A micromechanical model for predicting thermal properties and thermo-viscoelastic responses of functionally graded materials

This study introduces a micromechanical model for predicting effective thermo-viscoelastic behaviors of a functionally graded material (FGM). The studied FGM consists of two constituents with varying compositions through the thickness. The microstructure of the FGM is idealized as solid spherical particles spatially distributed in a homogeneous matrix. The mechanical properties of each constituent can vary with temperature and time, while the thermal properties are allowed to change with temperature. The FGM model includes a transition zone where the inclusion and matrix constituents are not well defined. At the transition zone, an interchange between the two constituents as inclusion and matrix takes place such that the maximum inclusion volume contents before and after the transition zone are less than 50%. A micromechanical model is used to determine through-thickness effective thermal conductivity, coefficient of thermal expansion, and time-dependent compliance/stiffness of the FGM. The material properties at the transition zone are assumed to vary linearly between the two properties at the bounds of the transition zone. The micromechanical model is designed to be compatible with finite element (FE) scheme and used to analyze heat conduction and thermo-viscoelastic responses of FGMs. Available experimental data and analytical solutions in the literature are used to verify the thermo-mechanical properties of FGMs. The effects of time and temperature dependent constituent properties on the overall temperature, stress, and displacement fields in the FGM are also examined.     

A micromechanical model of hardening, rate sensitivity and thermal softening in BCC single crystals

The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model, we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cross-slip; and dislocation pair annihilation. The model is found to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.     

A micromechanical model of surface steps

The surface of an epitaxial thin film typically consists of terraces separated by steps of atomic height and it evolves largely by the motion of steps. Steps are sources of stress that interact with other residual stress fields, and these interactions have a profound effect on surface evolution. A model of the elastic field arising from a two-dimensional step is presented as a departure from the commonly used half-plane point-multipole model. The field is calculated asymptotically for small step height up to second order in terms of ‘structural’ parameters that can be determined from empirical data or atomistic calculations. Effects of a lattice mismatch and surface stress are included. The model is shown to be in remarkable agreement with atomistic predictions. It is demonstrated that second-order terms are necessary for understanding non-trivial step-step interactions, and that these second-order fields cannot be described by point sources on a half-plane.     

A micromechanical explanation of the mean stress effect in high cycle fatigue

A micro–macro approach of multiaxial fatigue in unlimited endurance is presented in this study, as an extension of a previous model recently proposed by the authors [Monchiet, V., Charkaluk, E., Kondo, D., 2006. A plasticity–damage based micromechanical modelling in high cycle fatigue. C.R. Mécanique 334 (2), 129–136]. It allows to take into account coupling between polycrystalline plasticity and damage mechanisms which occur at the scale of persistent slip bands (PSB) during cyclic deformation. The plasticity–damage coupled model is obtained by adapting the Gurson [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth: part I – yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15] limit analysis to polycrystalline materials to take into account microvoids growth along PSBs. The macroscopic fatigue criterion corresponds to microcracks nucleation at the PSB–matrix interface. It is shown that this criterion accounts for the effect of the mean stress and of the hydrostatic pressure in high cycle fatigue. Such features of HCF are related to the damage micro-mechanisms. Finally, some illustrations concerning the particular case of cyclic affine loadings are presented and comparisons of the predictions of the fatigue criterion with experimental data show the relevance of this new approach.     

A molecular network model to describe the nonlinear viscoelastic behavior of polymers

A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories. The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes. Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity may be disclosed. The project supported by the National Natural Science Foundation of China and Doctorial Fund     

A two-dimensional micromechanical model of anisotropic elastic-microplastic damage evolution

Summary A two-dimensional micromechanically based model of anisotropic elastic-microplastic damage evolution is presented. The deterioration of the material is represented by equally oriented Dugdale microcracks. Assuming a physically plausible crack growth law a consequent homogenization gives the macroscopic nonlinear stress-strain behavior during a loading process as well as the evolution of the corresponding anisotropic damage and typical characteristics during a final unloading process.

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Ein zweidimensionales mikromechanisches Modell anisotroper elastisch-mikroplastischer Schädigungsentwicklung

Übersicht Es wird ein zweidimensionales mikromechanisch begründetes Modell anisotroper elastischmikroplastischer Schädigungsentwicklung dargestellt. Die Materialschädigung wird durch gleich-orientierte Dugdale-Mikrorisse modelliert. Unter der Annahme eines physikalisch plausiblen Rißwachstumsgesetzes liefert eine entsprechende Homogenisierung sowohl das makroskopische nichtlineare Spannungs-Dehnungs-Verhalten während eines Belastungsprozesses als auch die Evolution der entsprechenden anisotropen Schädigung sowie typische Charakteristika beim Entlastungsprozeß.

     

A multivariant micromechanical model for SMAs Part 2. Polycrystal model

An averaging scheme is developed to simulate the behavior of a polycrystalline shape memory alloy (SMA) specimen using the Multivariant Micromechanics approach. An untextured polycrystalline specimen is assumed to be formed by a number of randomly oriented single crystal grains. The previously developed Multivariant technique is used to model the response of each single crystal grain subjected to its stress field seen in the polycrystalline sample. Using spherical grains, the Eshelby–Kröner approach is used to formulate the interaction between grains and to determine the stress state in each individual grain. This model successfully captures the basic features of SMA polycrystalline response to loading and temperature. In addition, comparison is made to recent experimental data with fully triaxial load states. Reasonable qualitative agreement is obtained and some issues related to crystallography of the material model are addressed.     

A model to describe the flow curves of concentrated suspensions of spherical particles

Summary The explanation for the very common phenomenon of linearity of double logarithmic plots of stress and shear-rate for shear-thinning concentrated suspensions, proposed in earlier papers, has been much extended. A definite model is proposed which, while not claiming to describe real systems in detail, leads to the linearity of the log-log curves and probably represents fairly well the actual behaviour of such systems as thick fresh dairy creams at low temperatures.     

A micromechanical damage model for rocks and concretes under triaxial compression

Based on analysis of deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.     

A micromechanical model of toughening behavior in the dual-phase composite

The fabrication of a special kind of dual-phase composite consisting of a hard matrix and ductile phase, such as metals with bimodal grain size distribution, is a promising strategy for improving the tensile ductility of nanocrystalline (nc)/ultrafine-grained (ufg) materials (Wang et al., 2002). This strategy is, however, challenged by the low reproducibility from low controllability of microstructural parameters and the existence of counterexamples (Prasad et al., 2009). The key to meet these challenges is to control the bimodal microstructural parameters to enable quantificational investigation of the relation between mechanical properties and microstructural parameters, and then set up a correlative quantitative model. In this paper, a new micromechanical model based on the propagation and multiplication of localized deformation bands is developed. To assess the model, a series of hypo-eutectoid Cu–Al alloys with controllable bimodal structures are prepared and their stress–strain curves in tension, together with those of bimodal copper (Wang et al., 2002) and bimodal Al–Mg alloys (Han et al., 2005) are predicted. Close agreement between the model-predicted and experimental results is obtained. The strength and uniform ductility of bimodal materials are observed in strong relation to the microstructural and constitutive parameters of volume fraction, strain hardening coefficient, and size of the coarse-grained ductile phase. Additionally, appropriate microstructural and constitutive parameters to achieve effective toughening can also be estimated according to the model.     

A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial

The present study is devoted to the development and validation of a nonlinear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modeled as an heterogeneous composite composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill [Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101]. The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase. Due to the matrix/inclusion morphology of the microstructure of the argillite, a Mori–Tanaka scheme is considered for the localization step. The developed model is first compared to Finite Element calculations and then validated and applied for the prediction of the macroscopic stress–strain responses of argillites.     

A thermo-viscoelastic model for particle-reinforced composites based on micromechanical modeling

Acta Mechanica Sinica - Micromechanics-based constitutive models offer superior ability to estimate the effective mechanical properties for the composites, which greatly promote the computational...     

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.     

A micromechanical model for polycrystalline creep with grain boundary cavitation

Summary  A micromechanical model is developed to describe effects such as combined power-law creep and diffusion, grain boundary sliding and cavitation in polycrystals. Several aspects of creep-constrained cavitation are taken into account such as diffusion in a cage of creeping matrix material and cavitating facets in a cage of creeping grains. Grain boundary sliding is modelled by distributed micro-shearcracks. It is shown that the different physical mechanisms and their interactions are functions of a well-defined material parameter λ, which can be related to the material length scale L introduced by Rice. Received 18 January 2000; accepted for publication 17 May 2000     

A micromechanical model for effective conductivity in granular electrode structures

Optimization of composition and microstructure is important to enhance performance of solid oxide fuel cells （SOFC） and lithium-ion batteries （LIB）. For this, the porous electrode structures of both SOFC and LIB are modeled as a binary mixture of electronic and ionic conducting particles to estimate effective transport properties. Particle packings of 10000 spherical, binary sized and randomly positioned particles are created numerically and densified considering the different manufacturing processes in SOFC and LIB： the sintering of SOFC electrodes is approximated geometrically, whereas the calendering process and volume change due to intercalation in LIB are modeled physically by a discrete el- ement approach. A combination of a tracking algorithm and a resistor network approach is developed to predict the con- nectivity and effective conductivity for the various densified structures. For SOFC, a systematic study of the influence of morphology on connectivity and conductivity is performed on a large number of assemblies with different compositions and particle size ratios between 1 and 10. In comparison to percolation theory, an enlarged percolation area is found, es- pecially for large size ratios. It is shown that in contrast to former studies the percolation threshold correlates to varying coordination numbers. The effective conductivity shows not only an increase with volume fraction as expected but also with size ratio. For LIB, a general increase of conductivity during the intercalation process was observed in correlation with increasing contact forces. The positive influence of cal- endering on the percolation threshold and the effective conductivity of carbon black is shown. The anisotropy caused by the calendering process does not influence the carbon black phase.     

A novel quadratic yield model to describe the feature of multi-yield-surface of rolled sheet metals

Since Hill’s quadratic yield model [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. Lond. A193, 281–297] cannot address enough experimental results for fairly describing the “anomalous” yield behavior as observed in some of rolled sheet metals, a new quadratic yield model is proposed. As the concept of multiple yielding systems is introduced into the new quadratic yield model, seven commonly used experimental results, three uniaxial tension stresses, one equibiaxial tension stress and three strain ratios, can all be taken into account for characterizing the anisotropy of rolled sheet metals. If more experimental results are extra needed for further improving the prediction, this yield model is still workable. As the experimental parameters are defined as functions of loading direction of corresponding test separately from the major part of yield model, the increase of experimental results regarding the same test does not vary the quadratic form of yield model. The representation of this yield model with axes of principal stresses demonstrates the similar form to Hill’s quadratic model. Therefore, many previous studies developed from Hill’s quadratic yield model can be directly upgraded by the new model to reach a higher accurate level.