VELOCITY AND ATTENUATION OF SEISMIC WAVES IN TWO‐PHASE MEDIA: PART I. THEORETICAL FORMULATIONS

Geophysics ◽  
1974 ◽  
Vol 39 (5) ◽  
pp. 587-606 ◽  
Author(s):  
Guy T. Kuster ◽  
M. Nafi Toksöz
Keyword(s):  
Elastic Moduli ◽  
Seismic Waves ◽  
Matrix Material ◽  
Composite Medium ◽  
Solid Matrix ◽  
Seismic Velocities ◽  
Displacement Fields ◽  
Two Phase ◽  
The Matrix ◽  
In Series

The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and the matrix material. For long wavelengths the problem is formulated in terms of scattering phenomena in an approach similar to that of Ament (1959). The displacement fields, expanded in series, for waves scattered by an “effective” composite medium and individual inclusions are equated. The coefficients of the series expansions of the displacement fields provide a relationship between the elastic moduli of the effective medium and those of the matrix and inclusions. The expressions are derived for both solid and liquid inclusions in a solid matrix as well as for solid suspensions in a fluid matrix. Both spherical and oblate spheroidal inclusions are considered. Some numerical calculations are carried out to demonstrate the effects of fluid inclusions of various shapes on the seismic velocities in rocks. It is found that the concentration, shapes, and properties of the inclusions are important parameters. A concentration of a fraction of one percent of thin (small aspect ratio) inclusions could affect the compressional and shear velocities by more than ten percent. For both sedimentary and igneous rock models, the calculations for “dry” (i.e.,air‐saturated) and water‐saturated states indicate that the compressional velocities change significantly while the shear velocities change much less upon saturation with water.

scholarly journals Effect of Reactive SPS on the Microstructure and Properties of a Dual-Phase Ni-Al Intermetallic Compound and Ni-Al-TiB2 Composite

Materials ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 5668
Author(s):  
Paweł Hyjek ◽  
Iwona Sulima ◽  
Piotr Malczewski ◽  
Krzysztof Bryła ◽  
Lucyna Jaworska
Keyword(s):  
Intermetallic Compound ◽  
Tribological Properties ◽  
Matrix Material ◽  
Dual Phase ◽  
Compression Tests ◽  
Two Phase ◽  
Alloy Matrix ◽  
Plastic Properties ◽  
Mechanical And Tribological Properties ◽  
The Matrix

As part of the tests, a two-phase NiAl/Ni3Al alloy and a composite based on this alloy with 4 vol% addition of TiB2 were produced by the reactive FAST/SPS (Field Assisted Sintering Technology/Spark Plasma Sintering) sintering method. The sintering process was carried out at 1273 K for 30 s under an argon atmosphere. The effect of reactive SPS on the density, microstructure, and mechanical and tribological properties of a dual-phase Ni-Al intermetallic compound and Ni-Al-TiB2 composite was investigated. Products obtained were characterized by a high degree of sintering (over 99% of the theoretical density). The microstructure of sinters was characterized by a large diversity, mainly in regard to the structure of the dual-phase alloy (matrix). Compression tests showed satisfactory plastic properties of the manufactured materials, especially at high temperature (1073 K). For both materials at room temperature, the compressive strength was over 3 GPa. The stress–strain curves were observed to assume a different course for the matrix material and composite material, including differences in the maximum plastic flow stress depending on the test temperature. The brittle-to-ductile transition temperature was determined to be above 873 K. The research has revealed differences in the physical, mechanical and tribological properties of the produced sinters. However, the differences favourable for the composite were mostly the result of the addition of TiB2 ceramic particles uniformly distributed on grain boundaries.

Target Morphologies in Polymer Blends

2004 ◽  
Vol 856 ◽  
Author(s):  
Nigel Clarke ◽  
Ian Henderson
Keyword(s):  
Phase Separation ◽  
Polymer Blends ◽  
Selection Process ◽  
Matrix Material ◽  
Phase Region ◽  
Wavelength Selection ◽  
Two Phase ◽  
Inhomogeneous Surface ◽  
The Matrix ◽  
Separation Results

ABSTRACTWe model a novel process for obtaining controlled morphologies in polymer blends. Particles of one type of polymer are allowed to dissolve in a matrix of a dissimilar polymer. Prior to complete dissolution the blend is quenched into the two phase region, such that phase separation takes place. The combination of the incomplete dissolution and the wavelength selection process associated with phase separation results in particles that during the ‘intermediate’ stages have a core that is significantly rich in the matrix material. The concept is extended to consider the effect of phase separation on an inhomogeneous surface chemically patterned with regions which are more attractive to one component of the blend.

Stress Behavior at the Interface Junction of an Elastic Inclusion

2002 ◽  
Vol 69 (6) ◽  
pp. 844-852 ◽  
Author(s):  
Z. Q. Qian ◽  
A. R. Akisanya ◽  
D. S. Thompson
Keyword(s):  
Finite Element ◽  
Elastic Inclusion ◽  
Symmetric Mode ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Two Phase ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
The Matrix ◽  
Finite Element Prediction

The stress distribution at the interface junction of an elastic inclusion embedded in a brittle matrix is examined. Solutions are derived for the stress and displacement fields near the junction formed by the intersection of the interfaces between the inclusion and the matrix. The stress field consists of symmetric (mode I) and skew-symmetric (mode II) components. The magnitude of the intensity factor associated with each mode of deformation is determined using a combination of the finite element method and a contour integral. The numerical results of the stresses near the interface junction of two different inclusion geometries show that the asymptotic solutions of the stresses are in agreement with those from the finite element prediction when higher-order terms are considered. The implications of the results for the failure of particle-reinforced and two-phase brittle materials are discussed.

Micromechanics and Effective Elastoplastic Behavior of Two-Phase Metal Matrix Composites

1994 ◽  
Vol 116 (3) ◽  
pp. 310-318 ◽  
Author(s):  
J. W. Ju ◽  
Tsung-Muh Chen
Keyword(s):  
Metal Matrix Composites ◽  
Elastic Properties ◽  
Metal Matrix ◽  
Phase Particle ◽  
Matrix Material ◽  
Flow Rule ◽  
Plastic Behavior ◽  
Matrix Composites ◽  
Two Phase ◽  
The Matrix

A micromechanical framework is presented to predict effective (overall) elasto-(visco-)plastic behavior of two-phase particle-reinforced metal matrix composites (PRMMC). In particular, the inclusion phase (particle) is assumed to be elastic and the matrix material is elasto-(visco-)plastic. Emanating from Ju and Chen’s (1994a,b) work on effective elastic properties of composites containing many randomly dispersed inhomogeneities, effective elastoplastic deformations and responses of PRMMC are estimated by means of the “effective yield criterion” derived micromechanically by considering effects due to elastic particles embedded in the elastoplastic matrix. The matrix material is elastic or plastic, depending on local stress and deformation, and obeys general plastic flow rule and hardening law. Arbitrary (general) loadings and unloadings are permitted in our framework through the elastic predictor-plastic corrector two-step operator splitting methodology. The proposed combined micromechanical and computational approach allows us to estimate overall elastoplastic responses of PRMMCs by accounting for the microstructural information (such as the spatial distribution and micro-geometry of particles), elastic properties of constituent phases, and the plastic behavior of the matrix-only materials. Comparison between our theoretical predictions and experimental data on uniaxial elastoplastic tests for PRMMCs is also presented to illustrate the capability of the proposed framework. A straightforward extension to accommodate viscoplastic matrix material is also presented to further enhance the applicability of the proposed method.

An Examination of the Mori-Tanaka Effective Medium Approximation for Multiphase Composites

1989 ◽  
Vol 56 (1) ◽  
pp. 83-88 ◽  
Author(s):  
A. N. Norris
Keyword(s):  
Matrix Material ◽  
Anisotropic Elasticity ◽  
Effective Medium ◽  
Average Field ◽  
Two Phase ◽  
Stringent Requirement ◽  
Multiphase Composites ◽  
The Matrix ◽  
Differential Scheme ◽  
Generalized Differential

The Mori-Tanaka method is considered in the context of both scalar thermal conductivity and anisotropic elasticity of multiphase composites, and some general properties are deduced. Particular attention is given to its relation to known general bounds, and to the differential scheme. It is shown that the moduli predicted by the method always satisfy the Hashin-Shtrikman and Hill-Hashin bounds for two-phase composites. This property does not generalize to multiphase composites. A specific example illustrates that the method can predict moduli in violation of the Hashin-Shtrikman bounds for a three-phase medium. However, if the particle shapes are all spheres, then the prediction for the multiphase composite is coincident with the Hashin-Shtrikman bounds if the matrix material is either the stiffest or the most compliant phase. It is also shown that the generalized differential effective medium method yields the same moduli as the Mori-Tanaka approximation if certain conditions are satisfied in the differential scheme. Thus, it is required that at each stage in the differential process, and for each phase j (j = 1, 2, …, n) of new material, the average field in the incrementally added phase j material must be the same as the average field in the bulk phase j. For two phase media, n = 1, this condition reduces to the less stringent requirement that the ratio of the field in the incrementally added material to the average field in the matrix material is the same as the dilute concentration ratio. The cumulative findings of this paper, particularly those concerning bounds, suggest that the Mori-Tanaka approximation be used with caution in multiphase applications, but is on firmer ground for two-phase composites.

scholarly journals Effective modules of two-phase construction composites with grain filler

2019 ◽  
Vol 15 (6) ◽  
pp. 407-414
Author(s):  
Vladimir T. Erofeev ◽  
Aleksej S. Tyuryahin ◽  
Tatyana P. Tyuryahina ◽  
Aleksandr V. Tingaev
Keyword(s):  
Building Materials ◽  
Materials Science ◽  
Volume Fraction ◽  
Matrix Material ◽  
Flat Space ◽  
Upper And Lower Bounds ◽  
Two Phase ◽  
The Matrix ◽  
Dimensionless Function ◽  
Visual Graphic

In the book of R.M. Christensen, “Introduction to the Mechanics of Composites” (1982), a calculation formula is given for the bulk module of polydisperse composites with spherical inclusions. This formula has been known to the Russianspeaking reader for almost 40 years, but unfortunately, it is not used in the practice of building materials science. To identify applied possibilities, R.M. Christensen's formula is modified and reduced to a dimensionless function k = k ( w , η, θ), which depends on three dimensionless parameters, i.e., it depends on three quantities: w is the volume fraction of the inclusion, η - the ratio of the shear modulus of the matrix material to the volume modulus of the same matrix, θ is the ratio of the volume moduli of the matrix materials and inclusion. Numerical studies of this function reveal that in two-phase granular composites, the range of effective moduli is significantly narrowed compared to the region limited by Voigt and Reuss estimates (in the sense of the upper and lower bounds of real values). At the same time, the lower Christensen score is the same as the Reuss score. Numerical and graphically presented results are given on the examples of the study of two characteristic groups of composite materials. In addition, the dimensionless form of the effective module allows to construct a system of visual graphic dependencies of the functions k ( w ) in a flat space k - w . For different values of θ, the function k = k ( w , η) displays a bunch of curved segments, which sets the position of the plane figure in flat space. Examples of constructing figures for characteristic regions of the values of the function k (η, θ, w ) are given.

scholarly journals On Adequacy of Two-point Averaging Schemes for Composites with Nonlinear Viscoelastic Phases

10.14311/658 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
J. Zeman ◽  
R. Valenta ◽  
M. Šejnoha
Keyword(s):  
Finite Element ◽  
Shear Bands ◽  
Material Model ◽  
Finite Element Simulations ◽  
Composite Medium ◽  
Viscoelastic Response ◽  
Two Phase ◽  
Nonlinear Viscoelastic ◽  
The Matrix ◽  
Macroscopic Response

Finite element simulations on fibrous composites with nonlinear viscoelastic response of the matrix phase are performed to explain why so called two-point averaging schemes may fail to deliver a realistic macroscopic response. Nevertheless, the potential of two-point averaging schemes (the overall response estimated in terms of localized averages of a two-phase composite medium) has been put forward in number of studies either in its original format or modified to overcome the inherited stiffness of classical ”elastic” localization rules. However, when the material model and geometry of the microstructure promote the formation of shear bands, none of the existing two-point averaging schemes will provide an adequate macroscopic response, since they all fail to capture the above phenomenon. Several examples are presented here to support this statement. 

The effect of the extent of freezing on seismic velocities in unconsolidated permafrost

Geophysics ◽  
1986 ◽  
Vol 51 (6) ◽  
pp. 1285-1290 ◽  
Author(s):  
Robert W. Zimmerman ◽  
Michael S. King
Keyword(s):  
Elastic Moduli ◽  
Seismic Waves ◽  
Compressional Wave ◽  
Seismic Velocities ◽  
Wave Speeds ◽  
Direct Measurements ◽  
Two Parameters ◽  
Decreasing Functions ◽  
Increasing Function ◽  
Quartz Grains

We develop a model to relate velocities of seismic waves in unconsolidated permafrost is idealized as an assemblage of spherical quartz grains imbedded in a matrix composed of spherical water inclusions in ice. The theory of Kuster and Toksöz, based on wave‐scattering considerations, is used to determine the effective elastic moduli, and hence the wave speeds. The Hasin-Shtrikman theoretical bounds on the elastic moduli of heterogeneous materials and considerations establish the plausibility of the model. The model predicts [Formula: see text] and [Formula: see text] to be decreasing functions of both the porosity and the water‐to‐ice ratio, and the ratio [Formula: see text] to be an increasing function of these two parameters. The theory is then applied to laboratory measurements of shear‐ and compressional‐wave velocities in 23 permafrost samples from different sites in the Beaufort Sea, Mackenzie River Valley, and Canadian Arctic islands. Although no direct measurements were made of the extents of freezing in these samples, the data are consistent with the predictions of the model. We show the theory can be used to predict the extent of freezing of the water in the pore spaces, based on knowledge of the porosity and either of the two wave speeds.

Mechanically Tunable Solid/Solid Phononic Crystals Through the Rearrangement of Hard Scatterers Controlled by the Deformation of Periodic Elastomeric Matrixes

2020 ◽  
Vol 87 (10) ◽  
Author(s):  
Shaowu Ning ◽  
Chengcheng Luo ◽  
Fengyuan Yang ◽  
Zhanli Liu ◽  
Zhuo Zhuang
Keyword(s):  
Wave Propagation ◽  
Coupling Effect ◽  
Matrix Material ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Dynamic Responses ◽  
Two Phase ◽  
Elastomeric Matrix ◽  
The Matrix

Abstract The fixed band gap characteristic of passive phononic crystals (PCs) is possible to limit their applications in engineering. To overcome this shortcoming, inspired by the tunable mechanism of the spider silks, a new class of tunable PCs comprising periodic scatterers and periodic elastomeric matrix are proposed to effectively tune the band gaps and directionality of propagating waves. The orientation and arrangement of hard scatterers are controlled by the deformation of the periodic elastomeric matrix to enhance the tunability of their dynamic responses. According to this idea, PCs with differently shaped and arranged cylindroid scatterers are designed. Through introducing the multiple scatterers into the periodic elastomeric matrix, the scattering coupling effect between them is enhanced. The simulation results indicate that the orientation and arrangement of the scatterers could be altered continuously during deformation. During deformation, the number, position, and width of band gaps can be effectively tuned due to the geometric nonlinearity of the matrix and the rearrangement of multiple scatterers. The transmissibility of finite-sized structures without damping decreases significantly in the frequency ranges of band gaps. However, introducing the damping into the matrix material significantly enhances the ability to suppress elastic wave propagation but makes it difficult to identify the band gaps from the transmittance spectrum. The directionality of wave propagation can be also effectively tuned. In the low-frequency range, such as the first two phase constant surfaces, the phase and group velocity profiles and the anisotropy indexes are calculated and the results indicate that the deformation makes the wave propagation more isotropic. The schemes presented in this paper provide an effective approach to tune the band gaps of the solid/solid PCs and open avenues for the design of tunable PCs.

Analysis of Steady Compaction Waves in Porous Materials

1989 ◽  
Vol 56 (1) ◽  
pp. 15-24 ◽  
Author(s):  
J. M. Powers ◽  
D. S. Stewart ◽  
Herman Krier
Keyword(s):  
Porous Materials ◽  
Volume Fraction ◽  
Matrix Material ◽  
Wave Structure ◽  
Solid Matrix ◽  
Tait Equation ◽  
Two Phase ◽  
Piston Velocity ◽  
Zone Length ◽  
Compaction Waves

A two-phase continuum mixture model is used to analyze steady compaction waves in porous materials. It is shown that such a model admits both subsonic and supersonic steady compaction waves in response to a piston-driven boundary condition when a Tait equation is used to describe a solid matrix material and a generic static compaction relation is used to describe collapse of the matrix. Parameters for the Tait equation are chosen to match shock and compaction wave data. The model is able to predict compaction wave speed, final pressure, and final volume fraction in porous HMX. The structure of the compaction wave is also studied. A shock preceding the compaction wave structure is predicted for compaction waves travelling faster than the ambient sound speed of the solid. For subsonic compaction waves no leading shock is predicted. The compaction zone length is studied as a function of initial volume fraction, piston velocity, and compaction viscosity.

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