A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

MICROMECHANICAL DAMAGE MODEL FOR ROCKS AND CONCRETES SUBJECTED TO COUPLED TENSILE AND SHEAR STRESSES

Based on the analysis of the deformation in an infinite isotropic elastic matrix with an embedded elliptic crack under far field coupled tensile and shear stresses, the energy release rate and a mixed fracture criterion are obtained using an energy balance approach. The additional compliance tensor induced by a single opening elliptic microcrack in a representative volume element is derived, and the effect of microcracks with random orientations is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes is obtained and is verified with experimental results.

FRACTURE MECHANISM AND MICROMECHANICAL ANALYSIS OF POLYSYNTHETICALLY TWINNED CRYSTALS OF γTiAl ALLOYS

The fracture behavior and mechanism of PST crystals of a Ti 49%(mole fraction)Al alloy have been studied by using in situ straining and micromechanical calculation. The three dimensional micromechanical model representing the structure of PST crystal has been built, and the stress distribution ahead of the sharp and blunt crack tips either parallel to lamellar interface or perpendicular to the lamellae has been calculated by using finite element method based on linear elasticity of PST crystals. The experimental results show that the fracture behaviors and mechanisms are strongly dependent on the angle of loading axis to the lamellae. The calculation indicates that nucleation and propagation of microcrack along the interfaces are controlled by the normal stress and translamellar microcrack is controlled by shear stress ahead of crack tip.

A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material

Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components.However,high-precision numerical results cannot be achieved without reliable strain energy functions(SEFs)of the rubber or rubber nanocomposite material.Although hyperelastic constitutive models have been studied for nearly 80 years,selecting one that accurately describes rubber's mechanical response is still a challenge.This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019.A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed.The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index.The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists.Finally,some suggestions on how to select an appropriate hyperelastic constitutive model are given,and the perspective on the future progress of constitutive models is summarized.

Modeling of anisotropic polydispersed composites by progressive micromechanical approach

A progressive micromechanical method is presented in order to predict the elastic constants of polydispersed composites including multi-directional or randomly ori- ented reinforcement particles. Heterogeneities of various types are introduced into the matrices in a gradual manner. At each step, the Mori-Tanaka method is used to ob- tain the stiffness tensor of the intermediate medium used as a matrix of the following step. The proposed method is capable of introducing any kind of heterogeneities based on their dimensions, orientations, mechanical properties, and volume fractions to the ma- trix. Furthermore, suitable probability density functions can be defined for physical and structural parameters of the composite, including the level of the filler-matrix interfacial bonding, the aspect ratio, and the orientation of reinforcement particles. The efficiency of the iterative approach and the convergence of the solution are studied by computing the stiffness tensors of unidirectional and bidirectional particulate composites. The results of the present study are also compared with the literature data for a randomly oriented particulate composite.

High-temperature Creep Behavior Characterization of Asphalt Mixture based on Micromechanical Modeling and Virtual Test

The high-temperature creep behavior of asphalt mixture was investigated based on micromechanical modeling and virtual test by using three-dimensional discrete element method（DEM）. A user-defined micromechanical model of asphalt mixture was established after analyzing the irregular shape and gradation of coarse aggregates, the viscoelastic property of asphalt mastic, and the random distribution of air voids within the asphalt mixture. Virtual uniaxial static creep test at 60 ℃ was conducted by using Particle Flow Code in three dimensions（PFC3D） and was validated by laboratory test. Based on virtual creep test, the micromechanical characteristics between aggregates, within asphalt mastic, and between aggregate and asphalt mastic were analyzed for the asphalt mixture. It is proved that the virtual test based on the micromechanical model can efficiently predict the creep deformation of asphalt mixture. And the high-temperature behavior of asphalt mixture was characterized from micromechanical perspective.

A MICROMECHANICAL MODEL FOR γ-TiAl BASE PST CRYSTALS

An analytical micromechanical method is proposed to examine the dependence of plastic deformation on the microstructure for a PST crystal. The sub-domain microstructure of the γ phase and the effect of the α2 phase are taken into account by a proper micromechanical formulation, the dislocation slip and twinning deformation mechanisms are considered in the context of crystal plasticity. The model can well predict the dependence of stress-strain relations on loading angle with respect to the microstructure. The influence of the twinning and lamellar spacing on the deformation behavior and biaxial yield surfaces for PST crystals are also examined.

Nonlinear Micromechanical Modelling of Transverse Tensile Damage Behavior in Fiber-Reinforced Polymer Composites

The investigation focusing on the mechanical behaviors at the microstructural level in composite materials can provide valuable insight into the failure mechanisms at larger scales.A micromechanics damage model which comprises the coupling of the matrix constitutive model and the cohesive zone(CZM)model at fiber-matrix interfaces is presented to evaluate the transverse tensile damage behaviors of unidirectional(UD)fiber-reinforced polymer(FRP)composites.For the polymeric matrix that exhibits highly non-linear mechanical responses,special focus is paid on the formulation of the constitutive model,which characterizes a mixture of elasticity,plasticity as well as damage.The proposed constitutive model includes the numerical implementation of a fracture plane based ellipse-parabola criterion that is an extension of the classic Mohr-Coulomb criterion,corresponding post-yield flow rule and post-failure degradation rule in the fully implicit integration scheme.The numerical results are in good agreement with experimental measurements.It is found that directly using the matrix properties measured at the ply level to characterize the mechanical responses at the constituent level may bring large discrepancies in homogenized stress-strain responses and dominant failure mechanisms.The distribution of fracture plane angles in matrix is predicted,where it is shown to provide novel insight into the microscopic damage initiation and accumulation under transverse tension.

INFLUENCE OF MAGNETIZATION ROTATION ON MARTENSITE REORIENTATION IN MAGNETIC SHAPE MEMORY ALLOY

A large field-induced strain of magnetic shape memory alloy is developed by the martensite variant reorientation. It is widely recognized that the martensite reorientation in a magnetic shape memory alloy （MSMA） can develop if the magnetic field is large enough. However, it has been shown in the literature that the magnetization rotation may block variant reorientation via energy minimization approach. In this paper, based on a micromechanicat model associated with the thermodynamic theory, authors show that there are some limits for the martensite reorientation, which is hindered by the magnetization rotation. Some useful conclusions are obtained.

Modeling oxidation damage of continuous fiber reinforced ceramic matrix composites

For fiber reinforced ceramic matrix composites（CMCs）,oxidation of the constituents is a very important damage type for high temperature applications. During the oxidizing process,the pyrolytic carbon interphase gradually recesses from the crack site in the axial direction of the fiber into the interior of the material. Carbon fiber usually presents notch-like or local neck-shrink oxidation phenomenon,causing strength degradation. But,the reason for SiC fiber degradation is the aw growth mechanism on its surface. A micromechanical model based on the above mechanisms was established to simulate the mechanical properties of CMCs after high temperature oxidation. The statistic and shearlag theory were applied and the calculation expressions for retained tensile modulus and strength were deduced,respectively. Meanwhile,the interphase recession and fiber strength degradation were considered. And then,the model was validated by application to a C/SiC composite.

Nanomechanical Characteristics of Interfacial Transition Zone in Nano-Engineered Concrete

This study investigates the effects of nanofillers on the interfacial transition zone(ITZ)between aggregate and cement paste by using nanoindentation and statistical nanoindentation techniques.Moreover,the underlying mechanisms are revealed through micromechanical modeling.The nanoindentation results indicate that incorporating nanofillers increases the degree of hydration in the ITZ,reduces the content of micropores and low-density calcium silicate hydrate(LD C-S-H),and increases the content of highdensity C-S-H(HD C-S-H)and ultra high-density C-S-H(UHD C-S-H).In particular,a new phase,namely nano-core-induced low-density C-S-H(NCILD C-S-H),with a superior hardness of 2.50 GPa and an indentation modulus similar to those of HD C-S-H or UHD C-S-H was identified in this study.The modeling results revealed that the presence of nanofillers increased the packing density of LD CS-H and significantly enhanced the interaction(adhesion and friction)among the basic building blocks of C-S-H gels owing to the formation of nano-core-shell elements,thereby facilitating the formation of NCILD C-S-H and further improving the performance of the ITZ.This study provides insight into the effects of nano fillers on the ITZ in concrete at the nanoscale.

Micromechanics of Thermal Conductive Composites:Review,Developments and Applications

Micromechanics investigations of composites with fiber-shaped reinforcement are extensively applied in the engineering design and theoretical analysis of thermal composites in the aerospace engineering and high-tech industry.In this paper,a critical review of various classical micromechanics approaches is provided based on the classification framework and the development of micromechanics tools.Several numerical micromechanics tools have been developed to overcome limitations through exactly/approximately solving the internal governing equations of microstructures.The connections and limitations of those models are also investigated and discussed,based on which three recently developed numerical or semi-analytical models are explained,including finite-element micromechanics,finite-volume direct averaging micromechanics,and locally exact homogenization theory,as well as machine learning tools.Since it is almost inevitable to mention the interfacial effects on thermal behavior of fibrous composites,we review the new mathematical relations that interrupt the original continuity conditions due to the existence of interphase/interface within unit cells.Generally speaking,the interphase/interface is demonstrated to play a significant role in influencing the effective coefficients and localized thermal fields.The present work also briefly reviews the application of micromechanics tools in emerging engineered woven composites,natural fibrous composites,and ablative thermal protection composites.It is demonstrated that sophisticated micromechanics tools are always demanded for investigating the effective and localized responses of thermal fibrous composites.

A Dynamic Micromechanical Constitutive Model for Frozen Soil under Impact Loading

By taking the frozen soil as a particle-reinforced composite material which consists of clay soil （i.e., the matrix） and ice particles, a micromechanical constitutive model is established to describe the dynamic compressive deformation of frozen soil. The proposed model is constructed by referring to the debonding damage theory of composite materials, and addresses the effects of strain rate and temperature on the dynamic compressive deformation of frozen soil. The proposed model is verified through comparison of the predictions with the corresponding dynamic experimental data of frozen soil obtained from the split Hopkinson pressure bar （SHPB） tests at different high strain rates and temperatures. It is shown that the predictions agree well with the experimental results.

3D Micromechanical Modeling of Failure and Damage Evolution in Dual Phase Steel Based on a Real 2D Microstructure

A plate of dual phase steel was produced from low carbon steel with intercritical annealing treatment. Its optically determined surface microstructure was utilized to construct three different microstructural models. To describe the ductile damage in the ferritic matrix, the Gurson-Tvergaard-Needleman model was used with the failure in the martensite phase being ignored. The numerical results obtained for the mechanism of void initiation and coalescence were compared with the experimental observations. The numerical results obtained from the randomly extruded 3D model showed a significantly better agreement with the experimental ones than those obtained from the 2D model or the uniformly extruded 3D model.

Micromechanical modeling of polycrystalline high manganese austenitic steel subjected to abrasive contact

This study focuses on microstructural and micromechanical modeling of abrasive sliding contacts of wear-resistant Hadfield steel.3 D finite element representation of the microstructure was employed with a crystal plasticity model including dislocation slip,deformation twinning,and their interactions.The results showed that deformation twinning interacting with dislocations had a key role in the surface hardening of the material,and it was also important for the early hardening process of the sub-surface grains beyond the heavily distorted surface grains.The effects of grain orientation and microstructural features were discussed and analyzed according to the micromechanical model to give a perspective to the anisotropy of the material and the feasibility of using micromechanics in virtual material design.

Solute clusters-promoted strength-ductility synergy in Al-Sc alloy

Sc solute clusters with a high number density were produced in an Al-0.3 wt.%Sc alloy when aged at250℃,while fine Al_(3)Sc precipitates were predominantly formed in the same alloy aged at 300℃.The alloy strengthened by Sc solute clusters displayed higher yield strength and simultaneously greater ductility than its counterpart strengthened by Al_(3)Sc precipitates.This clearly demonstrates a superior strengthductility synergy promoted by the Sc solute clusters in Al-Sc alloys.The effects of Al_(3)Sc precipitates and Sc solute clusters on ductility were discussed in comparison by using a micromechanics fracture model.Since the Sc clusters were stabilized at 250℃,the Al-Sc alloys strengthened by Sc solute clusters should find extensive application fields within a wide temperature range,due to their high temperature resistance.

Mechanical properties of nanocomposites reinforced by carbon nanotube sponges

Carbon nanotube(CNT)sponge exhibits unique porous and hierarchical structure that are beneficial to the design of ultralight and tough composites.In this study,CNT sponges(undoped and boron doped)reinforced polydimethylsiloxane(PDMS)composites were fabricated.Mechanical properties of the composite,including compressive modulus,rate-dependent modulus,stress relaxation behaviors,dynamic viscoelastic properties,and their dependency on temperature,were systematically investigated.A micromechanical model,Mori-Tanaka model,was validated to describe the mechanical behaviors of CNT sponge reinforced composites.By coupling with boron-doped CNT sponge,PDMS composites showed remarkable improvement of mechanical properties,including compressive modulus(70%),viscous modulus(243%)and damping capacity(50%).Such reinforcement effects can be controlled by the morphology of CNT sponges,as the boron-doped and undoped nanocomposites showed distinct viscoelastic behaviors.The results proved that CNT sponge reinforcement is a promising strategy to develop engineering composites with both outstanding mechanical stiffness and controllable viscoelastic performances.

Research on failure criterion of composite based on unified macro- and micro-mechanical model

A new unified macro- and micro-mechanics failure analysis method for composite structures was developed in order to take the effects of composite micro structure into consideration. In this method, the macro stress distribution of composite structure was calculated by commercial finite element analysis software. According to the macro stress distribution, the damage point was searched and the micro-stress distribution was calculated by reformulated finite-volume direct averaging micromechanics （FVDAM）, which was a multi-scale finite element method for composite. The micro structure failure modes were estimated with the failure strength of constituents. A unidirectional composite plate with a circular hole in the center under two kinds of loads was analyzed with the traditional macro-mechanical failure analysis method and the unified macro- and micro-mechanics failure analysis method. The results obtained by the two methods are consistent, which show this new method＇s accuracy and efficiency.