specimens with UHPC jacket can move the damaged area away from PC base connection area and achieve seismic behavior equivalent to the cast-in-situ reference specimens. Nzabonimpa and Hong [] introduced the application of removable laminated high-yield metal plate in PC splicing and carried out tests and numerical simulation. Liu et al. [] introduced the test of seismic capacity of the connection between PC with GSC and foundation. Liu et al. [] proposed a new type of PC joint, with steel sleeve, which are used to fix the concrete core and the flexible plate connected by bolts, in order to realize rapid installation, created specimens, and conducted experimental research on seismic capacity under high axial compression ratio. Wang et al. [] studied the seismic performance of PC connected by bolt splicing, which is composed of column shoes, bolts and grouting, and six specimens were created and tested under different axial load ratios. Furthermore, Xue et al. [] studied the effects of impact location and two reinforcement technologies on improving the performance of PCS under transverse impact based on the numerical method. Xue et al. [] introduced two new types of PCS, and the failure modes, hysteretic characteristics, stiffness degradation, energy dissipation capacity, and ductility of twelve columns with low axial compression ratio were evaluated. Zhang and Li [] proposed a new type of energy dissipation bolt and prestressed reinforcement connection between precast concrete-filled square steel tubular (CFSST) column and reinforced concrete beam. A total of eight PCS specimens with different axial compression ratio, bolt diameter, steel pipe thickness, and beam end arrangement were tested under cyclic load. Chen et al. [] analyzed seismic performance of PC with GSC considering the debonding of longitudinal reinforcement, the results show that the partial debonding of longitudinal reinforcement seriously affects the damage propagation of flexural columns, but does not affect the damage of shear columns. Yu et al. [] proposed a new type connection for PC, and the connection of it has many advantages, and the post grouting process is simple, and the seismic performance tests were carried out.In the above research studies, the seismic performance of cast-in-situ concrete column or rectangular section PC were mainly studied; however, to the best of the authors’ knowledge, the seismic performance of PC with circular section has not been reported. Although circular section is not common in engineering, it is also an important section; therefore, it is necessary to study it to promote the use of PCS. Based on this, the experimental study on seismic capacity of circular section PC with GSC was conducted.Three circular CC and six circular PC with GSC were designed for the specimens. The specimens included three parts: column body, concrete upper end block, and concrete base, all of which were poured with concrete with strength of C60. The total height of each specimen was 2000 mm, and the size of the concrete base under the column was 500 mm × 1400 mm × 500 mm. The size of concrete end block on column was 500 mm × 500 mm × 300 mm, the column height was 1200 mm (net height from column bottom to loading point was 1350 mm), circular section column diameter was 400 mm, shear span ratio λ = 3.375. Holes were reserved for the concrete base and the upper end block of the concrete so that the screw could pass through it during the test loading. See for the size of the test specimens. The specifications and dimensions of sleeves were 48 mm × 310 mm and 52 mm × 370 mm, respectively. The processing and grouting process of concrete column specimens are depicted in The longitudinal reinforcement of the specimen adopts HRB400 hot-rolled ribbed reinforcement, and 8R16 or 8R20 reinforcements were evenly arranged along the column section. The connection length of the longitudinal reinforcement inserted into the sleeve was 153 mm and 183 mm, respectively. A 20 mm connection joint is reserved at the bottom of the column for grouting treatment. The thickness of the protective layer in the grouted sleeve area in the column was 40 mm and that in the non-sleeve area was 20 mm HPB300 reinforcements were used as the stirrup of the test piece, and the range 600 mm above the column bottom was designed as the stirrup densification area. In order to prevent column top concrete from being crushed, a layer of R10 HPB300 reinforcement mesh was arranged on the column top. The test parameters included LRR, SVR, and ACR. The test axial pressure is measured using the ACR, and the test axial pressure ratio n can be expressed as follows:The seismic performance of PC with GSC under different ACR is experimentally studied. Therefore, two different ACRs of 0.20 and 0.35 were designed for the test parameters, and the axial forces applied on the column top in the corresponding test were 790 kN and 1380 kN, respectively. The parameters of the test can be found in Three specifications of reinforcement are used in this test. Before making the test piece, three standard test pieces were reserved for each specification of reinforcement and the material performance test was conducted. The test was carried out according to the standard [The test specimen is poured with commercial concrete provided by a commercial concrete factory, and the concrete strength is C60. Three groups of standard concrete cube specimens were reserved and tested. The concrete cube specimens were loaded according to GB/T 50081-2012 [. The performance of grouting material is shown in The vertical axial pressure was applied by the vertical 200 tons electro-hydraulic servo actuator installed on the column top, and the horizontal repeated load of the column as controlled by the 100 tons MTS electro-hydraulic servo high-performance actuator installed in the horizontal direction. There was a concrete base at the bottom of each specimen, which was anchored with the ground using bolts. Two 100-ton screw hydraulic jacks were set on the concrete base along the horizontal loading direction to prevent the specimen from undergoing horizontal displacement, thereby simulating the boundary conditions of column bottom consolidation and collecting the load value and displacement value during loading. The loading device is depicted in The loading was controlled by displacement, and when the specimen is in the elastic stage, a single cycle is adopted. When the specimen enters the elastic-plastic stage, the displacement loading cycle of each stage shall be twice until the bearing capacity of the specimen is reduced to less than 80% of the maximum bearing capacity value or the specimen is damaged, and the test loading stops. The test loading displacement Δ is controlled by the drift ratio θ of the column, where θ=Δ/H (H = 1350 mm). The loading protocol was as follows: single cycle θ = 0.2%, 0.4%, 0.6%, and 0.8%; two cycles θ = 1.0%, 1.5%, 2.0%, 2.5%, 3.0%, 3.5%, 4.0%, 4.5% and 5.0%. The specific loading protocol is shown in The main failure model of nine specimens was bending failure. When CC-1, CC-2, and CC-3 were loaded to 0.4%, 0.4%, and 0.6% drift ratios, cracks appeared for the first time within 10–25 cm of the column bottom. On the other hand, when PC-1, PC-2, PC-3, PC-4, PC-5, and PC-6 were loaded to drift ratios of 0.8%, 1.0%, 0.8%, 0.6%, 0.6%, and 0.8%, cracks appeared for the first time within 20–30 cm of the column bottom. As the drift ratio increased step by step, the crack extended to the front and back of the column, the width also expanded, and new cracks simultaneously appeared. When CC-1, CC-2, and CC-3 were loaded to 1.5%, 1.5%, and 2.0% drift ratios, and PC-1, PC-2, PC-3, PC-4, PC-5, and PC-6 were loaded to 2.0%, 2.5%, 2.5%, 2.0%, and 2.0% drift ratios, the concrete in the compression areas at the bottom of the left and right columns were crushed and the horizontal bearing capacity reached the peak. As the drift ratios continued to increase, the horizontal bearing capacity continued to decrease. When CC-1, CC-2, and CC-3 were loaded with 2.5%, 3.0%, and 3.5%, and PC-1, PC-2, PC-3, PC-4, PC-5, and PC-6 were loaded with 3.5%, 5.0%, 4.5%, 5.0%, 4.0%, and 4.0% drift ratios, the horizontal bearing capacity decreased to a point lower than 80%, and the test was stopped. At this time, the concrete in the compression area on the left-hand and right-hand sides of the specimen was crushed in a large area, and the failure model is depicted in . The final failure of the specimen was concentrated at the junction of the left-hand and right-hand column bottom, and the cracks during loading were tensile cracks in the horizontal direction. The bottom joint sealing layer of fabricated concrete column was pulled off, and there was a small amount of relative slip between reinforcement and grouted material.The load-drift ratio hysteretic curves are shown in . It can be perceived that the shape of the hysteretic curve of all specimens is the same, the specimen is in the elastic stage at the initial stage of loading, the hysteretic curve is narrow and slender, the hysteretic loop area is small, the residual deformation during unloading is also small, and the hysteretic curve is prismatic. With the increase of cycle times and loading displacement, the column gradually enters the yield stage from the elastic stage. The slope of the curve decreases with the increase of displacement in each cycle loading process. Compared with the first cycle, the slope of the second cycle hysteretic curve in each stage loading process gradually decreases, the stiffness of the specimen degrades, the hysteretic loop area gradually increases, and the residual deformation of the column increases after unloading. When the horizontal load of the column reaches the maximum value, the horizontal bearing capacity of the column begins to decrease, and the load peak point of the column begins to decrease during each stage of displacement loading.The hysteretic curves of PC and CC depict a bow shape, and there is a small amount of pinch phenomenon. The pitching of CC is mainly caused by the crack closure of reinforced concrete columns in the process of low cycle reciprocating loading. When reverse displacement loading, the oblique cracks of columns will close under the action of small force, and there will be large displacement in the process of crack closure. The pitching of the hysteretic curve of the PC is mainly caused due to the opening of the joint surface of the bottom joint sealing layer and a small amount of relative slip between the reinforcement and the grouting material, thereby resulting in a large displacement and indicating that the two different construction methods have a great impact on the hysteretic characteristics of the column. Comparing specimens PC-1 and CC-1, PC-2 and CC-2, and PC-3 and CC-3, under the same parameters, the hysteretic curve of PC is fuller than that of CC, the change speed of slope is smaller, and the decline speed of peak horizontal bearing capacity is slower. Under the same conditions, the horizontal bearing capacity of PC is weaker than that of CC, and the stiffness degradation and bearing capacity decline speed are slower than that of the CC.The impact of longitudinal reinforcement ratio on the hysteretic curve of fully grouted sleeve connected fabricated column is obvious. Comparing specimens PC-1 and PC-5 and PC-2 and PC-3 under the same conditions of other parameters can offer effective results. In addition, increasing LRR of the column increases the hysteretic loop area of the fabricated column, and the peak point of horizontal load increases, the slope of the hysteretic curve increases, and the pinch phenomenon is alleviated. The influence of ACR on the hysteretic performance of PC is also obvious. Comparing specimens PC-2 and PC-6 and PC-1 and PC-4, when the ACR is increased under the same conditions of other parameters, the peak point of horizontal load of the hysteretic curve of PC significantly increases, the hysteretic loop area decreases, the curve slope increases, the slope change speed increases, and the peak value of horizontal bearing capacity decreases at a quicker rate.The SVR of stirrups has a small impact on the hysteretic performance of PC. Comparing specimens PC-1 and PC-6 and PC-2 and PC-4, under the same conditions of other parameters, when increasing the SVR, the peak point of horizontal load of hysteretic curve remains unchanged, the area of hysteretic loop slightly increases, and the change speed of curve slope and the decline speed of peak value of horizontal bearing capacity slightly slows down. By increasing the SVR, the horizontal bearing capacity of fabricated columns remains unchanged, the energy dissipation impact is slightly enhanced, and the rate of stiffness degradation and bearing capacity decline is slightly slowed down.(a–c) shows the skeleton curve of CC and PC with the same other parameters. The horizontal bearing capacity of CC is about 10% higher than that of PC. This is because the PC is prone to defects in the grouting process. When there are defects, the bonding force between the reinforcement and the grouting material in the grouting sleeve decreases, and the bearing capacity reaches the ultimate bearing capacity when the reinforcement and the grouting material are separated. In addition, when the horizontal load reaches the peak point, the skeleton curve of CC becomes steeper and the bearing capacity rapidly decays. However, after the skeleton curve of PC reaches the peak point, there is a long approximate horizontal section in the curve, and the horizontal bearing capacity of PC slowly decays. This is because when the horizontal bearing capacity reaches the peak, even though the reinforcement has a large relative slip with the grouting material, the reinforcement can still bear a large horizontal load before reaching the limit state.(d and e) shows the skeleton curve of PC with the same other parameters and different LRR. With the increase of LRR, the horizontal bearing capacity of PC significantly increases, but there is no significant difference in the slope of rising section. This is because the sleeve connection area of PC forms a rigid region due to a large number of sleeves, and the increase of LRR has little impact on the stiffness of the column bottom. With the increase of LRR, the horizontal bearing capacity of PC reaches the peak, the curve becomes steeper, and the decline speed of bearing capacity is accelerated; however, there is no significant difference in the final ultimate displacement.(f and g) shows the skeleton curve of PC with the same other parameters and different ACR. It can be perceived that with the increase of the ACR, the horizontal bearing capacity of PC increases, the slope of the rising section of the skeleton curve increases, the curve becomes steeper after the horizontal bearing capacity reaches the peak, and the decline speed of the bearing capacity accelerates. However, the specimen curve with small ACR has a significant horizontal section after reaching the load peak, and the final limit displacement is significantly smaller than that of the specimen with large ACR. This is because when the ACR is large, the axial force at the top of the column is large, which speeds up the failure speed of the specimen in the later stage.(h and i) shows the skeleton curve of PC with the same other parameters and different SVR. With the increase of SVR, the horizontal bearing capacity of PC has no obvious change, and the degradation of stiffness and the bearing capacity slows down slightly. In terms of comparison, the skeleton curve remains the same. This is mainly because the failure mode of long column under horizontal load is mainly dependent on the yield of longitudinal tensile reinforcement at the column bottom and the crushing of concrete in the compression area, and the connection area of grouting sleeve of PC due to a large number of GSC. Consequently, a rigid region is formed, which renders the impact of SVR on the bone frame curve of PC less obvious.The characteristic points of skeleton curve of restoring force model generally include yield point, peak point, and failure point. When the skeleton curve load reaches the peak, the corresponding point is the peak point, and the corresponding abscissa is θm. When the bearing capacity drops to 85% of the peak load, the corresponding point is the point of the ultimate failure state of the specimen, and the abscissa of the corresponding point is θu. As can be perceived from , the skeleton curve has no obvious yield point. Therefore, the geometric graphic method [] is used to capture its yield point, as shown in . The ductility coefficient of the specimen can be calculated by using Eq. The calculation results of ductility coefficient are shown in . It can be seen that the ductility coefficients of PC-1, PC-2, and PC-3 are significantly greater than CC-1, CC-2, and CC-3 under the same conditions; therefore, the ductility of PC is obviously better than that of CC. When other parameters are the same, comparing PC-1 with PC-5 and PC-2 with PC-3, it is found that the ductility coefficient of PC-1 is greater than PC-5, and that of PC-2 is greater than PC-3. When the LRR increases from 1.3% to 2.0%, the ductility coefficient increases by more than 1.0. The ductility coefficient and ultimate drift ratio of PC decrease, and the ductility decreases with the increase of LRR. Comparing PC-1 with PC-4 and PC-6 with PC-2, it is found that the ductility coefficient of PC-1 is less than PC-4, and that of PC-6 is less than PC-2. When the ACR increases from 0.2 to 0.35, the ductility coefficient decreases by more than 1.5. It can be perceived that the ductility coefficient and ultimate displacement angle of PC decrease, and the ductility decreases with the increase of axial pressure on the column top. The ductility coefficients of PC-1 and PC-6, PC-4 and PC-2, PC-1 and PC-6 are the same, and the ductility coefficients of PC-4 and PC-2 are the same, thereby indicating that the SVR has no obvious impact on the ductility of PC.Energy dissipation performance reflects energy dissipation capacity of structures or components under repeated loads during an earthquake. The energy dissipation characteristic is generally measured by the area enclosed by the hysteretic curve under the action of the reciprocating load. The larger the area enclosed by the hysteretic curve, the better is the energy dissipation performance and the seismic performance. The hysteretic energy consumption of each loop before the loading stage is superimposed, and the calculated result is the cumulative hysteretic energy consumption capacity of the specimen under the drift of the stage [(a–c) is the cumulative energy consumption curve of CC and PC with the same other parameters. During the initial stage of specimen loading, the specimen is in the elastic stage, the energy consumption per cycle is very small, and the energy consumption growth rate is also very small. When the specimen yields, the energy consumption per cycle increases, and the energy consumption growth rate is the same. Under the same level of loading displacement, the energy consumption of the second cycle is less than that of the first cycle. This is because the strength degradation and stiffness degradation reduce the bearing capacity of the specimen, the hysteretic loop area, and the energy consumption. Before the load reaches the peak point, the energy consumption of each cycle of PC and CC and the cumulative energy consumption are the same. After the CC horizontal load reaches the peak, the bearing capacity rapidly decreases to reach the failure load, and PC continues to consume energy.(d and e) is the cumulative energy consumption curve of PC with different LRR under the same other parameters. The cumulative energy consumption curve coincides before the specimen PC-1 reaches the ultimate failure point. After the specimen PC-1 is damaged, the column horizontal bearing capacity improves, and the cumulative energy consumption increases due to the increase of LRR. When the ACR is small, the cumulative energy consumption is not affected before the PC reaches the yield point. After the specimen yields, the cumulative hysteretic energy consumption increases with the increase of LRR, but the final cumulative energy consumption remains the same. It can be seen that when the axial pressure at the top of the column is small, the LRR has little impact on the final cumulative energy consumption effect of PC. When the column top axial pressure is large, the LRR increases, and the final cumulative energy consumption increases.(f and g) is the cumulative energy consumption curve of PC with different ACR under the same other parameters. When the ACR of PC increases, the cumulative energy consumption is the same as before the column yield. After the column yields, the cumulative hysteretic energy consumption increases with the increase of the axial pressure at the top of the column. This is because the increase of the axial pressure at the top of the column increases the horizontal bearing capacity of the column, and the single hysteretic loop of each displacement loading cycle is fuller even while the final cumulative energy consumption decreases. This is because the increase of the ACR weakens the ductility of the column, the bearing capacity rapidly decreases after the specimen reaches the peak load, and the total energy consumption is reduced.(h and i) is the cumulative energy consumption curve of PC with different SVR under the same other parameters. It can be perceived that the cumulative energy consumption curves of PC-1 and PC-6 are consistent. Furthermore, the cumulative energy consumption curves of PC-4 and PC-2 are also consistent, and the stirrup volume ratio has little impact on the energy consumption capacity of PC.In the test process, with the gradual loading of the test, the slope of hysteretic curve will decrease, which means that the stiffness of specimens will decrease as well. According to code [], Ki can be expressed in the form of the following formula:(a–c) shows the stiffness degradation curves of PC and CC with the same other parameters. When the ACR is small, the stiffness degradation of PC is slightly slower than that of the CC specimen, but the stiffness of specimen decreases in the same way as when it is finally destroyed, which can be reduced to less than 10%. When the column axial pressure is large, the stiffness degradation rate of PC is the same as that of CC. Through comparison, the final stiffness of CC is reduced to about 15% and that of PCs reduced to less than 10%.(d and e) shows the stiffness degradation curve of PC with different LRR under the same other parameters. When the column axial pressure is small, the stiffness degradation of PC slows down with the increase of LRR, and it can eventually degrade to about 10%. When the column axial pressure is large, then the stiffness degradation of PC remains unchanged with the increase of longitudinal reinforcement configuration. However, it can be perceived from the comparison of PC-5 and PC-1 that the LRR increases, and the stiffness degradation of the specimen is more when the column ultimate failure occurs. The increase of LRR can slow down the stiffness degradation rate of PC, and the increase of ACR can weaken the influence of longitudinal reinforcement configuration on the stiffness degradation of PC.(f and g) shows the stiffness degradation curve of PC with different ACR under the same other parameters. With the increase of axial pressure on column top, the stiffness degradation slows down, and the degree of slowing down gradually decreases with increase of horizontal loading displacement. Until PC reaches the ultimate load, the stiffness degradation remains the same, and it gets finally degraded to less than 10%. When the SVR is large, the influence of axial pressure on the stiffness degradation of specimen is weakened, and the increase of SVR can weaken the influence of axial pressure on stiffness degradation of specimen as well.(h and i) shows the PC stiffness degradation curve of different SVR under the same other parameters. When the ACR is small, the stiffness degradation slows down with the increase of SVR, the degree of deceleration gradually decreases with increase of displacement, and the later stiffness degradation remains the same. When the ACR is large, the impact of SVR on the stiffness degradation of PC is weakened. At the early stage of loading, the stiffness degradation of PC slows down with the increase of SVR. When the column yields, SVR has little impact on the stiffness degradation of PC. With the increase of SVR, the stiffness degradation of PC slows down. Increasing the axial pressure on the column top can weaken the influence of SVR on the stiffness degradation of PC.The curve of load force F- longitudinal reinforcement strain ε (F-ε) is shown in . At the initial stage of loading, before specimen yield, the curve of F-ε is narrow and slender, and residual deformation is small when unloaded to zero. As the load increases, the hysteretic curve F-ε is gradually full. When unloaded to zero, the residual deformation increases and the two cycle deviation of the same stage loading increases. There are different phenomenon in the forward (+) and reverse (−) direction of longitudinal reinforcement strain, which may be because the reinforcement position is offset when binding the reinforcement cage and is not completely in the loading direction.Comparing CC-1 with PC-1, CC-2 with PC-2, CC-3 with PC-3, with the increase of load, the longitudinal reinforcement strain increases, and the reinforcement strain of CC specimens increases faster than that of PC specimens. This is mainly because the reinforcement of PC is connected by grouting, and the bonding stress between reinforcement and grouting material is less than that between cast-in-situ reinforcement and concrete, Therefore, under the same horizontal load, the reinforcement is easy to be pulled out of the grouting material and the reinforcement strain decreases. As the load continues to increase, the strain of longitudinal reinforcement at the bottom of PC is less than that of CC.Compared with PC-1 and PC-5, PC-2 and PC-3, with the increase of LRR, the longitudinal reinforcement strain decreases and the load on the reinforcement at yield increases. This is because under the same load, the large-diameter longitudinal reinforcement and small-diameter longitudinal reinforcement are more difficult to deform and should be changed less.Compared with PC-1 and PC-4, PC-6 and PC-2, the strain of longitudinal reinforcement decreases with increase of ACR. For example, strain of longitudinal reinforcement at the grouting sleeve of PC-6 and PC-2. This is because when the ACR increases, the vertical pressure on the column top increases. Under the action of horizontal load on column top, tensile stress on the reinforcement decreases and the strain of longitudinal reinforcement decreases.Comparing PC-1 and PC-6, PC-4 and PC-2, the SVR has little effect on the strain of PC longitudinal reinforcement. This is because the bottom of PC is mainly the connection area of the grouting sleeve, the reinforcement is inserted in the grouting sleeve and wrapped by the grouting material, and the stirrup has no direct impact on the bonding stress between the longitudinal reinforcement and the grouting material.To study the seismic performance of PC with GSC, seismic performance tests were conducted on nine concrete columns, including six PCs and three CCs. The failure model, hysteretic behavior, ductility, energy consumption, and stiffness degradation of PC with GSC were analyzed. The conclusions have been outlined as follows:The failure model of the specimens comprised bending failure. When the PC was damaged, the sealing layer at the bottom of the column was pulled off, there was a small amount of relative slip between the reinforcement and the grouting material, the ultimate displacement angle was greater than 2.0, the displacement ductility coefficient was greater than 3.0, and the ductility performance was good. The hysteretic curves of all specimens had a small amount of pinch effect, and the PC was more obvious. Increasing the LRR can better weaken the pinch effect of fabricated column.Under the same LRR, ACR, and SVR, the hysteretic curve of the PC was fuller than that of the CC. Due to the slip of reinforcement, the horizontal bearing capacity decreases by about 10%, the drift ratio limit increases by more than 0.74%, the ductility increases, and the stiffness degradation speed remains the same.With the increase of LRR, the bearing capacity of PC increases. When the ACR is small, the LRR will have a greater impact on the bearing capacity of PC. In addition, the ultimate displacement of the specimen remains unchanged, the ductility weakens, the energy dissipation performance is enhanced, and the stiffness degradation slows down.With the increase of ACR, the bearing capacity of PC increases, the ultimate displacement decreases, the ductility weakens, the energy dissipation performance weakens, and the stiffness degradation slows down.The seismic performance of circular PC with GCS is similar or even better than that of that of CC. However, because the bond strength between the sleeve and the reinforcement is still less than the strength of the reinforcement itself, the strength of PC members is slightly lower than that of CC, and in the design, the strength of circular PC with GCS can be considered according to the reduction of 10% of the strength of circular CC.Zhixing Zeng: Conceptualization, Writing – original draft. Wenmao Yu: Data curation, Writing – original draft. Yi Luo: Funding acquisition, Conceptualization. Chen Wu: Writing – review & editing. Xiang Liu: Investigation, Supervision, Visualization.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Transparent, elastic and crack-free polymethylsilsesquioxane aerogels prepared by controllable shrinkage of the hydrogels in the aging processPolymethylsilsesquioxane (PMSQ) aerogels have gained extensive attention owing to their improved mechanical properties, good optical transparency and low thermal conductivity. However, the aerogels with high densities prepared by the conventional sol-gel method are fragile and opaque due to the increase in the particles size and the decrease in the uniformity of pore structure. In this research, transparent PMSQ aerogels over a wide range of densities from 0.15 g/cm3 to 0.25 g/cm3 are prepared by controllable shrinkage of the hydrogels in the aging process. Resulted PMSQ aerogels have smaller particle and pore size than that prepared by the conventional method. Surprisingly, the light transmittance of the aerogels with the density of 0.25 g/cm3 at 550 nm wavelength is up to 70%. Meanwhile, the Young's modulus of the aerogel is up to 4.33 MPa. The strength and resilience compressed to 50% can be 3.57 MPa and 99%, respectively. The thermal conductivities of the aerogels prepared by the novel method increase from 18.7 mW m−1 K−1 to 32.9 mW m−1 K−1, with the density increasing from 0.15 g/cm3 to 0.25 g/cm3. These results would extend the range of practical applications for the high density PMSQ aerogels such as the transparent insulators.Silica aerogels are a family of nano-porous materials with a number of desirable properties, such as high porosity, high specific surface area, high optical transparency, low thermal conductivity and low dielectric constant []. For these extraordinary characteristics, silica aerogels have gained extensive attention in the past decades and are presently of interest in Cherenkov radiation detectors []. However, their practical applications have always been narrowed due to the weak mechanical properties of the inorganic network structure. To overcome such challenges for silica aerogels, previous studies have been focused on cross-linking the skeleton with organic polymers [], interpenetrating a fibrous 3D scaffold within the silica matrix [], and using organopolysiloxanes instead of traditional tetrathoxysilane precursor to improve the silica aerogels' mechanical properties []. All the attempts lead to more widespread practical applications ranging from aerospace materials to industry products [], are reported to enhance the connection between the particles in these gels. However, the thermal conductivities of the composite aerogels are in the range of 28–170 mW·m−1 K−1, which are higher than that of the pure silica aerogels. The reported nanocellulosic scaffolds reinforced silica aerogels have low density (0.020 g/cm3) and low thermal conductivity (12–20 mW·m−1 K−1) []; whereas, multi-scale assembly of the pore structures resulted in the loss of transparency of the composite aerogels. Utilizing organopolysiloxanes as the precursor, the highly flexible aerogels are hydrophobic and the deformation is reversible after the release of the strain. However, the aerogels were usually opaque and the thermal conductivity were found in the range of 23–95 mW·m−1 K−1 because of large particles and pores size []. In fact, it is a challenging task to improve mechanical properties of aerogels with retaining their characteristic properties such as high transparency and low conductivity.Kanamori reported the synthesis of transparent monolithic polymethylsilsesquioxane (PMSQ) aerogels for the first time based on methyltrimethoxysilane, by exploiting appropriate surfactants to prevent the macroscopic phase separation []. All the transparent aerogels possess conventional silica aerogel-like microstructures, and show a sufficiently low thermal conductivity of 15 mW·m−1 K−1 []. Due to the incorporated methyl groups, the organic−inorganic hybrid aerogels are hydrophobic and show high reversible elastic deformation against uniaxial compression. After that, the polyethylsilsesquioxane (PESQ), polyvinylsilsesquioxane (PVSQ) and ethylene-bridged PMSQ aerogels have been reported []. The compressive strength of the vulcanized PVSQ aerogels with density of 0.15 g/cm3 can reach 2.6 MPa at 50% strain. This is superior to the value of 0.6 MPa for the PMSQ aerogels with the density of 0.14 g/cm3. In fact, the mechanical properties of the PMSQ aerogels can be significantly improved with the increase in density []. However, the light transmittance of the aerogels with a density higher than 0.20 g/cm3 was dramatically decreased. Because increasing the density in the conventional method is often achieved by increasing the precursor content, which requires a corresponding increase in the amount of surfactant. This will increase the viscosity of the sol system and the microstructure becomes coarser due to the inhomogeneous networks formation governed by a slow diffusion []. To improve the transparency of the aerogels, Tabata invented a novel pinhole drying method to make highly transparent aerogels over a wide range of densities []. Li deeply studied the effect of pinhole drying on the microstructure and transmission of aerogel. Results show that the clusters of the gel were becoming smaller during the shrinkage process and the pinhole dried aerogels have relatively transparent [In this research, PMSQ aerogels with different microstructure were controllably prepared via the simple, novel and low-cost shrinkage method of the hydrogel in the aging process. Compared with the conventional method of incremental addition of MTMS, the PMSQ aerogels resulted from the novel method have smaller particle size and pore diameter with the increase of density, which endow the PMSQ aerogels at 0.25 g/cm3 with high transparency of 70% at 550 nm wavelength. Furthermore, the aerogels after 50% compression can spring back to their original size. Novel shrinkage aging process provide a new version in synthesis of high performance PMSQ aerogel monoliths.Acetic acid, ethanol and ammonium hydroxide (NH3·H2O) were purchased from Beijing Chemical Works (China). Surfactant n-hexadecyltrimethylammonium chloride (CTAC) was supplied by Sinopharm Chemical Reagent Co. Ltd. (China). Methyltrimethoxysilane (MTMS) was obtained from Adamas Reagent Co. Ltd. (China). All the chemical reagents were used as received without further purification.PMSQ hydrogels were prepared through hydrolysis and polycondensation of MTMS in the aqueous solution according to the literature []. The molar ratio of the starting materials was MTMS: water: acetic acid: CTAC: NH3·H2O = 1: 24: 0.0014: 0.0089: 0.0038. The obtained sols were transferred into a beaker and would gel in about 2 h. The hydrogel was subjected to a shrinkage prior to aging in ethanol, which was driven by the evaporation of the solvent at 25 °C under ambient pressure without any protection as shown in . The hydrogels with different degrees of shrinkage were aged for 3 d in ethanol, followed by washing with ethanol three times (8 h at 60 °C each time) to remove the residual surfactant and other chemicals. The washed samples were dried by ethanol supercritical method at 255 °C and 8 MPa. The PMSQ aerogels with a series of densities from 0.15 g/cm3 to 0.25 g/cm3 can be obtained, which were labelled as CS-0.17, CS-0.19, CS-0.21, CS-0.23, and CS-0.25, respectively. By contrast, the aerogels with density of 0.15, 0.17, 0.19, and 0.21 g/cm3 were prepared by the conventional method of regulating the content of the precursor MTMS. These samples were marked as C-0.15, C-0.17, C-0.19, and C-0.21, respectively. The relationship between the densities and the shrinkage time or the content of MTMS are shown in The bulk density ρb of the PMSQ aerogels was obtained from the weight/volume ratio of specimens. Porosity was determined as ∅=1−ρb/ρs, where ρs represents the skeletal density that was fixed to be 1.40 g/cm3 according to literature []. The microstructure of the aerogels was studied using field-emission scanning electron microscopy (FE-SEM, Hitachi, S-4800). Specific surface area, pore volume, and pore size distribution were obtained from N2 adsorption-desorption (Autosorb-iQ, USA). The specific surface areas of the aerogels were determined by the BET method, based on the amount of N2 adsorbed at pressures 0.05 < P/P0 < 0.3. As we known, the analysis using N2 adsorption-desorption method only partially reveals the pore structure with the pore sizes within 100 nm []. The nanopore volume (VN2) is chosen the single point desorption volume of pores size smaller than 100 nm at P/P0 = 0.98. Total pore volume (Vt) was calculated according to the equation. Vt=1/ρb−1/ρs. The pore size distributions of the samples were obtained from desorption branch of the isotherm by using the BJH method. For light transmittance measurements, a UV-vis spectrometer UV-3600 (Shimadzu Corp. Japan) equipped with an integrating sphere was employed. The obtained transmittance data in the wavelength range of 400 nm–800 nm were normalized into those corresponding to the thickness of 10 mm using the Lambert-Beer equation. Mechanical properties of aerogels were investigated by a Universal Testing System (CTM5105, China). For uniaxial compression tests, the cube-shaped sample (typical length × width × height was 10 × 10 × 8 mm3) was placed between the testing plates and was compressed at a speed of 1 mm/min to 50% strain. Three replicates were done for each sample. The resilience of the aerogels is defined as the ratio of the final height dimension after compression to the original scale. Compressive modulus was calculated from the linear region of the stress-strain curves, which typically occurred from 1% to 5% strain. The thermal conductivities of the aerogel under room temperature were measured by transient hot wire method (XIATECH TC3000, China). The data was collected for five times with 5 min interval of each measurement.The PMSQ aerogels with a series of densities can be prepared by the controllable shrinkage method of the hydrogels and the conventional method. shows the shrinkage process of the hydrogel. In the new method, the crack-free aerogel monoliths with different densities from 0.15 g/cm3 to 0.25 g/cm3 can be obtained through the PMSQ hydrogels with low precursor concentration. As shrinkage proceeds, the capillary tension will cause the network to contract into the liquid. The density of the aerogels gradually increases and the network becomes stiff due to the formation of the new bonds []. In contrast, the PMSQ aerogels obtained from the conventional method are fragile when the density is higher than 0.21 g/cm3. Because PMSQ aerogels with higher density require more precursor and surfactant. Then the phase separation occurs, which is caused by incomplete dissolution of the excess MTMS. The PMSQ aerogels prepared by the two methods have significant differences in the particles and pores structure, which results in differences in optical transparency, mechanical and thermal insulation properties of the aerogels. shows the SEM images of the aerogels with different densities prepared by the controllable shrinkage method and the conventional method. It is obviously to find that all the aerogels prepared by the controllable shrinkage method have the 3D continuous network microstructure. With the density increasing from 0.15 g/cm3 to 0.25 g/cm3, the pore diameter and particle size gradually decrease. The aerogels' pore structure becomes more uniform. The macropores in aerogels with density of 0.25 g/cm3 are significantly reduced as shown in d. However, the uniformity of the pore structure in the aerogels obtained from the conventional method decreases with the density increasing from 0.15 g/cm3 to 0.21 g/cm3. Especially for C-0.21 in f, there are a large amount of particulate agglomerates and large pores in the aerogel. This is because the increase in precursor content in the conventional method requires high concentration of CTAC, which will increase the viscosity of the sol. The microstructure will become coarser due to the inhomogeneous networks formation governed by a slow diffusion []. For the controllable shrinkage method, the driving force during the hydrogel shrinkage will cause the deformation of the flexible network skeleton and change the complex hierarchy pore structures. It is well known that the shrinkage is driven by the capillary pressure, which is inversely proportional to the pore radius. During the solvent evaporation process, the smaller pores can hold the liquid and the larger pores are reconstructed by folding the flexible skeleton. As a result, the homogeneity of the pore structure in the aerogels is improved significantly. In this new method, the particle size gradually decreases with the shrinkage treatment. We attribute the result to the flow of liquid on the surface of the particles during the shrinkage treatment, which may promote the dissolution of the silica particles. In short, the new method can effectively prevent the formation of agglomeration and decrease the particle size in the preparation of the high-density aerogels.The N2 adsorption-desorption isotherms of PMSQ aerogels are depicted in a and b. All the isotherms show the type IV nature according to the IUPAC classification, demonstrating that the aerogels are typical mesoporous materials. The sharp increase in the high relative pressure region indicates liquid nitrogen condensation in the macropores. It is obviously to find that the hysteresis loops position of all the aerogels prepared by the new method are located at P/P0 > 0.8. While the hysteresis loop position of C-0.21 in b shift to P/P0 > 0.9, indicating that the pores in the C-0.21 aerogels are large. The pore size distributions of the aerogels obtained from the controllable shrinkage method in c are gradually narrowed with the density increase. The pore diameters are all concentrated at 13 nm. However, the pore size distributions of the aerogel prepared by the conventional method in d become wider with the density increasing from 0.15 g/cm3 to 0.21 g/cm3, and the pore diameters gradually increase from 13 nm to 26 nm. The results indicate that the shrinkage treatment for the hydrogels can effectively achieve the uniformity of the pore structure in the PMSQ aerogels at a wide density range.e shows that the nanopore volumes (<100 nm) in the PMSQ aerogels prepared by the controllable shrinkage method are about 3.00 cm3/g changing very slightly upon the density increasing. While the nanopore volume in the aerogels obtained from the conventional method decreases gradually from 3.00 cm3/g to 2.55 cm3/g with the increase of the density from 0.15 g/cm3 to 0.21 g/cm3. Correspondingly, the total pore volumes listed in decrease from 5.95 cm3/g to 3.29 cm3/g with density increasing from 0.15 g/cm3 to 0.25 g/cm3. The results suggest that the shrinkage treatment reduces the content of large pore (>100 nm) in the PMSQ aerogels. The specific surface area of the aerogels prepared by the controllable shrinkage method decreased firstly and then increased with the density increase as shown in f. The maximum value of 576.8 m2/g appears at sample CS-0.25. The specific surface area of the aerogels prepared by the conventional method decreases gradually from 558.3 m2/g to 431.9 m2/g with density increase. This is because the silica particles in the aerogels prepared by the new method may become smaller as the shrinkage proceeds []. On the other hand, high concentration of precursor in the conventional method result in the formation of large particles and aggregates.The photograph of crack-free aerogel monoliths is shown in a. It is clear that the aerogels prepared by the controllable shrinkage method still have good transparency when the density is as high as 0.25 g/cm3. Whereas the aerogels prepared by the conventional method have become opaque at the density of 0.21 g/cm3. b shows that the transparency of the PMSQ aerogels prepared by the new method improved with the increase of density and the light transmittance of the sample CS-0.25 at 550 nm wavelength is up to 70%. The peak pore size of CS-aerogels in c decreases slightly with the increase of the density, while the peak pore size of normal aerogels increases significantly at the similar situation. In addition, the shrinkage treatment reduces the amount of large pores in the CS-aerogels []. The nanopore volume in sample CS-0.25 is 2.99 cm3/g as noted in . The calculated volume ratio of large pore (>100 nm) is less than 10%. Because the scattering of light is mainly affected by the particle and pore sizes. Smaller pores and particles will decrease the scattering, leading the transmittance increase as predicted by the Rayleigh scattering mode []. While for the aerogels of C-0.21, the large aggregates and pores make the dominant light scattering mode transform from Rayleigh scattering to Mie scattering []. The controllable shrinkage method can effectively keep the homogeneity of the microstructure and realize the high transparency of PMSQ aerogels under high density.Mechanical properties of the aerogels are evaluated by uniaxial compression tests and shown in . It is noteworthy that the compressive strength of the aerogels has been significantly improved with density increase. The strength of the sample CS-0.25 at 50% strain is up to 3.57 MPa, which is comparable to the value for the PMSQ aerogels with the density of 0.27 g/cm3 prepared with F127 as the surfactant []. However, the sample C-0.21 is fragile so that it is difficult to compress to 50% strain in the compression test. It is interesting to find that, with the same density, the strength of the samples obtained from controllable shrinkage method is higher than that of the conventional method as shown in a. Similarly, the aerogels prepared by the new method are superior to that obtained from the conventional method in terms of Young's modulus and resilience. Young's modulus of the aerogels prepared by the new method increases from 0.68 MPa to 4.33 MPa with the density increasing from 0.15 g/cm3 to 0.25 g cm−3 as shown in b. It is well known that there is a power-low relationship between the Young's modulus (E) and density (ρ) of the aerogels according to the following equation [Where E is Young's modulus; ρ is the density of the aerogel; m is the power exponent, whose value is 2.5–4.0; and the index 0 denotes an arbitrary reference. c shows that the value of m was calculated to be 3.66 for the aerogels prepared by the novel method, which is agreement with the values reported in the literature []. Furthermore, these aerogels endure up to 50% linear compression and then spring back to more than 90% of their original size when the density is greater than 0.21 g/cm3 as shown in d. More importantly, the resilience of the sample CS-0.25 can reach 99%. The improvement in mechanical properties is attributed to the smaller particle size and the significant decrease in large pores content in the new method. The strength and modulus depend on the load-bearing faction of the cross-sectional area. The area of the neck joining a pair of particles is greater for smaller particles []. As a result, the PMSQ aerogel of CS-0.25 develop greater coalescence and strength.The microstructure and density of the nanoporous networks ultimately determine the thermal conductivities of these PMSQ aerogels. plots the thermal conductivity values of the PMSQ aerogels as a function of density and shows a curve characteristic of aerogels materials []. The results reveal that a minimum value of 18.7 mW·m−1 K−1 was obtained for aerogels with density of 0.16 g/cm3. The PMSQ aerogels are comparable to the commercially available insulation systems based on aerogel materials (19 mW·m−1 K−1) []. The thermal conductivities of the aerogels prepared by the controllable shrinkage method was observed to increase from 18.7 mW·m−1 K−1 to 32.9 mW·m−1 K−1, with density increasing from 0.16 g/cm3 to 0.25 g/cm3. For the aerogels with the same density, the samples prepared by the new method have a slightly lower thermal conductivity than that prepared by the conventional method. The high thermal insulating ability of the aerogels is mainly derived from the limited contributions from the conductions of the solid and gas phases. The radiative thermal conductivity at ambient temperature contribute little to the total thermal conductivity of the aerogel materials []. The solid thermal conductivity follows a scaling law as a function of the density with the scaling exponents in the range of 1.2–2 []. Therefore, the high density contributes greatly to the increase of the thermal conductivity. On the other hand, the gaseous thermal conductivity at given temperature is positively related to the pore size. Small pores size lead to low thermal conductivity. A comparison of the thermal conductivities between the prepared PMSQ aerogels and a number of representative aerogels is detailed in . The parameters concluding the density, thermal conductivity and the measurement method was listed in the table. The results suggest that the PMSQ aerogels prepared by the controllable shrinkage method have excellent thermal insulation properties even under high density [In summary, the transparent, high-strength and elastic PMSQ aerogels have been synthesized through the controllable shrinkage of the hydrogels. The obtained aerogels have small particles and pores, good transparency and low thermal conductivity. The light transmittance of the PMSQ aerogels with the density of 0.25 g/cm3 at 550 nm wavelength is up to 70%. The Young's modulus range from 0.68 MPa to 4.33 MPa with density increasing from 0.15 g/cm3 to 0.25 g/cm3; meanwhile, the strength and resilience when the aerogels are compressed to 50% increase from 0.76 MPa to 65% to 3.57 MPa and 99%, respectively. This facile method allows the flexible network skeleton to deform under the driving force during the shrinkage process. The high-density aerogels have the stiff skeleton and uniform pore structure without the occurrence of phase separation. Up till now, the PMSQ aerogels prepared by the new method are superior to that obtained from the conventional method in terms of transparency and mechanical properties. These results extend the range of practical applications for the PMSQ aerogels.The following are the supplementary data related to this article:Supplementary data related to this article can be found at © 2020 Elsevier Ltd. All rights reserved.Crack initiation and propagation in small-scale yielding using a nonlocal GTN modelThis study aims at investigating a non-local Gurson-Tvergaard-Needleman (GTN) ductile damage model at finite strains within the framework of small-scale yielding. This model solves the problems of spurious strain localization and volumetric locking. The model is applied to simulate large crack propagation under small-scale yielding and plane-strain mode I conditions. A new method to extract crack length from the porosity field is introduced. Besides, purely numerical parameters are introduced to help convergence. An adequate range is exhibited for each of them so that their impact on the J−Δa crack growth resistance curves remains negligible. A parametric study is performed for several values of the material properties in order to estimate their influence on the crack growth resistance. It is found that the relation between the non-local intrinsic length implicitly introduced by the hardening gradient terms and the width of the damage/strain localization band is quasi-linear; crack tip blunting, crack initiation and large crack propagation can be well captured with the modified GTN model; the numerical formulation is robust; wide ranges for material plasticity and damage parameters can be used in a reliable way so that toughness at crack initiation as well as ductile tearing behavior can be thoroughly studied.When aiming at predicting potential ductile fracture of metallic engineering structures, a streamlined approach, the global approach, is provided by Nonlinear Fracture Mechanics: the J path integral () is compared to a resistance curve in order to assess whether a crack propagates and to what extent (see e.g. SINTAP assessment procedure ()). However, it is restricted to pre-existing cracks and proportional loads. On the contrary, the local approach relies on damage plasticity constitutive models which describe the three main steps of ductile fracture: micro void nucleation, growth and coalescence. It is more complex but it covers a much wider range of applications: crack initiation and propagation along unknown crack path under any type of loading.The development of porous plasticity models traces back to the seminal work of () in which the growth of a single void was studied. The Gurson model () allowed accounting for a finite porosity and developing the first micro-mechanically based constitutive equations for porous plasticity. This first development was followed by the work of () who developed the so-called GTN model which is a pragmatic modification of the Gurson model allowing accounting for void nucleation, growth and coalescence as well as work hardening. The model was in particular successful in capturing “cup and cone” fracture. Almost at the same time, the more phenomenological but thermodynamically consistent Rousselier model was also proposed (). These works paved the way for the application of porous plasticity models to simulate crack initiation and growth in structures. They also led to the development of numerous porous plasticity models which, over the years, have allowed accounting for an increasing number of phenomena affecting ductile damage. Most of these models can be seen as extensions of the Gurson and GTN models. The models can first phenomenologically be extended to the case of rate-dependent materials () but a micro-mechanical approach can also be adopted (). The initial models were developed assuming a matrix following a von-Mises flow rule. It was then extended to account for a Hill-type matrix (), a matrix exhibiting tension-compression asymmetry (). Many extensions address the fact that voids cannot be considered as spheres and are in fact closer to ellipsoids. The first extensions () considered axisymmetric voids (oblate or prolate) but the model was later further extended to describe arbitrary ellipsoids including the description of the rotation of their main axes (). The combined effects of plastic anisotropy and void shape were studied in (). Coalescence is also largely investigated based on the initial approach proposed in () which described void coalescence as internal necking. The modeling approach was then improved by combining it with the Gurson model (). The resulting model can be formulated as a multi-surface model which can be used to perform finite element simulations (). This approach was also used in the case of anisotropic matrices (). Further developments include the description of coalescence under combined tension and shear (). More recent developments concern single crystals containing voids for which a yield surface was first proposed by (). In that case, the activation of each slip system depends on a GTN-like yield surface. An approximate treatment of the model was proposed in () so that only one surface can be considered. To account for the size effect due to the size of voids, the matrix can be assumed to be a strain gradient plasticity material () or one can also assume interfacial residual stresses at the interface between the matrix and the cavity (). Internal pressure inside voids can also be taken into account (). Models for void nucleation have been less developed even though attempts to describe these damage mechanisms have been made (see e.g. ()). Finally the effect of the Lode parameter can be described by adding a nucleation-like term in the model as in (). A detailed review of the applications, the advantages and the shortcomings of such continuum damage models can be found in (In the last years, these models have been successfully applied to model crack extension, see for instance (). However, due to the complexity of some of the extensions, most applications involving large crack propagation are restricted to the GTN model or its simplest extensions. In this work, for the sake of simplicity, we focus our attention on the isotropic GTN model.Damage at the continuum level results in strain-softening, i.e. the drop of the stress carrying capability with increasing damage. At the structure scale where constitutive behavior is combined with mechanical equilibrium, strain-softening is responsible for the spatial localization of the strain field, the plastic strain field and the damage field, in agreement with experimental evidences (). The scale of the macroscopic field variations becomes comparable to the microstructure scale (micro-void spacing, for instance). This is in contradiction with the length scale separation assumption which underlies the derivation of local constitutive relations, i.e. models that only depend on the point-wise state variables (strain, damage, plasticity, hardening and so on). Besides, such local models would lead to ill-posed boundary value problems resulting from loss of ellipticity of the rate operator (), spurious mesh-sensitivity and unrealistic physical predictions (). Therefore non-local constitutive relations are required as a consequence of overlapping micro and macro length scales. They account for a spatial coupling of neighboring material points: the material state is no more characterized by point-wise state variables and an interaction distance (also named internal length) appears. Different variants of non-local constitutive relations have been proposed in the literature, according to the choice of the effective non-local variables and the non-local operators, see () for specific choices. In particular, several non-local versions of the GTN model can be found in (). It is believed that the predictive capacity of the most advanced extensions (described above) of the GTN model can only be exploited in a regularized framework so as to be sure that numerical results are the outcome of the models and not due to uncontrolled localization. Here the gradient plasticity formulation () where the gradient of the hardening variable is introduced into the free Helmholtz energy is retained for its promising results. The formulation is expressed in the context of logarithmic finite strains () which tackles two issues: how to preserve the usual structure of return mapping algorithms at the integration point level and how to avoid volumetric locking caused by plastic quasi-incompressibility prior to significant damage. A mixed finite element is derived, the degrees of freedom of which are the displacement, the hardening variable, a non-local contribution to its driving force, the volume change and the pressure.The main purpose of the present article is to investigate how this non-local GTN model is able to construct a J−Δa resistance curve in the context of plane strain and mode I small-scale yielding, in order to establish a link between the streamlined J approach and the GTN-based approach. In particular, the effects of the GTN material parameters and the internal length of the model on the J−Δa resistance curve are thoroughly studied, in the spirit of the works (). The small-scale yielding conditions are fulfilled through the boundary-layer model developed by (), where the far-field is only characterized by the elastic stress intensity factor K related to J by Irwin's formula. The small-scale yielding framework hence reflects the vicinity of a crack tip without including any geometrical or constraint effect. This is the best adapted configuration to apply the global approach to ductile fracture. A second objective of the study consists in evaluating the robustness and the reliability of the non-local GTN formulation. A numerical enhancement related to the treatment of volumetric locking has been necessary due to the large amount of strain near the crack tip. Ranges of values for the numerical parameters of the model (including the radius of the notch which is used in lieu of a sharp crack tip) have been established so as to reach a trade-off between robustness and reliability of the predictions, enabling the simulation of relatively large crack propagations. These are necessary preliminary insights for the application of the model.The paper is organized as follows. A short summary of the non-local GTN model initially proposed in ( including the modification introduced to better stabilize volumetric locking. The numerical methodology applied to model small-scale yielding conditions and to extract pertinent data from the resulting mechanical fields is described in Section . The influence of the numerical parameters of the model on crack growth are first studied in Section in order to define an adequate range of values for each of them. Finally, a study of the influence of the physical parameters of the model is conducted in Section ; in particular, an empirical relationship between the internal length and the width of the localization band is exhibited.In this section, a non-local GTN model, which is originally proposed in () and improved in this paper, is summarized.), the GTN model is cast into the logarithmic finite strain formulation proposed by (). In this formulation, the logarithmic strain tensor E is defined as:where F is the deformation gradient tensor and C=FT.F is the Cauchy-Green strain tensor. Following (), the logarithmic strain tensor is divided into two parts:where Ee and Ep are respectively the elastic and plastic parts of the strain tensor E.The stress tensor T (work-conjugated with respect to E) is obtained by writing the internal work density:where S is the second Piola-Kirchhoff stress tensor.Under the assumption of pure isotropic hardening, hardening is characterized by a unique scalar variable which is referred to as κ in the following. The material state is then described by the current strain E, the hardening variable κ and the plastic strain Ep.In order to take into account the high gradients of the macroscopic fields which result from strain localization, a non-local constitutive relation based on the introduction of the gradient of an internal variable into the global Helmholtz free energy density is proposed in the work of (). In his work, the gradient of the hardening variable κ is introduced into the global Helmholtz free energy density F since this variable may reflect localization of both plasticity and plasticity-induced damage:where Fℓ is the global Helmholtz free energy density which would correspond to the local formulation of the constitutive law, Ω0 is the volume in the initial configuration and c is a parameter which weights the non-local interactions among neighboring material points. A non-local length scale can be introduced as:where σ0 stands for the initial yield stress., the free energy Fℓ is divided into an elastic part and a plastic (hardening) part:Fℓ(E,Ep,κ)=∫Ω0(φe(Ee)+φp(κ))dΩ0=∫Ω0(12Ee:E:Ee+∫0κ(σ‾(s)−σ0)ds)dΩ0where φe and φp are the elastic and plastic parts of the local Helmholtz free energy density, E is the elastic stiffness matrix, u‾ is the displacement, Ee is the elastic part of the strain deduced from E and Ep, σ‾ is the flow stress of the matrix material which is a function of the hardening variable κ. In this paper, the following form of σ‾(κ) is considered:where κ0 is a material constant, n is the hardening exponent with n>0.Note that on the one hand, the variation of F with respect to u‾ leads to as usual the equilibrium equation of the system:where W is the external work. On the other hand, with the definition of the global dissipation D=∫Ω0T:E˙−F˙, one can see that the variation of F with respect to the plastic strain tensor Ep leads to the driving force associated to Ep which is the stress tensor T and the variation of F with respect to κ leads to the driving force associated to κ which is referred to as Anl:{−∂φe∂Ep=E:(E−Ep)=TAnl≡−∂φp∂κ(κ)+div(c∇κ)=σ0−σ‾(κ)+div(c∇κ)In particular, it is assumed that no dissipation stems from the boundary, which leads to an additional boundary condition, expressed on the field κ:where n‾ is the normal vector to the surface ∂Ω0.Note that for the GTN damage model, the driving forces govern the evolution of the internal variables through local normality rules, as will be shown in Section On a numerical ground, the former non-local formulation leads to spatial gradients of state variables in the constitutive laws. Moreover, in quasi-incompressible situations, volumetric locking may appear. The numerical approach should deal with both difficulties. Following (), we introduce a relaxed formulation which is equivalent to the initial problem before spatial discretization by finite elements.More precisely, the decomposition-coordination technique proposed by () is used to treat the non-locality aspect. The hardening variable κ is duplicated: a first instance (named a) is used at the (global) scale of the structure while a second instance (still named κ) is used at the (local) constitutive law level. As a and κ reflect the same field, they should be equal. A Lagrange multiplier l is introduced to weakly ensure this equality, the corresponding augmented Lagrangian Lnℓ is:Lnℓ(E,Ep,κ,a,l)=Fℓ(E,Ep,κ)+∫Ω0(12c∇a.∇a+l(a−κ)+12rnl(a−κ)2)dΩ0The augmentation term 12rnl(a−κ)2 with rnl a penalty parameter, is introduced to provide an additional coercivity and to enforce the equality between a and κ.Regarding volumetric locking, the ideas of the Hu-Washizu mixed variational principle () are put in practice. The volumetric strain tr(E)=ln(J) with J=det(F) is duplicated: a first instance (still named ln(J(u‾)) is used at the global level while a second instance name θ is used at the constitutive law level. Since ln(J) and θ reflect the same filed, they should be equal. A Lagrange multiplier P is introduced to weakly enforce the equality, the corresponding augmented Lagrangian L is:L(E,Ep,κ,a,l,P,θ)=Lnℓ(E‾,Ep,κ,a,l)+∫Ω0(P(ln(J)−θ)+12rinco(ln(J)−θ)2)dΩ0where E‾ is the relaxed strain tensor defined as:), a new augmentation term rinco(ln(J)−θ)2/2 has been introduced, with rinco a new penalty parameter. Indeed, the Lagrange multiplier P only enforces the equality between lnJ and θ in a weak way: the difference θ⊥≡lnJ−θ is not equal to zero everywhere. The freedom brought by θ⊥ avoids the spurious stress oscillations due to quasi-incompressibility. Unfortunately, it was observed in () that this freedom may also result in ill-posedness of the problem in the context of finite strains and hence can lead to spurious plastic localization. The new quadratic term is designed to bring an additional coercivity so as to retrieve a well-posed saddle-point problem. A trade-off between stress oscillations control (quasi-incompressibility) and plastic localization (ill-posedness) should be reached and hence requires finding an optimal value for rinco. A range of satisfactory values is exhibited in section As the Lagrangian L corresponds to a relaxed numerical version of the physical Helmholtz free energy F, its variation should be equal to that of F for any variation of its arguments:Concerning the variation with respect to u‾, it results in the equilibrium variational equation:Here T‾ is the stress tensor used in the constitutive law:The variations with respect to (a,l,P,θ) should be equal to zero as F is not a function of these four arguments:{δaL=∫Ω0(c∇a∇δa+(l+rnla−rnlκ)δa)dΩ0=0δlL=∫Ω0((a−κ)δl)dΩ0=0δPL=∫Ω0((tr(E)−θ)δP)dΩ0=0δθL=∫Ω0((13tr(T‾)−P−rinco(tr(E)−θ))δθ)dΩ0=0It can be observed that the initial and the relaxed formulations are equivalent at the continuum level since the variations of L with respect to (l,P) result in the following relations:a=κ,θ=tr(E).Finally, the variations with respect to Ep and to κ lead to the expression of the driving forces:{−∂φe∂Ep=E:(E‾−Ep)=T‾A≡−∂φp∂κ(κ)+l+r(a−κ)=σ0−σ‾(κ)+l+r(a−κ)We can notice that the relaxed stress T‾ is equal to the driving force associated to the plastic strain. Moreover, the relaxed driving force A associated to κ involves the term l+r(a−κ) instead of the divergence term div(c∇κ) that appeared in the definition of the (unrelaxed) driving force Anl (See Equation ). Note that T‾ and A will be used in the evolution equations of the internal variables (plastic yielding and flow rules).The finite element associated with the five variables (u‾,a,l,P,θ) is a P2P1P1P1P1-type element where P1 stands for linear interpolation and P2 stands for quadratic interpolation. Example of non-local locking-free elements with reduced integration (four integration points in each quadrilateral element and three integration points in each triangle element) is shown in . Details of the implementation are given in (As the proposed model uses the accumulated plastic strain as the nonlocal variable, it shares some similarities with strain-gradient plasticity models (). Strain gradient models make use of the entire second gradient third order tensor which is bound to lead to very large computational costs. In addition, they are often restricted to incompressible plastic deformation. This issue can be addressed using micro-dilatational theories () using an implicit gradient formulation. The model developed in the present work is actually closer to micromorphic models based on the use of the accumulated plastic strain. In that case, the Helmholtz free energy is expressed as:F(E,Ep,κ)=Fℓ(E,Ep,κ)+∫Ω0(12Hx(κx−κ)2+12c∇κx.∇κx)dΩ0where κx is the micromorphic counterpart of κ,Hx is a model parameter which couples the two quantities. In finite element implementation of the model, κx is introduced as a new nodal unknown so that its gradient can be evaluated. For sufficiently high values of Hx, one has κx≈κ so that ∇κx=∇κ. The micromorphic model can then be seen as an implementation of the GEE model based on the use of a penalty method as stated in (). The micromorphic model is believed to be numerically less effective than the proposed method which uses Lagrange multipliers and augmentation terms.Strain gradient models can be used to represent plasticity related size effects (see for instance ()). In that case, the internal length is about 1–10 μm. For ductile fracture, the internal length should correspond to the inter-void ligament () which is about 100 μm in steels. Therefore the model parameters (when applied to a finite size problem) should be carefully chosen to represent experiments. As regularization is obtained by inducing additional hardening, the model will lead to global over hardening in the case of very small (i.e., with a size of the same order of magnitude as lb) specimens. This is however not the case for applications to laboratory size specimens or structures.The micromechanical-based model proposed by () for the description of ductile damage and fracture takes into account a strong coupling between damage and plastic strain. An equivalent expression of GTN yield function was proposed by () by introducing a scalar stress measure σ∗ which is a positive homogeneous function of degree 1 of the stress tensor σ. Then casted the GTN model into the logarithmic finite strain formulation proposed by (Within this finite strain framework, we note T∗ the scalar stress measure, which is implicitly defined by:G(TH,Teq,T*)≡(TeqT*)2+2q1fcosh(32q2THT*)−1−(q1f*)2=0, TH and Teq are the hydrostatic stress and the von Mises stress respectively. The parameters q1 and q2 are two material constants and f∗ is the effective porosity which is a function of the porosity f so as to account for the rapid drop in the stress carrying capacity at void coalescence:where fc and fF represent respectively the porosity at the onset of coalescence and the porosity at fracture.The evolution of f is given by the sum of the rate of the void growth fg and the rate of the void nucleation fn:where E˙p represents the rate of the plastic strain tensor and tr(E˙p) represents the trace of the rate of the plastic strain tensor which depicts the rate of volume change.For strain controlled void nucleation mechanism, the rate of void nucleation is defined on the rate of the hardening variable κ by:In the present study, we only focus on void growth and void coalescence, so we take Bn=0, i.e.,f˙n=0 in Equation . An exception will be made later, but only for some numerical purposes.As long as there is no rotation of the eigenbasis of the stress tensor, the scalar stress measure T∗ and σ∗ are linked by T∗=Jσ∗. Therefore, we write the yield function F as:where the expression of the driving force A is provided in Equation within the context of the relaxed numerical formulation.The Kuhn-Tucker consistency conditions are the following where the driving forces T‾ and A are defined in Equation in agreement with the relaxed formulation:The rate of the plastic strain tensor Ep and the rate of the hardening variable κ are given by application of a normality flow rule:Crack initiation and crack propagation under small-scale yielding and Mode I plane-strain conditions using the non-local locking-free GTN model (see Section . The main objectives of this numerical study are:To prove the reliability of the model to predict crack initiation and to achieve large amounts of crack extensionto establish a simple formula allowing to link the width of the localization band to the non-local length scaleto introduce a reliable way to compute crack lengthto investigate the influence of some parameters of the model on the crack resistance curveIn this section, the framework of the small scale yielding problem and the details of pre-/post-processing are introduced.The small-scale yielding model consists of a circular region of radius Rext→∞ containing a crack and subjected to increasing displacement of the elastic mode I singular field applied on the far outer boundary, as shown in Equation . The conditions of SSY model is fulfilled using the boundary-layer model developed by ({uxr,θ=K1+νEr2πcosθ23−4ν−cosθuyr,θ=K1+νEr2πsinθ23−4ν−cosθwhere ux and uy are the imposed displacement along x-axis and y-axis, (r,θ) is the polar coordinates, K is the stress intensity factor, ν is Poisson ratio, E is Young modulus. A schematic boundary-layer geometry is shown in This model is generally used to investigate the role of micromechanical parameters in relation to ductile crack initiation and growth. Under small-scale yielding and mode I plane-strain conditions, the path-integral J () is related to the stress intensity factor K, as established in (For dimensional analysis, the loading parameter J can be normalized as J/(σ0h) with h a length scale to be defined. We start by giving a short summary of different length scales which are involved in the current problem:The external radius Rext of the boundary-layer model: this quantity is considered as infinity.The size of the plastic zone Rp≈13π(Kσ0)2=13πJE(1−ν2)σ02 (). Small-scale yielding condition requires Rp≪Rext. In practice, it is suggested Rp≤0.05Rext. Note that Rp depends on the loading level.The size of the process zone Rpz=J/σ0. A finite deformation zone exists ahead of the crack tip within approximately 2Rpz. Outside this zone, the HRR fields () reasonably characterize the near-tip stress and deformation fields ahead of the crack. Note that Rpz also depends on the loading level.The non-local length scale lnl=c/σ0, as introduced in Section For the normalization of J, it is necessary to use a length scale which remains constant during the simulation. For example, in () in which a purely local model is used, the mesh size D is considered for the normalization. In this paper, the non-local length scale lnl is used. Note that mesh size in the process-zone should be sufficiently small compared to lnl so that the gradient in the localization band can be accurately discretized. In the case of ductile failure controlled by void growth and coalescence by internal necking, it is believed that the resulting band is about the mean distance between voids.A dimensional analysis shows that the crack-resistance curve J(Δa) can be expressed as follows:J(Δa)=σ0lnlFunction(Δalnl,Eσ0,v,κ0,n,f0,fc,fF,q1,q2)where Δa is the crack length. In Equation , the parameters (E/σ0,ν,κ0,n) characterize the elastic-plastic properties of the matrix material with (κ0,n) the hardening parameters (see Equation ) and the parameters (f0,fc,fF,q1,q2) characterize the GTN damage model.The boundary model is spatially discretized. Only half of geometry needs to be modeled due to symmetry of the geometry and the loading condition (except in the case of crack bifurcation). A typical mesh is depicted in . In this mesh, 12922 elements are used to discretize the circular domain with 11810 quadrilateral elements refined in the process zone of width B (as shown in (b)). In particular, a small initial notch radius Rn is added in the process zone to improve the computational convergence and to avoid excessive element distortion before crack initiation.Unless otherwise specified in the text, the normalized model parameters used in the simulations are listed in . Note that the yield stress σ0 and the non-local length lnl are used for dimensional analysis, so it is meaningless to modify them. Finite element simulations are performed using Code_Aster/Salomé-Méca, a software suite for finite element analyses.Two types of definitions of crack length Δa will be discussed. The initial crack tip is considered as the origin of the axes, as shown in . We use, in this paper, the uppercase letters (X, Y) for the coordinates in the initial configuration and the lowercase letters (x, y) for the coordinates in the deformed configuration. It is important to notice that both definitions of Δa are based on the deformed configuration, which is different from other studies such as (The crack length Δa is often defined as:where xref is the x-coordinates of a defined reference point in the deformed configuration, xtip is the position along the crack growth direction (in the present case the x-direction) of the most distant failed Gauss point from the reference point, so that: xtip=max(x,f(x)=fF) with f the porosity and fF the porosity at fracture (see (b) for the position of ligament). Both xref and xtip are computed in the deformed configuration. Intuitively, the reference point can be taken as the initial crack tip or some other points closed to the initial crack tip in the deformed configuration, for example the point just above the initial crack tip. Generally speaking, the position of the initial crack tip in the deformed configuration should not be used as the displacement of this point does not have too much meaning any more when the element containing this point fails or distorts.In this paper, the position of the farthest point satisfying f=fF in the ligament is used as an indication of the current crack tip. In the literature, instead of using the position of the farthest failure point, some authors used for example the position of the farthest point satisfying f=fc () or the position of the current maximum stress in the ligament (This method is based on the assumption that during deformation, the (upper part of the) notch remains almost a circle. This allows defining the center (xn,yn) and the radius of the current notch. At the beginning, we have (xn,yn)=(−Rn,0) and rn=Rn. We distinguish two stages: crack tip blunting stage if max(f(x))<fF and crack propagation stage if max(f(x))≥fF in the ligament. During crack tip blunting stage, the notch radius increases with increasing load and we note rblunt the radius at the end of the blunting stage. During crack propagation, we assume that the notch radius remains constant: rn≈rblunt (translation of the notch).. They will be numerically validated in Section . They enable two geometrical definitions of the crack extension, whether the blunting should be incorporated or not:Δa≡{xtip−(xn+Rn),incorporation of blunting stagextip−(xn+rn),otherwiseNote that the crack tip blunting length δ is shown in ; this length corresponds to the displacement of the initial crack tip. During crack tip blunting, the crack tip opening displacement CTOD is around 2δ.A further discussion on these two methods can be found in Section In this section, the influence of different numerical parameters on the global response (J resistance curve) is investigated. The proposed new method, which is presented in Section , will be used to compute the crack length Δa (see Equation ). The main numerical parameters involved in this paper are: the mesh size in the process zone, the non-local penalty parameter, the incompressibility penalty parameter, two artificial nucleation parameters, the external radius of the boundary layer model and the initial notch radius. The aim of these studies is to choose an appropriate (range of) value(s) for each numerical parameter, then these values will be used in the simulations presented in Section The boundary layer model is spatially meshed. Different element sizes le are used to discretize the process zone so as to find out a critical one below which the global response is spatially converged. shows the J resistance curves when le∈[0.35lnl,0.70lnl] with lnl the non-local length scale. On the one hand, crack initiation can be well captured for le<0.63lnl, on the other hand, the curves overlap for le≤0.42lnl. Thus, it is convenient to take 0.35lnl for the mesh size in the process zone for the study of crack propagation. This value is retained in the following study., a purely numerical parameter rnl is introduced in the non-local discretized formulation to enforce the equality between a and κ (see Equation ). Obviously, the value of rnl should not be too small, otherwise, its effect becomes negligible. observed oscillations on the κ field when rnl is not large enough in spite of the effect of the Lagrange multiplier l. On the contrary, one can take any large value for rnl as it will not affect the computational precision on a−κ.Since the influence of rnl on local responses has already been studied in the work of (), we only focus on the influence of rnl on the J resistance curves. Four values of rnl(rnl/σ0=0.1,1,10,20,100) are studied and no difference is found among the corresponding J resistance curves. It can be concluded that the value of rnl does not affect the global response. In view of the local/global responses and the computational convergence, the value of rnl/σ0 is set to 10from now on. Note that poor convergence is observed for rnl/σ0=0 due to strong plastic strain localization.In the locking-free mixed element formulation, we also added a purely numerical parameter rinco to add a control on the value of θ−tr(E) through a penalty term (see Equation ). Its effects on global and local responses are studied in this part.Five values of rinco (rinco/σ0=0,0.1,1,10,100) are used to perform the simulations. No difference is found among the corresponding J resistance curves. plots the porosity (f) profile along the ligament in the deformed configuration at a loading level of J/(σ0lnl)≈28. Spurious oscillations of f are observed for rinco/σ0=0 and rinco/σ0=0.1, they disappear for larger values of rinco. plots the field of the crack opening stress σyy for different rinco. It can be observed that stress oscillations are very important in case of rinco/σ0=100, especially in the initial crack tip nearby zone. They are much less pronounced for small values of rinco. In view of the local/global responses, rinco should not be too small neither too large since on the one hand, a too small value for rinco can lead to an incorrect local response (for instance the f field in our case) and can hinder the computational convergence, on the other hand, a too large value for rinco prescribes θ−tr(E)≈0 at each integration point, resulting in volumetric locking again. In the following study, the value of rinco/σ0 is set to 10.As said before, small-scale yielding condition requires that the size of the plastic zone Rp be much smaller than the outer radius Rext(Rext/Rp≥20). To check this requirement and choose a convenient value for Rext, we set a value for the maximal loading level J/σ0lnl≈58. In this case, the final size of the plastic zone is Rp≈2700lnl. Five values of Rext are studied (Rext/Rp=0.25,2.5,25,250,2500). shows the J resistance curves for different Rext. The global response does not depend on the value of Rext for Rext/Rp≥25. On the contrary, for Rext/Rp<25, the curve becomes steeper and steeper with the decrease of Rext as the small-scale yielding condition is not fulfilled anymore. Therefore, in the following study, in order to respect the small-scale yielding condition, Rext/Rp is set to 25 with Rp is obtained at maximal loading level.), pure crack tip blunting is expected in the initial stage of load, this phenomenon leads to element distortion (). To overcome this difficulty, McMeeking () suggested to introduce an initial notch radius Rn at the crack tip (see ). This study showed that the introduction of Rn only has little influence on the final results provided that δ/Rn≥5 (where δ is the crack tip blunting radius shown in ) as the theoretical solution for an ideal sharp crack tip can be obtained for this condition. This conclusion will be shown again in this part with a mesh size much smaller than that in the work of (Unlike in the other sections where the GTN damage law is used, the von-Mises law is used in this part, following the work of (). Several initial notch radii Rn are studied:Rn/lnl=1.4,2.1,2.8,3.5.The evolution of the maximum opening stress in the ligament σyymax as a function of δ/Rn is illustrated in (a). This figure shows that an asymptotic value is reached when δ/Rn≈8. This conclusion is in accordance with () as the asymptotic value is almost reached for δ/Rn≥5. In addition, σyymax belongs to the range from 4σ0 to 5σ0, a value increasing with the hardening level n. This observation agrees with the result obtained in (), who applied the slip line theory to estimate the stresses under plane-strain small-scale yielding conditions.However, it is observed that the stress tends to a very large value at the initial crack tip. This problem will be analyzed in the next part (Section (a), the stress in the vicinity of the crack tip was not accounted for.In this part, a special attention is paid to the spurious and extremely high crack opening stress in the vicinity of the initial crack tip, as mentioned in the previous part. It is observed that the crack opening stress at the initial crack tip is large compared to that at other positions when von-Mises law is used. This result is due to the very high gradient of plastic deformation which causes additional hardening in the yield function (cΔκ) in equation . The same problem can be found with the use of the GTN model when strain nucleation is not active. In addition, the material point (in the ligament) located at the initial crack tip never fails. This is mainly related to the low triaxiality at the initial crack tip. To illustrate it, a simulation without void nucleation is performed using the GTN damage model. (a) plots the evolution of the extended triaxiality Γ=TH/T∗ against the equivalent plastic strain defined as Eeqp=2/3Ep:Ep (including both volumetric and deviatoric parts) at four material points near the crack tip. It shows that at the beginning of load, triaxiality is very low at the material point located just against the crack tip (X=0.07lnl) and it increases along the ligament. (b) plots the hardening variable κ against the equivalent plastic strain Eeqp, it indicates that:Within a certain range for Eeqp, the equivalent plastic strain Eeqp is very close to the hardening variable κ.For the material point which never fails at the end of load(X=0.07lnl), κ increases much more slowly than Eeqp when Eeqp>2.3.For the material points near the initial crack tip, the deformation level at fracture decreases along the ligament.In some cases, for example when an element deletion technique is used, it is imperative that all the material points located in front of the current crack tip in the ligament be in failure. Indeed, with an element deletion technique, elements are removed when the necessary condition for element deletion is met, which would be for instance f=fF for all material points of an element. So it is interesting to introduce an artificial void nucleation fn,a. As regards the form of fn,a, a very simple formulation is used as below:fn,a={0ifEeqp<Eeq,cpb0(Eeqp−Eeq,cp)otherwisewhere b0 is a constant and Eeq,cp is the critical equivalent plastic strain. Note that instead of using κ, we use Eeqp as the argument of the function fn,a since κ is likely to be bounded, as shown in This formulation enables the material point near the crack tip to locally fail. Attention should be paid to the choice of b0 and Eeq,cp. The coefficient b0 should be large enough so that the material points can quickly fail and the deformation of the element containing these points would not be too large. Regarding Eeq,cp, on the one hand, it should not be too small, otherwise other undesired points may fail and the crack path may be physically incorrect; on the other hand, it should not be too large as the deformation of the desired point may be too large before its failure.In order to check whether the artificial nucleation affects the global material response, three complementary simulations are performed with Eeq,cp=100%,200%,300% and with the same value b0=0.25. The case without nucleation can be seen as b0=0.25,Eeq,cp=∞. No significant discrepancy has been observed. In this paper, we set b0=0.25 and Eeq,cp=2.This part aims at establishing the relation between the width of the localization band lb and the non-local characteristic length lnl. The former is defined as the width of the stable crack propagation zone where f≥2fc (see ) while we recall that lnl is derived from the non-local parameter c and the initial yield stress σ0 as:lnl=c/σ0.Simulations are performed with different value of κ0 and E/σ0: κ0=0.001,0.002,…,0.01 and E/σ0=200,300,…,800. gives the corresponding values of lb/lnl for each simulation. It shows that the relationship between lb and lnl is almost linear:This relation is in accordance with that obtained in the work of (), who performed some simulations with axisymmetric modeling with different values of c.The objective of this part is to verify whether the proposed new method is satisfactory for extracting Δa. For the detail of the literature method and the proposed new method, one can refer to Section . Firstly, the assumption stated in Section , i.e., the notch remains almost circular during crack propagation, can be simply validated by visualizing the notch shape at different load levels (see for example (a) plots the evolution of the notch radius rn with increasing load. It is shown that there is linear growth of rn during crack tip blunting while during crack propagation, rn increases very slowly. This is in accordance with our assumption.Secondly, two scenarios will be studied: with and without the consideration of crack tip blunting for the computation of Δa. The former corresponds to Δa=Δabl+Δatear and the latter corresponds to Δa=Δatear with Δabl crack growth due to blunting and Δatear crack extension corresponding to the actual ductile tearing. For the first scenario, only the proposed new method is used while for the second scenario, both the literature method and the proposed new method are used. For the second scenario, it is necessary to choose a reference point (i.e. xref in Equation ) for the literature method. As said in Section , the initial crack tip cannot be considered as a reference point as the element containing this point fails during load and the displacement of this point is not reliable any more. Instead of using the initial crack tip, we use the point located above the initial crack tip, as shown in (b) plots the evolution of the crack length Δa as a function of increasing load. It shows that:For the second scenario (without the consideration of crack tip blunting), both methods give almost the same results. It reveals that both the literature method and the proposed new method can be used to extract the physical crack extension.If we compare the two scenarios, the curve slopes during crack propagation are the same in the three cases.The literature method is rather simple but it cannot take into account the blunting. Therefore, in the following, the proposed new method is used and the crack tip blunting stage is taken into account for the computation of Δa in accordance with experimental procedure proposed in (In this part, several simulations are performed using the parameters introduced in (a) shows the evolution of the porosity f ahead of the notch with increasing load. From this figure, it is observed that the porosity at the crack tip grows slowly when compared to that at other nearby points, which results in the fact that the first failure (f=fF) does not occur at the crack tip (see the enlargement in (b) plots the corresponding crack opening stress σyy. It shows that during cracktip blunting, there is a single stress peak and it is far away from the crack tip. After crack initiation, another stress peak appears near the current crack tip and the crack propagates slowly at this stage. As load increases, the initial stress peak finally disappears and the crack propagates quickly. After the disappearance of the initial stress peak, the stress profile shifts along the ligament with increasing load. In particular, the maximum crack opening stress remains the same. At this stage, the stress profile ahead of the running crack is much steeper than that at crack initiation. plots the distribution of the hardening variable κ in the ligament at different loading levels. The κ profile moves along the ligament with increasing load, which is similar to that of σyy. One can observe that there exists a critical position xc such that κ at the failure points remain almost constant for x>xc. In the current case, this constant value is around κ=0.4. To further investigate this failure zone, we can, for example, plot the history curves at different points in the ligament. For instance, the f - κ curves at some points in the ligament are given in (b), their location is given in the initial configuration. One can see that the f−κ curves at the Gauss points located ahead of X≈18lnl almost overlap, i.e., all material points located at X≥18lnl have the same history which may correspond to a steady-state evolution. illustrates crack tip blunting, crack initiation and crack propagation with increasing load in the initial and deformed configurations. During crack tip blunting, the notch remains almost circular. As load increases, the crack appears near the initial crack tip and then propagates. Note that the notch still retains a circle shape during crack propagation; it is actually the prerequisite to the definition of the crack length Δa with the proposed new method. In addition, one can observe that damage forms in front of the current crack tip and moves along the ligament. A linear crack opening profile is obtained, as predicted by () in the experiments. This implies that a crack tip opening angle CTOA can be defined. In the present case, CTOA is around 16° at the end of load.At the final stage of load, nearly 180 finite elements have fully failed (violet part in ). Note that no element-deletion method is applied in our case. Some authors also succeeded in simulating large crack growth by means of local GTN model (). In both cases, the issue of volumetric locking was not dealt with. In the work of (), the mesh size is considered as a material parameter so that the mesh-dependency problem still exists. In the work of (), the large crack growth was performed with f0=0.1 or f0=0.01, values which are not adapted to most materials - modern steels and aluminum alloys are processed so that f0 is below 10−3. compares the energies dissipated during crack propagation in the localization band (Wlbp, the localization band is defined as the zone where f≥2fc) and in the entire volume (Wp). These two quantities are defined and computed as:{Wp=∫0t∫Ω0(T:E˙p)dΩ0dtWlbp=∫0t∫Ωlb(T:E˙p)dΩlbdtwhere t stands for the current loading level and Ωlb stands for the region in which f≥2fc. Note that Ωlb can change at each time step and Wlbp=0 if f<2fc for all material points.(a) plots the evolution of Wp and Wlbp. Wlbp varies linearly with crack advance which indicates that the energy dissipated in the localization band per unit crack advance is constant. The evolution of Wp is first rather quadratic and then becomes almost linear. To compare these two energies, (b) plots the evolution of Wlbp/Wp and ∂Wlbp/∂Wp. One can observe that Wlbp is very small when compared to Wp and Wlbp/Wp increases at the beginning and tends to a constant (around 0.001) as crack extends. On the contrary, the value of ∂Wlbp/∂Wp decreases at first and reaches to the same constant at Δatear/lnl≈10. This observation shows that the energy consumed for crack propagation tends to be proportional to the total dissipated energy for long cracks. In some ways, it indicates that the steady state may be reached which is consistent with the observed evolutions of opening stress, damage and plastic strain along the crack path (In this part, the hardening parameter κ0 remains constant. (a) shows the J resistance curves for different values of n. It is seen that n can affect crack tip blunting, crack initiation toughness Jc and tearing behavior. Larger values of n lead to steeper blunting lines. In particular, if σY=(σ0+σUTS)/2, with σUTS=σ0(nκ0)ne−n+κ0 for the selected hardening law, is used for the normalization of J, the blunting lines for different n would overlap. This result is in accordance with the ASTM standard which uses σY to define the blunting line. In addition, crack appears earlier with a smaller value of n. On the contrary, the tearing modulus (TE=ΔJ/(σ0Δa)) decreases for increasing values of n. One can notice that the simulations are performed for n≥0.12 as crack bifurcation is observed for n<0.12 as shown in (b). This could correspond to the competition between crack normal opening and shear cracking. Further investigations on crack bifurcation will be conducted in the future work.(a) plots the J resistance curves for different initial porosity f0. It shows that f0 affects both crack initiation and tearing behavior. To propagate the same crack length Δa, the smaller f0 is, the more energy should be provided. Indeed, the normal stress required to achieve material separation is high when f0 is low, so that a fully developed plastic zone is formed in front of the crack tip leading to large plastic dissipation as the crack advances (), this bifurcation was not observed as large values for f0 (f0≥0.01) were used.The J resistance curves with different fc are depicted in (b). From the obtained results, one can observe that the value of fc has influence on both crack initiation and tearing behavior: On the one hand, the critical toughness Jc increases with fc as the void coalescence (so the failure) is postponed with the increase of fc. On the other hand, the slope of J resistance curve, i.e., tearing modulus TE=ΔJ/(σ0Δa) increases with fc during crack propagation.Simulation of ductile fracture using damage models such as the GTN model or its numerous extensions faces two problems: dependence on the geometrical discretization (mesh) due to material softening and volumetric locking as the material is quasi-incompressible as long as damage by void growth is limited. A nonlocal formulation and a related numerical implementation were proposed in () to simultaneously solve these two problems. This initial formulation was slightly modified in this work to improve convergence by adding a penalty term which brings an additional coercivity so as to avoid the potential appearance of spurious plastic strain localization. In this study, this technique is used to simulate crack extension over relatively long distances (~200 elements) in the case of small scale yielding using the boundary layer model where the material is loaded applying a remote stress intensity factor. The use of the boundary layer model allows defining non dimensional quantities.This technique is first used to study the numerical stability. The effect of the penalty parameters rnl and rinco on the J−Δa curves and on the local values of plastic strain, damage and stresses is investigated. This allows defining ranges for both parameters so that they solve the purely numerical issues without affecting the computed physical quantities of interest. It is also shown that the mesh size in the crack propagation area must be at least three times smaller than the model intrinsic length defined as lnl=c/σ0 to obtain mesh independency.Using these optimal numerical parameters, a systematic study of the properties of the proposed model is carried out. The highly damaged zone surrounding the crack defined as the area where f≥2fc has a thickness which is about 1.3lnl. After an initial stage corresponding to blunting and initiation of crack growth, a stabilized crack propagation stage is reached with damage and stress gradients () much sharper than during initiation. The non-local framework can nevertheless describe these gradients. This steady state also corresponds to a constant cumulated plastic strain at failure (). Plastic dissipation in the highly damage zone (Wlbp) is evaluated as a function of crack advance and compared to the total dissipated energy (Wp). Both quantities increase as a function of crack advance and it is shown that Wlbp is much smaller than Wp. Their ratio tends to be constant for large crack advance which corresponds to steady state crack propagation. The effect of model parameters such as fc or f0 is also studied. Standard evolutions () are obtained. Increasing f0 or decreasing fc leads to lower values of J/(σ0lnl) for a given crack advance as well as to lower values of the tearing modulus ΔJ/(σ0 Δa). Finally crack bifurcation is observed when the hardening exponent n, decreases. The same phenomenon is observed when the initial porosity f0 decreases. The question of whether the effect is a purely numerical artefact or reflects some reality remains open. The simulated bifurcation could possibly represent the observed zigzagging cracks observed after blunting (see e.g. (Youbin Chen: Conceptualization, Methodology, Software, Validation, Investigation, Data curation, Writing - original draft, Writing - review & editing, Visualization. Eric Lorentz: Conceptualization, Methodology, Software, Validation, Resources, Writing - review & editing, Supervision, Funding acquisition. Jacques Besson: Conceptualization, Methodology, Validation, Resources, Writing - review & editing, Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Compressive behaviour of rubberized cement-stabilized aggregate mixturesAn investigation was undertaken to study the behaviour of cement-stabilized aggregate mixtures modified with small amounts of rubber under compressive loading with the aim of providing more sustainable and less brittle mixtures for use in semi-rigid pavements. Three rubber replacement levels (15%, 30%, and 45% by same volume of one aggregate fraction that has similar particle gradation) were investigated. The rubber particles have higher surface roughness than the aggregate particles they replace. To understand the behaviour, this study was conducted at both macro- and meso-scale levels utilizing mechanical testing, x-raying the internal structure and monitoring the crack propagation. The results showed a higher reduction in the compressive strength compared to the tensile strength. X-ray images confirmed an interconnected cracking network through/around the rubber particles. This resulted in a delay to crack development, with the velocity of crack propagation declining due to rubber incorporation. As the latter phenomenon is governed by the stress distribution inside the mixture, therefore a rubber distribution quantitative study confirmed a fairly uniform rubber distribution only for low and moderate rubber content, suggesting that the low rubber content can be used to ensure better properties and to overcome the shortcomings of normal cemented pavement mixtures.Expansion of the modern world in terms of population increase and in the quality of life have increased the number of the manufactured vehicles. This, in turn, has generated a significant number of old tires stockpiled year after year. Statistics indicate that about 300 million old tires are generated every year in the United States In many applications, waste tires have been used in form of rubber particles. Mechanical grinding of shredded tires is utilized to produce these particles of small sizes. The properties of resulted particles depend on grinding process conditions. Ambient grinding process produces rubber particles of irregular shape and rough surfaces while regular particles of smooth surfaces are normally obtained from cryogenic grinding process Over the past four decades, many scholars Recent investigations have focused on the use of recycled materials to ensure sustainable materials However, very few researchers have studied the compressive behaviour of cemented aggregate mixtures when modified with crumb rubber. Moreover, investigating issues related to cracking and crack propagation under compressive loading are seldom reported in the literature in the case of cement-stabilized mixtures. Therefore, this research has been conducted to fill these knowledge gaps which will help with understanding of the compressive behaviour and its related parameters and lead eventually to more sustainable highway construction.Failure criteria for conventional pavement structures, consisting of asphaltic surface layer and granular base and subbase, are the tensile strain at the bottom of the surface layer and compressive strain at the top of subgrade. For semi-rigid pavements that contain a cement-stabilized aggregate base/subbase layer, on the other hand, the first of these criteria shifts from the bottom of the asphaltic surface course to the bottom of the stabilized layer The compressive strength of the stabilized layer, however, might represent another criterion that needs to be taken into consideration during pavement structural design as recommended by the South African pavement design guide The motivation of this study is to investigate the behaviour of rubberized and cement-stabilized aggregate mixtures under compressive loading. This was conducted at both macro and mesoscale levels to investigate unconfined compressive strength, load-axial deformation and failure pattern. Another part of this study is to understand the failure mechanism of mixtures modified with different contents of crumb rubber particles. The latter objective was conducted by investigating the internal structures and also by monitoring the evolution of cracks due to compressive loading. Limited research, even for rubber-modified concrete, could be found in literature regarding the investigation of the meso-structure of failed specimens to reveal how the cracks evolved.Due to the high rigidity of cement-stabilized layer compared with other pavement layers, it is logical that such rigid layer will be the main structural layer. Hence, the rate of deterioration of this layer will likely govern the deterioration of the whole semi-rigid pavement structure. Therefore, studying how the embedment of rubber particles inside a brittle and rigid layer may affect the deterioration of the modified layer is an important issue that can help us to understand the failure mechanism and hence to assess the benefit of including such soft particles. To the best knowledge of the authors, this is the first study that investigates the effect of rubber inclusion on the propagation of cracks as a time-dependent process for both reference and rubberized mixtures under compression. Another novel objective is the study of the distribution of these rubber particles inside a cement aggregate mixture and, hence, to relate this to failure mechanisms.In this study, five crushed limestone aggregate fraction sizes were used. These ranged from 20 mm to less than 6 mm. Tire-derived rubber aggregate was used to produce rubberized cemented mixtures by replacing the natural aggregate. The gradation of each aggregate fraction size and rubber were measured on the basis of BS EN 933-1:2012. The grain size distribution of different aggregate fraction sizes are same as those used in Farhan et al. Different types of cement-bound granular mixture for highway construction are described in BS EN 14227-1:2013. Among these mixtures, Cement Bound Granular Material (CBGM) 2–0/20 was used for the purpose of this investigation since it represents a mixture with moderate maximum aggregate size. 11% of 20 mm, 20% of 14 mm, 11% of 10 mm, 13% of 6 mm and 45% of dust (<4 mm) were blended together to achieve the design gradation and to ensure uniform gradation in different specimens. This is because the strength of cemented mixtures is a density-dependent parameter A cement content of 5% was used for the purpose of aggregate mixture stabilization. This was selected based on a previous study Each mixture was designated by two letters each of which is followed by a number to indicate cement and rubber and their contents in the mixture. C5R45, for example, indicates the mixtures stabilized with 5% cement content and modified by replacing 45% of the 6 mm aggregate by crumb rubber.The mixing sequence was adopted as follows: first, cement was mixed with dry fine grain granular particles of less than 6 mm size until achieving a uniform colour. This was added to a mixture of the other aggregate fractions plus the crumb rubber particles and mixed for one minute. Then the resulting blend was again mixed for two further minutes after adding the designed water content.In this study, two sample sizes were manufactured and tested. These are small cylinders (100 mm dia. × 100 mm height) and prisms (100 mm × 100 mm × 200 mm). Once mixing was completed, the final product was placed in lubricated moulds in three layers and compacted utilizing a vibrating hammer for one minute as recommended in BS EN 13286-51:2004. Wet paper and polythene sheets were used to cover the specimens in their mould once the compaction process was completed to avoid moisture loss. On the next day, these were demoulded and wrapped with nylon film, placed in wet polythene bags and closed tightly and cured in the humid room at 20° C and a relative humidity of 90% for 28 days.Since the main items that will be investigated in this research are mechanical properties, it is logical to evaluate first the mechanical properties of the main component of the mixture which is the aggregate particles. This will give an idea regarding the strength of this component and help in understanding the behaviour and failure mechanisms of the various cement-stabilized mixtures. This was achieved as follows: firstly, large limestone blocks were brought from the same quarry that produced the different aggregate fractions used in this investigation. Then, four cylindrical samples with a dimension of 37.24 mm diameter × 74.08 mm height were extracted from these blocks by coring. These were tested for unconfined compressive strength (UCS) using a RDP Stiff Testing Machine (1000 kN capacity). Axial deformation was measured via two Linear Variable Differential Transformers (LVDTs) and the average value was used to calculate strains at each load increment. (a and b) illustrate the appearance of aggregate cores and the UCS testing setup for these samples.In general, the ability of compacted mixtures of adequate gradation to resist loading depends, to some extent, on the roughness of aggregate particles in this mixture where shear strength, for example, will be improved in proportion to the increase in the surface roughness of aggregate To achieve this objective, a three-dimensional (3D) non-contact profilometer (c) with laser scanner were used to measure the surface roughness of both natural aggregate and rubber. Three samples were selected randomly from each rubber and natural aggregate (of the 6 mm size). Each sample was mounted on an equipment holder and then scanned. Two measurements were performed for each sample.BS EN 13286-41:2003 was adopted throughout this project to assess unconfined compressive strength (UCS) of the cemented aggregate mixtures. To evaluate the behaviour with time, this test was conducted at ages of 7, 28 and 365 days using a 2500 kN testing machine. Three cylindrical specimens with dimensions of 100 mm dia. × 100 mm height were manufactured in accordance with BS EN 14227-1:2013 for each mixture and the average value was recorded as UCS. The latter parameter was computed from the following equation:A = Area of specimen cross-section (mm2).Failed specimens were visually observed to detect their failure patterns and, hence, to draw a picture about their probable failure pattern in the field. Then, these specimens were x-rayed along their height to provide a deeper investigation of internal structure, at the mesoscale level. This was conducted utilizing an x-ray machine at a focus of 300 kV since this power will ensure better penetration through stabilized aggregate mixtures. Five equally spaced scans at a resolution of 0.065 mm/pixel were conducted along the height of each failed specimen.Regarding damage propagation study, it was intended to study, quantitatively, the fracturing process of specimens as a time-dependent phenomenon. To this end, a non-contact technique called “Video Gauge” was utilized to observe the face of the specimen during the load application. This technique relies upon video-based two-dimensional measurement tools that use a special digital image correlation (DIC) algorithm. In parallel to this, the technique is also used to measure axial deformation along the specimen. The test setup is shown in . The specimens, in this methodology, need to be speckled first by applying thin black paint over previously prepared thin white matt. This was conducted to facilitate the tracking process. After placement and alignment of the specimen between loading platens, a source of lighting was placed in the front of specimen in order to ensure a bright monitored surface. Afterward, the camera was fixed in front of the prepared surface in such a way that ensures display of the prepared face. The application of compressive load was performed at a rate of 0.5 mm/min. The monitoring technique captured video at a rate of 1000 frames per second (fps). Images were then extracted from these captured videos for selected loading stages and used to calculate cracking velocities. The latter was computed as suggested by Pyo et al. Rubber particles have an important influence on tensile cracking Cylinders with dimensions of 100 mm × 100 mm, manufactured as previously described were used in this distribution study. Three mixtures were used: C5R15, C5R30 and C5R45. Cropping, scaling, filtering and thresholding of CT scan images were achieved using ImageJ software.It is generally accepted that the lower the scanning interval the more the information that can be obtained about the internal structure of the specimen. Since the idea behind this part of the study is to quantify the distribution of the rubber particles of sizes ranging from 2 to 6 mm, it was decided to x-ray the specimens at 1 mm intervals. The X-ray machine described previously () was used for scanning to produce a hundred two-dimensional images at 1 mm slice intervals for each specimen. Then, these images were converted to 8-bit format for more processing and analysis.Image thresholding is a process that allows separation and extraction of the desired objects of the image from the background of that image on the basis of pixel density. Images are normally produced with a grey scale ranging from 0 to 255 to represent darker pixels and lighter pixels, respectively. Thresholding of the image is then performed by selecting a value on the grey scale between 0 and 255 to define an area of interest. After thresholding of an image, pixels having a value less than the selected threshold value become black while those above become white i.e., conversion of image from grey scale to binary.The grey level of the rubber particles and of air-voids in the x-ray image is quite similar, as initial observation showed. Such inspection means, unfortunately, that it is extremely difficult to discriminate between these two components after thresholding of an image. Therefore, the following methodology was suggested and implemented to threshold an image. In the first place, an initial threshold value was chosen on the basis of visual observation. Then, specimen-based images were analysed and the amount of rubber in the rubberized specimen was estimated. The latter amount was compared with the actual rubber quantity used in the specimen based on the mix design. If these two amounts were similar, then the initial value could be considered as the precise threshold value. Otherwise, another threshold value was attempted until the rubber quantity estimated on the basis of image analysis equalled that originally used in mix design.Initial inspection of the X-rayed specimens showed existence of some rubber clusters in the horizontal plane at certain scanning levels as shown in a. Hence, better assessment of rubber distribution in cemented mixtures necessitates evaluation of the distribution of these particles not only vertically but also radially. Vertical distribution was performed by studying the change in rubber percentage from one image to the next above or below. Radial distributions, on the other hand, were evaluated by estimating the rubber contents and distribution in an internal core and external ring of equal cross-sectional areas (The stress–strain relationships of aggregate samples are illustrated in . As this figure indicates, moduli of elasticity of the four samples are similar with marginal differences whereas there is around 13% difference in the values of UCS. Therefore, this indicates that differences in the strength of mixtures may be partially explained due to the variation in the aggregate particle strength itself. The review of literature conducted by Yadav and Tiwari The surface topography of both natural and rubber and aggregate are illustrated in and the roughnesses of these surfaces are summarized in . Results show that the roughness of natural aggregates is around two-thirds that of the rubber particles. This indicates, from a frictional resistance point of view, that rubber particles have a positive effect, being even better than 6 mm size natural aggregate. This will lead to good interaction with natural aggregate particles when they are compacted together. Furthermore, better adhesion can be ensured when rough rubber particles are compacted with the matrix (fines and cement). This behaviour seems consistent with the conclusions reported by Segre and Joekes illustrates the effect of rubber modification on the compressive strength of cement–stabilized aggregate mixtures at ages of 7, 28 and 365 days. As is clear, replacement of natural aggregate by crumb rubber particles caused a decline in the UCS value. At 28-day curing period, for example, UCS was reduced by 12.35%, 29.35% and 37.7% due to replacing the 6 mm natural aggregate fraction size by 15%, 30%, and 45% crumb rubber, respectively. This is logical in the light of the fact that the rubber particles, of low strength and stiffness, replaced the natural aggregate of high strength and stiffness The final density was also negatively affected due to the incorporation of rubber particles of low specific gravity due to their detrimental impact on compaction efficiency as measured by Farhan et al. shows the relationship between ITS (as reported in a previous study conducted by Farhan et al. Regarding the curing period, there is an improvement in the UCS with time () which can be attributed fundamentally to an increase in the hydration products , the current results are in good agreement with the above-mentioned models. This, in addition, means that the rubber has no effect on these relationships. At 7 days age, however, the ACI model gives a conservative prediction for the stabilized materials’ strengths.In their report prepared for the Portland Cement Association, Scullion et al. illustrates the load-axial deformation relationship for cemented aggregate mixtures stabilized with 5% cement and containing different amounts of rubber particles. Qualitatively, the post-peak behaviour and the ductility of the rubber-modified mixtures improved proportionally as rubber content increased. This can be attributed to the presence of rubber particles in the path of the developed cracks which was assumed by Farhan et al. ) that the reference specimens with no rubber failed by crushing of large pieces from the specimens while the rubber-modified specimens showed longitudinal cracks with partial failure i.e. no complete failure. Such a failure pattern confirms an improvement in energy absorbency and the occurrence of ductile behaviour. In her investigation conducted on cement stabilized clayey sand soil, Chan Investigating internal structure by examining x-ray images of the failed specimens under compressive loading shows that the cracking network was interconnected through or around the rubber particles (). Such a finding supports the necessity of a rubber distribution study. Also, this observation of mesoscale structure reinforces the branching of cracks phenomenon suggested by Farhan et al. . Samples of these curves are provided in . The results reveal that there is a reduction in the velocity of propagated cracks in the cemented aggregate after rubber modification as shown in . The latter evidence clearly supports the crack growth delay hypothesis presented above. No doubt, the applicability of this proposed mechanism depends, to some extent, on the distribution of the rubber particles. The more uniform the rubber distribution, the more uniform the stress/strain distribution can be anticipated to be inside the mixture. On the other hand, non-uniform rubber distribution may cause asymmetrical stress distributions and help to accelerate the failure process. illustrates, the rubber distribution along the sample height is fairly uniform for mixtures of low and moderate replacement levels (i.e., C5R15 and C5R30) where the standard error was estimated as 7.9% and 7.6% for these two mixes, respectively. The mixture with higher rubber amount (C5R45), however, showed a larger variability where the standard error is about 14.8%. This is explained by the large decline in the value of UCS in the case of higher replacement level, which can be partially attributed to the non-uniformity of the rubber distribution.a, b, c shows the radial distribution of embedded rubber particles in the internal core and external ring for the examined rubber-modified mixtures. In general, there is a uniform rubber distribution throughout the sample height in both internal and external parts of the mixture with 15% rubber content as a indicates. The standard error of the mean in these two portions is 3.70% and 6.25%, respectively.Regarding the mixture containing 30% rubber content, b confirms a similar distribution; 4.7% and 5.3% are the standard error of the vertical rubber distribution in the internal and external parts, respectively. Finally, a large variability was observed (c) in the mixture of high rubber content (C5R45) where the standard error of the rubber distribution across the sample height was estimated as 10.4% and 9.1% for internal and external sample parts, respectively.The influence of tire-derived crumb rubber on the compressive properties, internal structural and damage propagation of cement-stabilized aggregate was investigated in this paper. Based on the outcomes of this study, replacing natural aggregate by rubber particles decreases compressive strength of cement-stabilized mixtures. Although the strength of rubber-modified mixtures increases with time as in case of rubber-free mixtures, a decrease relative to no-rubber mixes still occurs. From components of the mixture point of view, rubber particles used in this investigation showed better surface roughness than the natural aggregate of the same gradation. Nevertheless, reduction in the compressive strength occurred due to replacement of natural aggregate by rubber particles. This may lead to a conclusion that the strength and stiffness of aggregate particles, in the case of the compacted cemented mixtures, represents the governing factor in their behaviour.Failure patterns seem to be governed by rubber particles where the rubberized mixtures showed full intactness and ductile failure. Inspection of the internal structure revealed that the cracks were interconnected through rubber particles which indicates that the rubber particles have an impact on the cracking process. Moreover, an estimation of the crack velocity indicated that the presence of rubber in the path of cracks delays their propagation by reducing the velocity of propagation of these cracks. Therefore, the distribution of these particles influences the stress distribution inside specimens and hence the final strength and cracking. Quantitative rubber distribution analysis indicated a uniform vertical rubber distribution in line with each mixture’s rubber replacement levels. However, greater non-uniformity in this distribution occurred at the highest replacement level (45% of the 6 mm aggregate fraction). The radial rubber distribution, on the other hand, revealed that the vertical distribution in the internal core and external ring of the same cross-sectional area is fairly uniform especially in C5R15 and C5R30 mixtures. Consequently, the higher reduction in the UCS at higher replacement level can be partially attributed to the larger variability in the distribution of rubber particles inside the specimen.Based on the findings of this paper, it seems that the use of low rubber content to modify the normal cement-stabilized pavement mixtures will ensure better properties especially cracking behaviour and ductility. In addition, this modification will overcome the shortcomings of this type of pavement mixture in terms of reflection of cracks since branching of cracks due to uniform rubber particles will help to prevent stress concentration in the asphalt surface layer. However, durability of the rubberized cement-stabilized mixtures and the implication of such modification on critical stress/strain of the pavement structure are still questionable. Another paper is now under preparation to clarify the latter issues.Ahmed Hilal Farhan: Conceptualization, Formal analysis, Investigation, Methodology, Writing - original draft. Andrew Robert Dawson: Conceptualization, Methodology, Supervision, Validation, Writing - review & editing. Nicholas Howard Thom: Conceptualization, Methodology, Supervision, Validation, Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Failure assessment and virtual scenario reproduction of the progressive collapse of the FIU bridgeThe Florida International University pedestrian bridge in the United States is a two-span prestressed reinforced concrete bridge, which collapsed during its construction in March 2018. In this study, a finite element (FE) numerical simulation is performed to reproduce the virtual scenario of the bridge collapse and examine the cause of this accident. A refined FE model is established on the basis of the concrete plastic damage constitutive relations, and the damage factor is calculated using the Najar damage theory. When the model is combined with the alternative path method, the complete simulation of the structural damage and the collapse process is obtained. Especially, two key features of the structural response process, i.e. the instantaneous image of the collapse behavior and the total time of collapse 1.2 s, are almost identical with that recorded in the video. Simulation results can accurately reproduce the entire collapse process, indicating that the computational strategy used in this study are appropriate. Further investigation on the deformation and failure modes at different times during the collapse process and a discussion on the critical role of key components in the progressive collapse are presented. Analysis results show that the collapse of the structure is caused by the destruction of local nodes; the structural robustness analysis is crucial for the collapse resistance design. Numerical results and conclusions can provide a reference for the cause of bridge collapse accidents. The critical information of the finite element analysis process is presented in detail.On March 15, 2018, the Florida International University pedestrian bridge collapsed while under construction Computer numerical simulation is widely used to simulate structural behavior throughout the entire collapse process and determine the real cause of accidents. Abolhassan Despite the successful examples above, the simulation of the collapse behavior of complex large-scale structures remains challenging because the constitutive model and failure criterion of concrete materials are difficult to determine accurately. The constitutive properties of materials, such as yield, damage and softening behavior, and the contact relationship between concrete and rebar, are complex; thus, conducting an accurate simulation of the collapse behavior of complex structures, especially for reinforced concrete structures, remains challenging. Therefore, a corresponding experimental comparison is necessary. However, conducting a full-scale structural experiment is impossible even if a scale model test is conducted because of size effect deficiency.It is very rare that the video recording of the main process of the collapse of the FIU bridge can be used as a reference case for progressive collapse behavior of large and complex structures, and can be used to verify the reliability of numerical simulation results. Thus, it can be used as an effective means to verify the reliability of the numerical simulation of large-scale complex structures. Given the reasons stated above, this study performs a related analysis attempt and provides a reliable simulation result of the collapse behavior of the FIU bridge. This study then attempts to reveal the cause and mechanism of the collapse failure.The FIU bridge was a post-tensioned concrete structure. The rendering of the bridge design is shown in A photograph of the main span construction is shown in (b). The bridge construction adopted the accelerated bridge construction (ABC) technique, which allows bridges to be constructed or replaced with minimum traffic disruption. A prefabricated bridge is constructed on a site near the target building, and the bridge is lifted using self-propelled modular transporters (SPMTs). Then, the SPMTs lift the new bridge, transfer it to the worksite, and secure it in place. After the structure was prefabricated, it was placed on the two piers by transporters. At the time of the collapse, the main span was nearing completion, and it was still in a single state at this stage, a photograph of the collapsed structure is shown in (c). When the construction workers were adjusting the prestress, the local nodes of the structure suddenly broke and collapsed.A diagram of the structural cross section, pier and main span dimensions are shown in . The diagram shows the size and number of the components of each part. (The node number at the two connecting truss members is denoted by NP. For example, the node at the junction of the 11th diagonal member and 12th vertical member is denoted as NP 11–12.). The pylon tower and stay cable had not been constructed when the accident occurred; thus, only the main span portion was considered below. The main span was 53.34 m, and the total weight was approximately 861 tons. The canopy and deck and the diagonal members of the pedestrian bridge were prestressed using the post-tension method. The parameters of the material mechanical properties used in the structure are shown in A three-dimensional FE model of the structure is established in accordance with the structural design data of the FIU bridge and the actual loading situation at the time of the accident, as shown in . Among them, the main structure adopts the C3D8R element, and this element has high simulation precision for this problem. The transverse reinforcement applies a three-dimensional beam (B31) element, the road surface is considered a rigid body, and a discrete rigid body (R3D4) element is used. The rebar adopts the elastic-perfect plastic model and the concrete material adopts the concrete damage plastic model (CDPM). CDPM is currently one of the most common models used to simulate the mechanical behavior of concrete in ABAQUS. The model, which has been used in some studies, has good applicability to the simulation of the nonlinear deformation and irreversible damage of concrete, with high accuracy in all structural types and loading paths The yield criterion adopted by the CDPM was presented by Lubliner et al. F=11-αq¯-3αp¯+βε~plσ¯max-γ-σ¯max-σ¯cε~cpl=0where α=fb0/fc0-12fb0/fc0-1; β=σ¯cε~cplσ¯tε~tpl1-α-1+α; γ=31-Kc2Kc-1; q¯ is the Mises equivalent effective stress, and p¯ is the hydrostatic stress; σ¯max is the maximum principal effective stress, and 〈〉 denotes the Macaulay bracket defined as x=x+x/2; fb0/fc0 represents the ratio of the initial equi-biaxial compressive yield stress to initial uniaxial compressive yield stress; σ¯tε~tpl is the effective tensile cohesion stress;σ¯cε~cpl is the effective compressive cohesion stress; Kc is the ratio of the second stress invariant on the tensile meridian, q¯TM, to that on the compressive meridian, q¯CM, at initial yield for any given value of the pressure invariant p; and the condition 0.5 < Kc ≤ 1.0 must be satisfied. When Kc = 1 and Kc = 0.67, respectively, the corresponding Drucker–Prager yield surface and the Lublinear yield surface are shown in The concrete damage plasticity model assumes non-associated potential plastic flow. The flow potential G used for this model is the Drucker–Prager hyperbolic function:where ψ is the dilation angle measured in the p–q plane at high confining pressure, and ∈ is a parameter referred to as the eccentricity that defines the rate at which the function approaches the asymptote. The values are listed in For concrete materials, two failure modes are given in the ABAQUS: concrete crushing (compression fracture) and tensile cracking (tension break). When these failure modes are considered, the uniaxial tension and compression curves of the material will exhibit softening and damage behavior, as shown in where E0 is the elastic modulus before damage, and d is the damage factor. When the stress–strain curve transitions between the tension and the compression zones, the compression and tensile stiffness recovery coefficients (wc, wt) are introduced to determine whether the elastic modulus of the material can be recovered during the tension–compression transition; it cannot be recovered when 0 is taken. When 1 is made, it can be completely restored to the value of the previous unloading.In RC structures, the interaction between the two materials is involved. If concrete and rebars are treated as different parts, the calculation time will be lengthy. Therefore, the smeared model is used. In the model, all longitudinal reinforcements are dispersed into the section and treated as a continuous homogeneous material. The equivalent material stress–strain relationship curve is divided into phases, as shown in Elastic stage: When the material is in an elastic state (stage OAc, OAt), the elastic modulus E of the equivalent material is expressed aswhere the reinforcement ratio ρ = Ss/Sa (ρ = 0.0084), Es is the elastic modulus of the steel, Ec is the elastic modulus of the concrete, Ss is the cross-sectional area of the steel, and Sa is the effective area of the section.Compression nonlinear stage: When the material is under pressure, the modified equivalent method proposed in where σc1 is the equivalent material yield stress, fc is the concrete compressive strength, and E is the equivalent material elastic modulus.During the compression of concrete and in the nonelastic state, steel remains in an elastic phase. As the pressure increases, the rebar gradually reaches the yield point. At this time, the concrete also reaches the peak value of the compressive stress, and the equivalent material reaches the maximum yield limit.where σc2 is the equivalent material peak compressive stress, ρ is the reinforcement ratio, and σs is the steel yield stress. At this time, the strain of the equivalent material is the yield strain εc2 of the steel.After point Bc, the equivalent material enters the softening stage, the concrete crack increases gradually, and the stress begins to decrease. When the stress drops to 0.5fc, r (fc, r is the representative value of the uniaxial compressive strength of the concrete), the equivalent material reaches point Cc, and the stress at this time isWhen the curve reaches Cc, the concrete without lateral constraint is considered to have lost the bearing capacity, the remaining rebar are subjected to compressive stress, and the buckling occurs quickly. Therefore, point Cc is defined as the material failure point, and the strain εc3 of the equivalent material is the corresponding strain of the concrete stress 0.5fc.Tensile nonlinear stage: When the equivalent material is pulled, the concrete first enters the inelastic state, and the stress–strain values when the equivalent material enters the inelastic state can be expressed as:where ft is the tensile strength of concrete.When the tensile stress exceeds σt1, the concrete is cracked. At this time, the steel remains in the elastic phase (stage AtBt). When the strain of the concrete reaches the ultimate tensile strain εu, point Bt is reached, and the stress at this time is expressed as:where λ is tension stiffening coefficient. After the reinforced concrete member is cracked, the stress of the rebar between the cracks is reduced because of the presence of concrete. At this time, the average strain is smaller than the strain at the middle of the cracks, that is, the stiffness of the member is improved. The ratio of the average strain to the strain of the rebar at the middle of the crack is λ. take 0.2 before Bt, take zero after BtAfter point Bt, the tensile strength of the concrete decreases rapidly, and the stress of the steel increases continuously. When point Ct is reached, the steel yields. At this time, the stress and strain of the equivalent material are expressed asThe CtDt stage is the yielding stage of the rebar, and the Dt point strain is approximately considered to be 2εt3. Any point after the Dt point is completely cracked concrete. The rebar adopts the elastic-perfectly plastic model in this section; thus, the Dt point is used as the equivalent material failure point.The calculated material parameters are shown in Currently, many calculation methods for damage factor in the CDP model exist, such as the Najar damage theory, the Mander model, and the empirical formula method where W0=Eε22,Wε=∫fεdε, is the strain energy in a non-damaged state and a damaged state respectively.In order to avoid the numerical convergence problems caused by the excessive distortion of an element, the failure criterion for removing the element must be defined and used. For concrete materials, tensile damage and cracking failure are the primary causes of excessive deformation. Hence tensile strain can be used as a discriminant parameter for element removal, with the ultimate value without causing computational issues being referred as failure strain. It should be noted that the element removal criterion is only an algorithmic measure to overcome the convergence problem caused by excessive distortion of elements. As such, this value should be taken as high as possible to the extent that the failure strain has no physical significance. According to the recommendations in the references, the failure strain (erosion strain) is taken as 10−2 in this study In the FIU bridge’s design, the arrangement of the longitudinal and transverse rebar in the deck and canopy are different. However, material anisotropy cannot be considered in the CDP model; thus, the transverse reinforcing bar model is established in this study. Some rebar has been dispersed into the concrete due to the use of equivalent materials; the additional transverse rebar will lead to considerable lateral stiffness of the structure. However, the lateral stiffness does not affect the collapse mode of the structure because the collapse behavior of the structure mainly exists in the longitudinal direction. This simplification is therefore acceptable.For the transverse rebar, the elastic-perfect plastic model with an elastic modulus of 206 GPa and yield stress of 420 MPa is adopted.The bond-slip effect of the transverse rebar and the concrete is neglected, and the rebar are embedded in the concrete using the embedded region constraint. Some contact relations must be set between the structure, the pier, and the ground due to the collision during the collapse. The number of contact surfaces is large and complex; thus, the model uses the general contacts method. The coefficient of friction between concrete–concrete can be taken as 0.4 The number of elements has a massive effect on the results. Thus, mesh convergence analysis is required to avoid such effect. First, the total number of elements is chosen to be 10,000. Afterward, the total amount is increased by twice the initial number, and the maximum is selected to be 320,000. shows the strain energy variation with the number of elements. When the total number of elements exceeds 160,000, the effect on the results is minimal. Therefore, the seed size of the solid element is finally selected to be 0.15 m, the node portion is refined by 0.1 m, the beam element seed size is 0.2 m, and the total number is approximately 210,000 (the more detailed mesh convergence analysis are presented in ). Zero-energy mode may appear and affect the accuracy of the numerical results due to the use of the C3D8R element with reduced integration. Therefore, relevant energy change analysis is needed. presents the curve of artificial strain energy (ASE) and internal energy (IE) with time in the explicit analysis process; it shows that the ASE is always much smaller than the IE, and the maximum ratio of ASE to the total IE is 5.2%. This result indicates that the zero-energy mode in the analysis has minimal effect on the results.The progressive collapse behavior of the FIU bridge is a nonlinear dynamic response process. Thus, the FE simulation should also use the nonlinear dynamic method. The structural dead load includes the gravity load and post-tension prestressing force, and its loading process will have a substantial inertial effect on the explicit dynamic analysis, thereby affecting the static behavior before the collapse. To avoid this unrealistic structural response, this study uses the explicit/implicit conversion analysis method in ABAQUS. Static analysis is performed first, and then its results are transmitted to the explicit dynamic analysis. In the FE analysis process, the first static behavior of the structure under dead load is within a linear elastic range, but the subsequent explicit analysis involves the material inelasticity and large displacement of the structures. This result indicates multiple nonlinear characteristics of materials, such as geometry and contact relations.The video in site shows that the collapse of the FIU bridge can be divided into the following stages: ① The NP 11–12 are destroyed for unknown reasons; ② The 11th diagonal member lost, and the structure’s internal force is redistributed; ③ The structure collapses in a short period of time. For this structure, several factors influenced its construction, and the reasons for the failure of its nodes are highly complicated. However, the complicated failure process of the connected members caused by the NP11-12 failure can be simplified to the failure process of the 11th diagonal member. Therefore, the alternative path method can be used, indicating that the target member is replaced by a load, and a reaction force is applied to cancel the load for a certain period to calculate the response of the structure after the member is lost Static analysis is performed to determine the internal forces in the diagonal member to be removed;The structural geometry is changed by removing the load bearing element that will be damaged, and it is replaced by the internal force calculated in Step 1;The sudden force in Step 2 is removed from the system over a short impulsive time duration Tr. When the system’s dynamic response is dominated by one main vibration mode, Tr is commonly recommended to be 1/10 times the first natural period of the structural system.The FIU bridge has a large post-tension prestress, which was considered in the FE model. Although we lack detailed information on the construction process of the structure, public information shows that the prestress was adjusted during the construction process before the bridge collapsed, indicating that the prestressed sleeve in the structure may not have been cast with concrete. Before a structure collapses, the prestress remains constant. During the collapse stage of a structure, the prestress gradually disappears or even completely fails. If a fully realistic model is used to simulate this process, then solid elements must be used, and numerous contacts between the sleeve and the reinforcement must be established; such requirements are too complicated to achieve. Therefore, the present study used a simplified method to simulate the post-tension in the structure by applying external load, as shown in . Considering the structural state characteristics of the collapse process, the additional effect caused by longitudinal prestressed tendons is small and does not affect the overall behavior of the structure. During the collapse process, the longitudinal prestress of the structure is assumed to decrease with the increase in the maximum displacement of the structure and eventually decrease to zero.As observed from the published relevant information The accuracy of the progressive collapse process’ simulation results can be ensured by comparing it with the actual structural collapse behavior. The video was able to record the entire process of structural collapse; thus, it can be used to verify the FE results. The following is a real-time comparative analysis of the screenshots and the simulation results of each instant. is a comparison of the video screenshots and FE simulations of the collapse process. Video data was captured by a driving recorder at the time of the incident. The frame rate of the video was 10 frames/s. From the moment when the 11th diagonal member shows evident position changes, the images of the time of 0, 0.3, 0.6, 0.8, 1.0, and 1.2 s are respectively taken from the video. And compared with the results, which is the structural deformation at the corresponding time point after the removal of the 11th member in the FE simulation., large cracks occurred at NP 9–10 and NP 11–12 at 0.3 s, and the local bending deformation was severe. Afterward, the NP 9–10 were disconnected at 0.6–0.8 s, and the structure started to fall; At the time of about 1.0 s, the NP 9–10 of the structure first made contacts with the road surface.Comparison results show that the total collapse time of the simulated structure was precisely the same as that displayed in the video; both structures collapsed entirely at 1.2 s. In addition, the instantaneous simulation results are almost identical to the actual collapse configuration. Such high similarity also indicates that the FE model and calculation strategy used in this study can accurately restore the entire process of the FIU bridge collapse accident.The progressive collapse behavior of a structure is a dynamic process, and the dynamic analysis method should be adopted for the simulation analysis of the collapse behavior. However, before the collapse, the structure is already in a state of constant load, and its deformation and internal force have a considerable influence on the behavior of failure. Therefore, performing static analysis is necessary to obtain the initial deformation and internal force of the structure before the collapse.The maximum principal stress contours of the whole structure under the action of gravity is shown in . The diagonal member stresses of 1 to 8 are basically distributed alternately in accordance with tension and compression. The internal forces of the 9th and 10th diagonal members are more complicated due to the prestressing force effect, and the alternating change rule of tension and compression is no longer maintained. The maximum tensile stress is concentrated on the 1st, 5th, and 12th vertical members, and the maximum compressive stress is focused on the 2nd and 11th diagonal members. For the nodes, the maximum tensile stress is mainly concentrated at the ends of both sides of the bridge, and the outer edges of NP 11–12 and NP 1–2 are subjected to more stress.According to the static analysis results, the end node of the main span of the simply supported bridge are in an extremely dangerous state and easily susceptible to damage or destruction just by being under the action of self-weight load. This phenomenon may be an indication that the bridge is not structurally sound and has a congenital defect.The structure collapsed immediately after the 11th diagonal member failed during the course of this accident. The failure mode of the structure and the failure sequence of various parts of the structure during the collapse process are studied by analyzing several different instantaneous behavior characteristics. The displacement time history curve of each node after the removal of the 11th diagonal member is shown in , reflecting the vertical displacement variation characteristics of each node at different stages. The figure shows that NP 9–10 first falls to the ground at approximately 0.9 s, followed by NP 7–8 falls to the ground at approximately 1.1 s.The vertical displacement curves of the structure at different times is shown in , reflecting the collapse characteristics of the structure at different times. The 11th diagonal member is removed at the initial moment. At 0.3 s, severe local damage occurs at a position approximately 10 m from the north end of the structure (NP 9–10) and shows the characteristics of plastic hinges. The maximum displacement is approximately 1 m. In the next 0.6 s, the displacement of the structure continues to increase, gradually falling to the ground.The damage of the 12th vertical member and 9th diagonal members at each moment is shown in , respectively. The entire collapse process of the structure can be described by referring to Within 0.3 s after the failure of the 11th diagonal member, the tensile force of the 10th diagonal member increases, resulting in a sharp increase in stress at NP 10–11 and the subsequent failure of the node. Afterward, the canopy of the deck and the 9th diagonal member at NP 9–10 become bent and severely damaged [(a)]. The lower part of the 12th vertical member is destroyed, and cracks soon appear in the deck [(a)]. At this time, the structure has already shown prominent bending deformation characteristics [(b)], and the maximum displacement is at the bottom of NP 9–10.At 0.6–0.8 s, the deck at NP 9–10 is completely broken, and the canopy at the 9th diagonal member is severely damaged [(b) and (c)]. NP 11–12 is completely disconnected, and the deck begins to break away from the pier [(b) and(c)]. At this time, the structure cannot bear its weight, and the whole structure accelerates fall.At approximately 1.0 s, the deck at NP 9–10 first falls to the ground and breaks; the upper canopy at the 9th diagonal member is almost destroyed [(d)]. The 12th Vertical member slants down with the canopy, and the entire lower deck disengages from the structure and falls [At 1.2 s, the structure collapses entirely, and most of the bridge structure falls on the road [The analysis shows that the 2nd and 11th diagonal members are crucial for this simply supported concrete bridge. The nodes at the bottom of the two truss members are subject to complicated internal forces and are easily broken. Once the node fails, its connected components can no longer bear the load. Therefore, the actual video of the accident and the FE simulation results show that within 1–2 s after the failure of the 11th diagonal member, the overall structure cannot remain stable; total collapse occurs after severe local damage.The collapse and failure behavior of structures can be accurately simulated when the CDP model is adopted; however, the difficulty of calculation convergence considerably increases. A degraded CDP model that ignores damage evolution behavior can be used to examine the effect of material damage on structural collapse behavior. shows the calculation results using the CDP model, whereas shows the calculation results using the degraded CDP model. A comparison between the two results shows evident differences.In the case of the diagonal member No. 11 being removed and the simplified constitutive model being adopted, the displacement time histories of several nodes of the structure are presented in . As shown in the figure, the members NP9-10 and NP7-8 fall on the ground at 1.12 s and 1.28 s respectively, whereas they take 0.9 s and 1.1 s as shown in with the simulation using the complex constitutive model. This comparison indicates that the collapsing duration of the structure using the simplified model is longer. Obviously, this is due to the fact that the material damage softening is not considered in the simplified material constitutive model. shows the displacement profiles along the span at different instants with the simulation using the simplified constitutive model. It can be observed that the position where the structure initially contacts the ground is approximately at 17.2 m away from the end of the span, whereas the corresponding distance in is approximately 15 m. This is obviously due to the fact that the damage behavior is not taken into account in the simplified material constitutive model, which leads to the larger overall stiffness of the structure. Compared with the actual collapsing process, the complex constitutive model incorporating damage can yield the collapsing behavior of the structure more accurately.The collapse behavior of an engineering structure is a highly nonlinear and discontinuous dynamic process in reality. From the initial material yielding and damage to the subsequent cracking and failure of the component until the final structure falls and collides with other parts, such a process makes numerical simulation extraordinarily complicated. Moreover, the nonlinear behavior of the material also makes convergence difficult and the model difficult to refine. The complexity of the calculation increases greatly due to the damage softening effect of the material. In addition, severe local deformation also means that numerous concrete materials have begun to soften and become damaged or even fractured., thus increasing the difficulty of convergence during the analysis. In this study, the equivalent rebar smeared calculation model is adopted for simulate the FIU bridge collapse. The problem of numerical solution convergence difficulty due to material nonlinearity is solved, and a certain precision is ensured. Transferring results between the ABAQUS/Explicit and ABAQUS/Standard method is executed to avoid unrealistic structural response problems caused by the inertial effect in the dynamic analysis. On this basis, the study can simulate the entire process of structural collapse and reproduce the virtual scenario of the bridge collapse.Numerical analysis results show that (1) the total duration of the structural collapse process is approximately 1.2 s, which is the same as the result of the video recording; (2) the structural deformation and failure modes of each moment and the final collapse mode are compared with the video; both results are almost identical. Thus, the simulation results almost reproduce the actual collapse behavior. This result fully demonstrates that the FE technique and material damage and constitutive failure model used in this study are appropriate, and the numerical results obtained are accurate. The results obtained in this study are extraordinarily rare compared with most large-scale structural collapse behaviors in other literature because distinguishing their accuracy is difficult. Therefore, using FE technology to analyze the entire process of large engineering structure collapse and damage accidents is feasible. The calculation method used in this study can also provide a reference for the simulation of such structures.Based on these findings, this study profoundly analyzes the shape characteristics of each moment in the process of structural collapse and discusses the reasons for its structural collapse.Although the cause of the failure of the 11th diagonal member cannot be determined, its failure is the key to the collapse of the entire bridge. In the design of the structure, the 11th diagonal member is at the junction of the main span and the subspan (back span), and its position is crucial. However, this component is weak in terms of design. Once the 11th diagonal member fails, the entire FIU bridge will collapse.From another point of view, the entire process of the accident shows that the local damage of the structure eventually leads to a large-scale overall collapse, indicating a lack of structural robustness in the design process. If other components are present instead of the damage role, the structure may not have such a serious accident.In summary, the following conclusions can be drawn from the FIU bridge collapse analysis: (1) The collapse of the FIU bridge was caused by the failure of the 11th diagonal member. (2) The structural robustness of the FIU bridge is weak. The force transmission path is relatively simple, leading to a massive change of the internal force of the other parts of the structure once a breakdown occurs in an individual link. This change may cause a large-scale progressive collapse due to local damage or failure.Ya-Chao Hu: Software, Data curation, Investigation, Writing - review & editing. Ying-Hua Tan: Software, Investigation, Writing - original draft. Feng Xi: Funding acquisition, Methodology, Investigation, Resources, Project administration, Supervision, Conceptualization, Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.The plastic strain distribution of each part with different mesh density (10–320 K) models was compared to examine the mesh convergence. are the contours of the maximum principal strain at the 1st vertical member and NP 4–5 with different number of elements. As the mesh density increases, the distribution of the nonelastic region near the 1st vertical member gradually stabilizes and is mainly concentrated in NP 1–2. The distribution of the nonelastic region at NP4-5 also shows the same trend. Moreover, the plastic strain at the node is concentrated at the junction of the node and the canopy due to the prestress. An increase in mesh density causes the damage to concentrate in a small area, and the total strain energy of the structure decreases.Supplementary data to this article can be found online at The following are the Supplementary data to this article:Combinatorial development of the low-density high-entropy alloy Al10Cr20Mo20Nb20Ti20Zr10 having gigapascal strength at 1000 °CA pseudo-ternary combinatorial approach to AlxTayVzCr20Mo20Nb20Ti20Zr10 revealed the composition of refractory high-entropy alloys characterized by outstanding high-temperature yield strength. Compression testing of Al10Cr20Mo20Nb20Ti20Zr10 disclosed yield strengths of 1206 MPa at 1000 °C, one of the highest values reported for refractory high-entropy alloys. Ta-containing AlxTayVzCr20Mo20Nb20Ti20Zr10 presented a lower high-temperature strength, while characterization of Al10Cr20Mo20Nb20Ti20Zr10 showed C14 Al2Zr- and NbCr2-type hexagonal Laves intermetallics, with a hardness of ∼10.5 GPa (higher than that of the body centered cubic phase, at ∼9 GPa). The stronger bonds between Al and transition metals appear to give rise to extraordinary load-bearing capabilities in Al10Cr20Mo20Nb20Ti20Zr10, at high temperatures. Owing to this rare combination of relatively low density (6.96 g/cm3) and remarkable high-temperature strength, Al10Cr20Mo20Nb20Ti20Zr10 has emerged as a potential material for high-temperature structural applications.Refractory high-entropy alloys (HEAs, having 5–13 elements in 5–35 at.%) [] are being explored for possible applications in the aerospace, automobile, and power industries. Several refractory HEAs with promising heat-resistant properties, including high strength levels (e.g., MoNbTaW (405 MPa at 1600 °C) and MoNbTaVW (477 MPa at 1600 °C) []), and oxidation resistance (e.g., 0.5 mg/cm2 weight gain in AlCrMoNbTi after oxidation, for 1 h at 900 °C, in air [Exchanging constituents and varying element concentrations significantly affect HEA properties []. The replacement of Ta in HfNbTaTiZr, with Mo, to develop HfMoNbTiZr, improved its room-temperature compressive strength from 1250 MPa to 1719 MPa [], while adding Al to AlxNbTaTiV led to a yield strength improvement from 1092 MPa (x = 0) to 1330 MPa (x = 0.25) []. Composition modifications like these have led to the development of AlMo0·5NbTa0·5TiZr, which has shown an impressive combination of high-temperature mechanical properties, that is, a compressive yield strength of 745 MPa, and a fracture strain of >50% (at 1000 °C) [Although several HEAs with promising properties have been reported, the achievement of desirable properties remains somewhat unpredictable []. Studying combinatorial HEA libraries containing ranges of elements—with the aim of discovering promising compositions with improved properties for further development and commercialization—is therefore useful. In our previous study, we undertook the combinatorial development of the novel HEAs AlxCryMozNbTiZr (x, y, and z: 10–30 at.%), which revealed relatively good oxidation resistance, as Al20Cr10Mo10Nb20Ti20Zr20 and Al30Cr10Nb20Ti20Zr20 (21 mg/cm2 and 20 mg/cm2 weight gains, after 20 h of oxidation at 1000 °C, respectively) [], when compared to several other refractory HEAs and conventional alloys. We focused on Al20Cr10Mo10Nb20Ti20Zr20, as the presence of Mo in this HEA suggested it would exhibit good strength at high temperatures.In this study, we locked in the base composition as Cr20Mo20Nb20Ti20Zr10, and decided to vary the Al content, from 0 to 10 at.%, to achieve a balance between oxidation resistance and strength, with a gradual increase/decrease of Ta and V, at the cost of 10 at.% Zr (so that oxidation resistance could be improved []), considering their renown in HEA strengthening []. In this way, we designed a pseudo-ternary combinatorial system of HEA, that is, AlxTayVzCr20Mo20Nb20Ti20Zr10 (AlxTayVz-Q, where x + y + z = 10 at.%, and Q is the quinary Cr20Mo20Nb20Ti20Zr10).Arc melting of 99.9% metal sources to develop AlxTayVz-Q HEA samples () was carried out using an ACM-01 arc melting furnace (DAIA-VACUUM, Japan). Sample remelting (five times) and further homogenization (at 1200 °C for 24 h, followed by air cooling) were carried out to improve their chemical homogeneity. Microstructural examinations were carried out by X-ray diffraction (XRD, D/MAX-2500, Rigaku, USA), scanning electron microscopy (SEM, FEI Magellan 400, USA), and energy dispersive spectroscopy (EDS, coupled with SEM). The contribution of each phase to the respective alloy’s mechanical properties was analyzed by taking nano-indentation hardness measurements of each phase, using an iNano nano-indentor (Nanomechanics, Inc., USA). Cylindrical samples, with dimensions of 6 mm × 3 mm and 8 mm × 3 mm (length × diameter), were subjected to both room-temperature and high-temperature (1000 °C) compression tests, at a strain rate of 10−4/s, using an Instron 5982 device.The pseudo-ternary combinatorial library of post-homogenization microstructures, along with three representative X-ray diffraction analyses, are shown in . The SEM micrographs show a granular microstructure, with secondary phases in the intergranular region. Refractory HEAs typically show various types of hexagonal (C14) and cubic (C15) Laves intermetallics []. XRD analysis of homogenized AlxTayVz-Q revealed a major body-centered cubic (BCC) phase, along with secondary phases. The representative XRD patterns for homogenized AlxTayVz-Q are shown in Al10-Q, Ta10-Q, and V10-Q mainly show BCC phases, with 0.303, 0.303, and 0.319 nm lattice parameters, respectively, (). Al2Zr- and NbCr2-type C14 Laves were identified in Al10-Q, while Cr2Zr-type C14 and Cr2Ta-type C15 Laves were observed in Ta10-Q, with V10-Q showing (CrV)Zr-type C15 Laves. The volume% of the Laves phases in Al10-Q, Ta10-Q, and V10-Q, as determined by image analysis, were 30 vol%, 35 vol%, and 22 vol%, respectively. Laves phase formation was observed in HEAs using Allen electronegativity differences (ΔXAllen), atomic size differences (δr), and d-orbital energy levels (Md) exceeding 7%, 5%, and 0.915 eV, respectively []. The occurrence of the Laves phase in HEAs is estimated by comparing ΔXAllen, δr, and Md with these criteria, so using these methods, we calculated ΔXAllen, δr, and Md for AlxTayVz-Q, and found them to be in the ranges of 7.38–7.74%, 6.35–6.62%, and 1.865–1.933 eV. These values suggested the formation of Laves phases in AlxTayVz-Q.EDS analysis results for the Laves phases observed in V10-Q, Al10-Q, and Ta10-Q are shown in (a), (d), and (g), respectively. In addition to the main constituents of Laves phases identified by XRD, notable concentrations of other elements were also present in the Laves intermetallics, suggesting the possible formation of high-entropy intermetallics, which could be a promising area for future research [The literature shows higher high-temperature mechanical properties for Laves phase intermetallics than for BCC solid solutions []. The Laves phases maintain their strength at elevated temperatures and enhance high-temperature strength in Laves-containing HEAs []. In order to confirm the role of the continuous network of Laves phase intermetallics, with regard to the increased strength of Al10-Q, we carried out nano-indentation hardness tests on the dendritic (BCC) and interdendritic (Laves intermetallics) regions of V10-Q, Al10-Q, and Ta10-Q. These tests were repeated five times at different points in each region, and the average results are shown in (c), (f), and (i). High scattering in the nano-indentation hardness data was observed near the surface, and the hardness decreased with increasing indentation depth. The nano-indentation hardness data were processed using the Nix-Gao model, to extract the hardness of the sample. The Nix-Gao model, expressed as shown in Eq. (i) showed a gradual decrease in the measured hardness (H) up to the bulk hardness (H0), with increased indentation:The hardness at a critical depth (d∗) is regarded as the representative or bulk-equivalent hardness of the samples, with values listed in Although nano-indentation data can have errors—because the stress field generated during indentation is not limited to a single phase—it can be used for comparative analysis. The comparison of the hardness values of the BCC and Laves phases clearly showed significantly higher hardnesses for the Laves phases than those for BCC phases, which demonstrated the significant contribution of the Laves phases to the mechanical behavior of AlxTayVz-Q.This behavior, under a compressive load, is shown in . The interchange between 10 at.% V, Al, and Ta did not impart any significant alteration of the room-temperature compressive yield strength ( (a)), as V10-Q, Al10-Q, and Ta10-Q showed similar strengths—that is, 1572, 1692, and 1626 MPa, respectively. It should be pointed out that the newly developed RHEAs show brittleness at room temperature with the maximum compressive strain around 3%. However, as there are some promising examples of ductile RHEAs showing tensile ductility at room temperatures such as HfNbTiZr and HfNbTaTiZr [], a further study for the ductilization of the strong RHEA compositions should be necessary for their industrial applications in the future.The ductilization of the promising composition can be achieved by microstructural engineering. There have been remarkable achievements for the ductilization of RHEAs to overcome the conflict between high-temperature strength and room-temperature ductility. One such example has been reported by Soni et al. []. The change in strength due to phase transformation is inevitable, therefore the HEAs-based composites are also being exploited as reported in Mileiko et al. []. Waseem et al. were able to achieve significant enhancement in the toughness of W0·5TaTiVCr without sacrificing strength [], which suggests that the extrinsic toughening can potentially play an important role in the development of novel RHEAs with a good combination of high-temperature strength and room-temperature ductility.High-temperature strength is one of the most important characteristics of refractory HEAs; therefore, compression tests for AlxTayVz-Q were also carried out at 1000 °C, to assess the role of Al, Ta, and V in imparting high strength in AlxTayVz-Q.The results showed that Al10-Q exhibited a strength of ∼1200 MPa, at 1000 °C ( (b)), while, in contrast, V10-Q and Ta10-Q achieved values of ∼830 MPa and ∼500 MPa, respectively, under the same conditions. Published HEA literature includes reports of improved high-temperature strength due to the addition of Ta; for instance, HfMoNbTaTiZr and HfMoNbTiZr exhibited 814 MPa and 600/721 MPa strengths, respectively, at 1000 °C [], although our study has revealed rather different Ta behavior—that is, reduction in high temperature strength due to Ta addition.In order to compare the high-temperature yield strength and density of various HEAs, we extracted data from the literature, as shown in ]. We divided these HEAs into several groups, based on the degree of similarity between their compositions and ours. For example, the group/region marked as AlCrNbTiV (Zr) represents the high-temperature compressive strengths and densities of the HEAs AlCrNbTiV, AlCr0·5NbTiV, AlCrNbTiV, AlCr1·5NbTiV, Al0·5CrNbTi2V0·5, Al0·25CrNbTiVZr, Al0·5CrNbTiVZr, and AlCrNbTiVZr, in which Al, Cr, Nb, Ti, and V were present in every alloy, whereas Zr may or may not have been present. The actual HEA compositions are also shown in the legend. The strength–density regions of the various HEAs (as shown in ) show the extent to which the strength and density of certain HEAs can be varied by adding, removing, and/or changing the concentration(s) of the elements shown in parentheses. Reported refractory HEAs with density levels <7 g/cm3 showed relatively low high-temperature yield strength, which would hinder their high-temperature structural applications. In contrast, some stronger HEAs showed high density levels, and therefore would not suit the application to the automobile or aerospace industries, where light alloys are needed.The strength–density region of the AlxTayVz-Q HEA system can be seen to have covered a wide range of high-strength values, while maintaining relatively low density, indicating that AlxTayVz-Q provided the opportunity to design numerous new HEAs characterized by desirable combinations of high-temperature strength and lower density levels. These data also highlighted the outstanding high-temperature compressive strength of Al10-Q HEAs (higher than all other refractory HEAs known thus far).The mismatch between the atomic sizes of Al and the other Al10-Q constituents results in lattice distortion—and so, consequently, the mechanical strength of Al10-Q increases. However, the atomic size difference was relatively higher in the case of V10-Q (), so that the mismatch induced in Al10-Q by the atomic size of Al cannot have been the only reason for the promising strength of Al10-Q.In order to reveal the mechanism behind the strengthening brought about by the addition of Al in refractory HEAs that incorporate transition metals and Al, Qui et al. performed density functional theory (DFT) calculations []; these calculations revealed the hybridization of p and s states from Al atoms, with d states from transition metals, which resulted in the formation of strong, directionally angular bonds between the Al atoms and their neighbors in transition metals. Such strong bonds were not detected between the constituents of Al-free refractory HEAs [], supporting the fact that the addition of V and Ta in Cr20Mo20Nb20Ti20Zr10—to form V10-Q and Ta10-Q, respectively—did not result in a remarkably strong HEA. In addition to the hybridization of the p and s states from Al atoms, the presence of Mo in AlxTayVz-Q also facilitated high temperature strength, while Mo-free RHEAs, such as AlNbTiV(Zr) and/or AlCrNbTiV(Zr) () showed remarkably low strength, at 1000 °C.We have carried out combinatorial synthesis and analysis of a refractory HEA (AlxTayVz-Q), and explored a novel HEA, Al10Cr20Mo20Nb20Ti20Zr10, which exhibited gigapascal strength and low density, at 1000 °C, and showed that it possessed characteristics considered very desirable for the application to the aerospace, automobile, and power industries. To understand this potential better, additional research into high-temperature oxidation resistance of AlxTayVzCr20Mo20Nb20Ti20Zr10 has been reported [In summary, combinatorial synthesis and analysis of AlxTayVzCr20Mo20Nb20Ti20Zr10 (x, y, and z: 0–10 at.%) high-entropy alloys were carried out. Arc-melted samples were homogenized at 1200 °C for 24 h and air cooled. Considering the potential load-bearing applications of HEAs, quasi-static compression tests were conducted, at room temperature and 1000 °C, and analysis of the compressive stress–strain curves revealed outstanding high-temperature strength, for Al10Cr20Mo20Nb20Ti20Zr10 (Al10-Q) (1206 MPa), along with low density (6.96 g/cm3). Thorough characterization of the Al10-Q microstructure, using XRD and EDS analyses, revealed Al2Zr- and NbCr2-type hexagonal Laves. The BCC phase revealed a bulk equivalent hardness of 9 GPa, while for Laves intermetallics, the result was 10.5 GPa. These promising mechanical characteristics suggest that this low-density, ultra-strong HEA (Al10-Q) has very good potential for future, high-temperature applications.Both authors contributed to the manuscript preparation. Owais Ahmed Waseem performed the experiments and analyzed results under the direct supervision of Ho Jin Ryu. Both authors reviewed the manuscript.Owais Ahmed Waseem: Writing - original draft, Investigation, Methodology. Ho Jin Ryu: Conceptualization, Writing - review & editing, Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Ultimate resisting capacity of slender RC columnsIn this paper, nonlinear analyses of slender RC (reinforced concrete) columns are conducted, and an improved criterion to estimate the load carrying capacity of slender RC columns is proposed. To simulate material nonlinearity including the cracking of concrete, the layer model is adopted, and the initial stress matrix is considered for the simulation of the P–Δ effect. After correlation studies with previous experimental and numerical results to verify the accuracy of the numerical model developed, numerous parametric studies are conducted, and a regression formula that can give a more exact resisting capacity of slender RC columns is proposed on the basis of the numerical results obtained. Finally, the P–M interaction diagrams constructed from the proposed formula are compared with those constructed from a rigorous nonlinear analysis with the objective of establishing the accuracy of the proposed formula. From the results obtained, it is found that the proposed equation is effective in determining an initial section of slender RC columns at the preliminary design stage.A reinforced concrete (RC) column, which is one of the primary structural members, is subjected to axial force and bending moment which may be due to end restraint arising from the monolithic placement of floor beams and columns or due to eccentricity from imperfect alignment. Due to the combination of axial force and bending moment, the column section must be designed to ensure that the forces acting on a member fall inside the P–M interaction diagram representing the resisting capacity of the column. Recently, because of architectural aesthetics and efficiency in use of space, relatively slender columns have frequently been used in many building structures, either throughout the entire building or in some parts of the structure, e.g. the exterior of buildings and the interior of lobbies. Moreover, the use of higher strength steel and concrete has led to an increased use of slender members. However, as slender RC columns may fail not only by material failure in a section but also by instability of a structure, they require more rigorous numerical analyses which consider secondary effects such as the P–Δ effect and creep deformation of concrete in order to meet their strength and serviceability requirements.There has been a lot of research on the behavior and design of slender RC columns. On the basis of the force equilibrium equation and the strain compatibility condition at a section, Bazant et al. To permit the flexibility in structural design, specifications must provide for adequate determination of column strength with any slenderness ratio. Thus, most design codes In this paper, an analytical model to predict the resisting capacity of slender RC columns is introduced. Material and geometric nonlinearities are taken into account, and the layer approach is adopted to simulate the different material properties across the sectional depth. However, consideration of the time-dependent deformation of concrete is beyond the scope of this paper. The validity of the numerical model is established by comparing the analytical predictions with results from previous experimental and analytical studies Generally, the ultimate compressive force P and the ultimate bending moment M for an RC column section are related to each other by means of an interaction diagram (P–M interaction diagram). In the absence of second-order effects (P–Δ effect), as in very short columns, the cross-section would undergo proportional loading until reaching the material strength at point A of the cross-section interaction diagram (see ). Slender columns, however, will follow the loading path up to point B where the material strength is reached. Point B is on the cross-section interaction diagram but is at a smaller axial load, P2 than it would be if L/r were actually zero. If the column fails due to instability, it would follow the path up to point C, that is it would be unable to reach the cross-section interaction diagram. The larger the column slenderness ratio, the greater is the reduction in the axial force resistance.For not too slender columns with the slenderness ratio of L/r⩽100, the failure occurs at points rather close to the material strength. For very slender columns, on the other hand, the failure occurs well within the cross-section interaction diagram because of a pronounced second-order effect. Referring to the structural behavior of RC columns, material nonlinearity of steel and concrete is taken into account for more exact estimation of the ultimate resisting capacity of RC columns. Moreover, the failure of RC columns must be assumed to occur as a result of material failure only because the slenderness ratio in most RC columns designed in practice is smaller than the critical slenderness ratio that causes instability failure.The response of RC columns under loads depends to a large extent on the stress–strain relation of the constituent materials and the magnitude of stress. Since concrete is used mostly in compression, the stress–strain relation in compression is of primary interest. Among the numerous mathematical models currently used in the analysis of RC structures, the monotonic envelope curve introduced by Kent and Park , the monotonic concrete stress–strain relation in compression is described by three regions:where εc0 is the concrete strain at maximum stress, K is a factor which accounts for the strength increase due to confinement, Zi is the strain softening slope, fc′ is the concrete compressive strength in kg/cm2 (1 kg/cm2=0.098 MPa), fyh is the yield strength of the stirrups in kg/cm2, ρs is the ratio of the volume of hoop reinforcement to the volume of concrete core measured to the outside of the stirrups, h′ is the width of the concrete core measured to the outside of hoops or ties, and sh is the center to center spacing of tie or hoop sets.On the other hand, it is assumed that concrete is linearly elastic in the tension region. Beyond the tensile strength, the tensile stress decreases linearly with increasing principal tensile strain (see ). Ultimate failure is assumed to take place by cracking, when the principal tensile strain exceeds the value ε0=2·Gfft′·ln(3/b)/(3−b) in , where b is the element length and Gf is the fracture energy that is dissipated in the formation of a crack of unit length per unit thickness and is considered a material property. The value of ε0 is derived from the fracture mechanics concept by equating the crack energy release with the fracture toughness of concrete GfReinforcing steel is modeled as a linear elastic, linear strain hardening material with yield stress fy as shown in . The reasons for this approximation are: (1) the computational convenience of the model; and (2) the behavior of RC members is greatly affected by the yielding of reinforcing steel when the structure is subjected to a monotonic bending moment In order to formulate the constitutive relationships in a layer of an RC column, the following simplified assumptions have been made: (1) The element is divided into imaginary layers to describe the different material properties; (2) plane sections remain plane to represent the linearity in the strain distribution on any section at any loading history; (3) a perfect bond between the concrete matrix and reinforcing bars is assumed; and (4) the constitutive materials are assumed to carry uniaxial stress only. In addition, shear deformation is not taken into account in the formulation because the shear effect is expected to be very small in slender RC columns.Unlike a beam element subjected to a bending moment only, a column element is subjected to both axial force and bending moments, so that the neutral axis of a column section cannot be calculated directly by the equilibrium condition of normal force only. To determine the neutral axis while considering bending effects, the total strain (εt) in concrete and steel needs to be partitioned into an axial strain (εa) and a bending strain (εb). Since the axial strain is constant across the section and the bending strain is zero at the neutral axis, the bending strains of concrete and steel at any layer can be calculated by εb=εt−εa. Based on the assumed neutral axis, the stress corresponding to the total strain can be calculated from the stress–strain curves of the constitutive materials, and iterations using the bisection method are repeated until errors for the axial force and bending moment calculated by the total strain and bending strain are within the given tolerances.Based on the assumed displacement field formulation, all the constitutive equations including the element stiffness matrix are derived. As shown in , the nodal displacement vectors of a two-dimensional beam element in its local coordinate system can be expressed by and the nodal displacements of an element may be expressed as the column vector Assuming that the independent axial displacement U0(x) varies linearly with x, and the small rotation θi at each node can be calculated by derivation of the vertical displacement vi with respect to x, the displacements U0(x) and V(x) at any point within the element can be expressed bywhere φ=[(1−p),p] and ψ=[(1−3p2+2p3),(3p2−2p3),L(p−2p2+p3),L(−p2+p3)] are the displacement shape functions, and the non-dimensional parameter p denotes x/L, that is, the position along the axis of the beam element.Then, by adopting the plane section hypothesis, the x displacement U(x) at any point can be written by the relation . Accordingly, x displacement U(x,y) and y displacement V(x,y) may be expressed in terms of the displacement column vector r,where ψ,x is the first-order derivative of ψ with respect to x.In addition, the axial strain ε(x,y) can be defined bywhere the second term denotes the nonlinear displacement effect.When a finite change in the joint displacement Δr occurs, corresponding changes in the strain Δε can be expressed bywhere B=[φ,x,−yψ,xx]=[−1/L,1/L,y(1−2p)(6/L2),y(−1+2p)(6/L2),y(2−3p)(2/L),y(1−3p)(2/L)]. Moreover, the incremental strain–displacement relationship of dε=B·dr+drT·cT·c·Δr=drT·(B+cT·c·Δr) can be developed by taking the differential from Eq. Applying the virtual work principle to a finite element on the basis of the energy conservation law and neglecting a higher-order incremental term, the incremental of nodal force vector ΔRj applied at node j can be written from Eq. While calculating the elastic stiffness Ke and the geometric stiffness Kg, the value of E at each layer is assumed to be held constant along the element length. Thus the volume integration in Eq. can be represented by the inner product of the line integration along the element length and the area integration across the sectional depth. Moreover, employing the layer approach, wherein a typical section is divided into imaginary layers, the sectional stiffness terms of EA and EI in Eq. can be evaluated by summation over all layers, i.e. , where nc and ns denote the number of concrete and steel layers respectively, Ai and Ei are the sectional area and elastic modulus of ith layer, yi is the distance from the centroid, and P refers to the applied force.Every nonlinear analysis algorithm consists of four basic steps: the formation of a current stiffness matrix, the solution of the equilibrium equations for the displacement increments, the state determination of all elements in the model, and a convergence check. Since the global stiffness matrix of the structure depends on the displacement increments, the solution of the equilibrium equations is typically accompanied by an iterative method through the convergence check. The nonlinear solution scheme selected in this paper uses a tangent stiffness matrix at the beginning of each load step in combination with a constant stiffness matrix during the subsequent correction phase, that is the incremental-iterative method is employed.The criteria for measuring the convergence of the iterative solution are generally based on the accuracy of satisfying the global equilibrium equations or on the accuracy of determining the total displacements. The accuracy of satisfying the global equilibrium is controlled by the magnitude of the unbalanced nodal forces. Hence the convergence criteria for the unbalanced nodal forces are used in this paper, and these can be expressed as are the absolute values of the maximum unbalanced axial force and bending moment, respectively, and Tol.F and Tol.M are the specified tolerances corresponding to the axial force and bending moment. Tol.F=Tol.M=0.01 are taken as the tolerances in this study, and more details for the solution procedures can be found elsewhere The experimental results from several hinged RC columns tested by Kim et al. The ultimate loads of columns measured experimentally are compared with those obtained from the proposed numerical model in . Regardless of compressive strength of concrete and the slenderness ratio, good agreements were obtained for the individual columns, leading to the conclusion that the introduced numerical model can accurately predict the ultimate loads of hinged RC columns. In addition, , representing a typical relation between the axial force and lateral deflection at the mid-height The second group of specimens used to validate the proposed analytical model is a series of columns with a width × depth of 200 mm × 300 mm. These columns were tested by Chuang et al. , which shows the experimental results and the analytical predictions, it can be seen that the proposed numerical model accurately predicts the ultimate load regardless of the eccentricity ratio.An additional comparison with numerical calculations introduced by Bazant et al. . The same material properties of concrete and steel as those in the previous analytical study are used and have the following values: fc′=5000 psi (352 kg/cm2), Es=29×106 psi (2.04 × 106 kg/cm2) and fy=60,000 psi (4220 kg/cm2).For the design of slender RC columns, ACI318 Moreover, as mentioned in a previous study , the results from the proposed numerical model are in good agreement with those of Bazant et al. also leads to the following conclusions: (1) as the slenderness ratio increases, the difference between the ACI strength interaction curve and the proposed model gradually increases; (2) the ACI method may underestimate the resisting capacity of slender RC columns; and (3) the ACI method does not achieve a uniform safety margin, defined in this study as the uniform difference between the results predicted by the ACI method and the results calculated by a rigorous analysis, over the entire interaction diagram for columns with L/r=70 and 100.The ultimate resisting capacity of slender RC columns is affected by many variables in addition to the compressive strength of concrete, such as the slenderness ratio, steel ratio, eccentricity, etc. In order to isolate the effect of these variables, a parametric study is conducted. The same cross-section dimensions as those used in the previous analytical verification are used (see ). Two values of steel ratio (ρs=0.03 and 0.08) are investigated and the slenderness ratio is limited to a maximum L/r=70, because the slenderness ratio of RC columns generally used in design practice is less than 70. The following material properties are assumed: fc′=360 kg/cm2, Es=2.1×106 kg/cm2 and fy=4350 kg/cm2. The resulting strength interaction curves in terms of primary bending moments are given in , the P–Δ effect appears more significant as the steel ratio decreases. This seems to arise from the fact that columns with relatively small steel ratios have a smaller bending stiffness EI at the post-cracking state, leading to the increase in both the lateral deflection and accompanying P–Δ effect. On the other hand, the P–Δ effect is gradually reduced as the slenderness ratio decreases and finally disappears in short columns (L/r=10 and 30). Thus the steel ratio has a minor influence on the P–Δ effect in columns with low slenderness ratios (i.e., L/r⩽30).In addition, the P–Δ effect increases with an increase in the eccentricity until the eccentricity e reaches the balanced eccentricity eb. It then gradually decreases for e>eb and disappears when the applied axial force P becomes zero.It is apparent from the comparison of the ACI results with rigorous analyses shown in and related discussion on that the development of a simple design formula, which can yield results similar to those obtained from a rigorous analysis regardless of the slenderness ratio and eccentricity and which can also be readily applied for the selection of an RC column section at the preliminary design stage, become highly desirable.Since the ultimate resisting capacity of RC columns is governed by many variables and is gradually reduced as the slenderness ratio increases because of the P–Δ effect, it is necessary in many cases to conduct a rigorous numerical analysis that considers material and geometric nonlinearities to accurately predict the ultimate strength of slender RC columns. However, nonlinear analyses are time consuming and costly. To directly determine the ultimate resisting capacity of slender RC columns, a strength reduction coefficient is introduced in this paper. If a rigorous analysis is conducted at the final design stage, after selecting the section at the preliminary design stage with the proposed formula, then one can expect an efficient design, as the formula very closely estimates the ultimate resisting capacities determined through rigorous nonlinear analyses of slender RC columns.When the dimensions of the concrete section and the material properties of concrete and steel have been selected, the P–M interaction diagram of a section representing the ultimate resisting capacity is constructed through a section analysis on the basis of the force equilibrium and compatibility condition. However, as a long column is accompanied by the P–Δ effect, the P–M interaction diagram cannot be easily determined. If a strength reduction coefficient F is defined as the normalized ratio of the difference in the ultimate resisting capacities of an RC section and a slender column with respect to the RC section taken at the same eccentricity F=(OA−OB)/OA in , then the ultimate resisting capacity of a slender RC column can be easily determined from (Pn·(1−F),Mn·(1−F)) without conducting additional rigorous numerical analyses.To introduce a design formula for the strength reduction coefficient F, however, the following difficulties must be overcome: (1) the P–M interaction diagrams must be determined for a column section (equivalent to a short column) and for long columns with the same design variables; (2) the calculated strength reduction coefficient F does not maintain a constant value but changes according to the eccentricity and the slenderness ratio; (3) unlike structural steel members, RC columns do not use the commercially available standard sections. Theoretically, an infinite number of RC column sections can be designed for the applied external forces. Hence, in determining RC column P–M interaction diagrams, all the variables need to be assumed on the basis of practical limitations and the design code requirements. The commonly used compressive strength of concrete and yield stress of steel for column design are fc′=360 kg/cm2 and fy=4350 kg/cm2 (Grade 60 steel), respectively. In addition, the steel ratio ranges from 0.02 to 0.08, the slenderness ratio from 20 to 70, and the eccentricity from 0.04 to 1.1 h. These ranges of variables were selected for the numerical analyses conducted in this paper for developing the strength reduction coefficient F.The calculated strength reduction coefficients F for RC columns with ρs=2% and 6% are marked with different symbols for different eccentricities in , respectively. This figure shows that the strength reduction coefficients F increase in proportion to the slenderness ratio L/r and have larger values as the steel ratio decreases. Note that an increase in coefficient F indicates a reduction in the ultimate resisting capacity. also shows that the coefficient F of a slender RC column with ρs=2% is significantly affected by the eccentricity. From , it appears that the strength reduction coefficient F reaches its maximum value when the eccentricity e reaches a value near the balanced eccentricity eb.Hence, the regression formula for the strength reduction coefficient F is developed on the basis of the upper limit values in order to include the P–Δ effect conservatively. This is because the eccentricity e is not included in the regression equation for F for the sake of simplicity. Fortunately, as shown in , the scatter in values of the coefficient F over the practical range of eccentricity appears relatively small (from minimum values represented by dashed lines in to maximum values represented by solid lines in ). Therefore, the regression formula given in was chosen, and the regression results obtained are listed as Eq. The regression formula, noted above, was developed on the basis of the upper limit values for the strength reduction coefficients (see ). Hence, the direct application of this formula to regions with very small eccentricity (e⩽emin,emin=0.6+0.03 h (in) defined in the ACI318-02) and with very large eccentricity (e⩾1.2eb) will give conservative results because of the scatter of the coefficient F in these regions (see ). If the eccentricity e is infinity, then the strength reduction coefficient F must theoretically become zero. On the other hand, rigorous P–Δ analyses show a slightly steep decrease of the axial load carrying capacity at the region with very small eccentricity (e⩽emin). Hence, the corrected regression formulas of Eqs. are used for each boundary region, as shown in show the differences in long column design using the method involving proposed formula as opposed to the ACI method. As shown in this table, the ACI method requires the magnification of the applied ultimate moment Mu by multiplying it by a magnification factor δ. A column section is then designed to ensure that the ultimate load Pu and the magnified ultimate moment δ·Mu exist inside the P–M interaction diagram of the RC section in which the nominal strength of a column section is reduced by the strength reduction factor φ (see ). Conversely, the method involving the proposed formula does not magnify the applied ultimate loads, while the reduction of the P–M interaction diagram itself is taken into consideration according to the proposed formula (see ). However, all other design steps, including the application of the strength reduction factor φ, are the same as those of the ACI formula.To verify the effectiveness of the proposed formula, typical RC columns with different steel and slenderness ratios are analyzed; the results are given in . In order to review the structural response according to the compressive strength of concrete, RC columns with fc′=360 and 270 kg/cm2, which are the compressive strengths of concrete generally used for small to medium building structures, are analyzed. The proposed formula provides results that are reasonably close to, albeit somewhat conservative than those obtained from a rigorous P–Δ analysis for RC columns with small steel ratios (see ), because of the scatter of the strength reduction coefficient F (see ), through the entire eccentricity range regardless of the slenderness ratios.As opposed to the ACI formula, which gives very conservative results for a column with relatively high slenderness ratio (L/r⩾70 in ), the proposed formula effectively estimates the ultimate resisting capacity of slender RC columns (see Unlike an ideal RC column bent in a single uniform curvature, most RC columns used in practice are likely to be subjected to moment gradient. Many design codes that have adopted the moment magnifier method (the ACI Code As opposed to the moment magnifier method in which only an increase of the applied ultimate moment is magnified by a magnification factor δ to consider the P–Δ effect (see ) without any change in the applied axial force, the proposed formula is based on a strength reduction coefficient F (see Hence, the direct adoption of the equivalent uniform moment diagram factor Cm used in the ACI Code to the proposed method is not appropriate, because the axial force P and end moments MA and MB acting on the member (as shown in ) must be replaced by the equivalent axial force and equivalent end moments () to maintain consistency with the strength reduction coefficient F. This means that the magnitude of the equivalent axial force and end moments are such that the maximum moment Mmax produced by them will be equal to that produced by the actual axial force and end moments MA and MB.From the equality condition for the maximum moments of the two systems in The equivalent moment correction factor CmEQ in or it can be constructed approximately on the basis of the Austin expression, Pe=π2EI/(βL)2, EI=0.2EcIg+EsIse, where Ig and Ise denote the moment of inertia of the gross concrete section and reinforcement about the centroidal axis, as in the ACI Code, and βL=the effective length considering the end boundary condition The ultimate resisting capacity of a slender RC column subjected to unequal end moments of MA and MB as shown in in the case of the proposed formula because the transformed equivalent forces of (CmEQ·P,CmEQ·MB) in represented by (1−F)·(Pn,Mn). Note that the reduction rate (1−F)/CmEQ must be less than or equal to unity to have a physical meaning.To verify the applicability of the proposed formula to a slender RC column subjected to unequal end moments, typical slender RC columns with fc′=360 kg/cm2 are analyzed, and the results are illustrated in , the proposed formula, in conjunction with the equivalent moment correction factor CmEQ of Eq. , can effectively estimate the ultimate resisting capacity of these columns. The formula gives improved results than those given by the ACI method. However, significant differences exist between the numerical results of a rigorous nonlinear analysis and the estimated results of the analysis using the proposed formula, particularly for slender RC columns with a small steel ratio. These differences seem to arise from the adoption of the approximate expression of CmEQ (see Eq. ) and by excluding the eccentricity e from the strength reduction coefficient F. Nevertheless, the proposed formula can be effectively used for determining an initial section of slender RC columns.Furthermore, the most RC columns subjected to combined axial compression and bending moment occur as parts of rigid frames, rather than as isolated members. A correct rational analysis and design of long columns in such frames must include the actual end restraints provided by adjoining members. Nevertheless, in terms of design, a column may be considered as an isolated member removed from the frame and replaced by an equivalent pin-end column whose length is equal to the effective length βL for axial compression on the real column. The equivalent column is then analyzed for compression plus the end moments carried by the member.The most commonly used procedure for obtaining the effective length of an equivalent pin-ended column is the alignment chart from the Structural Stability Research Council Guide ) can be replaced by βL on the basis of β calculated from the ACI Code. However, more rigorous nonlinear analyses of RC columns may be required in the final design stage and could be conducted on the basis of the numerical model proposed in this paper.A numerical model to simulate the material and geometric nonlinearities of RC columns is presented in this paper, and the proposed model is verified by comparison with results from previous experimental and analytical studies. Moreover, through section failure and P–Δ analyses of slender RC columns, a simple but effective regression formula for the design of slender RC columns is also proposed. Based on the results of this limited investigation, the following conclusions are obtained: (1) the ACI procedure gives good agreement with the P–Δ analysis of RC columns with relatively small slenderness and large steel ratios; (2) the ACI procedure gives very conservative results as the slenderness ratio increases; and (3) the proposed formula shows good agreement with the P–Δ analysis while maintaining a consistent difference over the entire eccentricity for all slender RC columns.Although rigorous numerical methods considering material and geometric nonlinearities will play an increasingly important role and will become the standard for the final design checks, the simple formula introduced in this paper can be effectively used in determining an initial section of a slender RC column. Moreover, to reach a more rational approach, extensive studies for reliability assessment, including experimental studies, need to be followed.Production of Ti–6%Al–7%Nb alloy by powder metallurgy (P/M)The Ti–6%Al–7%Nb alloy, with α+β microstructure, was commercially developed aiming the replacement of Ti–6%Al–4%V alloy in the manufacture of surgical implants, taking into account of its enhanced biocompatibility. The processing of this alloy using powder metallurgy allows the preparation of parts with complex geometry, probably less expensive. Samples of this alloy were obtained from uniaxial hot pressing of the elemental powders in vacuum. The pressing was carried out in temperature range 1000–1500°C with pressures from 10 to 25 MPa. The influence of the processing parameters and chemical composition of the elemental powders on the final microstructure was investigated. The alloy was characterised using a scanning electron microscopy (SEM), X-ray diffraction, Vickers microhardness measurements, chemical composition determination and density measurement. The results show high densification, homogeneous chemical composition, high tensile strength and a Widmanstätten-like microstructure. The process parameters were defined aiming to reduce the interstitial pick-up (O, N, C) and to avoid grain growth during hot pressing.The metallurgy of titanium and Ti-base alloys have been developed during last 50 years. Titanium is a very light metal with unique mechanical properties and can be used over a wide range of temperatures. Despite of their great potential, the high production costs of titanium-based parts have limited their use to some specific applications in aerospace and chemical industries. Titanium alloys are expected to be much more widely used for implant materials in the medical and dental fields bearing in mind their superior biocompatibility, corrosion resistance and specific strength compared with other metallic implant materials. Among titanium-based materials, pure titanium and Ti–6%Al–4%V alloy are the mostly used implant materials. Vanadium-free alloys like Ti–6%Al–7%Nb have been recently developed for biomedical use The cost for the preparation of titanium alloys depends strongly on the cost of the titanium powder. Metallic titanium is produced on commercial basis using the Kroll process, which involves the reduction of titanium chloride (TiCl4) with magnesium resulting in a final product known as titanium sponge. Titanium shows high reactivity with oxygen, hydrogen, carbon and nitrogen. The existence of these elements increases hardness and strength. Because of significant decrease in toughness, mainly at low temperatures, it is strongly recommended the use of extra-low interstitial (ELI) alloys for cryogenic applications.By milling titanium sponge, it is possible to obtain titanium powder with irregular morphology and relatively low contents of chlorine and oxygen (≅2%). This powder allows the manufacture of low-cost parts. However, the resulting porosity levels and high interstitial contents hinder its use for high-performance applications.High quality titanium powders can be obtained using the rotating electrode process (REP). In this process, bars of high purity titanium obtained by electron beam or vacuum arc remelting are used as starting materials. The powders obtained have high purity and spherical morphology that provide parts with high density and excellent mechanical properties. This process has the disadvantage of high cost and is only justified when used in applications that demand high reliability, e.g. in the aerospace industry The hydride–dehydride (HDH) process method was used to produce titanium powder in this work. Among the reasons to justify this choice, low production costs and low-oxygen content are the most striking. The HDH process is commonly used for the preparation of metallic powders. This technique is preferentially applicable to titanium, zirconium and niobium, because these metals absorb large quantities of hydrogen at elevated temperatures. At room temperature, solubility of hydrogen in these metals is quite low. During cooling, brittle hydrides such as β-NbH0.89 are formed, in the case of niobium, and can be easily milled at room temperature. Heating of this powdered hydride in high vacuum allows hydrogen desorption yielding the respective metallic powders The processing of titanium alloy parts production via powder metallurgy involves two basic stages: powder production and compaction (sintering) to produce the solid part. An external pressure is applied to the loose powder to increase density. Uniaxial or isostatic pressing are commonly used. The pressure can be applied at room or high temperatures. Heat treatments are sometimes necessary to optimise the mechanical properties of the final compact One important point must be taken into account when powder metallurgy processing is chosen for the manufacture of Ti and Ti-base alloys. Extremely stable titanium oxides formed at the surface of titanium particles during its manufacture remain at the subsequent processing steps. Thus, the processing of titanium powders is limited to those methods that provide smallest oxidation of the powder particles The two major techniques used for the titanium alloys production by powder metallurgy are: the pre-alloyed (PA), and the blended elemental (BE) approaches The blended elemental technique aims to diminish the high production costs and has some advantages allows the use of low-cost powders like those obtained from the HDH process or from the milling of titanium sponge;the elemental blends can be easily cold compacted because of the relatively low-yield strength of the pure titanium powder.The blended elemental method followed by a sequence of uniaxial cold pressing, cold isostatic pressing and vacuum uniaxial hot pressing was chosen for the preparation of the Ti–6%Al–7%Nb alloy.Titanium powder was obtained by the HDH technique. Hydriding was carried out at 500°C in a vertical furnace for 3 h under a pressure of 10−5 |
Pa. After cooling to room temperature, the friable hydride was milled in a niobium container without protecting atmosphere. The dehydriding stage was carried out at 500°C in dynamic vacuum conditions. Niobium powder was obtained using the same route, however, hydriding–dehydriding temperatures were significantly higher (800°C). Aluminium powder was supplied by Valimet. shows the principal characteristics of those powders.The starting powders were weighed (25 g) and blended for 15 min in a double-cone mixer. After blending, powders were cold uniaxially pressed under pressure of 40 MPa in cylindrical 20 mm dia-dies. Afterwards, samples were encapsulated under vacuum in flexible rubber moulds and cold isostatically pressed (CIP) at 300 MPa for 30 s in an isostatic press with capacity of 450 MPa.Uniaxial hot pressing was carried out in 20 mm dia-graphite-dies in vacuum (10−2 |
Torr) with compaction pressures varying from 10 to 25 MPa using a Thermal Technology model 1400 equipment. Pressing temperatures ranged between 1000 and 1500°C. Heating rates varied from 10 to 30°C/min. After reaching the nominal temperature, samples were held at the chosen temperature for 1 h and then the furnace was cooled to room temperature. Dies were painted with a suspension of boron nitride in ethyl alcohol to avoid carbon pick-up. Metallographic preparation was carried out using conventional techniques. Specimens were etched with a Kroll solution: (3 ml HF, 6 ml HNO3, 100 ml H2O) to reveal its microstructure. Microhardness measurements were carried out in a Micromet 2004 equipment, Buehler, with the load of 0.2 kgf. The micrographs were obtained using an optical microscope LEO model 435VPi. The density of the sintered samples was determined by the Archimedes method.The specimens of the alloy Ti–6%Al–7%Nb prepared using the uniaxial hot pressing of elemental powders presented a Widmanstätten-like microstructure, two-phase (α+β), with low porosity and density varying between 99.3 and 99.8%. The amount of the Widmanstätten-like microstructure increased with the increased temperature and pressure and with the decrease of the heating rate. The values of hardness were the function of the sintering temperature, lying in the range from 370 to 400 HV for the specimens prepared at 1500°C. At lower sintering temperatures, the obtained microstructure is inhomogeneous and display coarse porosity. The hardness commonly reported for hot wrought alloys is about 350 HV shows the decrease of the hardness as a function of the increasing sintering temperature.The specimens pressed at 1500°C, 20 MPa and heating rate of 20°C/min, presented the best results when compared to the microstructure found in commercial samples. It can be observed that a Widmanstätten-like microstructure is distributed throughout the specimen (). Concerning the Widmanstätten microstructure, the white–contrasting areas are α-phase plates. The β-phase, present among the α-phase plates, gives rise to a dark contrast.The specimens processed at lower temperatures (below 1300°C) did not develop a Widmanstätten-like microstructure. It can be observed in where two-phase (α+β) areas are homogeneously spaced in the form of islands embedded in a titanium-rich matrix. In this titanium-rich phase, low amounts of Al and Nb are dissolved. These results indicate that there were not enough time for mutual diffusion (homogenisation) and further formation of a two-phase (α+β) microstructure throughout the specimens.Pressure-assisted sintering enabled the achievement of low-porosity specimens. During heating, aluminium melts and get into the pore structure. The flow of molten aluminium is driven by capillary forces, and the liquid tends to fill in the interparticle spacing found within the compacted microstructure (green compact). In addition, aluminium diffuses into niobium and titanium particles according to the respective solubilities.One of the main problem found in the manufacture of titanium alloys via powder metallurgy is the control of interstitial contaminants. Surface oxidation hinders the sintering of alloys containing very reactive metals like titanium and aluminium , reveal a very low interstitial contents, close to the ELI grade. Specimens were sampled in the central regions. Before painting with a BN suspension, carbon pick-up was observed to increase with increasing temperature and sintering time. After painting, TiB2 particles were found on the surface of the sintered specimens.The sequence of reactions which occur during heating of the blended elemental compacts will be the subject of a forthcoming paper. shows the EDS spectra, from α and β phases, regions in a specimen sintered at 1500°C. It can be observed that aluminium contents in α phase are slightly higher than those observed in β phase, as expected. On the other hand, niobium is preferentially dissolved in the b.c.c. β phase.Hot uniaxial pressing enhanced densification of Ti–6%Al–7%Nb. The obtained samples presented low porosity and a suitable α+β microstructure.The production of titanium powders by HDH process showed to be an efficient technique. The combination of relatively low-cost powders, compaction techniques with high productivity, minimal machining and good mechanical properties provide titanium parts more attractive in many applications.The results indicate that the Widmanstätten-like microstructure is obtained in the whole sample extension with the increase of the pressing temperature and decrease of the heating rate.Samples pressed at 1500°C with pressure of 20 MPa and heating rate of 20°C/min presented the best results. Higher pressing temperatures or longer holding times can lead to intensive grain growth.The hardness values observed in the samples are within the range used in commercially manufactured parts produced by powder metallurgy techniques.The final low interstitial contents in the sintered specimens demonstrate the efficiency of the process.Prediction of chevron crack initiation in inclusion copper shaped-wire drawingIn the copper superfine wire drawing, the internal cracks such as chevron cracks and breakage of the wire were fatal to the success of quantitative drawing operations. This paper shows how four of the main process parameters, the position, size and shape of an inclusion and drawing pass numbers, influence the plastic deformation, hydrostatic stress, maximum principal tensile stress and chevron cracks initiation by FEM simulation. The influence of the central and non-central cylindrical inclusion in the single-pass copper shaped-wire drawing was investigated. Influence of a central elliptical inclusion in the single-pass copper shaped-wire drawing was also investigated and compared. The effect of the lateral and longitudinal sizes of a central cylindrical inclusion in the multi-pass copper shaped-wire drawing was carried out. The plastic deformation, plastic strain, hydrostatic stress and maximum principal tensile stress of the copper shaped-wire containing an inclusion were obtained for the drawing condition, position, size and shape of the inclusion mentioned above. A ductile fracture criterion was chosen from literature, a large number of ductile fracture initiation criteria, to predict the chevron crack initiation of the drawn copper shaped-wire for this investigation. The problem of chevron cracks initiation for the investigated material was solved. This investigation gives very good results.Nowadays, various superfine wires are widely used in commercial products such as a fishing line, screw, pin, bolt, steel cord, sawing wire, cable, spring, screen mesh, mesh of filter, wire rope, stiffening wire, antenna, sensor, bonding wire, electronic wire, etc. Superfine steel wires are used for printing meshes, filters, steel cords, saw wires, wire ropes, precision springs, precision screws and precision pins. Superfine non-ferrous wires are used for ultra small motors, semiconductor bonding wires, magnet wires, materials for electronic components and electrode wires for electrical-discharge processing as shown in . A lot of research efforts have been made for development of ultra small motors in Japan. To further improve the performance and the efficiency of such motors, a cross-section of the magnet wire for the motor needs to be changed from circular to square as shown in . At present, the size of this shaped (square) wire is suggested to be in a range of 300–500 μm Superfine wire processing requires a large number of drawing passes and intermediate softening heat treatments. In some cases, the internal or chevron cracks and breakage of wires occur. This results in high manufacturing cost. In particular, for wire with diameters of 0.1 mm or less, the product price increases exponentially with the decrease of wire diameter . It is obviously seen that the most important problem of wire breakage while copper wires drawing is wire breakage due to inclusions. shows the wires fracture due to an inclusion while copper wire drawing.The inclusion/metal system may be simplistically considered as a composite material with the inclusions acting as the aggregate and the metal as the matrix are typical ductile fractures due to plastic deformation in wire drawing. shows the chevron cracks that occur along the non-inclusion wire centerline on the longitudinal cross-section of a copper wire. While the inclusion was passing through the reduction zone of the die, the highest tensile stress, the tensile stress at the inclusion-leading-edge strongly influenced this plastic deformation The wire breakage, defect and chevron cracks are fatal to industrial scale high-purity copper superfine wire production The wire drawing process is classified as an indirect compression process, in which the major forming stress results from the compressive stress as a result of the direct tensile stress exerted in drawing. A converging die surface in the form of a truncated cone is used. Analytical or mathematical solutions where Do and Df are the original and final diameters, respectively, and B is equal to μ |
cot |
α.The same approach can be used to yield equations of essentially the same form for such similar operations as drawing of a wide strip through a wedge-shaped die. In the case of the drawing of a strip through a wedge-shaped die in plane-strain, the following Eq. where S is the yield stress (2σo/√3) in a plane-strain compression test according to the von Mises criterion, σo is the yield stress in uniaxial tension, ho is the initial thickness and hf is the final thickness.The plastic work criterion is based on the assumption that the material can only absorb a certain amount of energy. This energy criterion was proposed in this form by Freudenthal Cockcroft and Latham have proposed that a criterion where ε¯ is equivalent strain, εf is fracture strain, σ∗ is maximum principal tensile stress attained in the specimen under axial loading, and C is constant for a material at a given temperature and strain rate as determined from an uniaxial tension test. A material will fracture when it achieves a strain-energy density equal to the above integral. C may be determined from independent test data such as for the tensile test using Bridgman’s analysis This criterion can be successfully applied to cold working processes The goal of this research is to predict the internal or chevron cracks initiation of the drawn copper shaped-wire. A ductile fracture criterion, Cockcroft and Latham criterion, was chosen for this investigation.The finite element method is a powerful tool for the numerical solution of wire drawing. With the advance in computer technology, wire drawing can be modeled with relative ease. In this, FEA have the following six steps. In the first step, Shape Functions, the finite element method expresses the unknown field in terms of the nodal point unknowns by using the shape functions over the domain of the element. In the second step, Material Loop, the finite element method expresses the dependent flux fields such as the strain or stress in terms of the nodal point unknowns. In the third step, Element Matrices, the finite element method equilibrates each element with its environment. In the fourth step, Assembly, the finite element method assembles all elements to form a complete structure in such a manner as to equilibrate the structure with its environment. In the fifth step, Solve Equations, the finite element method specifies the boundary conditions, namely, the nodal point values on the boundary, and the system equations are partitioned. In the sixth step, Recover, the finite element method recovers the stresses by substituting the unknown nodal values found in the fifth step back into the second step to find the dependent flux fields such as strain, stress, etc.A two-dimensional finite element method was used for analyzing the effects of a central and non-central inclusion on stresses, strains and plastic deformation in copper shaped-wire drawing. a–c shows the analytical model used. The black part was an inclusion in a copper shaped-wire. In the case of the non-central inclusion, the inclusion was eccentrically located from the copper shaped-wire centerline and the eccentric distance ratio was set as e/Do, the ratio of the inclusion eccentric distance to the lateral wire size. The authors assumed that the inclusion was a sintered hard alloy (WC). shows the material properties and the drawing conditions that were used in this analysis. The longitudinal inclusion size ratio (Li/Do), the ratio of the longitudinal inclusion size to the lateral wire size, was set to be constant at Li/Do |
= 0.26. The lateral inclusion size ratio (Di/Do), the ratio of the lateral inclusion size to the lateral wire size, was set to be 0.0, 0.2, 0.4, 0.6 and 0.8. The die half-angle (α), reduction of cross-sectional area (Re) and coefficient of friction (μ) were set at 8°, 17.4%, and 0.05, respectively.The model solution was obtained by using the MSC.MARC program. The element type, wire and inclusion material, die material, friction model and analysis type were set as quadrilateral, isotropic (elastic–plastic), rigid, Coulomb and plane-strain (large deformation), respectively. The authors assumed that the wire and the inclusion matrix were joined at the boundary during the process. In this analysis, the wire was considered as a copper shaped-wire with a hard inclusion subjected to steady deformation. It is also assumed that the inclusion can completely transfer the axial tensile stresses.A 2D FEM was also used for analyzing the effect of the size and aspect ratio of a central elliptical inclusion on stresses, strains and plastic deformation in copper shaped-wire drawing. The same finite element program as used in the case of the single-pass drawing of a copper shaped-wire containing a cylindrical inclusion was also used in this analysis. The analytical model used in this analysis is shown in a and d. The inclusion was located on the copper shaped-wire centerline. The black part was an elliptical inclusion in a copper shaped-wire. Seven longitudinal inclusion sizes, a/h |
= 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8, and five inclusion aspect ratios, b/a |
= 0.2, 0.4, 0.6, 0.8, and 1.0, of simulations were carried out. The die half-angle (α), reduction of cross-sectional area (Re) and coefficient of friction (μ) were set at 8°, 20%, and 0.05, respectively.A 2D FEM was also used for analyzing the effect of a central cylindrical inclusion on stresses, strains and plastic deformation in multi-pass copper shaped-wire drawing. The same analytical model (a and c) and finite element program as used in the case of the single-pass drawing was used in this analysis. The element type, wire and inclusion material, die material, friction model, and analysis type were set as in the case of the single-pass drawing. The longitudinal inclusion size ratio (Li/Do) equal to 0.05, 0.1, 0.2, 0.3 and 0.4 was used. The lateral inclusion size ratio (Di/Do) equal to 0.1, 0.2, 0.3, and 0.4 was also used. The die half-angle (α), reduction per pass (R/P) and coefficient of friction (μ) were set at 8°, 20%, and 0.05, respectively.The stresses, strains and plastic deformation behaviour of the drawn wire containing a non-central inclusion with Di/Do |
= 0.2 and e/Do |
= 0.0, 0.1, 0.2, 0.3, and 0.4 were obtained by the FEM simulation. shows the hydrostatic stress distribution and plastic deformation behaviour of a drawn wire containing a non-central inclusion for Di/Do |
= 0.2 where e/Do |
= 0.3.The copper matrix of the drawn wire that contained a non-central inclusion was deformed specifically around the inclusion. The inclusion was slightly deformed because of its hardness, resulting in large copper deformation. Necking, bending and misalignment due to a non-central inclusion in wire drawing occurred at some parts of the wire as an inclusion passed through the die. Necking occurred on the copper shaped-wire surface in front of the inclusion-leading-edge near the inclusion boundary, and the lateral neck size decreased as the eccentric distance increased. Bending and misalignment also increased as e/Do increased and occurred at the die inlet zone.During the drawing of the copper shaped-wire that contained a non-central inclusion, the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge decreased as e/Do increased. Extremely compressive stress or die pressure occurred on the die contact surface that was nearest to the inclusion and increased as e/Do increased. This caused a worn die contact surface, which easily occurred. The plastic deformation of the wire matrix around the inclusion boundary is very low and lower than the matrix plastic deformation that was far away from the boundary of the inclusion. This matrix plastic deformation increased as the distance from the inclusion increased. This caused wire bending and misalignment. It was found that the wire bending and misalignment increased when e/Do increased.When the lateral inclusion size was small, the inclusion was slightly deformed. Necking, bending and misalignment due to a non-central inclusion in wire drawing occurred at some parts of the wire for e/Do |
= 0.1, 0.2, 0.3, and 0.4 as the inclusion passed through the die. But for e/Do |
= 0.0, only necking due to a central inclusion in wire drawing occurred. In this case, the lateral neck size decreased as the lateral inclusion size increased. Bending and misalignment also increased as Di/Do increased, and occurred at the die inlet zone. During the drawing of wire that contained a non-central inclusion, the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge increased as Di/Do increased. Extreme die pressure still occurred on the die contact surface that was nearest to the inclusion and increased as Di/Do increased. Plastic deformation of the wire matrix around the inclusion boundary was low and increased rapidly as Di/Do increased.Li/Do strongly influenced hydrostatic tensile stress when Li/Do was less than 0.2. The hydrostatic and maximum principal tensile stresses rapidly increased as Li/Do increased. When Li/Do was between 0.2 and 1.0, Li/Do influenced hydrostatic tensile stress. The hydrostatic tensile stress was not affected by the longitudinal inclusion size when Li/Do was greater than 1.0.The stresses, strains and plastic deformation behaviour of the copper shaped-wire containing various longitudinal size ratios (a/h) and aspect ratios (b/a) inclusion for the case of the constant b/a |
= 0.6 and a/h |
= 0.5 while wire drawing were obtained by FEM simulation. shows the distribution of hydrostatic stress and plastic deformation in a copper shaped-wire for a/h |
= 0.5 where b/a |
= 0.6.The necking behaviour and the relationship between the lateral neck size and the longitudinal inclusion size are the same as described in the case of the single-pass drawing of copper shaped-wire containing a central and non-central cylindrical inclusion. While drawing the wire containing a central inclusion, it was found that the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge increased as both b/a and a/h increased. When the high tensile stress in front of the inclusion-leading-edge occurred during wire drawing, the internal crack or chevron crack easily occurred. The maximum hydrostatic tensile stress was found where the inclusion-leading-edge was located around the die exit.The stresses, strains and plastic deformation behaviour of the copper shaped-wire that contained a central inclusion for Di/Do equal to 0.1 and 0.3 where Li/Do was equal to 0.05 during five passes of drawing were obtained by FEM simulation. shows the distribution of hydrostatic stress and plastic deformation of the copper shaped-wires containing a central inclusion during multi-pass drawing for Di/Do |
= 0.1 and 0.3 and Li/Do |
= 0.05 where Re = 20% and α |
= 8°.For the first pass drawing, the inclusion was slightly deformed because of its hardness, resulting in large copper deformation. The inclusion deformation occurred when copper shaped-wire was repeatedly drawn. The necking behaviour and the relationship between the lateral neck size and the lateral inclusion size are the same as described in the case of the single-pass drawing of copper shaped-wire containing a central and non-central cylindrical inclusion. While drawing the wire containing a central inclusion, it was found that the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge increased as Di/Do increased.The highest value of the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge occurred where the inclusion-leading-edge exited and was outside the die. When we compared between the lateral and longitudinal inclusion sizes effects, the maximum tensile stress was stronger influenced by Li/Do than Di/Do. The wire deformation, inclusion deformation and maximum tensile stress also increased as the drawing pass numbers increased.The Cockcroft and Latham criterion was selected and used as the damage value to estimate if and where an internal or chevron crack will occur during the copper shaped-wire drawing. For the FEM simulation, the Cockcroft and Latham criterion can be written as follows:where n is the number of steps in the simulation, Δε¯ is the incremental effective strain (Δε¯=ε¯i-ε¯i-1), σ∗ is the maximum principal tensile stress in the element, and C is the material constant or the critical damage value. The critical damage value (C) of the material, copper, used in this investigation was determined to be 0.664 in the tensile test by a universal tensile testing machine at room temperature.From the results of the analysis described in Section , it can be seen that the maximum tensile stress over the entire FEM mesh in all cases of those simulations occurred in front of the inclusion-leading-edge. So if the summation of Eq. , C, exceeds the critical damage value, an internal crack or chevron crack should occur in front of the inclusion-leading-edge.It was reported that during the drawing of the copper shaped-wire that contained a non-central inclusion, tensile stress in front of the inclusion-leading-edge decreased as eccentric distance (e/Do), the distance between the centerlines of the inclusion and wire, increased. However, the maximum tensile stress over the entire FEM mesh still occurred in front of the inclusion-leading-edge. The maximum principal tensile stress over the entire FEM mesh was also found in this point. The greatest value of the maximum principal tensile stress that occurred in front of the inclusion-leading-edge was found when the inclusion position was at the wire centerline (e/Do |
= 0). The inclusion size directly and strongly influenced the strain-energy density (C) in the element which was located in front of the inclusion-leading-edge. The value of the summation of this strain-energy density (C) over the drawing pass increased as inclusion size increased. Since the chevron cracks initiation occurs when this summation value reaches the critical damage value, so we called the inclusion size in this case the “critical inclusion size”. This strain-energy density (C) was inversely influenced by eccentric distance. The influence of the lateral inclusion size and eccentric distance on the chevron crack initiation in front of the inclusion-leading-edge in the single-pass drawing of the copper shaped-wire containing a non-central cylindrical inclusion for Li/Do |
= 0.26 where Re/P |
= 17.4% was obtained as shown in shows the critical inclusion size and eccentric distance limit curve that divided the Di/Do–e/Do chart into three zones namely safe, dangerous, and unpractical zones. This critical inclusion size increases with increasing of the eccentric distance. In this case, the critical lateral inclusion size is equal to 0.77 when the eccentric distance is equal to zero. Since the maximum eccentric distance of an inclusion in a wire is limited by the inclusion size, the maximum eccentric distance linearly decreases with increasing of the inclusion size. The right-hand side of the eccentric distance limit curve is not a practical zone, so we called it the “unpractical zone”. Since the summation value of the strain-energy density (C) in the element which is located in front of the inclusion-leading-edge does not reach the critical damage value when the inclusion size is smaller than the critical inclusion size (safe zone), the internal or chevron cracks may not occur. But they may occur when the inclusion size is larger than the critical inclusion size (dangerous zone) and finally, wire breaks may also occur., we found that when the inclusion was located at the center of the wire or the eccentric distance was equal to zero, the value of the maximum tensile stress in front of the inclusion-leading-edge was at its greatest value. So the smallest critical inclusion size was found at this inclusion position. The influence of the lateral and longitudinal inclusion sizes on the chevron crack initiation in the single-pass drawing of the copper shaped-wire containing a central cylindrical inclusion where Re/P |
= 17.4% was obtained as shown in The critical lateral inclusion size rapidly increased as longitudinal inclusion size decreased when Li/Do was less than 0.8 and slightly decreased as Li/Do increased when Li/Do was greater than 0.8. It can obviously be seen that a very large (lateral size) inclusion can be included in the copper shaped-wire without chevron cracks initiation if that inclusion is very short. For Li/Do equal to 0.26, as an example, an inclusion with a lateral size of less than 0.77 can be included in the copper shaped-wire without chevron cracks initiation as shown in . A smaller inclusion can be included in the wire without chevron cracks initiation when the longitudinal inclusion size increases. For Li/Do greater than 0.8, an inclusion with a lateral size less than 0.078 can be included in the copper shaped-wire without chevron cracks initiation. The summation value of the strain-energy density (C) in the element which is located in front of the inclusion-leading-edge does not reach the critical damage value when the inclusion size is smaller than the critical inclusion size (safe zone), and internal or chevron cracks may not occur. They may occur when the inclusion size is larger than the critical inclusion size (dangerous zone) and finally, wire breaks may also occur.In comparison to the central cylindrical inclusion wire drawing, similar behaviour of the internal or chevron cracks initiation was found. The shape of the cylindrical inclusion differs from the elliptical inclusion shape. The flow of the wire matrix around the inclusion-leading-edge is smoothly changed due to the curvilinear boundary of the elliptical inclusion. Since there is a sharp-edge at each end of the cylindrical inclusion, the flow of the wire matrix around the inclusion-leading-edge is suddenly changed which is quite different from the case of the elliptical inclusion. Thus, the larger summation value of the strain-energy density (C), in the element which is located in front of the inclusion-leading-edge, is induced, resulting in a smaller critical inclusion size being obtained when compared to the case of the elliptical inclusion. The influence of the inclusion aspect ratio, lateral and longitudinal inclusion sizes on the chevron crack initiation in the single-pass drawing of the copper shaped-wire containing a central elliptical inclusion was obtained as shown in The critical lateral inclusion size rapidly increased as longitudinal inclusion size decreased when Li/Do was less than 0.8. When Li/Do was less than 0.8, a very large (lateral size) inclusion can be included in the copper shaped-wire without chevron cracks initiation when the longitudinal inclusion size decreased or when the aspect ratio, the ratio of lateral and longitudinal inclusion size (b/a), increased (a slim elliptical shape transform into a fat one). The critical inclusion size increased as the aspect ratio increased. Thus, the larger (lateral size) inclusion can be included in the copper shaped-wire without chevron cracks initiation if the elliptical shape of the inclusion is fatter. By comparison between the case of the spherical inclusion and the slim elliptical inclusion which can be included in the copper shaped-wire without chevron cracks initiation, we found that the lateral size of the spherical inclusion (b/a |
= 1.0) is larger than the slim elliptical inclusion. When Li/Do was greater than 0.8, the inclusion with a lateral size less than 0.128 can be included in the copper shaped-wire without chevron cracks initiation. When the inclusion size is smaller than the critical inclusion size (safe zone), the internal or chevron cracks may not occur.The influence of the lateral and longitudinal inclusion size on the chevron crack initiation in the multi-pass drawing of the copper shaped-wire containing a central cylindrical inclusion was obtained. shows the critical lateral inclusion sizes, 0.648, 0.134, 0.038, 0.009 and 0.001, in the first, second, third, fourth and fifth passes, respectively, for Li/Do |
= 0.05 where Re/P |
= 20%. shows the critical longitudinal inclusion sizes, 0.283, 0.072, 0.023, 0.006 and 0.001, in the first, second, third, fourth and fifth passes, respectively, for Di/Do |
= 0.1 where Re/P |
= 20%.These critical lateral and longitudinal inclusion sizes can also be plotted as a function of the total reduction of cross-sectional area as shown in , the initial inclusion size, mean the size of an inclusion in an undrawn wire.When the initial inclusion sizes (lateral and longitudinal inclusion sizes) are very small, a large number of drawing passes can be performed without chevron cracks initiation. As the result, more than five passes of the copper shaped-wire drawing can be performed without chevron cracks initiation when the initial inclusion size is less than 0.001. The number of the drawing passes that can be performed without chevron cracks initiation rapidly decreased as the initial inclusion size increased. In this case, chevron cracks initiation was found in the first pass of the copper shaped-wire drawing when the initial lateral inclusion size was equal to 0.648 for Li/Do |
= 0.05. Chevron cracks initiation was found in the first pass of the copper shaped-wire drawing when the initial longitudinal inclusion size (inclusion length) was equal to 0.283 for Di/Do |
= 0.1.Necking occurred on the copper shaped-wire surface in front of the inclusion-leading-edge near the inclusion boundary. The eccentric distance and lateral inclusion size inversely and strongly influenced the lateral neck size. They directly and strongly influenced bending and misalignment of the wire.The eccentric distance inversely influenced the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge for a drawing of the copper shaped-wire that contained a non-central cylindrical inclusion. The lateral inclusion size directly and strongly influenced these hydrostatic and maximum principal tensile stresses. The extreme die pressure occurred on the die contact surface that was nearest to the inclusion. The eccentric distance and lateral inclusion size strongly influenced die pressure and matrix plastic deformation.The aspect ratio and longitudinal inclusion size strongly influenced the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge for a drawing of the wire containing a central elliptical inclusion.Inclusion deformation occurred when copper shaped-wire was repeatedly drawn. The highest value of the hydrostatic and maximum principal tensile stresses in front of the inclusion-leading-edge occurred where the inclusion-leading-edge exited and was outside the die. The drawing pass numbers strongly influenced the wire deformation, inclusion deformation and maximum principal tensile stress in multi-pass copper shaped-wire drawing.The lateral and longitudinal inclusion sizes directly and strongly influenced the strain-energy density (C) in the element which was located in front of the inclusion-leading-edge. This strain-energy density (C) was inversely influenced by eccentric distance. A larger (lateral size) cylindrical inclusion can be included in the copper shaped-wire without chevron cracks initiation if it is a shorter (longitudinal size) one.A larger (lateral size) elliptical inclusion can be included in the copper shaped-wire without chevron cracks initiation if it is a fatter one. When comparing between a spherical inclusion and a slim elliptical inclusion that can be included in the copper shaped-wire without chevron cracks initiation, we found that the lateral size of the spherical inclusion (aspect ratio = 1.0) was larger than the lateral size of the slim elliptical inclusion.A large number of drawing passes can be performed without chevron cracks initiation when the initial inclusion sizes, lateral and longitudinal inclusion sizes, were very small. This initial inclusion size inversely and strongly influenced the number of the drawing passes that can be performed without chevron cracks initiation. More than five passes of the copper shaped-wire drawing can be performed without chevron cracks initiation when the initial inclusion size is less than 0.001.The internal or chevron cracks may occur when the inclusion size is larger than the critical inclusion size and finally, wire breaks may also occur.Spatial and time variations of radon-222 concentration in the atmosphere of a dead-end horizontal tunnelThe concentration of radon-222 has been monitored since 1995 in the atmosphere of a 2 m transverse dimension, 128 m long, dead-end horizontal tunnel located in the French Alps, at an altitude of 1600 m. Most of the time, the radon concentration is stable, with an average value ranging from 200 Bq m−3 near the entrance to about 1000 Bq m−3 in the most confined section, with an equilibrium factor between radon and its short-lived decay products varying from 0.61 to 0.78. However, radon bursts are repeatedly observed, with amplitudes reaching up to 36 × 103 Bq m−3 and durations varying from one to several weeks, with similar spatial variations along the tunnel as the background concentration. These spatial variations are qualitatively interpreted in terms of natural ventilation. Comparing the radon background concentration with the measured radon exhalation flux at the wall yields an estimate of 8 ± 2 × 10−6 s−1 (0.03 ± 0.007 h−1) for the ventilation rate. The hypothesis that the bursts could be due to transient changes in ventilation can be ruled out. Thus, the bursts are the results of transient increased radon exhalation at the walls, that could be due to meteorological effects or possibly combined hydrological and mechanical forcing associated with the water level variations of the nearby Roselend reservoir lake. Such studies are of interest for radiation protection in poorly ventilated underground settings, and, ultimately, for a better understanding of radon exhalation associated with tectonic or volcanic processes.Radon-222, a gaseous decay product of radium-226, is released from rocks and soils into natural systems by diffusion or fluid transport (e.g. ). This radioactive noble gas with a half-life of 3.8 days, together with its short-lived decay products, is responsible for more than half of the natural dose in the average population (). Most of the radiation dose is received in the tracheo-bronchial region of the lungs by inhaled solid radon-222 daughters (), and in particular the short-lived alpha-emitters 218Po and 214Po. The knowledge of the properties of radon-222 and its decay products in the environment is therefore a major health issue, in particular in work places where the radon-222 concentration is higher than 400 Bq m−3, such as mines (e.g. ) and also in poorly ventilated ground floor dwellings in high radon potential areas (e.g. ). Measuring the radon-222 concentration in various settings, from dwellings to underground workplaces, is therefore important, but it is only recently that techniques have allowed a reliable monitoring of the radon concentration as a function of time with comparatively short sampling intervals (e.g. for a review of the techniques see Transient variations of the radon-222 concentration also attract a lot of attention because anomalies have been repeatedly observed before earthquakes (e.g. ), and in the atmosphere of underground tunnels (e.g. ). These observations, combined with indications for a correlation between radon concentration in the soil and sismicity (e.g. ), suggest that radon-222 might be a valuable tracer of geodynamical processes, and maybe an earthquake prediction tool. The sensitivity of radon exhalation to crustal deformation is supported by laboratory experiments (e.g. ) which indicate that increased radon exhalation occurs before rupture.Furthermore, radon-222 bursts have been observed in the atmosphere of a tunnel, in association with mechanical deformation at the kilometer scale in the vicinity of the artificial Roselend lake in the French Alps (). However, transient radon-222 concentration changes can also be due to meteorological or hydrological processes (). Therefore, the signals observed near the artificial Roselend lake need to be analyzed in detail before a causal relationship between stress release in the crust and radon exhalation can be ascertained. In particular, natural ventilation is known to play an important role in the radon-222 concentration in the atmosphere of underground cavities (), and its effects have to be quantified carefully for the Roselend tunnel.In this paper, we present an expanded data set collected in the Roselend tunnel from September 1995 to June 2000. Some hypotheses made previously on the basis of the data collected before March 1998 () are reevaluated, and additional dedicated experiments have been performed. This study thus focuses on the characterization of the radon signal, without attempting at this stage a modeling of hydrogeological or mechanical effects. First, we describe the parameters of the Roselend tunnel relevant for radon physics in the tunnel atmosphere and bedrock, and we present the detailed time and spatial variations of the radon-222 concentration. Parameters of the radon source and the effects of natural ventilation are then estimated using radon and CO2 measurements and the support of a simple model. Implications for the modeling of transient radon-222 signals are discussed in the conclusion.The dead-end tunnel is located on the west bank of the Roselend lake ( at an average altitude of 1577 m, at a mean distance of about 800 m from the Roselend dam. It was drilled in the forties, before the construction of the Roselend dam, completed in 1960, and was then abandoned for over 30 years. It is hosted in fractured gneiss and has an irregular section with an average dimension of 1.8–2 m and a length of 128 m (, with a slight slope (1%) upward from the entrance. A side room with dimensions 3.6 × 8.8 × 1.8 m3, referred to hereinafter as the inner room, is located about 58 m from the entrance, with an alcove of dimensions 4 × 4 × 1.8 m3 (). The overburden has a thickness of 10 m at the entrance, 44 m at the inner room, and 55 m at the end (The entrances of the tunnel and of the inner room are closed by metal doors. The temperature of the tunnel is 6.7 °C, with yearly variations smaller than 0.1 °C, and the air humidity is close to saturation, suggesting low natural ventilation rates. The pressure difference between the outside and the inner room is smaller than 1 Pa. Tunnel confinement was further enhanced in October 1997 by the installation of two polymer curtains (), isolating zone 1 and zone 2 from the rest of the tunnel. These two curtains were originally thought to be sufficiently air-tight (), but the complementary radon measurements performed from 1999 to 2000 suggested that some low level of ventilation remained. Consequently, in 2001, two additional curtains were installed in the end section of the tunnel, defining zones 3, 4 and 5 (In 2002, the air exchange rate could be estimated from CO2 measurements. Indeed, after 8 h of the presence of one to three workers, the CO2 concentration reached 0.22% at the end of the tunnel, significantly higher than the background concentration of 0.03%, equal to the atmospheric concentration. This peak CO2 concentration due to respiration then decreased with a characteristic exponential time constant of 13 h, which indicates atmospheric mixing rates of the order of 0.05 h−1 (10−5 s−1) and thus an air renewal time of about 1.2 days (29 h). This latter value is actually a lower limit because part of the observed decrease of the CO2 concentration could be due, instead of air exchange with the outside atmosphere, to dilution within the whole tunnel volume of zone 4, or to CO2 solubility in water.The tunnel is located in the gneiss unit belonging to the Belledone crystalline basement. Bulk sample porosity has been measured in the laboratory and has an average value of 5%, with a range from 1 to 9%. The main geological structures cross the tunnel at high angle, are steeply dipping, and range from foliation (mm scale), cleavage (dm scale), quartz veins (cm to m scale), fractures and brittle to ductile shear zones (m to tens of m scale). The distribution of mapped fractures along the tunnel is roughly uniform (, with three sections of higher fracture density at distances of 35, 45 and 75 m from the entrance. Near the end of the tunnel, despite lower fracture density, large veins cross the entire tunnel. In addition, the major geological contact between the crystalline bedrock and the sheared and overthrust Permo-Triassic and Jurassic sedimentary units is a few hundred meters east of the tunnel (Groundwater trickles from the tunnel ceiling, with flow rates varying from 1 to 110 × 10−3 l m−2 h−1 (). Three segments can be identified: 0–50 m from the entrance, 50–100 m and 100–128 m, with typical values of 20, 5 and 100 × 10−3 l m−2 h−1, respectively. The larger flow rates at the end of the tunnel seem to be supported by few but comparatively larger fractures.The total gamma dose rate has been measured along the tunnel at 1 m above the ground level () using a Saphymo™ 61509ADb scintillator probe. The mean value is 215 × 10−9 Sv h−1, slightly higher than the dose rate measured in the open air, in the vicinity of the tunnel, with values ranging from 160 to 190 × 10−9 Sv h−1 typical of this altitude. This higher gamma dose rate in the tunnel, despite the shielding of the cosmic rays, is due to the larger solid angle of telluric radiation (contributions from minerals with U, Th, and K) sampled by the instrument. It may also include additional contributions from the radon daughter 214Bi present in the tunnel air, especially during episodes of high radon-222 concentration bursts. Spatially, the gamma dose rate is smooth along the tunnel (), suggesting the lack of major heterogeneity in rock chemistry, mineralogy and lithology, and in particular the absence of fractures with particular U, Th, K, and Ra content of their fillings. A maximum gamma dose value of 330 × 10−9 Sv h−1, observed at a distance of 100 m from the entrance (), is associated with a granitic body. This variation of the dose rate controlled by the lithology is confirmed by a shorter profile performed with the detector in contact with the host rock.The emanation coefficient of rock samples, defined as the ratio of the number of radon-222 atoms released in the pore space compared with the total number of radon-222 atoms produced from radium-226 radioactive decay, has been measured in the laboratory. A sample from the Roselend tunnel was machined into a cube with 4 cm sides (volume Vs=0.064×10−3 m3) and the equilibrium radon concentration was measured in a chamber of volume Vc=0.9×10−3 m3 with an Alphaguard™ counter from Genitron GmbH (Germany). Taking into account radon leakage from the imperfectly air-tight chamber (), the equilibrium concentration of radon is CRn=198 Bq m−3. Assuming that the diffusion length is larger than the sample size, the emanation coefficient E is given by (where CRa is the radium content (in Bq kg−1) and ρ is the rock density. The radium content of typical samples is measured to be 55±6 Bq kg−1 by germanium gamma spectrometry. Taking ρ=2720 kg m−3, the measured emanation coefficient is then 1.9±0.3%, which is small but compatible with the range of emanation coefficient from 1 to 14% reported for gneiss (). If the diffusion length is smaller than the sample size, however, is not valid, and the true emanation coefficient may be significantly higher (). Knowing the emanation E, the radon concentration in the rock pore space can be estimated as EρCRa/ε, where ε is the porosity (), which gives a value of 57×103 Bq m−3.The radon-222 exhalation flux at the wall surface was measured in situ with the accumulation method (e.g. ). The open base of a conical container of height 12 cm and diameter 29 cm is attached to the wall surface, with air tightness guaranteed by a moist cloth. The air inside the container is replaced by radon-free air and radon-222 from the rock is accumulated during 1.5 h. The air of the container is then sampled and inserted in Lucas scintillation cells (). The radon-222 concentration is measured using a photomultiplier counter and the radon exhalation flux is then obtained from:where Vcyl is the container volume, Scyl is its base surface area, CRn is the measured radon concentration and Tacc is the accumulation time. Six measurements were performed in June 2003 in three different locations in the tunnel. The average value of the inferred exhalation flux is 3.7 ± 1.0 × 10−3 Bq m−2 s−1, with values ranging from 1.4 to 9.3 × 10−3 Bq m−2 s−1 (The diffusive exhalation radon flux at the surface of a semi-infinite homogeneous source can be related to the emanation coefficient E, the radium content CRa and the density ρ by (where z∗ is the diffusion length of radon in the rock and λ is the decay constant of radon (2.1×10−6 s−1). Taking the numerical values, the obtained value of z∗ is 62±15 cm, which justifies a posteriori the use of above. Although larger, this value of z∗ is of the same order of magnitude as the value of 15 cm obtained in granite (). It is also similar to the estimated thickness of the excavation damage zone (EDZ), a zone of highly fractured rocks and increased permeability around the tunnel. The thickness of the EDZ in the Roselend tunnel has not been determined. However, for a tunnel of 2.4 m diameter in the Tono mine in Japan (), it is estimated to be around 30 cm. This number can be taken as a rough estimate only, as the cleavage and foliation structures in the Roselend tunnel could possibly enhance the damage zone, at least locally.From 1995 to 2000, the radon activity concentration was measured in the inner room of the tunnel (B5 in ) with a sampling time of 1 h, using Barasol™ probes from Algade (France). From June 1999 to June 2000, five additional probes were operating simultaneously at several locations in the tunnel (B1 to B6 in ). Probes at points B6 and B8 were also available from November 1998 to May 1999. In addition, Barasol sensors connected to a modem for transmission to the laboratory via a telephone line were available at point B7 from June 1996 to April 1999.) is based on the detection of alpha particles by a silicon junction in a chamber located behind a diffusion barrier (filter paper) that has a characteristic time of 20 min for radon and thus eliminates radon-220 (half-life of 55.6 s). Discrimination from radon-222 short-lived decay products deposited on the silicon junction is performed by an energy window from 0.1 to 6.1 MeV. The sensitivity of the probe is given by the least count sensitivity of 1 count per hour, corresponding to an activity concentration of 50 Bq m−3.The concentration of short-lived radon daughters was determined in September 2002 from the potential alpha energy concentration (PAEC) measured in the air of the tunnel using the WLM-plus™ monitor from Tracerlab GmbH (Germany). This monitor measures the alpha activity deposited on a membrane filter (0.8 μm pore size) by pumping the sampled air during a pre-determined measuring cycle. In one measuring cycle (24 h), the alpha activity equilibrium level corresponds to alpha-emitting short-lived decay products (218Po and 214Po) of radon-222. In addition, the alpha-emitting decay products of radon-220 (216Po, 212Bi and 212Po) are measured when the pump switches off at the end of each measuring cycle. The lower detection limit amounts to 2 × 10−9 J m−3 for a sampling time of 1 h. The measurements have been performed at a height of 0.8 m above ground at five different locations in the tunnel, labeled PAEv1 to PAEv5 in Simultaneously with the PAEC measurement, the radon-222 level was monitored with an Alphaguard™. This instrument is based on an ionization chamber (pulse mode) located behind a diffusion filter. The sensitivity is given by the least count sensitivity of 1 count per minute at a concentration of 20 Bq m−3. This instrument is thus about 120 times more sensitive than the Barasol monitor. Knowing the radon-222 short-lived daughters PAEC and the radon-222 concentration, the equilibrium factor F can be approximately determined using the simplified equation (where the PAEC is expressed in 10−6 J m−3 and the radon-222 concentration CRn is expressed in Bq m−3.The hourly radon concentration in the tunnel is shown in from June 1999 to June 2000. The radon concentration in the Roselend tunnel is characterized by a background level ranging from 400 to 1000 Bq m−3 in the inner room and bursts, or anomalies, with amplitudes ranging from several 103 Bq m−3 to a maximum value of 36×103 Bq m−3 in March 1999 (). The presence of radon bursts reported in the first paper () is confirmed by the additional 2 years of data collected from April 1998 to June 2000, which include three bursts of larger amplitude than observed previously. Data at point B5 are missing from July 1997 to October 1998 because of a failure of the Barasol sensor, replaced in November 1998.), the spatial variation of the radon background concentration and of the bursts can be studied in more detail. Four periods, labeled (a) to (d) in , can be defined as representative of the background concentration, and the average values measured during these time sections are shown in as a function of the position in the tunnel, normalized to the amplitude observed simultaneously in the inner room. Similarly, seven bursts, labeled A to G in , can be isolated during this time period, and their peak amplitude is shown in as a function of position, normalized to the peak amplitude observed simultaneously in the inner room. The amplitudes of the burst of March 1999 (labeled I in ), for which measurements were available at points B6, B7 and B8, are included for comparison. Both the background concentration and the amplitude of the bursts are lower in the tunnel with respect to the inner room, with the exception of the bursts D to G, as observed at the end of the tunnel at point B6. Both the background concentration () decrease toward the entrance (outward). A larger background concentration is observed at point B2 in zone 1 as compared with points B1 in the same zone and B3 in zone 2 (The general inward increase of the radon-222 concentration is confirmed by the measurement obtained in September 2002 using the Alphaguard™ sensor (). The spatial variation of the radon-222 PAEC () follows the same trend, whereas the radon-220 PAEC appears rather uniform along the tunnel (). Values of the equilibrium factor F, obtained using ). These values correspond to the background radon conditions. The factor F has not been measured so far during a burst.Incidentally, knowing the radon-222 concentration CRn and the equilibrium factor F of its short-lived decay products, the exposure of a person staying in a tunnel for a duration T can be calculated using:where the radon (and progeny) dose is expressed in mSv (millisievert), and the DCF is the dose conversion factor, expressed in mSv WLM−1. A working level month (WLM) is the exposure to the radon short-lived decay products in equilibrium with a concentration of 3700 Bq m−3 (100×10−12 Ci l−1) of radon-222 during a working month (170 h). The value of the DCF depends on the size distribution of the unattached and attached progeny clusters () and is not known for the conditions of the Roselend tunnel. Epidemiological studies (ICRP66) suggest a value of 5 mSv WLM−1 (), which may be underestimated for working conditions at an altitude of 1600 m. On the other hand, various lung deposition models () suggest values as high as 20 mSv WLM−1. To remain conservative, a value of 10 mSv WLM−1 is used here, in agreement with other workers (e.g. ). The exposure during an 8 h working session at CRn=1000 Bq m−3 and F=0.7 then leads to a radon dose of 0.09 mSv, or 3.2 mSv for the same session at 36 × 103 Bq m−3 (peak radon burst). This latter exposure is quite significant as compared with the total annual dose for the general population, which is of the order of 2.5 mSv (The radon-222 concentration observed in the Roselend tunnel is similar to levels observed in various tunnels and non-uranium mines (. For example, the mean radon concentration in the Zloty Stok former arsenic and gold mine in Poland () varies from 0.4 × 103 to 6 × 103 Bq m−3. A higher concentration of 55.5 × 103 Bq m−3 was observed in a sealed tunnel section of the Sorocco Peak silver mine (). Values of the equilibrium factor determined in the Roselend tunnel are rather high and uniform compared with published values as indicated by examples gathered in . In contrast to show caves and mines, characterized by high ventilation rates, multiple entries, repeated visits by large groups or the presence of dust, the conditions in the dead-end Roselend tunnel are expected to be more stable and uniform.In order to compare the observed radon concentration in the Roselend tunnel with the measured exhalation flux at the wall surface, the natural ventilation of the tunnel must be taken into account. Significant natural ventilation is suggested by the observable decrease of CO2 after release from respiration, but also by the radon data themselves. After the first polymer curtains were installed in October 1997, isolating zones 1 and 2 from the rest of the tunnel (), the background radon concentration increased () from 113 to 425 Bq m−3 at point B7 and from 435 to 985 Bq m−3 in the inner room. The mean background level then remained roughly stable until April 2000, without any clear seasonal pattern.The effect of ventilation was deemed negligible in the first analysis (). The expanded data set, however, is useful to provide more precise evidence to support this conclusion. Natural ventilation can indeed be subtler than we considered initially. Indeed, even though seasonal time variations of the radon concentration in underground cavities usually reflect the seasonal pattern of natural ventilation (), the converse is not necessarily true. For underground sites with vertical access pits, the situation is particularly simple (). In summer, the air inside the cavity is heavier than the outside air, and remains stable, with a maximum radon concentration. In winter, however, cold air avalanches occur and the cavity air is mixed with atmospheric air, lowering the steady state radon concentration. The situation is rather different for a horizontal dead-end tunnel. Indeed, in summer, the tunnel air is heavier than the outside air and flows out at ground level, letting warmer air enter from the top (). In winter, the cold outside air enters the tunnel at the ground level, and warmer tunnel air escapes from the top, neglecting the effect of the 1% tunnel slope. Therefore, although such natural ventilation exhibits a yearly cycle with a reversal of flow direction, the air exchange rate should be rather stable with time. The lack of clear seasonal variations of the radon concentration in Roselend consequently does not imply the lack of natural ventilation.Taking into account natural ventilation, the time variations of the radon concentration C observed in a cavity of surface area S and volume V is given by (where Cext is the outdoor atmospheric radon concentration and λV is the ventilation rate. Since the atmospheric radon concentration (10–100 Bq m−3; ) is negligible compared with the concentrations considered here indoors, the steady state radon concentration in the cavity in the presence of ventilation is therefore simply: is the steady state concentration without ventilation, which is related to the exhalation flux by: and taking C=883 Bq m−3, which is the average background radon concentration in the inner room measured from June 1999 to May 2000 (), the ventilation rate can then be obtained from:which gives λV=8±2×10−6 s−1 (0.03 ± 0.007 h−1). This value, which corresponds to an air renewal time of 35 h in the tunnel, is incidentally in good agreement with the estimate of 29 h obtained from the 2002 measurement of CO2 characteristic time. Larger ventilation rates would be expected outward, which accounts for the observed outward decrease of the radon concentration.The contribution of the trickling water to the radon concentration in the tunnel can also be estimated. Indeed, integrating the profile displayed in , the total water flow rate Qw in the tunnel amounts to about 5 ± 0.5 l h−1. If the radon concentration in the non-saturated pore space is of the order of 57 × 103 Bq m−3, then the expected radon concentration in the pore water Cw is of the order of 22 × 103 Bq m−3, taking into account the partition coefficient equal to 0.39 at 7 °C (). The equilibrium radon concentration in the tunnel due to degassing trickling water is then QwCw/λV, which gives 30 Bq m−3. Trickling water thus cannot be the main source of radon.Given the measured radon exhalation flux, the diffusion of radon can account for the background radon concentrations measured in the tunnel with a reasonable value of the ventilation rate. The peak concentrations observed during the bursts, however, with average values of 12 × 103 Bq m−3 in the inner room from 1999 to 2000 (), and a maximum value of 36 × 103 Bq m−3 (The radon bursts do not display any obvious relationship to the surface meteorology (), and, in particular, to rainfall or melting of the snow cover (). Nevertheless, the radon bursts, by contrast with the background radon concentration, are sometimes sensitive to atmospheric pressure variations (). This contrasted behavior is, for example, clearly visible for burst C (for which the high frequency fluctuations are associated with pressure variations) and background section (c) in (similar pressure variations as during burst C but no effect on the radon concentration). Atmospheric pressure variations are widely known to affect the radon concentration (), as radon-rich air can be drawn from the host rock during pressure drops. Atmospheric pressure variations definitely cannot be proposed as the mechanism producing the radon bursts (except possibly anomaly F in ), but can provide interesting clues on these mechanisms. Indeed, the sensitivity to some of the atmospheric pressure variation during the bursts therefore suggests an increased and independently driven connectivity of the air phase in the porous medium. Such modifications of the porous medium could be attributed to percolating rain or snow water from above, to variations in the water content of the unsaturated fractured medium, to mechanical transient changes induced by the level variations of the Roselend lake (), or to other causes from below such as hydrological effects involving the water table.Before a detailed analysis of such processes can be performed, however, the role of the natural ventilation in the Roselend tunnel needs to be clarified. Indeed, since the ventilation rate so far has not been measured during bursts, one may raise the hypothesis that the bursts could be due to transient variations of natural ventilation only. The maximum observed concentration (36 × 103 Bq m−3 in March 1999, ) would correspond to non-ventilated conditions. The onset of ventilation would reduce this concentration, and the minimal background level would then correspond to the maximum possible ventilation. The ventilation rate necessary to maintain this low level, given by , is 7.3 × 10−5 s−1, which would correspond to a renewal time of the tunnel air of 3.8 h, which is incompatible with the observed CO2 decrease rate and the corresponding lower limit of the air renewal time (ca. 29 h).This discussion thus supports the interpretation that the radon bursts are due to a change of exhalation radon flux at the tunnel walls. While natural ventilation therefore cannot be the origin of radon bursts, it plays an important role in the time structure of the anomaly, and, in particular, the return to background concentration. This end part of the anomalies can be characterized by an exponential characteristic constant, as shown with some examples in . The determination of this time constant depends on the choice of time section used for the fit and is affected by an uncertainty ranging from 20% to 50%.The distribution of the characteristic constants for all 26 radon bursts observed from 1995 to 2000 in the inner room is displayed in . From August 1997 to November 1998, the missing data from the inner room (B5) are replaced by data from point B7. A significant peak is observed, indicating the presence of a typical characteristic rate of 5.5 × 10−6 s−1. Before the installation of the polymer curtains, the average value is 5.4 × 10−6 s−1 in the inner room and 5.9 × 10−6 s−1 in the tunnel. After the installation of the curtains, the average value is 5 × 10−6 s−1 in the inner room. These values also include the radioactive decay constant of radon-222 and thus the inferred effective ventilation rate (3 × 10−6 s−1) agrees only moderately well with the values of the ventilation rate derived earlier (8 ± 2 × 10−6 s−1). This suggests that the return to the background concentration after the peak amplitude of the bursts must be controlled also by a slow decrease of the exhalation flux at the wall, at least for some anomalies, and not only by ventilation and radioactive decay. The characteristic time constant is also shown as a function of the position in the tunnel in . A larger time constant is observed in zones 1 and 2 () compared with the rest of the tunnel, compatible with larger ventilation near the entrance.Natural ventilation is mainly forced by temperature changes (). Therefore, daily variations of the radon concentration are expected in relation to diurnal forcing of ventilation. The amplitude of the 24 h line in the power spectrum is shown in as a function of the position in the tunnel. This figure confirms that the inner room is the most confined place in the tunnel and indicates that significant daily amplitudes are found only in locations B1 to B4, with a maximum for B1 closest to the entrance. Daily variations are also clearly observed on the time series at point B1 in October 1999 (). An enhanced daily peak is observed unexpectedly for sensor B4 in zone 2 (). This may indicate the presence of some air channel between the tunnel section around B4 and the outside air, for example through fractures. An enhanced fracture density is indeed observed near B4 (Ventilation also affects the rising part of the bursts, as indicated by , but it is hard to interpret the resulting pattern using this simple expression only. Indeed, the radon concentration in each zone is not only affected by mixing with outside air, but is primarily affected by the mixing with nearby zones. Zone 1, for example, bears an increased ventilation rate, but is also affected by the radon produced in the whole tunnel and transported towards the entrance. This effect is important to take into account to understand the time and spatial variations of the radon concentration, and the progeny levels as well, although the latter parameters should be more dependent on aerosol size distribution and concentration than on ventilation rate. It will therefore be necessary to consider a more detailed modeling of the air exchange processes in the tunnel.In this paper, we have described the parameters of the radon exhalation source in a dead-end tunnel and the measured spatial and time variations of the radon-222 concentration. Radon-222 is characterized by a background concentration of the order of 900 Bq m−3 in the most confined location of the tunnel. Comparing this value with the measured exhalation flux provides an estimate of the natural ventilation rate of 8 ± 2 × 10−6 s−1. On top of the background radon-222 concentrations, bursts with amplitudes reaching 36 × 103 Bq m−3 are observed, which must be due to transient increases of the radon exhalation flux, and cannot be attributed to a sudden lack of ventilation alone. Spatial variations of the radon concentration, both for the background concentration and the bursts, are due to spatial variation of the ventilation rate and also due to spatial variations of the radon exhalation flux. Time variations of the radon concentration during the bursts result from time variations of the exhalation flux modulated by natural ventilation, atmospheric pressure variations, and radioactive decay.Understanding the cause of transient changes of the radon-222 exhalation flux is important. Indeed such transient changes may be related to mechanical deformation of the rock mass, as suggested in the first analysis (), and therefore could shed light on a mechanism relevant for analyzing observed earthquake precursors. Possible alternative causes, such as meteorological or hydrogeological effects, should also be explored. Preliminary water level data obtained in 1999 and 2000 from two boreholes located near the tunnel indeed did not rule out purely hydrogeological effects, such as radon pumping into the tunnel by water level increases. Pending a better understanding of the mechanisms, alternative explanations that do not involve mechanical deformation cannot be excluded at this stage.To compare between different models and unravel the underlying physical processes, a comparison of the radon concentration in the Roselend tunnel atmosphere with the water geochemistry and the trickling rates is fundamental (). A detailed investigation of the radon sensitivity to barometric pressure could also provide significant information on the transport properties of the transient radon sources.In order to be able to interpret the spatial and the temporal structure of the transient variations of radon-222 exhalation in the Roselend tunnel, and thus to constrain the source mechanism, a better model of air exchange and circulation in the tunnel must be constructed. More data are also needed to constrain such a model. An independent assessment of the air exchange rates would be important, through, for example, temperature measurements () or the simultaneous monitoring of the CO2 level (e.g. ). Dedicated tracer tests or sealing experiments may also provide significant additional constraints. Finally, the time variations of the natural ventilation in the Roselend tunnel, and their relationship to the external temperature, humidity and atmospheric pressure variations remain unknown.Such detailed studies, with their necessary methodological investigations, could contribute to a better understanding of air circulation in underground cavities, which is important, first of all, for radiation protection of workers in such settings. In addition, air currents play an important role in the energy balance and long term stability of underground cavities, which has industrial and cultural applications, for example, for underground waste storage or in the context of the preservation of cultural treasures such as painted caves (e.g. ). Finally, a better understanding of time variations of radon-222 concentrations in natural settings may lead to a reliable earthquake prediction method.Geomechanical response of permafrost-associated hydrate deposits to depressurization-induced gas productionIn this simulation study, we analyzed the geomechanical response during depressurization production from two known hydrate-bearing permafrost deposits: the Mallik (Northwest Territories, Canada) deposit and Mount Elbert (Alaska, USA) deposit. Gas was produced from these deposits at constant pressure using horizontal wells placed at the top of a hydrate layer (HL), located at a depth of about 900 m at the Mallik site and 600 m at the Mount Elbert site. The simulation results show that general thermodynamic and geomechanical responses are similar for the two sites, but with substantially higher production and more intensive geomechanical responses at the deeper Mallik deposit. The depressurization-induced dissociation begins at the well bore and then spreads laterally, mainly along the top of the HL. The depressurization results in an increased shear stress within the body of the receding hydrate and causes a vertical compaction of the reservoir. However, its effects are partially mitigated by the relatively stiff permafrost overburden, and compaction of the HL is limited to less than 0.4%. The increased shear stress may lead to shear failure in the hydrate-free zone bounded by the HL overburden and the downward-receding upper dissociation interface. This zone undergoes complete hydrate dissociation, and the cohesive strength of the sediment is low. We determined that the likelihood of shear failure depends on the initial stress state as well as on the geomechanical properties of the reservoir. The Poisson's ratio of the hydrate-bearing formation is a particularly important parameter that determines whether the evolution of the reservoir stresses will increase or decrease the likelihood of shear failure.maximum and minimum compressive horizontal stresses [Pa]maximum, intermediate and minimum compressive principal stresses [Pa]Hydrates are solid crystalline compounds in which small gas molecules (referred to as guests) are lodged within the lattices of ice crystals (called hosts). The dominant gas in natural hydrate accumulations is CH4. Hydrates are stable under conditions of low temperature T and high pressure P in two different geologic settings: in the permafrost and in deep oceans.The assessment of the global inventory of hydrate distribution in geologic media is in an embryonic state, with estimates varying by several orders of magnitude (). However, the scientific consensus is that the total amount of CH4 (and other hydrocarbons) trapped in hydrates is enormous, and easily exceeds the equivalent of all the known conventional oil and gas reserves. The rapidly escalating global energy demand has forced the question of whether hydrates can be developed and exploited as a potential energy source. To address this issue, a significant international research effort has begun recently (). Of the three possible methods of hydrate dissociation () for gas production (i.e., depressurization, thermal stimulation, and use of inhibitors), depressurization appears to be the most effective and economically promising method (and currently the only viable alternative) for the commercial production of natural gas from hydrate deposits (Among the serious technical challenges concerning of gas production from hydrates (), geomechanical issues are particularly important, because they affect both the integrity of the formation and the well stability, and can by themselves prevent the exploitation of otherwise promising hydrate accumulations.Hydrate deposits that are suitable targets for gas production often involve unconsolidated sediments characterized by limited shear strength. The dissociation of the solid hydrates (a strong cementing agent) during gas production can undermine the structural stability of hydrate-bearing sediments (HBS). This is further exacerbated by the evolution of expanding gas zones, the progressive transfer of loads from the hydrate to the sediments, and subsidence. Additionally, the depressurization of a hydrate deposit can lead to a more anisotropic stress field, potentially causing shear failure within the dissociating hydrate accumulation. Thus, the potential geomechanical response of hydrate deposits, and their impact on the system flow behavior and resource recovery, needs to be carefully evaluated before commercial-scale gas production from permafrost deposits can be developed. This study focuses on this issue.The objective of this study is to analyze the simulated geomechanical response of two permafrost deposits under production, and to develop the first-ever assessment of the impact of production on the likelihood of formation failure, and the magnitude of reservoir compaction and ground settlement. The state of knowledge on the subject is embryonic at best, because the general dearth of information is compounded by the significant geomechanical complication of the “stiff” permafrost overburden. Although the geomechanical response of marine hydrate deposits with compressible overburdens has recently received some attention (), this analysis of permafrost systems is (to the best of our knowledge) the first study of its kind.The two hydrate deposits investigated in this study are (a) the Mallik accumulation in the Mackenzie Delta, Northwest Territories, Canada, and (b) the Mount Elbert deposit on the North Slope, Alaska, USA. Both deposits have been, and still are, the site of past and present studies, from which a large body of information has been acquired. Thus, it is no exaggeration that these two deposits are probably among the best characterized.The importance of these two deposits, and the reason for their selection for this analysis, stems from the likelihood of their being among the sites considered for the design, development, and execution of the first large-scale, long-term gas production test from a hydrate deposit (). The reasons for their suitability for such a long-term test include (a) the confirmed presence of hydrates at high saturations, (b) the occurrence of high-quality HBS, (c) site accessibility through proximity to infrastructure, and (d) knowledge of the site, as derived from past and present studies. This being the case, it is imperative to determine as early as possible whether there are any geomechanical limitations (or even barriers) to gas production from such permafrost hydrate deposits, and, should this be the case, whether strategies can be developed to overcome them.The numerical simulation studies discussed in this paper involve linking the TOUGH + HYDRATE simulator () of hydrate behavior in geologic media with the FLAC3D () commercial geomechanical code. In this simulation approach, the TOUGH + HYDRATE simulator solves governing equations related to hydraulic, thermal, and thermodynamic behavior in geological media containing gas hydrates. FLAC3D is used to calculate geomechanical responses as a result of changes in pressure, temperature, and hydrate saturation. This code has built-in constitutive laws suitable for soil and rocks, including various elastoplastic laws for quasi-static yield and failure analysis, and viscoplastic constitutive laws for time dependent (creep) analysis, that could be used directly or modified for analysis of geomechanical behavior of hydrate bearing sediments. In the resulting coupled simulator, the two constituent codes (TOUGH + HYDRATE and FLAC3D) are linked through a coupled thermal–hydrological–mechanical (THM) model of HBS. The basic couplings between hydrological and mechanical processes in the deformable porous media are considered through constitutive laws that define how changes in pressure, temperature, and hydrate saturation affect deformation and stress, and how changes in stress and strain affect fluid flow. The numerical approach, linking the processes and operation of the coupled codes, has been described in detail by in their analysis of the geomechanical behavior of oceanic HBS.The investigation approach involves 5 years of continuous gas production at the two sites, using horizontal wells that were kept at a constant bottom-hole pressure PW |
= 2.7 MPa, i.e., slightly above the quadruple point in order to prevent the formation of ice in the reservoir. The geomechanical properties of the hydrate bearing sediments and the initial stress field are treated as perturbation parameters in the sensitivity analysis component of the study. This approach is dictated by the lack of site-specific data and uncertainties in the estimation of these parameters at the two sites. During this production period, we monitor the production performance, and the evolution of key thermodynamic and geomechanical parameters, and we also provide side-by-side comparison of the geomechanical responses at the two sites.The discussion in this section follows closely the analyses of , which are the most thorough treatises on the subject.The Mallik field is probably the best-characterized gas hydrate accumulation in the world. It is located at the northeastern edge of Canada's Mackenzie Delta, within a sequence of Tertiary sediments in an area overlain by about 600 m of permafrost. The study of estimated the amount of trapped gas in the Mackenzie Delta to be in 1–10 trillion cm3 (TCM) range. Detailed geologic and engineering data on gas hydrates and associated sediments are available (). Quantitative well-log determinations and core studies reveal at least 10 discrete gas hydrate layers exceeding 110 m in total thickness, from approximately 900 to 1100 m depth. The gas hydrate intervals have high gas hydrate saturation values that, in some cases, exceed 80% of the pore volume (). In a recent study, industry-acquired 3D seismic reflection data were used to characterize the occurrence and spatial extent on the Mallik gas hydrate accumulation (). This investigation indicated that the deepest gas hydrate interval at Mallik covers an area of only 9 × 105 m2, and there is about 7.71 × 108 m3 (~ 27 billion ft3) of gas (at STP) within the Mallik gas hydrate accumulation. These attributes establish the Mallik field as one of the most concentrated gas hydrate reservoirs in the world.Recognizing that the Mallik gas hydrate accumulation was an ideal site for a field test of gas production from a natural gas hydrate, an international partnership was formed to carry out a production research program in 2002 (). Field operations for the 2002 Mallik program were conducted during the winter of 2001/2002 and provided an extensive data set covering a wide spectrum of subjects related to natural hydrate deposits: geology, geophysics, geochemistry, microbiology, kinetics of gas hydrate dissociation, geomechanics, petrophysical, thermal and hydraulic properties, etc. The production testing included short duration, small-scale pressure drawdown tests and a 5-day thermal stimulation test. This testing allowed the calibration of several numerical models, the determination of important properties and parameters, and an assessment of the long-term production response of a gas hydrate accumulation (Studies of pressurized core samples, downhole logs, and production testing at the Northwest Eileen State-2 well, located in the northwest part of the Prudhoe Bay Field (where the Mount Elbert deposit is located), provided the first direct confirmation of gas hydrates on the North Slope by identifying three hydrate-bearing stratigraphic units (). Based on downhole log data from an additional 50 wells in the same area, investigators identified hydrate units in six laterally continuous sandstone and conglomerate. The volume of gas within this area is estimated to be about twice that of the known conventional gas in the Prudhoe Bay Field, ranging between 35 and 42 trillion ft3 (TCF).A collaborative project that aims to determine the viability of the North Slope hydrates as an energy source is currently in progress (). In 2007, a well was installed at an accumulation named the “Mount Elbert” prospect to acquire critical reservoir data needed to develop a longer-term production test program. The well, named the “Mt. Elbert-01” well, was drilled through 590 m of permafrost to a depth of 915 m and achieved recovery of significant lengths of core of the hydrate intervals. These cores were used for subsequent investigations on the pore water geochemistry, microbiology, gas chemistry, petrophysical properties, and thermal and physical properties. A flow test conducted in two sandy hydrate-bearing sections (Units C and D) with high SH (60%–75%) yielded gas in both tests, and has provided one of the most comprehensive datasets yet compiled on a natural hydrate accumulation (Analysis of the data collected from the Mt. Elbert-01 well will be used to support decisions on the advisability, site selection, well type and location, production method, and timing of the next phase of the project. This is currently envisioned as a long-term production test to determine the reservoir deliverability and the gas production potential of permafrost deposits under a variety of well design and operation scenarios.Conditions in the relatively shallow and cold Mount Elbert hydrate accumulation we investigate in this study, it should be noted, are representative of only part of the Eileen gas hydrate accumulation on the Alaskan North Slope (). Large portions of the Eileen gas hydrate accumulations have physical characteristics similar to those of Mallik (), i.e., they involve thick, highly saturated gas hydrate occurrences at higher reservoir temperatures and pressures.Analysis of the geology of the two sites indicates that the HBS sequences at both Mallik and the Mount Elbert prospect are mainly composed of sand and weakly cemented sandstones with silt/shale interbeds, confined by nearly impermeable shale boundaries. As such, they are typical representatives of Class 3 deposits (). Although Unit C has a water contact and communicates with an underlying aquifer (i.e., it has the characteristics of a Class 2 accumulation), the presence of a shale interbed allows its study as a Class 3 deposit.The geometry of the rectangular 3D system (stencil) we consider in this study has a square cross section in the xz-plane and a side length of 800 m at both sites. Based on scoping studies that indicated a clear disadvantage in placing horizontal wells near the bottom of the hydrate layer (HL), a horizontal well is placed at the HL top along the x |
= 400 m axis. Because of symmetry (a) along the y axis and (b) about the x |
= 400 m axis, it suffices to simulate a 2D slice in (x,z) that has a unit thickness along the 3rd dimension (Δy |
= 1 m), includes the entire system profile (from the surface to 30 m below the HL into the underburden) along the z coordinate, and is Δx |
= 400 m long along the x coordinate (). The (x,z) plane of the simulated domain and the location of the horizontal well are shown in the lower part of . Because of symmetry, there is no flow of fluids and heat through the lateral boundaries (vertical sides) of the domain. For the same reason, we impose a restriction of zero-displacement normal to these boundary surfaces. The top boundary, representing the ground surface, is kept at constant T and P, but is allowed to move. The bottom boundary (placed 30 m below the HL) has a fixed P and T, and a restriction of zero-displacement along the z-axis, i.e., normal to the boundary.In the case of the Mallik deposit, the 2D domain was discretized in 120 × 100 = 12,000 elements in (x,z), resulting in 36,000 equations when the equilibrium dissociation option was invoked. The discretization of the 2D domain in the Mount Elbert cases resulted in 120 × 93 = 11,160 elements in (x,z) and 34,800 equations. In both cases, discretization along the x-axis is logarithmic (with an initial Δx |
= 0.1 m), and the vertical discretization is variable. The fine discretization of Δz |
= 0.25 m in the HL allows an accurate description of the dynamic processes occurring there. presents the initial conditions at the base of the HL at the two sites. The initial P, T and stresses are higher at the Mallik deposit because of a greater depth. The initial SH is about 75% at the Mallik deposit, and 65% at the Mount Elbert accumulation. The initial stress gradients for both sites are based on site geomechanical investigations at the Mallik area (). The vertical stress gradient is about σV |
= 19.6 MPa/km corresponding to a bulk density of the overlying permafrost zone of about 2000 kg/m3. Based on estimates by , the horizontal stresses σH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.