Wave propagation in micropolar mixture of porous media

This paper is concerned with the possible propagation of waves in an infinite porous continuum consisting of a micropolar elastic solid and a micropolar viscous fluid. Micropolar mixture theory of porous media developed by Eringen [A.C. Eringen, Micropolar mixture theory of porous media, J. Appl. Phys. 94 (2003) 4184–4190] is employed. It is found that there exist four coupled longitudinal waves (two coupled longitudinal displacement waves and two coupled longitudinal microrotational waves) and six coupled transverse waves in a continuum of this micropolar mixture. All the waves are found to attenuate and dispersive in nature. A problem of reflection of coupled longitudinal waves from a free boundary surface of a half-space consisting the mixture of a micropolar elastic solid and Newtonian liquid, is investigated. The expressions of various amplitude ratios and surface responses are derived. Numerical computations are performed to find out the phase velocity and attenuation of the waves. The variation of amplitude ratios, energy ratios and surface responses are also computed for a specific model. All the numerical results are depicted graphically. Some limiting cases have also been discussed.     

Reflection and Refraction of Micropolar Magneto-thermoviscoelastic Waves at the Interface between Two Micropolar Viscoelastic Media

Using micropolar generalized thermoviscoelastic theories, problems of reflection and refraction of magneto-thermoeviscoelastic waves at the interface between two viscoelastic media are studied when a uniform magnetic field permeates the media. Coefficient ratios of reflection and refraction are obtained using continuous boundary conditions. Some special cases are considered, i.e., the absence of micropolar and viscous effects. By numerical calculations, variations of the amplitude ratios of reflection and refraction coefficients with the angle of incidence are shown graphically for incident rotational and dilatational waves at the interface between two media (one medium is aluminium-epoxy micropolar iscoelastic material, and the other is magnesium crystal micropolar viscoelastic material). Comparing the generalized thermoelastic theories developed by Lord and Shulman (LS) and by Green and Lindsay (GL) in this paper to conventional dynamics (CD) theory the effects of a magnetic field and viscosity are shown numerically in this paper.     

Acoustic reflection from the boundary of anisotropic thermoviscoelastic solid with fluid

Vertical slownesses of waves at a boundary of an anisotropic thermoviscoelastic medium are calculated as roots of a polynomial equation of degree eight. Out of the corresponding eight waves, the four, which travel towards the boundary are identified as upgoing waves. Remaining four waves travel away from the boundary and are termed as downgoing waves. Reflection and refraction of plane harmonic acoustic waves are studied at a plane boundary between anisotropic thermoviscoelastic solid and a non-viscous fluid. At this fluid-solid interface, an incident acoustic wave through the fluid reflects back as an attenuated acoustic wave and refracts as four attenuating waves into the anisotropic base. Slowness vectors of all the waves in two media differ only in vertical components. Complex values of vertical slowness define inhomogeneous refracted waves with a fixed direction of attenuation, i.e. perpendicular to the interface. Energy partition is calculated at the interface to find energy shares of reflected and refracted waves. A part of incident energy dissipates due to interaction among the attenuated refracted waves. Numerical examples are considered to study the variations in energy shares with the direction of incident wave. For each incidence, the conservation of incident energy is verified in the presence of interaction energy. Energy partition at the interface seems to be changing very slightly with the azimuthal variations of the incident direction. Effects of anisotropy, elastic relaxation and thermal parameters on the variations in energy partition are discussed. The acoustic wave reflected from isothermal interface is much significant for incidence around some critical directions, which are analogous to the critical angles in a non-dissipative medium. The changes in thermal relaxation times and uniform temperature of the thermoviscoelastic medium do not show any significant effect on the reflected energy.     

Two-Temperature Effects on Plane Waves in Generalized Thermo-Microstretch Elastic Solid

In this article, the effect of two temperatures on plane waves propagating through a generalized-thermo-microstretch elastic half-space solid has been investigated. The surface of the medium is subjected to a mode-I crack, and the $z$ axis is pointing vertically into the medium. Two fascinating theories of generalized thermo-elasticity presented by Green and Naghdi and named as without energy dissipation (GN-II) and with energy dissipation (GN-III) have been used. Governing equations for each particular case are also derived, and a solution is obtained. An analytical technique of normal mode analysis is used to obtain the exact expressions for the displacement components, force stresses, the temperature, and the couple stresses distribution. The variations of the considered variables against the vertical distance are illustrated graphically. Comparisons are made with the results between type II and III in generalized-thermo-microstretch and in a particular case (without microstretch constants). Numerical work is also performed for a suitable material with the aim of illustrating the results. It is found that the maximum amplitude is obtained for the maximum value of the two temperature parametric constant.     

A mathematical model for wave propagation in a composite solid matrix containing two immiscible fluids

Constitutive relations and field equations have been extended for a porous medium composed of two solids and containing two chemically non-reactive immiscible fluids. By generalizing the closure relation of porosity change and employing this into the mass balance equations, the stress–strain relations have been developed. The idea of generalized compressibility tests is invoked to find the value of dimensionless parameters appearing in the closure relation of porosity change. By generalizing momentum balance equations of Lo et al. (Water Resour Res 41:1–20, 2005), the propagation of dilatational and rotational waves is explored. It is found that four dilatational and two rotational waves exist in the porous medium. In contrast to Biot’s theory, the presence of the second fluid and second solid in the porous medium gives rise to additional P- and S-waves. Variation of phase speeds and corresponding attenuation coefficients of existing waves versus frequency, saturation of the fluid phases and solid fraction are computed numerically and depicted graphically.     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Rayleigh waves at the boundary surface of modified couple stress generalized thermoelastic with mass diffusion

In this problem, we have studied propagation of Rayleigh waves in an homogeneous isotropic modified couple stress generalized thermoelastic with mass diffusion solid half space in the context of Lord–Shulman (L-S), Green–Lindsay (G-L) theories of thermoelasticity. Secular equations are derived mathematically by using appropriate boundary conditions. The values of determinant of secular equation, Rayleigh wave velocity and attenuation coefficient with respect to angular velocity for different values of wave number and relaxation times in the absence and presence of mass diffusion, are computed numerically. The numerical simulated results are depicted graphically for copper material.     

The effect of thermal radiation on the propagation of temperature waves in a semitransparent medium

The propagation of temperature waves arising as a result of periodic external thermal stimulation is investigated in a plane layer of semitransparent absorbing and radiating medium without scattering. The classification of temperature waves on the basis of two dimensionless parameters is suggested. It is rigorously demonstrated that not more than two temperature waves may simultaneously exist in a gray semi-infinite medium. The relative contribution of radiation to complex heat transfer is estimated. The system of equations of radiative-conductive heat transfer is reduced to a single integral equation on the boundary. The effect of reflection on the boundary is discussed.     

Unit-impulse response matrix of unbounded medium by finite-element based forecasting

In this novel forecasting algorithm to calculate the unit-impulse response matrix of an unbounded medium to analyse dynamic medium-structure interaction in the time domain based on the substructure method, a finite-element region adjacent to the structure–medium interface consisting of two or three rows only is introduced. Its exterior boundary is chosen to be similar to the interior boundary which coincides with the structure–medium interface. At similar boundaries of the unbounded medium the unit-impulse response matrices are a function of the dimensionless time. The unit-impulse response matrix at the exterior boundary can be forecasted from that at the interior boundary via this dimensionless time by taking advantage of the time delay of waves propagating between these two boundaries. The forecasting algorithm based solely on the finite-element method is exact in the finite-element sense in modelling the unbounded medium.     

Magnetic shape memory effect and highly mobile twin boundaries

Abstract

The magnetic shape memory effect can be classified as an example of the multiferroic effect combining ferro-elasticity and (ferro)magnetism. After short overview of all known effects the focus is on magnetic field induced structure reorientation (MIR) in the martensite of Ni–Mn–Ga. In this material giant deformations of up to 12% have been observed in moderate magnetic fields. The phenomenology of the effect is first discussed and a model presented. The properties of Ni–Mn–Ga relevant to MIR are then considered. One necessary condition for MIR is a highly mobile twin boundary or interface between two differently oriented martensite variants (ferroelastic domains). In 10M modulated martensite, two types of mobile twin boundary (type I and type II) are observed with complex layered microstructures consisting of a hierarchy of twinning systems. The boundaries strongly differ according to the magnitude and temperature dependence of the twinning stress. Finally, the nature of these boundaries and their different behaviour is reviewed.     

平面S波在非饱和土自由边界上的反射问题研究

运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面S波在非饱和土层自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波：反射P1波、反射P2波、反射P3波及反射S波的振幅反射率及能量反射率的理论表达式,并在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明：各反射波的振幅反射率及能量反射率不仅与入射角有关,也受到饱和度变化的影响,这些结论对土动力学的理论研究以及相关工程地震勘探具有一定指导意义。     

Development of structure and effect of processing parameters on Strength–structure relationships for two ferritic stainless steels

Abstract

The development of substructure as material passes through the roll gap has been examined for a ferritie stainless steel and it is shown that the final structure evolves close to the roll gap exit. Temperature variations as the material was rolled were monitored and the subsequent effect on substructure investigated. The variation of substructure with processing for two ferritic steels is discussed and the effect of this variation on room temperature properties is presented. It is shown that the strength–structure relationship is highly dependent upon retained martensite which degrades the tensile strength.

MST/380     

Diffusion of chromium in ferritic and austenitic 9–20 wt-%chromium steels

Abstract

Radiotracer ⁵¹Cr diffusion experiments were conducted on 9–20 wt-% chromium ferritic and austenitic steels. Volume diffusion coefficients have been determined in the temperature range 881–1281 K, and triple product values of grain boundary diffusion between 795 and 1281 K. Compared with dilute solid solutions, high ratios of grain boundary and volume diffusion activation energies have been obtained. This is discussed in view of the chemical composition of the grain boundaries measured by Auger electron spectroscopy. Furthermore, in the case of ferritic steels the effects of α–γand paramagnetic–ferromagnetic phase transitions are illustrated, while for austenitic steels a classical Arrhenius relationship has been found in the investigated temperature range.     

Accumulation of coincidence site lattice boundaries during grain growth

Abstract

Monte Carlo simulations were used to investigate the effect of grain growth on the coincidence site lattice (CSL) boundary content of randomly textured polycrystals. Each grain was assigned an orientation, and grain boundary properties were dependent on both the boundary misorientation and the CSL character. While low misorientation angle boundaries (LABs) increase during growth, the fraction of CSL boundaries does not change with time. Decreasing CSL boundary energy and mobility did not alter these results. In contrast with LABs, which are characterised by a scalar misorientation angle, a particular combination of three independent rotation variables is required to create a low energy CSL boundary; thus, these boundaries are unlikely to form or to persist in a random polycrystal. While texture influences boundary formation, a texture that can enhance CSL boundaries is not apparent. Boundary plane effects should not increase CSL fraction during grain growth.     

Mechanical properties of Al–Li alloys Part 1 Fracture toughness and microstructure

Abstract

Mechanisms influencing the ambient temperature mechanical properties of commercial Al–Li alloys 2090, 8090, 8091, and 2091 are examined as a function of plate orientation, with specific emphasis on the role of microstructure. In Part 1, results on the uniaxial tensile and plane strain fracture toughness properties are presented and the behaviour is discussed in terms of the role of the matrix and grain boundary precipitates, associated precipitate free zones (PFZs), and the occurrence of short-transverse delamination. It is seen that in general peak aged microstructures show an excellent combination of strength and toughness (L–T, T–L), equal to or exceeding that shown by traditional 2000 and 7000 series high strength aluminium alloys. The superior toughness of peak aged compared with naturally aged microstructures seems to be associated with widespread matrix precipitation of platelike precipitates (T₁ in Al–Li–Cu alloys and S in Al–Li–Cu–Mg alloys), β′-dispersoids and second phase particles which promote ductile (void coalescence) fracture, and with secondary cracking (through thickness delamination) caused by poor short transverse properties. By contrast, the deterioration in fracture toughness with overaging is primarily attributed to extensive grain boundary precipitation and corresponding formation of PFZs, similar to traditional aluminium alloys. All alloys show highly textured, predominantly unrecrystallised grain structures that render the properties to be strongly orientation dependent; specifically, fracture toughness values for the short-transverse orientations (S–L, S–T) are typically 50% lower than in the longitudinal and transverse orientations.

MST/926a     

Influence of grain boundary carbide thickness and grain size on cleavage fracture strength and Charpy impact behaviour of steels

Abstract

The cleavage fracture strengths and Charpy impact transition temperatures of plain C–Mn steels (0·12%C and 1–1·4%Mn) having ferrite–pearlite microstructures have been determined for ranges of grain size and grain boundary carbide thickness. Using appropriate heat treatments, ferrite grain size and carbide thickness were varied independently. Refining the ferrite grain size or grain boundary carbide thickness increased the fracture strength and decreased the impact transition temperature. Of the current theories for brittle fracture, an equation recently derived by Petch was found to give the most satisfactory agreement with the experimental data for cleavage strength.

MST/1424     

Numerical investigations on internal temperature distribution and refrigeration performance of reciprocating active magnetic regenerator of room temperature magnetic refrigeration

A two-dimension porous medium model for a reciprocating active magnetic regenerator (AMR) of room temperature magnetic refrigeration has been developed. The thermal diffusion effect, heat flux boundary effect and variable fluid physical properties are considered in the model. In the paper, we compare the numerical results of the porous medium model with the experimental data and the calculation results of one-dimension Schumann model to validate our model. Our model can simulate the operation of the reciprocating AMR effectively. With the present model, the internal heat exchange between the two phases is numerically investigated. The two dimensional temperature distributions of the magnetic refrigerant and the refrigeration performance of AMR are obtained, and the influence of the heat flux boundary effect and the variable fluid properties on them is discussed. AMR can achieve a maximum refrigeration capacity of 293.7 W with a corresponding coefficient of performance (COP) of 5.4.     

Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM

In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction–radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM). In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction–radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction–radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.     

Effect of aging and dispersoid content on tensile properties of Al–0·6Mg–1 Si alloys

Abstract

Slip distribution was varied in a series of Al–Mg–Si alloys by changing the amount of manganese-bearing dispersoid present and by under- and overaging, which also altered the grain–boundary precipitate-free zones and hence the grain–boundary strength. Dispersoids are shown to increase ductility by slip homogenization. Slip is more heterogeneous in underaged alloys, but these show greater ductility than overaged alloys because the grain boundaries are stronger. Work-hardening rates increase with dispersoid content, although for a given dispersoid content, the underaged alloys have higher work-hardening rates. This effect is interpreted in terms of the effect of aging upon the properties of the grain-boundary regions.

MST/340     

Microstructure and properties of warm worked medium carbon steels

Abstract

In response to the growing interest of the automotive industry in warm precision forging, a laboratory study has been conducted to examine the response of selected medium carbon steels to warm working in the range 650–1060°C. The microstructure and tensile and impact properties have been determined after single, double, and multipass rolling operations. The initial work on 080M40 steel was conducted in collaboration with Austin Rover for the production of stub axle forgings. Properties satisfying the BS970 ‘R’ condition were achieved after soaking at 820–900°C and finish working at 730°C, followed by air cooling. The induction hardening response of the warm worked steels was also satisfactory. The addition of vanadium can be used either to increase strength (by adopting a soaking temperature of 1150°C) or to give an improved strength–toughness combination (by using a soaking temperature of 900°C). The properties of warm worked steels are shown to be dependent upon chemical composition, soaking and working temperature, and subsequent cooling rate. The results have been explained in terms of classical structure–property relationships.

MST/727