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The object of the work is an experimental study of the features of the movement of viscous and anomalous fluids in plane-parallel and plane-radial microcracks. In the work, the unexplored problem of hydrodynamic features of fluid motion in the considered objects – channels is solved. It was experimentally revealed that various fluids, when moving in microcracked channels with micron-sized openings, acquire new mechanical properties, which differ from their properties in the usual condition. The effect in the “microcrack-fluid” system is the reason for changes in the mechanical properties of fluids in microcracks and equivalent ultra-low-permeable porous media. It was revealed that when a one-parameter viscous fluid moves in a crack with an opening h, Об'єктом роботи є експериментальне дослідження особливостей руху в'язких та аномальних рідин у плоскопаралельних і плоскорадіальних мікротріщинах. У роботі вирішується задача вивчення гідродинамічних особливостей руху рідини в розглянутих об'єктах – каналах. Експериментально встановлено, що різні рідини під час руху в мікротріщинних каналах з розкритістю мікронного розміру набувають нових механічних властивостей, що відрізняються від їхніх властивостей у звичайному стані. Причиною зміни механічних властивостей рідин в мікротріщинах та еквівалентних наднизькопроникних пористих середовищах є ефект системи "мікротріщина-рідина". Виявлено, що під час руху в'язкої однопараметричної рідини в тріщині з розкритістю h

YAG (Y3Al5O12) transparent ceramics have attractive application prospects for transparent armor protection modules because of their excellent light transmittance and anti-ballistic capability. Understanding the fracture behavior and damage mechanism of YAG is necessary for armor design. To explore the damage characteristics of YAG under compression and tension, shock compression and shockless spalling experiments with soft recovery technique are conducted. The spall strength of YAG is obtained and the recovered samples are observed by CT and SEM. It is shown that the macroscopic damage characteristic of YAG under compression is vertical split cracks with oblique fine cracks distributed in the entire sample, while that under tension is horizontal transgranular cracks concentrated near the main spall surface. The cracks generated by macroscopic compression, tension and shear stress extend in similar tensile form at the microscale. The proportion of transgranular fractures on spall surfaces is higher than that of cracks induced by macroscopic compression. Meanwhile, higher loading rate and longer loading duration increase the transgranular fracture percentage.

An experimental study of the process of friction between a steel spherical indenter and a soft elastic elastomer, with a strongly pronounced adhesive interaction between the surfaces of the contacting bodies, is presented. We consider sliding of the indenter at low speed (quasi-static contact) for different indentation depths. The forces, displacements and contact configuration as functions of time were recorded. The most important finding is that under conditions of uni-lateral continuous sliding, the tangential stress in the contact area remains constant and independent on the indentation depth and details of loading. We suggest a simple numerical model in which the elastic substrate is considered as a simple elastic layer (thus reminding a two-dimensional elastic foundation), although with in-plane elastic interactions. It is found that this model leads to the dynamic scenarios which qualitatively resemble the experimentally observed behavior of the considered system.

Tungsten as a material exhibits broad and increasingly important applications; however, the characterization of its ductile-to-brittle transition (BDT) is currently limited to large-scale scenarios and destructive testing. In this study, we overcome this challenge by implementing small-scale techniques to provide a comprehensive understanding of the BDT behavior of pure tungsten. In order to predict the failure mode at various temperature ranges, the practical fracture analysis diagram has been proposed to describe the resistance to shear flow and cracking behavior with temperature. High temperature nano-indentation tests have provided the inherent mechanical responses corresponding to the maximum shear stress at various temperatures, which is required for dislocation activities in an atomic scaled activation volume. On one hand, atomistic simulations have provided the temperature dependence of brittle fracture stress, where the atomic bonds break due to intergranular or intragranular fracture. We considered four tungsten specimens having various microstructures prepared using different processing conditions of cold-rolling and post-annealing, and their BDT ranges were inferred using the obtained fracture analysis diagram with the statistical data processing. The fracture analysis diagram of each specimen obtained were compared with the direct observation of fracture responses in macroscopic mechanical tests, which conclusively indicated that the small-scale inherent mechanical properties are greatly relevant to the macroscopic BDT behavior in pure tungsten. Based on the BDT estimations by small-scale characterization, we provided further insights into the factors affecting the BDT behavior of tungsten, focusing on the contributions of different types of dislocations.

A learning-based approach for solving wall shear stresses from Shear-Sensitive Liquid Crystal Coating (SSLCC) color images is presented in this paper. The approach is able to learn and establish the mapping relationship between the SSLCC color-change responses in different observation directions and the shear stress vectors, and then uses the mapping relationship to solve wall shear stress vectors from SSLCC color images. Experimental results show that the proposed approach can solve wall shear stress vectors using two or more SSLCC images, and even using only one image for symmetrical flow field. The accuracy of the approach using four or more observations is found to be comparable to that of the traditional multi-view Gauss curve fitting approach; the accuracy is slightly reduced when using two or fewer observations. The computational efficiency is significantly improved when compared with the traditional Gauss curve fitting approach, and the wall shear stress vectors can be solved in nearly real time. The learning-based approach has no strict requirements on illumination direction and observation directions and is therefore more flexible to use in practical wind tunnel measurement when compared with traditional liquid crystal-based methods.

In this work, supercritical n-decane flowing in ducts with different orientations is thoroughly investigated in terms of secondary flow, wall shear stress, and thermal acceleration. It is known tha...

Deformation behavior of a FeCrNi medium entropy alloy (MEA) prepared by powder metallurgy (P/M) method was investigated over a wide range of strain rates. The FeCrNi MEA exhibits high strain-hardening ability, which can be attributed to the multiple deformation mechanisms, including dislocation slip, deformation induced stacking fault and mechanical twinning. The shear localization behavior of the FeCrNi MEA was also analyzed by dynamically loading hat-shaped specimens, and the distinct adiabatic shear band cannot be observed until the shear strain reaches ~14.5. The microstructures within and outside the shear band exhibit different characteristics: the grains near the shear band are severely elongated and significantly refined by dislocation slip and twinning; inside the shear band, the initial coarse grains completely disappear, and transform into recrystallized ultrafine equiaxed grains by the classical rotational dynamic recrystallization mechanism. Moreover, microvoids preferentially nucleate in the central areas of the shear band where the temperature is very high and the shear stress is highly concentrated. These microvoids will coalesce into microcracks with the increase of strain, which eventually leads to the fracture of the shear band.

Advances in additive manufacturing have been paving the way for unconventional topologies in electromechanical systems. As such, topology optimization can be employed to uncover topologies that were once considered impractical. This paper investigates enhancing the shear stress of the reluctance trans-rotary magnetic gear (TROMAG) by optimizing the topology of the gear’s variable reluctance component. Reluctance TROMAG is a strong contender for force-intensive linear motion applications where a long stroke is required. Topology optimization is performed on the reluctance TROMAG with radially-magnetized permanent magnet (PM) configuration as well as with quasi-Halbach magnetized configuration. Results show that the use of elliptical iron teeth backed by non-ferromagnetic core can make 40% increase compared to the shear stress of the conventional (rectangular teeth) reluctance TROMAG with radial magnetization. The Halbach-magnetized TROMAG with elliptical iron teeth backed by non-ferromagnetic core achieves the same shear stress as the conventional reluctance TROMAG with Halbach magnetization, and the use of light weight non-ferromagnetic material for the variable reluctance component can make significant reductions in the total gear weight.

Epicyclic gears also known as Planetary Gears is a system which consists of planet gears, a sun gear, and a ring gear. The Sun gear is mounted and rotated about the centre and meshed with planet gears which are connected with the help of a carrier. These planet gears are meshed with ring gear. This type of gear has a wide range of application in wrist watches, automobiles, and hoist. This paper focus on epicyclic gear In Wind Turbine. Necessary calculation for design is done and the Gear System is modelled in Solidworks. Analysis of the gear system carried out through Ansys. Simulation for total deformation, von-Mises stress, Shear stress for two cases for two different materials. Finally results were concluded on the best material.

A rotating detonation engine (RDE) generates a continuous thrust with one or more rotating detonation waves. Because of the velocity on the order of kilometers/second, the reaction zone is relatively small. Therefore, the RDE realizes a short combustion chamber length. However, the detonation waves induce an azimuthal motion of propellant, resulting in torque around the thrust axis. Because the motion does not contribute to the thrust, the torque is important in terms of performance loss. Herein, we conducted combustion tests with a six-axis force sensor to simultaneously measure 0.149±0.009 Nm torque and 48.1±0.9 N thrust. A comparison of detonation waves captured by high-speed camera revealed that the torque followed the direction and was offset when the waves existed in both of two directions simultaneously, which indicates the possibility of controlling the torque. Under a mass flow rate at 87±9 g/s and an equivalence ratio at 1.43±0.28, when the azimuthal component of shear force was 8.8±0.6% of the thrust, 0.77±0.10% of the total kinetic energy of the exit flow was distributed to the azimuthal component of velocity and did not contribute to the thrust. We therefore concluded that the effect of the azimuthal motion on the RDE’s performance was small.

The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical separation techniques, etc. One of the most essential components of immiscible flow is the fluid interface, which must be consistently monitored. In this article, the unsteady flow of two immiscible fluids i.e., an Eringen micropolar and Newtonian liquid is considered in a horizontal channel. Despite the no-slip and hyper-stick shear stress condition at the channel edge, it is accepted that the liquid interface is dynamic, migrating from one position to the next and possibly get absolute change; as a result, The CS (continuum surface) model is integrated with the single moment equation based on the VOF (volume of fluid) approach to trace the interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant, decaying, and periodic) and flow is analyzed under seamless shear stress over the entire interface. The modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled partial differential equations for the fluid interface evolution. The advection and tracking of the interface with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of micropolar parameters affects the interface with time. The novelty of the current study is that previous studies (which considered the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes) are extended and generalized to consider the time-dependent flow of two immiscible fluids namely Eringen micropolar and Newtonian with a moving interface in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the steady-state, the peak of the waves resembles those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure gradient case i.e., weaker micropolar fluids encourage faster stabilization of the interface. With periodic pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

Lubricant behaves non-Newtonian at high shear stress and high shear rate. The non-Newtonian shear behavior of oil such as shear-thinning, viscoelasticity, and limiting shear stress could have influences on almost all characteristics of an elastohydrodynamic lubrication (EHL) contact, that is, the central film thickness, the coefficient of friction, and the temperature rise in the lubricating film. For example, for lubricants of large molecular weight or of polymer blended ones, there can be inlet shear-thinning, which would reduce the EHL film thickness. For the EHL traction in a rolling/sliding EHL contact, it cannot be reasonably predicted without the consideration of non-Newtonian rheology. In EHL numerical studies, the non-Newtonian properties and the constitutive equations are expressed by the concept of generalized viscosity [Formula: see text], which can be either a function of shear rate [Formula: see text] or a function of shear stress [Formula: see text]. In this way, a non-Newtonian lubrication problem could be solved as a generalized Newtonian problem based on solvers for a Newtonian EHL problem. According to the function of the generalized viscosity [Formula: see text], numerical solutions can be classified into shear rate-based ones and shear stress-based ones. In this work, these two kinds of numerical solutions are revisited. And their efficiency is compared for a two-dimensional (2D) non-Newtonian point contact EHL problem (here 2D means non-Newtonian flow in both the x and y directions). Results show that the shear rate-based numerical solution has a higher efficiency than the shear stress-based one. The shear rate-based 2D generalized Newtonian method is more suitable to analyze multiple EHL contacts in angular contact ball bearings and gears with complex 2D flow and/or transient EHL lubrication problems.

Multiple ballistic impacts are carried out on a 2024-T4 aluminum alloy by spherical steel projectiles (5-mm diameter) at ∼ 400 m s − 1 , to investigate its dynamic deformation and damage. The ballistic impact process is captured with high-speed photography. Postmortem samples are characterized with optical imaging, three-dimensional laser scanning, microhardness testing and electron backscatter diffraction. With increasing number of impacts, crater diameter increases slightly, but crater depth and crater volume increase significantly, and strain accumulation leads to microhardness increase overall. Crater parameters all follow power-law relations with the number of impacts. Twin-like deformation bands and macroscopic deformation twins are produced by impact as a result of spontaneous dislocation self-pinning under high strain rate, large shear deformation. Under multiple impacts, shear strain accumulation in the arc-shaped region of the crater induces deformation twinning when it exceeds a critical value ( ∼ 1.1 − 1.6 ). It is highly possible that the deformation twins are related to deformation bands, since they both share one set of the { 111 } pole with the initial matrix grain. A finite element method model is optimized to reproduce experimental observations and interpret deformation mechanisms.

Toward accurately simulating both hardening and softening effects for metals up to failure, a new finite strain elastoplastic J2-flow model is proposed with the yield strength therein as a function of the plastic work in the explicit form. With no need to identify any adjustable parameters, the uniaxial stress-strain response predicted from this new model is shown to automatically and accurately match any given data from monotonic uniaxial extension tests of bars. As such, the objectives in three respects are achieved for the first time, i.e., (i) both the hardening and softening effects up to failure can be simulated in the sense of matching test data with no errors, (ii) the usual tedious implicit procedures toward identifying numerous unknown parameters need not be involved and can be totally bypassed, and (iii) the model applicability can be ensured in a broad sense for various metallic materials with markedly different transition effects from hardening to softening. With the new model, the complete response features of stretched bars and twisted tubes up to failure are studied, including the failure effects of bars under monotonic extension and tubes under monotonic torsion and, furthermore, the fatigue failure effects of bars under cyclic loading. The results show accurate agreement with the uniaxial data, and the results for both the shear stress and the normal stress at the finite torsion display realistic hardening-to-softening transition effects for the first time.

In this paper, the real joint load transfer efficiency of airport pavement is calculated by combining the results of airport pavement deflection detection and ground-penetrating radar detection. Spring elements are used to simulate the actual load transfer efficiency of joints in ABAQUS. The impact of different asphalt overlays on the stress state of the critical point in the pavement is analyzed by the airport cement concrete pavement model. The result shows that adding a thin stress-absorbing layer with fine-graded and low modulus can effectively disperse the load transferred from the asphalt pavement to the cement pavement and the stress concentration at the joint under the asphalt overlay. Compared with airport pavement without a stress-absorbing layer, the tensile stress and shear stress at the critical point in the airport pavement asphalt overlay decreased by 24.62% and 22.49%, respectively. Therefore, the combination of the high-modulus upper layer and low-modulus lower layer can effectively reduce the tensile stress and shear stress at the critical point. In addition, increases in the thickness of the asphalt overlay can effectively improve the stress state at the critical point. When the thickness of the asphalt overlay changed from 13 cm to 21 cm, the maximum tensile and shear stress decreased by 8.82% and 8.92%, respectively. Finally, based on the analysis of the numerical simulation and field test verification, the optimal airport pavement asphalt overlay scheme is proposed.

Vertical rolling is an important technique used to control the width of continuous casting slabs in the hot-rolling field. Accurate prediction of vertical rolling force is a core point maintaining rolling-mill equipment. Owing to the limitation of the algorithm in use, the prediction accuracy of most vertical rolling force models based on the energy method can only reach more than 10%. Therefore, it is challenging to optimize the rolling-force model to improve prediction accuracy. An innovative approach for optimizing the calculation of vertical rolling force with a unified yield criterion is presented in this paper. First, the maximal width of a dog-bone region is determined by the slip-line method, and the dog-bone shape is described using a sine-function model. Second, the velocity and corresponding strain-rate fields satisfying kinematically admissible conditions are proposed to calculate the total power of the vertical rolling process. Finally, the analytical solution of the rolling force and the dog-bone-shape model is obtained by repeatedly optimizing the weighted coefficient b of intermediate principal shear stress on the yield criterion. Moreover, the effectiveness of the proposed mechanical model is verified by measured data in the strip hot-rolling field and other models’ results. Results show that the prediction accuracy of the vertical rolling force model can be improved by optimizing the value of b. Then, the impacts of reduction rate, initial thickness, and friction factor on dog-bone shape size and vertical rolling force are discussed.

The controlled pulse welding current combined with ultrasonic vibration was used to increase the keyholing/penetrating capability of plasma arc, and a mathematical model was developed to elucidate the underlying mechanism of periodic interaction between the ultrasound field and the plasma arc. The exerted ultrasonic vibration on the tungsten electrode increases the thermal conductivity of plasma arc, reduces the electrical conductivity of plasma arc, and then enhances the heat-pressure of plasma arc. The variations of the heat flux, current density, and the plasma arc pressure with time were quantitatively analyzed. Compared with the traditional controlled pulse plasma arc welding, the plasma arc heat flux, plasma arc pressure, and gas shear stress on the anode surface all increase in both peak and base stages of welding current after ultrasonic vibration is applied, which improves the keyholing/penetrating ability of plasma arc under the controlled pulse current. The experimental measurements were made to validate the numerical model indirectly.

This study provides an effective determination process of the interface microstructural parameters in the numerical modelling of the mechanical interaction between two different geomaterials involved with frictional-bonded interfaces, such as the interaction between backfill columns and the surrounding rocks, or the soil-structure interaction, by using the coupled finite-difference and discrete-element (FD-DE) method. Three-dimensional numerical direct shear tests were conducted on the coupled FD-DE model of the combined rock-cemented rockfill (R-CRF) specimens with the frictional-bonded interface. With the microstructural parameters determined, the macro-mechanical properties of the interface of the coupled model were calibrated to well fit with the theoretical values of the combined specimen under the direct shear condition assumed according to the Mohr–Coulomb strength criterion. Evident elastoplastic shear behaviour was observed on the interfaces, and excellent agreement was attained between the shapes of the theoretical and simulated shear stress-displacement curves of the coupled models at different servo-controlled normal stresses. Particulate-scale force chains inside the DE model of the CRF specimen were highly consistent with the force contour on the FD model of the rock specimen, demonstrating the shear stress evolution of the coupled model at different shear displacements. Parametric studies verified the effects of the deformation properties of the interface parallel bonds on the shape of shear stress-displacement curves of the coupled models. The test results validated the feasibility and rationality of the coupled FD-DE method for modelling the combined specimens with frictional-bonded interfaces or joints. Furthermore, this study provides valuable numerical modelling experience for investigating the shear behaviour at the interface between cemented backfill columns and surrounding walls by using the coupled FD-DE method.

This paper reports an experimental study on the supersonic jet surface flow structure visualization and shear stress field measurement issuing from a rectangular nozzle with extended shelf. The evolution of the near-field surface flow structures with an increased Nozzle Pressure Ratio (NPR) is successfully captured by the surface oil flow, infrared detection technology, and the Shear-Sensitive Liquid Crystal Coating (SSLCC) technique. Results reveal that under smaller NPR, the wall flow structure is similar to that of a jet without the extended shelf i.e., clean jets, and this is caused by insufficient effect on the boundary layer. However, at higher amplitudes of NPR, there exists a significant effect of the boundary layer, as a near triangular separation forms on the trailing edge of the Mach stem due to the adverse pressure gradient, which is visualized for the very first time in this paper. Furthermore, the vector field of shear stress is measured quantitatively by SSLCC technique. Results shows that the magnitude of shear stress heightened with NPR increasing, and the directions of shear stress changes across the shock wave and expansion fans. In addition, surface streamlines measured by SSLCC is significantly consistent with the streamlines visualized using the oil flow technique.

The mechanochemical effect on the microcutting of AA6061 alloy is studied through characterization on the chip. A pronounced reduction of machining forces and chip thickness was observed with mechanochemical effect during microcutting. Furthermore, electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM) observations were performed on the chips and shear bands. The result reveals much coarser grains (24.6 μm in size) in the surfactant-affected chip than that in the surfactant-free chip (13.5 μm). Different grain orientations are induced by microcutting. {100} and {110} grain orientations are majority for surfactant-free chip, and {110} and {100} dominate most for all grain orientations for surfactant-affected chip. Additionally, since less localized shear strain and lower temperature are generated inside the shear band with mechanochemical effect, almost no recrystallization phenomena can be observed in this region. TEM analysis shows that fewer subgrains and dislocations could be observed inside the shear band of the surfactant-affected chip in comparison with the surfactant-free chip. Based on the high-resolution transmission electron microscopic (HRTEM) observations, dislocations were observed at the atomic scale. The results show that the main dislocation motion mode in shear bands of surfactant-free and surfactant-affected chips are dislocation climb and dislocation glide, respectively.

We analyze transient dynamics during shear start-up in viscoelastic flows between two parallel plates, with a specific focus on the signatures for the onset of transient shear banding using the Johnson-Segalman, non-stretching Rolie-Poly and Giesekus models. We explore the dynamics of shear start-up in monotonic regions of the constitutive curves using two different methodologies: (i) the oft-used `frozen-time' linear stability (eigenvalue) analysis, wherein we examine whether infinitesimal perturbations imposed on instantaneous stress components (treated as quasi steady states) exhibit exponential growth, and (ii) the more mathematically rigorous fundamental-matrix approach that characterizes the transient growth via a numerical solution of the time-dependent linearized governing equations, wherein the linearized perturbations co-evolve with the start-up shear flow. Our results reinforce the hitherto understated point that there is no universal connection between the overshoot and subsequent decay of shear stress in the base state and the unstable eigenvalues obtained from the frozen-time stability analysis. It may therefore be difficult to subsume the occurrence of transient shear banding during shear start-up within the ambit of a single model-independent criterion. Our work also suggests that the strong transients during shear start-up seen in earlier work could well be a consequence of consideration of the limit of small solvent viscosity in the absence of otherwise negligible terms such as fluid inertia., 46 pages, 13 figures

Dynamic gut-on-a-chip platform allows better recreation of the intestinal environment in vitro compared to the traditional static cell culture. However, the underlying mechanism is still not fully discovered. In this study, the shear stress behavior in a gut-on-a-chip device with porous membrane subjected to peristalsis motion is numerically investigated using CFD simulation for three different pore sizes and two pattern layouts. The results reveal that, in the stationary microchannel, the average shear stress on the porous membrane is approximately 15% greater than that of the flat membrane, regardless of the pore size. However, when subjected to cyclic deformation, the porous membrane with smaller pore size experiences stronger variation of shear stress which is ±5.61%, ±10.12% and ±34.45% from its average for the pore diameters of 10 μm, 5 μm and 1 μm, respectively. The shear stress distribution is more consistent in case of the staggered pattern layout while the in-line pattern layout allows for a 32% wider range of shear stress at the identical pore size during a cyclic deformation. These changes in the shear stress caused by peristalsis motion, porous size and membrane pattern could be the key factors that promote cell differentiation in the deforming gut-on-a-chip model.

The split Hopkinson pressure bar and universal testing machine are used to study the dynamic response and failure behavior of U71Mn using a hat-shaped specimen under the compression-shear stress state. The shear stress–strain curves are presented at the shear strain rates ranging from 0.001 to 19,200 s−1 and temperatures ranging from 25 to 600 °C. It is observed that the effects of strain rate hardening, strain hardening, and thermal softening are closely related to the changes of the shear stress–strain curves. The coupling effects are very significant in the process of deformation failure. The fracture morphology and longitudinal section microstructures of U71Mn are investigated by scanning electron microscope. According to the results, the shear strain rates and temperatures greatly influence the failure mechanisms of the material. Furthermore, the increase in temperature promotes the occurrence of dynamic recrystallization and reduces the tendency of the pearlite flowing toward the center of the shear zone. Based on the quasi-static tensile tests and finite element analysis, the Johnson–Cook damage model parameters are fitted and applied to the finite element analysis of the hat-shaped specimen.

In this study, a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel. The stenosis disease is caused because of the abnormal narrowing of flow in the body. This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel. Mathematical modeling helps us analyze such issues. A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method. The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid. A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem. Moreover, the flow characteristics such as the impedance, the wall shear stress in the stenotic region, the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed. The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel, which has a direct impact on the wall shear stress. It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.

This paper describes experimental trials that were performed to increase the electrorheological (ER) effect in ER fluids (ERFs) by introducing piezoelectric particles (PEPs). Five sample solutions were made using different PEPs, ER powders, and liquids that included ERFs provided with different solutions and silicone oil. The shear stress of each sample was measured by shearing the sample between parallel plate electrodes. Samples containing the PEP showed the same shear stress under steady voltage inputs but showed somewhat higher shear stress under sinusoidal voltage inputs. This suggests that mixtures of the piezoelectric powders (at approximately 5 wt.%) and the ERF may shorten the response time of the ERF to DC inputs or increase the response frequency to AC inputs.

In roadways with high ground stress or burial depths, the joints distributed within rock formations are subject to complex stresses and interlayer misalignments frequently. Rock bolts and cable bolts anchored in the rock formations are subject to tensile and shear forces. Most of the bolts used in roadway engineering are local anchored, resulting in insufficient shear strength at the bolt free end close to roadway surface and increasing bolts breaking. The anchor cable and C-shaped tube (ACC) is a highly prestressed cable bolt that can withstand high shear force in its free end. This paper examines the effect of the relationship between C-shaped tube length and joint location on the shear resistance of ACC by double shear tests. To fully exploit the ACC’s shear resistance, the C-shaped tube ends should be at least 30 cm beyond the joint. The effect of preload and concrete spray thicknesses on roadway deformation and plastic zone is investigated by numerical simulation. Results show that ACC and concrete spraying layer can form a stable extruded arch structure, so that the broken and soft rock within the loosen zone is in three-dimensional-stress state, effectively improving surrounding rock properties and controlling its deformation size. Based on these results, the ACC support design method is proposed.

Shock compression subjects materials to a unique regime of high quasi-hydrostatic pressure and coupled shear stresses for durations on the order of 1–10 nanoseconds for laser-driven loading of samples. There is, additionally, an attendant temperature increase due to the shock and the mechanisms of plastic deformation in metals whereby dislocations, twins, and phase transitions nucleate and propagate at velocities near the sound speed. Covalently bonded materials have, by virtue of the directionality of their bonds, great difficulty in responding by conventional plastic deformation to this extreme regime of shock compression. We propose that the shear from shock compression induces amorphization, as observed in Si, Ge, B4C, SiC, and olivine ((Mg, Fe)2SO4) and that this is a general deformation mechanism in a broad class of covalently bonded materials. The crystalline structure transforms to amorphous along regions of maximum shear stress, forming nanoscale bands, and thereby relaxing the shear component of the imposed shock stress. This process is usually preceded by the emission and propagation of a critical concentration of dislocations.

Magnetic nanoparticles (MNPs) are very attractive components in many biomedical applications, particularly as therapeutic magnetic microcarriers (TMMC) for targeted therapy. Although MNPs can be effectively gathered and transported using external magnetic fields, the optimal delivery is yet to be fully investigated. In this letter, we discuss the modeling and the characterization of deformable soft magnetic microrobots under various magnetic field conditions. The microrobots considered consist of superparamagnetic iron oxide (SPIO) immersed in different carrier fluids, and the behavior of which has been characterized experimentally under weak magnetic fields. The experimental results clearly show that the observations properly follow the model prediction. Soft magnetic microrobots with controllable shape deformation have great potential for targeted drug delivery due to the adaptability of their characteristics to environmental conditions (e.g. vessel size, velocity, shear stress).

Cutting tools with round edge can enhance the performance of machining difficult-to-machine materials, while the complex contact mechanism related to micro cutting edge limits the deeper understanding of cutting mechanics. Material separation, which is associate to plough mechanism with formation of dead metal zone (DMZ), also requires the analysis of contact behavior. This study develops a contact model along the round edge together with the illustration of DMZ, with three contact feature points defined to explain the contact situation between workpiece and cutting edge. Among these feature points, two separation points related to DMZ classify the sliding and sticking region considering the dual-zone approach. The stagnation point is the zero shear stress point where a sudden change in shear stress direction happens. Besides, the parabolic stress model obtained from finite element simulations is established to define the normal contact distribution along the round edge. In this basis, the tool-based cutting forces are predicted with proposed contact model and two contact force components are classified for different contact regions. The proposed contact feature points and contact stress are validated through illustration with finite element simulations. Besides, orthogonal cutting tests ensure the practicality and accuracy of the proposed contact model and predicted cutting forces.

A phenomenological ductile fracture model is proposed by a careful consideration of void nucleation, growth and coalescence during plastic deformation. Within the model framework, void nucleation is controlled by an equivalent plastic strain function. Void growth takes place through two ways, namely void dilation and void elongation, which are characterized by the normalized hydrostatic stress and normalized maximum shear stress, respectively. Void coalescence is characterized by the maximum shear stress. Aluminum alloy (AA) 6016-T6 sheets are selected to conduct ductile fracture (DF) experiments on specimens with different geometries, which can cover a wide range of stress states from simple shear to balanced biaxial tension. Subsequently, the new DF model is calibrated by using a robust hybrid numerical-experimental approach with a three-dimensional (3D) fracture surface constructed for AA 6016-T6. Ductile fracture data of other two aluminum alloys (AA 2024-T351 and AA 5083-O) are also used to evaluate DF model performance by establishing their 3D fracture surfaces. Finally, a cup drawing test is conducted and simulated as a case study showing how an applicable way of using the new model. Furthermore, the predictive accuracy of the proposed DF model for fracture initiation is compared with other three uncoupled models (modified Mohr–Coulomb criterion (MMC), Lou-Yoon-Huh model and Mu-Zang model) by ABAQUS/Explicit with a user subroutine (VUMAT), which shows a good performance of the proposed DF model.

This paper presented an implementation of entropy generation analysis in the main flow field of a water jet pump via the CFD method. This study aimed to identify the inefficient location of energy conversion and to analyse entropy generation sources in each region of the water jet pump. The 2D-axisymmetric model and realisable k-ε (RKE) turbulence model at steady-state conditions were performed to validate jet pump performance and to assess the entropy generation. Likewise, the effects of the projection ratio and throat-aspect ratio as independent parameters were investigated. As a result, the throat is the most inefficient part due to the high total entropy generation rate, following by diffuser part. Also, the entropy generation rate was assessed dominant than viscous dissipation due to the turbulent dissipation, which was caused by a turbulent shear stress layer of mixing the streams. In conclusion, the projection ratio influenced the growth of the shear stress layer as well as the entropy generation. Further, the throat-aspect ratio affected the distribution of entropy generation in the throat section. An appropriate combination of both parameters has an impact on the jet pump performance improvements reducing the entropy generation rate in the future.

We present a combined simulation and experimental study of the structure and dynamics of dilute, semidilute, and concentrated graphene oxide aqueous alkaline dispersions. These materials behave as lyotropic systems, with phase ordering as the concentration increases. The sheet spacing in the ordered phases is much broader than that expected by the classical Derjaguin–Landau–Verwey–Overbeek theory. Rheological responses in the isotropic phase are similar to rod-like liquid crystals (LCs), which follow the simplified Leslie–Ericksen (LE) model. The dispersions in the biphase and the discotic phase behave similarly to polydomain LC polymers, following the mesoscopic LE model [Larson–Doi (LD) model]. The LD model fits the time evolution of shear stress at startup flow, re-startup flow after the cessation of flow, and reversal flow in the discotic phase. Further, the Folgar–Tucker–Lipscomb model fits the stress overshoot in a startup flow, but not the reversal flow.

Although the rheology of strong colloidal gels is predominantly concerned with either pure shear or pure compressive deformation, the vast majority of practical applications involves an arbitrary combination of shear and compressive stresses and strains. This situation demands a tensorial rheology of colloidal suspensions, where the multidimensional response of these complex materials to arbitrary superposed stress states needs to be characterized and constitutive models developed. In this study, we use 2D discrete element modelling simulations in the absence of hydrodynamic interactions to probe the behavior of a model strong colloidal gel under combined shear and compressive deformation. We consider the deformation and failure of these gels under strain-controlled conditions that range from pure compression to shear-dominated consolidation. Particle-scale observations uncover how shear stresses act to stimulate nonaffine buckling and rupture of force chains during consolidation, leading to augmented failure and collapse of the particle network. At the macroscopic level, we find that the energy required to consolidate a colloidal suspension from the gel point to close packing passes through a minimum that corresponds to weak shear strain, indicating that small amounts of shear play a critical role in destabilizing the colloidal network. These results represent an important step toward a complete understanding of the tensorial rheology of strong colloidal gels.

The flow behavior of nanocrystalline cellulose (CNC) hydrogels in the presence of a monovalent electrolyte (NaCl) as a function of CNC and salt concentration is explored using a variety of linear and nonlinear rheological tests. We have first observed an apparent “slip yield stress” at small wall shear stress values that is mainly due to the onset of solidlike slippage of the hydrogels before their true yielding and deformation. This flow regime and the “slip yield stress” can be eliminated using a sandpaper of an optimum grit size. At higher wall shear stress values, two yielding points for the CNC/salt network are seen in strain sweep tests due to network disruption and cluster deformation that depend on the concentration of both CNC (1–5 wt. %) and electrolyte (0–100 mM). The first yield stress is due to yielding and flow of clusters, while the second one is due to breakage of clusters to small flocs and individual fibers. These yielding stresses were obtained by a variety of tests including strain amplitude sweep, creep, and steady shear, and their values are compared confirming their existence. Rheo-SALS (small angle light scattering) measurements confirmed structural changes as the scattering patterns change from isotropic to highly anisotropic with an increase of deformation and rate of deformation. Moreover, confocal laser scanning microscopy and polarized microscopy images confirm the gradual breakup of clusters to smaller ones and eventually to nearly individual fibers with an increase in the applied shear strain and rate.

The experimental method of small punch tests (SPT) using miniature specimens has great advantages and broad application prospects for material research in space, nuclear plants and other extreme environments. However, at present, the application of this method lacks unified standards and norms, which affects its application effect. Based on these, the mechanical properties of φ3 mm disks miniature specimens of SIMP steel with different thicknesses are investigated through SPT experiments, finite element modeling (FEM) analyses and scanning electron microscopy observations. All the results demonstrate that the relationship of the mechanical properties of standard tensile test samples derived from the data of small punch test is established, and the method of establishing this mechanical relationship is also provided. Most importantly, based on the shear stress analyses of FEM calculations, most mechanical properties, such as yield strength, ultimate strength, fracture toughness and elastic modulus, can be obtained directly through SPT experiments. These findings may improve the possibility of establishing a widely accepted program for obtaining basic materials properties from SPT experimental data by using FEM simulations and provide a new comparison scheme (or norm) for obtaining accurate data from miniature specimens.

The purpose of this research is to improve the parameters of shear strength in granular volcanic soil, by adding a percentage of Portland type I cement. The first step for this research was to classify the soil through a Granulometry test, according to the Unified Soil Classification System (USCS), the result was considered as a poorly graded sand with gravel also considered by The American Association of State Highway and Transportation Officials (AASHTO) as “A-1-b”. In addition, the compaction curve of the volcanic soil has a Maximum Dry Density (MDD) of 1.21 kg/cm2 and an optimum moisture content of 17.8%. Also, the friction angle of 33.5° and a cohesion of 0 kg/cm2, and the results of the Direct Shear Test indicate the Residual Stresses of 0.63, 1.34 and 2.65 kg/cm2 according to the Normal Stresses 1, 2 and 4 kg/cm2, respectively. The second step was to apply a Modified Proctor Test as following: one sample for natural soil and four samples adding 3%, 5%, 7% and 9% of cement. Finally, applied the Direct Shear Test: one sample for natural soil and three samples adding 3%, 5%, and 7% of cement after 7 days of curing, then three more samples are taken adding 3, 5% and 7% of cement at 14 days of curing. The results of the Modified Proctor Test of the volcanic soil with the addition of 5% cement has a maximum peak of a Maximum Dry Density of 1.33 kg/cm2 and with an Optimal Moisture Content of 22.7%, improved the MDD by 10% in regard to the natural soil. And the results of the Direct Shear Test shown in each sample an increase from 14.6% to 79.1% in the friction angle in comparison with the natural soil from 25.8% to 161.5% in shear strength. Likewise, the behavior of the volumetric deformation is shown, presenting a greater contraction when a normal stress of 1 kg/cm2 is applied and a greater expansion when a normal stress of 4 kg/cm2 is applied. Also, the volcanic soil at 7 days of curing with 7% cement addition increases its resistance by 67.34% and the volumetric variation decreases by 50% and the volcanic soil at 14 days of curing with 5% addition of cement increases its resistance by 103.40% and the volumetric variation decreases by 25%.

Purpose This study aims to purpose the suitable location of slip boundary condition and microscale surface textures to enhance the tribological performance of the hydrodynamic journal bearings. Design/methodology/approach Mass conserving Elrod cavitation algorithm with considering slip boundary condition has been used for predicting the static performance characteristics (load carrying capacity, coefficient of friction and volumetric inflow rate) of finite cylindrical shape textured journal bearings. Findings It has been observed that the full textured bearing with slip boundary condition in between 0°–180° circumferential region gives a significant reduction in the lubricant rupture zone. However, the introduction of textures up to the interface of slip and the no-slip region is increasing the load-carrying capacity and reduces the shear stress. This reduction in shear stress with combined slip and surface textures is effective in increasing the volumetric inflow rate of the lubricant. Practical implications The combined effect of slip boundary condition and surface texturing is increasing the scope of liquid lubricants in hydrodynamic journal bearings and further contributing toward the development of small-scale rotating machines. Originality/value The study related to the use of mass conserving Elrod cavitation algorithm for finding the optimum location of slip and surface texture zones has been found rare in the literature. Previous studies show that the mass conserving Elrod cavitation algorithm gives realistic results for textured bearings and its findings show good agreement with the experimental observations.

The buckling behavior of functionally graded rectangular plates under mechanical and thermal loading is investigated using a four-node finite element based on a simple high-order shear deformation theory. Unlike other high-order shear deformation theories which employ a great number of unknown, the present element has only five degrees of freedom per node. The principle of total potential energy is used to derive the stiffness and geometrical matrices. Moreover, the assumed natural shear strain technique is introduced to elevate any shear locking phenomenon. The proposed model accounts for the quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate. Therefore, no shear correction factors are needed. Convergence and comparison studies showed the stability and accuracy of the present finite element in predicting the critical buckling load and the critical temperature rise of isotropic and functionally graded material plates. The effect of volume fraction exponent, side-to-thickness ratios, and loading types on the buckling behavior of functionally graded plates are also studied.

In this article, a grinding force model, which is on the basis of cutting process of single abrasive grains combined with the method of theoretical derivation and empirical formula by analyzing the formation mechanism of grinding force, was established. Three key factors have been taken into accounts in this model, such as the contact friction force between abrasive grains and materials, the plastic deformation of material in the process of abrasive plowing, and the shear strain effect of material during the process of cutting chips formation. The model was finally validated by the orthogonal grinding experiment of powder metallurgy nickel-based superalloy FGH96 by using the electroplated CBN abrasive wheel. Grinding force values of prediction and experiment were in good consistency. The errors of tangential grinding force and normal grinding force were 9.8% and 13.6%, respectively. The contributions of sliding force, plowing force and chip formation force were also analyzed. In addition, the tangential forces of sliding, plowing and chip formation are 14%, 19% and 11% of the normal forces on average, respectively. The pro-posed grinding force model is not only in favor of optimizing the grinding parameters and improving grinding efficiency, but also contributes to study some other grinding subjects (e.g. abrasive wheel wear, grinding heat, residual stress).

Tire burst is one of the hot issues in automobile market. Based on the tire burst problem of all-steel radial tire, the shear strain and strain energy density at the end of the belt layer are analyzed to extend the tire durability. A multi-objective optimization model was established by finite element analysis, and the function constraints conditions were set. The optimization scheme was determined using differential evolution (DE) method. The finite element simulation and the durability test of tire specimen show that tire performance has greatly improved after the optimization. The results show that the combination of the finite element analysis technique and the multi-objective optimization method can effectively reduce a lot of labor, material, and financial resources in the structural optimization of mechanical products.

The debris from exploded buildings can ricochet after colliding with the ground, thus increasing the debris travel distance and danger from any associated impacts or collisions. To reduce this danger, the travel distance of ricocheted debris must be accurately predicted. This study analyzed the change in the travel distance of ricocheted concrete debris relative to changes in the properties of a sand medium. Direct shear tests were conducted to measure the change in internal friction angle as a function of temperature and water content of the sand. Finite element analysis (FEA) was then applied to these variables to predict the speed and angle of the debris after ricochet. The FEA results were compared with results of low-speed ricochet experiments, which employed variable temperature and water content. The travel distance of the debris was calculated using MATLAB, via trajectory equations considering the drag coefficient. As the internal friction angle decreased, the shear stress decreased, leading to deeper penetration of the debris into the sand. As the loss of kinetic energy increased, the velocity and travel distance of the ricocheted debris decreased. Changes in the ricochet velocity and travel distance of the debris, according to changes in the internal friction angle, indicated that the debris was affected by the environment.

The tip leakage flow formed by the tip clearance of a semi-open centrifugal pump adversely affects the energy performance and the energy waste. A T-shaped blade is proposed to be used to improve the energy characteristics. The internal flow field is simulated via the shear stress transport turbulence model to analyze the influence of the T-shaped blade on the performance of a centrifugal pump. It is shown that with the T-shaped blade, the hydraulic loss can be reduced, the Euler head can be increased, and the external characteristics can be improved. The maximum head and efficiency improvements are 3% and 1.6%, respectively. The relative flow angle near the tip clearance of the T-shaped blade decreases, and the strength of the backflow region is remarkably weakened. The area of the high entropy production region decreases, and the trend of the upstream diffusion is restrained under the design condition. The T-shaped blade can help to inhibit the diffusion of the high entropy production region to the hub under the low flow rate condition, but the entropy production and the mixing losses at the tip clearance are slightly increased. This research provides a new method for improving the energy performance of the semi-open centrifugal pump.

Mechanical components are frequently subjected to severe cyclic pressure and/or temperature loadings. Therefore, numerical and analytical low cycle fatigue methods become widely used in the field of engineering to estimate the design fatigue lives. The primary aim of this work is to evaluate the accuracy of the most commonly used numerical and analytical low cycle fatigue life methods for specimens made of 316 LN austenitic stainless steel and subjected to fully reversed uniaxial tension–compression loading, in the room temperature condition. It was found that both maximum shear strain and Brown–Miller criterions result in a very conservative estimation for uniaxially loaded specimens. However, maximum shear strain criteria provide better results compared to the Brown–Miller criteria. The total strain energy density approach was also used, and both the Masing and non-Masing analysis were adopted in this study. It is found that the Masing model provides conservative fatigue lives, and non-Masing model results in a more realistic fatigue life prediction for 316 LN stainless steel for both low and high strain amplitudes. The fatigue design curves obtained from the commonly used analytical low cycle fatigue equations were reexamined for 316 LN SS. The obtained design curves from Langer model and its modified versions are nonconservative for this type of material. Consequently, the authors suggest new optimized parameters to fit the given test data. The obtained curve using the currently suggested parameters is in better agreement with the experimental data for 316 LN SS.

The investigation of deformation law is the theoretical basis for analyzing instability wrinkling and forming performance during the sheet-metal-forming process. In order to explore the deformation law in the flange area of box-shaped parts and conduct qualitative and quantitative analysis on stress and strain, it is assumed that the deformation law of the mass point on the zero line of shear stress in the corner area is equal to that of the axisymmetric parts. Based on the basic assumptions that the equivalent strain in the flange area is linear with the radius along the radial direction, the simple linear relationship between in-plane shear stress and geometric parameters and the expressions of stress and strain in each region of the flange area are derived. The theoretical derivation is compared and analyzed through finite element (FE) simulation and process tests. The results demonstrate that the theoretical calculation results are consistent with the trends of experimental and simulation results. The calculation accuracy of equivalent strain is higher than that of stress calculation, which reveals that calculation accuracy is sensitive to the parameters in the material constitutive model. The theoretical analysis has reference significance for exploring the law of deep drawing deformation, optimizing the forming process and guiding the actual production.

A magnetorheological shear thickening fluid (MSTF) is prepared through adding carbonyl iron particles and Al2O3 abrasives into the traditional shear thickening fluid (STF) to improve low shear stress characteristic of STF in this work. To select the optimal sample as base fluid for MSTF, a series of STFs was pre-prepared and its rheological characteristics were further tested, which contained different concentrations of starch polymer and abrasive. Furthermore, different character parameters of MSTFs, such as magnetic field intensity and carbonyl iron particle’s concentration, were experimentally tested to explore its rheological characteristics. Then, the magnetorheological effect on shear thickening formation of MSTFs was furtherly discussed. Experimental results show that with the same base fluid the viscosity and the shear stress of MSTFs are both higher than of STFs under the action of magnetic field. Moreover, the MSTF exhibits a good shear thickening effect under the weak magnetic field intensity and at low level of iron particle concentration, because the existence of hydrogen bonds and magnetic particle chains makes the shear thickening effect of MSTF enhanced by particle clusters. The results indicate that the MSTFs as polishing fluid contribute to develop a higher efficiency polishing method in the future.

Fiber-reinforcement is a common feature of many soft biological tissues. The response of fibrous biotissues to applied shear is thus of considerable current interest. We consider here the fundamental deformation of simple shear within the framework of transversely isotropic incompressible hyperelastic materials for fiber-reinforced specimens with a single family of parallel fibers oriented at a general angle to the direction of shear. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining an homogeneous deformation state in the bulk of the specimen. Here we investigate the effects of fiber-matrix interaction on the shear and lateral normal stresses. The inclusion of fiber-matrix interaction stiffens the shear stress response. As regards the normal stress, it is shown that the confining normal traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy, fiber-matrix interaction and on the angle of orientation of the fibers. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear so that one has the possibility of both a positive or negative Poynting effect. It is shown that the fiber-matrix interaction enhances both the positive and negative Poynting effects. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. In particular, it is shown that, for sufficiently small angles of orientation, a transition amount of shear exists at which the normal stress changes character from tensile to compressive with increasing amount of shear. An increase in the degree of fiber-matrix interaction enlarges the range of orientation angles for which this transition can occur and decreases the transition amount of shear. These transition amounts of shear are well within the physiological strain regime. The results obtained here are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fibrous biological soft tissues.

Fatigue cracking caused by repeated heavy traffic loading is a critical distress in asphalt concrete pavements and is significantly affected by the selected binder. In recent years, the growing use of recycled asphalt materials has increased the need for the production of softer asphalt binder. Various modifiers/additives are marketed to adjust the grade and/or enhance the binder performance at high and low temperatures. The modifiers are expected to alter the rheological and chemical characteristics of binders and, therefore, their performance. In this study, the damage characteristics of modified and unmodified binders, at standard long-term and extended aging conditions, were tested using the linear amplitude sweep (LAS) test. Current data-interpretation methods for LAS measurements (including AASHTO TP 101-12, T 391-20, and recent literature) showed inconsistent results for modified binders. An alternative method to interpret LAS results was developed in this study. The method considers the data until peak shear-stress is reached because complex stress states and failure patterns are observed in the specimens after that point. The proposed parameter (Δ| G*|peak τ) quantifies the reduction in complex shear modulus measured at the peak shear-stress. The parameter successfully captures the effect of aging and modification of binders.

The detachment of attached shock waves and the attachment of detached shock waves frequently occur for various supersonic air vehicles. The transitional boundary plays a crucial role in clarifying the detachment and attachment processes of shock waves, which are always accompanied by remarkable aerodynamic characteristic differentials. In this work, a computational study is performed to investigate the detachment and attachment conditions of shock waves for profound understanding of the shock wave dynamics. The result of computational fluid dynamics is validated against existing experimental data in the open literature. An excellent match is obtained using the shear stress transport k-omega turbulence model. From the theoretical analysis, attached shock waves can transform into detached shock waves abruptly and vice versa. Realistic transitional regions with a certain range are numerically established. The differences in the detachment and attachment phenomena of shock waves are produced as a hysteresis process.