A micromechanical model for porous materials with a reinforced matrix

In this study a micromechanical model is proposed for ductile porous material whose matrix is reinforced by small inclusions. The solid phase is described by a pressure sensitive plastic model. Based on works of Maghous et al. [6], a macroscopic plastic criterion is firstly obtained by using a two-step homogenization procedure. The effect of porosity at the mesoscale and the influence of inclusions at the microscale are taken into account simultaneously by this criterion. With a non-associated plastic flow rule, the micro-macro model is applied to modeling of mechanical behavior of a cement paste. In particular, we have considered at the microscopic scale the formation of calcite grains by carbonation process in the solid matrix. The studied cement paste is then seen as a reinforced matrix–pore system. Comparisons between numerical results and experimental data show that the proposed model is able to capture the main features of the mechanical behavior of the studied material.     

Nondestructive evaluation of the carbon content in steel

The aim of this work is to propose an experimental method to evaluate the steel carbon content by ultrasound. The sample is immersed in a water tank in order to analyze it under various incidences of sound waves. Longitudinal wave velocities are measured by immersion by using a 5-MHz frequency probe. Transverse wave velocities are measured in a contact mode by using a 4-MHz transverse wave transducer. The attenuation coefficients of ultrasonic longitudinal and transverse waves are deduced from three successive basic echoes through the sample. The effects of some heat treatments on ultrasonic parameters are also studied. The measurement of ultrasonic parameters in steel offers an interesting possibility of tracing the carbon content and, at the same time, provides information on the steel structure and its elasticity.     

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

Characterizing texture in polycrystalline materials by ultrasonic waves

A method for characterizing texture from measurements of ultrasonic wave velocities is proposed. In polycrystalline aggregates, ultrasonic wave velocities are strongly affected by orientation distribution coefficients (ODCs), which are usually used to describe the degree of preferred grain orientation in textured materials. In this work, velocities of longitudinal and transverse waves propagating into aluminum alloy 6061 were measured under pure shear, simple shear and uniaxial tension. From the measured ultrasonic wave velocities, the ODCs W₄₀₀ and W₄₂₀ were calculated to infer the deformation-induced texture. The predicted pole figures, obtained using ultrasonic velocities, were in good qualitative agreement with the finite element polycrystal model analyzed pole figures.     

Ultrasonic nondestructive material evaluation method and study on texture and cross slip effects under simple and pure shear states

Ultrasonic wave velocities propagating in a plastically deformed medium are known to depend upon its microstructural material properties. Therefore, the authors have proposed the theoretical modeling of an ultrasonic nondestructive method to evaluate plastically deformed states. In the present paper, we verify the proposed theoretical modeling of an ultrasonic nondestructive method and examine its accuracy by comparing the experimental results with the simulated subsequent yield surfaces, the longitudinal and transverse wave velocities under combined stress states of an aluminum alloy using internal state variables of an anisotropic distortional yield model which were determined to achieve a good fit for the experimental results of the longitudinal and transverse wave velocity changes under uniaxial tension test. As a special case, the velocity changes of longitudinal wave under pure shear state subjected to the combinations of tension and compression are also studied, it shows a different result compared with that of longitudinal wave velocity under torsional tests of thin thickness cylinders, i.e., simple shear state. The effects on ultrasonic wave velocity changes due to texture and cross slip under simple and pure shear states are studied via a finite element polycrystal model (FEPM).     

Dislocation density based constitutive model for ultrasonic assisted deformation

The mechanical behaviour of metallic materials subjected to plastic deformation is altered with the superposition of ultrasonic vibrations. A significant effect is the reduction of flow stress or acoustic softening. This phenomenon is utilized in metal forming and other deformation based manufacturing processes. Experimental investigations on ultrasonic assisted tensile tests focus on the effect of ultrasonic vibrations along the longitudinal axis of the specimen, whereas the manufacturing processes employs in transverse directions. In the present work, transverse ultrasonic vibrations are imposed during a uniaxial tensile test using an aluminium alloy. The trend of acoustic softening due to transverse direction vibrations is similar to that along longitudinal direction. A dislocation density based constitutive model is extended to model the softening due to ultrasonic effect. The predicted results agree well with the experimental observations.     

A micromechanical study of drying and carbonation effects in cement-based materials

This paper is devoted to a micromechanical study of mechanical properties of cement-based materials by taking into account effects of water saturation degree and carbonation process. To this end, the cement-based materials are considered as a composite material constituted with a cement matrix and aggregates (inclusions). Further, the cement matrix is seen as a porous medium with a solid phase (CSH) and pores. Using a two-step homogenization procedure, a closed-form micromechanical model is first formulated to describe the basic mechanical behavior of materials. This model is then extended to partially saturated materials in order to account for the effects of water saturation degree on the mechanical properties. Finally, considering the solid phase change and porosity variation related to the carbonation process, the micromechanical model is coupled with the chemical reaction and is able to describe the consequences of carbonation on the macroscopic mechanical properties of material. Some comparisons between numerical results and experimental data are presented.     

Thermal stress analysis of a silicon carbide/aluminum composite

Thermal deformations and stresses were studied in a silicon-carbide/aluminum filamentary composite at temperatures up to 370°C (700°F). Longitudinal and transverse thermal strains were measured with strain gages and a dilatometer. An elastoplastic micromechanical analysis based on a one-dimensional rule-of-mixtures model and an axisymmetric two-material composite cylinder model was performed. It was established that beyond a critical temperature thermal strains become nonlinear with decreasing longitudinal and increasing transverse thermal-expansion coefficients. This behavior was attributed to the plastic stresses in the aluminum matrix above the critical temperature. An elastoplastic analysis of both micromechanical models was performed to determine the stress distributions and thermal deformation in the fiber and matrix of the composite. While only axial stresses can be determined by the rule-of-mixtures model, the complete triaxial state of stress is established by the composite cylinder model. Theoretical predictions for the two thermal-expansion coefficients were in satisfactory agreement with experimental results.     

Analytical solutions for transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partial vegetation

The theory of poroelasticity is introduced to study the hydraulic properties of the steady uniform turbulent flow in a partially vegetated rectangular channel. Plants are assumed as immovable media. The resistance caused by vegetation is expressed by the theory of poroelasticity. Considering the influence of a secondary flow, the momentum equation can be simplified. The momentum equation is nondimensionalized to obtain a smooth solution for the lateral distribution of the longitudinal velocity. To verify the model, an acoustic Doppler velocimeter (ADV) is used to measure the velocity field in a rectangular open channel partially with emergent artificial rigid vegetation. Comparisons between the measured data and the computed results show that the method can predict the transverse distributions of stream-wise velocities in turbulent flows in a rectangular channel with partial vegetation.     

Ultrasonic Measurements of Residual Stresses Caused by Severe Thermomechanical Deformation during FSW

In engineering processes, residual stresses can be intense once high plastic deformation and temperature gradient are involved. This is exactly the case for friction stir welding (FSW) in which both rotational and translational movements of the tool induce extreme temperature gradient and plastic deformation. In this research, the extents of longitudinal and transverse residual stresses are measured within the AA7075-T6 plates welded through FSW process using ultrasonic method. According to the obtained results, it can be found that the residual stress is of the tensile type adjacent to the welding line whereas it is of the compressive type far from the welding line. Another observation is that the longitudinal residual stresses are considerably greater than the transverse residual stresses. Furthermore, with the aim of investigating the effects of rotation and traverse velocities of the tool on residual stress, experiments are carried out at three different rotation and traverse velocities. Based on the acquired results, it is observed that upon increasing the rotation and traverse velocities, the longitudinal and transverse residual stresses decrease and increase, respectively.     

Evolution of properties in hydration of cements—A numerical study

The present work develops a numerical method for analysis of the microstructure and property evolution in the hydration of the cement. A time-dependent micro-mechanical model is established to investigate the microstructure development and the effective property evolution of the cement paste, while the input parameters of the model are based on experimental data. It is assumed that the cement paste composite consists of the anhydrous cement particles, cement gel and pores. The cement particles have a periodically spatial array and are wrapped by the cement gel. The Young’s modulus and Poisson’s ratio of the cement paste are calculated by direct average method and two-scale expansion method. The comparisons between the numerical results and experimental data show that this model can simulate the evolution of the microstructure and properties during the hydration of the cements quite satisfactorily.     

Inelastic behavior of an AS4/PEEK composite under combined transverse compressionand shear.Part II: modeling

A micromechanical model is presented for simulating the nonlinearities exhibited by AS4/PEEK composites in shear and transverse compression, their interaction, and their rate dependence at room temperature. The fibers are assumed to be transversely isotropic and to be distributed in a hexagonal pattern in the matrix. The PEEK matrix is modeled as an elastic–powerlaw viscoplastic, isotropic solid through two related models. Model I is the simple J₂–type viscoplasticity; Model II is a rate dependent version of the non-associative Drucker-Prager model. Both models are calibrated so that they reproduce the shear response of the composite. Model II is also calibrated to its transverse compression response. Both models capture the rate dependence of the composite well. Model I is significantly less stiff in transverse compression than the experimental data. However, it does a reasonable job of predicting other aspects of the biaxial experiments and captures the important trends of behavior observed. Model II does better in transverse compression, but shearing in the presence of transverse compression is found to be stiffer than the measured responses. The unit cell model allows us to examine the stresses in the composite, providing an explanation for the lack of interaction between the constant stress and the increasing stress observed experimentally for certain loading paths.     

自然冷却和遇水冷却后高温花岗岩力-声特性试验研究

以松辽盆地露天花岗岩为研究对象，对自然冷却和遇水冷却后高温花岗岩进行单轴压、拉和声波测定试验。研究不同方式冷却后花岗岩温度（100℃、200℃、300℃、400℃、500℃、600℃、700℃、800℃，以下简称100℃-800℃）与表观形态、纵、横波波速、弹性模量、泊松比、抗压强度、抗拉强度间关系，并将纵、横波波速与抗压强度、弹性模量建立联系。同时考虑遇水冷却后静置过程对花岗岩力-声性质影响。研究表明：（1）静置0h-2h是质量损失、纵波波速下降主要时段，静置6h后变化率可以忽略；自由水损失量与力-声特性损失量存在一定线性关系；（2）温度升高，自然冷却后花岗岩纵、横波波速、弹性模量、抗压强度、抗拉强度呈线型下降，遇水冷却后呈凹线型下降；高于300℃，自然冷却后花岗岩力-声参数均大于遇水冷却，泊松比变化率与其相反，600℃时冷却方式不同对花岗岩纵、横波波速、弹性模量、抗压强度影响达到最大，遇水冷却比自然冷却分别低33.33%、31.88%、53.33%、31.74%，700℃-800℃时冷却方式对花岗岩力声特性影响减小；（3）温度变化，花岗岩纵、横波波速与抗压强度、弹性模量呈良好相关性。所得结论可以提高花岗岩力-声特性测量准确性，为力学特性预测提供一个可行方法，并为岩体工程安全稳定性评估提供依据。     

Ultrasonic assessment of rough surface contact between solids from elastoplastic loading-unloading hysteresis cycle

An ultrasonic method to characterize the elastoplastic contact between two rough surfaces is presented. Ultrasonic experiments are performed on three different interfaces formed by aluminum surfaces with different levels of roughness. The frequency-dependent ultrasonic reflection coefficient from the interface is measured during loading and unloading cycles as a function of pressure, from which the ultrasonic interfacial contact stiffness is reconstructed by the least-squares inversion procedure. It is shown that one should distinguish between the ultrasonic (dynamic) interfacial stiffness and static interfacial stiffness for rough surfaces in elastoplastic contact (they are identical for purely elastic contact). It is shown that ultrasonic stiffness is associated with local unloading stiffness. An elastoplastic micromechanical model is used to describe the plasticity-induced hysteresis in the ultrasonically measured interfacial stiffness during loading-unloading cycles. The topographic parameters of the interface contact are reconstructed by matching the model-predicted results with the experimentally determined ultrasonic stiffness. Using these parameters the real area of contact, which is not directly measurable, is predicted during loading-unloading cycles using the model.     

冻土纵,横波复合宽带超声换能器系列研制

根据冻土弹性波测试的要求,本文研制成功一种冻土测试用２５０ｋＨｚ、５００ｋＨｚ和１ＭＨｚ系列的纵波、横波复合宽带超声换能器。这种换能器具有灵敏度高、频带宽、声阻抗低的特点,适于冻土力学特性测试。作者介绍了它的结构及相应系统特性,并以１０ｐｓ的延时间精度,在零度以下气温条件下,实测了不同含水量（７％、１０％、１６％、２２％和２５％）及负温（－２℃、－４０℃、－６℃、－８℃、－１０℃、－１２℃、－１４     

Steady-State MHD Flows in Nozzles with an External Longitudinal Magnetic Field

Steady-state MHD flows in channels of the nozzle type in the presence of an external longitudinal magnetic field can be divided into two significantly different classes. Subcritical flows, in which the Alfvén velocity calculated from the longitudinal magnetic field is less than the plasma velocity, have mainly the same properties as flows in a transverse magnetic self-field and their quantitative characteristics depend only slightly on the longitudinal magnetic field strength. Supercritical flows with the opposite inequality for the velocities correspond to strong longitudinal magnetic field. The main difference is the transitions between different forms of energy (kinetic, thermal, and electromagnetic). The present study contains a classification of possible flows, namely, sub- and supercritical and sub-, super-, and transonic flows with respect to the fast and slow magnetosonic and Alfvén velocities. Examples of these flows are given. The effect of the problem parameters on the flow properties is investigated.     

Critical time for acoustic wavesin weakly nonlinear poroelastic materials

The final time of existence (critical time) of acoustic waves is a characteristic feature of nonlinear hyperbolic models. We consider such a problem for poroelastic saurated materials of which the material properties are described by Signorini-type constitutitve relations for stresses in the skeleton, and whose material parameters depend on the current porosity. In the one-dimensional case under consideration, the governing set of equations describes changes of extension of the skeleton, a mass density of the fluid, partial velocities of the skeleton and of the fluid and a porosity. We rely on a second order approximation. Relations of the critical time to an initial porosity and to an initial amplitude are discussed. The connection to the threshold of liquefaction is indicated.Received: 10 August 2004, Accepted: 3 December 2004, Published online: 4 March 2005PACS: 62.50, 81.40, 62.65 Dedicated to Prof J. L. Ericksen on the occasion of his 80th birthday     

The Peculiarities of Linear Wave Propagation in Double Porous Media

The features of propagation of longitudinal and transverse waves (LW and TW) in fractured porous medium (FPM) saturated with liquid are investigated by methods of multiphase mechanics. The mathematical model of FPM accounting for inequality of velocities and pressures of liquid in pores and fractures, liquid mass exchange and nonstationary interaction forces is developed. Processes of monochromatic wave propagation are studied. The dispersion relation is obtained and the effect of model parameters on wave propagation is analysed. It is established that one transverse and three longitudinal waves propagate in FPM saturated with liquid. The fastest LW is a deformational wave and the two others are filtrational. Filtrational waves attenuate much stronger than deformational and transverse waves. Distinction of velocities and pressures in liquid in various pore systems provides an explanation for the existence of the two filtrational waves in porous medium with two different characteristic sizes of pores.     

Modélisation probabiliste d'une expérience ultrasonore : calcul de la dispersion sur les mesures de célérité

This Note presents a probabilistic model of transient wave reflection at a fluid–solid interface. The configuration represents an ultrasonic experiment used for bone tissue evaluation. The parametric method is used to derive the probabilistic model for the mechanical parameters of the solid (bone); the associated random variables are derived according to the maximum entropy principle. A Monte Carlo simulation, associated with the Cagniard–de Hoop method to calculate the acoustic response, yields the probability density for an output ultrasonic parameter similar to the velocity of longitudinal waves in the solid. Results demonstrate the sensitivity of the probability density of this parameter to the experimental setup. To cite this article: K. Macocco et al., C. R. Mecanique 333 (2005).     

On the evolution of lattice deformation in austenitic stainless steels—The role of work hardening at finite strains

In this work, a three dimensional crystal plasticity-based finite element model is presented to examine the micromechanical behaviour of austenitic stainless steels. The model accounts for realistic polycrystal micromorphology, the kinematics of crystallographic slip, lattice rotation, slip interaction (latent hardening) and geometric distortion at finite deformation. We utilise the model to predict the microscopic lattice strain evolution of austenitic stainless steels during uniaxial tension at ambient temperature with validation through in situ neutron diffraction measurements. Overall, the predicted lattice strains are in very good agreement with those measured in both longitudinal and transverse directions (parallel and perpendicular to the tensile loading axis, respectively). The information provided by the model suggests that the observed nonlinear response in the transverse {200} grain family is associated with a competitive bimodal evolution of strain during inelastic deformation. The results associated with latent hardening effects at the microscale also indicate that in situ neutron diffraction measurements in conjunction with macroscopic uniaxial tensile data may be used to calibrate crystal plasticity models for the prediction of the inelastic material deformation response.