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θcritic.The determination of the phase velocity of the fundamental modes S0 and A0 was made using the phase-spectrum method demonstrated by Sachse and Poo where Δφ is the difference in the phase spectrum of two signals that were collected with a different distance between them of L, and f is the frequency.For a simpler visualization of the modes and to determine the group velocity of the Lamb wave we can use the method of a “spectrogram”, presented by Boashash The studied GFRP samples are all transversally isotropic, as was experimentally demonstrated. An elastic medium is transversally isotropic if the elastic characteristics remain invariant for all points in directions symmetrical with respect to an axis. Accordingly, if Z is the axis of transverse isotropy, then the material is “isotropic” in the planes normal to the Z axis.In the case of transverse isotropy, only five elastic coefficients can be independent, as shown by Lamaitre and Chaboche εxεyεzεxyεyzεxz=1Ex-υxyEx-υxzEx000-υxyEx1Ex-υxzEx000-υxzEx-υxzEx1Ez0000001+υxyEx00000012Gxz00000012Gxz·σxσyσzσxyσyzσxzwhere ɛ is the strain vector, σ is the stress vector, and A represents the tensor of elastic compliance.In addition, we have the following equalities:Ex |
= Ey – extensional moduli coefficients in the directions X and Y;υxz/Ex |
= |
υyz/Ey – contraction coefficients in the directions X and Y, for a tension applied in the direction Z;Gxz |
= |
Gyz – shear moduli for shear in the planes perpendicular to the axis Y and the axis Z;The five coefficients that characterize the material areTwo Young’s (or extensional) moduli Ex and Ez. can be expressed as a function using the Lamé coefficients λ and μ, taking into account the basic relationship:To determine the Young’s modulus Ex and the Poisson’s ratio υxy, the expression of the phase velocities of the fundamental modes of Lamb’s wave propagation can be used.where the sign “ + ” from the exponent corresponds to the symmetric (extensional) modes and the sign “−” corresponds to the anti-symmetric (flexural) modes.where k=ω/cph represents the wave number for the phase velocity of the Lamb wave; kpx=ω/cpx is the wave number for the longitudinal waves that propagate in the X direction; ksx=ω/csx is the wave number for the transversal waves that propagate in the X direction; and 2h is the plate thickness ( is rather complex, and it must be found numerically. However, some special cases can be treated analytically. At low frequencies, the hyperbolic tangent term in Eq. For the symmetrical modes at low frequencies, Eq. The phase speed for the fundamental anti-symmetrical mode, A0, can be obtained after a few algebraic calculations:where Dp is the flexural rigidity of the plate:By means of destructive procedures, the mechanical descriptors that define the compliance tensor from Eq. were determined. These data are for non-immersed GFRP specimens presented in as an average value of five samples from the same product. Menard Ez, υxz and Gxz were determined from measurements of the propagation speed of the ultrasound along the direction Z (according to ); the other mechanical properties being determined from the propagation speed of the Lamb waves, the fundamental modes S0 and A0.a presents the signal received by the reception transducer during the examination of the 7201 composite, where the modes A0, S0 and S1 can be distinguished. For a more reliable identification, the amplitude spectrum was traced and is presented in c presents the corresponding spectrogram. The signal is presented in the time-domain (Using the spectrum-phase method, the phase velocity of A0 and S0 were determined, and, using Eqs. , the other measures from the compliance tensor from Eq. can be determined. The data from the ultrasound measurements for all three types of composite are collected in , it is clear that there is a very good correlation between the mechanical measures that define the compliance tensor, which is determined by the destructive and non-destructive procedures.The water-absorption behaviors of three types of GFRP composite were recorded, and from these results we can conclude the following:The destructive tests showed good mechanical results for the composite 7524, where the polyester is produced in-situ. In-situ production means a cheaper process in comparison with the similar composite 7201. The glass-transition temperature is 10 °C higher in the case of the 7524 composite, compared to the 7201 composite.For a more effective use of the composite materials, the principal mechanical parameters, such as the compliance tensor, must be known. This can be obtained from destructive tests or by means of nondestructive tests using ultrasound.The measurement of the propagation speed of the longitudinal and transversal waves can be used with good results for the determination of the elastic modulus Ez, the shear modulus Gxz and the Poisson’s ratio υxz.For the determination of the elastic modulus Ex, the shear modulus Gxy and the Poisson’s ratio υxy, the use of Lamb waves is required, the phase velocity of fundamental modes being directly connected to the mechanical parameters.A method for the generation and reception of Lamb waves in plates of composite materials involves the use of air-coupling, low-frequency, ultrasound transducers in a pitch–catch configuration.The results of the nondestructive measurements described in this paper are in good agreement with those obtained using classical destructive tests.Use of infrared radiation as curing agent for bioactive paper fabrication in times compatible with industrial processIn this work, the use of infrared radiation as curing media to graft eugenol onto cellulose for bioactive paper obtaining is proposed with the aim to obtain a process compatible with typical processes for papermaking. Eugenol is grafted onto commercial papers using polycarboxylic acid as linking agent using infrared heating for reaction curing. The effect of different operation and design variables, such as power, time, and distance to heat source were analyzed using an experimental design. Optimal infrared curing parameters were determined analyzing reaction degree, mechanical properties and color by response surface methodology. The operation conditions were compared with laboratory, pilot and industrial scale background concluding that the bioactive paper production could be adapted with the current papermaking process doing feasible scaling the bioactive paper production. The modified paper presents insectifuge and antimicrobial properties. A decrease in the biodegradability rate was observed, however, the biodegradable characteristic is conserved.Infrared (IR) radiation technology can be applied in different industrial processes where products need to be drying, polymerized or curing in continuous processes, especially for surfaces coatings []. In this technology, a heat source (or emitter) at high temperature radiates energy at specific wavelengths, which are absorbed by another body (receiver) that is colder. Generally, industrial sources of infrared radiation are electrical and there is a multiplicity of designs depending on working wavelength. The most common designs involves tubes, panels and lamps in different oven configurations, open or closed [Infrared radiation is a versatile and sustainable technology. One of the infrared radiation main advantages is that their installations are generally smaller than hot air ovens, due to its high energy densities and the good heat transfer between the source and the cold object. It no generate emissions of combustion gases and changes in emission power are relatively accessible. This power changes they can be made without large investments by adding or removing infrared radiation emitters or by adapting the source of electrical energy. Also, power regulation is flexible, fast and precise. Furthermore, these systems can achieve production speeds significantly higher than hot air systems, due to the high densities of infrared radiation []. Also, this technology has low thermal inertia so that the entire production capacity is available quickly when turned on [Particularly in paper manufacturing process, infrared radiation technology is used as an efficient tool for drying, heating and curing of paper and board products []. It is important to note that the thermal conductivity of the material is not a limit for the rate of heat transfer. The heat is mainly produced at the surface, however infrared radiation is able to penetrate into the bulk of material, so it is well absorbed and passes a wet paper thickness []. Also, infrared radiation provides the benefit of contact free heating of products, making this application very interesting for the drying/curing of coated paper [Taking into account the advantages described above, infrared radiation technology is an interesting method to apply for active paper production for packaging applications, generally produced by coating or chemical reaction. Active packaging can be defined as packaging that interacts with the product in order to enlarge its shelf life. With this goal, several substances (aggregates) are been incorporated in/on packaging materials or in package headspace to improve the performance of the package system. In paper-based packaging, the most common methodology for the fabrication of active package is the use of different coatings for obtaining active paper. Several works reported the preparation of antimicrobial paper by coating it with soy protein isolate solution containing carvacrol []. Another kind of active paper reported is based on gelatin-coated paper, which has antimicrobial and antioxidant effect for beef packaging [The main disadvantages of this systems proceed from the free liberation of the active agent as it is dispersed in the coating material. A promissory alternative is the immobilization of the active agent onto paper using chemical linkages. This technique is convenient to produce food active paper packaging because chemical immobilization of active compounds could prolong the specific activity and reduce the migration to the food. An example is the preparation of an antimicrobial cellulose by laccase-mediated grafting of phenolic compounds for packaging applications [In previous works, the development of bioactive paper by eugenol grafting onto cellulose was investigated using a convection oven []. Optimal reaction conditions (eugenol amount, temperature and time) were assessed and final properties were determined. It was found that modified paper presents antioxidant and insect repellent activity, without modification of organoleptic properties of food product, making it attractive for food active packaging application []. However, the reaction time was too long for an industrial scaling of the process.For this reason, in this work we propose the use of infrared radiation to graft eugenol onto cellulose in order to obtain bioactive papers using a process with times and equipment closer to those used in the paper industry. Thus, eugenol is grafted onto commercial papers using polycarboxylic acid as linking agent using infrared heating. The effect of different operation and design variables, such as power, time and distance to heat source were analyzed using experimental design. Optimal infrared curing parameters were determined analyzing reaction degree, mechanical properties and color by response surface methodology, and this parameter were compared with laboratory, pilot and industrial scale background with the aim to analyze the technological feasibility of proposed process. Finally, to corroborate that the modified paper has characteristics of a bioactive paper some final properties related to the food active packaging like insecticide/insectifuge activity and antimicrobial activity were evaluated. Also, the effect of chemical modification on paper biodegradability was analyzed in order to corroborated that the proposed process does not alter this important property.Reaction was performed on a commercial paper (150 g/m2 basis weight) provided by Cartocor S.A. (Argentina). The active compound grafted was eugenol, CAS# 97-53-0 (mass fraction≥99 %), while 1,2,3,4 butanetetracarboxylic acid (BTCA), CAS# 1703-58-8 (mass fraction≥98 %) was used as ligand and sodium hypophosphite monohydrate (SHPI), CAS# 10039-56-2 (mass fraction≥ 99 %) as catalyst. All of non-cellulosic reagents were supplied by Sigma Aldrich.The IR oven consisted in an isolated metal chamber (1.1 × 0.35 × 0.35 m) with 15 quartz tubes. Each tube had a potency of 0.15 kW and had on-off switches. Maximum power density was 9000 W/m2, and the sample tray was located in one of three different positions: 0.1, 0.15 and 0.2 m (gap distances) from the heat emitters.In order to evaluate the best reaction conditions and their effects on paper final properties, an experimental design based on the response surface methodology was used. A Doehlert experimental array [] with three factors (reaction time, distance to heat source, and power) was applied. Experimental region was defined considering operational characteristics of the oven used and some preliminary test. The range of these variables was: 30−180 s for time, 10−20 cm for distance to heat source and 0.15 to 0.75 kW for power. Experimental matrix with the coded (Xi) and experimental (natural) values of these three factors are listed in . Eugenol, BTCA and catalyst amount remained constant for all the experiments. Concentration of eugenol was 5 wt% respect to paper mass, BTCA:eugenol molar ratio was 2:1 and catalyst:eugenol molar ratio 1:1.Multivariate polynomial models were used to fit experimental responses. Moreover, the factors and their interactions were subjected to analysis of variance (ANOVA). the effect of diverse factors effects on different responses were considered significant when p < 0.05.Desirability function (DF) was applied to obtain the optimal parameters, considering various responses at the same time []. This function was maximized using the software StatgraphicsStatAdvisor application.The reaction was performed directly on the paper by adding the reactive. Papers of 10 × 15 cm were uniformly wet with BTCA, eugenol and SHP dissolved in water and alcohol at room temperature. Then, in order to eliminate the solvent, samples were dried at room temperature for 12 h and cured in an infrared oven presented on . Reaction parameters (times, distance to heat source and power) were used according to experimental design. A blank sample was obtained following the same procedure but in absence of eugenol.For reaction occurrence analysis, samples were washed with abundant ethanol to remove the excess of reactants and treated with NaOH solution (0.1 M) at room temperature for 4 min to neutralize free carboxylic acid to distinguish their signal in infra-red spectroscopy.Evidence of the grafting reaction was obtained by Fourier transformed infrared (FTIR) and UV spectroscopy (UV). FTIR spectra of modified paper and unmodified paper were recorded using infrared imaging microscope (Nicolet iN10 MX, Thermo Fisher Scientific, USA). Reaction occurrence and reaction degree was determined following typical ester and carboxylate peaks and quantifying their relative absorbance values. Samples were analyzed at room temperature within the spectral region of 600−4,000 cm−1, with 16 scans recorded at a resolution of 4 cm−1. Also, UV–vis for solid in reflectance mode measurements of unmodified and modified paper were made over a range from 200 to 1100 nm at a spectral resolution of 0.5 nm using a StellarNet miniature UV–vis for solid.Color difference between modified paper and virgin paper were measured with a colorimeter (CR-400 Konica Minolta). Color values were measured using the CIE 1976 color space (Comission International d’Eclairage). Measurements were taken as the average of three points of each sample. Total color differences (ΔE*) were calculated as follows:where L*,a* and b* are the values of unmodified paper.Mechanical properties: Tensile mechanical behavior of modified and unmodified papers was determined using an Instron 2519−104 universal testing machine. The load cell was 500 N and the tensile velocity was set at 30 mm/min until break. All specimens were prepared in a rectangular shape, with a width of 10 mm and length of 120 mm. The initial grip distance was 100 mm. The main tensile properties, as young modulus, tensile strength and ductility, were obtained along each test. Results were expressed as the mean of ten measurements for each sample.Some final properties related to the food packaging of the modified paper compared with the unmodified paper were evaluated, in order to prove the paper modification effectiveness and the impact onto the material sustainability. Papers tested were modified using optimal conditions.Repellent and insecticide activity against to Tribolium castaneum were carried out using the area preference test []. This bioassay was performed on washed and non-washed modified paper with and without eugenol and compared with unmodified paper. For the preference tests, papers were cut in half circles and were placed in a dish (half of modified paper and a half of virgin paper). Then, 10 beetles of mixed sex were put at the center of dish and immediately the lid was placed. The dishes were checked after 24 h. Percentage of repellency (%R) was calculated as follows [where NC and NT is number of insects present on control and treated paper, respectively. Results are the average of three measurements.The percentage of microbial reduction (R%) was calculated according to Eq. where C (CFU) is the number of microbial colonies in the “control” and T (CFU) is the number of microbial colonies in the treated sample. Virgin paper was used as control.Biodegradation test: the degradation ability of modified paper was determined following the method described by González & Alvarez Igarzabal [] with a few modifications. Experiments were carried out in a plastic box (25 × 20 × 12 cm3) containing 3053 g (dry basis) of characterized soil. The main characteristics of the compost are the following: moisture content: 40 %; organic matter: 20 %; ashes: 45 %; C/N ratio: 7.7; pH: 6.2 and electrical conductivity: 1.1 mmhos/cm. Samples were cut into square shape (3 × 3 cm2), dried until constant weight in an oven at 105 ⁰C to remove the moisture and weighed. Then papers were buried at 8 cm depth from the soil surface favoring aerobic degradation conditions. Specimens were put between plastic meshes to easy retrieval of the degraded samples and to permit the access of microorganisms and moisture. Test was performed at 25 ± 2 ⁰C and 45 ± 5 %RH by adding water periodically. Soil moisture fluctuation was measured by Fieldscout TDR 150 soil moisture meter. Samples were taken from the soil at different times, cleaned with a brush and distilled water. After that, they were dried in an oven at 105 ⁰C until constant weight. Finally, the biodegradation capability of the papers was expressed as the average weight loss in relation to the initial weight of the samples, as weight loss percentage (%WL). All determinations were performed by triplicate.Commercial paper was treated with 5% wt. of eugenol at different times, power infrared and distance to heat source depending on experimental design (). BTCA and SHP were used as ligand agent and catalyst, respectively. Esterification between BTCA and hydroxyl groups of cellulose at high temperatures is well known []. In the same way, carboxylic groups of the BTCA can reacts with hydroxyl groups of the eugenol and simultaneously with cellulose, producing the eugenol grafting onto cellulose. The infrared spectra of the control paper and modified paper are shown in a. The main difference that it can observed is the appearance of two bands at 1720 and 1580 cm−1. First peak can be attributed to carbonyl band of the ester formed during the curing process and the carboxyl band of the BTCA []. However, before the analysis, samples were treated with 0.1 M NaOH to convert the free carboxylic group to carboxylate anion so that the intensity of the band around 1720 cm−1 is only attributed to ester bond formed on the treated paper. So, the other new peak, at 1580 cm−1, is attributed to carboxylate band formed during neutralization []. Eugenol bands are not detectable may be due to the overlapping of its characteristic peaks with cellulose ones, and/or its low relative concentration. For this reason, eugenol presence was corroborated using UV–vis spectrophotometric technique in reflectance mode. Thus, UV–vis absorbance spectrum of a reaction sample is shown in b. compared with the spectrum of virgin paper. In this figure, in modified paper spectrum is possible to note the presence of a peak at 280 nm, typical absorbance of aromatic ring of eugenol.Reaction progress obtained for each reaction condition was assessed following the intensity of the FTIR ester peak at 1720 cm−1. For a correct comparison the intensity of this peak was normalized against band associated with the CH bending mode of cellulose (1318 cm−1). Response surface was constructed using this information, for the three variables studied (time, power and distance to heat source). The response variable was correctly fitted with a determination coefficient of (R2) of 87.32 %.The effect of power and distance to heat source at constant time, and time and distance to heat source at constant power is shown in a and b, respectively. As expected, reaction progress increases as power and time increases. Nevertheless, ester peak intensity decreases when distance to heat source increases. This also was expected due to smaller values represent less distance to heat source.According to the ANOVA test, and the corresponding Pareto chart (Fig. S1), the three variables are significant factors (p < 0.05) on reaction advance, as well as power/time, power/distance and time/distance interactions.The effect of operative variables on paper properties was also analyzed in order to find the optimal curing parameters. Two properties were selected thinking in packaging application: color and mechanical properties.For the first one, total color difference (ΔE*) respect to virgin paper was evaluated based on the CIELAB system following the Eq. . The influence of power, time and distance to heat source on final paper color difference was analyzed by response surface methodology. For this response a determination coefficient R2 = 8355 % was obtained.In general, a yellowing of samples is observed as consequence of reaction, furthermore to the own eugenol coloration []. Color changes are mainly due to oxidation and chain scission of the cellulose and other non-cellulose components such as remnants of lignin or additives, which are favored by high temperatures and long times and produce colored substances []. Thus, it is expected that reaction variables have also influence on these color differences. The effect on color variation of power and time for constant distance to heat source is shown in a, while the influence of power and distance to heat source for constant time is presented in b. According to ANOVA test (Fig. S2), power and time are significant effects and power has the greatest estimated absolute effect, while distance is not a significant effect. Color increases with the time and power increment, as observed in a and b. In addition, it is observed that the cross effects of the power with the remaining variables have a greater absolute estimated effect than time.It is important to highlight that color difference obtained for this methodology was smaller than the obtained by convection curing [] and that paper appearance is good for the most samples analyzed, and only for samples with color difference higher than 4, the differences are noticeable [On the other hand, tensile strength tests were conducted for all samples and tensile mechanical behavior was analyzed by surface response methodology with the aim of analyzing the influence of the reaction in the paper modification. shows young modulus variation with power and time for a constant distance to heat source (a) and with power and distance to source for constant time (b). The effect of the same variables on ductility and tensile strength is shown in response surfaces of To analyze the effect of the operative variables, an ANOVA analysis was performed for each response and the results are presents in Fig. S3.Young modulus presents a quadratic behavior for the three variables, being all of them statistically significative according to ANOVA analysis (Fig. S3a). This behavior can be attributed to the secondary reactions produced during cellulose modification process: depolymerization/degradation and crosslinking. As it was mentioned above, the first one proceeds from the catalytic effect of BTCA due to low pH level, and favored by high temperatures []. In the same way, it was demonstrated [] that polycarboxylic acids produces cellulose crosslinking. Therefore, mechanical properties of modified paper will depend of the extent of each secondary reaction.Initially as the power or time increases the elastic modulus decreases, because the temperature rises and with it the degradation and depolymerization of the cellulose caused by the BTCA. Then, as the power or time continues to increase, the elastic modulus begins to increase, the degree of crosslinking of the cellulose molecules prevailing. This occurs due to an increase in the esterification reaction, which would cause a hardening of the macromolecular network of the paper. The same happens with the variable distance, since at distances close to the heat source the temperature is high enough so that the cellulose degradation prevails and with it the decrease of the elastic modulus. At greater distances, the previous phenomenon does not occur and the paper returns to its initial values of elastic constant. it can be observed that ductility decreases with the increment of power and time and decreases with the distance to source. This behavior can be explained by the secondary reactions mentioned. Both reactions (depolymerization and crosslinking) have the effect of reducing the ductility of the material. In the case of depolymerization, this effect is due to a reduction in the size of the polymer molecules, while the cross-linking reduces the mobility of the chains, producing a hardening of the material and the consequent reduction of the elongation at break. Therefore, as already discussed, the increase in time, temperature and decrease in the distance to the source, have a positive effect on both secondary reactions, thus producing a decrease in the ductility of the modified paper. For this response, the three variables were statistically significant as shown in Fig. S3b.Whereas, tensile strength decreases when power and time increase. According to the previous discussion, this decrement can also be because of secondary reaction. It is clear, that the occurrence of degradation [], favored by the increment of power and time, produces a decrease in tensile strength []. Also, the higher rigidity detected at high level of power and time as consequence of crosslinking could also generate a decrease in tensile strength. This asseveration is based on the stress-strain curve behavior. The tensile strength (calculated as the maximum tension that the specimen supports) decreases as a consequence of a decrease in the ductility of the material, and not because the material has a lower capacity to withstand the stress.Tensile strength presented a quadratic effect when distance to heat source was increased. This unexpected behavior may be due to experimental error, which can be corroborated because this variable is not statistically significant as shown in Fig. S3c.Based on the results of reaction extent, color and mechanical properties, optimal reaction conditions were determined. For this purpose, a useful tool as the function of desirability was applied. This procedure helps determine the combination of experimental factors that simultaneously optimizes several responses. It does this by maximizing the function of 'desirability'. For this case, proper selection of reactions conditions should be based on a good compromise between of reaction advance and final properties of material. To achieve this, it is necessary to maximize the reaction progress (peak ester intensity), without adversely affect the original properties of the paper, that is, to maximize the ductility and minimize the variation of color.Considering this analysis, a high time of reaction and a middle value for the power and distance to heat source was found to be the optimal reactions conditions to obtain modified paper. These optimal values are: 130 s for the reaction time, 0.45 kW for the power and 15 cm for distance to heat source. After that, papers were prepared under these optimized conditions and then they were characterized. shows the results of predicted and experimental values for each response variable. Predicted properties were obtained evaluating surface response functions at optimal conditions. It was found a great positive agreement between experimental and predicted values for ester peak intensity, difference color and ductility.Is important to mention that the optimal time obtained for this methodology is lower than the optimal time obtained by convection curing, color differences are also reduced and mechanical properties enhanced []. Mainly the reaction time reduction impact in energy consumption, a key parameter to select the most profitable methodology. For a better comparison between these technologies, some variables operation and responses were analyzed for the same reaction progress (ester intensity peak: 0.42) and the same eugenol amount (5% wt). To achieve this, operation variables like temperature for convection (160 °C), and power (0.45 kW) and distance for infrared (15 cm) were set in values obtained for optimal conditions each one technology while the reaction time and other response variables were calculated using the surface response equation. Thus, reaction times obtained were 10 and 2.95 min for convection and infrared curing, respectively. Infrared radiation curing reduced reaction time around 70 %, compared with conventional methodology. Based on these process times and equipment specifications, the electricity consumption was calculated, obtaining a consumption of 133.33 Wh for convection and 22.12 Wh for infrared curing for the same reaction progress. Therefore, significant electricity savings (around 80 % for the analyzed case) can be obtained by infrared curing. After that, the other responses like color difference and elongation at break were calculated from the corresponding surface response equation based using operating conditions used and obtained in previous step. The results obtained for color difference were 3.33 and 1.42 ΔE and for elongation at break were 2.53 and 3.79 % for convection and infrared curing, respectively. Thus, infrared curing provides a lower paper degradation in comparison with convection curing, giving lower difference color and higher elongation at break at same reaction progress each methodology. According to these results infrared curing methodology allows paper modification in short time, with low energy consumption, good mechanical properties and good appearance. Thus, IR curing could be considered an interesting tool for its use for bioactive paper production at industrial scale.The cellulose modification process presented in this manuscript is an interesting alternative to produce biactive paper to be used in food packaging application. In order to asseverate this claim, the technological feasibility of the process should be analyzed, exploring the possibility of combine this method with the current papermaking process.Paper production involves a series of steps for the transformation of fibrous raw material into the final product. First, the cellulose pulp is obtained separating the cellulose fibers by chemical or mechanical processes from a high cellulose content matrix like wood. This pulp is then bleached and further processed, depending on the type and grade of paper that is to be produced. The pulp could be blended with additives, fillers and additional water to produce the paper stock, with is a dry solids content of 0.5–1 % (100−200 kg of water for every kilogram of paper produced). The paper stock is fed to the paper machine, the fibers deposit on the wire and form a sheet, most of the water being drained through the wire or sucked off into suction boxes by vacuum, reducing the water content 80 %. After that, the paper sheet pass to a press section where the additional water is removed from the web by mechanical means. After this section, the dry solids content increase to about 45 %, that is, the paper web has from 1 to 1.5 kg of water per kg of dry paper. This excess of water is removed in dryer section. Usually, the dryer section consists of hot rotating cylinders with a diameter of 1.5−2 m, heated by water vapor. Depending of the kind of paper, the number of cylinders varies from 30 to 120 approximately, and dryer felts are used for pass the paper sheet from one cylinder to another.After drying, special processes can be performed in order to bring different paper finishing. For example, starch solution can be applied on pre dried sheet by size press to increase the surface strength of the paper. In the same way, a coating station can be present to apply special covering to improve the surface printability and finishing. In both special stations (size press or coating station), convective and infrared dryers are often used to remove the solvents and additional surface moisture.Thus, depending on paper specification (kind of pulp, basis weight, finishing, equipment, among others), paper is usually produced in the continuous operation of paper machines, which are up to 10 m wide, are normally 100−200 m long, and run at some 10−25 m/s, being in this way a relative fast process [In the last years, infrared dryers were introduced as new technologies in paper production, and in modern machines they are almost always present in dryer or coating sections. These dryers could be used in different sections of papermaking process.The first application of IR equipment is in the press section before the presses. The increase of temperature due to IR heat transfer to the very wet sheet reduce the viscosity of the water held by the sheet, improving the efficiency of pressing and increasing the dryness of the sheet before it reaches the dryer section.IR dryers are also used for preheating between the press section and the dryer section, with the aim to increase the web temperature and accelerate the drying starting in the dryer section, without.Another possibility of the use of infrared dryers is at the end of the dryer section to increase the drying rate when the paper sheet is already rather dry. Normally, in this conditions paper has low thermal conductivity and the driving force for heat transfer is reduced. Thus, the use of IR emitters in this zone allows reducing the number of dryers cylinders for a specific production rate. Last, a very common application of IR dryers in paper industry is the coating station, usually in combination with air dryers.In the drying of coating process, the power used is often very high, a simple machine has a rating of up to 36 MW in these installations []. The use of IR dryers in this station is justify by the initial rapid heat up and drying of the coated web and the transport of energy to the interior of the paper sheet which often provides of better coating quality.The bioactive paper preparation proposed in this manuscript could take place as a finishing section in the paper production, similar to coating steps. Then, the equipment requirements, production rate and other processes variables should be like those usually used for paper manufacturing, in order to guarantee the feasibility of coupling this process with the existing papermaking process. Thus, a research of industrial, pilot and laboratory scale experiences were performed in order to compare with the obtained results. As there is no similar process in the literature, comparison will be performed on IR applications for other step of papermaking, such a drying or coating of paper sheet.] investigates the heat transfer mechanism taking place in IR paper drying at pilot scale equipment. They found a drying time of about 5 s for a light paper with a basis weight of 46 g/m2 with an initial moisture content of 1 g of water/g fibre. The equipment consists of a winding system, an IR with a nominal input power of 126 kW and an air circulation system. The exposure distance between the IR emitter surface and the paper surface can be adjusted in a range of 0.1−0.3 m.On the other hand, Seyed-Yagoobi and Husain [] also carried out the study of heating/drying of moist paper sheet with a gas-fired infrared emitter. The experiments presented were carried out at an emitter fuel consumption rate corresponding to 50.1 kW, with classical radiation calculation of 66.0 kW/m2. They study the effect of different basis weight on IR drying. As expected, the higher basis weights the higher drying time. For samples with an initial dry basis moisture content of 1.5, samples with 100 g/m2 are completely dried in 4 s, while for papers with 200 and 300 g/m2 the drying time is higher than 10 s.] found that the IR efficiency, defined as the fraction of energy supplied to the heater that was transferred to the paper sheet, depends on power level of the dryer or the used electric voltage. For a coated fine paper grade (70 g/m2 base paper coated with 11.7 g/m2), the efficiency could be almost duplicated, taking values from about 20 % for low power level to about 38 % at high power. Additionally, in the same work [], they demonstrate that the moisture content has also an important effect on IR efficiency, increasing from 37 % for a dry 41 g/m2 sheet to above 44 % for a moisture ratio close to unity.There are some studies that use IR emitters during paper coating. Desmaisons et al. [] study and model the impregnation of paper with cellulose nanocrystal reinforced polyvinyl alcohol by means of infrared dryers. The experiments for heat transfer modelling during infrared drying were performed on a short-wave (2 × 1000 W tubes) electrical infrared dryer (234 V), with lamps located 22 cm above the paper sheet with a basis weight of 80 g/m2. The paper coating drying was reached at times between 90−130 s, depending on the coating characteristics.] also model a paper coating using both convection and infrared heating. To simulate the drying process, the available setup data has been collected from production setup with paper web of 47 g/m2 and 2 % moisture, 80 g/m2 end product and with a web speed of 1450 m/min. The upper surface of the paper is coated with 65 % solid content and 5 g/m2. The venting air had temperatures of about 650 °C and 700 °C. The temperature of IR heat source is about 1000 °C with an emissivity of unity due to small distance between the emitter and the drying surface. The distance from the emitter varies from 10 to 40 cm. No specifications are about infrared power. The drying process of this low water content paper coating is about 5–10 s. Thus, it is important to note that, the installed power of the equipment used in this manuscript is far below than the power density of industrial and/or pilot equipment used in mentioned experiments. So, the process studied in this work is slower than the recently cited investigations due to both, the lower power used and the lower IR efficiency related with it. Also, the dry character of paper samples used in the bioactive paper preparation could also reduce the energy efficiency in comparison with a typical drying process, due to the lower IR efficiency and the low thermal conductivity. Additionally, the paper basis weight of modified bioactive paper is quite high (150 g/m2) in comparison of the background paper analyzed.Taking into the account these facts, the optimal operation conditions are promising to think in a bioactive paper process scaling. In comparison with experiences performed with similar equipments characteristic, like the paper coating of paper with cellulose nanocrystal carried out by Desmaisons et al. [], time processes are very similar. However, the optimal process time is higher than the time used for paper drying performed in equipments with very high IR power installed []. Thus, it is expecting that the use of industrial equipments could help to reduce the optimal time found in this work, and thus make the process compatible with the existing paper preparation process.In order to prove the effectiveness in paper modification some final properties, mainly related to active food packaging applications, were evaluated using paper modified under optimal conditions.The first one was the insecticidal activity. One cause of significant quantitative and qualitative losses in food is the infestation by post-harvest insect pests. These can attack stored raw materials, as well as semi-finished and final food products, due to their ability to enter packaged food products during their distribution or storage. Some examples of insects capable of penetrating the package of stored products are: Plodia interpunctella (Hübner), Sitophilus spp., Tribolium castaneum, Lasioderma serricorne (F.), Rhyzopertha dominica (F.), among others. This activity was evaluated in previous work [] and it is checked in the present work as a test for validating the modification with IR heating.Repellency against to Tribolium castaneum of modified and unmodified is shown in . Test was performed on washed and non-washed modified paper with and without eugenol and compared with virgin paper. Clearly, samples with eugenol present high negative values, which denotes the good repellent activity to weevils. Moreover, after washing, eugenol modified paper retains a good repellent action. This shows that the repellent action is not modified when samples are washed. On the contrary, samples without eugenol have positive values, so it shows the lack of repellent activity. Furthermore, washed samples without eugenol showed an attractive effect. This demonstrates the importance of eugenol grafting on bioactivity. Similar behavior was found in previous work [], demonstrating that the heating technology does not alter this activity, this is, the eugenol grafting mechanism is the same and not eugenol degradation is produced.Another cause of food deterioration is the attack of microorganisms, such as molds, yeasts and bacteria, which produce food losses and can also be harmful to human health. Taking into account that both polycarboxylic acid and eugenol present antimicrobial activity, this property was also evaluated on modified papers, with the aim to extent the application of this new material.Thus, antibacterial activity of modified paper against E. coli was evaluated by a dynamic contact test method. A comparative analysis was performed evaluating the activity of virgin paper, modified paper with and without eugenol, before and after washing with abundant ethanol. This kind of comparative assay allows to confirm the activity proceeding from grafted molecules. presents results of the microbial reduction respect to VP (blank) for the tested samples.All samples present high antibacterial activity as expected, because intrinsic activity of both BTCA []. However, the presence of eugenol increases it. It is important to note that modified papers contain both, grafting molecules and free ones meanwhile washed ones only contain grafting molecules and retain high bioactivity against E. coli evidencing that the proposed methodology is successful for generate bioactive papers. In this way, it was proved an additional functionality of the proposed new material.One of the reasons of the predominant position of paper on packaging industry, is its biodegradability, in addition to its low cost, ready availability, and great versatility []. For this reason, it is important to study the effect of grafting reaction on the capacity for biological degradation.Thus, biodegradability test was carried out comparing the washed and non-washed treated papers (with and without eugenol), with the virgin paper. The test was performed monitoring the weight loss and macroscopic appearance for 75 days. shows the image of the papers after 75 days in soil burial conditions. Since fiber rotting is accompanied by a color change of the sample surface, the color difference determined after different periods of burial can also represent a measure of sample biodegradability []. Macroscopic observation revealed that the virgin paper was the one that suffered the most deterioration during the test, followed by the washed papers, while the non-washed papers were more resistant to the attack of the soil microorganisms.These results coincide with the weight loss analysis of the papers tested. shows the weight loss results of the samples tested over time. As can observed in , unmodified paper almost complete degraded in the period of time analyzed, meanwhile weight loss for modified papers decrease between 10 % and 50 % respect to unmodified paper, demonstrating that the progress of the rotting process, caused by microorganism in the soil, is faster for virgin than for modified papers. These results are expected because both reagents, BTCA [], have known antimicrobial activity, as it was demonstrated above, being more resistant to attack of the soil microorganisms. In this sense, non-washed samples degrade slower than washed samples. The non-reacted agents are removed during washing, reducing their amount in samples, and then, their activity. Same behavior was found for antimicrobial activity.Additionally, the crosslinking generated between cellulose chains can also decrease the degradation rate, as observed by other authors. The formation of new intermolecular bonds restricts the cellulose chain mobility and the space between molecules, decreasing the wettability. The decreased amount of moisture in the finished fibers impair the conditions for growth of microorganisms [Although, the modified paper degrades slower than virgin paper, it conserves its biodegradable characteristic.A technology for bioactive paper production using infrared heating as cured media is proposed. In this sense, it was tested for grafting eugenol onto commercial paper.For the proposed reaction, optimal operation conditions at pilot scale were assessed following either curing advance, paper color and mechanical properties. Thus, optimal conditions were: 130 s for the reaction time, 0.45 kW for the power and 15 cm for distance to heat source. Modified paper at these conditions presents insectifuge against Tribolium castaneum (between -100 and -80 % Repellency) and antimicrobial against E. coli (between 82 and 99 % microbial reduction) properties, demonstrating its capacity for different uses in food active application. This antimicrobial activity produces a decrease in the biodegradability rate; however, the important biodegradable characteristic is conserved.From studies at pilot scale it can be inferred that this process is compatible with typical processes for papermaking as drying and coating. This claim is based in several comparative studies from the time-power relationship between process at industrial and pilot scales. Also, from comparative results between convective and infrared curing technologies, it possible to conclude that infrared curing provides the best alternative, with the lowest reaction time and minimal paper degradation (see color and elongation at break). Reduction in reaction time is around 70 %, compared with conventional methodology. Also, the infrared curing achievement a reduction of consumed energy of 80 % compared to convection curing.From this process studies at pilot scale it can be concluded that this technology could be adapted to the current papermaking process doing feasible scaling of bioactive paper production.We the undersigned declare that this manuscript is original, has not been published before and is not currently being considered for publication elsewhere.We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us.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.Supplementary material related to this article can be found, in the online version, at doi:The following is Supplementary data to this article:Investigating the anisotropic mechanical properties of plasma sprayed yttria-stabilised zirconia coatingsThe adhesion and cohesion bond strengths of plasma sprayed yttria-stabilised zirconia (YSZ) coatings were measured by performing the tensile adhesion test (TAT) and the tubular coating tensile test (TCTT). The TAT allowed assessment of adhesive/cohesive bond strength of a coating microstructure perpendicular to the substrate. In contrast, the TCTT quantifies the strength of a thermal spray coating parallel to the substrate without the use of any adhesive. The failure strength of the coatings from the respective tests can be approximated to a Weibull distribution and indicated the anisotropic behaviour of plasma sprayed coatings. The average coating strength parallel to the substrate is approximately 1.5 times greater than the bond strength perpendicular to substrate. The anisotropic behaviour of the plasma sprayed YSZ coatings were also probed using Knoop hardness measurements that were orientated at a well-defined geometry with respect to the lamellar microstructure. In addition, uniaxial compression tests evaluated the Poisson's ratio of these anisotropic YSZ coatings when loaded with respect to the different microstructural orientations.The use of yttria stabilised zirconia (YSZ) ceramics as thermal barrier coatings (TBCs) has been established for applications in advanced gas turbine engine components operating above 1000 °C. The low thermal conductivity of certain zirconia-based ceramics leads to benefits that include reducing the component cooling requirement while maintaining suitable metal substrate temperatures. Coupled with complex air cooling designs and the use of high temperature nickel-based superalloys, improved engine performance and durability can be attained. Commercially viable TBC applications were developed at NASA Lewis Research Center (now NASA Glenn Research Center) The partially yttria stabilised zirconia coating in the as-sprayed state A YSZ coating may be manufactured via the air plasma spray process, which confers a lamellar microstructure that is formed by the rapid solidification of impinging molten droplets and cohesion among splats It is characteristic that the lamellar splat structures give rise to the highly anisotropic mechanical properties of thermal spray coatings The standard tensile adhesion test method for thermal sprayed coatings, as described in ASTM C633-08 There are several references that illustrate methods to measure the strength of a thermal spray coating parallel to the substrate. Different designs have been discussed The tubular coating tensile test (TCTT) Within the current work it should be cautioned that the term “elastic” is used for convenience since thermal spray coatings deform by inelastic splat sliding. The coating modulus is affected not only by the strength of lamellae cohesion but also by the distribution of the void and crack network. The inhomogeneous architecture of a thermal spray coating is likely to cause pseudo ductility because the lamellae are able to slide over each other The Poisson's ratio of thermal spray coatings, since it is mathematically related to “elastic” properties, should also be related to the unique lamellar microstructure and be direction dependent. It has been noted that the evaluation of coating bond strength, crack growth rates, and coating stresses during in-service loading requires accurate values of the coating modulus and also Poisson's ratio In this work, the mechanical strength of plasma sprayed YSZ coatings was determined (i) in the plane parallel to the substrate surface by TAT methods, and (ii) in the cross section orientation, perpendicular to the substrate that reflects the cross sections of splats by means of TCTT techniques. In addition, Knoop microhardness indentation tests were performed at specific orientations to establish the anisotropic behaviour of the coatings. Finally, coating removal techniques were applied to obtain free standing plasma sprayed YSZ specimens. Subsequently, the thermal spray coating modulus and Poisson's ratio were determined by uniaxial compression in different orientations. The measurements of such transverse and longitudinal strains were accomplished with mounted strain gauges on the coating.The use of YSZ ceramics in the context of this work considers thermal barrier coating (TBC) applications. TBCs can be found in advanced gas turbine engine components operating above 1000 °C Coatings were produced on TAT and TCTT specimens, both 25 mm in diameter, using an industrial air plasma spray system (Metco 7MB, Sulzer Metco Inc., Westbury, NY-USA). In these experiments, operating conditions corresponded to those typically recommended by the coating manufacturer, see . The plasma torch was mounted on a robotic arm (YR-SK16-J00 Motoman, Yaskawa Electric Corp, Japan) to transverse across the individual substrate holders. Specialized substrate holders were designed to allow batch thermal spraying of TAT and TCTT coupons. Detailed information concerning the specimen geometry and technical drawings for TAT and TCTT configurations can be found in reference The cross section profile of the TBC consisting of bond coat and YSZ top coat was prepared according to ASTM E1920: Standard Guide for Metallographic Preparation of Thermal Sprayed Coatings The microstructure of prepared samples was characterised using a field emission scanning electron microscope (Zeiss SUPRA™ 40VP FESEM system). Image analysis software (ImageJ, US National Institutes of Health, Bethesda, MD) was employed to process the FESEM images to evaluate the porosity according to the test method described in ASTM E2109: Test Methods for Determining Area Percentage Porosity in Thermal Sprayed Coatings The Bruker X-ray diffractometer (XRD) with Cu Kα radiation at 40 kV and 30 mA was employed to identify the phases in the feedstocks and coatings by comparison with standards from the International Centre for Diffraction Data's Powder Diffraction File (PDF).Once the thermal spraying of 25 mm diameter specimens was completed, they were individually checked with an electronic thickness gauge (Minitest 650, ElektroPhysik) to ensure that the thickness did not vary across the surface by more than 25 μm. TAT assembly employed a film epoxy (FM1000, Cytec Industries Inc., NJ, USA) that was placed between both mating surfaces. A vee block held the cylindrical specimens in a parallel position to maintain alignment during tightening. The assembly was tightened to approximately 150 kPa using a torque wrench and the specimens cured under gravity at a 70–75° angle with the pull-off bar placed in the bottom position of the assembly. Epoxy curing was carried out at 190 °C for 2.5 h under a soft vacuum of 70 kPa.A universal joint design was used for the tensile test rig as recommended by the ASTM C633 standard The cross sectional area of the TCTT specimens under test was small; therefore, a table-top electromechanical-type universal machine Z010/TN2S (Zwick GmbH & Co, Ulm, Germany) could be used without sacrificing data integrity. The Z010/TN2S crosshead was screw driven with a 500 W DC actuator and was equipped with an interchangeable load cell capable of measuring up to 1 kN. The constant crosshead speed of 0.008 mm/s was selected as the testing condition for all samples. This test speed was almost half that used for the conventional ASTM C633 standard since the intention was to maintain the strain rate range within the quasi-static or pseudostatic mode of tensile testing; i.e., between 10− 5 and 10− 1 |
s− 1. The time to failure, crosshead displacement and maximum failure load were recorded at 50 Hz for further analysis. It is noted that only the YSZ coating layer was tested and 35 TCTT assemblies were sampled.The effects of the indenter orientation with respect to the coating cross sectional lamellar microstructure were investigated by orientating the major diagonal of the Knoop indenter in two directions: (i) parallel to the lamellar layers, and (ii) perpendicular to the lamellar layers, see . This was accomplished for “Direction 1” by the alignment of the coating–substrate axis to the major diagonal of the Knoop indenter. For “Direction 2”, the entire sample stage was re-orientated at 90°, without moving the test specimen. The Knoop microhardness device uses a calibrated machine (Micromet 2103 Microhardness Tester, Buehler, USA) to force a pointed, rhombic base pyramidal diamond indenter having specified angles, under a predetermined load, into the surface of the cross sectioned YSZ coating sample.The rate of indenter motion prior to contact with the specimen was set to 0.060 m/s. The time of application of the full test load was selected as 15 s unless otherwise specified.Thermal spray ceramic coatings are known to exhibit a low tensile strength. Thus, the compression technique is preferred and permitted the YSZ specimens in this study to be loaded to representative stress magnitudes of between 60 and 120 MPa. The test method ASTM C1424 Additionally, the curves of transverse strain and longitudinal strain enabled calculation of Poisson's ratio. The measurements of transverse and longitudinal strains were accomplished with strain gauges (Micro-Measurements Model EA-06-031CF-120, Vishay Precision Group, USA) mounted on the coating perpendicular to each other. The loading directions, hence measured coating modulus and Poisson's ratios, relate specifically to these two test orientations, see . The first test orientation, Orientation A, comprises a uniaxial compression load applied on the coating plane sections while the coating cross-sections were measured for longitudinal and transverse strains. The specimen dimensions for Orientation A are 10 × 15 mm (loading area) by 5 mm thick. The other test, Orientation B, illustrates a uniaxial compression load that is applied on the cross section of the coating and indicates the corresponding coating cross-sections that were measured for longitudinal and transverse strains. Specimen dimension for Orientation B is 10 × 5 mm (loading area) by 15 mm thick. Note that variations in the test specimen dimensions from those of ASTM C1424 test standards were inevitable, due to limited size of the coating material. Longitudinal strain is determined by measuring the change in length in the loading direction which was divided by the specimen original length. On the other hand, transverse strain refers to the ratio of change in length to original length orientated perpendicular to the loading direction.Large micrometre-sized interlamellar pores in the order of 1 to 15 μm in diameter were widespread and well distributed among the microstructures for all of the YSZ coatings, see . The lamellar microstructure became evident at high magnification and splats of approximately 10 μm thickness were distinguished. These images also showed that the lamellar microstructure was highly defective with the presence of both fine interlamellar and intralamellar cracks. The predominant crack features were (i) interlamellar horizontal cracks, and (ii) vertical intralamellar cracks. The coating porosity level was 17.6 ± 2.7% (n = 32).The phases present in the YSZ material in the as-sprayed coating and the feedstock were similar, as observed from the diffraction peaks in . The coating showed strong diffraction peaks for the tetragonal phase of zirconia, which would be associated with the formation of non-equilibrium tetragonal (T′) phase from the rapid cooling of the molten splats during spraying. In addition, the peak signatures for the monoclinic phase diminished. Although quantitative analysis was not carried out to determine the phase concentrations, the reduction of the monoclinic peaks indicates that the addition of yttria into the feedstock inhibited the formation of the monoclinic phase The majority of YSZ coatings failed at the bond coat–ceramic coat interface and the failure mode can be termed as “internal adhesive”. shows the scanned image of a typical YSZ test sample exhibiting failure along the bond coat–ceramic coat interface. Conventional image processing techniques have been used to highlight the bond coat material in a red colour. Most of the YSZ material was transferred onto the pull off bar while the bond coat material was exposed along with some retained YSZ coating on the coated substrate. Tensile adhesion strength is calculated by taking the ratio of the failure load divided by the test area. The average adhesive strength of plasma sprayed YSZ coatings was 8.46 ± 2.01 MPa with a coefficient of variance (COV) of 23.8%.It is important to point out that since the principal load was applied normal to the plane of the substrate, the reported coating TAT strength is related to the distribution of an interlamellar horizontal crack network. Tensile fracture occurs in the coating's weakest plane The TCTT probed the mechanical response of the coating from the aspect of the influence of vertical intralamellar cracks and/or interlamellar cracks; i.e., the directionality and lay of defects. High resolution photo-scanned images of the cross sectional failure areas were used to calculate the coating inter-splat cohesive strength. Firstly, the scanned image was acquired and then post-processed using suitable image threshold methods to isolate the “ring” shaped coating from the substrate and scan background. Subsequently, the failure stress was calculated by dividing the failure load with the area of the ring-like cross section Finite element stress modelling of the TCTT method indicated that the geometrical design of mating two substrates via a thermal spray coated structure can lead to a local stress concentration along the plane of the two substrates The tensile loading conditions between the TAT and TCTT methods differ as highlighted in a, the test load is applied perpendicular to the substrate surface. The tensile fracture mechanism of the coating is caused by cumulative splat delamination due to poor intersplat cohesion or splat–substrate adhesion occurring along the weakest plane. In contrast, b illustrates the cross section view of a TCTT specimen and the potential crack propagation path across the coating as the specimen is loaded. The cracks that result in coating failure propagate parallel to the substrate surface. It is also important to note that the TCTT method does not represent Mode II coating failure as described by Callus et al. c. In other words, the compact tension measures the failure shear stress along the weakest plane of the coating while the TCTT provides the ultimate tensile strength of the entire intersplat layer.A fractured TCTT sample was also chosen for SEM analysis as shown in a image revealed interlamellar horizontal cracks and vertical intralamellar cracks, as well as interlamellar pores. Additionally, the SEM image in b provided evidence concerning incomplete splat stacking and the vertical columnar grain growth associated with rapid quenching and solidification of impacting splats. Cracks and pores would be arbitrarily scattered within the test plane that joins the two substrates together. These crack and pore networks had the damaging effect of acting as nucleation sites for coating failure during tensile loading.The TAT and TCTT measure coating strength under tensile loading but the principal stress orientations were different. The TAT assessed the tensile strength in the weakest plane parallel to the substrate while the TCTT was carried out to evaluate intersplat strength perpendicular to the substrate, see . A comparison of the mean values from the respective tensile tests is presented in . It was determined that the plasma spray coating intersplat cohesive strength was greater than the tensile adhesion strength. The difference in strength arose due to the anisotropic microstructure in the cross section plane of the coating. Since the test orientations were normal to each other, the higher TCTT results suggested that the strength in the spray direction, perpendicular to substrate, was greater.The mechanical property values for coatings were compared to dense sintered ceramics that were isotropic . It was determined that the strengths of thermal spray coatings were significantly less than the equivalent dense bulk ceramics. The reduction in coating strength arose from the lamellar microstructure that was defective in nature, and the disparity in material phases that existed within the as-sprayed coating.The failure distributions of TAT and TCTT data were examined for the APS YSZ coatings to further assess whether thermal spray ceramic coatings followed the Weibull theory . The R2 values from the regression analyses were above 0.9. The Weibull modulus (m), , is a measure of the variability in strength for the particular data set. The m value is estimated to be between 5 and 10 . A paired one way Student's t-test conducted at a 0.05 level significance produced a P value of 0.00030 and indicated that the data sets were statistically from different populations.Therefore, statistical analysis reveals that the coating microhardness property exhibited anisotropic behaviour and the value was sensitive to indenter orientation. These results are consistent with those gathered from the TAT and TCTT measurements in which the mechanical strength in the axis parallel to substrate was greater.The respective experimental stress–strain curves shown in , were recorded from one of the YSZ coating specimen compressed in Orientation B. The longitudinal strain, ε1, which represents the principal load direction, is always greater than the transverse strain, ε2. Importantly, the hysteresis of the stress–strain curves can be observed in all cases and the YSZ coatings cannot be described as linear elastic The hysteresis can be attributed to inelastic effects, such as crack evolution, splat debonding, and mutual splat sliding; but may also indicate that microstructural changes in the coatings, such as pores closing, may be reversible The values of effective coating secant modulus of elasticity and corresponding Poisson's ratio of free standing YSZ coatings evaluated via uniaxial compression tests are presented in . In both orientations, the YSZ coating modulus is lower than the bulk material properties, Y.Ebulk YSZ |
= 180–250 GPa The YSZ coating modulus, 72.0 GPa, in Orientation A, which is a widely adopted tested orientation, is comparable to reported literature values of 30–70 GPa Furthermore, the YSZ coating modulus in Orientation B, 40.1 GPa, is lower in value than that of Orientation A, 72.0 GPa; indicating that the test direction is critical. It is important to note that the principal load for Orientation B is aligned on the cross sectional plane of the coating. This load alignment is more susceptible to the influence of the interlamellar crack network; particularly the inelastic growth of interlamellar horizontal cracks caused by poor intersplat cohesion. This is also further evidence of anisotropic mechanical behaviour of the YSZ coating. The ratio of stiffness between Orientations A and B for a coating under uniaxial compression is about 1.79.In addition, the TCTT can be also seen as a representation of loading the coating in tension, specifically in Orientation B. Therefore, by applying Hooke's law where KM is the machine elastic deflection and is known as the machine stiffness, L0 is the initial specimen gauge length, S is the crosshead speed of the testing machine, and A0 is the initial cross-sectional area of the specimen. Ṗ0 is the specimen load rate obtained from the test curve profile. KM was determined to be 3.06 MN/m from a compliance calibration of the equipment. The YSZ coating modulus in tension was calculated as Et |
= 26.9 ± 4.0 GPa.The YSZ coating modulus values in Orientation B can be compared. The lower coating modulus in tension, Et |
= 26.9 GPa, compared to Ec |
= 40.1 GPa is consistent with data reported elsewhere The Poisson's ratio of YSZ coatings was obtained from the ratio of − Δε2/Δε1 and calculated to be ν = 0.222 in Orientation A and ν = 0.177 in Orientation B. These measurements are similar to those obtained using a cantilever beam test The mechanical strength of plasma sprayed YSZ coatings were measured by performing the tensile adhesion test (TAT), the tubular coating tensile test (TCTT), Knoop microhardness indentation, and the uniaxial compression test.The adhesion strength of the YSZ-bond coat system measured by TAT was 8.46 ± 2 MPa. The TCTT, measuring the coating's intersplat strength parallel to the substrate without the use of any adhesive, yielded strengths of up to 20.4 ± 11 MPa. In both data sets, the failure strength of the coatings from the respective tests can be approximated to a Weibull distribution and also indicated the anisotropic behaviour of YSZ plasma sprayed coatings. The average coating strength parallel to the substrate is approximately 1.5 times greater than the bond strength perpendicular to substrate.These tests revealed that the mechanical response of a thermal spray coating depends on microstructural alignment with respect to the unique lamellar features of these coatings. Anisotropic material properties are expected for coating strength, microhardness, coating modulus and Poisson's ratio. The test directionality with respect to the various coating microstructural features includes (i) splat dimensions, (ii) spherical pores, (iii) interlamellar vertical cracks, (iv) interlamellar horizontal cracks, and (v) intralamellar microcracks. These microstructural features significantly influence the measured material property.The influence of hydrostatic pressure on gas diffusion in polymer and nano-composite membranes: Application to membrane inlet mass spectrometry► A nano-composite membrane was directly coupled to the inlet system of a mass spectrometer. ► The nano-composite membrane was created by the deposition of a thin polysiloxane film on the surface of an anodic aluminum oxide (AAO) membrane, forming a polysiloxane nano-composite (PNC) membrane. ► The gas-permeation properties of the PNC membrane were compared to those of a conventional polydimethylsiloxane (PDMS) membrane over a range of hydrostatic pressures. ► Permeation of gases through the PNC membrane was much less affected by hydrostatic pressure than permeation through the PDMS membrane.A nano-composite membrane, created by coating a thin polysiloxane film to the surface of an anodic aluminum oxide (AAO) membrane, was directly coupled to the inlet system of a mass spectrometer. The gas-permeation properties of the polysiloxane nano-composite (PNC) membrane were compared to those of a conventional polydimethylsiloxane (PDMS) membrane over a range of hydrostatic pressures. Permeation of gases through the conventional PDMS membrane was reduced at high pressure by compression of the siloxane matrix. The PNC membrane had a much higher mechanical strength than the PDMS membrane, and exhibited little deviation in gas permeation at elevated hydrostatic pressure. Consistent with this difference in behavior, whereas the PDMS membrane exhibited hysteresis throughout cycles of increasing and decreasing hydrostatic pressure, hysteresis effects were substantially limited for the PNC membrane. The time required to attain steady-state diffusion through the PNC membrane was substantially reduced relative to the PDMS membrane.Mass spectrometer (MS) inlet systems have included capillary tubes, a variety of orifice-types, inorganic and organic membranes, and composite membranes MIMS is a valuable technique for analysis of volatile solution species, and is particularly useful for in situ or on-line applications. MIMS has been used to detect analytes at concentrations as low as parts-per-trillion Polydimethylsiloxane (PDMS) is currently the most frequently selected membrane for MIMS analysis of volatile, relatively non-polar analytes in aqueous solutions. Commercially available PDMS membranes have thicknesses on the order of hundreds of micrometers (microns), making them easy to mount without mechanical tearing. Under normal laboratory conditions, membrane inlet systems are generally used at atmospheric pressure. However, in some applications, including in situ measurements of dissolved volatile components of seawater and monitoring of analytes in bioreactors Polymer films have been reported to exhibit higher hardness than their bulk polymer counterparts when film thickness decreases In order to characterize the permeation properties of thin films with respect to variable hydrostatic pressure, we have fabricated and tested nano-composite membranes for MIMS analysis of dissolved gases in aqueous solutions. The nano-composite membrane was composed of an anodic aluminum oxide (AAO)-membrane substrate coated with a thin polysiloxane film. MS ion currents produced using polysiloxane nano-composite (PNC) membranes and conventional PDMS membranes were used to assess the gas permeabilities of each type of membrane over a range of hydrostatic pressures. To the authors’ knowledge this manuscript provides the first observations of the effects of hydrostatic pressure on a PNC membrane that have been obtained using membrane introduction mass spectrometry.A membrane module was created using vacuum epoxy to mount an AAO membrane (Whatman) on a stainless steel frit. Previous results demonstrated that the vacuum epoxy eliminates leaks around the edge of the oxide membrane a). The PDMS membrane module was purchased from MIMS Technology Inc. and was modified to incorporate a stainless steel frit that provided mechanical support for the membrane. The assembly for support of the PDMS membrane is shown in The AAO membranes used in this work had a uniform and monodispersed arrangement of pores (a). The AAO membranes were 60 μm thick and had channels (pores) with an average diameter of 200 nm. The polysiloxane films were uniformly deposited across the upper surface of the AAO membranes and, on average, were 11 μm thick (b). Scanning electron microscope (SEM) analysis showed polymer material to depths of 400 nm within the AAO pores (image not shown). The cumulative area of the four PNC membranes was ∼8 mm2. The PDMS membrane (Diversified Silicon Products, Inc.) was 304 μm thick and had a total area of 18 mm2 (Mass spectrometry measurements were conducted using the system shown in . The membrane module was connected directly to a quadrupole MS (Inficon, Transpector 2.0 Gas Analyzer System). The PNC and PDMS membrane modules were connected and disconnected from the MS via a Swagelok fitting. An HPLC pump (Shimadzu) transported experimental solutions from the sample reservoir (d, ) into the membrane module. The membrane modules had a built-in heater block for regulation of sample temperature at the membrane–water interface. A backpressure regulator (Swagelok) was used to control the hydrostatic pressure within the membrane module. Hydrostatic pressure was monitored with a digital pressure gauge (Cecomp Electronics Inc.). Sample flow rates were monitored using a rotameter (Omega) at the exit end of the backpressure regulator. Exiting fluid was returned to the sample reservoir. Gas-diffusion experiments, described in Section , were performed using a peristaltic pump on the retentate side of the membrane modules.Measurements were made using a Faraday cup detector. The ion currents produced by diffusion of CH4, N2, O2, Ar, and CO2 through the PDMS and PNC membranes were analyzed at m/z ratios of 15, 28, 32, 40, and 44. Background values were measured by stopping the flow of the sample and allowing the solution to degas through the inlet membrane. For direct comparison of the PNC and PDMS membrane introduction systems, overall inlet permeability rates were empirically matched, whereby the total pressure inside the vacuum chamber created similar ionization conditions. Experimental runs were performed at a steady flow rate over a range of hydrostatic pressures. The temperatures of the aqueous solutions that entered and passed through the membrane module were regulated at 30 °C for the PNC and PDMS membrane. Total pressure inside the ionization region was measured using the pressure-reading software of the Transpector mass analyzer, and ranged between 2.4 × 10−4 and 6.9 × 10−4 |
Pa.Permeating gases achieve a steady state gas flux (FG) into the MS vacuum system that is directly proportional to the concentration of a gas [G] or, ideally MS signal responses (ΦG) for transmitted gases, corresponding to their fluxes through the membranes, were determined at m/z ratios of 15, 28, 32, 40, and 44. The permeability properties of the PDMS and PNC membranes were observed at various hydrostatic pressures in the following manner. Observed ion currents produced by gas fluxes through the membrane were allowed to attain steady state at a hydrostatic pressure of ≈1 bar. Once ΦG signals were steady, the external hydrostatic pressure on the membrane module was increased, in steps, to approximately 41 bars for the PNC membrane and 14 bars for the PDMS membrane (the lower pressure limit for the PDMS membrane was caused by limitations of the membrane assembly). External hydrostatic pressure was then returned to 1 bar in a series of steps.Baseline or background levels were attained after stopping the pump and allowing the sample to degas through the membrane (). Baseline (background) values were taken as observed steady state values in the absence of dissolved gases. After the background signals reached a steady state, the pump was restarted. Ion currents were then measured as the system approached and attained steady state.Baseline normalized ion currents (IBN) were calculated (Eq. ) as a means of comparing the mass flux properties for both types of membrane.where ΦG(baseline) is a baseline current for a given gas, G, and ΦG is the ion current for gas G measured at any point in time. shows a comparison of background-normalized ion currents (IBN) for each gas permeating through the PDMS and PNC membranes. shows that gases permeating through the PNC membrane attain steady-state considerably sooner than is the case for permeation through the PDMS membrane. Diffusion properties for most non-porous membranes have been estimated by a time-lag technique and were calculated using the following equation where DG is the diffusion coefficient, L is the membrane thickness and t1/2 is the time required to achieve 50% of the final steady state permeation. Diffusion coefficients for the PNC membranes were calculated using the average thickness (11 μm) of the thin polymer films. An apparent diffusion coefficient, “DG”, for the PNC membrane was also calculated using the total thickness of the polymer film plus AAO membrane (11 μm + 60 μm). shows that t1/2(PDMS)/t1/2(PNC) ranges from 8.2 to 18.6 for gases permeating through the PNC membranes. Thus, the time required to attain steady state diffusion is approximately an order of magnitude smaller than is the case for the PDMS membrane. This attribute can be very useful for in situ monitoring of dissolved volatile species in aqueous environments. Diffusion coefficients for the PNC membrane, measured using the thin polymer film thickness, are approximately two orders of magnitude lower than those measured for the PDMS membrane. In contrast, apparent diffusion coefficients, “DG”, calculated using overall (combined) membrane thickness are roughly comparable to those calculated for the PDMS membrane. Notably, in spite of the much greater thickness of the PDMS membrane, the observed ion currents obtained with this membrane are uniformly greater than those obtained with the PNC membrane.The PNC membranes consist of a thin polymer film and a nano-porous support substrate. Transport through the thin polymer film can be described by Fick's law When exposed to aqueous solutions, thin-film membranes exhibit high water permeation rates The signal intensity of a gas is proportional to the rate of each gas permeating through the membrane. Both membrane systems produced similar pressures inside the vacuum chamber of the MS and, thereby, similar ionization conditions. An “enrichment factor” for each gas can be determined (at approximately identical ionization conditions) by measuring the ratio between the background-normalized ion currents (IBN) observed for the PDMS membrane and the PNC membrane. The observed PDMS/PNC enrichment ratios for each gas at steady state were: 1.28 for CH4, 3.24 for N2, 5.19 for O2, 3.59 for Ar, 1.92 for CO2, and 0.043 for H2O (m/z 18). Thus the PNC membrane had enrichment ratios that were roughly a factor of three lower than the PDMS membrane (with the exception of H2O).Hydrostatic pressure at the membrane module was increased in discrete steps. At each step the permeability (PG) for each gas was quantified using the following relationship where FG is the gas flux, A is the membrane surface area and Pp(G) is an upstream partial pressure of gas G. Permeability characteristics obtained for each increasing hydrostatic pressure were calculated as PG/PG(1 bar) and plotted ( clearly shows, for each gas, that the permeability of PNC membranes was much less affected by hydrostatic pressure than PDMS membrane. The PDMS membrane module obtained from MIMS Technology Inc. was only capable of tolerating hydrostatic pressures as high as 14 bars because higher water pressures caused water seepage through the seal that encased the PDMS membrane. The PNC membranes and custom-made supporting module were designed to tolerate hydrostatic pressures of 41 bars or more.The difference in the permeability characteristics of the two types of membranes is attributable in part to their mechanical properties. The compression properties of materials can be expressed in terms of Young's modulus where Γ̶/A is the force per unit area applied to the material and ΔL/L is a fractional change in the linear dimension of the polymer material. Elastic polymer films experience a compression that is perpendicular to the support axis (e.g., a frit or oxide substrate). The compressional change in thickness (ΔL) of a polymer film is directly proportional to the applied hydrostatic pressure (Ph), and polymer membrane thickness (L), and inversely proportional to E: ΔL |
= |
Ph |
· |
L/E, where Ph |
= Γ̶/A. The enhanced molecular bonding properties of thin films result in mechanically stronger films and higher E values PDMS membranes exhibit hysteresis when hydrostatic pressure is increased and decreased. Loops in PG/PG(1 bar) vs. pressure plots caused by hysteresis results in variable PG at identical hydrostatic pressure. The PDMS membrane used in these experiments exhibited substantial hysteresis during hydrostatic pressure cycling () for the PNC membranes were quite small. This attribute of the PNC membrane produced in this study should prove to be quite valuable in measurements of gas concentration profiles over the full range of ocean depth.Permeation of gases through PNC membranes was much less affected by hydrostatic pressure than permeation through a PDMS membrane. For a variety of gases, permeation through the PDMS membrane decreased by approximately 15% as pressure was increased to 14 bars. In contrast, gas permeation through the PNC membranes produced in this work changed by only few percent for hydrostatic pressures up to 41 bars. The relative insensitivity of PNC membranes to hydrostatic pressure greatly reduced the significance of hysteresis for PNC membranes relative to the PDMS.The response times of gases permeating PNC membranes were substantially reduced relative to the PDMS membrane. The time required to attain 50% of steady state permeation through PNC membranes was approximately an order of magnitude smaller than that required using a PDMS membrane. The PDMS membrane produced high analyte-water permeation ratios relative to PNC membranes.Nano-composite membranes are viable inlet devices for the detection and quantification of volatile analytes in solution. Thin polymer films can be used to minimize compression effects and provide improved linearity of MIMS responses to analyte concentrations over a range of hydrostatic pressures. This feature could be very important for use of MIMS over the wide range of depths and pressures in seawater.Effect of heat-treatment on the dynamic compressive strength of Longyou sandstoneTemperature plays an important role in many rock engineering practices. The increase or decrease of temperature induces the damage characterized by cracks/voids in the rock and thus reduces its strength. Therefore it is essential to quantify the damage induced by the heat-treatment and establish its correlation to the mechanical properties of rocks. In this study, X-ray Micro-computed tomography (CT), a non-destructive observation technique was utilized to quantify the damage induced by the heat-treatment. Using CT images, the damage variables were measured for Longyou sandstone (LS) at three heat-treatment temperatures, 250 °C, 450 °C, and 600 °C, and room temperature of 25 °C. The dynamic compressive strength of LS was then obtained by a modified split Hopkinson pressure bar system with the loading rate from 102 to 104 |
GPa/s. An empirical equation to quantify the correlation between the damage variable and the dynamic compressive strength was established from the experimental data.Thermal effect plays a key role in many rock engineering practices, including rock drilling, ore crushing, deep petroleum boring, geothermal energy extraction, and deep burial of nuclear waste (). The problem of the effect of temperature or heat-treatment temperature on the mechanical properties of rocks has been suggested as residing in the evolution of microstructure, such as size, number and orientation of microcracks and bedding planes in material, due to temperature variation. For instance, after the heat treatment (up to 850 °C), the increasing of both number and average opening distance of microcracks in Westerly granite has been reported by . Many other researchers have reported the influence of thermal treatment on the physical ( found that the P-wave velocity of five carbonate rocks increases as temperature increases from room temperature to 100 °C, and then decreases sharply with the heating temperature (up to 500 °C). measured the static fracture toughness of Kimachi sandstone and Tage tuff from room temperature up to 200 °C (0.075 mm/min loading speed). They showed that the fracture toughness first decreases as the temperature increases from room temperature to 75 °C, then increases with the temperature up to 125 °C. Similar results were reported by Balme et al. on igneous rocks ( measured the static fracture toughness of Fangshan gabbro and Fangshan marble after heat-treatment under high temperature (up to 600 °C). They reported that the toughness decreases with an increase of the heat-treatment temperature, due to the cracks induced by the heat-treatment.In part of the mentioned rock engineering practices, such as drilling, cutting, tunneling and blasting, rock might fail under the combination of high temperature and high loading rate conditions. Under high loading rate condition, the behavior of rock is different than that of rock under static loading condition. For example, reported that the compressive strength of Laurentian Granite increased from 240 MPa to 375 MPa when the loading rate increased from 4000 GPa/s to 10,000 GPa/s. Thus, dynamic tests are necessary to understand the failure progress of rock under both high temperature and high loading rate conditions. The thermal effects on dynamic strengths of rock were investigated in some literatures ( utilized the split Hopkinson pressure bar (SHPB) to measure the dynamic uniaxial compressive strength of Dresser basalt with ambient temperatures up to 527 °C (strain rate 670–1090 s− 1). They obtained an equation to correlate the ambient temperature, the strain rate, and the flow stress of Dresser basalt. measured the dynamic fracture toughness of Fangshan gabbro and Fangshan marble under high ambient temperatures, by employing a short-rod specimen in combination with the SHPB system. They concluded that the dynamic fracture toughness of such rocks was mainly determined by the loading rate within the limited range of temperature (up to 330 °C). reported that the dynamic fracture toughness of Laurentian Granite decreased as the heat-treatment temperature increases up to 850 °C (loading rate 25–164 GPa·m1/2 |
s− 1). From the above results, it can be concluded that both static and dynamic compressive strength and fracture toughness of rocks generally decrease with the thermal treatment temperature due to microcracks induced by heating. However, the mineralogical factors such as grain expansion, dehydration, phase transition, and re-crystallization may add more complexities to the experimental observations (). Thus the quantification of thermally induced damage of rocks is essential to interpret the macroscopic experimental observations, such as elastic wave velocity and strength measurements.There are several traditional methods to monitor the cracks induced by the thermal effect, such as acoustic wave measurement (), and the optical or electronic microscopic method (). During the last forty years, the flourishing development of X-ray computed tomography (CT) provides a unique non-destructive method for 3D microscopic examination in medical and industrial applications (). This technique has been adopted to investigate hydraulic and physical properties and failure mechanisms of geomaterials ( utilized X-ray CT to scan cracks inside rock samples, including gypsum, granite, sandstone and limestone, which were statically deformed and fractured in a triaxial cell. Later several studies were devoted into the observation of the fracture mechanism under static loading for soil (, in which the real-time 2D X-ray Micro-CT method was utilized, was conducted to observe the damage evolution of sandstone under triaxial compression. The size of sample was 50 mm in diameter and 100 mm in length with the space resolution of the CT machine 0.35 × 0.35 × 0.1 mm3. They reported that the CT value could be used as an index to describe the damage evolution during the test. Compared with the traditional 2D and destructive examination techniques, the X-ray CT technique has advantages of being non-destructive and presenting 3D damage information although the scanning is 2D. For example, utilized 3D X-ray CT and successfully investigated the damage evolution of granite under dynamic loading.Because the compressive strength of rock is one of the most important parameters in rock engineering practices, and the dynamic test method of compressive strength is less complex than that of the tensile strength test (), the specific problem investigated in this work is the accumulated damage in rocks due to heat-treatment and its effect on the dynamic compressive strength of rocks. introduces an experimental technique based on SHPB and sample preparation procedure. presents the CT data scanned by a 3D X-ray Micro-CT scanning technique. The CT values of rocks after heat-treatment are presented and an empirical model between the strength of sample and damage variable is established in A fine-grained homogeneous sandstone, Longyou sandstone (LS) is chosen in this study to demonstrate the influence of heat-treatment on the uniaxial compressive strength. The mineral composition and some physical properties of LS are listed in ). For the dynamic compressive test by SHPB, sandstone was first drilled into 25 mm in diameter cores. These cores were then cut into cylinder. Three groups, twenty one samples in total were prepared in this study: samples were thermally treated for 2 h under 250 °C, 450 °C and 600 °C, respectively. The heat-treatment was carried out in a servo-controlled electrical furnace with a 2 °C/min heating/cooling speed, which is sufficiently slow to avoid cracking due to thermal shock (). The average P-wave velocity of heat-treatment sample is listed in , and the difference in three directions is less than 5% overall. shows typical samples, and it can be observed that the sample treated at 600 °C is darker than other samples.The heat-treated samples were then scanned by the Scanning Electron Microscope (SEM) as in . In general, the size of particles of LS ranges from 0.02 mm to 0.15 mm. Small mica and calcite particles fill up the gaps between quartz and feldspar based on grain size provided by . There are more small particles attached on the surface of large particles as shown in a), which might be an indication of the cement decomposition (c) and d), cracks introduced by the heat-treatment can be clearly observed marked with circles. However, it is difficult to detect any evolution of damages in . Overall it is hard to carry out quantitative analysis of the damage introduced by heat-treatment using the non-destructive SEM technique.The split Hopkinson pressure bar (SHPB) system was used to conduct dynamic uniaxial compressive strength (UCS) tests of rocks, following the recent International Society of Rock Mechanics suggested method for dynamic rock tests (). The SHPB system consists of a striker bar (200 mm in length), an incident bar and a transmitted bar, as shown in . The diameter of bars is 25 mm. The incident (input) bar is 1500 mm long and the strain gauge is located 787 mm from the impact end of the bar. The transmitted (output) bar is 1000 mm long and the stain gauge is 522 mm away from the specimen–bar interface.The specimen is sandwiched between the incident bar and the transmitted bar. The striker bar is launched by a low speed gas gun. The impact of the striker bar on the free end of the incident bar generates a longitudinal compressive wave propagating in the incident bar as incident wave εi. When the incident wave reaches the incident bar–specimen interface, part of the wave is reflected back as reflected wave εr, and the remainder passes through the specimen and then enters the transmitted bar as transmitted wave εt (the symbol ε indicates strain here). These three waves were measured using the signals obtained from the strain gauges () and used to infer the dynamic response of the material (i.e., stress–strain curve) subsequently.Using these three waves, the forces P1 and P2 on both ends of the specimen can be calculated (where E |
= 200 GPa and A are Young's modulus and cross-sectional area of the bars, respectively.For brittle material under dynamic loading, the pulse shaper has been introduced to eliminate the inertia effect inside the sample subjected to dynamic loading (). In this work, a copper shaper (Multipurpose 110 Copper from McMaster-Carr®) with 3.175 mm diameter and 1 mm thickness was used for each test. With the shaper, the forces applied on the sides of the sample are approximately in equilibrium during test (), the histories of strain ε(t) and stress σ(t) within the sample in the dynamic compression tests can be calculated as:where C |
= 5051 m/s is the one dimensional P-wave velocity of the bar, L is the length of the sample and A0 is the initial cross-sectional area of the sample. For the typical SHPB test, the strain–stress curve obtained using Eqs. . The dynamic UCS is identified as the peak-value of the stress experienced by the sample, which is 89.4 MPa for the test shown in X-ray Micro-CT as a non-destructible method was used to examine the microcracks/voids inside the heat-treated sample. A GE Micro-CT system at STTARR, Canada was used to provide a high resolution scan with an 80 W X-ray source at 80 kV. During scanning, the sample was placed perpendicularly to the scanner, i.e. the X-ray beam scanned the sample vertically to its longitudinal axis. The scanned image consists of 311 × 311 × 292 voxels with 6.667 voxels per mm resolution. For each heat-treatment temperature, a rock sample was scanned and the average CT value was obtained. One typical heat-treated sample is shown in ). Inside the sample, the bright zone indicates high density minerals and the dark zone indicates low density minerals or voids. The CT value, or Hounsfield radiological density, is used to represent the attenuation of the X-ray passing through material and to indicate the density of material after scaled with standard materials with Unit Hu (− 1000 |
Hu for air and 0 |
Hu for pure water) (). The window level of these images, the number on the CT value of the middle gray value, is 2700. There is no significant difference/change in each image. Based on the above definition, the average CT value of rock sample was calculated from voxel by voxel of the whole rock sample and scaled by the reference pure water, and the results are shown in . In CT images, there are notable artifacts such as ring artifact and beam hardening (), most of which can be corrected by modern scanners (). However, the cupping artifact still can be observed in b) shows the CT value from one edge to the other edge passing the center of the sample of 550 layers (marked as black) and their average (marked as white). To compare the cupping artifact in different heat-treated temperatures, the scaled CT values of four different heat-treated temperatures are shown in c). The maximum difference along the axis is less than 5% for all heat-treated temperatures. Thus, the cupping artifact can be ignored if the average CT value is used to compare the damage between samples.The dynamic UCS of LS with a corresponding loading rate is listed in . In general, the strength of LS increases with the loading rate for all heat-treatment temperatures. For the same loading rate, the sample without heat-treatment has the highest strength, while the sample treated at 600 °C has the lowest strength. It is noted that the strength of the sample treated under 450 °C is higher than those treated under 250 °C and 600 °C. This trend is consistent with that shown in , where the sample at room temperature has the highest CT value, which means that it has the least amount of voids or microcracks, while the sample under 600 °C has the lowest CT value corresponding to the most damages (including both voids and microcracks). The CT value of the sample treated under 450 °C is higher than that treated under both 250 °C and 600 °C.This observation of the strength and CT values of samples treated under various temperatures can be explained as follows. The thermal decomposition of cement occurs at 250 °C, which leads to the decrease of the CT value and thus the strength of the sample. The strength increasing at 450 °C can be explained as the closure of original cracks/voids caused by the baking effect of clay minerals, which results in the increase of the CT value and thus the strength of the sample ( summarized literatures about the increasing of the static compressive strength of sandstones affected by heat-treatment temperature (from 100 °C to 950 °C). The maximum static compressive strength of samples under heat-treatment (from 250 °C to 600 °C) is 1.2 to 1.8 times compared with that of original samples. reported that the static compressive strength of a sandstone after a 450 °C heat-treatment is 3.5 times of that of the original sample. The elastic modulus of sandstone also has been reported to increase with the heat-treatment temperature (). In addition, the decrease of the strength at 600 °C can be explained by both thermal stress induced microcracks () as a result of phase transition from α quartz to β quartz at temperature 573 °C.The damage variable D is used to describe the damage induced by the heat-treatment based on the average CT values (where H is the average CT value of heat-treated sample and H0 is the average CT value of room temperature sample.Based on the continuum damage mechanics, suppose that the state of damage is isotropic and the loading is along the axis. The effective strength σ for the bulk material due to damage is related to its original strength σ0 by (Following this relation, to fully describe the dependence of the dynamic rock UCS on the strain rate and thermal damage effect, the following function is proposed:where UCS0 is the static UCS strength under room temperature, σ˙0=0.001GPa/s is the reference loading rate (i.e. strain rate under static loading), σ˙ is the loading rate, and α and β are fitting constants.The physical meaning of each term of Eq. is justified as follows. If there is no dynamic loading and the heat-treatment damage is zero, the UCS is simply the static compressive strength. On the right-hand side of the equation, the first term in the product describes the thermal damage term and the second term is the loading rate term. Using Eq. , we did fitting using the Genetic Algorithm, a method to find the best solution based on natural selection, as in , where α |
= 6.31 × 10− 6 and β |
= 0.844. It can be concluded that the equation represents the trend of the data well.In this work, the split Hopkinson pressure bar system and X-ray Micro-CT were used to investigate the influence of damage induced by the heat-treatment (250 °C, 450 °C, and 600 °C) on the strength of Longyou sandstone under dynamic loadings (ranging from 600 GPa/s to 3000 GPa/s). Compared with the 2D Scanning Electron Microscope method, the X-ray Micro-CT showed its advantage of quantifying the damage induced by the heat-treatment.The strength of Longyou sandstone was observed to increase with the loading rate at a given heat-treatment temperature, and generally decrease when the temperature of heat-treatment increases with the exception of 450 °C. This phenomenon was consistent with the average CT value of the samples for each temperature and can be explained as the closure of original cracks caused by thermal expansion of mineral grains. The decrease of strength at 600 °C was caused by the cracks introduced by the different densities between α quartz and β quartz.The damage variable utilizing the averaged CT value for specimens at each temperature was introduced to describe the damage due to heat-treatment. A model for dynamic strength based on damage mechanics was developed to describe the UCS of Longyou sandstone under dynamic loading and heat-treatment conditions. The model was able to predict the trend of the data.The results indicate that the heat-treatment significantly affects the dynamic compressive strength of rock, which should be considered in the rock engineering practices, especially in those practices under dynamic loading conditions. In addition, the empirical model introduced in this paper can be used in the engineering practices for numerical analysis and safety design.Stress concentration near stiff inclusions: Validation of rigid inclusion model and boundary layers by means of photoelasticityPhotoelasticity is employed to investigate the stress state near stiff rectangular and rhombohedral inclusions embedded in a ‘soft’ elastic plate. Results show that the singular stress field predicted by the linear elastic solution for the rigid inclusion model can be generated in reality, with great accuracy, within a material. In particular, experiments: (i.) agree with the fact that the singularity is lower for obtuse than for acute inclusion angles; (ii.) show that the singularity is stronger in Mode II than in Mode I (differently from a notch); (iii.) validate the model of rigid quadrilateral inclusion; and (iv.) for thin inclusions, show the presence of boundary layers deeply influencing the stress field, so that the limit case of rigid line inclusion is obtained in strong dependence on the inclusion’s shape. The introduced experimental methodology opens the possibility of enhancing the design of thin reinforcements and of analyzing complex situations involving interaction between inclusions and defects.denotes the derivative of ui with respect to the spatial coordinate xjparameter depending on Poisson’s ratio, defining plane stress or plane straindimension of the inclusion along the horizontal axis in Cartesian coordinatesdimension of the inclusion along the vertical axis in Cartesian coordinatespolar coordinates centered at the wedge cornerpower of r in the Airy function for the stress and strain fieldssemi-angle in the matrix enclosing the wedgecomplex variable in the physical z-planecomplex variable in the conformal ζ-planetranslation of the inclusion in the ζ-planerotation of the inclusion in the ζ-planepre-image of the j—th vertex in the ζ-planefraction of π of the j—th interior angle in the ζ-planecomplex constants of the perturbed complex potential φ(p)(z)complex constants of the conformal map function ω (ζ)parameter function of the rectangle aspect ratiocomplex constants of the perturbed complex potential ψ(p)(z)Experimental stress analysis near a crack or a void has been the subject of an intense research effort (see for instance Lim and Ravi-Chandar Though the analytical determination of elastic fields around inclusions is a problem in principle solvable with existing methodologies (Movchan and Movchan lack mechanical interpretation, in the sense that it is not known if these predict stress fields observable in reality. Moreover, from experimental point of view, questions arise whether the bonding between inclusion and matrix can be realized and can resist loading without detachment (which would introduce a crack) and if self-stresses can be reduced to negligible values. In this article we (i.) re-derive asymptotic and full-field solutions for rectangular and rhombohedral rigid inclusions (Section ) and (ii.) compare these with photoelastic experiments (Section Photoelastic fringes obtained with a white circular polariscope are shown in and indicate that the linear elastic solutions provide an excellent description of the elastic fields generated by inclusions up to a distance so close to the edges of the inclusions that fringes result unreadable (even with the aid of an optical microscope). By comparison of the photos shown in The stress/strain fields in a linear isotropic elastic matrix containing a rigid polygonal inclusion are obtained analytically through both an asymptotic approach and a full-field determination. Considering plane stress or strain conditions, the displacement components in the x-y plane arecorresponding to the following in-plane deformations εαβ (α,β=x,y)which, for linear elastic isotropic behavior, are related to the in the in-plane stress components σαβ (α,β=x,y) viaεxx=(κ+1)σxx+(κ-3)σyy8μ,εyy=(κ+1)σyy+(κ-3)σxx8μ,εxy=σxy2μ,where μ represents the shear modulus and κ⩾1 is equal to 3-4ν for plane strain or (3-ν)/(1+ν) for plane stress, where ν∈(-1,1/2) is the Poisson’s ratio. Finally, in the absence of body forces, the in-plane stresses satisfy the equilibrium equation (where repeated indices are summed)Near the corner of a rigid wedge the mechanical fields may be approximated by their asymptotic expansions (Williams ), the Airy function F(r,ϑ), automatically satisfying the equilibrium Eq. The following power-law form of the Airy function satisfies the kinematic compatibility conditions (Barber F(r,ϑ)=rγ+2A1cos(γ+2)ϑ+A2sin(γ+2)ϑ+A3cosγϑ+A4sinγϑ,and provides the in-plane stress components asσrr=-(γ+1)rγ[A1(γ+2)cos(γ+2)ϑ+A2(γ+2)sin(γ+2)ϑ+A3(γ-2)cosγϑ+A4(γ-2)sinγϑ],σϑϑ=(γ+2)(γ+1)rγ[A1cos(γ+2)ϑ+A2sin(γ+2)ϑ+A3cosγϑ+A4sinγϑ],σrϑ=(γ+1)rγ[A1(γ+2)sin(γ+2)ϑ-A2(γ+2)cos(γ+2)ϑ+A3γsinγϑ-A4γcosγϑ],where A1,A2 and A3,A4 are unknown constants defining the symmetric (Mode I) and antisymmetric (Mode II) contributions, respectively, while γ represents the unknown power of r for the stress and strain asymptotic fields, σαβ,εαβ∼rγ, with γ⩾-1/2.Imposing the boundary displacement conditions ur(r,±α)=uϑ(r,±α)=0 leads to two decoupled homogeneous systems, one for each Mode symmetry condition, so that non-trivial asymptotic fields are obtained when determinant of coefficient matrix is null, namely (Seweryn and Molski (γ+1)sin(2α)-κsin(2α(γ+1))=0,ModeI;(γ+1)sin(2α)+κsin(2α(γ+1))=0,ModeII.Note that, in the limit κ=1 (incompressible material under plane strain conditions), Eq. are the same as those obtained for a notch, except that the loading Modes are switched. Furthermore, according to the so-called ‘Dundurs correspondence’ Dundurs coincide with those corresponding to a notch.The smallest negative value of the power γ⩾-1/2 for each loading Mode, satisfying Eq. 2, represents the leading order term of the asymptotic expansion. These two values (one for Mode I and another for Mode II) are reported in (left), for different values of κ, as functions of the semi-angle α and compared with the respective values for a void wedge, For the rigid wedge, similarly to the notch problem:the singularity appears only when α>π/2 and increases with the increase of α;a square root singularity (σαβ∼1/r) appears for both mode I and II when α approaches π (corresponding to the rigid line inclusion model, see Noselli et al. while, differently from the notch problem:the singularity depends on the Poisson’s ratio ν through the parameter κ;the singularity under Mode II condition is stronger than that under Mode I; in particular, a weak singularity is developed under Mode I when, for plane strain deformation, a quasi-incompressible material (ν close to 1/2) contains a rigid wedge with α∈[12,34]π.Since the intensity of singularity near a corner is strongly affected by the value of the angle α, it follows that the stress field close to a rectangular inclusion is substantially different to that close to a rhombohedral one. Therefore, strongly different boundary layers arise when a rectangular or a rhombohedral inclusion approaches the limit of line inclusion.Solutions in 2D isotropic elasticity can be obtained using the method of complex potentials (Muskhelishvili In the case of non-circular inclusions, it is instrumental to introduce the complex variable ζ, related to the physical plane through z=ω(ζ) with the conformal mapping function ω (such that the inclusion boundary becomes a unit circle in the ζ-plane, ζ=eiθ), so that the stress and displacement components are given asσxx+σyy=4Reφ′(ζ)ω′(ζ),σyy-σxx+2iσxy=2ψ′(ζ)ω′(ζ)+ω(ζ)‾ω′(ζ)3φ″(ζ)ω′(ζ)-φ′(ζ)ω″(ζ),2μ(ux+iuy)=κφ(ζ)-ω(ζ)ω′(ζ)‾φ′(ζ)‾-ψ(ζ)‾.The complex potentials are the sum of the unperturbed (homogeneous) solution and the perturbed (introduced by the inclusion) solution, so that, considering boundary conditions at infinity of constant stress with the only non-null component σxx∞, we may writeφ(ζ)=σxx∞4ω(ζ)+φ(p)(ζ),ψ(ζ)=-σxx∞2ω(ζ)+ψ(p)(ζ),where the perturbed potentials φ(p)(ζ) and ψ(p)(ζ) can be obtained by imposing the conditions on the inclusion boundary, which are defined on a unit circle and for a rigid inclusionκφ(p)(ζ)-ω(ζ)ω′(ζ)‾φ(p)′(ζ)‾-ψ(p)(ζ)‾=σxx∞21-κ2ω(ζ)-ω(ζ)‾,forζ=eiθ,θ∈[0,2π].In the case of n-polygonal shape inclusions the conformal mapping which maps the interior of the unit disk onto the region exterior to the inclusion is given by the Schwarz–Christoffel integralwhere R,k0, and α0 are constants representing scaling, translation, and rotation of the inclusion, while kj and αj (j |
= 1,…, n) are the pre-images of the j-th vertex in the ζ plane and the fraction of π of the j-th interior angle, respectively. In the following the translation and rotation parameters for the inclusion are taken null, k0=α0=0.Assuming that the perturbed potentials are holomorphic inside the unit circle in the ζ-plane, φ(p)(ζ) can be expressed through Laurent serieswhere aj (j |
= 1, 2, 3, …) are unknown complex constants. Furthermore, since the integral expression in Eq. cannot be computed as closed form for generic polygon, it is expedient to represent the conformal mapping aswhere dj (j |
= 1, 2, 3, …) are complex constants.In order to obtain an approximation for the solution, the series expansions for ω(ζ) and φ(p)(ζ) are truncated at the M-th term. Through Cauchy integral theorem, integration over the inclusion boundary of Eq. yields a linear system for the M unknown complex constants aj, functions of the M constants dj, obtained through series expansion of Eq. . Once the expression for φ(p)(ζ) is obtained, the integral over the inclusion boundary of the conjugate version of the boundary condition is used to approximate ψ(p)(ζ), resulting asψ(p)(ζ)=∑j=1M+2bjζj-1∑j=1M+2cjζj-1Rσxx∞ζ.In this case the angle fractions are αj=1/2 (j |
= 1, … , 4) while the pre-images arek1=eηπi,k2=e-ηπi,k3=e(1+η)πi,k4=e(1-η)πi,where η (likewise R) is a parameter function of the rectangle aspect ratio ly/lx, with the inclusion edges lx and ly. Parameters η and R are given in The conformal mapping function and perturbed potentials obtained in the case of rectangle with ly/lx=1/4 are reported for M |
= 15:ω(ζ)=1ζ+0.5633ζ-0.1138ζ3-0.0385ζ5-0.0071ζ7+0.0042ζ9+0.0052ζ11+0.0022ζ13-0.0006ζ15R,φ(p)(ζ)=-0.2420-0.0264ζ2-0.0071ζ4+0.0003ζ6+0.0020ζ8+0.0012ζ10+0.0002ζ12-0.0001ζ14Rσxx∞ζ,ψ(p)(ζ)=-2.4454-54.9115ζ2+6.4081ζ4+5.5545ζ6+3.4073ζ8+0.6051ζ10-1.3007ζ12-1.0545ζ14+0.2727ζ16Rσxx∞ζ/109.8986-61.9012ζ2+37.5162ζ4+21.1312ζ6+5.4989ζ8-4.1163ζ10-6.2272ζ12-3.1597ζ14+ζ16. for the rhombus aspect ratios ly/lx considered here, where lx and ly are the inclusion axis.The conformal mapping function and perturbed potentials obtained in the case of rhombus with ly/lx=2/15 are reported for M |
= 15:ω(ζ)=1ζ+0.8312ζ+0.0515ζ3-0.0086ζ5+0.0068ζ7-0.0028ζ9+0.0025ζ11-0.0013ζ13+0.0013ζ15R,φ(p)(ζ)=-0.1628+0.0071ζ2+0.0001ζ4+0.0009ζ6+0.0001ζ8+0.0003ζ10+0.0001ζ12+0.0002ζ14Rσxx∞ζ,ψ(p)(ζ)=8.1122+28.1115ζ2+1.8150ζ4-0.6928ζ6+0.4105ζ8-0.4451ζ10+0.1665ζ12-0.3417ζ14+0.2727ζ16Rσxx∞ζ/-53.0727+44.1156ζ2+8.2012ζ4-2.2724ζ6+2.5225ζ8-1.3283ζ10+1.4453ζ12-0.9307ζ14+ζ16.Photoelastic experiments with linear and circular polariscope (with quarterwave retarders for 560 nm) at white and monochromatic light have been performed on twelve two-component resin (Translux D180 from Axon; mixing ratio by weight: hardener 95, resin 100, accelerator 1.5; the elastic modulus of the resulting matrix has been measured by us to be 22 MPa, while the Poisson’s ratio has been indirectly estimated equal to 0.49) samples containing stiff inclusions, obtained with a solid polycarbonate 3 mm thick sheet (clear 2099 Makrolon UV) from Bayer with elastic modulus equal to 2350 MPa, approximatively 100 times stiffer than the matrix.Samples have been prepared by pouring the resin (after deaeration, obtained through a 30 min exposition at a pressure of −1 bar) into a Teflon mold (340 mm × 120 mm × 10 mm) to obtain 3 ± 0.05 mm thick samples. The resin has been kept for 36 h at constant temperature of 29 °C and humidity of 48%. After mold extraction, samples have been cut to be 320 × 110 × 3 mm, containing rectangular inclusions with wedges 20 mm ×20;10;5 mm and rhombohedral inclusions with axis 30 mm ×18;8;4 mm.Photos have been taken with a Nikon D200 digital camera, equipped with a AF-S micro Nikkor (105 mm, 1:2.8G ED) lens and with a AF-S micro Nikkor (70–180 mm, 1:4.5–5.6 D) lens for details. Monitoring with a thermocouple connected to a Xplorer GLX Pasco©, temperature near the samples during experiments has been found to lie around 22.5 °C, without sensible oscillations. Near-tip fringes have been captured with a Nikon SMZ800 stereozoom microscope equipped with Nikon Plan Apo 0.5x objective and a Nikon DS-Fi1 high-definition color camera head.The uniaxial stress experiments have been performed at controlled vertical load applied in discrete steps, increasing from 0 to a maximum load of 90 N, except for thin rectangular and rhombohedral inclusions, where the maximum load has been 70 N and 78 N, respectively (loads have been reduced for thin inclusions to prevent failure at the vertex tips). In all cases an additional load of 3.4 N has been applied, corresponding to the grasp weight, so that maximum nominal far-field stress of 0.28 MPa has been applied (0.22 MPa and 0.25 MPa for the thin inclusions).Data have been acquired after 5 min from the load application time in order to damp down the largest amount of viscous deformation, noticed as a settlement of the fringes, which follows displacement stabilization. Releasing the applied load after the maximum amount, all the samples at rest showed no perceivably residual stresses in the whole specimen.Comparison between analytical solutions and experiments is possible through matching of the isochromatic fringe order N, which (in linear photoelasticity)where t is the sample thickness, Δσ=σI-σII is the in-plane principal stress difference, and fσ is the material fringe constant, measured by us to be equal to 0.203 N/mm (using the so-called ‘Tardy compensation procedure’, see Dally and Riley , where the full-field solution obtained in Section has been used under plane stress assumption and ν=0.49. This assumption is consistent with the reduced thickness of the employed samples, much thinner than the thickness of the samples employed by Noselli et al. The results show an excellent agreement between theoretical predictions and photoelastic measures, with some discrepancies near the contact with the inclusions where, the plane stress assumption becomes questionable due to the out-of-plane constraint imposed by the contact with the rigid phase. Moreover, microscopical views (at 31.5×) near the vertices of the inclusions, shown in the inselts of , reveal that the stress fields are in good agreement even close to the corners, where a strong stress magnification is evidenced near acute corners, while no singularity is observed near obtuse corners.The near-corner stress magnifications and comparisons with the full field solution (evaluated with M =15) are provided in , where the in-plane stress difference (divided by the far field stress) is plotted along the major axis of the thin and thick rhombohedral inclusions (, upper and central parts, respectively) and along a line tangent to the corner (and inclined at an angle π/6) of the rectangular thin inclusion. In particular, magnification factors of 5.3 (upper part, ly/lx=2/15 and α≈23π/24), 3.8 (central part, ly/lx=9/15 and α≈5π/6), and 2.7 (lower part, ly/lx=1/4 and α=3π/4) have been measured.It is interesting to note that according to the theoretical prediction (Section ), the singularity is stronger for acute than for obtuse inclusion’s angles and that the stress fields tend to those corresponding to a zero-thickness rigid inclusion (a ‘stiffener’, see Noselli et al. ) inclusions become narrow (from the upper part to the lower part of the figures).For Mode I loading the stress concentration becomes weak for angles α within [π/2,3π/4], see (compare the fields near the two different vertices).For Mode II loading the stress concentration is much stronger than for Mode I. Stress concentrations generated for mixed-mode at an angle α=3π/4 are visible in near the corners of rectangular inclusions. These concentrations are visibly stronger than those near the wider corner in (upper part), which is subject to Mode I;The stress fields evidence boundary layers close to the inhomogeneity, see lower part of : These boundary layers are crucial in defining detachment mechanisms and failure modes. Therefore, the shape of a thin inclusion has an evident impact in limiting the working stress of a mechanical piece in which it is embedded. This conclusion has implications in the design of material with thin and stiff reinforcements, which can be enhanced through an optimization of the inclusion shape.Photoelastic experimental investigations have been presented showing that the stress field near a stiff inclusion embedded in a soft matrix material can effectively be calculated by employing the model of rigid inclusion embedded in a linear elastic isotropic solid. The results provide also the experimental evidence of boundary layers, depending on the inhomogeneity shape, which affect the stress fields and therefore define detachment mechanisms and failure modes. Finally, the presented methodology paves the way to the experimental stress analysis of more complex situations, for instance involving interaction between cracks or pores and inclusions as induced by mechanical and thermal loading.Finite element study of headed shear studs embedded in ultra-high performance concreteA novel bridge repair method has been developed to strengthen steel bridge girders with section loss due to end corrosion. The repair comprises of welding headed shear studs to the non-corroded portion of the web plate and encasing them in ultra-high performance concrete (UHPC) to create an alternate bearing load path. The interaction between the headed studs and the UHPC panels is crucial in the force transfer. Therefore, a careful study is needed through high-fidelity finite element analysis to complement the experimental results. This paper presents the development of a model in Abaqus finite element software that enables capturing the behavior of studs embedded in UHPC. The model was validated using a series of experimental results from push-out tests with headed shear studs welded onto a thin web plate. Experimental results from push-out tests performed on stud diameters of 12, 16 and 19 mm and two levels of eccentric loadings were used to calibrate the modeling methodology. The model explicitly considers effects of material damage, contact between the studs and UHPC, and the precise geometry of the weld collar of studs. After validation, design parameters such as interaction of in-plane torsion and direct shear, and limits for web thickness-to-stud diameter ratio were studied to compliment the experimental data. The results are expected to inform engineers about the design of this novel repair method. In addition, this paper may enable future finite element studies on the performance of studs in UHPC.This paper focuses on finite element simulations of push-out tests with headed shear studs embedded in UHPC with the goal of investigating engineering parameters as concerned by a novel bridge repair method. This repair method has been proposed to remediate bridge girders suffering from corrosion at their ends shows a schematic of this repair design. The composite action between the headed studs and the UHPC develops an alternate load path for the bearing forces. The performance of this repair has been investigated through a series of small- and large-scale experiments complemented by finite element (FE) simulations. This paper aims to present the findings of the refined FE simulations to further the understanding of the behavior of studs in UHPC.The need for this study stems from the fact that the diversity of girder end geometry and corrosion patterns may require different stud arrangements for different bridges. For bridges with no bearing stiffeners in which corrosion is limited to the lower portion of the web, the stud layout is trivial. However, there are situations where the studs need to be offset, or larger stud diameters need to be used to accommodate complex geometries due to limitations from stiffeners, connection plates, diaphragms, and the corrosion pattern. As part of an extensive study supported by Connecticut Department of Transportation, USA, experimental studies have been conducted to evaluate the performance of headed shear studs embedded in UHPC Several studies relevant to finite element modeling of headed studs embedded in concrete have been conducted. Xu et al. investigated the performance of studs embedded in regular strength concrete (RSC) with tight spacing When high-strength concrete (HSC) or UHPC is used, the weld collar that is formed at the base of the stud as a result of the welding process increases the shear capacity of the stud by 15% This paper presents the results of finite element simulations of push-out experiments with headed shear studs welded on a 9.5-mm thick web plate and embedded in UHPC. First, physical coupons from the headed studs, the base beam section and UHPC were tested so that appropriate material models could be used in the finite element FE model. Using the calibrated material models, the experimental results from three stud diameters (12, 16 and 19 mm) and two eccentric loadings are validated to confirm proper model calibration. Novel contributions include advancement of a modeling methodology enable of capturing global force-slip behavior and local strains on the web plate adjacent to the studs for concentrically and eccentrically loaded stud groups embedded in UHPC. The experimentally validated model was used to perform a parametric study to determine the effect of stud diameter-to-web plate thickness on the load carrying behavior of the connection. For this purpose, performance criteria such as the yielding of the studs and the yielding of the web plate under bearing stresses were investigated. Finally, the effect of eccentricity is studied by analyzing stud groups with different levels of eccentricity with respect to the load to develop an interaction formulation for in-plane torsion and direct shear. The results are expected to facilitate the design of this novel repair. In addition, the details of the finite element methodology may enable future studies on the performance of headed studs in UHPC.Comprehensive details of the experimental portion of the work were presented by the authors in Kruszewski et al. A schematic of each push-out specimen is shown in . In this paper, four stud arrangements are considered for validation. The first stud pattern (a) consists of eight headed shear studs with a diameter of 12 mm. They are welded symmetrically into one column of four studs spaced at 50 mm on each side of the web plate. b shows the stud arrangement for the 16-mm and 19-mm studs. For these diameters, two studs were welded symmetrically on each side of the web plate. The 16-mm and 19-mm studs are spaced at 64 mm and 75 mm, respectively. The stud spacing is based on the minimum spacing of 4 times the diameter of the stud, db, as specified by the AASHTO bridge design specifications c and 2d show the two eccentric samples studied. The first sample contains the same stud arrangement as layout “A”, but the studs are offset by 50 mm from the centerline of the web plate. , Sv and Hs are the vertical spacing and height of the studs, respectively. provides more details regarding the geometry of each specimen. shows the experimental force-slip curves for all samples considered in this study. Slip is defined as the relative displacement between the steel beam and the UHPC panel. The slip was measured at the corners of the panels and interpolated such that the stud line behavior was generated. The figure shows the capacity of one single stud, taken as the total load bearing capacity of the sample divided by the number of studs. The 12-mm, 16-mm and 19-mm studs generated a shear capacity of 73.8 kN, 104 kN and 146 kN respectively. The 50-mm and 100-mm eccentrically loaded samples achieved a respective stud capacity of 60.4 kN and 23.2 kN. All samples failed via shear rupture of the stud shank except for the 100 mm eccentrically loaded sample, which was not loaded to failure due to excessive rotations of the UHPC panel. This failure occurs at the interface between the weld collar and the UHPC panel, as shown in . No damage is sustained from the UHPC panel except a small shear plane which was sliced from the panel from sliding of the weld collar during rupture. c shows the centerline section cut of the UHPC panel after failure. It is observed that no interior damage to the UHPC panel was observed other than the weld collar plane. There is little evidence of flexure of the stud shank, as the UHPC constrains the studs such that only the localized region at the edge of the UHPC panel deforms. The capacities and failure mechanisms observed in this study are consistent with findings by other researchers First, the experimental results presented in this study are validated to provide credibility to the finite element model before further parametric analyses are conducted. To simulate the experiments, ABAQUS/Explicit version 6.20 was used Before assembling the global model of the push-out specimen, material models were calibrated by modeling the coupons which were used for physical testing. It is important to accurately model the material behavior of each component due to the nature of the repair. Since headed studs, which are comprised of modern steel material, are being welded to an old, weathered bridge girder and embedded in a new material such as UHPC, the materials must be accurately modeled to capture the correct failure mechanisms. Steel coupons were modeled for the beam section and studs. A cylinder specimen was modeled for the UHPC material. The coupons were modeled with realistic geometry and boundary conditions to replicate the physical scenario. Reliable stress-strain relationships were generated and then input into the global model following a similar methodology to Pavlovic et al. Values for density and elastic properties were the same for the base beam section and headed studs. The density was assigned as 7833 kg/m3. The modulus of elasticity and Poisson’s ratio was 200,000 MPa and 0.3 respectively. The plastic material properties were assigned according to the experimental stress vs. strain curves which were extracted by testing coupons of each steel material. For the headed studs, small coupons were fabricated by removing the head of the stud and machining a dog-bone shaped section with a reduced throat area. The throat length was approximately 19 mm. Due to a small coupon size, the reduced area was machined to a diameter of 6.25 mm to avoid triaxiality effects during testing. A high-elongation strain gauge was used to extract the local strain in the necking region. After severe necking, machine displacement was used to complete the softening curve as it was assumed that further elongation after the onset of necking was applied only to the localized throat region. For the beam section, standard dog-bone coupons were fabricated in accordance with ASTM shows the experimental stress vs. strain response for both steel materials. The yield strength of the web plate is approximately 280 MPa, while the stud material yields at 405 MPa. This illustrates the variation in steel material which was used for structural steel from the 1950s. The ultimate strength of the beam and stud material is 452 MPa and 531 MPa, respectively. These results are consistent with the findings of Brockenbrough who reported that U.S. structural steel specifications called for A373-58T during that time . From these results, the true stress values were used so that damage models may be incorporated allowing the replication of the experimental results.The damage models were calibrated according to plasticity relationships and fracture laws developed by Rice and Tracey where εpl is the equivalent plastic strain, εu is the strain at ultimate engineering stress, β is a material parameter typically assumed as 1.5, and θ is stress triaxiality. Stress triaxiality values were considered from −0.33 to 2.0. Damage evolution was assigned to describe the accumulation of damage (and thus reduction in stiffness) after the necking point. Damage evolution was input in tabular form using the damage relationship as proposed by Lemaitre . In the equation, αD is a damage eccentricity factor introduced to account for the difference between observed and calculated damage values . In the equation, ufpl is the ultimate displacement at failure, εipl is the plastic strain after necking, and εfpl is the ultimate strain at failure. The ductile damage and damage evolution relationships for both materials are shown in a and b, respectively. When these damage models were incorporated to the true stress response, good agreement was achieved between the simulated and physical test coupons (). This ensured that an accurate steel material response would be incorporated into the global model.The Concrete Damaged Plasticity (CDP) material model was assigned to describe the UHPC behavior. This model was selected because it allows for calibration of damage parameters to represent the degradation of stiffness and plastic deformations in the material ). The dilation angle and eccentricity factors were assigned as 17° and 0.1 For the purpose of computational efficiency, quarter models were developed to validate the capacity of the 12-, 16- and 19-mm stud diameters. In the quarter model, two planes of symmetry were available. The push-out specimen was cut down the middle of the web plate and again down the middle of the stud line, such that only two full studs (four half studs) were embedded in half of a panel of UHPC. For the eccentrically loaded sample with a column of 12-mm studs, half models were created since only one plane of symmetry was present due to the in-plane rotation of the studs. Therefore, the symmetry cut was made longitudinally down the middle of the web plate. A schematic of the geometry of the models used for experimental validation is shown in . Several boundary conditions were imposed. First, the normal vector of each plane of symmetry was restrained to satisfy the quarter model and half model conditions. For the quarter models, the base of the UHPC panel was tied to a reference point which resembled the center of the spherical bearing, approximately 25 mm below the bottom of the UHPC panel. This was to replicate the rotational tolerance from the spherical bearing which was used to limit the rotations from imperfections during the physical experiment. Displacement was restrained in all directions except normal to the UHPC panel (i.e. slab splitting was allowed). Rotations were permitted to replicate the behavior of the spherical bearing. However, since perfect symmetry was maintained in the FE model, no rotation was observed and therefore the spherical bearing was not modeled. For the eccentrically loaded specimens, the spherical bearing was explicitly modeled to replicate the friction contribution during rotation.). Since it is known that the presence of a weld collar significantly contributes to the shear capacity of a stud when embedded in UHPC shows the geometry and mesh assignments for various components of the push-out model.Two interaction properties were assigned to the model. The first interaction was assigned as a surface-to-surface contact between the UHPC panel and the web plate. Tangential behavior with a penalty friction formulation and friction coefficient of 0.3 was assigned to represent the friction bond between the web plate and the UHPC. The second interaction defined the contact between the headed studs (inclusive of the weld collar) and UHPC. Here, surface-to-surface contact was assigned with tangential contact, normal contact, and damping. Tangential behavior was defined with a penalty friction formulation and a friction coefficient of 0.3. Normal contact was defined to simulate the bearing effect of the studs onto the UHPC panel. A damping coefficient of 0.8 was applied to promote stability during damage initiation of the studs and UHPC.To provide credibility to the finite element model so that further parametric analyses may be conducted, local and global behavior was captured and compared to the experimental results. shows the force-slip relationship for all three stud diameters. The figure shows good agreement between the FE analysis and experimental results. The model captures softening of the headed shear studs over a large slip range with reasonable agreement to the experimental results. For all three diameters, the failure mechanism involved shear rupture of the stud shank, similar to the physical scenario (). In the figure, the UHPC panels were removed from the viewport to clearly observe the deformation in the headed studs. a shows the initial loading on the headed stud with a stress concentration at the base of the stud near the weld collar. The figure shows that the weld collar is engaged even during the elastic stage. b displays the yield point of the stud just prior to significant deformation. Additional stress accumulation has developed at the base of the stud. Once yielding occurs, large deformations are experienced by the stud as shown in c. Here, because the beam is sliding against the UHPC surface, the weld collar becomes more engaged as indicated by the stress concentration just above the web plate. Finally, at a slip of approximately 5 mm, the studs rupture at the interface just above the weld collar as indicated by the stress release in shows the force vs. web strain adjacent to the base of the studs. The experimental results were captured through strain gauges which were installed approximately 8 mm from the base of the headed stud on the compression side. The FEA results show the average equivalent plastic strain calculated over the length of the strain gauge which was used in the experiments. The figure shows that there is some deviation of strain from the experimental results. Typically, the finite element model over-predicted the web strain compared to the strain gauges in the physical scenario. This is likely because the large stress concentrations adjacent to the stud base create a scattered strain field which changes rapidly as a function of distance away from the stud base. Therefore, an exact match for web strains may be difficult to capture. However, the observed strains are within a reasonable range compared to the experimental results and are therefore deemed sufficient. With global and local behavior validated, parametric analyses may be conducted with confidence in the results.Two experiments with 50 mm and 100 mm eccentricities are used to calibrate the finite element models for eccentricity. Since half models were used for these simulations, the back side of the web plate was restrained to satisfy the boundary conditions. To adequately model the rotational effect, the spherical bearing was modeled with realistic geometry. The spherical bearing was modeled with an elastic material model using an elastic modulus and Poisson’s ratio of 300,000 MPa and 0.3, respectively. To introduce the spherical bearing, two additional interactions were defined in addition to the existing interaction parameters as outlined in 3.2. Normal surface-to-surface “hard” contact was assigned between the bottom of the UHPC panel and the top of the spherical bearing. A tangential friction coefficient of 0.2 and a damping coefficient of 0.5 were incorporated to replicate the sliding friction of the UHPC panel and steel bearing. Next, an interaction between the bearing sphere and its nesting was modeled using normal surface-to-surface “hard” contact with a tangential friction coefficient of 0.05 to model the friction between the two steel surfaces during rotation. Since the bearing was treated with a lubricant prior to the physical tests, a smaller friction coefficient was appropriate. The nodes at the bottom of the spherical bearing were restrained in all directions and also constrained to a reference point such that the total reaction force could be extracted. shows the rotated specimens at an overall displacement of approximately 2 mm. It is observed that the rotations between both samples are reasonable. shows the force-displacement curves for the two eccentric samples used for model validation. The 50-mm and 100-mm eccentric samples generated a capacity of 61.1 kN/stud and 23 kN/stud, respectively. The finite element model predicted the total load bearing capacity well, but did not capture the ductility of the headed studs at higher displacements. This may be due to the material model which does not account for in-plane torsion of the stud material. In addition, there may be physical phenomena occurring in the experiment that is not captured by the finite element model such as shear friction between the UHPC panels and the web plate. However, for the purposes of this study, the results are sufficient to proceed with a force vs. eccentricity analysis as only the total load bearing capacity of the stud group is of interest.To guide engineers through the design process, parametric studies relevant to the repair were conducted. First, the performance of a stud group under various eccentric loadings is considered. Eccentricity must be carefully understood when headed studs cannot be welded along the centerline of the loading axis. Similar to bolt groups, studs may experience a decrease in capacity when subjected to an eccentric loading. For the purpose of demonstration, a single column of four headed studs is analyzed under several eccentricities ranging from 0 mm to 100 mm in 12 mm increments. Secondly, the influence of web thickness vs. stud diameter is studied. A critical aspect of the proposed repair is to preserve the structural performance of the intact web plate while providing support to the corroded region. While full plastic capacity was achieved for studs up to a 19-mm diameter, the demands on the web plate must be characterized to inform engineers during the design process. Through efficient simulations, various web thicknesses were assigned for the three stud diameters considered in this study. By analyzing the failure mechanisms when the web thickness is reduced, an acceptable ratio of web thickness-to-stud diameter can be generated to satisfy the stud yielding limit state.Eccentricity is an important design parameter which must be carefully assessed prior to field installation. Based on the experimental results presented in 3.5, it is shown that a larger eccentricity decreases the overall capacity of the stud group due to a combination of in-plane torsion and shear. These results are relevant to the bridge repair because an eccentrically loaded stud group may not perform as expected if this reduction is not anticipated during the design process. To gain a better understanding of the performance of headed studs under an eccentric loading, simulations were conducted with the benchmark stud arrangement (i.e. one column of four studs) welded to the web plate of the beam section at various offsets ranging from 0 mm to 100 mm (). The location of the stud group was shifted by 12 mm increments for each simulation for a total of 9 analyses. shows the summary of all simulations conducted. Eccentricity is defined as the distance from the centerline of the specimen to the centerline of the studs. Critical side cover is defined as the distance between the outer edge of the stud shank to the edge of the UHPC panel on the side where the studs are offset.The analysis showed that, when a 12 mm eccentricity was introduced, the stud capacity was approximately 71 kN/stud, about 96% of the capacity of the sample with no eccentricity. At 25 mm, the capacity was approximately 92% of stud capacity with no eccentricity, suggesting that the decrease in capacity may be linear. However, at an eccentricity of approximately 62 mm, the capacity significantly drops and breaks the linear trend as larger rotations are induced onto the stud group. shows the normalized stud capacity as a function of eccentricity. To provide a broader perspective on a single-column stud group, the capacity was plotted as a function of eccentricity divided by the height of the stud group, e/h. The height of the stud group is important because it may influence the torsion induced on each stud. For a stud group which contains more studs vertically, the moment resistance may be larger due to the rotational resistance generated from the inertia of the stud group. In the figure, the total capacity of the stud group for each eccentric sample Po was divided by the number of studs, n, and normalized by the expected capacity of a single stud with no eccentricity. It is observed that, at e/h ratios larger than 0.4, the capacity tends to reduce more significantly as indicated by the change in slope of the scatter plot. At an eccentric loading of 100 mm, the stud capacity is just 33% of the stud group with no eccentricity.To generate a formulation for the capacity of a single column stud group under an eccentric loading, the elastic rotation method was adopted which is traditionally used for bolts. This method assumes that the force in each stud is proportional to its distance from the center of gravity (CG). The capacity of a stud group comprised of a single column may be quantified as the sum of two components: the vertical component due to shear and the horizontal component due to the applied moment, summarized by the following equation from the elastic method:where P is the capacity of the stud group with no eccentricity (kN), Po is the capacity of the stud group under an eccentric loading (kN), n is the number of studs, e is the eccentricity (mm), and di is the distance from each stud to the CG. The first part of the equation, (Pon), represents the longitudinal shear contribution of each stud. The second portion of the equation Pedi∑di2 represents its rotational resistance as a function of eccentricity. Since the CG of the stud group is in the center of the stud group, the force applied due to the moment is purely horizontal. Eq. can be rearranged such that the normalized capacity of one single stud can be calculated under an eccentric loading, as follows:where α is a modification factor for curve fitting. To fit the simulated results, it was found that a value of 1.3 for α fits the data well as shown in b. However, the figure shows that the elastic method yields a conservative stud capacity at small eccentricities. This is because the use of principle superposition assumes that the translational and rotational actions are independent of each other, which is why the equation is comprised of two components. In reality, these actions are coupled together especially at lower eccentricities when the moment is less prominent. When a larger eccentricity is introduced, i.e. at e/h ratios greater than 0.5, the rotational moment is so large that the translation action of the stud is essentially independent of the rotation. Therefore, better agreement is achieved.a shows the rotated specimen under an eccentricity of 100 mm. Due to a large eccentricity, the rotational action of the studs around their instantaneous center of rotation (ICR) is more prominent (b). The ICR is a fictitious point in space around which the stud group rotates. It is observed that the two inner studs which are closer to the center of gravity of the group deform less than the two outside studs further away from the center of gravity. This behavior confirms the ICR assumption, which states that each stud deforms proportional to its distance from the ICR. In this behavior, the two outside studs yield first and transfer the forces to the two inside studs, which also yield upon further displacement. The stud group deforms in a counter clockwise manner with stress concentrations at the base of the studs until they rupture in a combination of shear and torsion.For the purpose of field implementation and design guidelines, the web thicknesses considered in this analysis are a ratio of the stud diameter. All three stud diameters (12, 16 and 19 mm) were analyzed. To allow comparison, two half-studs of each diameter were modeled on the web plate. The experimental portion of this work was conducted with 9.5-mm thick web plates, corresponding to an initial web thickness to stud diameter ratio (tw/db) of 0.75, 0.6, and 0.5 for 12-, 16- and 19-mm studs, respectively. These ratios were considered the upper limit because the headed studs were welded on a 9.5-mm thick web plate and thus the initial ratio was dependent on the stud diameter. Additionally, the aforementioned experimental results revealed that all three studs failed in shear rupture of the stud shank when welded on a 9.5 mm thick web plate. Therefore, only ratios smaller than the benchmark were considered as larger ratios were considered redundant. From the benchmark ratios, the web thickness was reduced by a tw/db increment of 0.1 for each stud diameter to observe the force vs. slip relationship, corresponding web strains adjacent to the studs, and failure mechanism. shows the results from these simulations. The table is arranged according to each stud diameter, as every ratio was evaluated for the three stud diameters considered in this study. It is important to note that these results are valid for the material properties assigned to this model as outlined in 3.1 and may be different for varying steel strengths. In this study, the failure mechanisms observed include stud yielding (SY), stud rupture (SR), web bearing (WB), and web shear (WS). Stud yielding occurs when plastic deformation is experienced at the base of the stud but no rupture. Stud rupture occurs when the stud fails in shear just above the weld collar. Web bearing is defined as typical bearing failure of the web plate where the stud is welded. Finally, web shear occurs when the shear capacity of the web plate governs due to a higher capacity of the studs. Web shear typically occurs at the loading interface where high shear forces are present. A representation of these failure mechanisms is shown in From the table, it is observed that a ratio of 0.5 is the threshold for development of full plastic capacity of the headed shear studs. When a tw/db ratio below 0.5 was implemented, the failure mechanism shifted away from stud rupture. For the 12 mm studs, a tw/db ratio of 0.4 resulted in a combination of stud yielding and web bearing failure as characterized by the large web strains experienced adjacent to the headed stud. This is because the bearing strength of the reduced web plate was lower than the shear strength of the stud. However, at a ratio of 0.4, some stud yielding was still observed. When a ratio of 0.3 was analyzed, complete web bearing failure was achieved with little to no stud yielding, resulting in very large strain demands on the web plate (462,000 με). Similar results were obtained from simulations with 16-mm studs. At a tw/db ratio of 0.4, a combination of stud yielding and web bearing was observed. At a ratio of 0.3, a combination of stud yielding, web bearing and global web shear was observed. Here, global web shear failure is defined as the web yielding at the location of the loading point. This is because the larger diameter studs generate a higher total bearing capacity, so the failure mechanism shifts to the next weakest link which is global web shear. For the 19-mm studs, similar results were achieved. At a tw/db ratio of 0.5, stud rupture is the controlling mechanism. At a ratio of 0.4 and 0.3, global web shear is observed because of the high bearing capacity generated by the larger studs. This is further confirmed through the lower web strains experienced at the stud interface (24,800 με and 26,200 με for 0.3 and 0.4, respectively). This indicates that the larger web strains resulting in significant yielding are experienced at the loading interface, causing the global web shear phenomenon. shows the force vs. slip relationships for all simulations conducted in this parametric study. a depicts the force-slip curves for 12-mm studs. For the experimental part of this work, an initial ratio of 0.75 was used, corresponding to a web thickness of 9.5 mm. From there, ratios of 0.5 and 0.6 generate at least 98% of the plastic capacity with a failure mechanism of stud rupture as characterized by significant softening after a slip of 4 mm. When a ratio of 0.4 was incorporated, no such softening was observed due to stud and web yielding (the combination of which produced more ductility in the system). At a ratio of 0.3, the connection was governed mostly by web bearing failure, as little demand was placed on the stud shank. For the 16-mm studs, the shape of the force vs. slip curves looks similar to the experimental benchmark sample when a ratio of 0.5–0.6 was used. When a ratio of 0.4 was considered, a combination of stud yielding and web bearing was the governing failure mechanism. At 0.3, a new mechanism was introduced as global web shear failure was observed. This is characterized by the sharper elbow at the yield point of the force vs. slip curve. Finally, the 19-mm studs only achieved full plastic capacity at a tw/db ratio of 0.5. Below this ratio, the failure mode shifted to global web shear because of the higher bearing strength generated from a larger stud. The force-slip graph for samples which fail via global web shear display no ductility because the failure mechanism occurs outside of the panel region, where slip is captured. Therefore, some elastic displacement is experienced by the system until the web begins to yield outside of the panel zone.This paper presents the validation of push-out experiments with headed studs welded on thin web plates of weathered girders and embedded in UHPC through finite element analysis using ABAQUS. Based on the physical material properties, material models were assigned with damage models developed through classical formulations. With good agreement achieved between the simulations and experimental results, two parametric analyses were conducted. One study focused on the effect of an eccentrically loaded stud group with various offsets. The second analysis captured the effect of web thickness to stud diameter assuming the defined material properties. The following conclusions are made from this study:Material models were calibrated for the base beam section, headed studs, and UHPC materials used in this study. Using classical formulations, damage models were incorporated into the true stress responses. Simulated coupon results showed good agreement to the physical coupon test results.The shear behavior of headed studs welded on a 9.5-mm thick web plate and embedded in UHPC was validated through finite element simulations. Five push-out samples were considered: three stud diameters (12 mm, 16 mm and 19 mm) and two specimens with an eccentricity of 50 mm and 100 mm. With proper boundary conditions and calibrated interaction parameters, good agreement was achieved.An eccentrically loaded stud group embedded in UHPC was studied under various eccentricities. It was observed that, as the eccentricity increased, the total load bearing capacity of the stud group decreased. The relationship between in-plane torsion and longitudinal shear capacity was studied and a formulation for the load bearing capacity of an eccentrically loaded single-column stud group was proposed.A parametric study was conducted to determine the influence of web thickness to stud diameter ratio with the given material properties. It was found that a minimum tw/db ratio of 0.5 should be maintained to generate full plastic capacity of the studs without significant yielding of the web plate.When a tw/db ratio below 0.5 was introduced, the failure mechanism shifted away from stud failure. For 16-mm studs, bearing of the web plate was the controlling mechanism. When larger stud diameters (i.e. 19 mm) were incorporated into the model, a larger bearing capacity of the web plate was generated. This shifted the failure mode to global shear failure of the web plate under the defined loading conditions.The results of this work provide credibility to the proposed repair method by understanding the local behavior of the stud, web plate and UHPC interaction. The high-fidelity FE simulations outlined in this paper provide a novel contribution to the understanding of eccentrically loaded stud groups and limitations of stud-to-plate thickness ratios.Laminate thickness and resin pressure evolution during axisymmetric liquid composite moulding with flexible toolingThis paper presents experimental observations from the filling and post-filling stages of 1D axisymmetric Resin Infusion (VARTM) and RTM Light. A series of experiments have been performed to investigate the influence of mould flexural stiffness and fill mode on fluid pressure, cavity thickness, filling stage time, and post-filling stage time. Observations are also made on the effect of those parameters on the repeatability of nominally identical experiments. This paper helps identify the circumstances where a RTM simulation would be sufficiently accurate for an RTM Light process, and consequently where a full flexible tooling simulation is necessary.Liquid Composite Moulding (LCM) describes a range of composites manufacturing processes where dry fibrous reinforcements are compacted in a mould before being impregnated with a liquid thermosetting matrix. Although all LCM processes use closed moulds, they vary in stiffness from fully rigid to fully flexible, with the heavy tooling of Resin Transfer Moulding (RTM) and Compression RTM (CRTM) processes at one end of the spectrum, and the thin films used in Resin Infusion (a.k.a. VARTM) at the other.This paper focuses on LCM processes with flexible tooling, in particular RTM Light and Resin Infusion (). RTM Light differs from RTM by replacing one rigid mould half with a lighter, less rigid component, often manufactured from an isotropic glass fibre composite. Clamping is usually provided by application of vacuum to a region at the periphery of the mould cavity, and resin flow is driven by a cavity vacuum, an external injection system, or a combination of the two. RTM Light can provide significant reductions in tooling costs when compared to RTM, while at the same time allowing for higher injection pressures, higher volume fractions, and reduced cycle times when compared to flexible film processes. RTM Light has been employed in the manufacture of a variety of composites products, including boat hulls, bath tubs and automobile chassis components, where part size or volume of production makes rigid tool processes economically or technically unfeasible, and lack of process control or slow cycle times rule out Resin Infusion.Numerical simulations of rigid tool LCM processes have been in development for over 20 years, with several academic and commercial packages now available Extending a rigid tool simulation to flexible tooling processes such as Resin Infusion and RTM Light introduces a number of complexities attributable to the deforming mould and the resulting coupling between laminate thickness and the fluid pressure field in the saturated portion of the part. In particular, a simulation requires a constitutive model for the fibrous reinforcement to link applied stresses to deformations in the fluid–fibre system. Given that reinforcements typically exhibit non-linear load–deformation behaviour with rate and path dependencies ). At the completion of filling, mould deflection and part thickness vary spatially, even between regions with the same initial thickness. This post-filling stage, which is not present in RTM, involves the equilibration of fluid pressure and part thickness through bleeding of excess resin. Because the speed at which this process occurs dictates the final part thickness at gelation, it is an important phenomenon for parts where consistency or control of final part thickness is necessary.Clearly, the interactions between fluid pressure, flow evolution, reinforcement deformation behaviour, and the structural response of the tooling present challenges to the modelling and simulation of flexible tool LCM processes. Despite this, there are still a number of benefits to be had from developing a good simulation of flexible tooling processes, including accurate predictions of filling and post-filling time, guidance over mould design, and laminate thickness predictions throughout the process. It must be recognised that the utility of a flexible tooling simulation extends well beyond fill time prediction, where the improvements over RTM based predictions may be small, by providing estimates of part thickness variation during and at the completion of processing. RTM simulations are unable to account for these effects, and as a consequence will not indicate when they can, and cannot, be discounted.An important and necessary step in the simulation development process is performing experimental studies to guide model design and to validate simulation results. Such studies help identify the effects of mould compliance and the point at which they necessitate inclusion in a simulation. While a number of experimental studies on Resin Infusion have been presented in the literature The experimental study in this paper adopts the common scientific approach of simplifying a problem that includes a large number of variables by selecting and varying those which the authors consider important and controlling for the rest. While typical industrial RTM Light processes may involve complex geometries, preform construction, heat transfer, and resin cure kinetics, they are controlled for or simplified here. The key variables in this study are mould stiffness and injection scheme, and their effect on fill time, post-filling time, fluid pressure and laminate thickness, and cycle-to-cycle variability is investigated. This provides results suitable for comparison to simulation as well as a basis and motivation for future experimental studies. shows a schematic of the experimental facility developed for this study, which is capable of performing and monitoring 1D axisymmetric infusions with partially and fully flexible upper mould components. This has been achieved using a circular mould with a rigid aluminium lower half and upper mould halves of either nylon vacuum film or polycarbonate plates, depending on whether a Resin Infusion or RTM Light process is under consideration (). Two polycarbonate plates with 6 mm and 10 mm thicknesses are used in this study, providing a low rigidity case and a high rigidity case.The lower mould half is divided into two isolated sections: a 4 mm deep mould cavity able to accommodate circular preforms up to 450 mm in diameter, and an annular outer region that can be evacuated to clamp the RTM Light moulds in place. Ports located at the centre and the periphery of the mould cavity function as either injection gates or vents depending on the fill mode required. For the Resin Infusion experiments, an aluminium spacer ring () is placed around the periphery of the preform to act as a vent line for radial filling or a gate line for peripheral filling; no spacer is required for RTM Light, as the polycarbonate plates have sufficient stiffness to maintain a clear channel.The design of this facility was motivated by a desire to have flow and deflection behaviour suitable for direct comparison to numerical simulations without deviating too far from the practices seen in industrial RTM Light processes. This is why a circular geometry was preferred over a rectangular or complex 2D mould cavity, and why vacuum clamping was used in favour of mechanical techniques.Five pressure transducers are fitted to the mould, measuring the fluid pressure at the gate, vent, and three evenly spaced points along the preform (). Fluid mass flow rate is monitored by a mass balance supporting the fluid container. The transducers and mass balance are connected to a data acquisition system, and their outputs are recorded on a PC running LabVIEW. Full-field upper mould surface deflection is measured with a stereophotogrammetry system comprising a pair of digital SLR cameras mounted above the mould and a high frequency speckle pattern on the mould surface (). The cameras are connected to and controlled by a pair of PCs, acquiring images at set intervals that can be processed and converted into mould cavity height measurements. This system, described in detail in The fibre reinforcement used in this study is an emulsion-bound E-glass chopped strand mat (CSM) with a nominal areal weight of 450 g/m2 (Owens Corning, product code M705). Actual areal weight measurements were conducted before each test, giving an average value of 454 g/m2 and maximum and minimum values of 469 g/m2 and 433 g/m2. The CSM has random fibre orientation, providing the in-plane isotropic permeability that is necessary for 1D axisymmetric flow. Preforms for all experiments comprised 10 layers of CSM cut into 450 mm diameter circular sections, with a 15 mm hole in the centre to further encourage 1D flow. Ten layers of CSM gave a nominal fibre volume fraction (Vf) of 44% at the mould cavity thickness of 4 mm, which is close to the volume fraction of that material under 1 atm of compaction pressure. This ensures that the initial volume fractions in the Resin Infusion and RTM Light experiments are comparable. The test fluid for all experiments was a Mobil DTE Heavy mineral oil with Newtonian behaviour and a viscosity of 0.35 Pa s at 20 °C, giving comparable flow properties to uncured infusion grade resin without the associated toxicity hazard. The viscosity was measured over a 10–40 °C temperature range with a Parr Physica UDS200 rheometer (). The temperature-viscosity behaviour can be modelled in that temperature range by a fourth order polynomial:μ(T)=4.32×10-7T4-6.51×10-5T3+3.73×10-3T2-9.74×10-2T+1.26,where μ is the viscosity in Pa s and T is the temperature in °C.A series of six experiments were performed, allowing two fill modes and three levels of mould compliance to be compared. The two fill modes were radial and peripheral, giving divergent and convergent flow front evolutions; the three upper moulds were a flexible nylon vacuum bag, a 6 mm thick polycarbonate plate and a 10 mm polycarbonate plate. Experiments using these upper moulds are hereafter referred to as Resin Infusion, low rigidity RTM Light, and high rigidity RTM Light respectively. Each experiment was repeated three times to account for variations in constituent materials and operating conditions, giving 18 tests in total.Fill mode was of interest since both radial-type (central gate, perimeter venting) and peripheral-type (perimeter gate, central venting) fill modes are used in industrial RTM Light facilities. Peripheral-type filling is often preferred because of the comparatively quick fill times when compared to centralised gate setups.Previous research on Resin Infusion has shown that a flexible mould, when compared to rigid tooling, can have a significant effect on fill times and laminate thickness distribution The preform was cut and weighed before being placed in the rigid lower mould and covered with a Nylon vacuum film (Resin Infusion) or a polycarbonate plate (RTM Light). Half of the upper mould surface was printed with a speckle pattern to allow out-of-plane thickness measurements using the stereophotogrammetry system (). The data acquisition and stereophotogrammetry systems were then activated to monitor and record fluid pressure, fluid mass flow rate, and out-of-plane thickness deviations.Before opening the injection gate, a pre-filling compaction cycle of 600 s full vacuum (∼15 mbar cavity pressure) followed by 300 s at zero vacuum (1 atm cavity pressure) and 300 s full vacuum was applied. Previous studies have shown this cycling reduces variability in the compaction response of the CSM reinforcement shows the fill time and post-filling time for each experiment, along with the ambient temperature. Fill time is defined as the time between the injection gate being opened and the preform being fully saturated, and post-filling time is defined as the time between the end of the filling stage and the time at which the thickness variation across the part is less than 2% of nominal part thickness (0.08 mm). reveals a strong correlation between process times and ambient temperature, which is likely due to the effect of temperature on viscosity. To account for this variation, the times may be normalised to a constant viscosity:where tadj and traw are the adjusted and raw times, μ(T) is the viscosity at the experiment temperature and μ(20 °C) is the viscosity at 20 °C (0.35 Pa s). shows the process time mean and standard deviation for each combination of mould type and fill mode, with all times adjusted to a constant viscosity of 0.35 Pa s. Accounting for temperature reduces the variation across the samples, although the peripheral Resin Infusion post-filling still exhibits a large amount of scatter. The likely cause of this is discussed in more depth in Section The first significant trend is the difference in fill time between peripheral and radial modes, with average radial fill times for the three mould stiffnesses between 1426 s and 1674 s, and average peripheral fill times between 280 s and 312 s. This difference is consistent with 1D RTM analysis of a circular part subject to constant pressure injection tradial=μ(1-Vf)KPinjro22lnrori-ro2-ri24,tperipheral=μ(1-Vf)KPinjri22lnriro-ri2-ro24,where K is the permeability, Pinj is the constant injection pressure, and ri and ro are the inner and outer radii of the part. Taking the ratio of fill times produces a function dependent on part geometry only:tradialtperipheral=R2lnR-12(R2-1)12(R2-1)-lnR,where R |
= |
ro/ri is the ratio of outer radius to inner radius. gives the ratio of radial to peripheral fill time and post-filling time for all mould stiffnesses based on experimental data, along with the analytical RTM fill time and ratio (Eq. ) for the mould geometry in this study (ri |
= 7.5 mm, ro |
= 225 mm). The analytical fill time ratio for RTM is 5.85:1, which is close to the experimental RTM Light values obtained in this study (5.79:1 and 5.53:1). In comparison, Resin Infusion radial fill times were only 4.6 times longer than peripheral fill times on average. The larger changes in cavity thickness occurring during Resin Infusion make it unsurprising that the RTM analysis, which assumes constant permeability and thickness throughout the part, is a poorer predictor in this case.When comparing post-filling times, the trend is reversed, with thicknesses settling much faster in the radial fill mode for all moulds. The average ratio of radial post-filling time to peripheral post-filling time was 1:9 for Resin Infusion, 1:15 for low rigidity RTM Light, and 1:29 for high rigidity RTM Light. As a result, there is less difference in the combined filling/post-filling time between the fill modes than there is between the individual stages. Peripheral filling is typically preferred in industry because of its comparatively fast fill times, but the data here indicate that much of this advantage is lost when the time taken for thickness consolidation to occur is included. Further insight into this behaviour is provided by the laminate thickness data presented in Section While there are clear differences between the fill modes, the effect of mould stiffness is less pronounced. For the radial mode, Resin Infusion fill times are faster than either RTM Light case on average, but not significantly so. Overall, for either peripheral or radial filling, the mould stiffness has little effect on the fill time. However, it does appear to have a much more noticeable effect on post-filling, with Resin Infusion taking longer in both fill modes.Previous work on Resin Infusion has shown that the high compliance of vacuum film leads to lower fibre volume fraction, higher permeability and hence faster fill times than RTM for a given injection pressure A 2D representation of the mould deflection at the completion of filling is provided in using data generated by the stereophotogrammetry system. The results are limited to a partial area of the mould surface by the field of view of the cameras, but are still sufficient to demonstrate the axisymmetry of the deflection. One dimensional thickness profiles can therefore be obtained by circumferentially averaging the full-field data. Fluid pressure and laminate thickness profiles for all fill modes and mould types are presented in at three instances during the process: halfway through filling, at the completion of filling, and at the completion of post-filling. Values are plotted as a function of distance from inlet, so the maximum pressure and thickness values occur at zero for both fill modes.Looking first at the influence of mould stiffness, the pressure profiles during filling become less concave for peripheral and more convex for radial as the mould stiffness increases, which leads to a smaller pressure gradient at the flow front and slower flow speeds. This is consistent with thickness profiles showing less deviation with increasing mould stiffness, which results in smaller increases in permeability at the flow front and slower flow front speed. The smaller thickness deviations also correspond to a shorter post-filling time, since there is less excess fluid to extract before thickness variation falls within 2% of part thickness.When considering the effect of fill mode, peripheral filling results in significantly larger thickness increases for a given mould stiffness. This can be attributed to a combination of two effects: the region of high pressure near the inlet acting over a larger surface area in peripheral filling, and the relative shapes of the pressure profiles – concave for peripheral and convex for radial. However, this is tempered somewhat by the small distance between the high pressure region and the cavity edge supports in peripheral filling. Both fill modes display a sizeable pressure gradient at the completion of post-filling for all test cases (c). The difference in pressure between inlet and vent ranges between 190 mbar and 420 mbar, or approximately 20–40% of the applied pressure difference during filling. shows pressure and thickness at the inlet for all mould stiffnesses and fill modes against normalised time. Behaviour at the inlet is consistent between repeats so each trace is taken from a single test. Although inlet pressure during filling is unaffected by mould stiffness, as expected for a constant injection pressure configuration, a gradual increase in pressure is observed in the peripheral mode because of frictional effects in the injection line connecting the fluid pot to the mould (approximately 1.0 m of 8 mm internal diameter tubing). The pressure loss is a function of flow speed, explaining why it is much more prevalent in the faster flowing peripheral mode. Mould stiffness has negligible influence on the post-filling pressure behaviour for radial filling, but for peripheral filling there is a trend of more rapid pressure decrease as the mould stiffness increases. c and d shows the magnitude and duration of thickness deviations to increase with decreasing mould stiffness. The difference in post-filling pressure behaviour is likely attributable to this variation in mould deflection because of the coupling between fluid pressure and laminate thickness in these processes.Increasing the mould stiffness reduces radial post-filling time from an average of 179 s for Resin Infusion to an average of 31 s for high rigidity RTM Light and the peripheral post-filling time from 1619 s to 872 s. This is predominantly caused by lower overall thickness changes during filling when mould stiffness is increased: in peripheral Resin Infusion the part thickness deviation reaches a maximum of 0.8 mm at the inlet on average, twice the deviation observed in low rigidity RTM Light, and four times that seen with the high rigidity mould. With lower overall deviation there is less excess fluid to extract, so it takes less time for the thickness gradient to fall within a prescribed percentage of nominal part thickness (2% or 0.08 mm in this case).Although the aggregate property of fill time showed good repeatability, pressure and thickness measurements exhibited significant variability between repeats for the peripheral fill mode, particularly for the Resin Infusion experiments. compares the pressure traces for all repeats, mould types and fill modes. Once again, time is normalised with respect to fill time. The general trend seen in is that increasing the mould stiffness or switching to radial filling gives more repeatable pressure profile development. Also note that the variations between experiments are largest during the periods where pressures are changing rapidly, and as the filling progresses the pressures converge at each measurement point. While some of the differences between repeats can be attributed to deviations from axisymmetry, indicated by the initial rise of in-preform pressure measurements occurring at different normalised times, it cannot account for all the variation. A similar pattern is exhibited in the laminate thickness traces shown in , with repeat-to-repeat variability reducing with increasing mould stiffness and from peripheral to radial filling. It was noted in Section that variability in post-filling time increased with mould compliance, and was particularly large for the peripheral Resin Infusion sample. The cause of this behaviour appears to be found in , with peripheral Resin Infusion showing a wider range of thickness distributions at the completion of filling than the other combinations. This in turn would affect the volume of excess fluid in the laminate and consequently the time taken to complete the post-filling bleed.A possible explanation for the trends in repeatability is in the unloading process of the reinforcement as the flow front passes and the fluid pressure rises. In Resin Infusion there are larger changes in thickness and more potential for influence from local reinforcement variability, since the film does not average out deflection like a semi-rigid mould. When the mould possesses some rigidity, deflection at any point depends on the overall pressure field, not just the local pressure at that point.For the radial fill mode, the pressure and thickness traces collapse with much smaller deviation, even for Resin Infusion, as seen in d–f. Given that radial filling generates smaller deflections at a slower rate, this is evidence that some combination of rapid and large unloading of the saturated reinforcement is linked to variable fluid pressure behaviour, although more work is necessary to determine the relative importance of the rate and magnitude of unloading.Previous research has shown fibrous reinforcements to exhibit complex load–deformation behaviour, including viscoelasticity, permanent deformation, and path dependency The standard analytical treatment of Resin Infusion applies a force balance based on Terzaghi’s relation It is assumed that the mould has zero flexural stiffness, so the total applied stress can be set equal to the external air pressure. Since this value is known and unaffected by the process, the local resin pressure can be expressed as a function of the local fibre compaction stress, and then through a compaction model as a function of laminate thickness or fibre volume fraction The assumption that the Resin Infusion film provides no resistance to deformation is critical to this analysis, and it appears to be reasonable when considering bending stiffness only. shows material and geometric properties for the three mould types used in this study, along with values for a rigid RTM mould. Flexural rigidity is a property that arises in Kirchhoff’s classical thin elastic plate theory to relate curvature to bending moments, and is determined by material properties and plate thickness:where E is the Young’s modulus of the material, h is the thickness of the plate, and ν is the Poisson ratio of the material However, a corollary of assuming negligible resistance to deformation is that all points in the part with identical resin pressure will be under the same fibre compaction stress, and provided the compaction history and preform layup is constant throughout the part, the thickness at those points should also be the same. shows contradictory behaviour in the Resin Infusion experiments in this study. At the completion of filling there is a 50% difference in deviation from initial thickness between fill modes despite there being negligible difference in fluid pressure at the inlet at that time (959 mbar for peripheral vs. 973 mbar for radial). This suggests that the film may be offering some resistance to local laminate thickness increase, particularly for radial filling.It is possible that the film is acting as an elastic membrane as it is deflected by the fluid pressure. Out-of-plane deflection requires the film to stretch in-plane, and given that the film is far stiffer in tension than in bending, it can provide considerable resistance to deflection despite negligible flexural stiffness. The smaller laminate thickness increases exhibited in radial filling are therefore a consequence of having high fluid pressure concentrated in a small area in the centre of the mould, just as they are in RTM Light. Following this same line of reasoning, the thickness at the inlet should increase as the flow front progresses and the area with positive resin pressure expands. d shows precisely this behaviour, with the inlet thickness increasing during filling despite that point being at the same fluid pressure throughout. For the CSM material, a 0.25 mm difference in part thickness at the inlet corresponds to a 6% change in Vf and a 30% change in permeability An experimental facility has been developed to monitor LCM processes under flexible and semi-rigid tooling. Pressure and laminate thickness data was presented from a series of experiments in which the influence of mould stiffness and fill mode was investigated, revealing key issues in performing and modelling LCM processes with flexible tooling. Investigating the effect of fill mode showed peripheral filling to result in shorter fill times but longer post-filling times when compared to radial filling. This means that the advantage of peripheral filling is much less pronounced when the combined time is considered, dropping from approximately five times faster to 1.5 times faster.Although mould stiffness had little discernable effect on fill time, its effect on post-filling time was far more substantial, with post-filling time increasing with mould compliance. Additional findings revealed variability of point pressure measurements, laminate thickness, and in turn post-filling time, in nominally identical experiments to be strongly related to mould stiffness and flow speed. It was also shown that Resin Infusion film may act as an elastic membrane and restrict laminate thickness and permeability increase during filling.These results indicate that the interactions between mould stiffness and injection scheme can affect fill time, post-filling time and laminate thickness during and at the completion of processing, motivating the need for flexible tooling simulation for applications where predictions of final part thickness tolerances are important. Furthermore, flexible tooling simulations could be employed to quantify the effect of material and process variability on process time, part quality, and manufacturing cost, as well as providing improved guidance over injection strategy and mould design compared to conventional RTM simulations.Fire performance of axially ductile connections in composite constructionTo enhance the robustness of steel-framed structures in fire, a novel, axially ductile connection has previously been proposed. In this paper its performance is investigated when it is used to connect composite beams to steel columns in composite steel-concrete construction. The ductile connection is designed to satisfy the ductility demands of the composite beam at elevated temperatures. A reinforcement component has been added to the bare-steel ductile connection model to establish a component-based model of the composite ductile connection. The connection model has been incorporated into the software Vulcan, and is validated against detailed Abaqus FE models using solid elements. Results show that the proposed component-based model can efficiently represent the behaviour of the connection given by the detailed Abaqus simulations. Parametric studies using Vulcan have been carried out, varying three parameters; the connection thickness, the semi-cylindrical section radius, and the density of longitudinal reinforcing bars. Finally, a 2-D Abaqus composite frame model has been created to investigate the influence of shear studs on the behaviour of the composite ductile connections under different stud spacings.Axial ductility demand of the beam at the rebar levelAxial ductility demand of the beam at the connection top surfaceAxial ductility demand of the beam at the connection bottom surfaceTotal rotation of the composite beam at beam endTotal deflection of the composite beam, δtotal=δexternal−load+δthermal−bowingThe vertical distance from the top surface of the slab to the neutral axisThe vertical distance from the top surface of the slab to the longitudinal rebarThe tensile force acting at the centroid of the slabThe compressive force acting at the centroid of the steel sectionThe Young's modulus of the steel sectionThe cross-section area of the steel sectionThe second moment of area of the steel sectionThe vertical distance from the neutral axis to the centroid of the slabThe vertical distance from the neutral axis to the centroid of the steel sectionThe bond stress when the rebar strain is lower than the yield strainThe bond stress when the rebar strain is higher than the yield strainThe development length of post-yield zoneThe regular spacing of the weld points on the transverse rebarsFailure of the connections of a composite floor in fire conditions may lead to the detachment of connected beams, causing the collapse of floors, spread of fire into other compartments, buckling of the adjacent columns and may even initiate the eventual collapse of the entire building. Therefore, connection performance has a crucial influence on the control of the fire-induced progressive collapse of a composite structure. The behaviour of connections at elevated temperatures is considerably more complex than that at ambient temperature, since the connections undergo different combinations of loads at different stages of a fire event. In the initial stage, the major forces carried by connections are vertical shear, accompanied by some moment, depending on the type of connection. With the increase of temperature, connections can experience additional compressive force due to the restrained thermal expansion of the connected beam. This compressive force may eventually change to tension at very high temperatures when the connected beam is under catenary action due to highly reduced steel strength. It is therefore very difficult to reproduce such complex loading conditions in experiments except in full-scale structural fire tests []. In addition, due to the large variety of connection types and dimensions, a large number of experiments would be required to cover the investigation of a representative range of different connections. Hence, numerical simulation is the feasible alternative to study the performance of connections under fire conditions. This may consist of detailed finite element simulations or more global numerical analyses representing connections using a component-based method. Among these, the component-based method can be a good compromise between accuracy of results and computational cost, compared with detailed finite element modelling. This method, which was initially developed for the design of semi-rigid joints at ambient temperature, based on principles initially proposed by Zoetemeijer [], has been introduced into Eurocode 3 Part 1–8 []. When creating the component-based model, the connection is divided into components representing basic zones of structural action, and each component is idealized as a nonlinear spring of known stiffness and strength.Compared with bare-steel framing, composite construction has higher structural efficiency and lower cost, because it allows the use of smaller steel sections. Therefore, in recent decades, composite structures have been widely used in multi-storey construction. The performance of composite structures at elevated temperatures has been studied by researchers across the world []. Accordingly, the degradation rate of the strength of a composite connection should in general be lower than that of an equivalent bare-steel connection, due to the beneficial effect of this partial temperature reduction. In addition, the composite slab restrains the thermal expansion of the steel beam in the initial stage of a fire, leading to thermal bowing, which also affects the performance of its connections by causing higher early-stage rotations. Leston-Jones [] conducted three tests on composite flush end-plate connections under constant moment with increasing temperature, to obtain their moment-rotation characteristics across a realistic range of temperatures. AI-Jabri [] continued Leston-Jones’ work by conducting high-temperature tests on two composite flexible end-plate connections of different sizes and developing component-based models of these connections. Liu [] further developed his three-dimensional finite element model FEAST, which was originally developed to simulate the response of steel structures in fire, to simulate the behaviour of composite connections at elevated temperatures. Li et al. [] carried out three tests to investigate the fire-resistance of flush end-plate composite joints considering the effect of axial force. After that, they developed a simplified component-based model to calculate the initial stiffness and ultimate moment capacity for flush end-plate composite joints at elevated temperatures [] conducted numerical and experimental investigations on welded composite full-strength beam-to-column joints under seismic-induced fires to develop fundamental data for composite beam-to-column joints with concrete-filled tubes.Current commonly-used connection types lack the axial and rotational ductilities required to accommodate the deformation of a connected beam under fire conditions. In order to improve the performance of connections and enhance the robustness of steel-framed or composite structures in fire, a novel ductile connection has been proposed by the authors []. A suitable component-based model of the bare-steel ductile connection has been developed and tested by the authors [] against detailed Abaqus simulations. Therefore, this component-based model has been incorporated into the software Vulcan, and has been used in global frame analyses to test the performance of ductile connections in bare-steel framed structures []. Since the behaviour of the ductile connections in bare-steel structures has already been well studied by the authors, it is appropriate now to investigate their performance in composite structures. In non-composite steel frames, the thermal expansion of a complete beam can be absorbed by plastic deformation of the ductile connections, thus greatly reducing the forces imposed on the surrounding structure. However, in composite construction, unless a large number of shear studs are fractured or highly deformed, the deformation of the ductile connections will mainly be caused by rotation at the column face, which will mainly be caused by thermal bowing of the composite beams. Hence the influence of these connections on the overall frame behaviour is less easily predicted.When exposed to fire, connections undergo large axial deformations applied by the connected elements. At the initial stage of a fire, connections are mainly subject to compressive displacement due to the beam's thermal expansion. This eventually changes to tensile displacement when the loss of strength of the connected beam makes it incapable of carrying its load in bending, so that it enters a phase of the tension at very high temperatures. Excessive axial displacement of the connection can lead to fracture, potentially causing the failure of other structural elements, and even the progressive collapse of the entire structure. Therefore, the axial deformation capacity of connections is of great significance in preventing their abrupt failure and improving the inherent robustness of the structure in fire. The design of the proposed connection is based on the concept of ductility demand, which is defined in Section The deformation of a typical composite beam as its temperature rises is illustrated in . The lever arms used are the distances between each key position and the neutral axis of the composite beam. As mentioned previously, the slab restrains the thermal expansion of the composite beam. This leads to thermal bowing, and the deflection due to thermal bowing needs to be included into the total deflection of the composite beam. The total deflection of the composite beam also includes the deflection caused by external load.Δcts=43δtotal2/l−tan(θtotal)⋅(h1+h2−Hcon2−hc)Δcbs=43δtotal2/l−tan(θtotal)⋅(h1+h2+Hcon2−hc)To calculate the thermal bowing deflection of the composite beam, several assumptions are made here:the slab is assumed to remain at ambient temperature;the temperature distribution within the beam section is uniform;full shear connection between the slab and steel beam is assumed. (a), the mechanical strain is obtained by subtracting the thermal strain from the total strain, and is then used to establish mechanical equilibrium.Due to the assumption of full shear connection, the curvature of the slab is equal to that of the beam (Equation The tensile force acting at the centroid of the slab Tslab, and the compressive force acting at the centroid of the steel section Csteel can be obtained using Equation According to the horizontal force equilibrium, the curvature can be expressed by a formula containing the two distances e1 and e2 from the neutral axis to the centroids of the slab and steel section respectively (Equation Tslab=Csteel⇒E1A1y″e1=E2A2(αT−y″e2)⇒y″=E2A2αTE1A1e1+E2A2e2Moment equilibrium is then used to obtain the values of e1 and e2, as shown in Equation Tslabh1+h22=M1+M2⇒e1=2(E1I1+E2I2)E1A1(h1+h2)e2=e1+h1+h22Once the curvature is determined using Equation , the deflection due to thermal bowing is calculated using Equation β=sin−1(l/2rcurvature)Def=rcurvature(1−cosβ). This figure shows that the connection should have an axial deformation capacity of at least 28.1 mm in “closing” and 10.7 mm in “opening”, in order to meet the ductility demand of the composite beam in fire, if the composite beam is designed to survive to 800 °C. The elastic modulus of steel decreases with the increase of temperature. When the temperature reaches 600 °C, the elastic modulus of steel decreases considerably, to the same order of magnitude as that of concrete, which leads to the rapid change of thermal bowing deflection slope, as shown in To meet the ductility demand of the beam in fire, a novel ductile connection has been proposed by the authors [. The most critical parameter of the ductile connection in terms of the ductility demand in fire (Equations ) is the diameter of the semi-cylindrical section. All other parameters, such as the thickness and depth of the plate and the number of bolt rows, can be determined in accordance with EC3 [Component-based modelling of bare-steel connections has been well studied in recent years. However, few studies have been conducted on the component-based modelling of complete composite connections. Madas [] proposed a component-based model of composite end-plate connections for use in the analysis of composite frames under dynamic loading at ambient temperature. In the Madas model, the concrete slab is divided into a finite number of layers and each layer considered is subject to a uniform strain between studs and across the slab's effective width. Al-Jabri [] developed a high-temperature composite end-plate connection model by adding two additional components, representing the reinforcement and shear studs, to his steel end-plate component-based connection model. Rassati et al. [] developed an ambient-temperature component modelling approach for the simulation of composite connections, which is capable of accounting for the influence of partial interaction between the slab and beam, and the cracking and crushing of the slab. Li et al. [A component-based model of the non-composite ductile connection has already been developed by the authors [] and has been implemented into the Vulcan software for global frame analysis []. Vulcan is a finite element software developed by the Structural Fire Engineering Research Group at the University of Sheffield. It can be used to simulate the behaviours of 2-D or 3-D bare-steel and composite structures at elevated temperatures, considering both geometrical and material non-linearities. The 2-noded spring element in Vulcan can model ideally rigid or pinned connections, as well as the traditional connection types (e.g. end-plate connections) using a component-based method. Using the same method as the bare-steel ductile connection, the composite ductile connection will be implemented into Vulcan as a 2-noded spring element. Since the connections are within the hogging bending moment zone, and the tensile strength of concrete is negligible, the concrete in tension is ignored. In the following section, a reinforcement component is added to the non-composite ductile connection model to establish a suitable model of the ductile connection in a composite structure. This component-based composite ductile connection model has also been incorporated into Vulcan, and several case studies are carried out to test its performance.Depending on its effective depth within the slab, the reinforcement above the connection may be subject either to tensile or compressive strain due to the combination of hogging moment and thermally-induced rotation. In the case where the reinforcement strain becomes tensile, as the tensile strength of the concrete is very low, cracks usually occur, leading to reinforcement pull-out within these cracks. The part of the rebar within the crack width is under uniform stress, which is equal to its ultimate strength. However, the part of the rebar within the embedded length is subject to stresses lower than those within the crack width, due to the surface bond stress. The further away from the crack-face, the smaller the stress is. Sezen and Setzler [] considered the pull-out of the rebar at concrete cracks when modelling the lateral deformation of a column caused by rebar slip in the anchorage zone. Their simple model of rebar slip, shown in (a), was verified against 12 tests conducted by Sezen [In this model, a bilinear stress-strain relationship is assumed for the rebar, with a shallow gradient between the yield and ultimate stress points. The bond stress within the embedded length is assumed to be locally constant, at either ub and ub′. When the rebar strain is lower than the yield strain, the bond stress is ub=1.0fc, but when the rebar strain is above yield, the bond stress is ub′=0.5fc. This assumption is reasonable because only high rebar strain (above yield) and the resulting high slip at the rebar perimeter can cause real damage to the adjacent concrete. The slip of the rebar can be calculated using Equations . In the extreme case of rebar fracture within the crack, fs=fu and εs=εu. In the context of The total slip of the rebar from the crack-face, assuming that it is anchored in the concrete either side of the crack is] further considered the contribution of the weld points on the transverse reinforcing bars in the mesh when calculating the crack width at which rebar fractures using the simple slip model presented above. In fact, the weld points on the transverse bars at regular spacing sb can provide physical anchorages to the longitudinal bars. The strength of each weld should be at least 25% of the bar strength in accordance with Eurocode 2 []. If the rebar stress at a weld point exceeds the strength of the weld, then the weld will fracture. The distance from the crack-face to the next weld point is then used as the development length. In this case, the pull-out of the rebar will increase suddenly when weld fracture occurs. Considering different combinations of development length, rebar stress and weld strength, three typical cases are shown in (b). The first weld is positioned at a distance of sb/2 from the crack face, and the subsequent welds are at a regular spacing sb. In Case 1, the development length of the rebar does not go beyond the first weld; this is likely to occur to deformed bars with very high bond stress. If the development length reaches the first weld-point, there are two possible scenarios, according to the relationship between the rebar stress and the weld strength.Case 2: If the rebar force is less than or equal to the weld strength, the first weld does not fracture, but becomes a positive anchorage point. The development length and crack width are both reduced compared to when weld points are neglected;Case 3: If the rebar force exceeds the weld strength, the first weld fractures and the remaining anchoring force is borne by the bond stress developed beyond the broken weld. For bars with low bond stress, such as plain circular bars, there may be more welds broken before sufficient anchorage is accumulated.], for plain rebars the bond stresses are reduced to ub′=0.15fc and ub=0.3fc. For deformed bars, the two values (ub′=0.5fc and ub=1.0fc) mentioned earlier remain valid. The weld strength is assumed to be 25% of the rebar strength according to Eurocode 2 [The force-slip curve of a bar is generated by using the rebar slip model considering the weld anchorage described above. If the concrete crack occurs in the middle of the slab and there is enough length on both sides of the crack to develop the anchorage, the crack-width should be twice the slip from a single crack face. The tensile force of the rebar is obtained by multiplying the rebar stress by its cross-sectional area. Taking deformed and smooth A252 meshes at 200 mm × 200 mm spacing as two examples, the properties of these two meshes and their weld fracture predictions are listed in The calculated force-slip curves are shown in (a). This figure shows that only the first weld of the deformed A252 breaks, whereas three successive welds break for the smooth A252 bar. The location of the concrete crack must be determined when the rebar component is incorporated into the component-based model of the connection. Based on the results of the tests conducted by Al-Jabri [The development length on the right side of the crack is assumed to be limited by the first three weld points, since previous research indicates that the rebar development length usually does not exceed the third weld point []. The development length on the left side of the crack is assumed to be limited by the first weld point and the centre line of the column section, depending on whether the first weld point fractures. The slip on the left and right sides of the crack should be calculated separately. The sum of the slips on both sides is the crack-width, or the total displacement of the rebar component.The rebar component described above has been added to the component-based model of the bare-steel connection [] to form the component-based model of the composite ductile connection. As shown in (a), the proposed component-based model includes components representing the face-plate and cylindrical section, the column web in compression, bolt pull-out, rebar, fin-plate in bearing, beam web in bearing and bolt in shear. The gap between the compression spring row and the column face is designed to represent the maximum compressive displacement before internal contact occurs. The component-based model is then converted into a connection element, following the principles of the finite element method. The method is introduced in detail in a previous paper [], and so is not repeated here. The 2-D composite frame model shown in (b) is used to test the performance of the composite connection element. The height of the upper and lower columns is 3 m, and the beam span is 10 m. The rebar is assumed to be anchored to the centre line of the column section for both the inner and outer column cases. For an inner column, the inherent symmetry of deflection about the column line makes this assumption generally valid. For the outer column case, the rebar is assumed to be anchored, generally by a hook, to the column, which would be normal good design practice. In order to reduce the size of the model to save computation cost, only half of the frame is modelled, and symmetric boundary conditions are applied at the mid-span of the beam and slab. The bottom of the column is fully restrained, and the top can only move vertically. It is further assumed that fire only occurs in the lower storey. Lawson [ for a perimeter column connection. As can be seen from this figure, the proposed ductile connection exhibits satisfactory deformability.The results of the Abaqus and Vulcan models are compared in . Looking at the mid-span deflections and end rotations shown in (a) and (b), the Abaqus model appears to be stiffer than the Vulcan model at temperatures above 200 °C. These differences can be explained by two different aspects of the respective models:In its plastic phase, the push-pull analytical model of the semi-cylindrical section used in the component-based model of the ductile connection is softer than the detailed Abaqus connection model [The concrete cracking and the pull-out of reinforcing bars are only introduced in the Vulcan connection element; they are not considered in the Abaqus model, making the composite slab of the Abaqus model apparently stronger than that of the Vulcan model.The differences between the Abaqus and Vulcan models occur above 200 °C, since all the spring rows of the Vulcan connection element are within their linear-elastic phase below 200 °C, and the difference between the push-pull analytical model used in Vulcan and the detailed Abaqus model in the linear-elastic range is small ( (d)). The comparison of the connection axial forces obtained from the Vulcan and Abaqus models is shown in (c), which shows that above 200 °C the connection axial force of the Abaqus model is larger than that of the Vulcan model. This is also due to the fact that the Abaqus detailed connection model is more rigid than the push-pull analytical model in the plastic stage. At around 690 °C, the compressive axial force of the connection in the Vulcan model decreases rapidly and changes temporarily into tension at about 800 °C. Above this temperature, the connection axial force becomes compressive again. During heating, the behaviour of the connection is affected by the combined effects of thermal expansion and material degradation. In the beam temperature range 700 °C–800 °C, the change of steel crystal structure causes a pause in the beam's thermal expansion, which resumes when the transition is complete. This can be seen ( (b)) to cause a temporary change of direction in the connection rotation. This causes the connection spring rows to reverse direction, causing their forces to change rapidly into tension because of the rather stiff nature of the elastic unloading curves []. When the thermal expansion re-commences, the connection force again rapidly changes to compression, as shown in (a) and (b) show the temperature-force and temperature-displacement curves of each spring (component) row in the Vulcan model, indicating that the decrease in connection rotation leads to unloading of all the spring rows. Among all the five spring rows, the reduction in the compressive displacement of the bottom spring row (Row 5) is the largest, whereas the displacement reduction of the top spring row (Row 1) is the smallest. Therefore, Row 5 enters the so-called pulling-back stage [], and its force temporarily changes into tension, whereas Row 1 is within the unloading stage before the compressive displacement increases again, and its force remains as compressive. (c) and (d) show the temperature-force and temperature-displacement curves of the rebar component of the Vulcan model, which works only in tension. It is temporarily active at ambient temperature due to the hogging moment applied to the connection; it then remains inactive until about 600 °C, since the beam's thermal expansion compensates for the tensile displacement of the rebar component. After the activation of the rebar component, the discrepancy between results from the Vulcan and Abaqus models begins to increase, as shown in (a) and (c). At 689 °C, the force in the rebar component increases almost vertically; this is caused by a sudden increase of beam deflection (shown in (a)), as all the spring rows enter the unloading stage, which is manifested by the sudden decrease of the compressive forces of all the spring rows, as shown in (a). Most Vulcan results show a slight oscillatory pattern, which is caused by the large unloading stiffness of the connection element. It is assumed that the unloading stiffness of the spring row in the connection element is the same as the initial elastic loading stiffness, and the initial elastic loading stiffness of the ductile connection is very large []. This leads to a sudden change of the spring force when unloading occurs, which is manifested by the slight oscillatory pattern of the Vulcan result curves. In addition to this, the concrete model used in the slab elements models cracking at different levels within the elements. This causes the tensile stresses at various locations to vanish abruptly as the loading or heating proceeds. In general, the performance of the Vulcan connection element is satisfactory compared with the detailed model in Abaqus, indicating that the Vulcan composite connection element which has been developed can be used to investigate the effect of utilising the ductile connection within a composite structure in fire conditions.In this section, the 2-D composite frame model shown in (b) is used for a series of parametric studies. The effects of three parameters (the connection thickness, the inner radius of the semi-cylindrical section and the number of longitudinal bars within the effective width of the slab) are studied. As shown in , an increase in connection thickness leads to a decrease in connection ductility. Frames experience lower mid-span beam deflection, smaller connection rotation, larger connection axial force, larger rebar component force, and smaller axial displacement at the beam end, as their plate thickness increases. As mentioned previously, the inner radius of the semi-cylindrical section is a key parameter, determining the connection's axial deformation capacity, and should be determined on the basis of the ductility demands obtained using Equations The effect of the semi-cylindrical section's inner radius on the connection's behaviour is shown in . This figure shows that connections with larger inner radii have higher axial ductility, which can significantly reduce the forces in the connection and reinforcing bars, compared with connections of smaller inner radii. However, the influence of the cylindrical section radius on the mid-span beam deflection, connection rotation and beam end axial displacement are not obvious below about 500 °C. Above 500 °C, the mid-span beam deflection and connection rotation of the composite frame models with larger cylindrical section radius are smaller than those of the same frame with smaller radii. Although increasing the cylindrical section radius can effectively improve the axial deformation capacity of the ductile connection, it should be noted that an excessive increase in this radius may hinder the installation of bolts in the end-plate part of the connection, and may lead to hard contact between the semi-cylindrical section and the end-plate. Therefore, the limitation on the dimensions of the various parts of the ductile connection does not generally depend on the analytical aspects of its behaviour, but on the constraints of practical construction.The difference between the component-based model of the bare-steel ductile connection and that of the composite version is the introduction of the rebar component. Therefore, the effect of the number of longitudinal bars on the behaviour of the composite connection is also worth attention. In general, composite ductile connections with fewer longitudinal bars are prone to premature failure. It can be seen from (a) and (b) that the mid-span beam deflection and connection rotation of the composite frame model with 7 bars increase rapidly at 688 °C. This is caused by the failure of the rebar component ( (d)). The connection axial force of this model changes suddenly from compression to tension at 688 °C, when the bars fail, and then carries on increasing in tension from this point ( shows the temperature-force and temperature-displacement curves of each spring row of this model. Row 1 fails at 831 °C, at which point the forces in the remaining spring rows increase suddenly. Among these, the force increase in Row 2 is the largest, and this spring row fails at a slightly higher temperature (859.5 °C). The failure of Rows 1 and 2 results in an increase of connection rotation and the axial displacement at the beam end in a stepped manner, as well as a stepped decrease in connection axial force, as shown in . Although increasing the number of longitudinal bars can effectively delay the failure of the composite ductile connection, the additional cost of doing so should also be considered. In addition, the spacing of rebars should not be less than the minimum spacing specified in the Eurocode. The minimum spacing of reinforcing bars should be greater than the reinforcing bar size, the maximum aggregate size + 5 mm or 20 mm []. In the immediate vicinity of the connection the spacing has to be sufficient to bypass the column with an adequate clearance.The function of shear studs is to connect the slab and steel beam, transmitting the horizontal shear force between the two. The moment capacity of the composite beam can be reduced if partial-strength shear connection is applied. Therefore, shear studs are very important components in composite structures. It is therefore useful to investigate the influence of shear studs on the performance of the composite ductile connection. However, the shear studs are not included in the Vulcan composite connection element, and so it was decided to establish a composite frame model ( (b)) in Abaqus to study the influence of shear studs. The behaviour of the steel decking on which the concrete is cast cannot be guaranteed in a fire. The thin steel deck heat much more quickly than the concrete, and usually separates from it under the influence of its own local thermal expansion. The steel deck is of little importance at high temperatures, and is therefore neglected to simplify the Abaqus model, and to save computational cost.The nonlinear behaviour of uniaxially compressed concrete at different temperatures is represented by a series of stress-strain curves as shown in In compression, the stress-strain relationship given by EC2 [] is used, in which a linear descending branch is adopted for each curve. As for concrete in tension, it is assumed that the tensile stress increases linearly with respect to strain until concrete cracking occurs, after which the stress decreases linearly to zero, and the strain corresponding to zero stress is taken as 10 times the cracking strain, as suggested by the Abaqus user's manual []. In this work, the tensile strength of concrete is set to be 10% of the compressive strength [], and the total tensile strain of concrete is assumed to be 0.1 []. The Concrete Damage Plasticity model in Abaqus, which is suitable for materials with different tensile and compressive strengths, is adopted for concrete solid elements in this model. This material model combines the concepts of isotropic damaged elasticity and isotropic tensile and compressive plasticity to represent the inelastic behaviour of concrete. The yielded parts of the tensile and compressive stress-strain curves of concrete are entered separately into the model. The material dilation angle and eccentricity parameter are taken as 20° and 0.1, respectively. The ratio of biaxial to uniaxial compressive strength is taken as 1.16. The stress-strain relationship of carbon steel without consideration of strain-hardening specified in Eurocode 3 Part 1–2 [] at elevated temperatures is adopted to simulate beam, column and ductile connection. This is widely used, although it is an implicit-creep model based on transient testing. The current analysis does not consider the effects of high-temperature creep explicitly.In order to reduce the model size and to save computational cost, only a quarter of each model was built, as shown in Limited research exists on the performance of composite connections in fire, and there is limited experimental evidence for comparison. The experiments used to validate the modelling methodology are a series of tests carried out by Al-Jabri []. Al-Jabri used a cruciform test arrangement with a furnace wrapping the connection zone to conduct these high-temperature experiments. His Group 5 (FLC-5) tests are selected for this validation. The experimental setup of FLC-5 consists of a pair of UKB 610 × 229 × 101 sections connected to a UKC 305 × 305 × 137 column by 10 mm thick flexible end-plates with 14 M20 Grade 8.8 bolts, as shown in . This figure shows that the overall trend of the connection rotation-beam temperature curves obtained from the experiments is very similar to those obtained from the Abaqus models. However, the temperatures at which run-away failure occurs in the experiments are lower than those of the Abaqus models. This is because, in the tests, run-away failure was caused by longitudinal splitting of the slab. This kind of cracking might cause the shear studs to separate from the slab, essentially turning the composite beam to non-composite, and eventually leading to a sudden increase in the connection rotation. Since such localised cracking is not considered in the Abaqus models, the beams in these models always remain composite. This may explain why the connection rotations of the Abaqus models are lower than those of the experiments. Other than this, the comparisons between the modelling and test results are satisfactory, validating the simulation method of the Abaqus models.In this section, the Abaqus model shown in As mentioned previously, the moment capacity of the composite beam could be reduced in cases of partial shear connection. Three different shear stud spacings are selected here, and their corresponding degrees of shear connection are listed in The comparative results for the composite frame models with different shear stud spacings are shown in A component-based model of the composite ductile connection has been established by adding the reinforcement component to the bare-steel ductile connection model developed previously []. The proposed reinforcement component can consider the pull-out of longitudinal bars across a discrete crack above the connection, and the physical anchorages provided by the weld points to transverse bars in the welded mesh. The component-based composite ductile connection model has been converted into a connection element following the principles of the finite element method, and incorporated into the software Vulcan. A 2-D composite frame model with ductile connections has been modelled using both Vulcan and Abaqus; the latter has used a detailed model of the connection's geometry using solid elements. A comparison of the results shows that although the connection in the Abaqus model is stiffer than that in the Vulcan model, the proposed component-based composite ductile connection model can efficiently represent the behaviour of the composite ductile connection without going to the extent of creating a full model using solid elements. Parametric studies on three design parameters were carried out, including the connection thickness, the cylindrical section radius and the number of longitudinal bars in an effective width. It was found that thinner plate thickness and larger cylindrical section radii lead to higher axial ductility, which significantly reduces the axial force carried by the connection. Lower numbers of longitudinal reinforcing bars tend to lead to early failure.As for future developments, it is certainly necessary to validate the analytical results experimentally, possibly using composite frames/subframes with ductile connections at reduced scale. In addition to experiments, 3-D composite frame models will be built using Vulcan, to investigate the influence of out-of-plane structure, particularly slabs, on the performance of the composite ductile connections. In practical terms, the performance of the composite ductile connections should be compared with traditional connection types, including connection types which are normally designed as “simple” in the sense that they are not assumed to transfer moments. These include the commonly-used web-cleat, fin-plate and flexible end-plate connections.Yu Liu: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft. Shan-Shan Huang: Conceptualization, Methodology, Supervision, Writing - review & editing, Project administration, Resources. Ian Burgess: Conceptualization, Methodology, Supervision, Writing - review & editing, Project administration, Resources.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.Preparation and characterization of modified polypropylene by using electron beam irradiationThe modification by electron beam irradiation was applied to polypropylene (PP). In this process it is tried to add low density polyethylene (LDPE) and talc in the blend to check effects on its rheological property and thermal stability. The decrease in Tm could be the result of chain scissioning which decrease the number of tie molecule in the amorphous regions and consequently weakens the laminar connections. LDPE incorporated sample was comparatively better in shear thinning effect, zero shear viscosity, and thermal stability. Power law index, n, was 0.30 and 0.89 for the modified PP with LDPE and pure PP, respectively.Polypropylene (PP) is extensively used in many fields because of its outstanding chemical and moisture resistance, low density, easy processability and relatively low cost. However it has very low impact toughness, especially at low temperature Radiation process for polymer processing these days is gaining attention from the research as the alternate method for modifying the structure to chemical methods The toughness and radiation resistance of PP is expected to increase by addition of PE, as it undergoes predominantly cross-linking on high energy radiation Another field of interest with the cross-linked PP was that melts possess unusual viscoelastic properties such as non-terminal dynamic moduli at low frequency and a high shear-thinning tendency The purpose of this study is to characterize modified PP by irradiation process, and then analyze the effect of co-agent and LDPE on the rheological and thermal property of modified PP. DSC, FT-IR and parallel plate oscillator is used to analyze the characterization and physical properties of the modified PP.Block PP which is propylene and ethylene polypropylene rubber blend (MI 30) was supplied by SK energy. Irganox-1010 was used as antioxidant and the amount used was 1 phr (part per hundred resins) with all samples. Talc was used as nucleating agent and trimethylolpropane-trimetacrylate (TMPTMA, Sigma Aldrich) was used as the co-agent for cross-linking. LDPE/PP blend was also prepared and tested in order to check the effect of LDPE on the cross-linking kinetics of PP by electron beam irradiation. First of all, for the preparation of talc containing sample, talc and TMPTMA was mixed for 30 min and all other constituents (LDPE/PP/Irganox) were added and melt mixed for next 30 min. For the sample without talc, Irganox-1010 and TMPTMA was mixed and was then added to PP. shows the composition and constituent of all the samples. After compounding, the samples were pressed as sheet with 1 mm × 120 mm × 120 mm dimension at 190 °C and were exposed to electron beam irradiation with 500 MeV.Thermal analysis was done with TA Q20 differential calorimeter (TA Instruments, Newcastle, DE, USA). Samples were heated to 250 °C at the rate 10 °C min−1 and cooled to 40 °C with same rate. Then, again sample were heated to 250 °C with same rate. The sample weighing in between 0.2 g and 0.4 g was sealed inside an aluminum pan and with aluminum as the reference; DSC was carried out in a nitrogen atmosphere. Thermogravimetric analysis (TGA) was done using SDTQ 600 thermal analyzer (TA Instruments, Newcastle, DE, USA). Samples were cut into small pieces, placed in platinum pan and weighed in microbalance. The samples were heated to 800 °C from room temperature at the rate of 10 °C min−1 in nitrogen condition. The resulting weight loss is attributed by the chemical reaction in the sample, decomposition, solvent and water evolution, oxidations etc. An oscillatory viscometer (Anton Par, MCR 301, Austria), a parallel type geometry (12.5 mm), was used to monitor the rheological property. The temperature at which test conducted was 200 °C. The gap between the plates was 1.2 mm. Fourier transformation infrared (FT-IR) was used to analyze the chemical structure of modified Polypropylene. The chemical structure of the modified samples were recorded in absorbance mode making use of Perkin Elmer Spectrum 1000 spectrometer, keeping air as reference. The remaining gel after the extraction in xylene was prepared as a thin sheet and the infrared was passed through it to measure its absorbance. Hardness of the samples was measured under shores unit (Trade SATO mark, D-5014, Japan).In order to certify the cross-linking reaction, the infrared spectra of irradiated and non irradiated samples are shown in . The TMPTA cross-linking reaction was confirmed from the intensity of 1700 cm−1 for the O group in the FT-IR spectrum. The co-agent used constituted of the carbonyl group and the presence of carbonyl group in the extracted sample showed the cross-linking of the sample. The cross-linking amount was calculated relatively from the intensity of 1700 cm−1 for the O group in the FT-IR spectrum and the thickness variation of each sample was corrected by 3000 cm−1 intensity for CH stretching which is corrected by 6 for pure PP and 5.6 for PP/LDPE blend. The calculated values were summarized in . Other absorbed frequency corresponds to the propylene and polyethylene structure.The heating and the cooling curves are shown in . The modified PPs were heated twice to investigate the melting and the enthalpy changes of the samples. It was seen from the scan that there are some significant changes in all of the samples. It was found that, the samples with co-agents, excluding PP-TP-non, the melting point in second scan decreased. This may be due to thermal history and re-crystallization . From the graph it is clearly seen that except PP-TP other irradiated sample started slower degradation, i.e. degradation started at higher temperature. Irradiation can crosslink polymers, and more complex network structure is formed which can improve thermal stability, as this network is more stable against formation of gaseous product The melt rheological properties are very sensitive to change of molecular structure such as chain branching and cross-linking. Oscillatory measurements were used to observe the effects of the molecular structure on the rheological properties of the modified PP. The measured temperature and strain were 200 °C and 20%, respectively. All data presented in this paper was verified to be in the linear regime at 200 °C and 20% strain. shows the relation between complex viscosity and angular frequency of the samples. PP-LDPE-TC-TP-irr showed high complex viscosity at low frequency region comparative to other samples. The sample showed good shear thinning property too. All the irradiated samples had comparatively higher complex viscosity compared to respective non-irradiated samples. Also, some shear thinning activity was seen in case of irradiated samples. This may be attributed by some cross-linking or branching of the irradiated samples. The shear thinning tendency was predicted by power low index calculated from linear regression (see ). PP-LDPE-TC-TP-irr showed the lowest power law index and it indicates high shear thinning tendency.Loss modulus (G″) was plotted against storage modulus (G′) (Han plot) to understand the effect of radiation on the rheological property of PP. The slope of PP without irradiation was found to be 1.53 as shown in . Isotropic homogenous melts and solutions yield a slope of 2 on Han plot, whereas heterogeneous polymeric systems, such as mesophase and block copolymers, have slope less than 2 , the slope of irradiated sample for PP-TC-TP and PP-TP has seen decreasing after irradiation. Hence we can say these samples cross-linked or branched with irradiation. The slope PP-LDPE-TC-TP sample was seen to increase with irradiation. The un-irradiated sample also have slope lower than the slope of PP, and this may be due to the presence of LDPE with long chain branch.Further tan δ against frequency was plotted to study the rheology of the samples. Sugimoto et al. . The sample PP-LDPE-TC-TP-irr loss tangent is approaching to value 1.0 indicating some structural change suggesting cross-linking within the PP. It is believed that this cross-linked character is related to the structural change that results from the irradiation process. From these results, it is concluded that LDPE is beneficial for modification of PP using by electron beam irradiation.It is expected that cross-linking or degradation in the polymer due to the irradiation is related to the hardness of sample, as the change in the structure generally changes its physical and mechanical property and thus hardness, which is the resistance of the material to the local deformation. All the irradiated and non-irradiated samples were tested for hardness and compared. shows the result of the test. It was seen that there was not much increase in the hardness of talc and LDPE added, sample with irradiation. Yasin et al. O) at 1700 cm−1 in the FT-IR analysis supported that some cross-linking was there. The modified PP without LDPE was found less thermally stable compared to modified PP with LDPE. The modified PP with LDPE also showed high complex viscosity at low frequency, high shear thinning tendency, and an increase in elasticity. These properties can be beneficially used for industrial application and processing. We found, some test suggested cross-linking of the sample and some test suggested degradation. This is because of PP, which has both probability of cross-linking and degradation. The hardness can be increased with the cross-linking of PP but its actual influence i.e. its proportionality could not be explained in this test. Hence with the addition of co-agents and some filler/additive to PP, it can be cross-linked better and its properties can be altered.Influence of Nb on the β → α″ martensitic phase transformation and properties of the newly designed Ti–Fe–Nb alloysA series of Ti–7Fe–xNb (x = 0, 1, 4, 6, 9, 11 wt.%) alloys was designed and cast to investigate the β → α″ martensitic phase transformation, β phase stability, the resulting microstructure and mechanical properties. Phase analysis revealed that only Ti–7Fe–11Nb alloy shows a single body-centred cubic β phase microstructure while the others are comprised of β and orthorhombic α″ phases. Moreover, Nb addition up to 11 wt.% enhances the stability and volume fraction of β phase in the microstructure, hence reducing the propensity of the alloy system to form α″ phase during quenching. Compressive yield strength and hardness of the alloys are (985–1847) MPa and (325–520) Hv respectively. Additionally, Ti–7Fe–11Nb possesses the lowest Young's modulus (84 GPa) and the highest deformability (42% strain) among the designed alloys due to the single β phase microstructure. This high deformability is also corroborated by the large plastic deformation zone underneath the Vickers indenter. In contrast, the fractured surfaces of Ti–7Fe and Ti–7Fe–1Nb alloys after compressive tests mostly contain shallow dimples, verifying their low ductility. The good combination of mechanical properties obtained for Ti–7Fe–11Nb renders it more desirable than commonly used CP-Ti and Ti–6Al–4V materials and makes it a promising candidate for biomedical application.Titanium and titanium alloys have been extensively used for manufacturing load-bearing orthopaedic implants Because of their body-centred cubic (bcc) crystalline structure, the β-type titanium alloys exhibit an elastic modulus lower than α and (α + β)-type alloys, which may mitigate the stress shielding phenomenon While Fe is an attractive low cost β-stabilizer element along with the β-stabilizer and biocompatible component, Nb, for developing β-type titanium alloys Ti–7Fe–xNb (x = 0, 1, 4, 6, 9, 11 wt.%) alloys were designed and fabricated from 99.9% pure raw Ti, Fe and Nb metals using cold crucible levitation melting (CCLM) under an argon atmosphere. The CCLM furnace, a type of induction melting furnace, was composed of a water-cooled crucible made from high purity copper segments. Induction coils were wrapped around the crucible and connected to a frequency inverter power supply. After complete melting of the raw metals and subsequent mixing, the electric power was turned off and the molten metals were solidified into an ingot in the water-cooled copper crucible. The alloy ingots were flipped and re-melted four times to promote their chemical homogeneity. The as-cast alloy ingots (hereafter referred to as the “as-cast” samples) were 8 mm in diameter and 100 mm long. The as-cast samples were sectioned using a Buehler Isomet low speed diamond saw to obtain specimens for various purposes. The phase constitution in the alloys was identified by X-Ray diffraction (XRD) using a PANalytical EMPYREAN diffractometer with Cu Kα radiation (λ = 1.5406 nm). XRD patterns were recorded at a step size of 0.01° and scanning speed of 1°/min. The integrated areas for α″ and β diffraction peaks in the XRD spectra were determined by using the peak-fitting program, Fityk, with Pearson VII function where Vf(α״)and Vf(β) are the volume fractions and Aα״ and Aβare the total integrated areas, corresponding to α″ and β phases, respectively.To characterize microstructural features, samples surfaces were prepared using conventional grinding and polishing procedures followed by etching in Kroll's solution (5 vol% HF, 30 vol% HNO3 and 65 vol% H2O). The microstructures of the alloys were examined using a Zeiss optical microscope (OM) and elemental mapping was conducted by scanning electron microscopy (SEM, Jeol JSM 6000) with an energy dispersive X-ray detector (EDX). To evaluate the mechanical properties of the as-cast titanium alloys, compressive and hardness tests were conducted. To determine the compressive yield stress, plastic strain and modulus of elasticity, a compressive test was carried out on the cylindrical specimens of 8 mm in diameter and 16 mm long using an Instron 5980 universal testing machine at a crosshead speed of 0.001 mm/s at room temperature. To ensure the accuracy of Young's modulus, a clip-on extensometer attached to the specimen was used to measure the strain. Young's modulus was determined for each specimen as the slope of the linear portion of stress–strain curve Vickers hardness measurements of the polished samples were carried out using a ZwickRoell hardness testing machine with a load of 5 kgf and a dwell time of 30 s. The average hardness values were obtained from at least 10 measurements. To characterize the deformed morphology beneath the Vickers indentation, the bonded interface technique was employed shows the XRD profiles of Ti–7Fe and the ternary Ti–7Fe–xNb alloys, which indicate that all alloys except Ti–7Fe–11Nb are comprised of bcc β and orthorhombic α″ phases. Additionally, the TiFe intermetallic compound is not presented in all alloys because of the low Fe content in the studied alloys , Ti–7Fe contains the lowest β volume fraction (Vf |
= 62%) and the highest volume fraction of α″ phase (Vf |
= 38%). This athermal α″ orthorhombic structure, induced by fast cooling, was attained from a distorted hexagonal unit cell in which the c-axis of the orthorhombic unit cell correlates with c-axis of the hexagonal unit cell whereas a and b correspond to the orthogonal axis of the hexagonal unit cell , when 1 wt.% Nb is introduced into the Ti–7Fe alloy, the intensity of the peaks corresponding to α″ phase decreases, hence the volume fraction of this phase (Vf |
= 34%) reduces. With addition of 4 or 6 wt.% Nb to Ti–7Fe alloy, the number of the α″ phase peaks (i.e. around 53°, 63° and 76°) decreases suggesting that the formation of α″ phase is greatly suppressed whereas the intensity of β phase peaks and concentration of β phase increase (). When Nb content is 9 wt.%, the alloy exhibits the weakest peak of α″ phase, while β phase peaks become sharper, hence a significant amount of β phase with bcc crystal structure is retained (). Finally, the addition of 11 wt.% Nb to Ti–7Fe leads to the retention of only β phase as verified by its XRD pattern.The stability of β phase is determined by its ability to undergo martensitic transformation (β → α″, β → α′, β → ω) upon quenching to room temperature or upon deformation The stability of β phase can be predicted based on the DV-Xα cluster method where Xi is the atomic fraction of element i in the alloy, (Bo)i and (Md)i are the bond order and metal d-orbital energy level values for element i, respectively Additionally, the Moeq of an alloy can be expressed by the following formula Moeq=Mo+Ta5+Nb3.6+W2.5+V1.5+1.25Cr+1.25Ni+1.7Mn+1.7Co+2.5Fewhere [x] indicates the concentration of element x in weight percent The stability of β phase improves by increasing Bo or decreasing Md and by increasing Moeq summarizes the calculated values of Moeq, Bo¯ and Md¯ of the designed alloys. As indicated, the values for Moeq are higher than 10 wt.% thus classifying all of the alloys into the metastable β category , with an increase in Nb content of the alloys, the values of Moeq and Bo¯ increase, but Md¯ decreases, indicating the enhancement in the β phase stability of the metastable alloys against martensitic (β → α″) transformation The optical microstructures of the Ti–7Fe and Ti–7Fe–xNb alloys after etching are shown in . All alloys, except Ti–7Fe–11Nb, have a two-phase morphology comprising β and α″ martensite phases. Ti–7Fe alloy ((a)) exhibits the coexistence of β phase grains and a dense α″ martensite phase precipitated in the β matrix.When 1 or 4 wt.% β-stabilizer Nb is added, the quantity of α″ phase is decreased ((b) and (c)). Similarly, introducing 6 or 9 wt.% Nb to the Ti–7Fe alloy leads to the significant reduction in the amount of α″ martensite phase, hence β phase becomes more dominant ((f), further addition of Nb to 11 wt.% enhances β phase stability so that the microstructure overwhelmingly contains only β phase. The complete retention of β phase by adding 11 wt.% Nb is also proved in the X-ray spectra in . Therefore, based on these results, a higher concentration of Nb increases the stability of β phase and decreases the possibility of α″ martensite formation in these metastable β alloys during rapid cooling. The existence of α″ martensite phase in the microstructure has also been recognised in other studies which verify the martensitic transformation of β to α″ phase The dendritic substructure in the β grains of the as-cast Ti–7Fe–xNb alloys containing the two highest concentrations of Nb can be seen in displays the back scattered electron (BSE) image and associated Ti, Nb and Fe distribution EDX maps obtained for Ti–7Fe–11Nb alloy. The contrast in the BSE image ((a)) indicates that the dendritic structure in (e) is related to chemical segregation during the solidification process of these specified alloys.(b) and (c) illustrate that due to solute redistribution during solidification, Nb is accumulated in β dendrites, whereas Ti is rejected into the liquid resulting in higher concentration of Ti in interdendritic zones. This segregation pattern is a consequence of higher melting point of Nb which causes this element to have a partition coefficient higher than one when it dissolves in Ti. In contrast, (d) indicates that Fe presents a more uniform distribution across the whole area which is due to its high diffusion rate in Ti Studies show that the presence of more β-stabilizer (e.g. Nb) in dendrites and its lower concentration in interdendritic regions can cause martensite transformation e.g. β → α″, mainly in interdendritic zones ) and it is expected that this minor martensitic transformation occurs mainly in the interdendritic zones which contain less Nb. The presence of α″ can affect the mechanical properties of Ti alloys which will be discussed in the next section. In the case of Ti–7Fe–11Nb alloy with the highest Nb content and Moeq value, and despite its dendritic microstructure, the martensitic transformation is suppressed, suggesting that the Nb concentration in the interdendritic regions may still be high enough to stabilize β phase during quenching of the alloy.The mechanical properties of the titanium alloys are largely affected by the constituent phases and their volume fraction displays the typical compressive stress–strain curves of the series of Ti–7Fe–xNb alloys at room temperature. The compressive test was stopped either after failure of the alloy or when the maximum load capacity (100 kN) of the test machine was reached. According to , Nb addition impacts strongly the mechanical properties of the alloys. With the exception of Ti–7Fe and Ti–7Fe–1Nb, the alloys did not fail during compressive testing even after being largely deformed by ~ 42% in the case of Ti–7Fe–11Nb alloy. From , the 0.2% proof compressive yield stress and the plastic strain of the alloys were measured and their variations, with respect to the concentration of Nb (wt.% Nb) are presented in that the compressive yield strength of all alloys are higher than those of CP-Ti (552 MPa) (a). Since the orthorhombic crystal structure of α″ phase contains less slip systems than the bcc crystal structure of β phase, higher stress is needed for plastic deformation of α″ phase than for the β phase matrix , the yield strength of the alloys is reduced and their plastic strain is improved substantially with increasing Nb concentration. It is widely known that Nb is a β stabilizer element . Consequently, in the present study, Ti–7Fe–11Nb alloy with the highest Nb content and dominant β phase microstructure possesses the lowest yield strength which is still greater than those of the best commercial Ti-based biomaterials, e.g. CP-Ti and Ti–6Al–4V as mentioned above. The higher yield strength enhances the capacity of the alloy against its permanent shape change which could benefit the patient The elastic modulus values of the alloys are shown in , the Young's modulus values of the alloys decrease with the increase in their Nb content. Among all alloys, Ti–7Fe, which has the least stable β phase microstructure (Moeq |
= 17.5 wt.%) and contains the greatest proportion of α″ phase, presents the highest Young's modulus (129 GPa). When 1 or 4 wt.% Nb is added to this alloy, the Young's modulus reduces subsequently. Further increases in Nb content (6, 9, 11 wt.%) and hence β phase stability, lead to more reductions in the values of Young's modulus of the alloys as displayed in . These results may be associated with the formation possibility of martensitic α″ phase during quenching shows the SEM micrographs of the fracture surfaces for the Ti–7Fe and Ti–7Fe–1Nb alloys after a compressive test. Since the Ti–7Fe–xNb (x = 4, 6, 9, 11) series alloys did not fail during a compressive test, their fractographies were not examined. As shown in (a), Ti–7Fe is characterized by cleavage facets together with some dimpled surfaces which are shallow, smooth and small in size. This feature corresponds to the less ductile nature of the specimen as is also indicated by the low value of compressive strain (8%). As can be seen in (b), the fracture surface of Ti–7Fe–1Nb alloy contains more dimples which are larger and rougher in some areas. This is related to the increase in the ductility of this alloy with addition of 1 wt.% Nb, which is consistent with the compressive strain of 11%. displays the Vickers hardness values of the studied alloys. The results show that the Vickers hardness of all alloys are higher than those of commercially used biomedical Ti alloys, e.g. CP-Ti (190 Hv) . The measured Vickers hardness values are very similar to those for other titanium alloys containing Nb. For example, the Vickers hardness values are between 289 and 479 Hv for Ti–xNb–3Fe alloys (x = 10, 15, 20, 25 wt.%) Researchers have demonstrated an association between the wear characteristics and hardness of the materials which suggests that wear resistance improves with increasing hardness illustrates the deformation region underneath the Vickers indenter in Ti–7Fe, Ti–7Fe–4Nb and Ti–7Fe–11Nb alloys. Notably, with the increase in Nb content of the alloys, hence decrease in their Vickers hardness values, the penetration of the indenter in the alloys' surface and the lateral size of the indentation both increase. Additionally, in all three alloys, immediately surrounding the bulge area (tip of the indent), several semi-circular slip-steps called primary shear bands (b) and (c)) with higher Nb content, additional radial slip-steps named secondary shear bands, initiating along the indentation surface in a form of straight lines It is clear that the density of primary shear bands is greater than that of the secondary ones. The shear bands are produced when the local stress exceeds the yield point Generally, for materials with good plastic deformation ability, when the indenter penetrates their surface, the subsurface materials near the indenter tip are deformed due to hydrostatic pressure and are hardened subsequently by the applied plastic deformation. Under such conditions, the stress is not enough to produce further plastic deformation in this region. However, this hardened area could compress the near materials and cause this area to deform plastically which results in the formation of shear bands. Likewise, once this part also becomes hardened, it could produce plastic deformation in the adjacent materials, therefore shear bands formation could extend to adjacent areas beneath the indented surface (c)). This is due to its microstructure which consists of β phase with higher plastic deformation ability than α″ phase (b)). This can be attributed to its higher concentration of α″ martensitic phase and an associated lower plastic deformation ability than β phase Based on these experimental results, it is suggested that addition of Nb can considerably reduce the formation of α″ martensite and enhance the stability of β phase, hence improving the mechanical properties of Ti–Fe based alloy required for biomedical application. However, it would be interesting to compare Nb with other alloying elements (e.g. Mo, Zr, Ta) for their effects on the phase stability and the mechanical properties of the Ti–Fe alloy and then select the best alloying element for future studies.This work investigated the effects of Nb on the β phase stability and the resulting microstructure and mechanical properties of the designed Ti–Fe–Nb alloys. The results revealed that Ti–7Fe–xNb alloys can include β and α″ phases, the proportions of which depend on the amount of β-stabilizer Nb. As more Nb (1, 4, 6, 9 wt.%) is introduced into the Ti–7Fe alloy, the proportion of α″ phase declines until at 11 wt.% no α″ phase remains. Instead, the alloy microstructure only includes β phase with a bcc crystal structure. It is proposed that increasing the Nb content enhances the β phase stability of the designed alloys against β → α″ martensitic transformation during rapid cooling.The hardness (325–520 Hv) and compressive yield strength (985–1847 MPa) of Ti–7Fe and Ti–7Fe–xNb alloys varied depending on the relative proportions of β and α″ phases. However, they were better than for the best commercial Ti-based biomaterials, CP-Ti (190 Hv, 552 MPa) and Ti–6Al–4V (294 Hv, 970 MPa) alloys. Progressively increasing the Nb content from 0 to 11 wt.%, reduced the Young's modulus values from 129 GPa to 84 GPa, thus providing a much lower elastic modulus than for CP-Ti (104 GPa) and Ti–6Al–4V (114 GPa). Moreover, Ti–7Fe–11Nb alloy exhibited the highest plastic deformation, indicating its good workability at room temperature. It also presented the highest numbers of primary and secondary shear bands beneath the Vickers indenter due to its dominant β phase microstructure.Non-uniqueness in cylindrical shells optimizationCylindrical shells are widely used in many structural designs, such as offshore structures, liquid storage tanks, submarine hulls, and airplane hulls. During the optimization process of cylindrical shells, one is faced with a set of very unique challenges. Unlike that of simpler structures such as beams or plates, the modal spectrum of cylindrical shell exhibits very unique characteristics. Mode crossing, uniqueness modal spectrum, and redundancy of modal constraints are just a few of the unique attributes faced during the optimization process.In cylindrical shells, the lowest natural frequency is not necessarily associated with the lowest wave index. In fact, the natural frequencies do not fall in ascending order of the wave index either. Solution of the vibration problem of cylindrical shells also indicates repeated natural frequencies. These modes are referred to as double peak frequencies. Mode shapes associated with each one of the natural frequencies are usually a combination of (i) radial (flexural), (ii) longitudinal (axial), and (iii) circumferential (torsional) modes.When a uniform shell is segmented longitudinally along its axis, the thickness optimization of the segment thicknesses will yield in a segmented shell with varying thickness segments. In this paper, the non-uniqueness in optimum design of cylindrical shells for vibration requirements is presented, and its implications are discussed. Related issues such as the new mode sequence, mode crossing, repeated natural frequencies and stationary modes are also discussed. The numerical results were compared with those obtained analytically. The analytical expressions for the equations of motion for segmented circular cylindrical shells are derived using Donnell–Mushtari. The eigenvalue problem of the analytical solution is then solved using a MATLAB program script to predict the natural frequencies and strain energy distribution for the various mode shapes in the modal spectrum.The modal spectrum of cylindrical shell exhibits very unique characteristics. Unlike that of simpler structures such as beams and plates, the lowest natural frequency in cylindrical shells does not necessarily correspond to the lowest wave index shown in . In fact, the natural frequencies do not fall in ascending order of the wave index either as indicated in Mode shapes of a cylindrical shell can be categorized in three orthogonal directions that are associated with radial (flexural), longitudinal (axial), and circumferential (torsional) displacement components.Due to the shell curvature there is coupling between the transverse and in-plane vibration. The eigensolution of cylindrical shells indicates multiple eigenvalues, i.e. repeated natural frequencies with similar mode shapes. These are referred to as double peak frequencies Modes shapes associated with membrane shell deformations require a lot of strain energy, while mode shapes associated with bending deformation require less strain energy. Since the total potential strain energy in a shell is the summation of both membrane and bending strain energy, the first mode shape corresponds to the lowest total energy that might not necessarily be at the lowest wave index n.The ratio between the membrane strain energy and the kinetic energy (or the total strain energy) is high for modes with simple modal patterns n and decrease toward zero as the number of nodal lines increases, while the ratio of the bending strain energy to the kinetic energy (or the total strain energy) is small for simple nodal patterns and increase with the increase of wave index nNatural frequencies dominated by the membrane strain energy are approximately independent of the shell thickness change The fact that the optimization process results in a segmented cylindrical shell, it would be required that an analytical approach for the modal characteristics of segmented shells be developed. This approach will serve two purposes: First, is for the validation of the natural frequencies obtained through the finite element analysis. Second, is to identify the strain energy distribution and the stationary mode. This approach will focus on developing analytical expression for the modal characteristics of segmented cylindrical shells.The equations of motion of the segmented cylindrical shell are derived by suitably modifying the strain displacement and energy equations used in deriving the equations of motion for uniform circular cylindrical shell The segmented cylindrical shell is a chain of segments of uniform thin circular cylindrical shells of same radius, but each segment can have different length and thickness. We consider here an elastic, isotropic thin-walled circular cylindrical shell of total length L, and mean radius R. The cylinder is assumed to be made of p segments, and Li and hi are used to denote the length and the thickness of the ith segment, where i=1 to p. The material parameters of the shell are represented as Young's modulus (E), Poisson's ratio (v), and material density (ρ). The axial, circumferential and radial co-ordinates of the middle surface of the segmented cylindrical shell are represented by x, ϕ and z in cylindrical co-ordinate system as shown in , and the corresponding orthogonal components of displacements are represented by u, v, and w. A segmented circular cylindrical shell made of nine segments (p=9) is shown in Rayleigh–Ritz displacement functions satisfying the above boundary conditions take the form:These functions imply separation between time and the spatial variables, i.e. the shell will undergo simple harmonic motion in which both period and phase are identical at all points of the shell The strain displacement equations for the thin shell in orthogonal curvilinear coordinates are derived using three-dimensional theory of elasticity. Total strain at any point can be represented as the sum of strains due to bending and stretching. The strain components of the midsurface of the shell are normal (εxx and εφφ), shear (εxφ) strains, change in curvature (kxx and kφφ) and change in twist (kxφ). Using Donnell–Mushtari shell theory, those terms are expressed asIn Donnell–Mushtari shell theory, the tangential displacements and their derivatives are neglected for the midsurface changes in curvature and twist. Also, as the strains and displacements are sufficiently small, the second and higher-order magnitudes in the strain–displacement relations are neglected in comparison with first order terms.Furthermore, the total strain energy (V) of a uniform thin cylindrical shell of radius R can be expressed in terms of the strain components as a combination between the membrane strain energy (Vm) and bending strain energy (Vb)Vm=E2(1−v2)R∫−h/2h/2∫02π∫0L[εxx2+εφφ2+2vεxxεφφ+1−v2εxφ2]dzdxdφVb=E2(1−v2)R∫−h/2h/2∫02π∫0L[kxx2+kφφ2+2vkxxkφφ+2(1−v)kxφ2]z2dzdxdφAt a time t, the expression for kinetic energy T of the vibrating shell can also be expressed asT=ρ2R∫−hi/2hi/2∫02π∫0li[(∂u∂t)2+(∂υ∂t)2+(∂w∂t)2]dzdxdφ=ω2m(A2+B2+C22)where m is the mass of the segmented cylindrical shell given by m=∑i=1plihi(πρR/2).Substituting the respective strain and curvature displacement terms in Eqs. Vm=EπR∑i=1plihi4(1−v2)[A2{(mπL)2+(1−v2)(nR)2}+B2{(1−v2)(mπL)2+(nR)2}C2(1R)2−2AB(1+v2)(mπL)(nR)−2ACv(mπL)(1R)+2BC(1R)(nR)]Vb=EπR∑i=1plihi348(1−v2)[+C2{((mπL)2+(nR)2)2}]Now, applying Hamilton principles to the Lagrangian energy functional (F=V−T), would result in an eigenvalue problem that can be solved using a MATLAB program script to predict the natural frequencies and their corresponding energy distribution.A baseline cylindrical shell model shown in A series of four design optimizations were performed using SOL 200 module of MSC.NASTRAN software In the first design optimization, one modal constraint is imposed on the first natural frequency corresponding to mode (n=4, m=1) to achieve a desired increase of approximately 15% in natural frequency. Accordingly, the frequency f1=12.89 Hz is constraint as follows: f′1=14.92 Hz. The modal characteristics of the optimized design (Design I) are shown in Upon close examination of the results listed in , there was mode crossing in which mode 3 (n=5, m=1) moved past mode 5 (n=5, m=1). Also the natural frequency of mode 5 (n=3, m=1) in the baseline design remained in close proximity to the original natural frequency.In the second design optimization, the modal constraint is imposed on the third natural frequency (n=5, m=1). The frequency f3=14.13 Hz is constraint as follows: f′3=18.66 Hz. The modal characteristics of optimized Design II are shown in indicates the same mode crossing observed in Design I. Also the natural frequency of mode 5 (n=3, m=1) in the baseline design remained in close proximity (stationary) to the original natural frequency. In fact the modal characteristics of Design II are almost identical to the Design I.In the third design optimization, the modal constraint is imposed on the seventh natural frequency (n=6, m=1). The frequency f7=24.92 Hz is constraint as follows: f′7=24.92 Hz. The modal characteristics of optimized Design III are shown in On further examination of the results listed in , one can observe the same modal characteristics of Design I and Design II despite the fact that each model was optimized for different modal constraints.In the forth design optimization, the modal constraint is imposed on the ninth natural frequency (n=7, m=1). The frequency f9=23.54 Hz is constraint as follows: f′9=31.50 Hz. The modal characteristics of optimized Design IV are shown in Again, examination of the results listed in shows the same modal characteristics of Design I, Design II and Design III despite the fact that each model was optimized for different modal constraints.The modal characteristics of all four optimized designs indicate that the natural frequencies of a cylindrical shell are interlinked. They can be uniquely determined based upon one of the natural frequencies. A summary of the modal characteristics of all optimized designs is listed in . One can also observe mode crossing. Modes dominated by membrane strain energy remain stationary during the optimization process. Those are the modes represented by wave index (n=3, m=1), and (n=2, m=1). Attempts to optimize the cylindrical shell for multiple modal constraints would yield no solution except for the case of compatible constraints, i.e. constraints consistent with the modal spectrum as obtained for single modal constraint Despite the fact that the four optimized designs, Design I, Design II, Design III, and Design IV, exhibited identical modal characteristics as shown in , the values of the design variables, i.e. the segments' thickness are not, yielding different weight for each optimized design as indicated in The values of the design variables in each of the optimized designs are listed in . They show that the symmetry of the design was preserved even though it was not explicitly imposed. They also indicate non-uniqueness of optimal design points. Thickness variation for each design model is shown graphically in Using the analytical approach derived, one can validate the results of the finite element analysis obtained through the optimization process. The natural frequencies and energy distribution of Design I are shown in The design optimization of cylindrical shells for modal characteristics is of very unique. The uniqueness of the modal spectrum causes redundancy in modal constraints. The natural frequencies are often interlinked resulting in no optimum solution for optimization for incompatible multiple modal constraints. It is very clear that Design I and Design III are almost identical, yet they were obtained using different modal constraints. The non-uniqueness in optimum design of a cylindrical shell for modal constraints lead to different segments' thickness. The new modal spectrum shows a new frequency sequence, mode crossing, repeated natural frequencies, and stationary modes.Review on self-lubricant transition metal dichalcogenide nanocomposite coatings alloyed with carbonIn this paper, we review the results on the tribological behavior of nanocomposite coatings composed of nanoplatelets of transition metal dichalcogenides (TMD) immersed in a C-rich amorphous matrix. It is shown that such a microstructure produces low friction coefficients under different operating conditions such as air humidity, contact pressure or temperature. Special attention is paid to the analysis of the worn surfaces after the tests by Raman spectroscopy, Auger electron spectroscopy and transmission electron microscopy. Nanoscale analysis of the wear track has revealed the formation of a thin tribolayer exclusively consisting of TMD platelets oriented to exhibit the lowest friction. In some cases, the depth reorientation of the originally randomly oriented TMD platelets as a reaction to the sliding process has been observed. This self-adaptation explains the low friction coefficient together with a high load-bearing capacity and a limited sensitivity to air humidity. Finally, future perspectives for self-lubricant nanocomposite coatings based on the TMD-C concept are presented.The lamellar crystal structure is found in many chemical substances, and several of these have lubricating properties, such as naturally occurring micas, talc and graphite or synthetically prepared compounds. However, many of them were found to be unsatisfactory for friction applications and many of those found satisfactory cannot be applied directly as solid lubricants.Transition metal dichalcogenides (TMD) are, in many ways, a gift of the Nature to the mechanical engineers looking for friction reduction. TMDs exist in two crystal forms, hexagonal and rhombohedral. We will only deal here with the hexagonal structure, which is the most common and important for low-friction applications. The hexagonal crystal structure with six-fold symmetry, two molecules per unit cell, exhibits a laminar, or layer-lattice structure. Each chalcogenide atom is equidistant from three metal atoms, end each metal atom is equidistant from six dichalcogenide atoms. The attraction between the metal and dichalcogenide atoms is due to powerful covalent bonding; however, there is only weak Van der Waals attraction between the lattice layers To reduce friction, TMD is often used either as an oil additive or as a coating. The latter could be prepared as a thick film (e.g. burnished Recently, attention has been paid to fullerene-like TMD Thanks to its unique highly anisotropic crystal structure, TMD could behave as an excellent solid lubricant, i.e. a material with friction lower than 0.01. Martin et al. Friction lower than 0.001 is not necessary for mechanical applications; even a two orders of magnitude higher friction would be sufficient in many applications. Why is it so difficult to use pure TMD films deposited by conventional magnetron sputtering in terrestrial atmosphere?Deposition of TMD by magnetron sputtering leads inevitably to a disordered structure. The low-friction prominent orientation, (0002), cannot be achieved except for a very thin film not exceeding tens of nanometers TMD films are extremely sensitive to environmental attacks. When sliding in air, a very likely reaction is their oxidation producing metal oxides. The presence of WO3 − x and MO3 − x oxides increases the friction, although there is still controversy in the estimation of how detrimental such oxides are TMD films are very porous (partially due to their columnar morphology), as demonstrated in The hardness of TMD is very low compared to other competitive low-friction coatings, such as diamond-like carbon (DLC). It is typically in the range from 0.3 to 2 GPa depending on the stoichiometry, morphology, and deposition conditions. The adhesion to steel substrates could be improved by a thin metallic interlayer, typically Ti or Cr; however, it is still limited. Consequently, the load-bearing capacity is very low and TMD coatings peel off the substrate under high contact pressures.Various countermeasures have been applied to remedy the above referred limitations. The reduction of water in the residual chamber atmosphere to diminish the oxygen content in the film The first attempts to modify TMD films by alloying were aimed to increase density and consequently reduce porosity, improve adhesion and significantly increase of the hardness. In general, the aims have been achieved. Among many metals for alloying (Ti Non-metallic element and compound alloying, such as ZnO All films referred to above show two general features: prevalence of the TMD phase (maximum content of alloying is about 20 at.%) and limited interaction between the TMD phase and the alloying element (contamination of oxygen and carbon from the residual atmosphere during the sputtering process is not considered here as alloying).Compared to the previous section, the TMD coatings alloyed with non-metallic elements usually show a higher non-TMD content; moreover, alloying elements might react either with the transition metals or the dichalcogenides. A typical example is nitrogen forming tungsten nitride In the late nineties, a new concept of coatings based on the alloying of transition metal dichalcogenides (TMDs) with carbon started to attract the attention of several scientific groups. The original idea was to combine the excellent frictional behavior of TMDs in vacuum and dry air with the tribological properties of DLC coatings. Moreover, an increase in the coating compactness in relation to TMD and an improvement in the mechanical properties, particularly the hardness, was expected. Zabinski et al. W―S―C coatings prepared by magnetron sputtering have been intensively studied by Cavaleiro et al., with respect to the structure clearly shows that the main disadvantage of TMD films, the detrimental effect of the humid air, was not overcome and the friction in these conditions was relatively high whatever the carbon content was b), this result was attributed to the significant increase of the hardness, from 0.5 GPa (WS2) up to ~ 10 GPa, achieved by incorporating carbon.The analysis of the microstructure of the reactive deposited W―S―C coatings ), or just by WS2 nanograins dispersed in an amorphous carbon matrix (low carbon content). A similar behavior was observed elsewhere for WS2/DLC/WC coatings showing a huge friction coefficient difference when sliding in humid or dry air All these three different coating microstructures schematically shown in proved to be unsatisfactory for reducing the friction coefficient in humid air sliding conditions. The multilayer films are vulnerable to cohesion damage, since the interlayer sliding could occur in the interior of the film where the shear stresses are larger than at the surface. This problem could be partially solved by thinning layers down to nanometer thicknesses; however, such a nanolayered structure is difficult to achieve on typical industrial substrates with standard surface roughness.On the other hand, the other two microstructures could not simultaneously guarantee that either the TMD nanocrystals could be re-oriented with the basal planes parallel to the sliding distance or the oxidation of the dangling bonds would not occur. In fact, during the re-orientation process the extremities of the grains will be directly in contact with the atmosphere and therefore be immediately oxidized.It has been obvious that a new concept is required for a modern low-friction universal coating exhibiting high wear resistance, load-bearing capacity and, particularly, low friction in various sliding environments (vacuum/dry air or nitrogen/humid air; elevated temperature, etc.). This paper summarizes recent research in the area of nanocomposite TMD-C coatings, their deposition, structural and mechanical characterizations, and tribological properties.The W―S―C and Mo―Se―C coatings were deposited on steel substrates (chromium steel, quenched and tempered with a final hardness of 62 HRC) polished to a final roughness, Ra ≤ 30 nm. A two planar cathodes Edwards E306 machine with a 20 dm3 chamber was used for the depositions. A rotating substrate holder placed 60 mm from the cathodes allowed the substrates to be placed over one or another cathode for depositing the titanium interlayer or the W―S―C or Mo―Se―C films, respectively. The Ti thin interlayer (~ 300 nm) was deposited in order to improve the adhesion of the coatings to the substrate. The coatings were deposited by r.f. magnetron sputtering in an argon atmosphere from a graphite (99.999% purity) target with pellets of WS2 or MoSe2. The pellets (99.8% pure) were positioned in the erosion zone of the 100 mm diameter graphite target (hereinafter denominated “composite target”). The dimensions of the pellets were 1.5 × 3 × 4 mm and their number varied between 16 and 72. The discharge pressure and the power density were 0.75 Pa and 8 W cm− 2, respectively. Mo―S―C and W―Se―C films were deposited using two targets, WSe2 or MoS2 and graphite (i.e. the films were deposited directly on the substrate without Ti interlayer). The carbon content in the films was controlled through the number of the pellets or power applied to the C and TMD targets. No bias was applied to the substrate holder during the deposition (floating bias); the substrate temperature was about 200 °C. The deposition time was one hour.The coatings microstructure was studied by X-ray diffraction (XRD) in glancing mode (Co Kα radiation) and by high resolution transmission electron microscopy (HRTEM); the chemical composition was determined by electron probe micro-analysis (EPMA) whereas the chemical bonding was accessed by Raman (Ar+ laser, 514.5 nm wavelength) and X-ray photoelectron spectroscopies (XPS-Mg Kα radiation). The hardness (H) and Young's modulus (E) of the coatings were evaluated by depth-sensing indentation (maximum indentation load of 50 mN).Wear testing was performed using pin-on-disc and reciprocating (SRV) tribometers adapted to work in a controlled atmosphere; the sliding partners were 100Cr6 steel balls with a diameter of 6 and 10 mm, respectively. The air humidity (RH) was controlled by a precise hygrometer (error 1%). The number of laps (pin-on-disc) or cycles (SRV) is stated in the text. The morphology of the coating surface, the ball scars, the wear tracks and the wear debris were examined by scanning electron microscopy (SEM) and Raman spectroscopy; the chemical analysis of the wear tracks and the wear debris was obtained by energy-dispersive X-ray analysis (EDS). The chemical depth profiles in the wear track were obtained by Auger electron spectroscopy (AES). The profiles of the wear tracks were measured by a mechanical or 3D optical profilometer. The wear rate of the coating was calculated as the worn material volume per sliding distance and normal load. The average value of three profiles measured on the same wear track was used to calculate the coating wear rate.The basis for producing a low friction coating in a great variety of environments could be envisaged as a micro(nano)structure where TMD nanocrystals could be deposited completely enclosed within a protective C-rich matrix. If possible, these nanocrystals should have shapes that allow an easy reorientation of the basal planes parallel to the sliding direction. The carbon matrix will contribute to improving the hardness and the compactness of the coatings as well as protecting the TMD crystals from oxidation until the moment that they are completely aligned and risen the contact surface. For its part, TMD should assure the low friction coefficients, due to the easy sliding of the basal planes, and only a few strong bonds, promoted by the oxygen, should exist. In parallel with this approach, the use of other types of TMDs with less sensibility to oxidation than tungsten and molybdenum disulphides, such as MoSe2During sliding in pin-on-disc testing, strong shear stresses arise which could contribute to the re-orientation of the TMD crystals in the C-based amorphous matrix. However, during the alignment of the TMD nanocrystals parallel to the sliding direction, the dangling bonds of the end planes are exposed to the atmosphere and oxidized, leading to a consequent increase in friction. In pure TMD coatings, the porous structure and very low hardness give rise to a very high wear rate. Therefore, as generally accepted in the wear models, it is expected that the worn out TMD material adheres to both surfaces in the contact and is also subjected to the high stresses developed there. This tribolayer is very thin (nanometer scale) with the TMD phase highly oriented, mainly with the basal planes parallel to film surface The problems referred to above could be avoided if the crystals were already aligned in the material, since in this case almost no dangling bonds would be available for the reaction Deposition by co-sputtering from TMD and C sources, either from separate targets or by a combined target with both materials () was chosen in order to produce coatings containing simultaneously C and the TMD phase with a new microstructure different from that achieved in reactive deposited coatings. The TMD-C coatings were deposited with a carbon content in the range of 25–70 at.%. Since the best tribological properties were achieved for a carbon content of approximately 50 at.%, we selected films with this composition to be presented in this paper. The deposition conditions, chemical composition and hardness of the films are shown in . It is clear that alloying with carbon significantly improves the hardness, since that of pure sputtered TMD films were lower than 0.5 GPa . TMD peaks observed in Raman spectra were very broad compared to bulk TMD, which was related to a high degree of structural disorder. Finally, the Mo―Se―C and W―S―C films with ~ 50 at.% C were analyzed by HR-TEM technique. The nanostructure was quite different from the reactive deposited C + TMD films (see ) particularly regarding the TMD crystals, i.e. randomly oriented TMD platelets with only a couple of stacked basal planes can be observed (). The platelets are completely enclosed within the C-matrix TMD-C coatings were intensively tested under different conditions, such as relative air humidity (RH from dry air to 90%) The detrimental effect of air humidity on the friction coefficient was decreased compared to pure TMDs; however, the coatings are still sensitive to air humidity (see ). The friction coefficient in dry nitrogen is in the range of 0.01–0.08, whereas values from 0.10 up to 0.25 were measured in humid air (RH ~ 50%). In general, the friction coefficient of Mo-based films was lower than that of W-based. However, the increase in the friction coefficient was not followed by rapid coating destruction, since the wear rate was relatively low. The coatings based on diselenides exhibited lower friction in humid air.When the test temperature was increased, the friction dropped to a very low level, typically about 0.02 lower than the friction measured in dry air. In our previous study, we suggested that the higher temperature facilitated the slipping of the weakly bonded TMD basal planes The main drawback of pure sputtered TMD coating is the low load-bearing capacity. On the other hand, their friction decreases with increasing contact pressure and working in high-load conditions would further reduce the loss of energy due to friction. shows that the friction of TMD-C coatings decreases with the applied load and, thus, deviates from Amonton's law. For pure TMD films, it has been shown that the friction could be calculated using the formula for shear stress of solids at high pressures, where the contact pressure is calculated from the ideal Hertz contact model; however, such formula is not applicable to TMD-C. The evolution of the friction could be approximated to a power law fit μ |
≈ |
Lb, where b depends on the material (i.e. it is different for various TMD-C systems or for one TMD-C system with different carbon content); b is in the range (− 0.4 to − 0.6). Compared to pure TMDs where b = − 0.33 The evolution of the friction coefficient during the sliding process largely depends on the contact conditions. Typically, the initial friction is relatively high and drops to a low level after a short running-in process. When the contact pressure is higher, the running-in is shorter, as demonstrated in . However, we observed that the low friction level reached after several tens of laps (see ) was not a typical steady state sliding. shows the average friction coefficient obtained in tests with increasing duration times when a low load (5 N) is applied to the ball. As can be confirmed, there is a steep decrease in the friction coefficient in the first thousands of cycles and it is possible to reach a steady state value (~ 0.05), close to 100,000 cycles, which is not far from the lowest value shown in for these coatings when tested with much higher loads. Such an observation is supported by the evolution of the friction coefficient as a function of the number of cycles for a W―S―C coating tested by changing the humidity in the atmosphere every 10,000 cycles In conclusion, low friction coefficients can be achieved in any environment providing that sufficient contact pressure or long test duration is used.The progressive way in which the formation of the TMD tribolayer occurs can be demonstrated experimentally by the analysis of the top surface of the sliding track after wear testing. shows the Raman spectra of TMD-C films obtained after tribological tests carried out with either the same number of cycles but different loads or the same load but a different number of cycles. It is clear that the increase in the load, and/or the number of cycles, gives rise to a more intense signal in the bands assigned to the TMD phase in comparison to those of the C-based material (G and D bands). This result confirms an increasing agglomeration of TMD material close to the contact zone.Auger spectroscopy (AES) chemical depth profiles show the thickening of the surface TMD tribolayer when the contact pressure and/or number of laps (i.e. test duration) is increased The microstructural observation of the cross section of the top layer of the wear track by HR-TEM (high-resolution transmission electron microscopy) reveals platelets of TMD aligned parallel to the surface covering most of the zones which were analyzed, see . Furthermore, in the same micrograph it is shown that as the analysis is being moved to the interior of the film, the alignment is less and less evident. The observation of a great number of micrographs of different zones of the wear track The initial coating microstructure, the formation of a thin TMD tribolayer and the re-orientation of the TMD platelets inside the carbon matrix benefit the low friction behavior of the TMD-C coatings. The TMD platelets inside the carbon matrix are protected against environmental attacks; the coating is much denser compared to pure sputtered TMD films. The tribolayer, i.e. the outermost surface of the wear track, exhibited a (002) orientation, which is optimal for low friction and oxidation resistance. Moreover, the tribolayer was very thin (several monolayers) limiting coating wear. The sub-surface re-orientation inside the carbon matrix keeps the friction low and stable. When the top TMD tribolayer is worn out, the carbon matrix is worn out quickly revealing well oriented TMD platelets. However, two fundamental questions emerge: the role of carbon in the sliding process and the platelet re-orientation mechanism inside the carbon matrix.In WS2/DLC/WC coating, Wu et al. demonstrated using Raman spectroscopy the existence of a graphitic layer in the wear track when the tribotest was carried out in humid air, whereas the peaks of WS2 were measured after tribotesting in dry nitrogen Before any discussion about the feasibility of subsurface re-orientation, we should confirm that such a process is genuine. The formation of a tribolayer for TMD or DLC coatings is typically described as the detachment of worn coating particles and their agglomeration in the contact. They could form an adhered layer on the counterpart In general, the presented TMD-C coatings exhibit excellent load-bearing capacity and low friction in humid air. We believe that the self-adaptation of the coating microstructure as a reaction to the sliding process is vital to achieve desired tribological properties and should be considered when new self-lubricant TMD-based films are designed. Despite their advantages, TMD-C coatings must be further improved. The adhesion of the films must be increased, since in some cases catastrophic events, such as the detachment of the coating, occurred Based on the fundamental analysis of the coating composition, structure, morphology, and mechanical and tribological properties of W―S―C, W―Se―C, Mo―S―C and Mo―Se―C sputtered coatings, we can draw the following general conclusions:The coatings exhibited a nanocomposite structure composed of TMD platelets embedded in a C-rich amorphous matrix; carbides were not observed.The coatings showed reduced sensitivity to air humidity and excellent wear resistance. The load-bearing capacity outperformed that of sputtered pure transition metal dichalcogenides.Friction and wear decreased with the contact pressure.The formation of a thin TMD tribolayer and the sub-surface re-orientation of the TMD platelets inside the carbon matrix were observed as a result of the sliding process.It was demonstrated that the C-matrix had two roles: (i) contribution to the increase in the hardness and the load-bearing capacity and (ii) avoiding oxidation of the TMD platelets during the re-orientation permitting low friction coefficients in O-containing and humid environments.Implementation of a constitutive model in finite element method for intense deformationSince the constitutive information is one of the most important aspects of material deformation analysis, here a new constitutive model is proposed that can investigate the behavior of material during intense deformation better than existent models. The model that is completely based on physical mechanisms can predict all stages of flow stress evolution and also can elucidate the effects of strain and strain rate on flow stress evolution of material during intense plastic deformation. Here as an application, implementation of the constitutive model in finite element method (FEM) is used to compare two methods of sever plastic deformation (SPD) processes of copper sheet; repetitive corrugation and straightening (RCS) and constrained groove pressing (CGP). The modeling results are in good agreement with the experimental data and show that the hardness uniformity and its magnitude for RCSed sheet are higher than that for CGPed sheet. However, the prominence of these processes in strain uniformity depends on pass number.Nowadays, it is well known that theoretical and experimental approaches are two master pillars of scientific research activities. Computer simulation techniques have been widely used in scientific study and in some circumstances, they can be reasonable substitutes to physical experiments. One of the most accurate approaches of computer simulation is finite element method (FEM) that now is being used in all branches of science.Of the most prosperous applications of FEM is on the material deformation modeling In small deformation modeling, usually isotropic or perfectly plastic conditions are considered as a constitutive behavior. However, using these assumptions, it is not possible to make predictions with sufficient accuracy However, for finite element modeling of intensive deformation, the situation is more complex than that in small deformation. As mentioned, simple definitions such as isotropic hardening or perfectly plastic conditions cannot generate acceptable FEM results The processing of materials through the application of severe plastic deformation (SPD) has become attractive recent years, because it provides the capability of achieving remarkable grain refinement in polycrystalline materials, typically to the submicrometer or even to the nanometer scale However, the process is carried out in two major approaches that are shown in b, the dies constrain the sheet length. This approach although solves the elongation problem, has a problem in the case of strain and strain rate localization. As shown in b, the grooves in dies have sharp edges, while contacting to sheet, they cause to some extend of strain and strain rate localization in the surface of sheet. In this approach, the regions of this localization are invariable and repeating the process causes to intense localization. However, in RCS, the regions of the localization are variable and the intensity of the localization is negligible. However, considering both approaches, it is not clear that which approach is more efficient.In contrast to the extensive investigations on other elderly SPD processes, there are few works on GP process Therefore in this paper after proposing a new constitutive model which considers the effects of strain, strain rate, chemical composition and temperature on flow stress through intense deformation, as an application it is implemented in FEM for comparing CGP with RCS processes of copper.As mentioned, the mechanical response of materials due to deformation is related to strain, strain rate, temperature and chemical composition. Therefore, it is expected that in a constitutive model, the effects of all above parameters would be considered.Two major mechanical responses of materials due to deformation are work hardening and work softening. Work hardening describes the increasing of flow stress due to deformation, while work softening is the decreasing of flow stress due to straining. The common belief is that, the work softening occurs in warm or hot deformation and the mechanical response of material in cold deformation is work hardening or steady flow stress shows the values of flow stress measured in tension as a function of strain imparted on the materials by ECAP.This figure can show that in strains larger than four, dynamic recovery causes to work softening, so this behavior should be predictable in constitutive models.However, the classical engineering description that was developed by Ludwik–Hollomon cannot explain this trend at all , EM model cannot predict the work softening in cold deformation. However Estrin et al. dIdt=c1Mε˙W3Lb-c26Mε˙LbD(1-v)1/3-c32ν0LcIexp-Q(1-τG)KT-exp-QKTdWdt=c26Mε˙(1-v)2/3LbDv+c23Mε˙(1-v)WLbv-c4DlW2GLb3KTwhere I is the cell interiors dislocation density, W is the cell walls dislocation density, M is the Taylor factor, ε˙ is the strain rate, Lb is the length of Burgers vector and Lc is the length of potential sites for cross slip. Also, ν0 is the attack frequency, Q is the activation energy of cross slip, G is the shear modulus, K is the Boltzmann’s constant, T is the absolute temperature and Dl is the lattice diffusivity. In addition, D is the cell size that is a function of total dislocation density, v is the volume fraction of cell walls that is related to the magnitude of accumulated strain and τ is the magnitude of stress field in cell interiors that is related to cell interiors dislocation density. The parameters c1–c4 are the model constants. As can be seen, in this model all parameters (strain, strain rate, temperature and chemical composition) are considered. It should be noted that the effects of parameters such as temperature and chemical composition on work hardening are negligible and the main parameter affecting the work hardening is the strain.The three terms on the right-hand side of the first differential equation are the contributions from different dislocation mechanisms. The first one describes the rate of cell interiors dislocations generation by Frank–Read sources, the second term is related to the migration of some cell interiors dislocations to the walls Therefore, the mentioned set of coupled differential equations for the evolution of the cell interiors and the cell walls dislocation densities provides a full constitutive model for dislocation densities evolution and considering the Taylor relation, it is possible to investigate the evolution of material flow stress. For simply using of this model, the authors have represented the values of needed material parameters in The FE meshes used in these simulations are shown in Based on the comparison concepts, the node numbers and element shapes are similar in both models. In addition, considering the width to thickness ratio of sheet, a plane strain model with 3-node linear triangle elements is used. The number of nodes and elements used in the simulation were 726 and 1200, respectively.The simulations are carried out for both models in the sheet with length of 72 mm and thickness of 3 mm. The Poisson’s ratio is 0.33, Young’s modulus is 120 MPa and the friction is considered to follow the modified Coulomb friction model. In this simulation considering the large interface of sheet and die, variation of sheet temperature due to heat of deformation is neglected.As mentioned, the concept of constitutive model is to predict the flow stress evolution through deformation. Considering room temperature deformation, shows the flow stress in a strain and strain rate field for copper.As can be seen, the constitutive model predicts that the flow stress arises strictly due to strain accumulation in small magnitude of deformation. However, in larger strains, the flow stress raising stops and the flow stress shows some dropping. Also, at very large magnitude of deformation, a saturated flow stress is obtained. It should be noted that with increasing the strain rate, the described stages occur in higher strains. In addition, it is shown that increasing the strain rate causes to increase the flow stress. These trends are in agreement with the experimental work carried out by Torre et al. The model predicts that during small magnitude of deformation, work hardening is the prominent phenomenon and the softening driving force is small. However, increasing the strain causes to increase the driving force energy for softening mechanisms Common belief about the effect of strain rate in cold working is that it has not any significant effect on the flow stress evolution Considering the symmetry of the CGP and RCS processes, the distributions of strain in half length of processed sheets are shown in The results show that the average of strain magnitude in RCSed sheet is less than that in CGPed sheet. This phenomenon can be described by considering that in RCS some regions of sheet get thinner than the initial thickness of sheet. Therefore, these regions accept low magnitude of deformation in further processing that causes to decrease the average strain magnitude in this process.The groove pressing process, in its ideal state, exerts extremely uniform strain The condition of RCS process is different; the RCS process is not an ideal GP process. In this process, the sheet elongates during the deformation One more important phenomenon, that can influence the strain distribution, is related to sheet elongation during the process. As said in each step of GP process, certain regions of sheet are strained It should be noted, the friction between dies and sheet causes to that the surface of sheet accepts little strain than the center of sheet. This can be seen in the FEM results of both processes.Therefore, it can be concluded that the strain distribution is more uniform in RCSed sheet after one pass and in CGPed sheet after two and three passes.Considering the coefficient of 3 in relation between hardness and strength, the evolutions of hardness in processed sheets by RCS and CGP are shown in , the two primary passes of GP in both approaches cause to increase the hardness of sheet, while the third pass causes to decrease it. This trend is reasonable considering constitutive model descriptions. Also, as can be seen the agreement between the modeling results and experimental data is acceptable The distributions of hardness in processed sheets by RCS and CGP at different passes are shown in As shown in this figure, the analysis predicts that the hardness distribution of RCSed sheet is more uniform than that of CGPed sheet. This condition is related to the effect of described strain and strain rate localization in sheet surface that is intensive in CGP process. Also, as can be seen in hardness profile of RCSed sheet, the middle region in length of sheet has similar non-uniformity, because the middle region of RCSed sheet is affected by strain and strain rate localization, similar to that of CGP process.In the present work, the following items can be concluded:The proposed constitutive model, predicts that plastic deformation in small magnitude of strain causes to strict increase in the flow stress of materials, however, more deformation leads to stress dropping. In addition, larger deformation creates a permanent saturated flow stress.The results show that strain rate has clear effects on the flow stress evolution of material under intense deformation. The model shows that higher strain rate leads to higher flow stress, and also causes to shift the described stages of flow stress evolution to larger strains.The FEM results show that the average magnitude of strain in CGP process is larger than that in RCS. Also, the model predicts that the strain uniformity of RCS is higher in first pass of process, while it is higher in CGP for following passes.It is shown that the groove pressing process causes to increase the hardness of sheets in two first passes, while it leads to little hardness dropping in third pass. Also, the model shows that the hardness of produced sheet by RCS is higher than that of produced sheet by CGP. In addition, it is predicted that the RCSed sheet has more uniform hardness distribution in all passes. Comparing the modeling hardness results and experimental hardness data, a good agreement is achieved.Study on plastic damage of AISI 304 stainless steel induced by ultrasonic impact treatment► FEM coupled GNT damage model was developed. ► FEM was used to study the plastic damage of steel induced by UIT. ► The damage area was annular and only 0.07 mm from surface after UIT. ► Remove 0.1 mm surface after UIT could enhance the properties of materials.The plastic damage of AISI 304 stainless steel induced by the ultrasonic impact treatment has been studied by using finite element model based on Gurson–Tvergaard–Needleman (GTN) ductile damage constitutive equations in this paper. There is a maximum compressive residual stress with −370 MPa when the impact velocity is 5 m/s, and the location of maximum residual compress stress is at the depth of 0.2 mm from the treated surface. Meanwhile, the depth of the compressive residual stress increases from 0.65 mm to 0.85 mm when the impact velocity changes from 3 m/s to 5 m/s. The damage area is annular and the indent center is not affected. The damage depth is only 0.07 mm from the specimen surface. It is reasonable to remove about 0.1 mm thickness material from the treated surface which can not only keep the compressive residual stress and hardened surface but also avoid the surface roughness and plastic damage to material surface.The material failure including wear, corrosion and fatigue is dependent on the surface states UIT has been studied from the early 1970s The finite element method provides a powerful method for simulating the single/multiple shots/pins impact on a target. Several models conducted to simulate the impact process by using the finite element method. Some of them were axi-symmetric models to simulate the single shot/pin impact UIT is an effective way to enhance the properties of the materials, and the main benefits get from the treatment including surface gain refinement, surface compressive residual stress, and increasing surface hardness. However, the rough surface generated by UIT may mask the beneficial effects of UIT. The collision between the material surface and the pin may also cause the microstructure damage on the material. In this paper, a finite element model based on Gurson–Tvergaard–Needleman (GTN) ductile damage constitutive equations is established to study the plastic damage of AISI 304 stainless steel during UIT A UIT equipment consists of ultrasonic generator with a frequency of about 21 kHz and an output power of about 1.5 KW, piezo-ceramic transducer, step-like ultrasonic horn made from strength material, and the impact head installed on the horn tip. The impact head contains cylindrical pin(s) which can free move between the horn tip and the treated surface. The schematic diagram of UIT is shown in P(W/g/impact)=fiEkm=fim(Eus+Er)≈fim[2π2fus2ξ2mP+Er]where fi |
≈ 3 ± 0.5 kHz is an impacting frequency, m is the coefficient with the mass dimension, which takes into account the correlation between the pin mass mP and the sample mass ms. During the treatment, the repeated multidirectional impact at high rates onto specimen surface leads to severe plastic deformation on the surface. The main parameters of the ultrasonic impact treatment process are as follows: the vibration frequency driven by an ultrasonic generator is 20 kHz, the pin’s diameter and length are 3 mm and 25 mm, respectively. In this study, the peening velocity changed from 3 mm/s to 5 mm/s, in which the Er was ignored.It is considered that the ductile damage is induced by the evolution of micro-void under local stress–strain field, and it is nearly impossible to observe it experimentally because the time between the growth of void and the last failure of material is too short. The Gurson–Tvergaard–Needleman (GTN) model could simulate the micro-voids nucleation, growth, coalescence effectively. The GTN model is first proposed by Gurson where σe is von Mises stress, σy is the yield stress of material, σm is mean stress, q1, q2 and q3 are the constitutive parameters, f* is the current effective void volume fraction (VVF), which considers void coalescence phenomenon, in the definition of the yield criterion:f∗(f)=fiff⩽fcfc+q1-1-fcfF-fc(f-fc)iffc<f<fFwhere fc is the critical VVF, referring to the beginning of void coalescence, and fF is the final failure VVF, that is to say, material will be failure completely when the current VVF equal to fF.The evolutional rate of VVF consists of void volume grow rate of existing voids f˙growth, and new nucleation rate ·fnucl, that is:where f0 is initial VVF of intact material, which represents the initial damage induced by slag inclusions.f˙growthdepends on plastic volume strain rate, described as:Nucleation is considered to base exclusively on effective plastic strain and the void nucleation follows normal distribution, characterized as follows:where fN is the maximum volume of micro-particles which have potential to turn into voids through new nucleation in the material, εN is the critical mean value of plastic strain referring the beginning of void coalescence, SN is the corresponding standard deviation, εMpl is equivalent plastic strain, and ε˙Mpl is equivalent plastic strain rate.fc could be confirmed using the expression proposed by Benseddiq fF could be obtained from Zhang’s empirical relation between f0 and fFThe values of q1, q2 and q3 are fixed to 1.5, 1.0 and 2.25 as suggested by Tvergaard and Needleman.The two-dimensional axi-symmetric FE model was developed using the commercial finite element code ABAQUS Explicit 6.6 to investigate the damage on the materials during UIT for single impact (, the target was modeled as a rectangular body (6 mm × 15 mm), which was large enough to avoid the effects of the boundary conditions on the results. The impact area was (2 mm × 2 mm) located in the contact side of the rectangular. Target mesh was set by CAX4R: 4-node bilinear axisymmetric quadrilateral element with reduced integration and hourglass control. The diameter and length of the steel pin were 1.5 mm and 5 mm, respectively. The steel pin was modeled as a rigid whose element was CAX 3-node linear axisymmetric triangle. A sensitivity study had already been carried out to optimize the dimensions of the element in the refine zone. The size of the target was 0.1 × 0.05 mm2 and 0.1 × 0.1 mm2, and in the contact area was refine into 0.05 × 0.05 mm2.To simplify the damage analysis, AISI304 stainless steel was adopted in this model, and the mechanical properties of AISI304 stainless steel were presented in (σb= 668 MPa, σs= 286 MPa, υ |
= 0.3). The parameters of GTN were the same as mentioned in Section The bottom of the model was restrained against all displacements and rotations. The left was the axial symmetry boundary condition. The impact velocities employed were 3 m/s, 4 m/s and 5 m/s, respectively. shows the residual stress distribution obtained by numerical simulation as functions of impact velocity. The maximum compressive residual stresses are all located at the depth of about 0.2 mm from the treated surface at three different impact velocities. The similar results can be seen in Ref. , the injected energy per impact is square of the velocity that the impact velocity has little effect on the locations of maximum compressive residual stress, but it shows significant effect on the maximum compressive residual stress and the depth of the compressive stress zone. The results agree well with the result obtained in Ref. is the displacement of the points on the contact surface at different impact velocities. The displacement is 0.012 mm when the impact velocity is 3 mm/s. However, the displacement increases to 0.019 mm at the impact velocity of 5 mm/s. Considering the basic concepts of the various peening method, the surface roughness behavior is evidently due to the random nature of impact of the metallic balls. Comparing with such peening method, like shot peening, the roughness magnitude after UIT in this paper is larger. It is because the impaction of the metallic balls or pins with lateral load can lead to the shallow indent and the broader indent width The damage evaluation in the process of UIT is presented by using the parameter VVF in this paper. The plastic damages of AISI 304 stainless steel at different impact velocities are shown in . It can be seen that the plastic damage increases with the increasing impact velocity. According to the GTN equations, nucleation is considered to base exclusively on effective plastic strain and the void nucleation follows normal distribution, characterized as Eq. . The increase of the impact velocity enhances the equivalent plastic strain εMpl and also the equivalent plastic strain rate ε˙Mp in the UIT process. Meanwhile, the damage is caused by the tension in the process of UIT. So the damage value VVF increases with the impact velocity , it is reasonable to remove about 0.1 mm thickness material from the treated surface, which means the compressive residual stress and hardened surface can be kept. In addition, the surface roughness and plastic damage to materials could be avoided.The plastic damage of AISI 304 stainless steel induced by UIT has been studied by using finite element model based on GTN ductile damage constitutive equations. The results show that the maximum compressive residual stress changes from about −320 MPa to −370 MPa and locates at the depth of 0.2 mm from the treated surface when the impact velocity changes from 3 m/s to 5 m/s. Meanwhile, the depth of the compressive residual stress increases from 0.65 mm to 0.85 mm. The damage area in the process of UIT is annular and the indent center is not affected. The damage depth is only about 0.07 mm from the contact surface. Removal of surface layer with 0.1 mm thickness material from the treated surface is an effective method, which not only keeps the compressive residual stress and hardened surface but also avoids the surface roughness and plastic damage of material surface.Hydrogen assisted stress corrosion crackingInvestigation of hydrogen assisted cracking of a high strength steel using circumferentially notched tensile test► Novel CNT testing was successfully employed for HASCC study of a high strength steel. ► Effects of both internal and external hydrogen were examined. ► Fracture toughness KIcH |
relates to theoretical hydrogen distribution at/around crack tip. ► KIcH |
for lower loading rates agree with published threshold fracture toughness data. ► Utility of CNT tests for study of HASCC in steels was established.The novel circumferentially notched tensile (CNT) test technique is used for the first time for an investigation of hydrogen assisted stress corrosion cracking. Effect of hydrogen on the fracture strength of high strength steel AS-4340 is examined in neutral 3.5% NaCl solution at room temperature and under hydrogen supply from within the material and/or external environment. A progressive drop in the stress intensity factor at the fracture was observed as a result of: (a) increasing span of hydrogen pre-charging (hence increasing internal hydrogen) and (b) decreasing rate of loading (hence increasing external supply of hydrogen). The measured critical stress intensity factors corresponding to varying degrees of supply of internal hydrogen are consistent with the computed hydrogen concentrations ahead of the crack tip. The experimentally determined threshold for hydrogen embrittlement in the regime of slower loading rates are consistent with the published data. The results presented here establish the usefulness of the CNT test technique for the investigation of HASCC in high strength steel over a wider range of loading rate.Hydrogen assisted stress corrosion crackingHydrogen is one of the most common causes for accelerated damage of engineering materials. Specifically, the cracking caused under the combined action of hydrogen (which is generally produced as a result of corrosion reaction) and tensile stress is termed as hydrogen assisted stress corrosion cracking (HASCC). The sudden and generally insidious nature of HASCC pose a serious challenge in design, safety and maintenance for several industries, viz., aviation, marine, nuclear, offshore oil, and energy, to name a few. Presence of hydrogen dramatically diminishes fracture toughness of high strength alloys The hydrogen required for HASCC may become available in two ways. Firstly, the hydrogen may be present within the material itself prior to the application of stress, such as by prior diffusion of hydrogen atoms into the material from external surface. Such pre-existing hydrogen atoms can combine to form H2 molecules within voids and at precipitates and become immobile because of large size of the molecular hydrogen. The pressure build-up due to gradual accumulation of such molecules eventually leads to cracking. The presence of stress amplifies this effect. HASCC caused by the internal hydrogen is termed as internal hydrogen assisted cracking (IHAC) Major parameters influencing the HASCC in high strength alloys are: (a) stress intensity factor K; (b) rate of loading; (c) hydrogen distribution around crack tip; (d) corrosion electrode potential; (e) factors influencing hydrogen concentration in environment, such as pH; (f) yield strength σy and (g) temperature. Quantitative investigation of HASCC has generally focused on characterisation of the material in terms of critical stress intensity factor (KIcH) for a particular rate of loading and threshold stress intensity factor (KTH) below which the crack growth is insignificantly slow or negligible.The present study investigates application of a new testing technique for determination of KIcH |
for a high strength steel, AS-4340, under the conditions of IHAC, HEAC and both IHAC and HEAC. The KIcH |
data generated under IHAC condition have been further examined on the basis of the hydrogen enhanced decohesion (HEDE) mechanism The influence of different parameters on HASCC for 4340 steel has been widely investigated by fracture mechanics approach using double cantilever beam (DCB) In the light of potential advantages of CNT tests for HASCC studies, experimental investigation of HASCC has been performed using this type of specimens for a high strength alloy steel. The study focuses on the evaluation of influence of two parameters, hydrogen distribution around crack tip and rate of loading on the KI |
at the time of failure.The fatigue pre-cracking of CNT specimens (), which is done through rotating bending loading generally leads to crack profiles which are eccentric with respect to the axis of test specimen (). Therefore, the calculation of KI |
must incorporate the effects of the additional bending moment arising out of this eccentricity. For this purpose, a method developed by Ibrahim and Stark σt and σb are tensile and bending stresses, respectively. F0 |
and F |
are geometric factors for the round specimen with and without eccentricity respectively. α is a constant. P is the applied load, D is the specimen diameter, d is the equivalent ligament diameter, ϵ is the eccentricity and a is effective crack length. The values of d, ϵ and a are calculated using the procedure given in The initial KI |
is first estimated using Eq. for a given crack length a. This is corrected to a¯ using the Irwin correction factor ry computed from the estimated value of KI. That iswhere σy is the 0.2% offset tensile yield stress. KI is then recalculated from Eq. The concept of KI is based on the theory of linear elastic fracture mechanics (LEFM) which is valid for situations where the size of plastic zone near the crack tip is sufficiently small as compared to the specimen geometry. Accordingly, validity requirements for the CNT testing have been established Fatigue crack depth af should be at least twice the Irwin correction factor ry:where af |
= |
ϵ |
+ (D |
− 2am |
− |
d)/2, am is the machined crack length.Nominal stress in the final ligament σN should be less than 2.5 times the yield strength:where the nominal stress σN |
is the sum of tensile stress and the maximum bending stress.Both these requirements have been ensured for all the tests reported here.) consists of a loading arrangement, CNT test specimen, environmental cell, and instrumentation to measure load and specimen elongation. The set-up was specifically designed for this study. The loading axis was vertical. The machine was operated by an electric DC motor with reduction gear box to achieve cross-head linear speeds between 0.1 mm/h and 0.0015 mm/h. The tensile load was applied to the test specimen through gradual motion of the cross-head. The details of machine loading system can be found elsewhere The test specimens were machined from a bar of high strength alloy steel AS-4340 of composition () to a size of 7 mm outside diameter and 5 mm notch diameter (). These were heat treated by normalising at 835 °C for 0.5 h and followed by tempering at 300 °C for 2 h. The mechanical properties of test specimen after heat treatment are: ultimate tensile strength 1740 MPa, yield strength 1525 MPa and hardness 48 HRC. These test specimens were then fatigue pre-cracked using a rotating bending machine. The parameters for rotating bending were selected to achieve a crack root diameter of around 4 mm. The final KI |
during pre-cracking was limited to 20 |
MPam. After pre-cracking, the specimens were ground with SiC papers upto 1200 grit followed by cleaning with acetone and distilled water. The specimens were also wrapped with Teflon tape all over except over a 2.5 mm span on either side of the notch.An acrylic environmental cell was assembled with the specimen with Teflon end seals. The cell was filled with 3.5% (weight) neutral NaCl solution. The top cover of cell had openings for insertion of reference and counter electrodes. The specimen was mounted vertically into the loading machine with a spherical washer provided at the bottom support to accommodate minor misalignment, if any, in the loading axis.For measurement of applied force, a load cell was fitted in between the cross-head and the specimen grip. For measurement of specimen elongation, a special arrangement with two LVDTs was used (). The arrangement consisted of two extension arm assemblies attached to the specimen at a distance of 40 mm, one above and other below the notch. Readings from both load cell and LVDTs were acquired electronically by the data acquisition system. The specimen elongation data though collected is not used in the present study; it will be used in the future study on crack growth rate.All tests were conducted at room temperature for four cases: air, IHAC, HEAC and combination of IHAC and HEAC. For the IHAC investigations, the span of time for hydrogen charging was varied; whereas for the two latter cases, the rate of loading (i.e., cross-head speed) was varied (For the HEAC tests carried out at the lowest cross-head speeds (0.0015–0.0020 mm/h) the durations of loading (130–230 h) were much longer as compared to the durations (3–20 h) for the other cross-head speeds. Because of the prolonged durations of the tests at the lowest speeds, the hydrogen distribution can be presumed to be uniform and the material can be considered to be saturated towards the later part of the tests. The additional pre-charging time span of 12 h for the combined IHAC–HEAC tests was assumed to have an insignificant effect on the hydrogen distribution, and hence negligible influence on the KIcH |
at failure. Hence KIcH |
data for the pure HEAC tests can be easily considered to correspond to the combined IHAC–HEAC situation.During the HASCC experiments, the specimen was cathodically charged at a potential of −0.865 V (SCE) using a potentiostat for the entire duration of the test. For the IHAC study, the hydrogen charging was stopped and solution was drained from the environmental cell just before the cross-head motion commenced.For each test, the load at the failure of specimen was recorded. Using this load and the crack profiles at the fractured surface, the KIcH |
was computed.The fractured surface of the test specimens was ultrasonically cleaned for removal of corrosion products and then examined using scanning electron microscope (SEM). The solution used for ultrasonic cleaning contained 6 mL concentrated hydrochloric acid +10 mL of 30 g/L of 2-butyne-1,4-diol + 100 mL distilled water.The fracture toughness (KIcH) for the quenched and tempered AS-4340 steel undergoing HASCC was determined under the conditions of IHAC, HEAC and combined IHAC-HEAC.For the IHAC experiments, the hydrogen distribution around the crack tip was varied by changing the duration of the pre-charging time. This is consistent with the practice in the literature . As expected, the fracture toughness reduces with an increase in the average level of hydrogen concentration in the material immediately ahead of the crack tip (as a result of the increasing pre-charging time). The failure always occurs at KIcH>KTH |
for each duration of pre-exposure. The reported KTH data for C–Mn and alloy steels including AS-4340 at 23 °C in NaCl and other environments for hydrogen evolution lie in the range of 10–15 |
MPamThe average hydrogen concentration immediately ahead of the crack tip was computed through finite element analysis. The hydrogen distribution ahead of the crack tip is governed by the diffusion process. The diffusion of hydrogen during the pre-charging for the axi-symmetric geometry is governed by the following diffusion equation:where t is time, r is radius, C is hydrogen concentration and Deff is effective diffusivity of hydrogen in the material.The diffusion equation was solved using finite element code ABAQUS® (version 6.6) The effective diffusivity Deff for steel is in the range of 2 × 10−6 to 2 × 10−3 |
mm2/s. Due to their relatively higher trap density, Deff of the high strength steels tends towards the lower values of this range The average hydrogen concentration Cavg was computed for different pre-charging durations and at different spans from the crack tip. A variation of average concentration Cavg over a distance of 0.3 mm from the crack tip with time is presented ( shows plots of both (1 − |
Cavg) and KIcH against the pre-charging time for the two values of Deff. The plots clearly show the dependence of the fracture toughness on the hydrogen concentration ahead of crack tip.For the HEAC and combined IHAC–HEAC experiments, the cross-head speed was varied for the purpose of changing the crack tip strain rate. respectively present the variations of stress intensity factor at failure (KIcH) against the cross-head speed for the two situations, HEAC and combined IHAC–HEAC. The slower crack tip strain rate is reported to have an adverse effect on the fracture strength during HASCC ). The presence of additional hydrogen due to pre-charging in the case of combined IHAC–HEAC testing is manifested as a further drop in KIcH (). KIcH |
approached the KTH |
towards the lowest range of the cross-head speed (0.0015–0.0020 mm/h). This regime corresponds to an infinitesimally slow cross-head speed.The theoretical investigations into HEAC and combined IHAC–HEAC are more involved compared to the case of IHAC due to the additional influences of the crack tip stress field and the strain rate on the hydrogen transport. This will be considered in a future study.a represents the overall fractograph of a failed CNT specimen under HEAC condition. Overall fractograph consist of four regions: machined notch, fatigue pre-crack, HASCC and mechanical failure zone. The distinct features of each region become clear at higher magnification. The fatigue pre-crack region is exclusively characterised by striation marks running from the circumference (c shows the transition from fatigue pre-crack zone to HASCC zone. HASCC region was exclusively characterized by intergranular cracking/fracture (d). This presence of intergranular fracture is a typical hydrogen effect, which is generally caused by the preferential crack growth along the prior austenite grain boundaries, and is consistent with the features of hydrogen embrittlement reported for this steel e), confirming that the final failure indeed occurs by mechanical overloading.The HASCC behaviour of high strength alloy steel AS-4340 has been investigated experimentally, employing the novel CNT tests. During the IHAC, a progressive reduction in KIcH |
for higher amount of hydrogen ingress is observed; likewise, during the HEAC and combined IHAC–HEAC tests, a reduction in the value of KIcH |
for reduced rates of loading is noticed. The fracture toughness (KIcH) approaches the threshold fracture toughness (KTH) reported in the literature for similar material, both for the long range of pre-charging time during IHAC tests and the lower range of loading rates for the HEAC and combined IHAC–HEAC tests. The computed hydrogen distribution ahead of the crack tip is observed to have a distinct influence on the fracture data obtained during the IHAC tests; conforming the HEDE mechanism. The present results and their agreement with the published data confirm the utility of the CNT tests as a valid experimental approach for the study of HASCC behaviour of high strength steels. The study also provides distinct fractographic evidence for intergranular HASCC, which is consistent with the literature.A damage parameter for HCF and VHCF based on hysteretic dampingThe fatigue limit of materials, due to the improvement of fatigue life of structures and mechanical components should be extended from the traditional 106–107 cycles up to 109 and more, but with traditional testing hardware this is a difficult technical task due to the length of time needed for the completion of tests. Ultrasonic fatigue testing machines seem to be adequate for very high cycle fatigue (VHCF) tests. We propose here to evaluate the behavior of the hysteretic damping in an attempt to associate that with damage parameter. The approach here presented is based on the fact that the fatigue issue can be understood in terms of the energy available for irreversible process triggering. This nonconservative energy will be involved in micro-structural changes in the material before being dissipated as thermal energy. In fact, the balance between the energy supplied to and returned by the material is positive and the hysteretic damping factor represents the inelastic fraction of energy in each cycle. Aiming at building a model to correlate the hysteretic cycle parameters and the fatigue process, both energy loss and material response of the specimens are measured during the fatigue test. The fatigue tests are carried out with an ultrasonic machine test, operated at 20 kHz with amplitude or temperature control, under HCF and VHCF for copper specimens. The results show the behavior of hysteretic damping parameter during fatigue life, the equivalent dissipated energy per cycle and a good correlation between the hysteretic damping factor parameter and the fatigue process S–N curve, suggesting that factor as a promising fatigue life parameter useful for some cases of fatigue life prediction.Experimental evidence from tests performed on a large variety of materials, mainly metallic materials, show that material hysteresis is nearly independent of the forcing frequency over a wide range of frequencies. Accordingly, the hysteretic model has been extensively used to model damping in forced vibrations, both in harmonic and random processes. From the above, it is assumed that the accurate measurement of this energy per cycle, once integrated over a very high number of cycles, could be correlated with the fatigue damage that occur in initial phases of the fatigue process.Ultrasonic fatigue testing machines are being used to perform materials testing in the range of 107–1010 fatigue cycles. Since, in VHCF fatigue, this phase constitutes a very important fraction of the total life of the material, the understanding of the mechanisms acting during this phase may be of paramount importance for evaluation of the fatigue limit.In the past, when engineering components were not expected to endure more than 107 load cycles, the S–N results were often limited to 107 load cycles, considered as unlimited life but, nowadays, it is important to know the fatigue behavior of material above this limit. In conventional fatigue testing, this type of experiment become very difficult, time consuming and expensive. Meanwhile, piezoelectric fatigue machines are being developed which enable efficient and reliable testing in 1010 cycle domain in less than one week. With these developments and the ability of testing the materials for a very high number of cycles, authors like Bathias Given the high level of interest in this field of research, there are many authors dealing with this issue and publishing their work in VHCF. For instance, Xue et al. VHCF tests performed in ultrasonic fatigue testing machines have the particularity of being performed for one specific resonant frequency of the system, all resonant system needs to be designed for a specific frequency, such as the horn, the length and radius used to obtain a desired amplification, the specimen dimensions to obtain a specific stress level, references When a specimen is subject to cyclic loads, the work done by such external loads is available to trigger internal changes in the material The present work is part of a project aimed to relate the imaginary part of the Young modulus to the fatigue process. Very high frequency tests needed to assess the VHCF behavior with laboratory testing machines will be carried out in this study. In this paper, some equipment, methodologies and the algorithms that will be used to evaluate the evolution of the hysteretic damping factor (η) at 20 kHz frequency fatigue tests are described. A method to obtain the damping factor during VHCF fatigue tests and the S–N experimental fatigue life results under HCF and VHCF are presented for copper specimens, aiming at building a model to correlate the hysteretic cycle parameters and the fatigue process. Looking for this relation is the main objective of this work and if it exists, it could be highly important since it could be the basis of a promising new health monitoring tool. Consequently, this paper presents some promising initial experimental results for launching such search.Considering a general system, the harmonic dynamic load/deflection curve exhibits an elliptic loop denoting the energy dissipation phenomena. The energy ΔW dissipated per cycle of oscillation is given by the area enclosed in the oscillation loop, If a hysteretic damping model is applied where f(u) represents the dynamic force, U is the amplitude peak per cycle and d the constant damping coefficient of the hysteretic damper model.And by steady-state equation of motion of a hysteretically damped single-degree-of-freedom system:where U‾ represents the complex amplitude, F is the force excitation, k and m, the stiffness and mass, respectively, and ω the frequency.The damping loss factor is defined η by:This model provides a damping force proportional to the displacement of system and in phase with the velocity, a different state is achieved if a viscous model c is used where this vary inversely with frequency c |
= |
d/ω.To hysteretic damping the maximum amplitude X occurs when ω |
= |
ωn and the maximum for viscous damping model occurs when ω=ωn1-2ξ2, but assuming low damping values, a maximum amplitude to the system with viscous damping may be assumed at ω |
= |
ωn, and the two models (viscous and hysteretic) at resonance are sufficiently close to be assumed equivalent.The hysteretic damping factor η and the viscous damping factor ξ at resonance are related by: is plotted the hysteresis loop for different values of damping loss factor at fixed frequency for a single degree of freedom system (SDOF).Regarding this relation is possible to correlate the two models of damping and it allows to estimate the damping value by a very simple method like a logarithmic decrement. This method will be described in Section . Using the estimated damping factor and an equivalent system is possible to evaluate the behavior of dissipated energy per cycle along VHCF tests. For this analysis, we assume as equivalent system with keq, meq representing the dynamic response of specimen. Using Eq. The ultrasonic fatigue testing machine is an integrated system with several elements, each one of them with a specific task. The ultrasonic energy must be transmitted between resonant elements in an efficient way, starting in the actuator and ending at the specimen bottom.In order to perform ultrasonic test, it is needed to design a specimen with longitudinal natural frequency to the same work frequency. The specimen design is easily determined using elastic wave theory Considering the appropriated boundary conditions, resonant boundary conditions and defining the different parts of specimen see , by cylindrical parts at the ends and a profile of hyperbolic cosine for reduced section, the analytical solution representing the displacement behavior at longitudinal mode, is defined by:u1(x,t)=A0cos(kL1)cosh(αL2)sinh(βL2)sinh(βx)cosh(αx)sin(ωt),|x|<L2u2(x,t)=A0cos(k(L-x))sin(ωt),L2<|x|⩽LL1, |
L2, |
R2, |
R1, represent the different dimensions and radius of the specimen, Ed and ρ are the young modulus and the density of the material, and ω represents the resonant frequency. the strain and stress behavior in specimen can be determined:To determine the correct specimeńs dimensions, the static and dynamic mechanical properties of the material are needed. For the accomplishment of fatigue tests, a copper material was chosen. Static and dynamic mechanical properties of copper were previously estimated using tensile test and modal test and are presented in Knowing the properties of material of copper and using Eqs. , it is now possible to estimate the dimensions of specimen with resonant frequency equal to 20 kHz (actuator work frequency) which are shown in Finally is presented the evolution of displacement and stress on specimen previously design, The ultrasonic high frequency machine used to perform tests was developed by the same authors of this work and described in detail in In resonant system all elements are mechanically connected by a screw connection, piezoelectric actuator, booster, horn and specimen. These four elements form the resonant system of the testing machine. Power delivered to the piezoelectric is controlled by signal generator which is permanently in search for the natural frequency of the mechanical system; amplitude power can also be controlled by LabView® software.The measurement system is composed by a laser, measuring the displacement in the bottom of the specimen and if necessary the use of a strain gauge is possible in another channel. A third channel is used by a pyrometer, to monitor on-line the temperature of the center of the specimen.The cooling system, at this time is composed by two fans, helping to cooling the resonant system during the different phases of test.All information delivered by the monitoring elements and commands necessary to control the resonant system are processed by a data acquisition device which is the interface between the perifericals and the LabView® routine. This LabView® routine, establishes the power delivered to the piezoelectric actuator to achieve the desired axial tension, indicate the specimen temperature history, displacement, frequency and the number of cycles during test or at rupture time. When the fatigue test is finished a summary with the monitoring history is shown and registered in data file.This LabView® routine also allows to perform two types of control during fatigue test, amplitude control and temperature control.In order to obtain the desired data to estimate damping ratios in following sections, it is necessary to define some parameters in the LabView® routine, for the test machine proceeds by the desired mode, such as amplitudes of vibration, temperature range and type of control (temperature, amplitude or both).If only the power provided to the piezoelectric actuator is defined, the fatigue test start and run without interruption, performing 20 k cycles/s, the signals from the laser and pyrometer are acquired and stored in order to monitor the specimen behavior. Consequently in this case, the temperature may rise to a value outside the acceptable range, and an important fact, a unique free decay to estimate the damping ratio is obtained, corresponding to the end of fatigue test. Moreover more free decay to estimate the behavior of damping ratio along the fatigue test is needed. This problem is overcome when the fatigue test is carried out within temperature control, with variation ΔT, as illustrated in . In this case, a range of temperature is defined and the fatigue test is controlled by a LabView® routine, when the temperature of specimen reaches the maximum value defined by the user, the test is interrupted and the specimen is cooled, the test is restarted when specimen reaches the minimum value. In the process is illustrated: the test is in progress, the temperature is continuously checked, the LabView® routine process signals and record the mean values of temperature, amplitude, frequency and power in each period of time (block) defined by the user, when temperature reaches the maximum value, the routine interrupt the test to cool the specimen and record the last block in a data file with the number of correspondent block. With this procedure the necessary free decay along fatigue test is obtained.Setting a narrow range of temperature of the control parameters implies also a similarly narrow range on amplitude parameter, as was previously shown by the authors in Concerning the displacement amplitude measurement and control, two possibilities can be achieved on the test: (a) with power fixed, i.e. setting the power on the piezoelectric actuator and having no control on the amplitude of the displacement and (b) with amplitude displacement control, i.e. setting a fixed displacement amplitude at the bottom of the specimen which is related to the strain and stress at the centre of the specimen and therefore with the variation of the power.The operating temperature range ΔT and type of control used to perform the fatigue tests are presented at results section; here it is defined the sampling frequency with 400 kHz, the period of each acquisition block 0.125 s, and activate option to record the time signal only for the last block of each runs. Hence, with this block period the feedback loop for controls was updated every 2500 cycles.As mentioned before, to avoid the excessive heating of the specimen that happens in practical cases of fatigue testing at this frequency, the machine is programmed to stop exciting the specimen when the temperature reaches the allowed maximum and resumes when cooling brings it down to a given minimum. The effect is a time series of test blocks separated by cooling gaps. Each time the excitation stops, the system – machine + specimen – is left free to vibrate by itself until it comes to a rest.The energy loss in free vibration implies decreasing amplitude of the vibrations when the exciting load ceases to resupply the energy lost per cycle. Since, according to equations of motion for single degree of freedom linear and viscous system, such decrease can be modeled by a negative exponential curve, as follow:where ωn represent the natural frequency, ωd is the damped natural frequency and U and φ are constants determined by initial conditions. Then, the decrease rate can be measured by its logarithmic decrement ratio δ and related to the viscous damping factor ξ and hysteretic damping η equation.δ=1nlnUiUi+n=2πξ1-ξ2orδ=2πξ(assumingξ≪1)where Ui represents the first peak of the first cycle considered and Ui+n the last peak after n cycles.Finally viscous damping is related by hysteretic damping by η |
= 2ξ according to Eq. , is defined by a traditional logarithmic-decrement method, but in This new approach consists in using the area under the displacement amplitude, rather than only two points (first and last peak).S1+S2+⋯+SNSN+1+SN+2+⋯+S2N=S1+S2+⋯+SN(S1+S2+⋯+SN)e-ξωnnTd=eξωnnTd=e2nπξ/1-ξ2where, SN represents the absolutes areas, N the number of areas and n number of cycles. In analogy with method presented in , first area (S1) corresponds to the first peak (U1), but if we consider n numbers of peaks, in this case we have twice as many areas 2N, because we have two areas for one peak, one cycle. results with both methods are presented.The estimation of the hysteretic damping factor is not a direct process, and in this study we use one of the methods described in Section for the damping factor and correlated by Eq. . In this first section of results the estimation of η (hysteretic damping factor) are presented, obtained by the designed traditional logarithmic-decrement method (Eq. The following results concern a copper specimen tested in VHCF machine subjected to different loads, for each load we estimate hysteretic damping on three final blocks of cycles, considering different number of cycles. The first cycle considered for the calculation of areas needed to estimate damping factor is chosen when amplitude reaches 66.7% of maximum amplitude recorded during last block or 4/6 of the amplitude required during the fatigue test. we present the evolution of η with increasing the power supplied to piezoelectric actuator and the convergence of damping factor values when we increase the parameter n of Eq. corresponding to the number of cycles considered in estimation., we note that the values obtained for hysteretic damping factor by the two methods are very similar and consistent. We note that the trend of damping by the supplied power is similar for all number of cycles considered and that the convergence of the values is visible by the second method to considering a 800–1000 range of cycles. As explained by the authors In this section the behavior of hysteretic damping factor during the fatigue tests is described. These fatigue tests are performed with a VHCF machine for different stress amplitudes and different type of control (amplitude control and power control).Using the new approach for logarithmic-decrement previously validated, the estimation of hysteretic damping factor along life of specimen is carried out. The damping factor estimation is performed for the last block, corresponding to the fatigue test interruptions due the temperature control. The first cycle considered to calculus of areas is chosen when amplitude reaches 66.7% of maximum amplitude recorded during last block (4/6 Umax), and we chosen n |
= 600 cycles to estimate the damping factor, and so N |
= 600, a total of 1200 areas. The results are shown in respectively for VHCF tests carried out with Power control and Amplitude control as described in Section . A wide range of cycles to failure (from 106 up to 109) are presented allowing an acceptable range of damage variation during fatigue cycles. It is clearly observed that for higher stress amplitude in fatigue testing a higher damping factor is estimated and a shorter life is obtained. Nevertheless, a difference in the estimated values of damping are obtained for amplitude control tests and power control tests, therefore in order to evaluate this difference that corresponds to different inputs energy to the specimen, which will be analyzed in the next section.We can also observe that the behavior of the hysteretic damping factor parameter is similar for all the performed tests, which increases the level of confidence of the results. Another important aspect that should be noted, concerns the final region of fatigue life, which states a strong growth of the damping factor. Of course this is related to the occurrence of the crack in the specimen, and depending of the type of applied load this region can represent several thousand load cycles on the specimens, showing a region with high interest for future work.Using the formulation described in the Section , the energy dissipated per cycle is estimated by Eq. are represented the behavior of the dissipated energy per cycle along the same fatigue tests present in , tests with power control and amplitude control respectively. In this case, it is clearly observed that for higher stress amplitude in fatigue testing corresponds a higher dissipated energy. This estimated energy results show a very accuracy with the fatigue life of specimens.Finally we can compare the results of fatigue tests carried out before for both Power control and Amplitude control, on a classical S–N curve, the stress amplitude as a function of number of cycles to failure, and the new fatigue curve which correlates the hysteretic damping factor as a function of the number of cycles to failure, which are shown in (a and b) respectively. The hysteretic damping factor value used in (b) corresponds to the stabilizing value for each of curves presented on . With that comparison we do not intend to replace the estimator obtained by the S–N curves, but we seek by similarities that can justify the use of hysteretic damping factor by their advantages. Contrary to the S–N curves, this procedure does not depend on knowledge of the type of applied load, but only the response of the specimen. With this type of approach could be possible to monitor structures and perhaps predict his life to fatigue. It is clear that similar trends are obtained (); while considering these results as preliminary, it is our opinion that the hysteretic damping factor seems to be an acceptable parameter to measure the damage of the material during fatigue tests.The method used to estimate hysteretic damping factor has demonstrated a very good accuracy along the life of specimen.The analyzed results, so far, show a systematic correlation between damping factor and the life of the specimens for each type of control used .The hysteretic damping factor discrepancies, observed between the two types of control are corrected when we analyze fatigue life by the dissipated energy. The dissipated energy, showed a very good correlation with the life of the specimens.The trend line for the data plot between the damping factor and the logarithm of the number of cycles is very acceptable, considering the small number of data points and the difficulties in obtaining precise experimental damping values.This conclusion, if validated by further and more extensive tests, may be an important initial step for a promising new health monitoring tool, since it may allow for the prediction of in-service components without knowledge of the stress level (difficult to measure in some complex geometry mechanical components). In fact, just by measuring the vibration decay after a transient excitation at a convenient point, it shall be possible to obtain the damping factor and, if a correlation model can be established between this parameter and the number of cycles to failure, the remaining life of the component can be estimated.Finite volume simulation framework for die casting with uncertainty quantificationThe present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. State of the art uncertainty quantification technique is included in the framework to incorporate the effects of stochastic variations in the input parameters. Rigorous validation is presented using published experimental results of a solidification problem.Die casting is an important manufacturing process used when high production rates and complex geometries are required to be manufactured. shows a typical schematic of the die assembly. The die is generally made out of steel consisting of two halves which are separated along the parting line and held in place by multiple ejector pins. Cooling lines are designed in the die to flow a coolant, typically water. The mold cavity is sprayed with a lubricant which helps to control the die temperature and also reduces the sticking of the molten metal to the die during the removal. Then the two die halves are closed and liquid metal is filled in the cavity. The flowing coolant maintains temperature of the die and extracts heat from the molten metal. After solidification, the two halves are separated by sliding along the ejector pins. The last step is shakeout in which the scrap (gates, runners etc.) are separated from the casting and the casting is further cooled to room temperature either by quenching in water or leaving open to air. Cycle times vary from a couple of seconds for small components weighing less than one ounce, to thirty seconds for a casting of several pounds. Aluminum, magnesium and zinc alloys are the most popular materials used in die casting. Die cast products are more commonly used in automotive and housing industries. Several complex processes involving a large number of process parameters affect the final product quality. Due to the recent advances in computing hardware and software, it is now possible to simulate the physics of these processes using numerical simulations. These simulations provide detailed flow and temperature histories and can be used to estimate the final product quality. Frequently, it is difficult to measure and tightly control the process parameters like initial melt temperature, mold temperature and alloy component concentration. However, they can have a significant impact on the process as well as the predicted product strength.Temperature evolution and velocity distribution during solidification of pure metals and metal alloys has been analyzed by many researchers. Solidification phenomena of die casting involves interplay between heat transfer and flow due to natural convection. All the references discussed above simulated solidification on rectangular or cuboidal geometries and hence, structured Cartesian grids were used. Practical die casting geometries are complex and thus, unstructured hexahedral elements are utilized in this work. Multiple algorithms are discussed in the literature to simulate fluid flow on unstructured grids For die casting, the microstructure parameters like grain size and dendritic arm spacing are important as they affect the final product quality. Phase field modeling Use of deterministic simulations alone to analyze the engineering systems is incomplete due to the lack of precisely defined input data. Thus, there has been a growing interest In this paper, the traditional fractional step approach is modified to deal with the additional terms in the Navier-Stokes equation due to solidification. The discretized system of equations is altered in a way so as to simulate only in the liquid zone thus, increasing computational efficiency. In order to incorporate the effects of stochastic variations in the input process parameters, a parameter uncertainty propagation module has been developed in conjunction with the deterministic simulations. The method of polynomial chaos expansion is used to estimate the relation between input and output parameters and stochastic collocation is used as a wrapper on the underlying deterministic simulation. The framework has been validated against published experimental results followed by demonstration for solidification of two complex geometries. The novelty lies in the overall idea of coupling uncertainty quantification and sensitivity analysis techniques with the numerical simulation of solidification during die casting. We have shown the importance and advantages of such a coupling for validation and process improvement.Solidification, heat transfer and fluid flow due to natural convection are modeled. It is assumed that there is no macro-segregation during solidification and the metal is solidified at nominal composition. It is further assumed that the solutes do not contribute to buoyancy and the flow is incompressible. Thus, the set of governing equations consists of the standard Navier-Stokes equations with additional terms for solidification ρ∂u∂t+∇·(ρu⊗u)=∇·(μ∇u)−∇P−μKu−gρβ(T−Tref)Here, u is the velocity vector, ρ is density, t is time, μ is dynamic viscosity, g is gravity vector, β is coefficient of thermal expansion, P is pressure, K is isotropic permeability of the dendritic array, λ is dendrite arm spacing and fs is solid fraction.To model the effects of natural convection, the Boussinesq approximation is used. This is a valid assumption for problems with moderate density variations in the domain. The fluid is modeled as a constant density fluid except for the additional buoyancy term −gρβ(T−Tref) in the momentum The Darcy drag term (μKu) represents increased resistance to the flow in the mushy zone. We have used the Blake-Kozeny model () which estimates the isotropic permeability (K) of the dendritic array. In the liquid region, solid fraction is zero and permeability tends to infinity making the Darcy drag term to go to zero. When solid fraction is unity, permeability tends to zero and thus the coefficient of Darcy drag term goes to infinity. For stability, this coefficient is added to the diagonal term of the discretized momentum equations. As a result, the velocities in the solid region go to zero. In the mushy zone, the drag term reduces the velocities compared to the liquid zone.The energy equation is written in terms of temperature as:fs(T)={0ifT>Tliq1ifT<Tsol1−(T−TfTliq−Tf)1kp−1otherwiseHere, T is temperature, Cp is specific heat, k is thermal conductivity, Lf is latent heat of fusion, kp is partition coefficient, Tf is freezing temperature and Tliq is liquidus temperature. Note that the term dealing with advection of latent heat given by ρLf(∇·u)We have developed a new software OpenCast in an object oriented C++ environment. A finite volume method on a collocated grid is used to discretize the governing equations. The fractional step method without the pressure gradient term is solved to estimate an intermediate velocity (u*) field. The buoyancy and Darcy drag terms are included in this step. Second order accurate Crank–Nicolson scheme for the diffusion terms and the Adams-Bashforth scheme for the convection terms are used for temporal discretization. The coefficient of the drag term (μK) in the mushy zone is treated fully implicitly as:ρu*−unΔt+μKu*=−Conv(un,un−1)+Diff(u*,un)+Buoy(Tn)where, the operators Conv, Diff and Buoy represent the discretized convection, diffusion and buoyancy terms respectively. The full momentum equation is similarly discretized with an implicit pressure gradient term, given as:ρun+1−unΔt+μKu*=−Conv(un,un−1)+Diff(u*,un)−(∇P)n+1+Buoy(Tn) gives the velocity correction equation.Taking divergence of the velocity correction and invoking the continuity constraint gives the equation for pressure:The overall solution algorithm to advance from time-step n to n+1 is as follows:. Since the diffusion term is implicit, solution is obtained iteratively together with solid fraction relation () to estimate temperature and solid fractionEstimate micro-structure parameters such as grain size and yield strength using the empirical relationsIn this work, we have used the fractional step method instead of the semi-implicit methods like SIMPLE, SIMPLER, PISO Practical die casting geometries are quite complex. Cartesian grids introduce high stair-casing errors near the boundaries. Thus, OpenCast uses unstructured grids with tetrahedral and hexahedral finite volumes. First, a tetrahedral mesh is generated using the open source software GMSH can be written as a transport equation for a general scalar ϕ:where, ϕ is any scalar field, Γ is the diffusion coefficient, and Sϕ is the source term. shows two adjacent hexahedral control volumes sharing a common face with vertices V1, V2, V3 and V4. C1 and C2 are cell centers and f is the face center. n^ is the unit vector normal to face and in an outward direction with respect to cell C1. d→ is the distance vector from C1 to C2. We use a collocated finite volume formulation with all the field variables stored at cell centers.The surface integral of the diffusion term is approximated as a summation over all the six faces of the cell. The inner product of the normal and the face centered gradient at each face is split into two terms n^·∇ϕ|f=(d→·∇ϕ|fn^·d→)−(d→·∇ϕ|fn^·d→−n^·∇ϕ|f)=(ϕC2−ϕC1n^·d→)+(n^−d→n^·d→)·∇ϕ|f are direct and cross diffusion terms, respectively. For a structured grid, n^ is parallel to d→ and the cross diffusion term is identically zero as the direct diffusion term reduces to the central difference approximation of first derivative at face center.In order to estimate the face centered gradient, the strategy used by ) as the three axes. x, y and z are the axes of the global frame of reference. The gradients in both these frames are related by the chain rule of differentiation.where, the subscripts denote derivatives. The Jacobian matrix entries come from the co-ordinates of the cell centers and the vertices. Value of ϕ at each vertex is estimated by averaging from the neighboring cells of the vertex. Thus, the face centered gradient ∇ϕ|f=[ϕx,ϕy,ϕz]T is estimated by inverting the Jacobian matrix in The surface integral of the convection term is approximated as a summation over all the six faces of the cell. The face value of the field ϕ is estimated by interpolating from the two neighboring cells which share the face. The volume flux passing through the face (n^·uΔA) satisfies the discrete continuity equation. The cross diffusion term has to be accounted for in the computation of the volume flux. The details are given in For solidification problems, some additional steps are needed in order to handle the extra terms such as the Darcy drag and the latent heat terms in the momentum and energy equations respectively. The velocities in the solid region should go to zero and in the mushy zone, velocities should be significantly lower than the fully liquid region. Simultaneously, the continuity equation has to be satisfied by the face velocities for each control volume. Thus, special care has to be taken in the solution process of the pressure Poisson equation and the velocity correction step. shows a typical distribution of phases during the solidification process. For ease of visualization, a two dimensional schematic is shown and the same idea has been generalized to three dimensions. The dotted line shows a solid-mushy zone interface. The control volumes (cells) on the left of the line are solid and on the right are either liquid or in mushy zone. Cells are labeled with tags S:Solid, LM: Liquid or Mushy. The S or LM tag is assigned to each cell based on the temperature at the previous time step and the liquidus and solidus temperatures of the alloy. are solved to estimate the intermediate velocities (u*). After discretization, the Darcy drag coefficient (μK) is added to the diagonal term of the linear equations. In the pure liquid region, this coefficient is zero and thus, it does not have any effect. In the mushy zone, it is finite and non-zero and thus, it acts like a resistance to the flow. In the fully solidified region, it is a large number and thus, the u* tends to zero. From computational efficiency point of view, it is not necessary to solve for u* in the solidified cells since it is zero. Therefore, at each time step, before solving the linearized system of equations, the matrix rows corresponding to solidified cells are removed. As these solidified cells are connected to the neighboring mushy or liquid zone cells, the rows corresponding to the neighboring cells have to be modified in a consistent manner. Consider the row corresponding to cell number 1 in [A1,A2,⋯,A10][ϕ1,ϕ2,⋯,ϕ10]T=[S1,S2,⋯,S10]Twhere, ϕ is any component of u*=[u*,v*,w*]. Originally, ϕ1 is connected to all the neighboring cells from 2 to 10. But since cells 6, 7, 8 and 9 are solidified and their velocity is zero, those rows and columns are deleted from [A1,A2,A3,A4,A5,A10][ϕ1,ϕ2,ϕ3,ϕ4,ϕ5,ϕ10]T=[S1,S2,S3,S4,S5,S10]TSimilar to the momentum equations, the matrix rows corresponding to solidified cells are deleted from the discrete pressure Poisson equation. But in this case, the rows of the neighboring liquid or mushy cells cannot be updated by just deleting the connections of the solid cells as Neumann boundary conditions have to be applied. For any solidified cell, incoming or outgoing flow through all of its faces should be made zero. This is achieved as follows. Each face is shared by exactly 2 cells (face owners). All the cells which share a common vertex with a face are known as its neighbors. The face centered gradient is computed using the values at all connected neighboring cells. For example, cell numbers 1 and 2 are the owners of face F1 whereas, cells 1, 2, 3, 4, 5, 9 and 10 are its neighbors. The following cases arise for each face:None of the neighbor cells is solidified: no change in the face centered gradient coefficient (eg. all the faces of cell number 3) is requiredNone of the owners are solidified but at least one neighbor cell is solidified: flow through the face is allowed but the face centered gradient coefficient has to be modified as the solidified cells are removed from the linear set of equation (eg. faces F1 and F2)At least one owner is solidified: flow through the face is blocked; ∇P·n^=0 thus, contribution of this face in the integrated diffusion term (∯SΓn^·∇PdS) is zero (eg. faces F3 and F4)Consider the face F2 for modification of face centered gradient coefficient. Original coefficients for gradient computation at face F2 which are valid if none of its neighbor cells are solid are given by:[∂P∂x∂P∂y]F2≈[Ax1Ax2Ax3Ax4Ax5Ax6Ax7Ay1Ay2Ay3Ay4Ay5Ay6Ay7][P1P2P3P4P5P6P7]TSince cell numbers 6 and 7 have solidified, their contribution has to be removed from . Thus, the last 2 columns are deleted and those coefficients are smeared equally in the remaining columns for ex., Ax1 is modified to Bx1=Ax1+(Ax6+Ax7)/5 and Ay1 to By1=Ay1+(Ay6+Ay7)/5. Since there are 5 cells remaining, the division by 5 is required. After modification, [∂P∂x∂P∂y]F2≈[Bx1Bx2Bx3Bx4Bx5By1By2By3By4By5][P1P2P3P4P5]TThe steps for modification of the discretized pressure Poisson equation are as follows:Identify the faces with none of the owners solidified but at least one neighbor cell is solidified and smear the coefficients as described aboveIf at least one owner of the face is solidified, set all of its coefficients to zeroIf none of its face coefficients are modified, its coefficients do not changeIf at least one of its face coefficients is modified, re-assemble its coefficientsThese steps remove the contribution of the solidified cells carefully and reduce the computational effort significantly.The collocated finite volume formulation uses the face centered volume fluxes (n^·uΔA) in the continuity equation so as to avoid the checker-boarding of pressure. If there is an inconsistency in the numerical formulation of the pressure Poisson equation and the flux computations, there can be a gain or loss of mass and convergence problems. This section describes a consistent method used in the current code to handle solidification.The volume flux is obtained by taking inner product of the velocity correction at the face center with face normal and multiplying by face area:u*|f is estimated by averaging the cell values from the two owner cells of the face. n^·(∇P)n+1|f is computed exactly in the same way as the regular diffusion term by splitting it into direct diffusion and cross diffusion terms ( with ϕ=P). The face centered pressure gradient required in the cross diffusion term is estimated by the modified coefficients (). This volume flux estimate satisfying the discrete continuity equation to a specified tolerance is used in the convection term (The cell centered velocities do not satisfy the discrete continuity equation. They are computed from and cell centered pressure gradient is estimated by averaging the face centered gradients. which relates temperature with solid fraction is a non-linear model. The easiest way to numerically couple this with the energy equation is to model the Gulliver-Scheil equation fully explicitly as a source term. The problem with an explicit approach is that the source term destabilizes the discretized energy equation due to high magnitude of the latent heat coefficient. Thus, we use the source term linearization concept discussed by Patankar when integrated over time and control volume gives:where, superscripts old and m denote last time-step value and iteration number respectively. The value of solid fraction in the subsequent iteration (fsm+1) can be estimated from its latest value (fsm) by a first order Taylor expansion:∫V∫tLf∂fs∂tdVdt≈LfΔV(fsm+{dfsdT}m[Tpm+1−Tpm]−fsold)=[LfΔV{dfsdT}m]Tpm+1+[LfΔV(fsm−fsold−{dfsdT}mTpm)]=SpTpm+1+ScSp and Sc are functions of last iteration and last time-step values and thus can be computed first. Note that Sp is always negative and when taken to the left hand side of the equation, it becomes positive and is thus added to the diagonal of the linear system matrix. Adding a positive term to the diagonal helps in stabilizing the system and speeds up convergence. Hence, this approach is found to be much better than the fully explicit method.a for a typical aluminum alloy shows that there is a discontinuity at the solidus temperature. Thus, the derivative dfsdT cannot be computed. To deal with this difficulty, the original equation is modified by smearing the discontinuity near the solidus temperature:fs(T)={0ifT>Tliq1ifT<Tsol−Tϵfs^−(T−Tsol−Tϵ)(1−fs^2Tϵ)ifTsol−Tϵ<T<Tsol+Tϵ1−(T−TfTliq−Tf)1kp−1otherwisewhere, fs^=1−(Tsol+Tϵ−TfTliq−Tf)1kp−1 and Tϵ is the width of linear smear which can be set to a reasonable value like 2 K. Thus, the derivative can be computed analytically. b and c plot the modified solid fraction relation and its derivative respectively.The overall iterative procedure to obtain the variables at the new time step from values at the old time step can be summarized as:Compute Sp and Sc using last iteration values (Tpm and fsm) by and solve the linear system of equations to estimate next iteration value Tpm+1Update the solid fraction: fsm+1=(1−λ)fsm+λfs(Tpm+1) where, 0 < λ ≤ 1 is an under relaxation parameter (Note that fs(Tpm+1) is the solid fraction evaluated as a function of temperature at iteration m+1)Estimate the relative change between the successive iteration values of temperature and solid fractionRepeat steps 2–4 until the relative change drops below a desired threshold. For the aluminum alloy used here, it is found that under relaxation is not required i.e., λ=1 and the solution converges in 5–10 iterations.Typical die cast geometries have high aspect ratios i.e., thin cross sections compared to the lateral dimensions. It is found that single grid iterative solvers for the elliptic pressure Poisson equation converge slowly for such geometries. Hence, in this work a multigrid solver is used. The central idea of a multigrid solver is to solve the equations on multiple coarse grids and couple the corrections from all the grids through prolongation and relaxation. The high frequency component of the residual converges fast on the fine grids while the coarse grids are used to accelerate convergence of the low frequency residual. Thus, the coarse grid solutions are used to accelerate the convergence while maintaining the discretization accuracy of the solution at the finest level.Geometric multigrid is a technique in which multiple levels of grids are generated physically and the matrix vector system is estimated by discretizing the governing equations at each level. The main benefit of this approach is that the matrices at all the levels are obtained directly from the governing equations and thus, good convergence is observed. The main drawback is that generating coarse grids for a complex geometry with unstructured elements is non-trivial. Algebraic multigrid (AMG) tries to address this problem by coarsening the matrix using heuristics based algorithms. This is a black box approach which does not need any physical grids at coarse levels.The BoomerAMG routine along with Krylov solvers of the open source library HYPRE without difficulty. However, some consistency issues have been observed during the solution of the pressure Poisson when extensive solidification happens. In complex geometries, as solidification proceeds, there can be disjoint pockets of metal which are yet to solidify. shows an example of the disjoint regions formed near the end of solidification. The area with solid fraction of unity (red in b) is fully solidified and thus, has zero velocity and the pressure is also set to zero. The blue regions indicate liquid/mushy zones which are yet to solidify. These regions are solved with zero normal velocities on their boundaries. Each region is solved with Neumann pressure boundary conditions corresponding to fixed velocities on the boundary. We have checked that the sums of the local sources/sinks of the pressure Poisson equation for individual regions are zero. Thus, the pressure Poisson equation is well formulated whether solved separately for each domain or as a single linear system. As these pockets are far enough from each other, they are decoupled numerically in the discrete reduced pressure Poisson equation (). This is seen to cause convergence difficulties with AMG. The AMG solver has been coupled with a single grid BiCGSTAB solver, also from HYPRE, to be used when AMG is unable to solve the pressure Poisson equation. This issue arises towards the end of the simulation when only a few cells are liquid (for instance 20%). Thus, the reduced system is much smaller in size compared to the original problem and a single grid solver is reasonably well convergent.Grain size and Secondary Dendrite Arm Spacing (SDAS) are two important parameters used to characterize the microstructure. OpenCast uses empirical relations from the literature for estimation of microstructure parameters and mechanical properties such as yield strength.SDAS is predicted based on the empirical relationship proposed by Backer and Wang The model parameters Aλ and Bλ are chosen to be 39.4 and -0.317, respectively based on the model for microstructure in aluminum alloys Here, σ0.2 is in MPa, λ2 (SDAS) is in µm, Aσ=59.0 and Bσ=120.3Grain size estimation is based on the work of where, r is the grain size, Ds is the solute diffusion coefficient in the liquid and t is the time. The parameter λs is obtained by invariant size approximation:where, Cl=C0(1−fs)(kp−1) is solute content in the liquid, Cs=kpCl is solute content in the solid at the solid-liquid interface and C0 is the nominal solute concentration. Thus, using the prescribed partition coefficient (kp) and estimated solid fraction (fs), are solved to get the final grain size.The final product quality in die casting is influenced by process parameters like alloy material properties, interface conditions at the mold, thermal boundary conditions etc. Due to the complexity of the process, accurate measurement and control of these parameters is difficult. Conventional deterministic simulations alone are not sufficient to estimate the effect of any stochastic variations on the product quality, thus parameter uncertainty quantification is important. From modeling point of view, parameter uncertainty quantification is a set of stochastic partial differential equations with variation in initial conditions, coefficients and boundary conditions. Stochastic variables are considered as dimensions of the problem in addition to space and time.To estimate the relation between stochastic process parameters and output parameters, various methods have been proposed in the literature. A popular method is to use a linear combination of polynomial basis functions in the stochastic dimension to expand the output variables. Since orthogonality helps in convergence, orthogonal polynomials are used as basis functions. Wiener’s polynomial chaos ). For all practical purposes, the series is truncated to order n.w(x,ξ(θ))=∑i=0∞wi(x)Ψi(ξ(θ))≈∑i=0nwi(x)Ψi(ξ(θ))where, w is the quantity of interest, x is a vector of all the deterministic inputs including space and time (if applicable), Ψi is the multi-dimensional orthogonal polynomial of order i, ξ is the random variable vector (ξ1,ξ2,⋯ξn) and θ is an elementary event.In this work, stochastic collocation method is used to estimate the deterministic coefficients of the polynomial chaos expansion. Collocation is a non-intrusive method and thus, modification of deterministic software is not necessary. It acts as a wrapper around existing deterministic software. The deterministic simulation is run at M sample points (ξm) and a condition w(x,ξm)=wsim(x,ξm) is imposed. The right hand side comes from each deterministic simulation and left hand side from polynomial expansion. This gives M constraints written in a matrix vector form ) is overdetermined. Solving in the least-squares sense gives [w0(x)⋯wn(x)]T.[Ψ0(ξ1)⋯Ψn(ξ1)⋮⋮Ψ0(ξM)⋯Ψn(ξM)][w0(x)⋮wn(x)]=[wsim(x,ξ1)⋮wsim(x,ξM)]Sample points (ξm) have to be chosen wisely for successive implementation of stochastic collocation method. For instance, uniformly distributed samples can lead to highly oscillatory basis functions and thus poor convergence. Thus, for one dimensional stochastic problems The strategy described above is quite general and can be applied to any numerical solution framework. In this case, the output variables (w of ) are temperature and microstructure parameters like grain size and dendritic arm spacing. The stochastic input parameters are boundary conditions, initial conditions and alloy and material properties. The polynomial chaos expansion with stochastic collocation is combined with the deterministic computational fluid flow and heat transfer solver to estimate the sensitivity and uncertainty propagation.Due to the complexity of the die casting process, controlled experiments with accurate temperature measurements inside the casting during solidification are difficult. To validate our code, we have therefore used the experimental results of ingot solidification made of Sn–Bi alloy reported by Quillet et al. As a first step, validation was attempted without incorporating the effects of uncertainty. a plots the experimental measurements of temperature from the 25 thermocouples as a function of time beginning from solidification. b is the computed plot assuming a constant conductivity at an averaged temperature, while is the corresponding plot with temperature dependent thermal conductivity. It is seen that both the computed deterministic thermal histories do not compare well with the experimental data.Local values of the thermo-physical properties such as thermal conductivity and density depend on grain structure. At the length scale of current simulation, it is not possible to predict the grain structure and hence the properties from first principles. Thus, there can be some uncertainty in the input properties. Also, when the alloy solidifies and cools, there is a thermal contraction. This creates a gap between the mold wall and the casting and adds thermal contact resistance, reducing the amount of heat extracted. Further, the experimental measurements are also subject to sensor noise. For example, the thermocouples used by Quillet et al. The specific heat plays a role only in the energy equation. When the energy equation is divided by product of density and specific heat, the thermal diffusivity (kρCp) is a coefficient of the diffusion term and the ratio (LfCp) is the coefficient of the latent heat term. Thus, introducing uncertainty in any two parameters is sufficient. Hence, thermal conductivity and latent heat are chosen to introduce uncertainty. Additionally, density is also modeled as a stochastic quantity since it is a part of the momentum equations. Considering stochasticity in specific heat is not required as it does not add any new information to the problem. Uncertainty is therefore added only to wall temperature, latent heat, density and thermal conductivity. Since it is difficult to estimate the thermal contact resistance, the wall temperature is specified as a Dirichlet boundary condition by adding an offset to the cooling rate of 5 K/min. The offset is estimated from the experimental temperature plot (a). In order to take into account the errors in the temperature measurement, an uncertainty is added on top of the offset. All the four input stochastic parameters are assumed to follow a normal distribution with mean (μ0) and standard deviation (σ0) as follows:Wall temperature offset: μ0=0∘ C, σ0=0.5∘ CTemperature dependent thermal conductivity: μ0=[61.282,57.42,30.1,37.7] W/mK, σ0=[2.5,2.5,2.5,2.5] W/mK at temperature [273.2, 373.2, 573.2, 973.2] KAll the thermo-physical properties are estimated as a weighted average of individual properties of Sn and Bi taken from the online version of Kaye and Laby In order to make a comparison with the experimental data, the experimental temperature-time data plot (a) is digitized. Since it is difficult to distinguish between the 25 temperatures, the thermocouple with the highest temperature is used for validation. Stochastic collocation is done with three accuracy levels of sample points in order to study its convergence. For estimating the interpolation error, 60 Latin Hypercube samples are used as test points. Deterministic simulations and polynomial chaos give two independent estimates of the same output parameter at the test points. The non-dimensional error is defined as the root mean square of difference between these two estimates divided by the maximum value of the parameter. First column of denotes the accuracy level of sample points. Accuracy level l integrates polynomials upto order 2l−1 exactly ). The last column lists the non-dimensional RMS error in computation of the temperature. It can be seen that the error is of order 10−4 for all the accuracy levels and it decreases with increasing level thus, showing convergence. Hence, level 6 is used for validation.The Polynomial-Chaos-Kriging (PCK) module of UQLab plots the maximum temperatures (with error bands) from OpenCast simulations and experiments ). This effect starts near the solidus line and continues for around 200 s beyond which again the curves overlap. Thus, except for the initial 60 s and near the solidus line, the agreement is good.This study validates solidification with the fluid flow due to natural convection and heat transfer models implemented in OpenCast since all these phenomena occur in the experiments. It should however be noted that the microstructure parameters and yield stress empirical models are directly taken from the literature. Validation of these models is normally done by conducting solidification experiments.In order to demonstrate the utility of the developed software, some complex die casting geometries were simulated. Most of the die casting geometries have thin cross section and thus, the solidification times are of the order of s. For any geometry, before starting uncertainty quantification, simulations are performed for two cases: with and without natural convection and a comparison is made to assess the effect of natural convection. lists down various outputs for the clamp geometry simulated with and without natural convection. The maximum and minimum are taken over the entire physical domain. The same outputs are used for uncertainty quantification in this work. It can be seen that the effect of natural convection is insignificant. Same thing is observed for the pulley geometry. Thus, simulating without natural convection is acceptable as it saves significant computational effort. Hence, in all the simulations of this section, natural convection was neglected. However, in other processes such as sand casting, natural convection can be important. Therefore, OpenCast is validated with natural convection so that it can be applied for simulation of other casting processes. Note that the validation is performed for a Sn–Bi alloy whereas, the subsequent results presented here are for an aluminum alloy. Aluminum alloys are the most common in die casting and thus, such an alloy is used for deterministic and stochastic simulations in this paper. For validation, it is difficult to measure temperatures inside the casting during solidification of die casting. Thus, we used experimental solidification data from the literature which was available for a Sn–Bi alloy. Since the focus of validation is on the temperature evolution with time, the alloy used is immaterial as long as appropriate material properties are specified in the simulation. shows the hexahedral grids of two selected geometries. Both the clamp and the pulley have approximately 300,000 control volumes each. Initially, the mould is filled with a liquid alloy at 1000 K and the walls are held at 500 K. Aluminum alloys with around 8–12% Silicon content are popular in die casting. Thus, for this simulation, an Al-10%Si binary alloy is chosen. The liquidus, solidus and freezing temperatures are taken from the phase diagram. plots the temperature contours for the clamp geometry along the mid-plane in Z-direction at different time-steps during the solidification. shows the corresponding solid fraction contours. plots micro-structure parameters SDAS, grain size and yield strength estimated using the previously described empirical models. As time progresses, the cooling rates and temperature gradients decrease. Hence, the regions with highest thickness or the core take longer time to solidify. The core regions typically have higher SDAS, grain size and lower yield strength as the grains have longer time to grow. Such trends are seen in . The pulley is axisymmetric in geometry and loading conditions. Thus, SDAS, grain size and yield strength are plotted only along the XY plane as shown in . Even for this case, the core region has higher SDAS and grain size and lower yield strength.The clamp geometry is subsequently used to study the effect of stochastic variation in the process parameters on the outputs. The process parameters which can be tuned in a die casting foundry are alloy composition (the solute percentage), initial melt temperature and the wall temperature. It is assumed that these three parameters follow normal distribution (N) with the following means (μ0) and standard deviations (σ0):Solute concentration C0∼N(μ0=10,σ0=0.2) wt %Initial molten alloy temperature Tinit∼N(μ0=1000,σ0=1%μ0=10) KWall temperature Twall∼N(μ0=500,σ0=1%μ0=5) KThermal properties like thermal conductivity, density and specific heat are estimated as a weighted linear combination of the properties of aluminum and silicon with solute concentration as the weight. Since there is a significant variation with temperature The impact of the three input parameters is studied on the following four outputs: where, the maximum or minimum is taken over the entire domain. The polynomial chaos method with stochastic collocation described in is used for uncertainty propagation. The error due to stochastic interpolation is estimated using 60 Latin hypercube samples. Estimates of the same output are obtained from the complete simulation and the polynomial chaos expansion (PCE) independently. The difference between these quantities non-dimensionalized by their mean value is defined as the error. Since the errors in estimating all the four outputs reduce by using higher accuracy levels (), it can be seen that the collocation method has converged. The results presented correspond to the accuracy level 6. In order to get an idea of the interpolation error visually, both the simulation and PCE estimates can be plotted on the same graph. In the hypothetical scenario of exact interpolation, all the points should lie on the Y=X line. However, there is a deviation from the line because of the interpolation error. shows plots for each of the four outputs. Each output is normalized by subtracting its mean and dividing by its standard deviation and thus, is non-dimensional. Most of the points follow the trend of the Y=X line except some outliers. The outliers correspond to those random samples which are too far from the means of the input parameters. prove that the polynomial chaos has converged and is accurate enough for further use.A brief grid independence study is performed in order to make sure that the mesh resolution is sufficient and that the truncation errors are smaller than the uncertainty. Two unstructured hexahedral grids are chosen and the four outputs are evaluated. shows that the difference between the coarse and fine grid estimates of all the four outputs is much smaller compared to the final stochastic variation in the outputs.Sensitivity of each output with respect to each input can be easily estimated once an accurate polynomial chaos expansion is obtained. The sensitivity analysis tool of the software UQLAB ). It can be seen that each output is highly sensitive only to one input parameter. Sensitivity is practically important as it gives an idea as to which input parameter should be tightly controlled. Thus, other parameters can be loosely controlled saving cost but yielding desired product quality at the same time. The amount of heat extracted from the wall is proportional to the temperature gradient near the wall and hence, solidification time is highly sensitive to the wall temperature. On the other hand, the microstructure parameters like SDAS, yield strength and grain size depend on the solute concentration. Thus, these three parameters are more sensitive to solute concentration than the wall and initial temperatures.), the most important input is plotted on the x-axis. For solidification time response surface, the wall temperature (x-axis) and initial temperature (y-axis) are chosen. For other three outputs, solute concentration (x-axis) and wall temperature (y-axis) are chosen. It can be seen that all the response surface contours are nearly vertical. This confirms that the output is most sensitive to the input parameter plotted on the x-axis. The maximum grain size contours are non-linear. This implies that the sensitivity varies locally in the input parameter space. For other three outputs, the contours are almost linear and thus, it can be concluded that the local sensitivity is similar everywhere and independent of the input parameter value.This paper describes a numerical software framework OpenCast for simulations of solidification problems, including natural convection. Microstructure parameters and mechanical properties are estimated using published empirical relations. The flow equations are solved only in the liquid zone by modifying the coefficients of the discrete equations. The algebraic multigrid solver together with a Krylov subspace solver is used to solve the pressure Poisson equation. Complex geometries are meshed with unstructured hexahedral elements. Parameter uncertainty quantification is used as a wrapper over the deterministic simulations in order to assess the effect of stochastic variations in the inputs on the outputs.The software is validated against published experimental results of solidification. This validation study shows the significance of stochastic analysis since it is observed that validation without uncertainty is unsuccessful. The validated software is used to simulate two practical die casting geometries. Sensitivity and uncertainty analysis is also performed. Sensitivity analysis shows that the product quality given by grain size and yield strength is highly sensitive to the solute concentration whereas, the productivity given by the solidification time is sensitive to the mold wall temperature. These results are practically useful as it gives an idea about the important input process parameters. The response surfaces show the variation of the outputs with the important input parameters. They can be used to get quick estimates of the outputs without running full deterministic simulations and also to get local sensitivities.Although this paper demonstrates the ability of OpenCast to simulate die casting problems, it is a general purpose software. OpenCast can also be used to simulate other manufacturing processes such as sand casting, additive manufacturing, welding etc. The use of unstructured elements together with algebraic multigrid method adds complete flexibility to simulate arbitrary geometries. The coupling of uncertainty and sensitivity analysis tools enhance the power of the deterministic numerical method.Effect of processing parameters on microstructure and properties of tungsten heavy alloys fabricated by SLMSelective laser melting (SLM) was used to fabricate tungsten heavy alloy (WHA) with a nominal composition of W-7Ni-3Fe (wt%). Depending on the processing parameters (laser power, scanning speed, preheating, etc.), three different bonding mechanisms were observed, i.e., liquid phase sintering, partial melting and complete melting. The difference in applied energy density also reflected in a variation of the final composition, amount of W dendrites in γ-phase and the W grain contiguity. High density materials (>95%TD) were produced under optimal processing conditions. The effect of the as-built microstructure and post-process heat-treatment on the properties of WHA processed by SLM was evaluated. In the as-built condition, the WHA exhibited an UTS of 871 ± 30 MPa with a brittle fracture behaviour regardless of the applied processing parameters. With a suitable post-process heat-treatment, a material with a more optimal microstructure was obtained, with properties comparable to those of WHAs produced by conventional powder metallurgy (UTS of 850 ± 21 MPa with an elongation of 10.2 ± 1.0%).Tungsten heavy alloys (WHA) are two-phase composites of tungsten with a transition metal binder (Ni, Co, Fe, and Cu) in various combinations, namely W]. Due to the outstanding combination of properties such as high density (16–18 gcm−3), strength (1000–1700 MPa), ductility (10–30%), thermal conductivity, and good corrosion resistance, WHAs are widely used as counterweights, rotating inertia parts, X-ray and γ-radiation shields, collimators, rigid tools for machining, as well as for defence purposes (kinetic energy penetrators, fragmentation devices, etc.) [] and are even considered as plasma facing components in fusion reactors []. The properties of WHA and their consequential use depend mainly on the tungsten content (ranging from 80 to 97 wt%) and the exact composition of the binder phase. WHAs are typically fabricated by conventional powder metallurgy (PM) techniques. Pressed powder compacts are sintered to final density, usually at 1480–1500 °C in (wet) hydrogen atmosphere where the binder forms a liquid phase through eutectic reactions with tungsten [Selective laser melting (SLM) is an additive manufacturing technique which enables fabrication of 3D parts with high geometrical complexity by sequential deposition of powder layers, selectively fused together with a focused laser beam according to a predefined computer model. By utilizing a high energy density laser, even refractory metals like Mo []. However, SLM of W remains challenging due to the high melting point, high thermal conductivity, high melt viscosity, its affinity for oxygen at high temperatures and brittle nature at room temperature, resulting in cracked and porous microstructures []. Addition of a low melting point binder phase, as in the case of WHAs, can facilitate the densification and potentially lead to high density crack-free parts. Literature reports on additively manufactured WHAs mainly focused on compositions with high binder concentrations (≥20 wt%) in the W] systems, fabricated by direct laser deposition or laser sintering. For the W-7Ni-3Fe system investigated in this paper, literature data on SLM is rather limited. Zhang et al. [] observed melt pool instability and dendrite formation during processing with a 100 W laser, but the final density of the material was not reported. Wang et al. [] concluded that a high energy density needs to be applied to achieve a high degree of densification for W-7Ni-3Fe processed from a premixed powder. One of the main challenges in processing WHAs by SLM lies in the immense differences in thermo-physical properties between tungsten and the elements of the binder phase (). The melting temperatures (Tm) of the binder elements are much lower in comparison to tungsten, whose melting point exceeds even the boiling temperature (Tb) of Ni and Fe. According to the Ni-Fe-W ternary phase diagram [], an eutectic phase is formed at 1465 °C, with gradual increases in tungsten content until complete melting is achieved above 3200 °C. Due to the very high binder element vapour pressures above the melt with increasing temperature, preferential evaporation of binder elements can be expected during SLM.In the present work, the effect of various processing conditions, build platform preheating and post process heat treatment on the microstructure and properties of selective laser melted W-7Ni-3Fe WHAs were investigated.Spherical tungsten (TEKMAT W-45, TEKNA, d50 = 30.6 μm), nickel (Ni-110, AEE; d50 = 4–8 μm) and iron (CIP SE, BASF; d50 = 3.4–4.5 μm) powders were mixed in sealed polymer containers under argon atmosphere using a multidirectional mixer (Turbula T2F, WAB) for 24 h. The powder mixture contained 90 wt% W with a Ni/Fe ratio of 7/3 which corresponds to Class 1 tungsten heavy alloy (ASTM B777–15). The flowability of the powder mixture was assessed by Hall flow meter (ASTM B213–17) and angle of repose (AoR) measurements. Particle size distribution was measured by laser diffraction (LS 13320, Beckman Coulter).Selective laser melting was conducted on an in-house developed machine, equipped with a 1 kW Nd:YAG laser with a wavelength of 1.070 μm. The machine is also equipped with a preheating module which enables preheating of the baseplate up to 400 °C []. All experiments were conducted in a flowing Ar atmosphere with an oxygen content in the chamber <50 ppm. All samples were built on a stainless steel substrate.To evaluate the effect of the processing conditions (laser power, scanning speed, hatch spacing and scanning strategy) on the microstructure and densification, cube shaped test samples of 10 mm3 were fabricated using a bidirectional (“zig-zag”) scanning strategy, an intra-layer misorientation of 67° and sequentially depositing layers with 30 μm layer thickness. File preparation, positioning and slicing was performed with Magics software (Materialize, Belgium). The laser energy density parameter (E) was used to compare the different parameter sets and their influence on the densification.where P is the applied laser power [W], v scanning speed [mms−1], t layer thickness [μm] and h hatch spacing [μm]. To evaluate the effect of preheating, a set of experiments was conducted with a preheated baseplate of 400 °C.After fabrication, parts were removed from the baseplate by wire electrical discharge machining (EDM) (GF Cut E600, AgieCharmilles). The density of the produced parts was measured by the Archimedes method in ethanol using lacquer encapsulation (Enplate Stop-off No.1, Enthone) in case of open porosity. Theoretical densities for W, Ni and Fe of 19.250, 8.908 and 7.874 gcm−3 respectively, were used to calculate the density of the WHA using the rule of mixtures. The surface of the as-built samples and polished cross-sections were examined by optical and scanning electron microscopy (SEM, XL-30 FEG, FEI Dual Beam). EDXS analysis (Oxford Instruments) was performed on polished cross-sections to determine the final composition of the material after SLM. EPMA (JXA-8530F FEG-EPMA) was used to determine the exact composition of selected samples. Post-process heat-treatments were conducted in a high temperature box furnace (HT 1800, LINN) under dry hydrogen atmosphere up to 1500 °C for 30–60 min. During cooling, the atmosphere was changed to argon to avoid hydrogen embrittlement [The morphology of the used powder mixture is shown in . After mixing, Ni and Fe powders with smaller particle size were distributed among larger spherical W particles. A small fraction of Ni and Fe powder also adhered to the surface of the W (inset in a) spheres. Therefore, the resulting powder mixture had a bimodal particle size distribution (b), with a slight increase in the larger fraction (30–40 μm), due to adhered particles, and a broad distribution of smaller particles (1–20 μm). The addition of smaller powder fractions deteriorated the flowability of the powder mixture in comparison to pure W powder. Nevertheless, the measured angle of repose of the powder mixture was only 35.5 ± 2.3° and satisfactory stable layers could be produced during powder spreading.Density optimisation was carried out by varying the process parameters in a broad range of laser power (50–350 W) and scanning speed (100–600 mms−1). The majority of the samples had an in-plane crack at the bottom part of the cube, typically close to the build platform (). Crack formation can be related to the build-up of residual stress and baseplate preheating was suggested as one of the most effective ways to mitigate this type of cracking []. Therefore, with the aim to prevent cracking, baseplate preheating up to 400 °C was evaluated. Unfortunately, in the case of WHA, the use of preheating did not have the desired effect and the amount of cracks in the final material increased, especially near the surface of the samples.b) of the as-built samples witout and with preheating shows the presence of W and smaller peaks at 43.4° and 50.5° corresponding to the formed γ-phase. In contrast to the SLM-ed parts, the starting powder mixture contains only peaks for W, Ni and Fe. The height of the γ-phase peaks in the sample produced with preheating is comparably smaller indicating that less binder remained in the final part.The morphology of the melt pool observed at the top surface of the as-built samples was unstable (), with poor spreading of the melt. When applying higher energy densities and especially when slow scanning was used, the stability of the melt pool was improved and individual scan tracks could be discerned (b). However, the overall melting behaviour was still unstable, especially in comparison to pure W [In order to elucidate the melting behaviour of the material during SLM, selected single-track experiments were performed. Apart from the typical meltpool shape, consisting of a melted track on the surface and a meltpool volume in the substrate, a large amount of unmelted W particles bound by a binder phase was observed on both sides of the track in a similar manner as was observed at the sides of the parts (see ). The following laser track would scan on the already bound powders with variable height, resulting in an uneven surface. This, in combination with keyhole defects observed in the melt tracks at higher laser powers, led to a high surface roughness and consequently poor powder spreading, bridging effects and lack-of-fusion porosity (Furthermore, upon cooling, tungsten solidifies first in the form of tungsten dendrites, causing the viscosity of the melt to increase significantly [] over the solidification temperature range of the molten binder. The increased viscosity, in combination with an inward flow of metal due to a higher surface tension towards the centre of the meltpool, oppose the spreading of the melt. Therefore, in order to obtain a stable scan track with sufficient melt spreading and overlap, low scanning speeds have to be applied. The need for low scanning speeds to obtain a high density part was also observed experimentally, however, too low scanning speeds caused deformation of parts (curling, delamination).After SLM, the produced parts had a layer of powder sintered at the sides, around the initial sample contour (). The effect was especially pronounced at high energy density or when preheating was applied. There is a clear correlation between the thickness of the adsintered powder layer and the applied energy density (b). The microstructure of the adsintered layer reveals that the surrounding Ni and Fe powder were melted, which resulted in liquid phase sintering of the surrounding powders. The Rosenthal equation [] was used to analytically correlate the processing parameters to the extent of the heat affected zone where only the binder phase is melted (1436–3250 °C). The analytical solution in the case of specimens fabricated without preheating is in good agreement with the experimental data. When preheating was used on the other hand, the experimental thickness of the adsintered layer exceeds considerably the predicted value, which is merely 35% higher than without preheating. Although, the exact cause for the high amount of sintered powder is unclear, a possible explanation can be linked to the increase in crack susceptibility. A higher crack density lowers the heat conduction and consequently increases the temperatures in the part and surrounding powder bed.The adhered powder could be easily removed by sandblasting, however when building more complex shapes with internal structures, this feature has to be taken into account.Densification followed a similar trend as was described by Wang et al. [], requiring a high energy density (> 300 Jmm−3) to obtain maximum densification. As is evident from , the density increased with increasing energy density from 12.9 gcm−3 at 40 Jmm−3 up to 16.5–17.5 gcm−3 at 300 Jmm−3 where it reached a plateau. The large scatter in measured densities at high energy densities corresponds to different processing conditions - a higher density was achieved at slow scanning speeds. Surprisingly, a similar trend was also observed for the composition, where the amount of tungsten was reduced in comparison to the initial powder mixture at low applied energy densities (see b). The uneven surface due to the incomplete melting, combined with poor spreading of the powder led to the formation of lack-of-fusion defects. During the deposition and melting of successive powder layers, some of the molten binder phase most likely infiltrated the residual pores, thus contributing to a higher binder content.Conversely, in the case of WHA fabricated at high energy density, and especially with baseplate preheating, where full melting of all constituents was observed, the amount of tungsten in the final composition increased to 97 wt%. This can be attributed to Ni and Fe evaporation during processing, as the melting temperature of tungsten exceeds the boiling temperatures of Ni and Fe (). With the addition of preheating to 400 °C, the overall processing temperature is increased and therefore, the amount of evaporated binder elements is higher.The microstructure of WHAs processed by SLM varied significantly with respect to the used processing conditions (). According to the classification proposed by Kruth et al. [], three major binding mechanisms were identified: liquid phase sintering, partial melting and complete melting.At low applied energy density (<200 Jmm−3), only nickel and iron powders were melted and formed a binder phase between the non-melted tungsten particles which predominantly retained their initial size and shape (a), analogously to the conventional liquid phase sintering. Due to the rapid nature of SLM, the densification is governed by wetting and particle rearrangement. However, as the amount of binder phase (~20 vol%) is insufficient to form a dense material (minimum 35 vol% of liquid phase is required in case of a chemically stable solid phase) [], the samples produced with low applied energy density exhibited a high residual porosity with lack-of-fusion type defects.With an increased energy density (>250 Jmm−3), partial melting and dissolution of tungsten resulted in higher density values. Wang et al. [] noted that longer solidification times as a result of high laser input are beneficial for densification as they facilitate particle rearrangement in the liquid NiFe binder. However, with increased energy density, the melting and densification behaviour is clearly far more complex and cannot be described merely by rearrangement mechanisms. Melting and reprecipitation of tungsten during solidification as well as binder evaporation contribute to a higher final density. As shown in b, a layered microstructure was obtained, with complete melting on top and un-melted W particles in the binder phase at the bottom of the melt pool (). Upon solidification the dissolved tungsten precipitated in the form of W dendrites in the binder phase (The formation of W dendrites was already observed by several authors during SLM of different grades of WHA []. However, due to the broad distribution of dendrite size and orientation, no clear conclusions can be made regarding the solidification behaviour (solidification rate, direction). The resulting microstructure is most likely the consequence of unequal uneven conditions during SLM due to differences in composition and surface roughness (see ) and remelting of the binder phase during the melting of succeeding layers.With preheating, the melting behaviour was completely different, which resulted in complete melting and a unique microstructure (). The effect of preheating on SLM of WHA was already discussed by Zhang [], who predicted complete melting with high applied energy and/or the use of preheating based on FE simulations. However, when only a high energy density is used without preheating, deformation of the samples prevents a successful fabrication of parts.With baseplate preheating at 400 °C, the increase in the maximum process temperature led to complete melting of all constituents, accompanied by an enhanced evaporation of binder elements (b). The amount of binder phase was reduced and was located primarily along the grain boundaries as well as small “precipitates” within the W grains (With complete melting, the amount of cracks in the material increased, especially near the surface of the samples which can be attributed to an almost complete continuity of the tungsten phase and thus intrinsically more brittle material.Based on the discussed microstructure and the final composition of the WHA, the processing parameters can be divided into three groups, as depicted in . At low E (< 200 Jmm−3), the microstructure is governed by liquid phase sintering and the resulting material has low density with lack-of-fusion porosity. At high E (>350 Jmm−3), higher density samples could be produced, however with an increased crack density and distortion (curling, warping). A higher E also resulted in a higher amount of sintered powder around the sample contour and evaporation of binder elements, thus altering the initial target composition. Optimal processing conditions were determined in the E region between 250 and 350 Jmm−3 (laser power of 150–250 W and scanning speed of 200–400 mms−1), where samples with targeted composition and high density (>16.2 gcm−3) could be obtained. In general, lower scanning speeds resulted in a better melt spreading and lower surface roughness values.A post-process heat-treatment was applied in order to obtain a more homogeneous microstructure and eliminate the remaining defects. During heat treatment, spheroidized tungsten grains are formed by dissolution and reprecipitation of W from the binder phase (), the microstructure was comparable to the microstructure of liquid phase sintered WHAs [] with rounded W grains embedded in a W-Ni-Fe binder (γ-phase) (b). EPMA analysis of the binder and W grains revealed that the γ-phase contains 22 wt% W, while the W grains contained traces of Ni. A comparable microstructure was obtained regardless of the initial microstructure of the as-built material. However, a larger shrinkage was observed (up to 4% for samples with 87% initial density) with inhomogeneous distribution of W and residual defects (unfilled pores) in the final material in case of an initially more porous sample.Properties of the as-built and heat treated WHA are summarized in The tensile properties were evaluated on the as-built as well as heat-treated WHA. As built WHA were produced with optimal conditions (e.g. P = 250 W, v = 400 mms−1) where the targeted composition (90 wt% W) and high density (>95%TD) could be obtained.The non-uniform microstructure and high tungsten contiguity throughout the as-built material resulted in a high hardness and a brittle fracture behaviour. The ultimate tensile strength (UTS) of the as-built WHA was 871 ± 30 MPa (b) with a total elongation below 1%. The fracture surface of the as-built material is depicted in , where intergranular fracture is observed with evidence of residual porosity.After heat treatment, a typical WHA microstructure is obtained with a more ductile fracture behaviour with UTS of 850 ± 21 MPa and 10.2 ± 1.0% elongation (b). The fracture surface of the heat treated WHA reveals a mixed mode of fracture comprised of cleavage of the W grains and ductile tearing of the binder phase (b). Furthermore, the reduced W connectivity in the heat-treated material can also be related to the decrease in resistivity, E-modulus and hardness after heat treatment.The overall properties of the heat treated WHA are comparable to LPS sintered WHAs in the as-sintered state []. In order to obtain optimal mechanical properties with enhanced elongation, subsequent solution annealing and quenching (typically applied for the LPS materials) would be required to further decrease the contiguity of tungsten grains and avoid impurity segregation at the tungsten binder interface []. Further optimisation of the heat treatment cycle by lowering the sintering temperature and prolonging the heat-treatment time, might also result in a material with reduced W grain size which is also beneficial for tensile behaviour of the material.High density tungsten heavy alloy with a nominal composition of 90 wt% W with a Ni/Fe binder ratio of 7/3 was successfully produced using selective laser melting. Three distinct bonding mechanisms were observed depending on the applied energy density – liquid phase sintering (<200 Jmm−3), partial melting, and complete melting (>350 Jmm−3, with preheating). At optimal processing conditions (250–350 Jmm−3), high density (>16.2 gcm−3) material could be produced. When the applied energy density was too low, the density of the WHA was low and the amount of binder phase in the final parts increased in comparison to the initial powder composition. On the other hand, at higher applied energy, and especially with applied preheating of 400 °C, W-rich WHA was produced due to evaporation of Fe and Ni. Complete melting of WHA during SLM and the formation of a unique microstructure consisting of W grains with a γ-phase binder present in small intragranular precipitates along the grain boundaries was observed. With increased applied energy density, the amount of cracks in the material increased. Due to the change to complete melting and formation of a more brittle material, preheating to 400 °C was not successful in preventing the formation of cracks.In the optimal as-built condition with an energy density of 250–350 Jmm−3, the WHA exhibited an UTS of 871 ± 30 MPa with a brittle fracture. However, with a suitable post process heat treatment (30–60 min at 1500 °C in H2), the microstructure and the properties of the SLM WHA parts are comparable to those produced by conventional powder metallurgy (UTS = 850 ± 21 MPa with 10.2 ± 1.0% elongation).Stress–strain relations in elastoplastic solids with Dugdale-type cracksMechanical behavior of a two-dimensional elastoplastic solid with rectilinear cracks is investigated. Plastic strip model is used to reduce plasticity problem to the equivalent linear elasticity formulation. Two realizations of the mixed mode plastic strip model are considered: in-line plastic strips as proposed by Becker and Gross [Int. J. Fract. 37 (1988) 163], and inclined plastic strips of Panasyuk and Savruk [Appl. Mech. Rev. 47 (1994) 151]. The effective mechanical response predictions are based on the procedure presented in Kachanov et al., [Appl. Mech. Rev. 47 (1994) 151]. Stress–strain relations are obtained for parallel and randomly oriented non-interacting cracks. Results are compared with known elastic solutions.The effective properties of the elastic material with cracks are well investigated in literature (see, for example, review of Kachanov The effect of plastic deformation on the stress distribution around cracks can be included using the plastic strip model originally proposed by Dugdale To analyze the overall behavior of elastoplastic solid with cracks the following micromechanical approach is used. We select a representative area A that contains a statistically representative number of cracks and calculate its total (macroscopic) strain . As discussed, for example, in Kachanov et al. in the crack-free material and the additional strain where the additional strain due to the presence of each 2D crack is expressed in terms of the crack opening displacement (COD) function are the dyadic products of two vectors.For a solid with multiple cracks, we accept the non-interaction approximation, and obtain the stress–strain curve by evaluation of every crack’s contribution into the total strain. Note that the approximation of non-interacting cracks in elastic materials remains accurate even at relatively high crack densities, see Kachanov The outline of the paper is as follows. describes the plastic strip model which reduces elastoplastic problem to elastic one by accepting the stress distribution law in the plastic zone. The model allows to obtain analytical solution for a solid with parallel cracks and to develop an efficient numerical procedure for non-parallel cracks under arbitrarily inclined tension. The elastoplastic response (stress–strain dependence) of solids with multiple parallel cracks is studied in . Materials with randomly oriented cracks are analyzed in . Dependence of the effective response on both crack density and load-to-yield-strength ratio is investigated.As an illustration of the plastic strip approach, let us consider a rectilinear crack in mode I loading. It is assumed that the crack of length 2l0 is located in the infinite 2D solid having Young’s modulus E, Poisson’s ratio ν and plastic yield strength σY. The solid is subjected to the remotely applied tension p. According to classical Dugdale model, the crack with plastic zones at its tips is represented as one fictitious cut of length 2l with the following distribution of traction on its faces (To find the COD using well-developed elasticity technique, the problem with boundary conditions can be represented as a superposition of two problems: (A) infinite homogeneous solid under stress p and (B) solid with no stresses at infinity and tractions on the crack contour that are obtained by subtracting p from the right-hand side of Eq. . Problem (A) is formulated for continuous solid and will not generate any crack opening. Thus for the purpose of current study only problem (B) must be considered.where E′ denotes the Young’s modulus E for plane stress, and E/(1−ν2) for plane strain. Application of the Muskhelishvili The length of the fictitious cut in Dugdale model is expressed by the following formula to derive the effective stress–strain relations for the elastoplastic solids with mode I cracks.There are two approaches to model elastoplastic cracks under remotely applied mixed mode loading. The approach proposed by Becker and Gross assumes that the plastic strips are located on the continuation of the crack line for any loading. Also, the stresses in the plastic zone σ0 and τ0 satisfy von Mises yield criterion. Then, the COD under the remotely applied stresses σxx∞, σyy∞, τxy∞ is given byAn example of the COD calculated using formula This analytical solution for mixed mode loading is obtained under the assumption that plastic zones are parallel to the initial cut. However, plastic zone orientation is dependent upon the direction and magnitude of external load. An efficient approach to account for this dependence using plastic strip model was proposed by Panasyuk and Savruk where traction pn specified on the faces of Ln is determined by a yield stress of the material σY. This traction and the choice of local coordinate system is illustrated in . Note that real and imaginary parts of traction pn in Eq. correspond to y and x components of pn in the local coordinate system xnOnyn. This model thus reduces the elastoplastic formulation to the problem of 2D elasticity for a branched cut with a given traction on its faces. The 2D elasticity problem is tackled using complex variables approach as described in Muskhelishvili where tn∈Ln, and overbar denotes the complex conjugate. Savruk where (un+−un−) and (vn+−vn−) are the x and y components of the COD vector in the local coordinate system.Let us examine the solid containing a crack directed along x-axis (α0=0). Uniaxial tension p is inclined at angle γ (). For this loading, only one plastic strip appears at each tip of the crack, i.e N=2. Note that due to symmetry, α1=α2−π. The elasticity problem for a three-section cut with traction σY acting on the contours of the side cuts is reduced to the system of singular integral equations as follows. First, we introduce functions ϕ0(ξ)=g′0(l0ξ), ϕ1(ξ)=g′1(l1ξ). Note that the argument of these functions changes from −1 to 1. The stress potentials Φ and Ψ are expressed in terms of these functions and substituted into boundary conditions . Due to the symmetry of the problem, L1=L2, g′1(t1)=g′2(t2) and the system of singular integral equations for ϕ0, ϕ1 is obtainedHere pr=−p(1−exp(2i(γ−αr)))/2 and the explicit formulae for kernels Mnk(ξ,η) and Nnk(ξ,η), n=0,1; k=0,1,2 are presented in . The condition of displacement single-valuedness must be added for the system are solved using the numerical procedure based on the following quadrature formula:where ξk=cos((2k−1)π/2N), k=1,2,…,N and ηm=cos(πm/N). As this formula is applied to the singular integrals in Eq. , the integral equation system is reduced to the system of linear algebraic equations for unknowns ui(ξk)=ϕi(ξk)(1−ξk2)1/2, i=0,1:After the system is solved, the COD for ith cut is interpolated over the values of ui(ξk) at the nodes ξk of quadrature formula In this formula, Tr(x)=cos(rarccos(x)), x∈[−1,1] and the constant Ci is defined by the opening at the end of the ith cut, i=0,1,2. The example of the COD calculated using this technique is shown in contains plastic strip length l1 and angle α as unknown parameters. Thus the system must be solved by successive approximations, using the condition that the stress intensity factor is equal to zero at the end of the plastic strip:The optimization problem for the system of linear equations with two unknown parameters α and d=l1/l0 is solved efficiently using the Nelder–Mead simplex method implemented in Matlab In this section, we analyze a solid with a family of parallel cracks, arbitrarily oriented with respect to the applied load. We use the plastic strip model to estimate the effect of plastic zones at the crack tips on the stress–strain behavior. When stress σij is applied, the total strain response is represented as the sum of εij0, the elastic strain of a uniform solid, and Δεij, the additional strain due to cracks (Eq. ). Part of this additional strain is caused by initial cuts, and part is produced by plastic strips. The influence of plastic deformation on the effective response is the main focus of this paper.The contribution of each crack into the effective mechanical response is given by integral . For mode I crack (uniaxial tension σ22=p), this integral is calculated in closed form using the expression for the displacement function. The only non-zero component of additional strain is Δε22, since there is no relative displacement of crack faces in x1 direction:For multiple non-interacting cracks, we assume that each crack is placed in the external stress field undisturbed by the presence of other cracks. Then, the total additional strain of a representative area may be obtained by summation of the additional strains from all individual cracks. To characterize the density of cracks in 2D solid, the crack density tensor (see where the summation over the number of cracks in the representative area A is performed. For parallel cracks, the traditional scalar crack density parameter can be usedThus, based on classical Dugdale model for mode I loading, the additional strain is expressed in terms of the crack density asThis dependence between the applied stress and additional strain for several crack densities is depicted in . The results for effective properties of elastic solids with cracks are also shown for comparison. Note that the elastic prediction of the additional strain (see, for example, paper of Kachanov et al. presents how total macroscopic strain ε22 depends on crack density for various levels of remote mode I loading σ22. As can be seen from , the effect of plastic zones becomes significant for σ22/σY>0.5, especially for high crack densities.For the crack array under mixed mode loading, the closed form solution for additional strain can be obtained using COD given by Eq. (in-line plastic strip model of Becker and Gross). This will produce two components of additional strain in the coordinate system associated with the cracksThese additional strains are plotted in along with the numerical results based on Panasyuk and Savruk model.Let us consider the elastoplastic solid with a set of parallel cracks subjected to a uniaxial tension σ22 inclined at an angle γ to the crack line. According to Panasyuk and Savruk model presented in , each crack is represented as three rectilinear cuts. Thus, formula for additional strain due to one crack is written aswhere index i denotes the quantity related to the ith cut.In the coordinate system xOy associated with the crack direction (), the components of the additional strain are represented as sumswhere nx(i), ny(i) are the components of the unit normal to the ith cut, and and αi is the angle between the ith cut and the x direction.To observe the effect of plastic zones, we compare the numerically obtained predictions of stress–strain response to elastic solutions. Note that the purely elastic behavior of a solid with parallel cracks of density ρ is characterized by components of additional strain show how the components of macroscopic strain ε12 and ε22 depend on the applied stress σ22. As expected, the effective stiffness decreases as either crack density or applied load increases. An interesting observation is that the predictions of normal strain in the direction of loading are the same for both plastic strip models (Becker–Gross and Panasyuk–Savruk), while the shear strain predictions differ noticeably. This can be explained by the shape of crack opening in the models, see The dependence of additional strain on the direction of loading is shown in . The cracks produce maximum contribution into the total strain when the tension is orthogonal to the crack array; this effect almost vanishes at γ<10∘. suggest that for considered range of crack densities, the effect of plastic deformation becomes significant when σ22⩾0.4σY.Consider a body containing sufficiently large number of cracks. We introduce a random variable γ that represents the orientation of a given crack to the direction of load. We assume that γ changes within the interval (0,π) and has a uniform distribution density 1/π (randomly oriented cracks). We use the solution for additional strain due to a crack under arbitrarily oriented load to find the expected value of . Assuming that orientation of the cracks is uncorrelated with their length, we derive the additional strain as can be numerically evaluated to obtain the stress–strain dependence shown in for various crack densities. No significant difference is observed between Becker–Gross and Panasyuk–Savruk predictions for this particular case of the orientational distribution. The elastic response curves, provided in for comparison, are constructed using formulawhich is a modification of the results that can be found in Kachanov Two realizations of the mixed mode plastic strip models can be used to predict elastoplastic behavior of 2D cracked solids: in-line plastic strips (Becker and Gross) and inclined plastic strips (Panasyuk and Savruk). The first realization yields closed form expressions, the second one requires numerical solution. For arrays of parallel cracks, the predicted response in the direction normal to cracks coincides for both approaches; shear strain obtained using Becker and Gross approach is higher than the Panasyuk and Savruk predictions. The analysis suggests that the contribution of plastic zones into additional strain is insignificant at low magnitude of load (σ22<0.4σY) and crack density (ρ<0.01), getting more pronounced as these quantities increase.Kernels of the integral equation system obtained for the plastic strip model of Panasyuk and SavrukMechanical structure–property relationship of aerogelsThe elastic moduli (E) of high-porosity materials (such as aerogels) exhibit power-law scaling with their relative densities (ρ), E∝ρm, where 3⩽m⩽4, but the physics responsible for this behavior is not well-understood. Computer models of aerogels were generated by diffusion-limited cluster–cluster aggregation (DLCA) algorithms, and their linear elastic properties were examined by the finite element method (FEM), assuming that the stiffness of each interparticle bond can be represented by a beam element. The simulation yields m≈3.6 for perfectly connected structures, contradicting the consensus that the dangling mass on the gel gives rise to the exponent. The results suggest that the high exponent is largely because of the reduction in the connectivity of the material with decreasing density. The open-cell foam model, which predicts m=2, is valid only when the connectivity remains unchanged upon variation of the density. The mechanical structure–property relationship in the gel can be described by the `blob-and-link' model. The bonds (links) between the fractal clusters (blobs) are more sparsely distributed than those inside the clusters, and therefore the strain energy is localized at the cluster boundaries during deformation. This model is consistent with the experimental evidence.The mechanical structure–property relationship of high-porosity materials, such as aerogels illustrates some of the scaling exponents found from a number of different materials using different characterization techniques. Gibson and Ashby , through the use of the computer models of the gel network, with FEM as the characterization tool.Computer models of the gel network at various densities and sizes were generated by a diffusion-limited cluster–cluster aggregation (DLCA) algorithm. A backbone algorithm was executed to trim off the dangling mass from the network, so that the scaling behavior of the perfectly connected models could be studied. The pair correlation function was measured on both the trimmed and untrimmed models, from which the fractal dimension and the mass correlation length were extracted for analysis. After that, the network connectivity information was transferred to the finite element analysis program. By representing every interparticle bond as a stiff beam element, the mechanical properties of the model were evaluated as a framework of beams, and the modulus was calculated from the energy stored during deformation. The finite size effect on the properties of the models was studied, and was subsequently eliminated by using only the results from models big enough to produce size-invariant results. The scaling relationship, defined by , was then compiled from the simulation results and compared with the experimental observations. Attempts were made to identify and characterize the load-bearing structure in the DLCA network. In addition, percolation clusters were generated for referencing and validating the methods and the results of this study.The sol–gel process involves the assembly of small particles to form clusters and networks ), the choice of any particular aggregation algorithm should be of secondary importance.The on-lattice DLCA process begins with dispersion of unit-diameter particles randomly in a three-dimensional cubic lattice with unit lattice spacing. The particles are allowed to diffuse randomly along the lattice connections. When they collide, they bond irreversibly and continue to diffuse as a dimer, trimer and so on, until one single cluster is left. Periodic boundary conditions are imposed so that when the particles diffuse out of, or the branches extend beyond, the surface, they are recovered in the opposite side of the lattice. As a result, when the aggregation is over, parts of the cluster that are only connected to the main cluster via a periodic face appear to be isolated inside the lattice. To avoid a singularity during the computation in the finite element analysis, a burning algorithm was used on the lattice to remove these `disconnected' pieces. The algorithm works by setting a `fire' on a particle. The cluster containing that particle will then be burnt. If the fire does not reach all six sides of the lattice, the cluster is not percolating, and is removed. Otherwise the whole cluster is defined as percolating and is preserved. The burning process is repeated on all the particles that have not been burnt in the previous runs, until all the disconnected pieces are removed.Dangling mass, in the context of the computer model, is defined as a particle or a branch of particles hanging on the percolating backbone by a single bond. While the percolating backbone, which spans between the lattice surfaces, presumably carries the load during deformation, the dangling mass by definition does not contribute to the mechanical stiffness. Instead, it reduces the overall mechanical efficiency by adding dead weight to the network. Since it was believed that the dangling mass accounts for the high-scaling exponent m, a backbone algorithm was developed to remove all the dangling mass from the model, so that the scaling behavior of the `perfectly' connected models, free of dangling mass, could be investigated. The algorithm is an extension of that developed by Herrmann et al. The relative density ρ of the aggregate model is defined bywhere n is the number of unit-diameter spherical particles in the cubic lattice of size L, in which there are L sites with (L−1) unit spacing along each axis, and π/6 is the volume of one such particle. Networks of seven different density levels were generated by the DLCA algorithm, including ρ=0.026, 0.042, 0.052, 0.063, 0.079, 0.13, 0.18. The network densities after burning and trimming were calculated using the same formula.The pair correlation function g(r) is a higher-order parameter for characterizing the microstructure of random heterogeneous materials. The function g(r) can be calculated by counting the number of particle centers δn at a distance between r and r+δr from a particle center, and then normalizing with the relative density of the model The small-angle scattering technique measures the pair correlation function where ρn is the number density of the fully occupied lattice (which equals 1 for the cubic lattice models in which there are a total of L3 sites in the lattice volume of L3). The dimensionality of the system d equals 3 for Euclidean structures, but is less than 3 for fractals. As a result, the fractal dimension of the model can be directly determined by plotting F(r) against r on a double logarithmic scale and reading the slope in the small r region. When r becomes bigger, the structure will become Euclidean and so the slope will steepen towards 3. The mass correlation length signifies the cut-off between the fractal and the Euclidean regimes. The df and ζ were determined as functions of density of both the original and the perfectly connected (trimmed) models. The functions g(r) and F(r) were verified to be dependent only on density, but independent of size and realization when the lattice size is big enough. Since ρ, df and ζ can be determined experimentally, these parameters were therefore useful for correlating with the mechanical properties of the material.The FEM is a numerical technique for solving complex engineering problems by discretization of the system of interest and modeling each discretized element using the relevant constitutive equations. The connectivity information of the DLCA network was input to the program by the position of the bonds in the lattice space. Each particle in the network was regarded as a rigid node, while each bond was treated as a beam element. A beam element is defined as a straight cylindrical bar of uniform cross-section; it possesses a finite elastic modulus and moment of inertia so that it can resist axial force (1 degree of freedom), shear forces (2 degrees of freedom), bending moments (2 degrees of freedom), and twisting moments (1 degree of freedom) in three-dimensions. Thus the network is represented as a network of cylindrical beams joining the particle centers. The formulation of the stress–strain relationship in beams is a system of linear equations The linear elastic properties of the DLCA model were studied by simulating the hydrostatic compression on the network, and then solving for its bulk modulus K. A volumetric strain εv of −1% was imposed on the lattice; it has been verified that the same modulus could be derived using different values of εv. The strain was implemented by defining one corner of the lattice as the origin, and then each node in the lattice was displaced to a new position given by is the original position vector of the node and is the new position. With the nodes on the lattice surface held fixed, the network inside the lattice was allowed to relax in accordance with the connectivity and the beam theory. The nodal displacements, the nodal forces on the lattice surface, and the strain energy of every beam were obtained from the finite element analysis. The bulk modulus K of the model is given bywhere Es,j is the strain energy of an arbitrary beam j and is the summed over the total number of beams Nel.Alternatively, K can be found from the force applied to the surfaces to sustain the compression. Both methods were confirmed to give the same results. Moreover, the isotropy of the models can be judged from the resultant forces in the three orthogonal directions. Since these forces were found to be within ±20% of each other in each of the models tested, the models were regarded as isotropic.The Poisson’s ratio of aerogels is generally insensitive to their densities The generation of the DLCA models and the finite element analysis were carried out in three SGI R10000 workstations. DynaFlow™ Before any realistic mechanical data could be obtained from the finite element analysis, the critical lattice size was determined for each of the density levels, beyond which the models are big enough to contain all the necessary microstructural information that accounts for the mechanical properties. Four density levels () were selected to conduct the finite size effect analysis. The DLCA models were grown with lattice sizes from L=50 to 159. Larger models were inhibited by the memory requirement (about 2.2 GBytes) for the finite element analysis. Ten realizations were generated at each density level and each lattice size as a compromise between the confidence of the statistical results and the computation time involved in each realization (up to 3 days for one realization). Since the scaling relationship is interpreted on a logarithmic scale, the results and the statistics were calculated on a logarithmic scale, too. To determine the critical lattice size Lc (beyond which the properties were size-independent) at each density level, the convergence and the statistical variation of the density after trimming, and the bulk modulus of the model, were compared at successive lattice size intervals. The following set of criteria was designated for determining Lc: indicates an arithmetic average, σ is the standard deviation and subscript Lc−1 signifies the level of the lattice size immediately smaller than the critical one. The threshold values were chosen as a compromise between the confidence of the result and the acceptable error for deriving the scaling exponent.An immense number of studies have been conducted to understand or derive the scaling relationship with various properties in the vicinity of the percolation thresholdwhere P is the property of interest, p the probability of sites occupied, pc the percolation threshold, which equals 0.3117 for site percolation on a cubic lattice, and λ is the critical exponent for that particular property PThe structural features of the original and the perfectly connected DLCA networks were studied and compared. There is an abundance of dangling mass in the low-density models, and the relationship of the densities before and after trimming can be represented bywhere ρ0 and ρ are the relative densities of the original and the perfectly connected DLCA networks, respectively. As little as 10% of the total mass is perfectly connected when the initial density is about 0.03. The amount of dangling mass diminishes as the density goes up to about 0.2.demonstrates how the fractal dimension df and the mass correlation length ζ were determined from the plot of F(r) versus distance r. The df is given by the slope of the points at 3<r<6, which is about 1.8. The ζ is deduced by the intersection of the regression lines of the fractal regime and the Euclidean regime (d=3), and is about 10. The fractal dimension and the mass correlation length as a function of density for both trimmed and untrimmed DLCA models are shown in a) and (b), respectively. The measured df of the original models are consistent with the reported values in the literature The size dependence of the relative density after trimming and the bulk modulus of the DLCA networks at different initial densities were studied to eliminate the finite size artifact. a) and (b) illustrate the convergence and the statistical fluctuation of these two variables with respect to the lattice size of initial density 0.052. The critical lattice size Lc at this density is determined as 100. Similar analyses were performed on the other densities and the result is summarized in together with the mass correlation length of the perfectly connected models. While the Lc is larger than the limiting size of 159 for ρ<0.01, the Lc was predicted to be much smaller than the lower bound of 50 for ρ>0.1. There seems to be a constant order of magnitude difference between the ζ and Lc over the density range explored. All the results reported later from the finite element analyses were obtained from the models with L⩾10ζ, and so the finite size error could be eliminated.The scaling relationship of bulk modulus against relative density, derived from the computer simulation, is illustrated in The untrimmed DLCA models show a scaling behavior with an exponent of 7.6. However, the data points of the perfectly connected (trimmed) networks, do not fall on a single regression line. Instead, the four data points at lower density exhibit a power-law relationship with an exponent of 3.6.The effect of the beam parameters on the modulus of the models during compression was tested. The bulk moduli vary linearly with the elastic modulus of the beams, but scale with an exponent q with the aspect ratioThe qs at different densities are tabulated in Except for the two uncorrelated points of the regression in , q is constant at 4. Therefore, the scaling exponent m≈3.6 derived from the perfectly connected models is independent of the beam properties.The spatial distribution of the strain energy in a low density perfectly connected DLCA network upon compression is illustrated in which is a zoom-in view through the diagonal of the three-dimensional model of lattice size L=100 and density ρ=0.017. The reddish and the yellowish beams are the load-bearing bonds and account for the majority of the total network energy. The bluish beams carries much less energy and contribute very little to the total network energy. However, even though the network is already `perfectly connected', there is still an abundance of unloaded bonds. No distinctive load-bearing backbone is observed from the network. Conversely, the load-bearing bonds are found scattered all over the network. Moreover, these bonds appear in the more open spaces, while the unloaded bonds are concentrated in the blob-like structures between the loaded bonds.Statistical interpretation of the energy distribution in the network was performed by analyzing the probability density function (pdf) of the strain energy in a beam. The result is shown in Both spatial and statistical distributions indicate that there is an abundance of unloaded bonds, while the stiffness of the network is determined by only a few percent of heavily loaded bonds. The shape of the pdf is similar for the other densities, and the first and the second moments of the pdf at different densities are given in Since the number of bonds increases with the density, the number of load-bearing bonds therefore increases with the density too. In a fully occupied cubic lattice, the total number of bonds Neltot is given byThe relative density of the DLCA model is, of course, directly related to the fraction of occupied bonds in the lattice. From the simulation results, this relationship can be approximated bywhere Nel is the number of bonds in the lattice model. By counting the number of bonds in the descending order of energy that cumulatively accounts for, say, 99% of the total strain energy, the load-bearing volume fraction in the network could be estimated using the scaling relationship . The volume fraction of the network that bears load is found to increase with increasing density, as illustrated in Again divergence from the scaling line is observed for the models of higher densities.a) shows the gel fraction plotted against the deviation from the percolation threshold of the site percolation clusters. The deviation from the predicted slope of 0.4 can be attributed to the finite size of the percolation clusters. At the percolation threshold, the cluster is supposed to have an infinite correlation length (b). Subject to the errors from the finite size effect, the data points are fairly close to the estimated slope of 3.75. These results have validated the methodology and the finite element analysis used in the investigation of the DLCA models.The scaling exponents observed for various types of high-porosity aggregates in nature have been captured in the computer simulations of this work. The scaling exponent of the bulk modulus against density of the perfectly connected DLCA models was evaluated to be about 3.6, while the exponent is about 7.6 for the original on-lattice DLCA models with dangling mass (). Recalling that a number of those high-porosity materials exhibit fractal geometry and scaling behavior with exponent around 3 to 4 (), the perfectly connected DLCA models exhibit a close resemblance to both the structural features (relative density, fractal dimension and mass correlation length) and the mechanical stiffness (scaling relationship).The increase in the load-bearing volume fraction of the network at increasing density accounts for the high-scaling exponent. Gibson and Ashby Assuming the network is made up of square beams of aspect ratio ac (=beam width/beam length) in the cellular structure, the relative density ρc is given by Therefore, if the beams in the network are evenly loaded, then the elastic modulus varies with density according to is fulfilled when the aspect ratio is varied in a model. If the density of the material varies in the way described by , i.e., the density of the network changes by varying the bond thickness but the connectivity is unaltered, is then recovered. This explains why some materials follow the open-cell foam model.The scaling exponent of 3.6 was obtained in by considering only the lower density part of the data. If bending is the dominant mode of deformation, which is a reasonable assumption for the highly porous chain-like structure, the models should follow , and this is verified for the regression models as shown in . However, since the models are on-lattice type, the axial compression dominates in the high-density limit. In axial deformation, the elastic modulus relates to the beam aspect ratio by If the axial stress of the beams becomes significant during compression, the exponent q in would then drop from 4 towards 2. This effect is observed for the deviating data points at high densities. As a result, the models with density higher than about 0.05 are considered to contain an artifact of the lattice model (viz., excessive axial compression), so the omission of the high-density data is justified.In the present study, the dangling mass refers only to the clusters attached to the percolating backbones by one single bond. The other dangling mass attached by two or more bonds is not trimmed in the perfectly connected network defined above. Elimination of such dangling mass may enhance the efficiency of the connectivity and thus the overall stiffness. However, the loop structure that is formed between the percolating backbone and the dangling mass by the two or more connecting bonds is itself a mechanically efficient structure. Removal of these loops will also weaken the network to some extent, and therefore such a structure is not classified as dangling mass here.Unfortunately, although the pair-correlation functions of the perfectly connected DLCA models are similar to those of the untrimmed ones with the same density, the trimming itself is too artificial as a mechanism for explaining the structure and the mechanical properties of the materials of interest. Taking into account the artifact of the lattice model, the importance of `loop' structures for the mechanical stiffness and the unrealistic abundance of dangling mass in the original DLCA model, we have developed a new aggregation algorithm targeted to capture the structural and mechanical properties of the gel-type materials. This model allows physically realistic internal bond vibration and rotation within a cluster, leading to higher connectivity. A description of the new model will be published in the near future.The strain energy distribution in the gel network during compression is generalized in . Only a few percent of bonds bear the majority of the load. While the unloaded bonds form blobs of high-particle density, the few load-bearing ones connect between these blobs in the less crowded spaces.Gel is formed when the fractal clusters percolate A similar structural model was proposed by Shih et al. To verify the `blob-and-link' hypothesis (proposed after the visual inspection of the spatial distribution of strain energy), a more quantitative examination of the load-bearing pattern of the perfectly connected DLCA network was performed, using the four models in . The bonds in the network were marked one by one in descending order of strain energy, until the marked bonds began to percolate. Over 90% of the total strain energy was recovered in each of these models at the percolation threshold, and the marked bond that was least loaded (i.e., the last marked one) carried only ppm level of the total energy. The burning algorithm was then executed on each of the resultant clusters of marked bonds. More than half of the marked bonds were found not connecting to the percolating backbone, but scattered all over the volume. The summary of the result is illustrated in The `blob-and-link' model is again able to explain the scattered load-bearing bonds on the network. Moreover, a percolating path through the network must pass through the inside of the cluster and so the percolating backbone was found including the bonds with a very small fraction of the total strain energy.There is experimental evidence supporting the hypothesis of the `blob-and-link' model. Woignier et al. Using the finite element analysis and the beam theory to represent the interparticle bonds, the scaling relationship between the linear elastic bulk modulus and the relative density of the DLCA model was found to beafter the dangling mass on the network was trimmed. The scaling exponent agrees well with many of the gel-derived materials. In the sol–gel process, density determines the network connectivity, which in turn controls the mechanical stiffness, as illustrated in the simulation result. It is the increase of the mechanical efficiency of the connectivity with respect to the increasing density that accounts for the high exponent. Dangling mass is not a key factor for determining the scaling exponent. If the density of the network changes by varying the network thickness without altering the connectivity, the open-cell foam model, for which the exponent equals 2, is then applicable. The linear elastic and plastic deformations of the gel network can be described by the `blob-and-link' model. The bonds (links) form between the fractal clusters (blobs) when the clusters percolate at the gel point. Since the links are more sparsely distributed than the bonds within the blobs, the strain energy is more concentrated at the cluster boundaries, and therefore the deformation is bigger at the boundaries. This model is consistent with the experimental evidence that the mass correlation length shortens and the big pores collapse preferentially upon compression.A unified modeling method for dynamic analysis of GPLs-FGP sandwich shallow shell embedded SMA wires with general boundary conditions under hygrothermal loadingIn this research, the dynamic analysis of graphene platelets (GPLs) reinforced functionally graded porous (FGP) sandwich shallow shell embedded shape memory alloy (SMA) wires with general boundary conditions under hygrothermal loading is conducted. Four different porosity distributions of FGP reinforced with four various GPLs dispersion patterns are considered. Based on the Brinson formulation, the constitutive equation of the SMA is established. The energy functional of the sandwich shallow shell is constructed by employing the Hooke’s law and the first-order shear deformation theory (FSDT). Ultimately, the dynamic characteristics of the sandwich shallow shell are obtained by solving the energy functional with the Rayleigh-Ritz method. After the verification of accuracy and reliability, parametric studies on the effects of material properties, geometrical parameters, and boundary conditions are investigated.In recent decades, with the rapid development in the aerospace field, increasing demand has been raised for the structure’s mechanical performances. Due to its high stiffness and lightweight, the sandwich shallow shell has been widely used in many fields, such as aviation, aerospace, and military industry It can be found that the mechanical performance of the structure can be enhanced by adding composite materials To meet the application requirements, it is crucial to investigate the dynamic behaviors of the structure The hygrothermal loading has a significant influence on the dynamic performances of the structure Based on the above analyses, the main goal of this paper is to construct a GPLs-FGP sandwich shallow shell embedded SMA wires and investigate its dynamic behaviors by considering the effect of hygrothermal loading. The innovative points of this work can be summarized as: 1) The GPLs-FGP and the SMA wires are introduced to improve the mechanical performances and the thermal stability of the sandwich shallow shell; 2) A complex dynamic model of the sandwich shallow shell affected by many factors is constructed, based on the Jacobi-Ritz formulation; 3) The hygrothermal loading model of the sandwich shallow shell is derived by utilizing the energy method. The framework is organized as follows. First, a theoretical model of GPLs-FGP sandwich shallow shell embedded SMA wires is established with general boundary conditions under hygrothermal loading. Second, the accuracy and reliability of the proposed model are verified, and the parametric analysis is carried out. Finally, the conclusions are provided at the end of the article.In this work, a sandwich shallow shell model with general boundary conditions subjected to hygrothermal loading is considered, as displayed in . Rx and Ry denote the principal radii of curvature. The length and width of the structure are indicated by a and b, respectively. The total thickness is h=ht+hc+hb, where the thickness of the top layer, core, and bottom layer is expressed by ht, hc, and hb, respectively. The Cartesian Coordinate System is established at the middle surface, i.e., the coordinate x refers to the length direction, the coordinate y is in the width direction, and z is in the thickness direction. Four typical sandwich shallow shells are obtained by changing the principal radii (Rx and Ry): 1) sandwich plate (Rx = Ry = ∞); 2) sandwich circular cylindrical shell (Rx = ∞ and Ry = R); 3) sandwich spherical shell (Rx = Ry = R); 4) sandwich hyperbolic paraboloidal shell (Rx = R and Ry = -R).The sandwich shallow shell has three layers: the top face sheet, the bottom face sheet, and the core layer. The isotropic nickel material is employed as the face sheets material, and the GPLs-FGP is introduced as the core material. This paper considers four types of FGP porosity distributions to describe the volume fraction of internal pores. For the symmetric porosity distribution, Type 1 disperses more pores around the surface areas, and Type 3 disperses more pores near the central areas. For the non-symmetric porosity distribution, the porosity distribution of Type 2 varies along with the sandwich shallow shell thickness, and Type 4 is the uniform distribution of the pores. Therefore, Young’s modulus Ez, shear modulus Gz, and mass density ρz of the FGP can be expressed as [E(z),G(z),ρ(z)]=[E1Λi(z),G1Λi(z),ρ1Φi(z)]where E1,G1, and ρ1 represent the effective Young’s modulus, shear modulus, and density, respectively; Λi(z) and Φi(z) (i = 1, 2, 3, 4) can be further expressed as Λi(z)=1-e0ψi(z) and Φi(z)=1-emψi(z), in which ψi(z) corresponding to four types of FGP porosity distributions; e0 and em, respectively, denote the porosity coefficient and the mass density coefficient; and the range of variable z is from -hc/2 to hc/2.Based on the closed-cell Gaussian Random field scheme, the Poisson’s ratio v(z) of FGP material can be expressed as follows v(z)=0.2211-ρ(z)ρ1+v11-1.211-ρ(z)ρ1+0.3421-ρ(z)ρ12where the FGP Poisson’s ratio is indicated by v1 when the porosity coefficient is zero.For the GPLs-FGP material, E1, ρ1 and v1 is derived by utilizing the mixture rule and the Halpin-Tsai micromechanical model, and they can be expressed as followsE1=Em381+ζLυLVGPLs1-υLVGPLs+581+ζTυTVGPLs1-υTVGPLswhere Ei (i = m, GPLs) represents the effective Young’s modulus, ρi is the density, vi stands for Poisson’s ratio, Vi represents the volume fraction, and the subscripts ‘m’ and ‘GPLs’ represent the matrix material and the GPLs, respectively; ζT, υT, ζL, υL indicate the size coefficients of the GPLs. As shown in , the volume fraction of different GPLs dispersion patterns can be given asin which Pti indicates the largest GPLs volume fraction, Ψi(z) (i = 1, 2, 3, 4) are the different GPLs dispersion patterns. Furthermore, the relation equation between Pti and Ψi(z) is given as followsℵGP∫-h/2h/2HdzℵGP+(1-ℵGP)(ρGP/ρm)= Pti∫-h/2h/2HΨi(z)dzwhere ℵGPL represents the weight fraction of GPLs; the term related to porosity coefficient and distribution can be indicated by H, and it can be expanded as In this work, the sandwich shallow shell is embedded SMA wires in the top and bottom sheets, and the SMA wires are parallel to the coordinate x, as shown in . The effective thermomechanical properties are obtained by utilizing the multi-cell micromechanical method as follows α2=E2mE22α2m1-Vs+VsαsVs+α2m1-Vs/1-Vs1-E2mEsξwhere the metal matrix and SMA wires are indicated by the subscripts ‘m’ and ‘s’, respectively. Additionally, E represents the Young’s modulus, G indicates the shear modulus, υ is Poisson ratio. The density, the volume fraction, and martensite fraction of SMA are indicated by ρ, Vs, and ξ, respectively.in which the parameter with the subscript ‘0′ denotes that it is in the initial state. Additionally, σ indicates stress, ε stands for strain, Eξ represents Young’s modulus, Θξ is thermoelastic tensor, ΔT is the temperature variation, and Ωξ is transformation tensor. The Young’s modulus and transformation tensor can be derived through the rule of mixtures as belowwhere the martensite and austenite phases are expressed by subscripts ‘M’ and ‘A’, and εL is the maximum recoverable strain. The martensite volume fraction during conversion to austenite can be expressed aswhere the ξS and ξT denote the martensite fraction induced by stress and temperature, respectively, and the total martensite fraction ξ equal to ξS+ξT. In addition, the start and finish temperatures of austenite are indicated by As and Af, respectively; T1 = ΔT + T0 (T0 = 20 ℃) denotes the temperature; and CA represents the influence coefficient of austenite stress. The material properties of SMA wires are provided in Appendix A.In this study, the FSDT is applied to establish the displacement field of the sandwich shallow shell as followswhere the middle plane displacements along the x, y, and z directions are denoted by u, v, and w, respectively. ϕx and ϕy are the rotations of transverse normal relative to y and x coordinates, and t represents time. Based on the small deformation assumption and the linear strain–displacement relation, the normal strains and shear strains of the sandwich shallow shell can be derived as where εx0, εy0, γxz0, γyz0 and γxy0 are the strains in the middle plane, χx, χy and χxy denote the curvature changes. The strains and curvature changes can be further expressed asFurthermore, based on the Hooke’s low, the stress–strain relationships in the kth layer of the sandwich shallow shell subject to hygrothermal loading can be written asσxσyτyzτxzτxyk=Q11Q12000Q12Q2200000Q4400000Q5500000Q66εx-α1ΔT-β1ΔCεy-α2ΔT-β2ΔCγyzγxzγxyk+Vsσxrcos2θσyrsin2θ000k=t,b,ckwhere superscript ‘t’ and ‘b’ represent the top layer and bottom layer, and the core layer is indicated by ‘c’; σx, σy represent the normal stresses; εx, εy represent the normal strains; τxy, τxz, τyz are the shear stresses; γxy, γxz and γyz are the shear strains; the thermal expansion coefficients are denoted by α1 and α2 in x and y directions, respectively; the hygroscopic expansion coefficients are indicated by β1 and β2 with respect to x and y directions, respectively; ΔT is the temperature variation relative to T0 = 20 ℃; ΔC is the moisture variation; the volume fraction of SMA is denoted by Vs, and Vs is equal to zero when k takes t or b; θ is the angle between SMA wires and coordination x. The elastic stiffness coefficients Qiji,j=1,2,4,5,6 are obtained as followsQ11(z)=Q22(z)=E(z)1-μ2(z),Q12(z)=Q21(z)=μ(z)E(z)1-μ2(z)Q44(z)=Q55(z)=Q66(z)=E(z)21+μ(z)Based on the above equations, the calculated results of force and moment of the sandwich shallow shell can be given asNxNyNxy,MxMyMxy=∫-h/2-hc/2σxσyτxyb1,zdz+∫-hc/2hc/2σxσyτxyc1,zdz+∫hc/2h/2σxσyτxyt1,zdzin which the force resultants of the structure are represented by Nx, Ny and Nxy; the moment resultants are indicated by Mx, My and Mxy; Qx and Qy denote transverse shear force resultants; κ is the shear correction factor, usually set as κ = 5/6; Finally, the constitutive equation of the sandwich shallow shell under hygrothermal loading as followsNxNyNxyMxMyMxy=A11A120B11B120A21A220B21B22000A6600B66B11B120D11D120B21B220D21D22000B6600D66εx0εy0γxy0χxχyχxy-NxTNyT0MxTMyT0-NxCNyC0MxCMyC0+NxrNyr0MxrMyr0where εx0, εy0 are the normal strains of the sandwich shallow shell in the middle plane, γxz0, γyz0 and γxy0 are the shear strains in the middle plane, χx, χy and χxy are the bending curvatures; Aij (i, j = 1, 2, 6) indicate the stretching stiffness coefficients; Bij (i, j = 1, 2, 6) represent the coupling stiffness coefficients under stretching-bending; Dij (i, j = 1, 2, 6) are the bending stiffness coefficients; They can be written as follows(Aij,Bij,Dij)=∫-h/2h/2Qij(1,z,z2)dz,(i,j=1,2,4,5,6)The total energy functional representation of the sandwich shallow shell includes strain energy and kinetic energy. The strain energy of the sandwich shallow shell can be calculated asUS=12∫0b∫0aNxεx0+Nyεy0+Nxyγxy0+Mxχx+Myχy+Mxyχxy+Qxγxz0+Qyγyz0dxdyFurthermore, considering the hygrothermal loading with evenly temperature and moisture, the corresponding strain energy can be expressed as UT=-12∫0b∫0aNxT+MxT∂w∂x2+NyT+MyT∂w∂y2dxdyUC=-12∫0b∫0aNxC+MxC∂w∂x2+NyC+MyC∂w∂y2dxdyIn this study, the strain energy of SMA wires is described by Subsequently, the kinetic energy functional of the sandwich shallow shell can be derived asT=12∫0a∫0bI0∂u∂t2+∂v∂t2+∂w∂t2+2I1∂u∂t∂ϕx∂t+∂v∂t∂ϕy∂t+I2∂ϕx∂t2+∂ϕy∂t2dxdyin which the inertia terms can be defined asThe virtual spring technique is adopted to construct the different boundary conditions Usp=12∫-h2h2∫0bka0uu2+ka0vv2+ka0ww2+Ka0xϕx2+Ka0yϕy2x=0ka1uu2+ka1vv2+ka1ww2+Ka1xϕx2+Ka1yϕy2x=adydz+12∫-h2h2∫0akb0uu2+kb0vv2+kb0ww2+Kb0xϕx2+Kb0yϕy2y=0kb1uu2+kb1vv2+kb1ww2+Kb1xϕx2+Kb1yϕy2y=bdxdzIn this study, the Jacobi orthogonal polynomials are employed to expand the displacement and rotation components of the sandwich shallow shell. The i order classical Jacobi polynomial is expressed by Pi(α,β)(ϕ), where α, β are Jacobi parameters and the range of ϕ is defined on the interval of [-1,1]. For classical Jacobi polynomials, the recurrence relation of Pi(α,β)(ϕ) is shown asPi(α,β)(ϕ)=(α+β+2i-1)α2-β2+ϕ(α+β+2i)(α+β+2i-2)2i(α+β+i)(α+β+2i-2)Pi-1(α,β)(ϕ)-(α+i-1)(β+i-1)(α+β+2i)i(α+β+i)(α+β+2i-2)Pi-2(α,β)(ϕ)For the classical Jacobi polynomials, the orthogonality condition can be expressed as followshk=2α+β+12k+α+β+1Γk+a+1Γk+β+1Γk+a+β+1k!,j=k0,j=kThe Legendre, Chebyshev, and Gegenbauer polynomials are the particular forms of Jacobi polynomials. The variation of the Jacobi parameters α, β, i.e., the change of orthogonal polynomials. The Legendre polynomials can be achieved by choosing α = β = 0 while α = β = -1/2 and α = β = 1/2 lead to two kinds of Chebyshev polynomials. Finally, by setting α = β, the Gegenbauer polynomials can be obtained. Therefore, the admissible displacement function of the sandwich shallow shell is expanded by utilizing the Jacobi polynomial, and it can be written asϕx=∑n=0N∑m=0MϕmnPm(α,β)(x)Pn(α,β)(y)eiωtϕy=∑n=0N∑m=0MΓmnPm(α,β)(x)Pn(α,β)(y)eiωtin which Umn, Vmn, Wmn, ϕmn, Γmn are the Jacobi coefficients for different displacement functions; Pm(α,β)(x) and Pn(α,β)(y) are the Jacobi polynomials in the x and y direction, where the order numbers are denoted by m and n; t denotes time, and ω is the angular frequency. The number of the polynomial terms are presented by M and N, respectively.Based on the above equation, the Lagrange functional of the sandwich shallow shell is given asAccording to the Rayleigh-Ritz approach, the variational minimum of the Lagrange functional with respect to the undetermined coefficients can be derived asFurthermore, substituting Eqs. (19)-(24), (27), , and then the eigenvalue equation can be defined aswhere K, M, P, and F are the stiffness matrix, mass matrix, undetermined coefficient vector, and external force vector. Obviously, by solving Eq. , the natural frequency and mode shape of the sandwich shallow shell are easily acquired.Furthermore, four types of pulses are considered in this work, which can be defined as followswhere the rectangular pulse, triangular pulse, half-sine pulse, and exponential pulse are represented by frt, ftt, fht, and fet, respectively; τ is the pulse width, and t is the time variable. The external loading vector can be further expressed as Fit=q0fit, i=r,t,h,e, in which q0 denotes the pulse amplitude.Besides, the forced vibration of the sandwich shallow shell can be express aswhere u¨ denotes the acceleration vector, u is the displacement vector. The average acceleration based Newmark-β method where γ and β are set as 1/2 and 1/4, respectively.The dynamic characteristics of the GPLs-FGP sandwich shallow shell embedded SMA wires are investigated in this section. For simplicity, shows the boundary condition abbreviations and spring stiffness. It is mentioned that the convergence of the model will affect the prediction results with the frame of the Rayleigh-Ritz method. Therefore, it is necessary to verify the convergence condition of the present method before the parametric analysis. investigated the effect of truncated numbers M and N on the dimensionless fundamental frequencies Ω=ωa2π2ρmhDD=Emh3/12∗1-vm2. As can be seen from this table, the truncated numbers M = N = 8 are acceptable to obtain a reasonable solution.After the convergence is verified, the parametric studies on the dynamic analysis are carried out. The dynamic analysis is divided into two parts: First, the validity of the proposed modeling method needs to be verified; Second, the dynamic analysis of the sandwich shallow shell is studied.The validity of the method proposed in this work is verified via comparing with the results from the open literature and finite element method (FEM). shows the comparison of the first six frequency parameters Ω∗=ωaρm(1-vm2)Em of the GPLs-FGP plate with uniform porosity under CCCC boundary condition. illustrates the contrastive study of the first eight non-dimensional frequencies between the proposed method and FEM with CCCC boundary condition. The model parameters are set as a = b = 1 m, h = 0.2a, ht = hb = 0.05 h, hc = 0.9 h, Rx = ∞, Ry = ∞, Em = 200GPa, EGPLs = 200GPa, vm = 0.31, vGPLs = 0.186, ρm = 8908 kg/m3, ρGPLs = 1062.5 kg/m3, Vs = 0, ε0 = 0, ΔT = 10 °C, ΔC = 0, e0 = 0.4 and weight fraction (wet) of GPLs is 5%. In the following study, the material definition remains unchanged if no special reminder. illustrate that the proposed method is in good agreement with the existing data and FEM. Therefore, further investigations of the sandwich shallow shell can be continued.The dimensionless fundamental frequency of the sandwich shallow shell versus porosity coefficient e0 curves under CCCC and SSSS boundary conditions are plotted in . It can be noted that the porosity distribution 3 (T = 3) has a significant effect on the vibration behaviors than others, and the dimensionless fundamental frequency drops evidently with the increase of porosity coefficient as T = 3. It is obvious that only slight variations can be observed with the growth of the FGP porosity coefficient while the porosity distribution is T = 1. The results show that the porous structure with a hard surface and soft middle layer is less affected by internal pores. studied the effects of GPLs weight fraction and pattern on the dimensionless fundamental frequency of the sandwich shallow shell under CCCC and SSSS boundary conditions. It can be seen that the most effective reinforced pattern of GPLs is pattern 2 (P = 2), and P = 4 is an ineffective pattern. However, under SSSS boundary and the fourth FGP distribution, the linear distribution along the z coordinate (P = 3) is the best distribution pattern to improve the stiffness of the sandwich shallow shell. These findings suggest that the symmetric pattern distributing more GPLs around the top and bottom surface of the sandwich shallow shell provides the highest rigidity.In order to further investigate the effect of porosity coefficient e0, shows the first six dimensionless fundamental frequencies of the GPLs-FGP sandwich shallow shell. With the increase of porosity coefficient e0, the dimensionless frequency decreases, but this occurrence is not apparent. The results are fitted into the previous study displays the comparison of dimensionless frequency parameters Ω with different geometric parameters between the proposed method and the FEM, and the GPLs-FGP distribution is set as T = 1; P = 1. The present result fits into the FEM simulation, as shown in . Consequently, the numerical discussions and geometric parameters studies of the sandwich shallow shell are carried out in the following section (see list the first six frequency parameters Ω for four kinds of the sandwich shallow shell with different boundary conditions. Through , the following points can be obtained: 1) The largest first six dimensionless fundamental frequencies appear while the boundary condition is CCCC; 2) The dimensionless fundamental frequencies of the sandwich spherical shell are the largest as a/h = 10 and the sandwich hyperbolic shell possesses the largest with a/h = 50. This is because the CCCC boundary condition can achieve the highest structural stiffness. Another reason is that the spherical and hyperbolic shells have higher structural stiffness than other shallow shells. Therefore, it can be known that the spherical shell and hyperbolic shell perform better anti-vibration ability, and the structural stability can be further improved by setting the clamped boundary condition. Additionally, the first six frequencies with different thicknesses and boundary conditions are given in . It is noteworthy that the corresponding frequency parameters increase with the growth of the absolute value of a/Rx, a/Ry. As a result, it can be inferred that the vibration resistance increases with the growth of thickness. To further understand the vibration resistance of the sandwich shallow shell, the corresponding first four mode shapes are displayed in The effect of the hygrothermal loading on free vibration is studied in this part. Based on previous discussions, a tiny difference can be found between the 2nd and 3rd modes. Hence, the effect of the thermal loading on the first f1ive dimensionless fundamental frequencies of the sandwich shallow shell except the third mode is shown in . As the temperature increases, the frequency parameters decrease, but this phenomenon is not apparent. illustrates that the dimensionless fundamental frequencies vary with moisture. The variation of the dimensionless fundamental frequencies is unnoticeable with the increase in humidity. This is because the strains of the sandwich shallow shell are more sensitive to the temperature than humidity. It also should be noted that the change of natural frequencies is more significant than the dimensionless frequencies, and the instability situation also should be prevented with the growth of the temperature and humidity.Besides, investigating the effect of the SMA wires is another objective of this work. The phase of the SMA wires remains the reverse martensite phase transformation during the dynamic analysis. shows the effects of the SMA volume fraction (Vs) and Pre-Strain (ε0) on the dimensionless fundamental frequencies of the sandwich shallow shell. The research work discovered that increasing the SMA wires volume fraction is an effective approach to reduce the effect of temperature on the vibration characteristics. However, the effect of Pre-Strain on temperature stability is not obvious. A credible explanation for this is that the structures embedded with SMA wires have excellent temperature stability. The findings demonstrate that SMA wires have an outstanding contribution to the thermal stability of the sandwich shallow shell. Furthermore, with the increase of SMA wires volume fraction and Pre-Strain, the improvement of the thermal stability becomes obvious.Another primary objective of this paper is to study the forced vibration. Therefore, this section is devoted to the forced vibration analysis, including the transient and steady-state response. Two typical loads are considered in this study: point force and surface force.Similarly, the reliability and accuracy of the proposed dynamic analysis method should be verified first. shows the contrastive study of the steady-state response obtained by the FEM and present method. The material and geometric parameters are define as T1-P3, Vs = 0.4, ε0 = 0.5%, ΔT = 200 °C, h = 0.2a, ht = hb = 0.05 h, hc = 0.9 h. The results obtained from the present method are consistent with the FEM. The tiny difference is because that the proposed modeling method is simplified.After the verification, the forced vibration characteristics are investigated. shows the effect of GPLs-FGP dispersion patterns on the steady-state forced response with CCCC boundary condition, and the detection point is (0.6, 0.6). It can be found that only a slight difference can be obtained by changing the FGP porosity distributions, but a noticeable difference can be observed with the change of the GPLs patterns. The findings reveal that the FGP porosity distributions slightly affect the steady-state response, while the GPLs patterns have a significant effect. Regarding the forced vibration, the magnitude of the resonance frequency is crucial to the structural characteristics. The least resonance frequencies occur while P = 4 and the largest appear as P = 2. That is due to the fact that P = 2 is the best GPLs pattern to improve the structural stiffness, but the reinforcing effect of P = 4 is insignificant. shows the coupling effect of the SMA wires volume fraction and the boundary condition with the detection point (0.8, 0.8). From this graph, it can be seen that the shape of the resonance frequencies curve has a significant change with the variation of the boundary conditions, and increasing the SMA wires volume fraction slightly affect the resonance characteristics of the sandwich shallow shell. The results prove that the forced vibration of the sandwich shallow shell is greatly affected by the boundary conditions. However, the improvement of SMA wires on structural resonance is not apparent, which can be attributed to that the GPLs-FGP contributes more effect to the structure stiffness than the SMA wires. The findings reveal that the effect of SMA wires on stiffness is slight than GPLs-FGP. investigates the effect of the hygrothermal loading on steady-state response with the detection point (0.6, 0.6). It can be easily observed that the resonance frequencies decrease with the increase of temperature, and the humid loading affects the steady-state forced response inconspicuously. This is because only a tiny strain is produced for the sandwich shallow shell under hygrothermal loading. Therefore, the effect of hygrothermal loading is unnoticeable. In other words, for the steady-state response, the sandwich shallow shell embedded SMA wires has excellent hygrothermal stability. displayed the effect of loading types on steady-state response with different weight fractions. It is apparent that the resonance frequencies of the sandwich shallow shell impressive decrease with the growth of the GPLs weight fraction under the same loading type. Besides, the amplitude of resonance in surface loading type is higher than the point loading, which is caused by the larger area of the loading force. The results show that the GPLs weight fraction improves the steady-state behavior of the shallow sandwich shell, regardless of the loading type.In this subsection, the transient response of the sandwich shallow shell is studied. The transient response of the sandwich shallow shell is obtained by utilizing the Newmark-β method. First, the contrastive study on the result of the proposed method and FEM software are carried out at different detection points with T1-P3 and CCCC boundary condition, as depicted in . The proposed method are in good agreement with the FEM and can be considered as acceptable. The comparison gaps in can be attributed to three kinds of errors as follows: the model error caused by the approximation and hypothesis in the modeling process; the truncation error resulting from the discretization of motion equation; and the integral error stemming from the Gauss-Legendre quadrature formula. illustrates the effect of the GPLs-FGP dispersion patterns on transient response with CCCC boundary condition. A significant difference can be observed by employing different GPLs-FGP dispersion patterns. As shown in (a), with the same FGP distribution pattern T = 1, the minimum amplitude of the response curve appears as P = 2. Similarly, (b) illustrates that the porosity distribution T = 1 has the smallest amplitude with the same GPLs dispersion pattern P = 1. It can be concluded from the above analyses that T1-P2 is the most effective GPLs-FGP dispersion pattern for the improvement of the structure performance as the GPLs-FGP dispersion pattern T1-P2 can achieve the highest structural stiffness. examines the effect of different pulse loads in transient response with different loading types. The displacement of the surface force load is much lower than the point force load in the transient response curve. It is worth noting that the pulse has a significant effect on the transient response, such as rectangular and exponential pulse. However, the effect of the triangular and half-sine pulse on the transient response is not apparent. It can be inferred from the above analysis that the point loading has a significant effect on transient response than surface loading. For the steady-state response, the result reverses.The dynamic behaviors of the GPLs-FGP sandwich shallow shell embedded SAM wires, considering the effects of general boundary conditions and hygrothermal loading, were investigated in this work. Some conclusions are drawn as follows:GPLs can significantly improve the stiffness of porous structures weakened by the internal pores. Compared with the traditional sandwich structure with the FGP core layer, the sandwich shallow shell with the GPLs-FGP core layer shows better mechanical performance.The FGP porosity coefficient and GPLs weight fraction remarkably affect the stiffness of the sandwich shallow shell, and the extent of the effect is different with various distributions. The highest stiffness of the sandwich shallow shell can be achieved by setting FGP symmetric distribution (Stiff-Soft-Stiff) and dispersing more GPLs around the top and bottom layers.The SMA wires have been proved to be effective in reducing the strains caused by the hygrothermal loading as well as improving the structural thermal stability. By increasing the volume fraction and Pre-Strain of the SMA, the thermal stability of the sandwich shallow shell can be further improved.The sandwich shallow shell proposed in this work has excellent dynamic characteristics. However, the vibration resistance of the structure will be inevitably reduced when the external excitation frequency changes. Changing the structure’s mechanical properties in real-time as the external conditions change is an effective method to solve this problem. Therefore, the adaptive sandwich shallow shell should be further investigated in future work.Jing Zhao: Conceptualization, Writing – review & editing, Resources, Supervision, Funding acquisition. Jinzhai Hu: Writing – review & editing, Methodology, Software, Validation, Formal analysis, Investigation, Visualization. Tianhao Wang: Methodology, Software, Formal analysis. Hui Li: Conceptualization, Resources, Supervision. Jialin Guan: Data curation, Investigation, Validation. Jincan Liu: Conceptualization, Software. Zhijiang Gao: Formal analysis, 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.Young’s modulus of Austenite: EA = 67GPa; Young’s modulus of Martensite: EM = 26.3GPa; Thermoelastic tensor: Θ = 0.55Mpa/°C; Pre-Strain: ε0 = 0.067;The influence coefficient of austenite stress: CM = 8 MPa/°C;The influence coefficient of martensite stress: CA = 13.8 MPa/°C;The start temperature of martensite: Ms = 18.4 °C; The finish temperature of martensite: Mf = 9 °C;The start temperature of austenite: As = 34.5 °C; The finish temperature of austenite: Af = 49 °C;M=∫0b∫0aMuu00Mux00Mvv00Mvy00Mww00MuxT00Mxx00MvyT00MyydxdyMuu=I0UTU,MVV=I0VTV,MWW=I0WTW,Mxx=I2ΦTΦ,Myy=I2ΘTΘ,Mux=I1UTΦ,Mvy=I1VTΘKξ=∫0b∫0aKuuKuvKuwKuxKuyKuvTKvvKvwKvxKvyKuwTKvwTKwwKwxKwyKuxTKvxTKwxTKxxKxyKuyTKvyTKwyTKxyTKyydxdyKuu=A11∂UT∂x∂U∂x+A66∂UT∂y∂U∂y+κA66Rx2UTUKvv=A22∂VT∂y∂V∂y+A66∂VT∂x∂V∂x+κA66Ry2UTUKww=A44∂WT∂y∂W∂y+A55∂WT∂x∂W∂x+A11Rx2+A12RxRy+A22Ry2WTW-2NxT+NxC+MxT+MxC∂WT∂x∂W∂x-2NyT+NyC+MyT+MyC∂WT∂y∂W∂y+Nr∂2WT∂x2∂2W∂x2Ksxi=∫0bKx0Kx1Kx1TKx2dyKx0=diagKuiui,Kvivi,Kwiwi,Kxixi,KyiyiKx1=diagKuiui+1,Kvivi+1,Kwiwi+1,Kxixi+1,Kyiyi+1Kx2=diagKui+1ui+1,Kvi+1vi+1,Kwi+1wi+1,Kxi+1xi+1,Kyi+1yi+1Kuiui=kuUiTUiKvivi=kvViTViKwiwi=kwWiTWiKxixi=kxΦiTΦiKyiyi=kyΘiTΘiKuiui+1=-kuUiTUi+1Kvivi+1=-kvViTVi+1Kwiwi+1=-kwWiTWi+1Kxixi+1=-kxΦiTΦi+1Kyiyi+1=-kyΘiTΘi+1Kui+1ui+1=kuUi+1TUi+1Kvi+1vi+1=kvVi+1TVi+1Kwi+1wi+1=kwWi+1TWi+1Kxi+1xi+1=kxΦi+1TΦi+1,Kyi+1yi+1=kyΘi+1TΘi+1Ksyi=∫0aKy0Ky1Ky1TKy2dx,Ky0=diagKujuj,Kvjvj,Kwjwj,Kxjxj,KyjyjKy1=diagKujuj+1,Kvjvj+1,Kwjwj+1,Kxjxj+1,Kyjyj+1Ky2=diagKuj+1uj+1,Kvj+1vj+1,Kwj+1wj+1,Kxj+1xj+1,Kyj+1yj+1Kujuj=kuUjTUjKvjvj=kvVjTVjKwjwj=kwWjTWjKxjxj=kxΦjTΦjKyjyj=kyΘjTΘjKujuj+1=-kuUjTUj+1Kvjvj+1=-kvVjTVj+1Kwjwj+1=-kwWjTWj+1Kxjxj+1=-kxΦjTΦj+1Kyjyj+1=-kyΘjTΘj+1Kuj+1uj+1=kuUj+1TUj+1Kvj+1vj+1=kvVj+1TVj+1Kwj+1wj+1=kwWj+1TWj+1Kxj+1xj+1=kxΦj+1TΦj+1,Kyj+1yj+1=kyΘj+1TΘj+1Kbx=diagKxl,0,…,KxrKxl=∫0bdiagKxl,uu,Kxl,vv,Kxl,ww,Kxl,xx,Kxl,yyx=0dyKxl,uu=ka0uUTUKxl,vv=ka0vVTVKxl,ww=ka0wWTWKxl,xx=Ka0xΦTΦKxl,yy=Ka0yΘTΘKxr=∫0bdiagKxr,uu,Kxr,vv,Kxr,ww,Kxr,xx,Kxr,yyx=adyKxr,uu=ka1uUTUKxr,vv=ka1vVTVKxr,ww=ka1wWTWKxr,xx=Ka1xΦTΦKxr,yy=Ka1yΘTΘKby=diagKyl,0,…,KyrKyl=∫0adiagKyl,uu,Kyl,vv,Kyl,ww,Kyl,xx,Kyl,yyy=0dxKyl,uu=kb0uUTUKyl,vv=kb0vVTVKyl,ww=kb0wWTWKyl,xx=Kb0xΦTΦKyl,yy=Kb0yΘTΘKyr=∫0adiagKyr,uu,Kyr,vv,Kyr,ww,Kyr,xx,Kyr,yyy=adxKyr,uu=kb1uUTUKyr,vv=kb1vVTVKyr,ww=kb1wWTWKyr,xx=Kb1xΦTΦKyr,yy=Kb1yΘTΘThe effect of sulphuric anodisation of aluminium alloys on contact problemsDamage of aluminium alloys is a major problem in industrial applications. Especially under contact loadings, aluminium alloys show surface degradation independently of contact configurations and operating conditions such as fretting in bearing holder for gear box and abrasion in buckets of trucks. To improve wear resistance, some surface treatments have been performed, particularly sulphuric anodisation (SA) which is often used.The present work deals with the effect of such treatment in two different contact problems. The first concerns abrasion of the 5xxx alloy, whereas the second treats fretting of the A357 alloy. It was found that SA treatment effect depends on the contact configurations. It has been shown that SA treatment decreases wear resistance and provides a transition wear mechanism from ploughing to cutting under scratch. However, in fretting mode, SA treatment eliminates wear kinetics transition and maintains a low wear regime.For some time now, the use of aluminium alloys in the transport industry, has increased enormously. Their use has extended to cars, trucks, planes, etc.Aluminium alloys are omnipresent because of the need to lighten these structures and thus save energy in transport.In addition to their relatively low density, aluminium alloys offer certain interesting properties such as corrosion resistance. Nevertheless, surface damage arise due to friction, depending on loading conditions, especially when normal and tangential forces are superimposed. According to the nature of tangential displacement and contact configuration, many specific mechanisms can be found.To improve wear resistance, surface treatment is often used. In this paper two particular cases were considered: aeronautical application in which there is a fretting damage of the A357 aluminium alloy, whereas the second is transport application in which scratch damage of the 5xxx aluminium alloy is found. For these two applications effect of sulphuric anodisation (SA) surface treatment of aluminium alloy was investigated.Fretting is a process in which material is removed from one or both of two contacting surfaces when the surfaces undergo cyclic tangential displacement with respect to each other Abrasive wear can be classified into two-body and three-body categories In order to improve surface properties (especially hardness) and then wear resistance, SA treatment has been made. As there is no deep study of the effect of such treatment on surface contact problems, the objective of this paper is to investigate the effect of SA treatment on the tribological behaviour of two aluminium alloys used in two different contact configurations, namely fretting and scratch.Qualitative and quantitative analyses of wear are used to identify different contact damage and to evaluate the effect of SA treatment under such configuration.Simulation of gear box and buckets of trucks damage is carried out through two laboratory tests: fretting and scratch. Loading conditions (pressure, velocity, frequency) are chosen to be as similar as possible to real cases.Fretting test: We consider a sphere on plane contact under a normal force and a geometry creating 250 MPa as a maximum Hertz pressure. Alternative tangential sliding strokes are then applied at the contact interface to generate fretting damage. shows a schematic outline of the fretting-wear rig used in this study Concerning the scratch test configuration, a contact between a diamond cone and aluminium alloy is considered (b). After applying a normal force on the indenter, a sliding movement is carried out and the normal force (P) and the tangential force (Q) can be simultaneously measured, using a piezo-electric transducer located underneath the sample. A single scratch test is carried out on the aluminium alloy with a conical indenter (120° point angle and 10 μm radius of its spherical ends). Normal force is varied from 1 to 20 N whereas the scratching length is fixed at 3 mm. The sliding velocity is fixed at 250 μm/s.For fretting, the A357 alloy is brought into contact against the AISI 52100. Both treated and untreated A357 are tested. The thickness of sulphuric anodised layer is about 20 μm.In scratch experiments, a 5xxx aluminium alloy is used to simulate damage of truck buckets. This alloy is obtained by a rolling process. For the treated specimen, an anodised layer of 18 μm thickness is tested.A summary of the mechanical properties of tested materials and coating layers is presented in To investigate the effect of SA treatment, the specimen has been tested before and after treatment under the same condition. After test, analysis of wear quantitatively and qualitatively has been investigated.For each test, scratch section (material below the initial surface b illustrates the variation of scratch section versus the normal load (for treated and non-treated case). It shows that the scratch section increases after SA treatment. So increasing hardness by anodisation process decreases abrasive wear resistance. For a normal load P≤1 N, the depth of the scratch is less than the anodised layer thickness. In this case, only the layer anodisation has been loaded. However, for a normal load greater than 15 N, the depth scratch is much greater than the thickness of anodised layer. Both curves, for treated and non-treated case, became closer for high values of normal load.In abrasive wear, it is generally considered that the hardest material has the best resistance. But much research has drawn contradicting conclusions and shown that the correlation between hardness and abrasive wear is not so clear. On one hand, this contradiction is due to the different operating conditions, configuration parameters and types of test used To better understand the SA treatment effect, wear mechanisms have been analysed. Scanning Electronic Microscopy (SEM) has been employed. presents wear mechanisms before and after SA treatment. Before SA treatment, the main wear mechanisms are ploughing appearing as wedges on the side and the front of the scratch. However, after SA treatment, a transition of wear mechanisms from ductile to brittle damage has been observed. Fracture and formation of wear particles have been located. So, SA treatment induces the transition of wear mechanism from ductile to brittle damage () and decreases therefore, the abrasive wear resistance (The transition of wear mechanism has been confirmed by the measurement of the friction coefficient. presents the friction coefficient variation versus the length scratch respectively before and after SA treatment. It shows that after SA treatment, the friction coefficient presents some fluctuation compared to the case with no SA treatment. This result confirms those found by Kayaba In summary, SA treatment, on one hand increases hardness and decreases wear resistance (), and on the other hand, it induces the transition of wear mechanism from ploughing to brittle with presence of wear particles.To appreciate the effect of the anodised layer on wear, fretting tests under gross sliding regime are carried out. Typically, displacement amplitudes varying from 50 to 200 μm are investigated. In parallel, tests on bulk material are performed under the same conditions.These amplitudes are rather large and seem to be related more to the reciprocating condition. However, it is fundamental to relate the displacement value to the contact dimension. The boundary between fretting and reciprocating conditions can be related to the ratio between the displacement amplitude and the contact radius, e=d/a shows the evolution of wear volume versus displacement amplitudes for both treated and non-treated aluminium alloy. Two main results can be emphasised:There is a kinetics transition in the wear of A357, which is marked by an increase of wear volume at a critical displacement amplitude The anodised layer eliminates this transition and keeps a linear variation of wear volume versus displacement amplitudes.Under gross slip regime, fretting scars relative to the anodised material show a maximal wear depth much higher than the SA layer thickness. This means that fretting through occurs and there is contact between A357 and the AISI 52100 steel. However, there is no wear kinetics transition when displacement amplitudes increase. Such results could be explained by contact configuration changes with respect to the presence of the SA layer. In fact, using such surface treatment induces a reduction of the adhesion phenomenon especially at the beginning of fretting tests. Furthermore, removal of the anodised layer gives rise to wear debris, which will be trapped in the third body bed and continue to accommodate the tangential displacement. Hence, the wear volume measured on the anodised aluminium alloy presents a linear variation versus the displacement amplitude without any wear kinetics transition.Effect of sulphuric surface anodisation was investigated in two real cases: bearing holder for gear box and buckets of trucks. In the first one, SA treatment was used to avoid fretting damage observed in the A357 aluminium alloy. However, in the second case, SA treatment was employed to perform wear resistance of the 5xxx aluminium alloy under scratch. It was found that the anodisation effect depends on the tribological system:For scratch test, SA treatment decreases abrasive wear resistance despite the increase of the anodised layer hardness. In fact, presence of SA layer induces transition of wear mechanism from ductile to brittle damage. The SEM observations showed ploughing phenomena before anodisation and fracture with presence of wear particles after anodisation. The variation of friction coefficient confirms this behaviour.However, for fretting test sulphuric anodised layer on the A357 eliminates wear kinetics transition and maintains a low wear regime even under large displacement amplitude. Although fretting-through occurs under the gross slip regime, the effect of the oxide layer is maintained in the third body bed allowing wear reduction.Method of evaluating workability in cold pilgeringA new method of evaluating the workability of a tube in cold pilgering has been studied on the basis of material deformability and the effects of process conditions. A circumferential compression test of a tube is confirmed to be an effective evaluation method for deformability. The critical reduction in height upon crack initiation in the compression test is also found to be a good measure of material deformability. Systematic cold pilgering tests and the numerical analysis of cold pilgering are conducted. As a result, the ratio of radial strain to circumferential strain during pilgering is a good indicator of process conditions, and a common mechanism of inner fissure formation during pilgering in stainless steel, titanium alloy, and zirconium alloy is proposed. Finally, a suitable expression for workability is obtained by considering material deformability and the effects of pilgering conditions. These findings will assist the selection of appropriate pilgering conditions to prevent the formation of fissures on the inner surface of a tube.High-quality metallic seamless tubes, including those made of stainless steel, titanium (Ti) alloy, and zirconium (Zr) alloy, are generally fabricated by cold working followed by a subsequent heat treatment to obtain dimensional accuracy and good mechanical properties, i.e., high strength and high ductility. shows the process flow of a seamless tube fabricated by cold working. First, a heat-treated hollow billet is extruded. The extruded tube is annealed if necessary. Subsequently, the tube is repeatedly cold-worked and heat-treated. Finally, the surface of the tube is finished by pickling, polishing, or blasting. Cold working includes cold drawing and cold pilgering. Cold pilgering is suitable for metals that are difficult to deform owing to its compressive reduction mode; reported that it is widely applied to tube manufacture and plays an important role in high-quality tube making. The objective of the present study is to develop a method of evaluating the workability of a tube in cold pilgering. shows an illustration of the cold pilgering process. The tools used are a pair of roll dies and a mandrel. The roll dies have a decreasing caliber from the inlet to the outlet on the outer surface. In pilgering, the roll dies are rotated and simultaneously reciprocated, and the rate of reduction of the outer diameter depends on the caliber. The mandrel, which has a tapered shape in the rolling direction, is located inside the tube. The diameter and wall thickness are gradually reduced with increasing number of forming steps while applying a lubricant, and the tube is elongated in the axial direction. In each forming step, the mother tube is advanced and rotated in the idle zone at a predetermined feed rate and turn angle, respectively, to repeatedly perform rolling during cold pilgering.Various studies on fissure formation in cold pilgering have been reported. conducted cold working tests on austenitic stainless-steel tubes and quantitatively discussed the relation between the reduction mode and inner fissure formation. They indicated that a suitable ratio of wall reduction to diameter reduction (i.e., the reduction mode or Q-factor) was crucial for preventing inner fissures. reported the results of cold working tests on Ti alloy and Zr alloy tubes, which indicated that a reduction with high Q-factor is effective for preventing fissures. reported the formation of inner fissures in the case of reduction with a Q-factor of less than 1. studied the effect of the Q-factor on the inner fissure formation of a Zr-lined Zircaloy-2 tube by performing systematic cold pilgering tests and considering the plastic deformation state during cold pilgering.However, the formation of inner fissures was subsequently observed in the cold pilgering of Zircaloy-2 tubes subjected to rapid quenching during the process, and their formation could not be explained by only the Q-factor. investigated the effects of cold pilgering parameters, including the Q-factor and reduction in area, on the inner fissure formation of Zr alloy tubes subjected to rapid quenching. In their study, a compression test was performed on Zr alloy tube shells to evaluate material deformability, and the relation between cold pilgering parameters and fissure formation was obtained. studied the effect of the roll die caliber on the quality of Zr alloy tubes and proposed an appropriate caliber design for high-reduction cold pilgering. studied inner fissure formation and the factors affecting it in Zr alloy tubes. In their study, a compression test was proved to be a useful measure for evaluating the deformability of Zr alloy tube shells. The compressive properties of the tube shells, which were related to the heat treatment conditions in the process, affected inner fissure formation in cold pilgering.In the present paper, we present a comprehensive study of inner fissure formation in cold pilgering, in which both material deformability and the effects of cold pilgering conditions are considered. The test materials used are two stainless steels, a Ti alloy, and two Zr alloys. The investigation of material deformability includes the metallurgy and compressive property of each test material. Systematic cold pilgering tests and the numerical analysis of cold pilgering are conducted to determine the effects of pilgering conditions on inner fissure formation. From the investigation results, a common mechanism of inner fissure formation for the test materials is revealed. In the discussion, the results in the above-mentioned previous studies () are referred to. A circumferential compression test is proposed as a means of measuring deformability. Finally, the relationship between the material deformability of tubes and the pilgering conditions is discussed.The chemical compositions of the five materials tested, i.e., two stainless steels (M1 and M2), one Ti alloy (M3), and two Zr alloys (M4 and M5), are shown in . M1 is a typical austenitic stainless steel (Type 304), and M2 is a dual-phase stainless steel (Type 329). M3 is an α + β-type Ti alloy that is widely used as an aerospace material. M4 and M5 are Sn–Fe–Cr–Ni–Zr alloys; M4 is a typical material used in the nuclear industry called Zircaloy-2.A billet of each tested material was extruded to form a tube shell, as shown in . The tube shells of the two stainless steels and Ti alloy were cold-worked and heat-treated twice before the cold pilgering tests. The Zr alloy tube shells were annealed at about 650 °C before the cold pilgering tests. The β-quenching method for the billets differed between the two Zr alloy tubes. The billet of M4 was quenched from the β-phase to the α-phase in the solid state using water, whereas that of M5 was quenched with ice-mixed brine while in a hollow shape to obtain a high cooling rate. All the tubes were fully annealed to remove the residual stress before the cold pilgering test.The sampling of specimens and the compression test method are shown in . Specimens were obtained from three directions, i.e., the radial, circumferential, and axial directions, of the tube. The specimens were solid cylinders of 4 mm or 8 mm diameter and 8 mm height; their surfaces were finished to form smooth surfaces with a roughness of 0.8 μm Ra. The compression test was performed in an Instron test machine at room temperature. Both the top and bottom sides of the specimens were lubricated with oil, and the compression speed was kept constant at 5 mm/min. During compression, the actual displacement and load were recorded continuously; thus, crack initiation in the specimens was clearly observed. The critical reduction in height, ϕc, upon crack initiation was calculated usingwhere H is the height of the specimen before the test and h is the height of the specimen upon crack initiation. Also, the yield strength was obtained from the recorded displacement and load.The stainless-steel and Ti alloy specimens were obtained from extruded tube shells of 45 mm outer diameter (OD) and 7 mm wall thickness (WT). The Zr alloy specimens were obtained from tubes of 63.5 mm OD and 10.9 mm WT before the cold pilgering test.In the cold pilgering test of the stainless steels and Ti alloy, the mother tubes tested had an OD of 16 mm, a WT of 1.3 mm, were 2 m long, and were fabricated from tube shells by several cold working and annealing processes. The test tubes were fully annealed and surface-conditioned to a roughness of 0.2 μm Ra by pickling or blasting. The test machine was a small cold pilger mill with a roll die diameter of 100 mm and a working zone length of 180 mm. The feed rate was 2.5 mm and the turn angle was 75°.The five test pass schedules for the stainless steels and Ti alloy are shown in , together with the two cold pilgering parameters, i.e., the reduction in area [Rd(%)] and reduction mode (Q-factor). The Q-factor represents the ratio of wall thickness reduction to diameter reduction and is defined as Q |
= ln(t1/t0)/ln(d1/d0), where t0 and t1 are the wall thicknesses before and after pilgering, and d0 and d1 are the average diameters before and after pilgering, respectively. In the test, Rd was fixed at 80% and the Q-factor was widely varied from 0.7 to 4.2. The depth of the inner fissures was measured by observing the cross section of the cold-pilgered tubes using optical microscopy, and the inner fissures that formed during pilgering were observed by scanning electron microscopy (SEM). Also, the effect of the mother-tube grain size on the workability of M1 was investigated by performing annealing at different temperatures before the pilgering test.In the cold pilgering test of the Zr alloys, the mother tubes of 63.5 mm OD, 10.9 mm WT, and 2 m length were fully annealed and surface-finished to a roughness of 0.2 μm Ra by pickling. The cold pilgering test was performed using a 75VMR-type mill manufactured by Meer with a roll die diameter of 370 mm and a working zone length of 760 mm. The feed rate was 2 mm and the turn angle was 57°. The test pass schedules for the Zr alloys are shown in . M4 and M5 were cold-pilgered using schedules Z1 and Z2, respectively. The reductions were 91% and 87%, respectively, which are relatively high. The other five pass schedules from Z3 to Z7 were used in previous studies (Typical graphs showing displacement versus compression load obtained from the compression test of the stainless steels and Ti alloy are shown in . In all three directions, the two stainless steels did not form cracks up to a displacement of 5 mm, whereas the Ti alloy had slanting cracks. The two Zr alloys formed cracks in the compression test similar to those in the Ti alloy; the appearance of M5 specimens after the compression test is shown in The compression test results of all five materials are shown in . In all three directions, M1 and M2 showed a critical reduction in height, ϕc, of more than 1, and hardly any difference in yield strength (0.2%YS) was observed. Even M2, which has high strength, did not exhibit cracks in any direction. For the Ti alloy, a difference in yield strength was observed among the three directions, and both the circumferential and axial specimens had a much lower ϕc. Both M4 and M5 had a difference in yield strength among the three directions and also had lower ϕc values in all three directions. In particular, M5 had an extremely low ϕc in the circumferential direction.The Ti alloy and Zr alloy tubes had lower compressive deformability than the stainless-steel tubes and significant anisotropy in the yield strength and ϕc among the three directions. This result is related to the fact that Ti and Zr have only a few slip systems causing crystal deformation owing to their hexagonal close-packed (hcp) structure. reported that Ti and Zr exhibit inherent crystallographic and mechanical anisotropies, and that an hcp structure has least deformability in the c-axis direction. In , the existence of a relationship between the c-axis orientation ratio and the ϕc values for the three directions in Zr alloy tube shells was confirmed.The difference in ϕc between M4 and M5 can be explained by the effect of the cooling rate in billet β-quenching, as described in . Namely, the cooling rates of M4 and M5 were about 30 °C/s and over 100 °C/s, respectively. The difference in the cooling rate affected the compressive deformability of the tube shells. The compressibility is related to the dislocation density in the matrix. studied the dislocation behavior of Zircaloy-4 during quenching and annealing, and found that the rapid water quenching of a Zircaloy-4 specimen induced a large amount of dislocation in the matrix that could not be annihilated by subsequent annealing at 650 °C or a lower temperature. reported that the channeling of dislocations led to inhomogeneous plastic deformation in Zircaloy-2. stated that dislocation channeling is produced by quenching or irradiation in many metals, including Zircaloy-4. Thus, the tube shell M5, which was fabricated by extremely rapid quenching and annealing at 650 °C, exhibited less deformability than M4 owing to its larger number of remaining dislocations. studied the relation between stress and crack initiation during compression tests on annealed steel samples. The obtained reduction in height was from 0.6 to 1.8. The compression test results revealed that the Ti alloy and Zr alloy tube shells in the present test had lower deformability than the annealed steel samples.The measurement results for the inner fissure depth of the cold-pilgered stainless-steel and Ti alloy tubes are shown in . A marked difference could be seen among the five test passes as well as among the three materials. In the lower-Q-factor passes (P1 and P2), deep fissures were observed, whereas in the higher-Q-factor passes (P3, P4, and P5), shallow wrinkles were observed. This result is in agreement with those in In pass schedule P1, where the effect of the cold pilgering conditions was significant, the Ti alloy tube (M3) had the deepest fissures of 10 μm, followed by the dual-phase stainless steel (M2) with 8 μm fissures and the austenitic stainless steel (M1) with 6 μm fissures. In pass P2, where the effects of the pilgering conditions as well as the material were observed, the Ti alloy had deep fissures, while the two stainless steels had shallow fissures. In passes P3 and P4, where a difference among the materials was observed, only the Ti alloy had fissures. In pass P5, where the effect of the pilgering conditions was manifest, all material tubes had shallow wrinkles. The Ti alloy had deeper inner fissures than the stainless steels in all the passes. The pilgering test results correspond to the behavior of ϕc for the materials.The result of the test on the austenitic stainless steel with different mother-tube grain sizes is shown in . A mother tube with coarser grains had deeper fissures after pilgering than that with finer grains. shows the inner surface during pilgering. Images were obtained by SEM observation of the austenitic stainless-steel tube during P1, which resulted in the deepest fissures for all three materials. Even when the mother tube (Position 1) had a smooth surface, the tube had a rough inner surface in the early stage of pilgering (Position 2). The roughness on the inner surface changed into wrinkles at Position 3. Eventually, deep fissures were formed on the inner surface at the finishing point of pilgering (Position 4). Similar results were observed for the other materials in this study. A similar result for a Zr-lined Zircaloy-2 tube was also reported in The effect of the grain size of the mother tube on the inner fissure depth, as shown in , is related to the roughness observed at Position 2. In general, a metal workpiece with coarser grains is likely to exhibit roughness on the surface after cold working; such roughness is referred to as “orange peel”. Because the roughness is formed in the early stage of pilgering, the grain size of the mother tube affects the depth of fissures in pilgering. In addition, the inherent deformation systems of materials, such as slip and twin systems, are expected to affect the formation of fissures.The results of the cold pilgering test of the Zr alloy tubes are shown in , together with the pilgering parameters and the ϕc values in the circumferential direction. In the present study, pilgering tests No. 1 and No. 2 were conducted for tube shells M4 and M5, respectively. The results of 16 other tests were reported in . The 18 tube shells had various ϕc values from 0.29 to 0.73; this variation is caused by the different thermal histories of the process, as already mentioned. That is, tube shell M4 in test No. 1 was subjected to a moderate cooling rate (about 30 °C/s) during billet quenching, while tube shell M5 in test No. 2 was subjected to an extremely high cooling rate (over 100 °C/s). The tube shells in tests No. 3 to No. 8 were fabricated by a method involving rapid billet quenching (about 100 °C/s). In contrast, the tube shells in tests No. 9 to No. 18 were fabricated by a combination of three different cooling rates (i.e., 100 °C/s, 30 °C/s, and 15 °C/s) during billet quenching and various annealing temperatures from 649 °C to 788 °C as described in Tube shell M4 in test No. 1, having the higher ϕc of 0.59, had no fissures on the inner surface after the cold pilgering with 91% reduction. In contrast, tube shell M5 in test No. 2, having the lower ϕc of 0.29, had deep fissures of about 0.2 mm after the pilgering with 87% reduction. The relative values of ϕc for the two materials in the compression test are in qualitative agreement with the degree of fissure formation obtained in the cold pilgering test.However, the 18 cold pilgering test results shown in cannot be explained by only considering the circumferential ϕc. Neither can they be explained by only considering the cold pilgering parameters (Rd and Q-factor). Hence, it is necessary to discuss the workability of cold pilgering by considering both the measure of material deformability ϕc and the pilgering conditions. This will be discussed in the next section. developed a method of numerical analysis for investigating cold pilgering. Their analytical model was the first attempt to estimate the plastic deformation state in pilgering. Most subsequent studies on the analysis of cold pilgering have cited this study. reported an improvement in the lifetime of cold pilgering tools by applying results obtained using the analysis method. Finite element (FE) analysis has also been used to investigate cold pilgering. reported a three-dimensional FE analysis of tubes subjected to cold pilgering, citing the study of Furugen and Hayashi, and their results corresponded well with those obtained using the analytical model. Hence, the analysis method of Furugen and Hayashi is useful for estimating the plastic deformation state and is utilized in the following discussion.. In each section, the average stress σ and strain ɛ are calculated in the radial (r), circumferential (θ), and longitudinal (l) directions. The analysis using the method of Furugen and Hayashi was performed to enable a discussion of the pilgering test results.The analysis results of austenitic stainless steel at pass P3 are shown in , as an indicator of the pilgering conditions.. The pilgered tubes are classified into three groups by inspection, namely, no fissures (○), fissures (▵), and deep fissures (●). The figure clearly shows the workability of the Zr alloy tubes in cold pilgering. When the material has good deformability, that is, a high ϕc, severe cold pilgering with a large strain ratio (−ɛr/ɛθ)max is possible. In contrast, when the material has a low ϕc, cold pilgering must be carried out with a small (−ɛr/ɛθ)max to prevent fissure formation.A criterion curve for fissure formation is next discussed on the basis of the theory of ductile fracture, assuming the relation (function of process condition indicator) × (measure of material deformability) = constant. studied the criteria leading to ductile fracture strain in metal forming. The proposed formula of the criterion curve isFrom all 18 cold pilgering test results of Zr alloys, we obtain a |
= 0.45 and b |
= 0.25 and the obtained criterion curve is shown in . The test results of the stainless steels were referred to in the discussion of workability in the case of a high ϕc; namely, even when ϕc is higher than 1, cold pilgering at a strain ratio higher than 0.35 is impossible. Moreover, the pilgering test results of the Ti alloy tube are consistent with the relation shown in . These results will enable a manufacturer to choose appropriate cold pilgering conditions for Zr alloy tubes.Incorporation of carboxylation multiwalled carbon nanotubes into biodegradable poly(lactic-co-glycolic acid) for bone tissue engineering▶ The carboxyl acid groups of acid-treated MWCNTs can form hydrogen bond with polymer matrix to enhance the dispersion of c-MWCNTs in the PLGA matrix. ▶ The incorporation of c-MWCNTs enhanced the mechanical strength of the nanocomposites due to the homogeneous distribution of c-MWCNTs in PLGA matrix. ▶ Addition of c-MWCNTs allowed a better hydrophilicity in the polymer matrix. ▶ The PLGA/c-MWCNT nanocomposites promoted the attachment, proliferation, and differentiation of rat MSCs, which would provide new insights in the PLGA/c-MWCNT nanocomposites for bone tissue engineering.Biodegradable poly(lactic-co-glycolic acid) (PLGA)/carboxyl-functionalized multi-walled carbon nanotube (c-MWCNT) nanocomposites were successfully prepared via solvent casting technique. Rat bone marrow-derived mesenchymal stem cells (MSCs) were employed to assess the biocompatibility of the nanocomposites in vitro. Scanning electron microscopy (SEM) observations revealed that c-MWCNTs gave a better dispersion than unmodified MWCNTs in the PLGA matrix. Surface properties were determined by means of static contact angle, X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM) analysis. The presence of c-MWCNTs increased the mechanical properties of the nanocomposites. Seven-week period in vitro degradation test showed the addition of c-MWCNTs accelerated the hydrolytic degradation of PLGA. In addition, SEM proved that the cells could adhere to and spread on films via cytoplasmic processes. Compared with control groups, MSCs cultured onto PLGA/c-MWCNT nanocomposites exhibited better adhesion and viability and also displayed significantly higher production levels of alkaline phosphatase (ALP) over 21 days culture. These results demonstrated that c-MWCNTs modified PLGA films were beneficial for promoting cell growth and inducing MSCs to differentiate into osteoblasts. This work presented here had potential applications in the development of 3-D scaffolds for bone tissue engineering.Rapid advancement in the field of tissue engineering has led to an increased interest in the use of synthetic biodegradable polymers as scaffold material. Biodegradable polymers such as poly(Recently, carbon nanotubes (CNTs) have been effectively reinforced for polymer composites due to their exceptional mechanical properties, large surface area to volume ratio and easy functionalization capability -lactide-co-epsilon-caprolactone) could increase the mechanical strength of the polymer It has been shown that PLGA/c-SWCNT nanocomposite scaffolds can be used as an improved scaffold for neural tissue engineering Poly(lactic-co-glycolic acid) (PLGA) (Mw = 100,000 g/mol), a copolymer with a lactide/glycolide ratio of 75:25, was purchased from Jinan Daigang Bio-Tech Co. Ltd. (Jinan, China). The MWCNTs of over 95 wt.%, 30 μm length and 20–30 nm diameter were purchased from Chengdu Organic Chemistry Co. Ltd. (Chengdu, China). All other reagents were of analytical grade. Milli-Q water (18.2 MΩ) was used in all of the experimental processes.PLGA/MWCNT nanocomposite films were prepared by the solvent casting technique as previously described The surface morphology of PLGA, PLGA/MWCNTs, and PLGA/c-MWCNTs films was observed using a scanning electron microscopy (SEM) (LEO1530, Germany) at an accelerating voltage of 1 kV. A contact angle goniometer (Krüss DSA100, Germany) was employed to measure the static contact angles of the various samples. The initial distilled water volume of 5 μL was used in each measurement after 15 s exposure to ambient temperature. The images of water drops on the sample surface were recorded by a camera and analyzed with software supplied by the manufacturer. Measurements were performed on five replicate samples for each substrate. Surface chemical compositions of films were characterized by X-ray photoelectron spectroscopy (XPS) (PHI Quantum 2000 Scanning ESCA Microprobe, America). Surface properties of the nanocomposites were examined using a nanoscope atomic force microscope (MI5500, Agilent Technologies, America), in the tapping mode and expressed as height and phase images. Tensile properties of the nanocomposite films were determined with an electronic universal testing machine (WDS-5, China) at a constant crosshead speed of 10 mm/min. Rectangular specimens of dimensions 10 mm × 50 mm were used for testing, and the tensile strength was determined as the maximum point of the stress–strain curve. The elastic modulus was calculated as the slope of initial linear portion of the stress–strain curve. Three samples from each composition were tested to get statistical data of the tensile strength for the composite films.The degradation behaviors of neat PLGA and its nanocomposites were determined by the variation of water absorption and weight loss. All the samples were weighted (W0), immersed in phosphate buffer solution (PBS) solution (pH 7.3) and kept under slow agitation at 37 °C for periods of up to 7 weeks. The PBS was exchanged every week. At desired time intervals, the films were collected and analyzed for water absorption and weight loss behavior. For measuring the water absorption of the samples, the immersed samples were extracted and weighed (Ww) after surface wiping. Similarly, for measuring the weight loss, the dry samples (Wt−dried) were weight after being air-dried and vacuum-dried for 24 h, respectively. Water absorption and weight loss were evaluated by the following equation:Wabsorption(%)=100×Ww−Wt−driedW0,Wloss(%)=100×W0−Wt−driedW0where Wt−dried was the weight of sample subjected to hydrolytic degradation for time t and dried in vacuum.A protein adsorption assay was carried out on the samples using fetal bovine serum (FBS, Gibco), as developed by Cai et al. Mesenchymal stem cells (MSCs) were isolated from bone marrow of rats’ femur and tibia (SD rat, with four or five-week-old) using well-established methods -glutamine (Gibco), and 1% penicillin and streptomycin (pen/strep, Gibco) at 37 °C under 5% CO2 atmosphere. MSCs were selected from the marrow aspirate on the basis of their ability to adhere to tissue culture plastic. Nonadherent cells were removed in repeated washes with PBS two days later and the medium was changed every three days. Primary culture MSCs were subsequently detached using 0.25% trypsin (Sigma), replaced at a lower density, and cultured until confluency to generate first passage MSCs. The cells between the third and the fourth passages were used in the following studies. For osteogenic differentiation, the MSCs were treated with a cocktail of 10−8 |
M dexamethasone, 10 mM β-glycerophosphate and 50 μg/ml ascorbic acid (Sigma).For morphological observation, MSCs were seeded on the PLGA, PLGA/MWCNTs and PLGA/c-MWCNTs films at a density of 2 × 104 cells/well in a 24-well plate. The cells adhering to the films were washed with PBS after 24 h of incubation, and then fixed with 2.5% glutaraldehyde solution at 4 °C for 3 h and rinsed three times with PBS. Next, the samples were dehydrated in an ethanol gradient series, air-dried in a laminar air flow cell culture hood, lyophilized, and sputter coated with gold to be visualized by SEM at low (100×) and high (1000×) magnification at 5 kV.Cell attachment assay was performed on different films and tissue culture polystyrene (TCPS; control group) as described previously Cell proliferation was using WST-1 assay according to the manufacture's protocol. MSCs at a density of 5 × 103 cells/well in 96-well plates were seed on different films or TCPS for 3, 7, 14 and 21 days culture, respectively. Then 10 μl of WST-1 (2-(4-iodophenyl)-3-(4-nitophenyl)-5-(2,4-disulfophenyl)-2H-tetrazolium salt) reagent (Beyotime, Shanghai, China) was added to each well and incubated at 37 °C, 5% CO2 for another 2 h, followed by recording the absorbance of the samples using a microplate reader (Model 680, Bio-Rad, USA) at a wavelength of 450 nm with the reference wavelength 650 nm. Each treatment was performed five times. The cells cultured on TCPS at the same time intervals were used as controls (100% viability).Cell differentiation was assessed by measuring the alkaline phosphatase (ALP) activity of cells cultured on the films. The procedure was performed as described previously All assays were repeated with a minimum of n |
= 3 independent determinations for each data point and were expressed as means ± standard deviation (SD). The differences among the samples were tested by Student's t-test with a significance level of P |
< 0.05 or P |
< 0.01.The morphological characteristics of the polymer/CNT nanocomposites were essential to investigate the dispersion of the CNTs in the polymer matrix. The SEM images (, which could lead to a decrease in the interface area between CNTs and polymer. In contrast, PLGA/c-MWCNT nanocomposites (b) showed uniform distribution of CNTs (shown in red) in the matrix very distinctly (For interpretation of the references to color in this text, the reader is referred to the web version of the article.). The presence of carboxylic acid groups on the fabricated nanocomposites was verified by FTIR spectroscopy, as shown in , wherein the characteristic bands at 1051 and 1720 cm−1 can be observed. What's more, the TEM images () showed that the c-MWCNTs were shorter than pristine MWCNTs. The length shortening of MWCNTs is because of purification and carboxylation of MWCNTs using strong acid treatment. Because the carboxyl acid group of c-MWCNTs could form the hydrogen bonding with polymer matrix and shorter CNTs tend to avoid agglomeration, the c-MWCNTs achieved better dispersion in PLGA. This was further confirmed by optical micrograph of PLGA and its nanocomposites (). Another study also revealed that the functionalization of CNTs offered better possibilities for their dispersion in the PLGA matrix XPS is capable of providing both qualitative and quantitative information about the presence of different elements on the surface. lists the similar surface chemical compositions of the films, indicating CNTs covered by PLGA for nanocomposites. The presence of the silicon at the surface of the samples as seen in the XPS data may be partly due to the silicon substrate interface.Contact angle generally indicated the wettable properties of measured substrates , the wettability of the nanocomposites in comparison with the neat polymer (which was measured to be 83.0 ± 0.8°) increased significantly, further confirming the hydrophobic nature of the polymer. The decrease in water contact angle was more prominent for the PLGA/c-MWCNT films with 76.8° than for the PLGA/MWCNT films with 81.1° (n |
= 5, *P |
< 0.01) due to the fact that the acid-treated MWCNTs were more hydrophilic than pristine MWCNTs Surface topographies of nanocomposite films were shown in . Analysis on the surface topography revealed that root mean squared roughness (RMS roughness, Sq = |
SRMS) Sq was 0.28 ± 0.02, 0.81 ± 0.12 and 0.45 ± 0.05 nm for PLGA, PLGA/MWCNTs, and PLGA/c-MWCNTs (), respectively. It can be clearly seen that CNTs modified PLGA had higher surface toughness than neat PLGA. The difference in surface roughness originated from the distribution of CNTs in the matrix and their interaction with the polymer at the solution stage The protein adsorption study showed that the total amount of protein adsorbed on the surface was higher for the nanocomposites compared to the unfilled polymer (which was measured to be 169 ± 19 μg/cm2), as evident from the results in . For example, nanocomposites with c-MWCNTs and pristine MWCNTs resulted in 124% and 144% increase (n |
= 3, **P |
< 0.01), respectively. The presence of pristine MWCNTs in the matrix resulted in higher protein binding compared to the c-MWCNTs but this difference was not statistically significant. Material surface chemistry and surface topography strongly influence protein adsorption behavior. Such a difference in protein adsorption capability is thought to be related to the marked differences in surface morphology and surface area available for protein adsorption for each of the three films as shown in . This result was consistent with previous study The typical stress–strain curves of the pure PLGA and its nanocomposites were shown in . The results of tensile test indicated that the stress increased sharply during the initial stage of stretching and reduced subsequently until finally fracture. The tensile strengths of PLGA/c-MWCNTs and PLGA/MWCNT nanocomposites were 11.3 ± 1.3 and 6.7 ± 0.8 MPa, respectively, in comparison to 4.1 ± 0.5 MPa for PLGA (). The tensile strength of PLGA/c-MWCNT nanocomposite film was enhanced by nearly three-fold compared to those of pure PLGA films and by nearly two-fold compared to those of PLGA/MWCNT nanocomposite film. PLGA/c-MWCNT nanocomposites had an average elastic modulus of 375 ± 20 MPa, which was an 82% improvement over PLGA (67 ± 10 MPa). PLGA/MWCNTs also showed an improvement of 73% in the value (248 ± 38 MPa) as compared to the PLGA matrix. Tensile tests demonstrated that the presence of functionalized MWCNTs in nanocomposites could efficiently enhance reinforcement by improving solubility and dispersion in the polymer. Previous studies have reported that the reinforcement effect depends on the interfacial adhesion and interface area between CNTs and polymers The addition of MWCNTs on the hydrolytic degradation of PLGA was of great interest. reveals that the water absorption of the PLGA/c-MWCNT nanocomposites was higher than that of the PLGA/MWCNT nanocomposites. There were significant increase (*P |
< 0.05) in water absorption and weight loss of the PLGA/CNT nanocomposite films in comparison with the unfilled PLGA films, and this result further confirmed the hydrophobic nature of PLGA. The ultimate values of the weight loss reached around 6.94%, 7.08%, and 7.65% for pure PLGA, PLGA/MWCNTs and PLGA/c-MWCNTs films, respectively after exposure to PBS solution for 7 weeks as shown in b. Obviously, the pure PLGA degraded slowly while the incorporation of CNTs filler accelerated the degradation process. Moreover, the weight loss of PLGA/c-MWCNT nanocomposite was slightly higher than that of PLGA/MWCNT nanocomposite, and this result was similar with previous reports on the mass loss behavior of PLLA/MWCNT nanocomposite The cellular behavior on biomaterials was an important factor to evaluate the biocompatibility of biomaterials, while spreading was crucial for cell growth and differentiation. shows the morphology of the MSCs cultured on the PLGA and MWCNT-modified PLGA films. The cells were found to be typical MSCs morphology, linked with fibers via cytoplasmic processes, and spread on all the substrates, which reflected the overall good adherence of the cells to the surfaces of the nanocomposite films. However, the cell growth was influenced by the surface type. also provides a comparative picture of the population of cells on the three films. Broadly speaking, MSCs cultured on unfilled PLGA adopted a less well-spread morphology as compared to the cells grown on the nanocomposites (a–c respectively). The edge of the cell was characterized by the presence of lamellipodia which are membrane protrusions extended over a substratum to form new cellular contacts d–f) showed extensive formation of filopodia on nanocomposite films with higher protein absorption.The result of the cell attachment test was shown in . The number of adherent MSCs on the PLGA was 70% of the controls, and MSCs did attach and spread on the PLGA/MWCNTs film at a compatible level with the controls, while PLGA/c-MWCNTs showed more attached cells than the controls, and this difference was statistically significant (*P |
< 0.05) (e). The CNT-modified PLGA films dramatically improved the ability of MSCs by increasing protein absorption and decreasing contact angles. Indeed, as reported by the literature, the surfaces with contact angles ranging from 60° to 80° allowed good cell attachment ). In addition, Lee et al. demonstrated that the hydrophobic surfaces can cause the denaturation or conformational changes of the adsorbed proteins a factor which would limit cell adhesion, as the appropriate integrins were not available for binding The difference of protein absorption for CNTs-modified PLGA was not statistically significant. However, higher surface roughness obstructs cell proliferation and attachment due to its increased surface tension and reduced contact angle shows the proliferation of MSCs growing on various materials over 21 days. The enhanced cell attachment on the nanocomposites affected further proliferation level. Compared to the control group (TCPS), a comparable level was found in cell viability of MSCs adhering on PLGA/c-MWCNTs film on day 3 and 7, however significantly increased (**P |
< 0.01) on day 14 and 21. The MSCs proliferation on the PLGA/c-MWCNTs film was higher than that on the PLGA and PLGA/MWCNTs films for all the culture time points. It was worth noting that the MSCs growing on PLGA/MWCNTs film were significantly higher than those growing on PLGA film until 3 weeks (*P |
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