Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks

The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.

Generalized thermoelasticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

EFFECTIVE ELASTIC MODULI OF INHOMOGENEOUS SOLIDS BY EMBEDDED CELL MODEL

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites.

EFFECTIVE ELASTIC MODULI OF AN INHOMOGENEOUS MEDIUM WITH CRACKS

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material.

A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials

We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation rondel was based on the large deflection of the inclined members of the cells of celluar materials, The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensioned cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.

Expansion of spherical cavity of strain-softening materials with different elastic moduli of tension and compression

An expansion theory of spherical cavities in strain-softening materials with different moduli of tension and com-pression was presented. For geomaterials,two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of elastic theory with different moduli and stress-softening models,general solutions cal-culating Tresca and Mohr-Coulomb materials' stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression and strain-softening rates on stress and displacement fields and development of plastic zone of expansion of cavity were analyzed. The results show that the ultimate expansion pressure,stress and displacement fields and development of plastic zone vary with the different elastic moduli and strain-softening prop-erties. If classical elastic theory is adopted and strain-softening properties are neglected,rather large errors may be the result.

An anisotropic micromechamcal model for calculation of effective elastic moduli of Ni-based single crystal superalloys

An anisotropic micromechanical model based on Mori-Tanaka method is developed to calculate the effective elastic moduli of

Influence of loading and heating processes on elastic and geomechanical properties of eclogites and granulites

Increased knowledge of the elastic and geomechnical properties of rocks is important for numerous engineering and geoscience applications(e.g. petroleum geoscience, underground waste repositories,geothermal energy, earthquake studies, and hydrocarbon exploration). To assess the effect of pressure and temperature on seismic velocities and their anisotropy, laboratory experiments were conducted on metamorphic rocks. P-(Vp) and S-wave(Vs) velocities were determined on cubic samples of granulites and eclogites with an edge length of 43 mm in a triaxial multianvil apparatus using the ultrasonic pulse emission technique in dependence of changes in pressure and temperature. At successive isotropic pressure states up to 600 MPa and temperatures up to 600 ℃, measurements were performed related to the sample coordinates given by the three principal fabric directions(x, y, z) representing the foliation(xy-plane), the normal to the foliation(z-direction), and the lineation direction(x-direction). Progressive volumetric strain was logged by the discrete piston displacements. Cumulative errors in Vpand Vsare estimated to be <1%. Microcrack closure significantly contributes to the increase in seismic velocities and decrease in anisotropies for pressures up to 200-250 MPa. Characteristic P-wave anisotropies of about 10% are obtained for eclogite and 3-4% in a strongly retrogressed eclogite as well as granulites. The wave velocities were used to calculate the geomechanical properties(e.g. density, Poisson’s ratio, volumetric strain, and elastic moduli) at different pressure and temperature conditions. These results contribute to the reliable estimate of geomechanical properties of rocks.

Band structure,Fermi surface,elastic,thermodynamic,and optical properties of AlZr3,AlCu3,and AlCu2Zr:First-principles study

The electronic properties（Fermi surface,band structure,and density of states（DOS）） of Al-based alloys AlM3（M=Zr and Cu） and AlCu2Zr are investigated using the first-principles pseudopotential plane wave method within the generalized gradient approximation（GGA）.The structural parameters and elastic constants are evaluated and compared with other available data.Also,the pressure dependences of mechanical properties of the compounds are studied.The temperature dependence of adiabatic bulk modulus,Debye temperature,specific heat,thermal expansion coefficient,entropy,and internal energy are all obtained for the first time through quasi-harmonic Debye model with phononic effects for T = 0 K-100 K.The parameters of optical properties（dielectric functions,refractive index,extinction coefficient,absorption spectrum,conductivity,energy-loss spectrum,and reflectivity） of the compounds are calculated and discussed for the first time.The reflectivities of the materials are quite high in the IR-visible-UV region up to ~ 15 eV,showing that they promise to be good coating materials to avoid solar heating.Some of the properties are also compared with those of the Al-based Ni3 Al compound.

Quantitative Analysis on the Elastic Behaviour of Borotellurite Glass

Borotellurite glasses show potential application in nonlinear devices and are of interesting materials to he studied due to their low melting points, high refractive index, high dielectric constant and good infrared transmission. In this work, a systematic series of horotellurite glasses （B2O3）1-x （TeO2）x with x=0.6 - 0.80 were synthesized by rapid quenching. Longitudinal and shear ultrasonic velocities were measured in each horotellurite glass samples at room temperature and at 5 MHz frequency. Ultrasonic measurements were carried out by using the MBS8000 Ultrasonic Data Acquisition System. Densities of the glass samples were measured using displacement method while acetone was used as immersion liquid. Elastic constants were calculated as well as Poisson＇s ratio, Dehye temperature, softening temperatures and microhardness for all glass samples. Makishima-Mackenzie theory and bond compression model were applied to compare between the experimental elastic moduli data and the calculated theoretically.

PREDICTION OF THE OVERALL MODULI OF A CYLINDRICAL SHORT-FIBER REINFORCED COMPOSITE

With respect to obtaining the effective elastic moduli of the composite, the present theory dif- fers from both Eshelby's equivalent inclusion method and Hill's self-consistent one, both of which only consid- er the mechanical properties of the matrix and inclusions(fibers). In fact, the inclusion-inclusion interaction is more pronounced when the volume fraction of inclusions of the composite increases. Hence, in this paper the effective elastic moduli of the composite are derived by taking into account the shapes, sizes and distribution of inclusions, and the interactions between inclusions. In addition, it is more convincing to assume short-fibers as cylindrical inclusions as in the present paper than as ellipsoidal ones as in others. Finally, numerical re- sults are given.

Structural and Elastic Behavior of Chromium Doped Pr_0.5Sr_0.5MnO₃System

A series of colossal magneto resistance (CMR) materials with compositional formula Pr0.5Sr0.5Mn1-xCrxO3 (x = 0, 0.1, 0.2, 0.3, 0.4) were prepared by sol-gel technique using pure metal nitrates as the starting materials. These samples were characterized structurally by X-ray diffraction, FTIR and SEM. All the samples exhibit orthorhombic structure without any detectable impurities. The bulk densities for all the compositions were measured from the pellets. The Young’s and Rigidity moduli, Poisson’s ratio and Debye temperature of all the compositions were calculated with the experimentally measured ultrasonic longitudinal and shear velocities at room temperature using pulse transmission technique. As the materials are porous, zero porous elastic moduli have also been calculated using a well-known Hasselmann and Fulrath model. The observed variation of elastic moduli with varying chromium doping concentration has been studied qualitatively.

Mixed Alkali-zinc Effects on Thermo-mechanical Properties in Borosilicate Glasses

A series of mixed alkali-zinc borosilicate glasses with various r values(r=molar ratio of[ZnO]/([R^(2)O]+[ZnO]))from 0.00 to 1.00 were fabricated to probe the mixed alkali-zinc effects on thermo-mechanical properties.The nonlinear evolution of glass transition temperature(T_(g))with the addition of ZnO is ascribed to the competition of two converse factors,i e,the T_(g)depression as one of the colligative properties for a solution,on the one hand,and the enhancement of T_(g)due to the higher field strength of zinc cations compared to that of alkali ions.However,the nonlinear evolution of elastic moduli and coefficients of thermal expansion with r is attributed to the variance of intermediate-range clusters,which is confirmed by infrared and Raman scattering spectra.These findings are very helpful in tailoring the performance of borosilicate glasses.

Study on conveyor non-linear dynamics and its effect on dynamic behavior

A conveyor linear system assumption is based on an approximate description of belt mechanics behavior and constant elastic moduli. It produces analysis errors and improper dynamics simulation in large conveyors. The belt non-linear characteristics based on sag are described and the belt equivalent elastic moduli expression is deduced. The relationship between belt-equivalent elastic module and elastic module is studied, and their ratio varies from 0.1 to 1.0. The non-linear motion equation with a lumped element model is put forward. Its increment equation and numerical solution are built. A dynamics simulation on a conveyor is carried out, mainly to calculate and compare belt speed, acceleration, tension, displacement of gravity take-up and wave period with linear and non-linear models. It shows that the simulation errors between two models vary from 6% to 50%.

Calculation on uniaxial compressive strength of high strength concrete after wrapped by FRP

A theoretical calculation method of the axial compressive strength of a high strength concrete with fibre reinforced plastics (FRP) constraint is proposed. It is shown by test verification that the FRP strength devotion factor used for this method is in accordance with actual conditions. FRP is not up to the ultimate strength when the concrete reaches the ultimate strength, whose strength devotion factor is in the range of 0.28 to 0.59, which is related to an elastic modulus. The method can be used to estimate axial compressive strength of the concrete strengthened with FRP. The theoretical strength is 10% to 30% higher than the measured one. The deviation comes mainly from a non-ideal bonding condition of FRP-concrete interfaces and discrete property of the testing data of compressive strength.

Properties of high calcium fly ash geopolymer pastes with Portland cement as an additive

The effect of Portland cement （OPC） addition on the properties of high calcium fly ash geopolymer pastes was investigated in the paper. OPC partially replaced fly ash （FA） at the dosages of 0, 5%, 10%, and 15% by mass of binder. Sodium silicate （Na2SiO3） and sodium hydroxide （NaOH） solutions were used as the liquid portion in the mixture： NaOH 10 mol/L, Na2SiO3/NaOH with a mass ratio of 2.0, and alkaline liquid/binder （L/B） with a mass ratio of 0.6. The curing at 60℃ for 24 h was used to accelerate the geopolymerization. The setting time of all fresh pastes, porosity, and compressive strength of the pastes at the stages of 1, 7, 28, and 90 d were tested. The elastic modulus and strain capacity of the pastes at the stage of 7 d were determined. It is revealed that the use of OPC as an additive to replace part of FA results-in the decreases in the setting time, porosity, and strain capacity of the paste specimens, while the compressive strength and elastic modulus seem to increase.

Evaluation of the microstructure,thermal and mechanical properties of Cu/SiC nanocomposites fabricated by mechanical alloying

Nano-sized silicon carbide(SiC:0wt%,1wt%,2wt%,4wt%,and 8wt%)reinforced copper(Cu)matrix nanocomposites were manufactured,pressed,and sintered at 775 and 875℃in an argon atmosphere.X-ray diffraction(XRD)and scanning electron microscopy were performed to characterize the microstructural evolution.The density,thermal expansion,mechanical,and electrical properties were studied.XRD analyses showed that with increasing SiC content,the microstrain and dislocation density increased,while the crystal size decreased.The coefficient of thermal expansion(CTE)of the nanocomposites was less than that of the Cu matrix.The improvement in the CTE with increasing sintering temperature may be because of densification of the microstructure.Moreover,the mechanical properties of these nanocomposites showed noticeable enhancements with the addition of SiC and sintering temperatures,where the microhardness and apparent strengthening efficiency of nanocomposites containing 8wt%SiC and sintered at 875℃were 958.7 MPa and 1.07 vol%^(−1),respectively.The electrical conductivity of the sample slightly decreased with additional SiC and increased with sintering temperature.The prepared Cu/SiC nanocomposites possessed good electrical conductivity,high thermal stability,and excellent mechanical properties.

Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

DELAMINATION FORMATION AND DELAMINATION PROPAGATION OF COMPOSITE LAMINATES UNDER COMPRESSIVE FATIGUE LOADING

Fatigue tests of the smooth composite laminates and the notched composite laminates under compressive cyclic loading have been carried out. The damage mechanism is discussed and analyzed. Damage evolution is monitored using stiffness decay. From these tests, it is found that the initial delamination occurs at the free boundary of smooth specimens, or the notch boundary of notched specimens, subjected to the compression-compression cyclic load. A point of view in relation to two-phases of compression fatigue delamination of composites is proposed, namely, compression-compression delamination consists of the delamination formation phase and the delamination propagation, and there is a 'damage transition point' to separate this two-phases. Furthermore, an empirical modulus degradation formula and its parameters fitting method are presented. According to the test data handling results, it is shown that this formula is univocal and can fit the test data conveniently. In addition, two kinds of new anti-buckling devices are designed for these tests. At last, the E-N curves, the D-N curves and the S-N curve of the smooth carbon fiber reinforced composite laminates of T300/648C are determined to predict the fatigue life of the notched composite laminate. And the E-N curve of the notched specimens at the given load ratio R = 10 and minimum load Pmin = -0.45 kN is also measured to verify the estimated result of fatigue life.

Channel Stability Analysis by One-Way Fluid Structure Interaction: A Case Study in China

Channel engineering stability with underground goafs is a complex three-dimensional problem, especially when considering channel leakage, and is influenced by a number of processes, such as seepage, fluid structure interaction (FSI), modeling, and selection of geological mechanical parameters. In this study, stability finite element analysis by one-way FSI was performed by establishing an integrated 3D engineering geological model. The extended Fourier amplitude sensitivity test was used to quantitatively assess the first-order and total sensitivities of the engineering model to critical geological mechanical parameters. Results illustrate that the channel engineering deformation is under a reasonable range and the elastic modulus is the highest total sensitivity parameter for the channel tilt and curvature at 0.7395 and 0.7525, respectively. Moreover, the most observable coupling effects for the curvature and horizontal strain are cohesion (0.1933) and density (0.7410), respectively. © 2017, Tianjin University and Springer-Verlag GmbH Germany.