Large Transverse Deformation Research Articles

The effect of the coefficient of friction between the roller and the powder on the rolling process

The friction coefficient between the roller and the powder is one of the important factors affecting the rolling process. Since the friction coefficient is difficult to measure during rolling, it is usually regarded as a constant value in previous studies. However, the friction coefficient changes with the changes in process parameters such as the gap size and the rolling speed. In order to study the effect of the friction coefficient between the roller and the powder on powder rolling, the Drucker Prager Cap model for nickel powder rolling was established by ABAQUS. Firstly, the changes of contact stress (CPRESS) between the roller and the powder, the width (PE33), and relative density (SDV1) of the strip during rolling were analyzed. Then, the effect of the friction coefficient between the roller and the powder on the contact stress, the width, and the relative density of the strip was studied especially. The results show that during the rolling process, the contact stress remains basically unchanged. However, a large transverse deformation occurs on both sides of the strip, and the deformation in the middle is basically small. The relative density is greatest at the smallest seam between the rollers, and it decreases slightly after moving away from the roller, and then it remains stable. The coefficient of friction between the roller and the powder has an impact on the rolling result, in which the contact stress between the roller and the powder, the width, and the relative density of the strip will increase as the friction coefficient increases.

Deformation recoverability of longitudinal joints in segmental tunnel linings: An experimental study

The shield-driven tunnel is a fabricated lining structure. The existence of longitudinal joints between segments in a ring makes the entire tunnel lining vulnerable to deformations, because the rigidity of longitudinal joints is lower than that of the main concrete segments. Large transverse deformation, accompanied by joint opening, is a common disease of shield tunnels. The aim of this work is to explore the deformational behaviors and mechanical properties of tunnel longitudinal joints under overloading, unloading, and soil grouting conditions, with emphasis on the recoverability of joint deformation. For this purpose, a series of laboratory tests have been carried out on the full-scale longitudinal joints at tunnel crown adopted in Shanghai metro tunnels, including three parallel tests with different overload levels and one cyclic overloading and unloading test. The full-scale testing considers the actual stress state of the longitudinal joint under different working conditions in real environments. The specimen of the longitudinal joint at tunnel crown adopts the actual three-segment-two-oblique-seam structure, which is different from the simplified two-segment-one-straight-seam form used in previous studies. Multiple deformation indicators, including joint opening, concrete strain, and bolt strain, are monitored and analyzed. Based on the test results, the effects of restoration actions, i.e., unloading and soil grouting, on joint deformation recovery under different overload levels are discussed. The change of recovery efficiency with the degree of joint deformation is also obtained. In addition, the deformation recoverability and rotational stiffness are compared between the longitudinal joint at tunnel crown which is subjected to positive bending moment and the longitudinal joint at tunnel springline which is subjected to negative bending moment. The test results show that the larger the joint deformation caused by overload, the lower the recovery efficiency. From a mechanical perspective, soil grouting is an effective measure to recover the large deformation of shield tunnels.

Dynamic Response Analysis of Super Shallow‐Buried Rectangular Tunnel

Relying on the project of the open‐cut municipal tunnel undercrossing Ankang Freight V yard, the train dynamic response and seismic response of ultrashallow‐buried rectangular tunnel of the lower interchange are studied, respectively, by combining the method of field measurement and numerical simulation. The results show that under the action of train vibration load, the dynamic stress response of the top plate midspan and the upper end of the side wall of the tunnel cross section directly below the rail is the most significant, and the dynamic stress response of the bottom plate is the smallest. Under the rare earthquake, the tunnel structure has large transverse deformation, in which the transverse displacement of the tunnel roof is the largest. At the same time, there is a large stress concentration at the variable section of the tunnel.

Evidence of charge density wave transverse pinning by x-ray microdiffraction

Incommensurate charge density waves (CDW) have the extraordinary ability to display non-Ohmic behavior when submitted to an external field. The mechanism leading to this nontrivial dynamics is still not well understood, although recent experimental studies tend to prove that it is due to solitonic transport. Solitons could come from the relaxation of the strained CDW within an elastic-to-plastic transition. However, the nucleation process and the transport of these charged topological objects have never been observed at the local scale until now. In this paper, we use in situ scanning x-ray microdiffraction with micrometer resolution of a ${\mathrm{NbSe}}_{3}$ sample designed to have sliding and nonsliding areas. Direct imaging of the charge density wave deformation is obtained using an analytical approach based on the phase gradient to disentangle the transverse from the longitudinal components over a large surface $(90\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\text{m})$. We show that the CDW dissociates itself from the host lattice in the sliding regime and displays a large transverse deformation, ten times larger than the longitudinal one and strongly dependent on the amplitude and the direction of the applied currents. This deformation continuously extends across the macroscopic sample dimensions, over a distance 10 000 times greater than the CDW wavelength despite the presence of strong defects while remaining strongly pinned by the lateral surfaces. This two-dimensional quantitative study highlights the prominent role of the shear effect, which should be significant in the nucleation of solitons.

Experimental and empirical study of large transverse deformation of triangular plates subjected to water hammer shock loading

In this paper, the dynamic plastic response of isosceles triangular plates under hydrodynamic loads was investigated experimentally using a drop hammer machine. To do this, a series of experimental tests were carried out on mild steel triangular plates with different thicknesses to bring insight into the effect of geometry and mechanical properties of the plate on the deformation of specimens, which were impacted by a piston-induced pressure wave inside a water tube. The effects of various impact loads originated from different drop hammer standoff distances, and hammer weights concerning variations of deflection of the center of mass were described. The experimental results were presented in terms of deflection of the center of mass of the plates and deflection profiles. The experimental results showed that the plate with lower thickness experienced higher deflection-to-thickness ratio. An empirical model was also proposed based on new dimensionless numbers for triangular plates in order to predict the ratio of deflection of the center of mass to thickness. The dimensionless numbers considered the effects of plate geometry, hydrodynamic applied load, and mechanical properties of materials. Comparison between the experimental results and empirical predictions demonstrated that the suggested model is accurate enough to predict of the response of isosceles triangular plates under hydrodynamic loads.

Large transverse deformation of double-layered rectangular plates subjected to gas mixture detonation load

A series of twenty experimental tests were first carried out to assess the large transverse deformation of double-layered rectangular plates subjected to gas mixture detonation load. Specimens were made from a combination of an aluminum alloy front layer (the impulse-receiving face) and a mild steel back layer. Four different types of thickness configurations, namely, 1 mm + 1 mm, 2 mm + 1 mm, 1 mm + 2 mm, and 2 mm + 2 mm were selected to bring an insight into the influence of back and front layer thicknesses on the deformation resistance of double-layered plates. Each specimen group was subjected to five different pre-detonation pressures of acetylene and oxygen mixture. Quantitative experimental results were obtained and discussed in detail. The experimental results showed that the back layer deflection was approximately equal to the front layer deflection when there was no gap between the layers and the front layer had a lower strength and density than the back layer. A closed-form analytical model based on energy method was developed for double-layered plates subjected to the uniform impulsive loading. Furthermore, empirical design formulae were derived based on new dimensionless numbers to predict the maximum permanent deflection of back and front layers. The influence of strain rate sensitivity of materials was considered in both analytical and empirical models. An encouraging agreement between the experimental, analytical and empirical results in terms of the normalized deflection was achieved.

Determination of Materials for Hybrid Design of 3D Soft Body Armour Panels

In order to optimise the construction of soft body armour panels by hybridization, this study aims to identify materials determination for hybrid panel. Different ballistic characteristics of aramid woven fabrics and Ultra High Molecular Weight Polyethylene uni-directional laminates were investigated through ballistic test and fractorgaphic analysis. With an increasing of total layer numbers in a panel, specific energy absorption of Twaron woven panel shows a decrease trend, and Dyneema UD panel exhibits an increasing trend. Such reverse trend of ballistic performance is due to different failure modes of two materials. According to fractorgraphic analysis, Twaron fabric has large transverse deformation for back layers in a perforated panel. This results in higher energy absorption in back layers. For Dyneema UD, thermal damage is the dominant failure mode, which can result in performance degradation especially for front layers on the strike face. In addition, Dyneema UD exhibits significant advantage of minimize Backface Signature (BFS) and a little higher perforation ratio than that of Twaron woven panels. Based on these findings, an optimized hybrid panel is designed by combing Twaron woven fabric before Dyneema UD. In comparison with other panels with different layer sequences, this hybridization manner exhibited better ballistic performance, including improvement of energy absorption, minimized BFS of the non-perforated panel and reduction of perforation ratio. These findings indicated that material determination for hybrid design should be based on ballistic characteristics of different materials and requirements of different regions in a panel.

Dynamic modeling and analysis of a flexible sailcraft

The coupled orbit, attitude and structural dynamics is very important for an orbiting sailcraft because the orbit is determined by the attitude, and the attitude and structural vibrations are affected mutually. Thus it is critical to derive the coupled dynamics and analyze how the vibrations are excited by the attitude motions, and how the orbit and attitude motions are affected by the vibrations. To solve this problem, the coupled orbit, attitude and structural dynamics is established for the sailcraft modeled by the Euler beam with large deformations merely experiencing the pitch motion in this paper. The Von-Karman’s nonlinear strain-displacement relation is adopted to consider the sailcraft with large transverse deformations, moderate rotations and small strains. The external loads include the torques by the control vanes, the offset between the center-of-mass (cm) and center-of-pressure (cp) and the gravity gradient force. The full nonlinear coupled dynamics denoted by “model 1” is established using Lagrange equation method based on the calculation of the kinetic energy, strain energy, the dissipation function and the external loads respectively. “model 2, 3” are obtained by neglecting the geometrically nonlinear terms, the second and higher terms including the vibration displacement, velocity and acceleration in “model 1” respectively, and “model 4” is a rigid body model. A 90deg pitch maneuver will be performed for the sailcraft initially on the geostationary (GEO) orbit for all the four models. The control torque generated by the control vanes is obtained based on the nonlinear optimal proportional–integral controller considering the saturation problem of the control vanes. The attitude, orbit and vibration responses are presented and compared to see the differences between the four models, some discussions and conclusions on the dynamics and control are also given, all based on the dynamics simulations.

Vibration Mode Analysis of a Rotating Circular Membrane under Transverse Distributed Load

Vibration modes of an extremely thin rotating circular membrane subjected to transverse distributed load are investigated. In the previous paper, the author proposed an analytical method to obtain equilibrium states with large transverse deformations employing the von Karman theory and taking account of buckling under the assumptions of rotationally symmetric deformations. In this paper, transverse vibration equation around the equilibrium state under transverse load is derived and modal equation is formulated. The equation is numerically solved and modal frequencies and modal shapes are obtained. Typical vibration modes are illustrated. In order to confirm the validity of the analysis, eigenvalue analysis of a spring-mass system model for the membrane are performed to obtain vibration modes. A fairly good agreement is found between the theoretical and numerical results. Experiments of thin rotating circular membranes under gravity in vacuum are also conducted and transverse vibration frequencies are measured for a variety of rotation speed and air pressure. Analytical results are compared with the experimental results to verify the validity of the present analysis.

Shear mechanism modelling of heavy tow braided composites using a meso-mechanical damage model

Abstract Heavy tow braid reinforced composites are a potential substitute for metals in automotive and other transport applications. These composites, if properly designed, can provide lightweight efficient load bearing structural members that can also absorb high specific energy under impact and crash loading. Many of these components are ‘beam like’ members that must resist large transverse deformations at high force levels, thereby absorbing high levels of energy. This class of composite component is particularly considered in this paper. An effective means to achieve high energy absorption is careful design of the fabric architecture so that shearing mechanisms of the fibre/matrix interface, without premature fibre failure, are possible. Characterisation and modelling of progressive shear damage and failure occurring in biaxial carbon and glass braided composites are investigated. Fibre re-orientation and fibre/matrix interface damage is measured using an optical strain measuring method based on digital image correlation (DIC). This is then used to provide input to a meso-mechanical damage model in an explicit finite element code. A modelling approach using coupled layers of equivalent unidirectional plies is used to represent the biaxial braid composite and validation of the approach has been performed against test coupons and beam structures loaded transversally to failure.

Equilibrium of a Rotating Circular Membrane under Transverse Distributed Load

Equilibrium states of a rotating circular membrane subjected to a transverse distributed load are investigated. In order to analyze large transverse deformations of an extremely thin membrane, rotationally symmetric deformations are assumed and the membrane theory of shells of revolution and the von Karman theory are applied to formulate basic equilibrium equations. Numerical integration method of the equilibrium equations are proposed taking account of buckling due to large transverse deformation and approximate displacements, stress and strain distributions in equilibrium states are obtained while the method cannot give buckling waves. The results based on the two theories are compared and it is found that the results are approximately the same even when the transverse deflection is extremely larger than the thickness and the applicable scope of the von Karman theory is estimated. An experiment is also conducted to measure transverse displacements of a rotating circular membrane under gravity in vacuum with a wide range of rotation speeds. It is shown that the displacements given by the analyses fit into the displacements measured by the experiment.

Experimental investigation of the transverse mechanical properties of a single Kevlar ® KM2 fiber

A new experimental setup is developed to investigate the transverse mechanical properties of Kevlar ® KM2 fibers, which has been widely used in ballistic impact applications. Experimental results for large deformation reveal that the Kevlar ® KM2 fibers possess nonlinear, pseudo-elastic transverse mechanical properties. A phenomenon similar to the Mullins effect (stress softening) in rubbers exists for the Kevlar ® KM2 fibers. Large transverse deformation does not significantly reduce the longitudinal tensile load-bearing capacity of the fibers. In addition, longitudinal tensile loads stiffen the fibers' transverse nominal stress–strain behaviors at large transverse deformation. Loading rates have insignificant effects on their transverse mechanical properties even in the finite deformation range. An analytical relationship between transverse compressive force and displacement is derived at infinitesimal strain level. This relation is used to estimate the transverse elastic modulus of the Kevlar ® KM2 fibers, which is 1.34 ± 0.35 GPa.

The Impact of a Sphere on a Timoshenko Thin-Walled Beam of Open Section With due Account for Middle Surface Extension

The problem on the normal impact of an elastic sphere upon an elastic Timoshenko arbitrary cross section thin-walled beam of open section is considered. The process of impact is accompanied by the dynamic flexure and torsion of the beam, resulting in the propagation of plane flexural-warping and torsional-shear waves of strong discontinuity along the beam axis. In addition, the process of impact is accompanied by large transverse deformations and large deflection of the beam in the place of impact, with the consequent generation of longitudinal shock waves and large membrane contractive (tensile) forces. Behind the wave fronts up to the boundaries of the contact region (the beam part with the contact spot), the solution is constructed in terms of one-term ray expansions. During the impact, the sphere moves under the action of the contact force which is determined due to the Hertz’s theory, but the contact region moves under the attraction of the contact force, as well as the twisting and bending-torsional moments and transverse and membrane forces, which are applied to the lateral surfaces of the contact region. Simultaneous consideration of the equations of sphere and the contact region motion leads to the Abel equation of the second kind, wherein the value characterizing the sphere and beam drawing together and the rate of change of this value are used as the independent variable and the function, respectively. The solution to the Abel equation written in the form of a series allows one to determine all characteristics of the shock interaction of the sphere and beam.

Non-axial Muscle Stress and Stiffness

A generalization is developed of the classic two-state Huxley cross-bridge model to account for non-axial active stress and stiffness. The main ingredients of the model are: (i) a relation between the general three-dimensional deformation of an element of muscle and the deformations of the cross-bridges that assumes macroscopic deformation is transmitted to the myofibrils, (ii) radial as well as axial cross-bridge stiffness, and (iii) variations of the attachment and detachment rates with lateral filament spacing. The theory leads to a generalized Huxley rate equation on the bond-distribution function, n(ς, θ, t), of the form where the D ij are the components of the relative velocity gradient and ρ and ñare functions of the polar angle, θ, and time that describe, respectively, the deformation of the myofilament lattice and the distribution of accessible actin sites (both of these functions can be calculated from the macroscopic deformation). Explicit expressions, in terms of n, are derived for the nine components of the active stress tensor, and the 21 non-vanishing components of the active stiffness tensor; the active stress tensor is found to be unsymmetric. The theory predicts that in general non-axial deformations will modify active axial stress and stiffness, and also give rise to non-axial (e.g., shearing) components. Under most circumstances the magnitudes of the non-axial stress and stiffness components will be small compared with the axial and, further, the effects of non-axial deformation rates will be small compared with those of the axial rate. Large transverse deformations may, however, greatly reduce the axial force and stiffness. The theory suggests a significant mechanical role for the non-contractile proteins in muscle, namely that of equilibrating the unsymmetric active stresses. Some simple applications of the theory are provided to illustrate its physical content.