Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Microstructure characteristics and solidification behavior of thixomolded Mg-9%Al-1%Zn alloy

Experimental investigation and theoretical analysis of the microstructure of thixomolded AZ91D were carried out to comprehensively understand the morphology transformation of solid particles and the solidification behavior. Typical microstructure of thixomolded AZ91D is composed of a-Mg and β-Mg17Al12, characterized with aun, aprim and eutectic. Four kinds of aun are classified according to the morphology and generation mechanism, such as spherical （al）, irregular （a2）, entrapping liquid alloy inside （a3） and entrapping pool inside （a4）. Under the effect of heating, shearing, collision, agglomeration or fragmentation, a2 and a4 can be the middle states ofal and a3. Similarly, a4 and a3 can also break into a2 and become al at the end. Controlled by undercooling, aprim nucleates and spherically grows within the remaining liquid alloy of thixomolded AZ91D until instability growth. The investigated microstructure was theoretically proved according to the analysis of Mg-Al binary phase diagram.

Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beams with(Damage) on a Viscoelastic Foundation

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential (equations) were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.

Hydrodynamics and Solids Mixing Behavior in a Riser with Blunt Internals

The hydrodynamics and solids mixing behavior in a riser with blunt internals are studied. A uniform radial distribution for solids fraction and particle velocity achieves near the internals. The turbulent velocity of particles near the wall increases with the addition of the internals, with the lateral solids mixing enhanced significantly. Probability density distribution of particle velocity is bimodal in the riser with internals, which is similar to that in the conventional riser, indicating that no significant difference in the micro flow structure exists between the riser with internals and the conventional riser. At the same time, the axial solids mixing behavior changes insignificantly with the addition of internals. These results indicate that the micro flow structure in the riser is very stable, which changes insignificantly with the change of the bed structure.

High temperature tribological behaviors of aluminum matrix composites reinforced with solid lubricant particles

The AA6061-10 wt.%B4 C mono composite, AA6061-10 wt.%B4 C-Gr(Gr: graphite) hybrid composites containing 2.5, 5, and 7.5 wt.% Gr particles, and AA6061-10 wt.%B4 C-Mo S2 hybrid composites containing 2.5, 5, and 7.5 wt.% Mo S2 particles were fabricated through stir casting. The dry sliding tribological behaviors of the mono composite and hybrid composites were studied as a function of temperature on high temperature pin-on-disc tribotester against EN 31 counterface. The wear rate and friction coefficient of the Gr-reinforced and Mo S2-reinforced hybrid composites decreased in the temperature range of 30-100 ℃ due to the combined lubrication offered by the wear protective layer and its solid lubricant phase. Scanning electron microscopy(SEM) observation of the worn pin surface revealed severe adhesion, delamination, and abrasion wear mechanisms at temperatures of 150, 200, and 250 ℃, respectively. At 150 ℃, transmission electron microscopy(TEM) observation of the hybrid composites revealed the formation of deformation bands due to severe plastic deformation and fine crystalline structure due to dynamic recrystallization.

Experimental Study on the Viscoelastic Behaviors of Debris Flow Slurry

The rheological properties of most liquid in nature are between liquids and solids, including both elastic changes and viscosity changes, that is socalled ＂viscoelastic＂. Dynamic oscillatory test was used to quantitatively study the distinct viscoelastic behaviors of debris flow slurry in the shear stress conditions for the first time in this study. The debris flow slurry samples were from Jiangjiagou Ravine, Yunnan Province, China. The experimental results were found that at the low and middle stages of shearing, when the angular velocity 09〈72.46 s-1, the loss modulus （G was greater than the storage modulus （G3, i.e. G＂〉G＇. At the late stage of shearing, when the angular velocity co-72.46 s-x, the storage modulus was greater than or equal to the loss G = G, tan -〈 1 （where phase-shift modulus, i.e. ＇ 〉 ＂ angle 5=G＂,/G3, and the debris flow slurry was in a gel state. Therefore, the progress of this experimental study further reveals the mechanism of hyperconcentrated debris flows with a high velocity on low-gradient ravines.

Prediction of Viscoelastic Behavior of Unidirectional Polymer Matrix Composites

To develop a novel method predicting the viscoelastic behavior of polymer matrix composites according to the viscoelasticity of the matrix, we used the viscoelastic model of the matrix to build new models for unidirectional composites in both 0° and 90° directions. Viscoelastic parameters for both new models were derived, and the obtained equations shared the same form as the viscoelastic constitutive equation of matrix material. The viscoelastic behaviors of matrix material and unidirectional composites were also tested. Results showed that fitting parameters of creep compliance equation were close to the theoretical values of viscoelastic constitutive parameters of the unidirectional composites, proving the validity of the models. A new method was obtained to predict the viscoelastic property of the unidirectional composites based on the viscoelastic property of composite matrix and elastic property of the unidirectional composites. This method provides a theoretical basis for future studies on the viscoelasticity of composite laminates.

Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials.The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics.The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution.Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators.The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials.Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed.As a result of the numerical investigations,in particular,it is established that in the case where the rheological parameters of the components of the compound cylinder are the same,the viscosity of the layers’materials causes the axisymmetric wave propagation velocity to decrease.

Size-dependent behaviors of viscoelastic axially functionally graded Timoshenko micro-beam considering Poisson effects

A size-dependent continuum-based model is developed for the functionally graded(FG)Timoshenko micro-beams with viscoelastic properties,in which material parameters vary according to the power law along its axial direction.The size effect is incorporated by employing the modified couple stress theory and Kelvin-Voigt viscoelastic model,so that viscous components are included in the stress and the deviatoric segments of the symmetric couple stress tensors.The components of strain,curvature,stress and couple stress are formulated by combining them with the Timoshenko beam theory.Based on the Hamilton principle,the governing differential equations and boundary conditions for the micro-beam are expressed with arbitrary beam section shape and arbitrary type of loads.The size effect,FG effect,Poisson effect,and the influence of the beam section shape on the mechanical behaviors of viscoelastic FG micro-beams are investigated by taking the simply supported micro-beam subjected to point load as an example.Results show that the size effect on deflection,normal stress and couple stress are obvious when the size of the micro-beam is small enough,and the FG effects are obvious when the size of the micro-beam is large enough.Moreover,the Poisson ratio influences the size effect significantly and the beam section shape is also an important factor influencing the mechanical behavior of the micro-beam.

Rheological Behavior for Polymer Melts and Concentrated Solutions——Part Ⅶ: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.

Rheological Behavior of Semi-Solid AZ91D Alloy

The rheological behavior and microstructure of semi-solid AZ91D was studied using a Couette type viscometer. The results show that the apparent viscosity of semi-solid AZ91D increases with the cooling rate increasing when it is continuously cooled and mechanically stirred and the empiric relation of the apparent viscosity with the cooling rate and solid fraction at shearing rate 93.7 s-1 is expressed as η=[0.66-0.63e(-ε/3.01)]e(fa/0.14), and with the shearing rate and solid fraction at cooling rate 4℃/min is shown as η=0.55e(fa/0.11-γ/87.59), as well as the cooling rate and shearing rate have an important effect on the microstructure of the semi-solid AZ91D alloy slurry, and decreasing the cooling rate and increasing the shearing rate are favorable to the nondendritic evolution of the primary grains.

Rheological behavior of semi-solid Mg_2Si/AM60 magnesium matrix composites at steady state

The microstructure and rheological behavior of semi-solid Mg2Si/AM60 magnesium matrix composite at steady state were investigated.The results show that the primary α-Mg phases are knapped by mechanical stirring and the Chinese script type reinforced Mg2Si phases exist in liquid phase and grain boundary.The analysis of apparent viscosity indicates that the apparent viscosity of semi-solid Mg2Si/AM60 magnesium matrix composite at steady state increases with increasing the volume fraction of Mg2Si and solid fraction of primary α-Mg,but decreases with increasing the shearing rate and shearing time,and the apparent viscosity keeps stable when shearing time reaches 300 s.

Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion

The time-dependent electro-viscoelastic performance of a circular dielectric elastomer(DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH FADING MEMORY

We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approach- ing to predetermined diffusion waves, Pointwise estimates on the convergence details are obtained.

Rheological behavior of semi-solid TiB_2/7075 composites and simulation of their rheocasting processes

In the present study, in-situ Ti B2 particle-reinforced 7075 aluminum alloy was produced by adding a mixture of K2 Ti F6 and KBF4 to the molten base alloy. The effects of the addition of 4.5wt.% and 9wt.%Ti B2 on the apparent viscosity and microstructure were investigated. The results showed that adding Ti B2 is effective for optimizing primary α-Al, but compared with the 4.5wt.%Ti B2/7075 composite, the addition of 9wt.%Ti B2 had no further significant refinement role in the 9wt.%Ti B2/7075 composite due to particle aggregation. The viscosities of semi-solid 7075 alloy and Ti B2/7075 composite slurries increased with an increase in solid fraction, but decreased with an increase in shear rate. The viscosity of 4.5wt.% Ti B2/7075 was the lowest among the three samples, and that of 7075 alloy was the highest under the same conditions. The primary α-Al grain size was decreased, and the dendritic grains grew into spherical shapes after shearing. Based on the experimental results, viscosity models of the semi-solid 7075 alloy and 4.5wt.% and 9wt.%Ti B2/7075 composites were formulated. According to the simulation results, the shrinkage porosity of the 4.5wt.%Ti B2/7075 wheel was lower than those of the 7075 alloy and 9wt.%Ti B2/7075 wheels.

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third_order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third_order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.

Thixotropic behavior of semi-solid AZ91D magnesium alloy

The thixotropic behavior of semi-solid AZ91D slurry was studied through a Couette type viscometer. The results show that the apparent viscosity of semi-solid AZ91D magnesium alloy slurry increases after being isothermally held, but the apparent viscosity quickly falls down to a steady state value after being stirred again and it takes on a sharp shear-thinning behavior. With the same shearing rate and the rest time increasing, the steady apparent viscosity increases because of the agglomeration of the solid particles, and the time required for the slurry to reach the steady state also becomes longer. If the solid fraction increases, it takes longer time for the slurry to reach the steady apparent viscosity with the same shearing rate and the same rest time. If the solid fraction and the rest time are the same, but the shearing rate rises, it takes shorter time for the slurry to reach the steady apparent viscosity and the final steady apparent viscosity also decreases.

Mechanical behavior of LC_4 alloy in semisolid state at high volume fractions of solid

The mechanical behavior of LC 4 alloy in the semisolid state at high volume fractions of solid has been studied through unconstrictive compressing test. The results show that peak stress mainly depends on grain boundary’s cohesion and instantaneous strain rate sensitivity in the semisolid state, which is similar to that in the solid state. Analyses on microstructures and status of compressive stress of specimen demonstrate that segregation of liquid solid phase is mainly affected by strain rate and deformation temperature. There are mainly two kinds of flow in liquid phase: either from the region with relatively large hydrostatic compressive stress to the region with relatively small hydrostatic compressive stress or from the grain boundaries perpendicular to the compression axis to the grain boundaries with a certain directional angle to the compression direction. Based on the above results, compressive deformation mechanism mainly depends on deformation temperature, strain rate and stress state.

Study on Viscoelastic Behaviors of Waxy Crude Water-in-Oil Emulsion

Emulsion of waxy crude oil is one of the common states in the subsea pipeline. At low temperatures in offshore environment, waxy crude oils with water could form the crude oil emulsion gel of oil-in-water emulsion. Thus, the waxy crude oil emulsion viscoelastic behavior for deep sea transportation and restarting pipeline safety is particularly important. By means of MASIII HAAKE rheometer which is produced by German company, waxy crude oil emulsion viscoelastic behavior is explored at different volumetric water contents and different shear stresses. By analyzing the rate of change of shear rate in the initial stage, the influence rules of viscoelastic properties were summarized, with the change of volumetric water content and the applied shear stress and based on the experimental results, the law of emulsion is explained from the micro level. It is proposed that brittle fracture exists between wax crystals, and flexible fracture was found in the interaction between water droplets and wax crystals.

Blocking Behavior of Organic Solid Phase in the Carbon Dioxide Multiphase and Multicomponent Displacement Process

Better dealing with carbon issues can support the management of current greenhouse gas emissions while achieving energy economic diversification and energy security. Carbon dioxide displacement has become the most acknowledged and practical method in enhanced oil recovery system. This is because of its oil sweep efficiency and ability to reduce the level of greenhouse gas emission. Nevertheless, it would lead to the organic solid phase deposition, which causes the changes of the wettability and the damages of wellbores and reservoirs. In this study, we used slim tube test and component test to research the dynamic characteristics of displacement process. In addition, the mechanism of porous media blockage was also investigated. Results show that when the displacement pressure closed to the minimum miscibility pressure, reservoir blockage in pore throat could happen. Component test characterizes that during near miscible displacement process, the components of oil sample varied obviously, the variation range of peak component carbon marks fluctuated strongly. Crude oil component differentiation could happen after carbon dioxide fully contacted with oil. Besides, the rapid extraction mechanism of aromatic hydrocarbons played a significant role in this process under such condition. The reason is that the solubility of saturated hydrocarbons to asphaltene and non-hydrocarbons is obviously weaker than aromatic hydrocarbons. Controlling the pressure is considered as an important link to prevent the occurrence of blocking in the carbon dioxide multiphase and multicomponent displacement process.