Axial Stress Research Articles

Experimental and numerical study on dynamics of viscoelastic liquid cone in flow focusing

The effects of viscoelasticity on the stability and morphology of the liquid cone in liquid–liquid flow focusing are investigated experimentally and numerically. The particle tracers are utilized in experiments to visualize the flow fields, and the Oldroyd-B model is applied in numerical simulations to describe the viscoelastic characteristics of the liquid cone. Based on the quantitative analyses on the elastic stresses and forces inside the cone, the influence of viscoelasticity on the startup process of the liquid cone is first investigated. The stretching and shrinking stages of the viscoelastic cone are identified, and the startup process of the Newtonian cone is also studied for comparison. By considering the force balance at local jet position, a scaling analysis is proposed to give the criterion for the establishment of the stable cone, which indicates that the axial elastic stress can promote the cone stability. Upon a stable liquid cone, the influences of viscoelasticity on the interface profile and flow field of the cone are further analyzed, indicating that an increase in viscoelasticity leads to more shrinkage of the cone interface. The shrinkage of cone leads to the acceleration of focused liquid and thus the decrease in the recirculation flow size. This fundamental work provides scientific guidance for understanding the influences of viscoelasticity in flow focusing process, contributing to the industrial applications of microdroplets production.

Optimization of functionally graded materials to make stress concentration vanish in a plate with circular hole

This paper is devoted to the minimization of the stress concentration factor in infinite plates with circular hole made of functionally graded materials and subjected to a far-field uniform uniaxial tension. Despite the vast literature on the versatility of these materials, the novelty of the results is that the material distribution is not limited to prefixed laws, as in many works available in the literature. Instead, it is assumed to be an unknown piecewise constant function, thus aiming to derive the material distribution by exploiting, at best, the inhomogeneity concept associated with functionally graded materials. After a brief review of the governing equations, the motivation, the statement and the mathematical formulation of the optimization problem are given under the hypothesis of axisymmetric material distribution. Still, the problem could not be solved analytically, therefore a direct transcription approach by the aid of finite difference method has been followed to convert it into a nonlinear programming problem, whose solution has been obtained numerically by dedicated gradient-based solvers. Numerical optimal solutions are reported in graphical forms, thoroughly discussed and validated by means of the finite element method. The developed numerical approach yields a material inhomogeneity obeying a sigmoid-like function and a uniform hoop stress along the radial direction, thus making the stress concentration factor at the rim of the circular hole vanish.

Overcoming the brittleness of sustainable compression-cast recycled aggregate concrete through steel spiral confinement

The loose and porous adhered mortar of recycled aggregates produces concrete with low strength and poor durability. The newly developed compression casting technology applies pressure to fresh concrete to squeeze out excess water and air in the recycled aggregate concrete (RAC) and force the cement paste into the old adhered mortar to strengthen it, thereby effectively solving the aforementioned problems. However, the significant increase in the compactness and compressive strength of the RAC is accompanied by a pronounced increase in compression brittleness. Hence, this study attempts to overcome the brittleness of sustainable compression-cast RAC through proper design of transverse reinforcement. To achieve this objective, the axial compression behaviour of steel spiral-confined RAC specimens was experimentally investigated. It is found that the compression casting approach almost doubled the compressive strength of the unconfined RAC and improved the ultimate axial stress of the steel spiral-confined RAC by up to 69.9 %. The steel spiral-confined normal-cast RAC exhibited typical compression failure accompanied by a stress–strain curve characterised by strain hardening, whereas the steel spiral-confined compression-cast RAC exhibited localised shear failure accompanied by a stress–strain curve characterised by strain softening. The strain-softening behaviour of steel spiral-confined compression-cast RAC can be significantly improved by reducing the spiral pitch. Based on the test results obtained in this study and in the literature, stress–strain models were proposed separately for the steel spiral-confined compression-cast RAC and normal-cast RAC. The stress–strain models exhibited a significantly higher prediction accuracy than the selected models in the literature.

Prediction of fatigue life of a bolted joint in railway steel arch bridge using multiaxial fatigue criteria

Fatigue represents a critical condition for infrastructure subjected to repeated cyclic loads, such as steel railway bridges. The literature offers several methods to estimate fatigue life, consisting of three main phases: cycle counting, fatigue damage criterion, and damage accumulation criterion. Applying S-N curves might not be conservative in the case of railway bridges subjected to traffic because the stress-time history is complex and cannot be reduced to a sinusoidal history. Additionally, the presence of a multiaxial stress state must be considered. Therefore, this work compares eight multiaxial fatigue damage criteria for evaluating fatigue life in a scenario between high and low-cycle fatigue. Specifically, the authors considered four low-cycle fatigue criteria, namely Smith–Watson–Topper (SWT), Kandil, Brown and Miller (KBM), Glinka, Fatemi and Socie (FS), and four high-cycle fatigue criteria, Crossland, Basquin and the methods recommended by Eurocode 3 and British Standard. The rainflow counting method in ASTM E1049-85 (2011) and Miner’s rule for damage accumulation were used. The Polcevera railway steel bridge was selected as a case study. A 3D numerical model was developed for this purpose using Midas Civil software, taking into account the material non-linearity of the bridge’s elements. Once the area with the highest stress concentration was identified, a detailed analysis was conducted to estimate the stress and strain time histories induced by train traffic. A sensitivity analysis was conducted after critically comparing the eight methods for predicting fatigue life to assess the impact of traffic parameters, train velocity, axle load, and convoy length on fatigue life. It has been found that the criteria considering axial stress tend to overestimate the number of fatigue cycles to failure compared to the criteria, including the effect of shear stress components.

Production of rubberized concrete utilizing reclaimed asphalt pavement aggregates and recycled tire steel fibers

The integration of waste tire elements into concrete, specifically granular rubber and discrete steel fibers, signifies a substantial advance in the pursuit of sustainable alternatives for rigid concrete pavements. This incorporation not only improves the ductility of rigid concrete pavements, but also augments their energy absorption capabilities. Similarly, replacing natural aggregates in concrete with reclaimed asphalt pavement (RAP) aggregates makes a large contribution to the reduction of negative environmental impacts, while conserving natural resources from depletion. This investigation explores the potential application of recycled rubber particles from waste tires (WTRR) and RAP aggregates as partial substitutes for natural fine aggregates, and evaluates their impact on the performance of rigid concrete pavements. Eight mixes were cast, each with two variables: (i) fine aggregate type (fine rubber (FRu) aggregates, fine asphalt (FAs) aggregates, and combinations of both types of aggregate) replacing 50 % of the natural fine aggregate; and (ii) waste tire recycled steel fibers (WTRSF) content (0 and 40 kg/m3). The axial compressive stress–strain, flexural load–deflection, and direct shear strength behaviors, together with the dry unit weight and volume of permeable voids for all concrete mixes were investigated and compared. The results show that, although the flexural and shear strengths decrease with the inclusion of FRu and/or FAs, the use of WTRSF noticeably mitigates the losses in strength that arise from the use of WTRR and/or RAP aggregates alone. The inclusion of WTRSF enhances the strain capacity of the concrete and allows the development of adequate post-peak energy absorption capacity in flexural and shear loading. Additionally, the dry unit weight of the proposed composites decreased by as much as 8 %, and their volume of permeable voids lies within the limits of high-durability concrete mixes (9–12 %). Hence, the proposed sustainable concrete composites are promising composites for rigid concrete pavement construction.

Stress relaxation assessment of high-temperature bolts under combined biaxial loads: Theory and simulation

Estimating bolt stress within high-temperature bolted connection systems is crucial for determining bolt preload and assessing bolt assembly integrity. This work proposes a theoretical model for estimating high-temperature bolt load under combined tension, bending, torque, and shear loads, considering the characteristics of bolt stress distribution and relaxation. To assess the model's accuracy, finite element analysis was employed to examine the impact of various creep parameters and load combinations on bolt stress relaxation. The results indicate that the introduction of bending moments, torque, and shear loads accelerates axial stress relaxation in bolts. Under a high-temperature load for 300,000 h, the stress relaxation predicted by the theoretical model aligns well with the results from finite element analysis.

Compressive behaviour of concrete columns confined with textile reinforced concrete composites

The enhancement of strength and deformation capacity in confined concrete members could be achieved through the application of advanced composite materials. Textile reinforced concrete (TRC), a novel cement-based composite material, is considered as a viable alternative to fiber reinforced polymer (FRP) sheets, addressing the limitations associated with organic resins. This study delved into the impact of various parameters, such as cross-section shapes, concrete strengths, and the number of TRC layers, on the confinement effect. The results reveal a consistent augmentation in both axial compressive strength and deformation capacity of confined concrete with an escalation in the number of TRC layers, irrespective of the cross-sectional configurations. Notably, the maximum enhancements in axial peak stress for rectangular, square, and circular specimens are recorded at 45.96 %, 49.98 %, and 90.06 %, respectively, accompanied by corresponding increases in axial strains of 56.28 %, 53.74 %, and 86.00 %, respectively. The effectiveness of TRC confinement exhibits a substantial correlation with the geometry of the cross-sections. The circular ones have higher utilization rates followed by the square ones, and the rectangular ones with section aspect ratio greater than 1.0 have the lowest utilization rates. Furthermore, an evaluation of existing confinement identification models indicates that both the Mirminan Model and Wu Model could effectively delineate the hardening and softening characteristics of circular and rectangular specimens. However, there exists scope for improving the accuracy of these models. Therefore, a novel modified identification model, predicated on the Mirminan model, was proposed to refine the confinement assessment process. The revised modified confinement ratio (MCR) is recommended at a value of 0.045, aiming to elevate the precision and reliability of confinement evaluations in concrete structures.

Mechanism of uneven densification in PBX compression molding

The uneven density distribution during compression molding of polymer bonded explosive (PBX ) seriously affects the mechanical properties of high-energy material components and the precise output ability of shock waves. Investigating the multi-scale densification evolution laws and density non-uniformity mechanism of PBX composite powders is crucial for understanding the density non-uniformity phenomenon of energetic material components and evaluating the differences in macroscopic mechanical response. To this end, we developed a new dual-scale 3D discrete element method (DEM) model for PBX compression molding, which can increase the computational quantity of macroscopic powders by about an order of magnitude while considering the true morphology of mesoscopic explosive crystals. First, the densification behavior at different scales were analyzed using the developed 3D DEM models, including the rearrangement of macroscopic powder during the low strain stage, the deformation of macroscopic powders and mesoscopic bonding failure inside the powders during the high strain stage. Furtherly, the types and percentages of microcracks at the crystal-binder interface and inside the binder at the mesoscale during the macro powder deformation in the compression densification process were quantified. The characteristics of pore distribution and evolution laws of porosity and density uniformity during compression densification were revealed by simulations and X-ray μCT scanning. Finally, the mechanism of density non-uniformity was elucidated from multiple perspectives including displacement, force chain, contact fabric, and stress distribution. Subsequently, different degrees of energy dissipation behavior and the same gradient attenuation pattern were captured at different scales. This indicates that axial stress attenuation and density inhomogeneity are co-dominant results of the gradient attenuation of different scales of energy during layer-by-layer transfer along the loading direction. The potential induced mechanism of uneven density and stress attenuation were explained for the first time from the perspective of energy dissipation by this finding.

Strength Model for Prestressed Concrete Beams Subjected to Pure Torsion

A torsional strength model for prestressed concrete beams was proposed considering the initial crack angle, principal stress angle, and longitudinal strain, which are affected by the axial stress induced by the effective prestress. The use of the torsional effective thickness was also proposed to calculate the torsional strength of prestressed concrete beams by considering the effect of prestress. The shear element in the torsional member was simplified under the assumption that the principal tensile stress and principal compressive strain were negligible in the ultimate state. The torsional strength was determined when the principal compressive stress or shear stress at the crack surface in the shear element reached the failure criterion according to the multipotential capacity model, which considers concrete crushing and aggregate interlocking as the main resistances to the applied load. The proposed strength model was verified using test specimens collected from existing experimental studies. The proposed model accurately evaluated the torsional strength of prestressed concrete beam specimens, regardless of the key variables of the prestressed concrete specimens, where the mean value of the tested results to the calculated torsional strengths was 1.123, and the corresponding coefficient of variation was 17.7% for 104 prestressed concrete beam specimens, while the ACI 318-19 torsional design method gave the mean and coefficient of variation of 0.880 and 24.3%, respectively.

Thermo-hydro-mechanical behaviour of energy tunnel in unsaturated soils

Soils surrounding energy tunnels are often unsaturated, particularly in areas with a low water table. All studies of the mechanical behaviour of energy tunnels focused on saturated or dry soils. Through numerical simulations using a coupled thermo-hydro-mechanical model for unsaturated soils, this study aims to improve the understanding of the interactions between energy tunnels and unsaturated ground. The influences of water table position and soil type on the mechanical behaviour of energy tunnels were investigated. Results show that the thermally-induced lining convergence of energy tunnels does not change much with the water table position. Nevertheless, the other mechanical responses (e.g., settlements of ground and tunnel and lining stress changes) highly depend on the water table position. These mechanical responses are more significant when the water table is higher than the tunnel center, except for the larger settlements at a lower water table in clay. Furthermore, the above responses are underestimated if soils above the water table are assumed to be completely dry. The degree of underestimation is most significant for the clay, followed by silt and sand, e.g., a maximum of 54%, 23% and 10% in the change of circumferential stress, respectively. These results highlight that the unsaturated soil model should be used to evaluate the thermo-hydro-mechanical responses of energy tunnels in unsaturated soils, particularly for the clay ground.

Axial stress-strain behavior of pre-stressed CFRP confined concrete columns

Bonded carbon fiber reinforced polymer (CFRP) confined concrete presents issues such as stress hysteresis and easy detachment at the interface between CFRP and concrete. Applying prestress to CFRP can improve this situation. To investigate the stress-strain behavior of prestressed CFRP strengthened plain concrete columns (PC) under axial compression, a total of 1 unreinforced concrete column, 9 bonded CFRP strengthened concrete columns, and 27 prestressed CFRP strengthened concrete columns were designed. Including CFRP layers and the level of prestress were taken as the study factors, and axial compression tests were conducted on each specimen to analyze their axial compression performance. The test results indicated that applying prestress to CFRP results in the core concrete being constantly subjected to triaxial compression, with initial transverse compressive strain and longitudinal tensile strain, thereby increasing the initial stiffness of the core concrete. In contrast to bonded CFRP-strengthened columns, the ultimate axial stress, ultimate axial strain, and initial stiffness of prestressed CFRP-strengthened columns increased with the level of CFRP prestress, with a more pronounced improvement observed in columns wrapped with a higher number of layers of CFRP. For a 4-layer CFRP strengthened column prestressed at 0.3, the ultimate axial stress and ultimate axial strain increased by up to 13 % and 20 %, respectively, compared to bonded 4-layer CFRP strengthened columns, with the initial stiffness increasing by up to 30 %. On the other hand, applying prestress to CFRP can significantly enhance the effective utilization of CFRP, but it is negatively correlated with the number of CFRP layers. Compared to bonded 1-layer CFRP strengthened columns, the effective utilization rate increased from 0.63 to 0.91, a 44 % increase, when prestressing CFRP at 0.3. Finally, based on existing relevant research, a peak stress and strain model considering the ratio of confinement stiffness to strain ratio was proposed. Based on the fundamental assumptions of curve analysis, the design-oriented axial stress-strain model suitable for prestressed CFRP strengthened concrete columns was established, with good match between theoretical and experimental curves.

Changes in magnetic characteristics of pipes during hydraulic and pneumatic tests of trunk pipelines

To identify the zones with the highest tensile stresses and deformations, a two-parameter magnetic method based on the measurement of coercive force and residual magnetic induction was applied. For realization of the method a mobile hardware and software complex DIUS-1.21M with an electromagnetic U-transducer was used, which was located along the pipe axis and along the pipe ring. Measurements were carried out on three pipes: in the first one magnetic characteristics were measured in the absence and under the influence of internal pressure; in the second and third ones — before the test and after the pipe fracture. It was revealed that internal pressure leads to the growth of residual magnetic induction in all zones both along the axis and along the ring, which indicates the occurrence of axial and circular tensile stresses in these zones, and the change of coercivity occurred ambiguously. It was found that fracture significantly increases the scatter of magnetic characteristics, which is explained by the complex nature of the stress-strain state of the fractured object.

An experimental and theoretical investigation on residual stress of 7075-T651 aluminum alloy hole under electromagnetic cold expansion

The electromagnetic cold expansion process (ECE) was adopted in this work. The theoretical plastic radius, hole wall stress, radial stress, circumferential stress and release stress under different expansion rates (ER) were studied based on thick cylinder theory and ECE experiments. The released strain, residual stress (RS) and failure force were measured. The tensile fracture morphology was characterized. The results showed that the theoretical plastic radius (maximum 15.87 mm), internal stress (maximum 982.9 MPa), radial stress (maximum −820.9 MPa) and circumferential stress (maximum −271.4 MPa) increased with the increase of ER. The absolute radial and circumferential stress decreased and increased in negative and positive ranges respectively with distance increased. The release strain (maximum −3033 με, 10−6 microstrain), radial RS (maximum 600.9 MPa) and circumferential RS (maximum 601.1 MPa) also increased with the increase of ER, and the minimum relative error of the plastic zone radius of the theoretical model was 3.78 % proving the reliability of the model. In addition, ECE increased the release stress (the maximum radial and circumferential release stresses were 1402.6 MPa and 747.5 MPa) and decreased the failure force (minimum 44.7kN) with increased ER. The initial crack position tended to transition from the inlet and outlet surfaces to the middle position, and the crack propagation angle and axial crack size gradually decreased with the decreased ER and stress level.

Sensitivity analysis and fuel performance of a control rod withdrawal in the generic fluoride-salt-cooled high temperature reactor

The purpose of this study is to develop boundary conditions with respect to input parameter uncertainty for fuel performance assessment of a control rod withdrawal transient in a fluoride-salt-cooled high-temperature reactor (FHR). Sensitivity analysis was performed to determine how certain key input parameters impacted the uncertainty of the outputs needed for the boundary conditions. The generated boundary conditions can be used in fuel performance codes to obtain failure probabilities and fuel performance envelopes. To accomplish this, we utilized a KP-AGREE model of the generic fluoride-salt-cooled high-temperature reactor (gFHR) and a pebble bed benchmark developed by Kairos Power. The key boundary conditions that were developed included the total power, maximum fuel region temperature, maximum fuel kernel temperature, and maximum moderator (graphite) temperature within the core. The sensitivity analysis was run until the Sobol indices and output converged within a 95 % confidence level; it was found that the coolant inlet temperature consistently had the highest impact on the uncertainty of the key core temperature values. The maximum bound of these temperatures also did not exceed 1123.5 °C for the fuel kernel and 973.7 °C for the moderator after the transient, demonstrating that there is a large margin between the predicted fuel and moderator temperature and accepted safety limits, given a 1650 °C limit for Tristructural Isotropic (TRISO) fuel. These boundary conditions were implemented into a BISON model to demonstrate their use in fuel performance and obtain a brief failure profile of the fuel. The maximum magnitude of the hoop stress on the SiC layer was −12.02 MPa, resulting in a failure probability of 4.90·10−19. Thus, the fuel performance simulations also emphasized the robustness of the TRISO fuel design utilized in the gFHR, as the predictions reveal substantial margin of the TRISO particles relative to temperature limits during the control rod withdrawal. The limiting temperature is expected to be the reactor vessel temperature and the fuel is not expected to be challenged at all by mechanical failure of the SiC layer during these events.

Stress–strain behaviour and degradation mechanism of low–carbon MgO–C refractories at 900–1100 °C: role of TiB2–BN–AlN waste

The use of boron–containing additives often raises concerns when exposed to high temperatures. In this study, the high temperature stress–strain behavior and degradation mechanism of low–carbon MgO–C refractories containing TiB2–BN–AlN waste were investigated. Stress–strain curve, peak axial stress, Young’s modulus, cohesion, and residual strength ratio after thermal shock tests were thoroughly analyzed. The findings suggest that the mechanical properties of refractories remain unimpaired within the temperature range of 900–1100 ℃, and can even be enhanced through the synergistic effect of TiB2–BN–AlN waste and Al powder. The optimized axial stress increased from 55.0 to 62.0 MPa at 1100 ℃, while the cohesion increased from 10.0 to 13.8 MPa, respectively. The observed enhancement can be primarily attributed to the effective healing of pores and cracks, reduction in oxidation, and improved material cohesion. However, the excessive incorporation of boron–containing waste may compromise the performance of refractories, leading to instability or degradation.

Effects of CO2-saturated brine imbibition on the mechanical and seepage characteristics of Longmaxi shale

Supercritical carbon dioxide (SC– CO2) serves as a promising anhydrous fracturing fluid that has the potential to simultaneously enhance shale gas recovery and accomplish CO2 sequestration within shale reservoirs. However, the hydromechanical properties of shale are considerably affected by CO2-brine-shale interaction. This study conducted shale imbibition experiments involving subcritical/supercritical CO2 saturated brine (Sub/SC-CO2+brine). Triaxial compressive strength tests were performed to evaluate the impact of Sub/SC-CO2+brine imbibition on the mechanical properties of shale, as well as the influence of SC-CO2+brine imbibition on shale permeability. The results indicate that, after SC-CO2 brine imbibition, noticeable macroscopic cracks are formed parallel to the bedding plane. The imbibition of Sub/SC-CO2+brine results in the reduction in axial stress and Young's modulus, while simultaneously increasing the axial strain of shales. Compared to Sub-CO2+brine, SC-CO2+brine exhibits a higher imbibition pressure and a more intense geochemical reaction with shale. Due to increased compressibility sensitivity, the averaged permeability after SC-CO2+brine imbibition shows a reduction of nearly 70 % compared to that before imbibition. The insights from this research are expected to provide theoretical support for shale gas recovery and CO2 geological sequestration.

Three-dimensional numerical analysis of twin tunnelling in two-layered soil strata

Tunnelling induces stress change and displacement in the ground. The excavation of a new tunnel in stratified soil can trigger different patterns of stress redistribution, which may adversely influence nearby tunnels. Research on multi-tunnel interaction has mainly been performed on the assumption of a uniform ground. The effects of different soil stratifications on tunnelling interaction remain poorly understood. In this paper, three-dimensional numerical parametric studies verified by previous centrifuge tests were carried out to analyse the twin tunnelling effects in two-layered soil. An advanced hypoplastic constitutive model that can capture stress-, path-, and strain-dependency of soil behaviour is adopted. Numerical cases investigated include perpendicular twin tunnelling in two sand layers with different relative densities and the location of the interface between the two sand layers. It is revealed that larger settlements and a wider surface settlement trough occur when tunnelling in two-layered soil strata than in a uniform ground. This is because of the wider and larger soil arch induced in two-layered soil strata. The structural response including tunnel deformation, induced bending moment, and induced hoop stress of the existing tunnel can be greater when tunnelling in layered soil strata than in a uniform ground owing to larger stress relief. Moreover, the combination of bending moment and hoop stress can exceed the M−N failure envelope of the structure in layered soil. A conventional simplified assumption of a uniform ground can underestimate of the influence of new tunnel excavation on existing tunnels, resulting in unsafe designs.

A Biomechanical Comparison Study of Plate-Nail and Dual-Plate Fixation in AO/OTA 41-C2 Tibial Plateau Fractures.

This study's purpose was to evaluate the biomechanical performance of plate-nail and dual-plate fixation for the treatment of AO/OTA 41-C2 tibial plateau fractures. Twenty synthetic tibias were selected and randomly divided into a plate-nail group (n = 10) and a dual-plate group (n = 10). After the artificial tibias were osteotomized to simulate AO/OTA 41-C2 tibial plateau fractures in both groups, the plate-nail and the dual-plate methods, respectively, were used for fixation, and then axial compression loading, three-point bending, torsion, and axial failure tests were carried out. The data of each group were recorded and statistically analyzed. In the axial compression test, the average stiffness of the plate-nail group was higher than that of the dual-plate group (p < 0.05). The displacement generated in the plate-nail group was significantly smaller than that in the dual-plate group (p < 0.05). In the resisting varus test, the stress of the plate-nail group was significantly higher than that of the dual-plate group (p < 0.05). In the resisting valgus test, the stress of the plate-nail group was slightly higher than that of the dual-plate group, but the difference was not statistically significant (p > 0.05). In the static torsion test, the load applied to the plate-nail group was smaller than that of the dual-plate group when rotated to 5° (p < 0.05). In the axial compression failure test, the average ultimate load of the plate-nail group was significantly higher than that of the dual-plate group (p < 0.05). The treatment of AO/OTA 41-C2 tibial plateau fractures with plate-nail fixation is superior to that with dual-plate fixation in resisting axial stress and preventing tibial varus deformity, while dual-plate fixation has better resisting torsional ability.

Mechanical response and failure mechanism of circular inclusion embedded in brittle materials under dynamic impact

Inclusions are prevalent in both natural and synthetic materials. Gaining a comprehensive understanding of their dynamic response and interaction with the surrounding matrix is essential in fundamental mechanics and engineering applications. This study aims to achieve such understanding through theoretical analysis, experimental investigations, and numerical simulations, focusing on the dynamic destruction of inclusions and the underlying mechanisms. Firstly, the circumferential, radial, and shear stresses around elastic heterogeneous inclusions were derived by the wave function expansion and Duhamel integration methods. Subsequently, a set of experiments on sandstone specimens containing three types of inclusions (plaster, epoxy resin, cement) were conducted utilizing the Split Hopkinson Pressure Bar (SHPB) system in conjunction with high-speed photography and Digital Image Correlation (DIC) techniques to obtain the surface deformation of inclusion specimens. Eventually, a series of Finite Element Method (FEM) numerical simulations adopted suitable materials were also carried out to investigate the fracture process of inclusion and matrix under dynamic impact. The results demonstrate that the stress distributions and fracture mode of matrix and inclusion are highly dependent on the physical and mechanical properties of the inclusions and the surrounding matrix, specifically, density ρ, elastic modulus E, Poisson's ratio v, and strength. With an increase in the E and v, there is a reduction in the concentration of circumferential stress, while the radial and shear stresses experience an increase. The experimental and numerical results corroborated the theoretical findings and indicated that the localized dynamic stress concentrations induced by wave scattering around the inclusions directly dominated both local and overall specimen failure. Due to the dissimilarities in elastic parameters and strength between the inclusion and the matrix, the stress state of the inclusion and the interface is not homogeneous. Under dynamic loading, the weaker inclusion experiences tensile cracking at both ends of the loading, and as the mechanical properties (ρ, E, v, and strength) of the inclusion rise, a transition from tensile- hybrid-shear failure occurs within the inclusion. The findings of this study help us understand the dynamic failure mechanisms of dissimilar inclusions in brittle material.

Experimental research on the flow field and flame geometry of free buoyant diffusion flames with low dimensionless heat release rates

The flame geometry of turbulent diffusion flames is dominated by the turbulent mixing between the gaseous fuel and the entrained air. The significant variations of the power law for the mean flame height regarding the dimensionless heat release rate (Q˙*) in different Q˙* ranges implied that the turbulent mixing characteristics would change greatly among these Q˙* regimes. This paper presents a combined experimental and analytical study to reveal the turbulent transport properties and flame shape of free turbulent buoyant diffusion flames of relatively low Q˙* prevalent in large-scale fires. The instantaneous velocity fields of free buoyant methane diffusion flames (burner diameter: d = 0.30 m, Q˙*= 0.22–0.40) were measured by the stereo particle image velocimetry (SPIV) technique. The results indicate that the radial profiles of the time-averaged axial velocity, axial normal stress, radial normal stress, shear stress, and turbulent kinetic energy exhibited self-similarity at different heights under all the heat release rates. The turbulent flow in the buoyant flame was found to be anisotropic. Based on the gradient transport approximation, the mean turbulent viscosity within the mean flame height (νt=) was scaled by g1/2d3/2, where g is the gravitational acceleration. The semi-physical correlations for the mean flame height and width were derived based on the concepts of turbulent mixing and equal axial convection and radial diffusion times, respectively. The two correlations agreed reasonably with the experimental data of this work.