Low Elastic Modulus Research Articles

Comparative Analysis of Water Hammer Performance in Different Pipe Parameters with FSI

Water hammer (WH) is a critical phenomenon in fluid-filled piping systems that can lead to severe pressure surges and structural damage. The characteristics of the pipe material, geometry, and support conditions play a crucial role in the fluid–structure interaction (FSI) during WH events. This study investigates the impact of various pipe parameters, including material, length, thickness, and diameter, on the WH behavior using an FSI-based numerical approach. A comprehensive computational model was developed based on the algorithm presented in Delft Hydraulics Benchmark Problem (A) to simulate the WH phenomenon in pipes made of different materials, such as steel, copper, ductile iron, PPR (polypropylene random copolymer), and GRP (glass-reinforced plastic). This study examines the influence of pipe parameters on WH performance in pipelines, utilizing FSI to analyze the phenomenon. The results show that the pipe material has a significant influence on the pressure wave speed, stress wave propagation, and the overall system response during WH. Pipes with lower modulus of elasticity, such as PPR and GRP, exhibit lower pressure wave speeds but higher stress wave speeds compared with steel pipes. Increasing the elastic modulus, pipe wall thickness, length, and diameter enhances the pipe’s stiffness and impacts the timing, magnitude of pressure surges, and the likelihood of cavitation. The findings of this study provide valuable insights into the design and mitigation of WH in piping systems.

Improvements in manufacturability, bonding strength, and curing efficiency of a silicone adhesive

Two-component room temperature vulcanizing silicone adhesive RTV566 with a lower elastic modulus has been widely used in precision optomechanical products such as remote sensors and aerospace infrared cameras. However, the silicone adhesive is of poor manufacturability due to its extremely high viscosity, and the bonded joint usually exhibits low bonding strength and requires a long curing time. This paper investigates a way to improve both the adhesion strength and curing efficiency of Invar alloy and optical glass with RTV566 through single-lap experiments. It is found that adding small amounts of acetone and water can significantly reduce the viscosity, enhance the bonding strength, and shorten the curing time. The viscosity can be reduced by 63.4 % and the bonding strength can be improved by 136.4 % with the weight ratio of adhesive to acetone being 20:2. Moreover, a little amount of water in the weight ratio of 100:10:0.1 (adhesive: acetone: water) can shorten the curing time from 7 days to 4 days without harms to the bonding strength and elastic modulus. As to the mechanism, the silicone adhesive can be dissolved by acetone and its sulfuration reaction can be enhanced by water, resulting in good manufacturability and high curing efficiency. This work contributes a novel and easy-to-use method to greatly improve the performances of the bonding process of precision optical structures.

Analysis of Rock Mechanical Characteristics and Establishment of an Evaluation System for Coal Measures in the Longtan Formation, Guizhou Province.

The mechanical properties of coal measure rocks and their evaluation significantly impact the process and efficacy of coal measure exploration and development. This study focuses on the Guizhou Longtan Formation coal measure. The mechanical and fracturing characteristics of coal measure rock samples are analyzed via well coring, geophysical logging, and indoor experiments. Additionally, predictive models for rock mechanical parameters are developed, and an evaluation system for the Longtan Formation coal measure rock mass is established. The findings are as follows: (1) Coal measure rocks in Guizhou's Longtan Formation exhibit a relatively low elastic modulus and tensile strength, but a substantial variation in compressive strength. The triaxial compressive strength, elastic modulus, and residual strength increase nonlinearly with increasing confining pressure. As the confining pressure increases, the failure mode of the mudstone and siltstone transitions from primarily splitting failure to shearing failure. (2) Strong correlations are calculated between logging parameters and rock mechanical parameters and are used to construct three regression prediction models, yielding an average prediction accuracy of approximately 85% for rock mechanical properties. (3) Considering the rock mechanical properties, rock mass structure and stratigraphic characteristics, and the occurrence environment related to the characteristics of rock mass affecting coal measure gas development, eight evaluation indices are selected. The analytic hierarchy process-entropy weighting method is used to determine the weights of the comprehensive evaluation indices, and a coal measure rock mass evaluation system is established by utilizing gray clustering analysis. The evaluation results categorize the mudstone group (mudstone and silty mudstone) as Classes III-IV, the fine sandstone group as Classes I and II, and the siltstone group (muddy siltstone and siltstone) as Classes II and III. A comparative analysis with fuzzy comprehensive evaluation results and extenics theory evaluation results demonstrated a high level of consistency. These findings benefit coal measure rock mechanics classification and quantitative research on rock mechanics properties, providing a solid foundation for efficient coal measure gas exploration and development.

Study on Key Parameters and Design Methods for the Density-Mix Proportion of Rubber-Foamed Concrete

Rubber-foamed concrete demonstrates exceptional toughness, a low elastic modulus, and significant sensitivity to density. It is necessary to parameterize the density mix of rubber-foaming concrete to meet engineering design requirements. Density-mix design methods for foaming concrete rely mainly on empirical knowledge or trial-and-error approaches. In this paper, with numerous parametric tests and regression analysis based on general principles for density-mix designs applicable to both foamed and rubber-foamed concretes, the key design parameters, such as volume correction coefficient, rubber size effect coefficient, and water-reducing agent effect coefficient, have been proposed in order to optimize their respective densities more accurately. The tests demonstrated an optimal water-to-cement ratio of 0.45, corresponding to a volume correction factor of 1.027. Incorporating rubber particles and water-reducing agents has a more significant effect on the cement-paste volume. Controlling fluidity in the 200 to 300 mm range is crucial when designing foamed concrete with varying densities. The regression equation accurately predicts the paste’s measured volume and wetting density by incorporating volume corrections, size, and water reduction effect coefficients. By employing a foam excess coefficient of 1.1 and a mass coefficient of 1.25, the dry and wet density error of foam concrete is less than 5%. A comprehensive framework for optimizing mix design in terms of density is provided for applications in foamed concrete and rubber-foamed concrete, facilitating researchers in designing mix ratios for additional novel mixture-based foamed-concrete applications.

The influence of different diagenesis on the elastic properties of different shale lithofacies: a case study of the upper Permian Wujiaping formation in East Sichuan Basin, China

Understanding the impact of diagenesis on the elastic properties of organic-rich shale reservoirs is essential for evaluating unconventional hydrocarbon reservoirs and interpreting seismic data. Recent advancements in the exploration of the Permian Wujiaping Formation in the eastern Sichuan Basin indicate its potential to become a significant succession within the Sichuan Basin. However, the effect of different lithofacies in the Wujiaping Formation on shale elastic properties under varying diagenetic conditions remains unclear, hindering detailed reservoir interpretation. This study employs X-ray diffraction, thin section analysis, scanning electron microscopy, organic geochemistry, and dynamic elastic property tests to investigate the Wujiaping Formation shale. The results reveal three primary lithofacies types: argillaceous shale, mixed shale, and siliceous shale. Argillaceous shale, subjected to intense compaction, forms a dense rock framework of oriented clay minerals, characterized by low porosity (1.66%), low elastic wave velocity (4122.30 m/s), low elastic modulus (2174.59 m/s), and high Poisson's ratio (32.24 GPa). Mixed shale, dominated by carbonates and quartz, exhibits a rock framework formed through dissolution and cementation, with high elastic wave velocity (5196.54 m/s), relatively high elastic modulus (2975.86 m/s), and moderate Poisson's ratio (58.53 GPa). Siliceous shale, comprising biogenic quartz particles, shows strong resistance to compaction. During hydrocarbon generation, it develops abundant organic matter pores, resulting in the highest porosity (2.36%), high elastic wave velocity (5177.92 m/s), high elastic modulus (2975.86 m/s), and low Poisson's ratio (62.23 GPa). The significant differences in mineral composition and diagenetic processes across the lithofacies lead to distinct elastic properties. This study provides a rock physics framework for the detailed seismic prediction of "sweet spots" in the Wujiaping Formation shale reservoirs and offers new insights into characterizing the diagenesis of unconventional shale reservoirs using geophysical properties.

Influence of prosthetic index structures and implant materials on stress distribution in implant restorations: a three-dimensional finite element analysis

BackgroundMechanical complications affect the stability of implant restorations and are a key concern for clinicians, especially with the frequent introduction of new implant designs featuring various structures and materials. This study evaluated the effect of different prosthetic index structure types and implant materials on the stress distribution of implant restorations using both in silico and in vitro methods.MethodsFour finite element analysis (FEA) models of implant restorations were created, incorporating two prosthetic index structures (cross-fit (CF) and torc-fit (TF)) and two implant materials (titanium and titanium-zirconium). A static load was applied to each group. An in vitro study using digital image correlation (DIC) with a research scenario identical to that of the FEA was conducted for validation. The primary strain, sensitivity index, and equivalent von Mises stress were used to evaluate the outcomes.ResultsChanging the implant material from titanium to titanium-zirconium did not significantly affect the stress distribution or maximum stress value of other components, except for the implant itself. In the CF group, implants with a lower elastic modulus increased the stress on the screw. The TF group showed better stress distribution on the abutment and a lower stress value on the screw. The TF group demonstrated similar sensitivity for all components. DIC analysis revealed significant differences between TF-TiZr and CF-Ti in terms of the maximum (P < 0.001) and minimum principal strains (P < 0.05) on the implants and the minimum principal strains on the investment materials in both groups (P < 0.001).ConclusionsChanges in the implant material significantly affected the maximum stress of the implant. The TF group exhibited better structural integrity and reliability.

Multiscale exploration of Ti-Nb-Zr-based alloys for enhanced bioimplant performance

Beta-titanium alloys (β-Ti alloys) with low elastic modulus are metallic materials of great technological interest for high-performance bioimplants. This study employs a comprehensive multiscale approach to investigate alloys from the Ti-Nb-Zr-Sn system, exhibiting desired bioimplant properties such as low elastic modulus and high β-phase stability. The multiscale strategy encompasses electronic structure calculations, integrating them with device simulations through a coupling of calculation of phase diagrams, density functional theory (DFT), machine learning (ML), and finite element analysis (FEA). Utilizing ML and DFT methodologies, we predict and analyze the elastic and electronic properties of the optimized ternary and quaternary alloys. DFT calculations point to elevated β-phase stability compared to omega-phase, suggesting a potential formation of orthorhombic martensite in the Ti-22Zr-11 Nb-4Sn (at%) alloy. Incorporating small amounts of Sn changes the nature of the bonds, resulting in structural and electronic stabilization of the beta-phase. FEA further validates the mechanical performance of the proposed alloys, demonstrating their potential compared to the well-established Ti-Nb-Ta-Zr (TNZT) alloy, a reference in the field. Our findings underscore the effectiveness of multiscale methodologies in advancing the understanding of alloy design for bioimplant applications. We conclude that this multiscale strategy not only elucidates the compositions of interest but also serves as a catalyst for innovation and progress in the field of bioimplantation.

Relationship between elastic properties and energy absorption of different types of aramid and UHMWPE composites used in ballistic protection

This study aimed to analyse composite materials' mechanical and elastic properties from various aramid and ultra-high- molecular-weight polyethylene fabrics used in ballistic armour materials. Furthermore, a comprehensive analysis was conducted to examine the correlations between the energy absorption data acquired from the low-velocity impact, dynamic compressive, and ballistic impact V50 tests performed in our prior investigations and the tensile test outcomes of these composites. The research revealed a notable correlation between Poisson's ratio, elasticity modulus values, and energy absorption capability. The composite material with the lowest Poisson ratio exhibited superior energy absorption performance in all tests. Composites reinforced with unidirectional textiles have attracted attention due to their low Poisson ratio and high elasticity modulus values, resulting in exceptional energy absorption capability.

Investigating dilation response in PET FRP-confined reinforced concrete: Experimental study

In compression, concrete undergoes dilation due to the Poisson’s effect. Beyond the elastic limit, rapid crack propagation causes unstable expansion, leading to stiffness degradation, reduced strength, and ductility. External confinement with fiber-reinforced polymer (FRP) composites effectively manages this dilation, maintaining core integrity at high strength and deformation levels. However, internal steel reinforcement, especially when poorly detailed, can hinder FRP's efficacy by inducing stress concentrations from longitudinal bar buckling, resulting in premature FRP failure. This study addresses this challenge by utilizing polyethylene terephthalate (PET) FRP with a large rupture strain (LRS) capacity to delay premature rupture to high strain levels. Experimental results on poorly detailed reinforced concrete (RC) externally confined with PET FRP are presented, with variables including PET FRP layers, longitudinal bar buckling length, and cross-sectional aspect ratio. Detailed discussions on the effects of these variables on lateral to axial strain ratio, dilation rate, and volumetric response of confined concrete are provided. Test results have shown that PET FRP effectively managed the unstable dilation of confined concrete, even with internal steel reinforcement. Following the yielding of lateral ties and the buckling of longitudinal bars, PET FRP efficiently handled local stress concentrations and redistributed internal concrete damage. Despite PET FRP's low elastic modulus causing significant lateral expansion, its LRS capacity maintained the integrity of the entire column under high deformation.

Compressive Behavior of Novel Additively Manufactured Ti-6Al-4V Lattice Structures: Experimental and Numerical Studies.

This paper presents novel configurations for additively manufactured lattice structures, including helical and elliptic designs, in addition to the pyramid base model. Functionally graded versions of the pyramid and elliptic lattice structures are developed by considering desirable relative densities in each layer. The lattice structures were manufactured using Ti-6Al-4V powder in a three-dimensional selective laser melting printer. The averaged porosities are 0.86, 0.91, 0.916, 0.93 and 0.74 for pyramid, functionally graded pyramid, elliptic, functionally graded elliptic and helical, respectively. The mechanical behavior of the lattice structures was characterized through compression tests using a universal testing machine and computationally analyzed using finite element code. The results indicate that the elliptic and functionally graded elliptic lattices have elastic moduli of 0.76 and 0.67 GPa, while the yield strengths are 41.32 and 32.24 MPa, respectively, in comparison to cancellous bone. Moreover, pyramid, functionally graded pyramid, and helical lattices show relatively lower elastic moduli of 0.57, 0.65 and 0.41 GPa and higher yield strengths of 54.1, 52.15 and 61.02 MPa, respectively. This could be an indication that they are fit for cortical bones. All samples have low elastic moduli coupled with high yield strengths. This could reduce or eliminate stress shielding, making them suitable for some load-bearing bio-inspired applications. A comparative study utilizing experimental and numerical models was conducted to evaluate the performance of the proposed designs.

Effectiveness of hybrid textile bars in tensile and bond stresses as an alternative to concrete reinforcement

Development for low and/or middle-income countries is not an option anymore. Therefore, developing Egyptian society must create its own sustainable model based on the ability to leverage the existing resources. Hybrid Textile Fiber Reinforced Polymers (HTFRP) introduce an innovative and/or alternative approach to replace traditional steel bar. Our study aims to introduce HTFRP to overcome the poor elastic modulus of existing FRP bars when utilized as a structural element in reinforced concrete constructions. In the proposed hybrid rebar, the steel core is protected through winding of various textile materials as an out layer. Thus, the relatively cheap cost of steel improves the viability of utilizing HTFRP. In addition, the behavior of HTFRP with varied volume fractions under uniaxial tensile load is investigated. Moreover, the bond stress of various HTFRP texture treatments is assessed. During the experimental investigation of the study, four groups were involved: Group A contains ten samples of natural and synthetic ropes which were used either before treatment or after being immersed in polyester resin to form the matrix. Group B contains five samples of Glass Fiber Reinforced Polymer (GFRP) bars made of glass fiber and matrix with variable volume fractions. Group C contains seven samples of hybrid/core-steel bars. The types of steel include wires steel, threaded steel, and mild steel. Finally, group D contains two samples of hybrid/powder bars. To assess the bond stress, four groups with various surface treatments of hybrid GFRP bars, including rib yarn, rib knotted yarn, braided yarn, and uniform sand-coated, are considered. The results showed that increasing the volume fraction of the GFRP rods increases the number of fibers, which leads to a significant improvement in the properties of the GFRP rods. In addition, the hybridized bars have more balanced tensile behavior that not only enhanced the ultimate tensile strength compared to steel reinforcement but also overcame the limitation of GFRP bars’ low elastic modulus by introducing a 220% improvement. The results showed also that braided yarn treatment has the highest pullout strength of 15.03 MPa, while the rib knitted treatment showed the lowest pullout test of 10.61 MPa. Moreover, the braided, rib yearn, and sand samples showed increased pullout results of 41.65%, 16.68%, and 12.06% respectively, compared to the rib-knotted sample. Finally, the rib-knotted and sand-coated samples illustrated sudden failure, whereas the rib knotted and rib sample had a ductile failure.

Production and performance evaluation of chitosan/collagen/honey nanofibrous membranes for wound dressing applications

Persistent bacterial infections are the leading risk factor that complicates the healing of chronic wounds. In this work, we formulate mixtures of polyvinyl alcohol (P), chitosan (CH), collagen (C), and honey (H) to produce nanofibrous membranes with healing properties. The honey effect at concentrations of 0 % (PCH and PCHC), 5 % (PCHC-5H), 10 % (PCHC-10H), and 15 % (PCHC-15H) on the physicochemical, antibacterial, and biological properties of the developed nanofibers was investigated. Morphological analysis by SEM demonstrated that PCH and PCHC nanofibers had a uniform and homogeneous distribution on their surfaces. However, the increase in honey content increased the fiber diameter (118.11–420.10) and drastically reduced the porosity of the membranes (15.79–92.62 nm). The addition of honey reduces the water vapor transmission rate (WVTR) and the adsorption properties of the membranes. Mechanical tests revealed that nanofibers were more flexible and elastic when honey was added, specifically the PCHC-15H nanofibers with the lowest modulus of elasticity (15 MPa) and the highest elongation at break (220 %). Also, honey significantly improved the antibacterial efficiency of the nanofibers, mainly PCHC-15H nanofibers, which presented the best bacterial reduction rates against Staphylococcus aureus (59.84 %), Pseudomonas aeruginosa (47.27 %), Escherichia coli (65.07 %), and Listeria monocytogenes (49.58 %). In vitro tests with cell cultures suggest that nanofibers were not cytotoxic and exhibited excellent biocompatibility with human fibroblasts (HFb) and keratinocytes (HaCaT), since all treatments showed higher or similar cell viability as opposed to the cell control. Based on the findings, PVA-chitosan-collagen-honey nanofibrous membranes have promise as an antibacterial dressing substitute.

Synthesis of a novel flocculant with dimethylamino propylmethacrylamide and polyether and its flocculation performance

The widespread use of polymer flooding has resulted in a large number of produced liquids consisting of crude oil emulsions and oily wastewater. Efficient flocculants are required to treat these produced liquids till the oily wastewater satisfies the requirements for reinjection formation in order to maintain the regular manufacturing process. In this work, an unsaturated polyether macromonomer (PEP-30) was prepared by ring-opening polymerization using isobutenol as a starting material. Subsequently, a novel flocculant (PMAP) was obtained by copolymerization of dimethylamino propylmethacrylamide (DMAPMA) and PEP-30. For the produced liquids with different crude oil emulsion content, the oil removal rate of PMAP at a dosage of 150 mg/L was more than 75%, and the oil removal rate and versatility were better than those of conventional cationic flocculants. Furthermore, the findings of the flocculation mechanism investigation demonstrated that PMAP had a low interfacial elastic modulus and a large interfacial adsorption mass. Specifically, the optical tweezers were used to detect the interaction force between oil droplets. PMAP effectively strengthened the attraction between oil droplets, extending their duration in contact during flocculation and promoting their coalescence.

Enhanced sintering resistance in LaYbZr2O7 system through HfO2 doping for thermal insulation ceramic materials

AbstractThe increase in operating temperature contributes to improving the performance and fuel utilization efficiency of gas turbines. However, it also places thermal barrier coatings (TBCs) in a more demanding working environment, requiring higher sintering resistance and better mechanical properties. In the present study, HfO2 was introduced into the dual‐phase LaYbZr2O7 system as a doping oxide to form the LaYb(HfxZr1−x)2O7 system. The research concentrated on its phase composition, mechanical properties, and thermophysical properties. The results show that substituting Hf for Zr does not alter the dual‐phase structure of the system. The mutual inhibition between the two phases and the inherent material‐binding capability of Hf further reduce the grain size compared to pure LYZO. Additionally, the presence of Hf reduces the tendency of Frenkel defect formation and cation migration frequency, effectively inhibiting ion diffusion and thereby suppressing the densification and shrinkage trends of the material. The system retains relatively high hardness, fracture toughness, and low elastic modulus of the LYZO matrix, with a decrease in thermal conductivity and an increase in infrared reflectivity. These results suggest that Hf doping enhances the sintering resistance of LYZO material, making them promising for high‐temperature TBCs. Our study presents a viable approach to enhance the sintering resistance of LYZO, and this methodology can be extrapolated to other rare‐earth zirconates.

Experimental study on the shear and slip behaviors of perfobond strip connectors with low elastic modulus material wrapped perforated rebars

Adopting Ultra-high performance concrete (UHPC) endows steel-UHPC composite beams with numerous benefits, including high cracking capacity, high durability, light self-weight, etc. However, the cracking load of the steel-UHPC composite beams under negative moments reaches only 13–40 % of their ultimate load, with cracking properties being the primary constraint to the development of steel-UHPC composite beams. This study proposed a novel uplift-restricted and slip-permitted (URSP)-PBL connector to improve the crack resistance in the negative moment regions of continuous steel-UHPC composite beams. A total of ten push-out tests were conducted to investigate the behaviors of the URSP-PBL connector. The effects of perforated rebar diameter, rubber thickness, and row numbers on the URSP-PBL connector were investigated by evaluating the failure mode and the load-slip relationship of the push-out specimens. Additionally, numerical analyses were carried out to investigate the effect of various parameters on the mechanical properties of the connector. Based on the analysis results, a load-slip curve model of the URSP-PBL connector was established as a reference for the promotion of the URSP-PBL connector in steel-UHPC composite structures.

Cooperation mechanism between the vacuum levels and interface dipole energy of triboelectric materials for real-time vibration recognition

Triboelectric Nanogenerator (TENG) device, acting as sensors of energy harvesting and material identification, are attracting intensive attention. Nevertheless, vibration wave recognition cannot be achieved by the developed devices owing to device structure and working mechanism limitations. Here, a cooperation mechanism between the vacuum level and interface dipole energy of triboelectric materials is proposed to explore triboelectric charge generation and migration. Hence, metallized cottons of high specific surface area encapsulated by polydimethylsiloxane (PDMS) of low elastic modulus are developed as TENG-based sensors to realize vibration recognition. The results indicate electrons flow from PDMS to metallized cotton with the generation of an extremely thin interfacial dipole barrier layer because the vacuum level of metallized cotton is higher than that of PDMS, resulting in the accumulation of triboelectric charges on the PDMS surface under vibration, further leading to generating distinct triboelectric signals that can be simply differentiated using signal amplitude or peak shape with 98.3 % recognition accuracy for vibration waveform. Besides, combined with the deep machine learning and triboelectric effect, a vibration perception system integrated with a TENG-based sensor, data processing and display modules is also developed for real-time vibration monitoring. This work contributes to further clarifying the theoretical mechanisms of triboelectric charge excitation under vibration.

The evolution of microstructure and mechanical properties of Inconel 625 alloy fabricated by laser powder bed fusion via novel hybrid scanning strategy

Four innovative hybrid scanning strategies (0° + 67°, 45° + 67°, 67° + 67° and 90° + 67°) of laser powder bed fusion (LPBF) have been proposed to tailor the microstructure and mechanical properties of Inconel 625 alloy for the first time. The experiment results revealed in sample I (0° + 67°) and sample IV (90° + 67°) a gradient structure is formed, progressing from randomly textured slender columnar crystals (001) to randomly textured equiaxial fine crystals, and finally to equiaxial and fine columnar crystals. In samples II (45° + 67°) and III (67° + 67°), isometric and columnar crystals are uniformly distributed throughout the sample. The tensile strengths of samples treated via hybrid scanning strategy in LPBF (sample I: 1270 ± 8 MPa, sample II: 1400 ± 6 MPa, sample III: 1390 ± 5 MPa and sample IV: 1360 ± 5 MPa) surpassed those of conventionally manufactured samples, including Inconel 625 alloy fabricated by LPBF using a single scanning strategy. This superiority can be attributed to the presence of fine grains, elevated residual stress levels, and the formation of stacking faults. The results of the nanoscratch test reveal that the bottom surface of samples I and IV demonstrates superior abrasion resistance in comparison to the top surface, which can be attributed to the higher relative density, finer grain size, lower elastic modulus and lower Schmidt factors in the bottom surface. These findings hold significant implications for tailoring the microstructure and properties of Inconel 625 alloy, especially in the realm of additively manufactured materials featuring heterogeneous structures.

Exact solution for mode shapes of cracked nonuniform axially functionally graded beams

This paper established the exact formulas for mode shapes of cracked nonuniform axially functionally graded (AFG) beams. The formula of the mode shape of cracked nonuniform AFG beam is derived in the form of a power presented as a recurrent relation. The power series solution of cracked beam is the same with the intact beam where the effect of cracks contributes to only the first four coefficients of the power series. The derivation of the formula of mode shapes is presented in details. Numerical simulations show that these effects on the natural frequency and mode shape are quite significant. The natural frequency and mode shape are more sensitive to cracks located at positions with low elastic modulus, small cross section and high mass density. For the case of tapered AFG cantilever beam, it is important to consider not only cracks located close to the fixed end but also cracks located close to the free end, especially when the free end has lower elastic modulus and higher mass density.

Geomechanical properties of laminated shale and bedding shale after water absorption: A case study of the Chang 7 shale in Ordos basin, China

There are abundant oil and gas resources in China's continental shale formations, and these formations often contain sandy lamina, tuffaceous lamina and carbonate lamina parallel to the bedding planes, resulting in complex geomechanical properties. During the drilling process, the mechanical weak surface structure inside the shale and the hydration effect of drilling fluid may easily cause wellbore instability, which reduces the safety and benefit of drilling. To explore the geomechanical properties of laminated shale and bedding shale after water absorption, a series of tests were conducted on the Chang 7 laminated shale and bedding shale in the Ordos Basin. The result indicates that the compressive strength and elastic modulus of laminated shale and bedding shale show a trend of decreasing first and then starting to drop as β (the angle between bedding/lamina and the direction of stress) keeps increasing, and laminated shale has stronger anisotropy, lower compressive strength and elastic modulus. The moisture content of laminated shale and bedding shale increases as the soaking time increases, which leads to a decrease in the compressive strength. Compared to bedding shale, laminated shale reaches water saturation faster and has a higher moisture content. Based on the macroscopic and microscopic images before and after shale hydration, it can be concluded that natural microfractures are easily formed at the interface between the lamina and shale matrix, and brittle minerals at the edges of natural microfractures are prone to detachment, thereby increase the hydration area and intensify the hydration process. Compared to bedding shale formations, laminated shale formations have a higher hole-size elongation ratio and are more prone to collapse according to on-site data. This study reveals the geomechanical properties of laminated shale under the dual influence of anisotropy and hydration, provides support for drilling design in such formations.

Effects of aging on the microstructure and mechanical properties of metastable β-type Ti-23.6Nb-5.1Mo-6.7Zr alloy with low elastic modulus

In this study, the influence of thermomechanical treatments on the microstructure and mechanical properties of a new metastable β-titanium Ti-23.6Nb-5.1Mo-6.7Zr alloy was assessed. The objective was to determine if the alloy is a potential candidate for a future fabrication of orthopedic implants, in particular prosthetic hip stems with a functional gradient of mechanical properties. Two thermomechanical processing routes were investigated: (a) 90% cold-rolled, (b) 90% cold-rolled, followed by annealing at 950 °C for 1 h. After these initial processing steps, samples were aged between 300 °C and 500 °C from 0.5 h to 4 h. Microstructural characterization was conducted by optical microscopy, transmission electron microscopy and x-ray diffraction. Young's modulus and microhardness were measured. Young's modulus of the sample annealed after cold rolling is lower than that after the cold rolled one. Aging was effective at increasing hardness but also increasing Young's modulus. The hardening during aging resulted from fine ωiso and α precipitation. The transmission electron microscopy investigations indicated that an aging treatment at 500 °C leads to a fine (α + β) microstructure, avoiding brittle ωiso precipitation. For these reasons, this alloy is a potential candidate for the manufacture of a hybrid hip prosthetic stem by employing localized aging treatment at 500 °C in the neck region, creating a functional strength gradient and maintaining a low Young's modulus in the distal part, which is needed to mitigate the stress shielding of the bone.