Microstructures and micromechanical behaviors of high -entropy alloys investigated by synchrotron X-ray and neutron diffraction techniques: A review

High-entropy alloys(HEAs)possess outstanding features such as corrosion resistance,irradiation resistance,and good mechan-ical properties.A few HEAs have found applications in the fields of aerospace and defense.Extensive studies on the deformation mech-anisms of HEAs can guide microstructure control and toughness design,which is vital for understanding and studying state-of-the-art structural materials.Synchrotron X-ray and neutron diffraction are necessary techniques for materials science research,especially for in situ coupling of physical/chemical fields and for resolving macro/microcrystallographic information on materials.Recently,several re-searchers have applied synchrotron X-ray and neutron diffraction methods to study the deformation mechanisms,phase transformations,stress behaviors,and in situ processes of HEAs,such as variable-temperature,high-pressure,and hydrogenation processes.In this review,the principles and development of synchrotron X-ray and neutron diffraction are presented,and their applications in the deformation mechanisms of HEAs are discussed.The factors that influence the deformation mechanisms of HEAs are also outlined.This review fo-cuses on the microstructures and micromechanical behaviors during tension/compression or creep/fatigue deformation and the application of synchrotron X-ray and neutron diffraction methods to the characterization of dislocations,stacking faults,twins,phases,and intergrain/interphase stress changes.Perspectives on future developments of synchrotron X-ray and neutron diffraction and on research directions on the deformation mechanisms of novel metals are discussed.

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.

Micromechanical adaptation as a treatment for spinal cord injury

Spinal cord injury: Thus far injury of the spinal cord is incurable and, in the majority of cases, a devastating and life-changing event. The worldwide incidence rate of spinal cord injury (SCI) ranges from 250,000 to 900,000 (www.who.int, 2013;Kumar et al., 2018) new cases per year. SCI outcome includes the damage of axons, demyelination of axons, loss of signal transduction, and consequential long-lasting motor and sensory deficits. Additionally, the non-use of muscles can lead to atrophy and joint contractures, thereby further reducing the possibility of recovery. Depending on the spinal level and the severity of the injury, the extent of the damage can vary and spontaneous recovery is possible to varying degrees.

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),the micromechanisms of damage in quasi-brittle materials subjected to triaxial either tensile or compressive loading are investigated and the complete strew-strain relation including four stages is obtained from micromechanical analysis.The regime of pre-peak nonlinear hardening corresponds to the distributed damage,i.e.the stable propagation of microcracks.After the attainment of the ultimate strength of load-bearing capacity, some microcracks experience the second unstable growth and the distributed damage is transmitted to the localization of damage.These analyses improve our understanding of the hardening and softening behaviors of quasi-brittle materials.

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.

Micromechanical analysis on tensile properties prediction of discontinuous randomized zalacca fibre/high-density polyethylene composites under critical fibre length

In this research,the tensile properties'performance of compression moulded discontinuous randomized zalacca fibre/high-density polyethylene under critical fibre length was analysed by means of experimental method and micromechanical models.These investigations were used to verify the tensile properties models toward the effect of fibre length and volume fraction on the composites.The experimental results showed that the tensile properties of composites had significantly increased due to the enhancement of fibre length.On the contrary,a decline in the tensile properties was observed with the increase of volume fraction.A comparison was made between the available experimental results and the performances of Tsai-Pagano,Christensen and Cox-Krechel models in their prediction of composites elastic modulus.The results showed that the consideration of fibre's elastic anisotropy in the Cox-Krenchel model had yielded a good prediction of the composites modulus,nevertheless the models could not accurately predict the composites modulus for fibre length study.

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.

Effect of heat treatment on the microstructure and micromechanical properties of the rapidly solidified Mg61.7Zn34Gd4.3 alloy containing icosahedral phase

In this paper, the microstructure evolution of the rapidly solidified (RS) Mg61.7Zn34Gd4.3 (at%, atomic ratio) alloy at high temperatures was investigated. The hardness and elastic modulus of the main precipitated phases were also analyzed and compared with those of the α-Mg matrix on the basis of nanoindentation tests. The results show that the RS alloy consists of either a petal-like icosahedral quasicrystal (IQC) phase (~20 μm) and block-shaped H1 phase (~15 μm) or IQC particles with an average grain size of ~107 nm as well as a small proportion of amorphous phase, which mainly depends on the holding time at the liquid temperature and the thickness of the ribbons. The IQC phase gradually transforms at 400?C to a short-rod-shaped μ-phase (Mg28.6Zn63.8Gd7.7) with a hexagonal structure. The hardness of the IQC phase is higher than that of H1 phase, and both phases exhibit a higher hardness than the α-Mg matrix and the μ-phase. The elasticity of the H1 phase is superior to that of the α-Mg matrix. The IQC phase possesses a higher elastic modulus than H1 phase. The easily formed H1 phase exhibits the poorest plastic deformation capacity among these phases but a higher elastic modulus than the α-Mg matrix.

A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

The current work models a weak(soft) interface between two elastic materials as containing a periodic array of micro-crazes. The boundary conditions on the interfacial micro-crazes are formulated in terms of a system of hypersingular integro-differential equations with unknown functions given by the displacement jumps across opposite faces of the micro-crazes. Once the displacement jumps are obtained by approximately solving the integro-differential equations, the effective stiffness of the micro-crazed interface can be readily computed. The effective stiffness is an important quantity needed for expressing the interfacial conditions in the spring-like macro-model of soft interfaces. Specific case studies are conducted to gain physical insights into how the effective stiffness of the interface may be influenced by the details of the interfacial micro-crazes.

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.

Optimization of Micromechanical Cleavage Technique of Natural Graphite by Chemical Treatment

In this work,we report a method to improve the efficiency of the micromechanical cleavage technique to obtain few-layers graphene samples, from natural graphite flakes, which were previously submitted to two chemical treatment times with H2SO4(17 and 25 hours). After the chemical treatment times, Raman spectroscopy reveals a hydrogenation of the few-layer graphene samples, which were obtained from the treated graphite flakes. To analyze the hydrogenation of the samples, the G and 2D bands of the Raman spectra of the treated and un-treated samples were analyzed and compared, as well as the I(2D)/I(G) ratio, revealing a p-doping on the treated samples when compared with the untreated samples. Our studies could be of great importance to obtain larger and greater amount of few-layer graphene samples.

Discrete Element Modeling of Asphalt Concrete Cracking Using a User-def ined Three-dimensional Micromechanical Approach

We established a user-defined micromechanical model using discrete element method （DEM） to investigate the cracking behavior of asphalt concrete （AC）. Using the ＂Fish＂ language provided in the particle flow code in 3-Demensions （PFC3D）, the air voids and mastics in asphalt concrete were realistically built as two distinct phases. With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes, the three-dimensional （3D） discrete element model was able to account for aggregate gradation and fraction. Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation. A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature, i e, -10 ℃ and 15 ℃. The predicted results of the numerical simulation were compared with laboratory experimental measurements. Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures. Based on the DEM model, the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.

Micromechanical analysis of the behavior of stiffclay

Cementations formed in geological timescale are observed in various stiff clays.A micromechanical stress strain model is developed for modeling the effect of cementation on the deformation behavior of stiff clay.The proposed approach considers explicitly cementations at intercluster contacts,which is different from conventional model.The concept of inter-cluster bonding is introduced to account for an additional cohesion in shear sliding and a higher yield stress in normal compression.A damage law for inter-cluster bonding is proposed at cluster contacts for the debonding process during mechanical loading.The model is used to simulate numerous stress-path tests on Vallericca stiff clay.The applicability of the present model is evaluated through comparisons between the predicted and the measured results.In order to explain the stress-induced anisotropy arising from externally applied load,the evolution of local stresses and local strains at inter-cluster planes are discussed.

Effects of Aggregate Size and Specimen Scale on Asphalt Mixture Cracking Using a Micromechanical Simulation Approach

A micromechanical model based on discrete element method（DEM） was employed to investigate the effects of aggregate size and specimen scale on the cracking behavior of asphalt mixture. An algorithm for generating three-dimensional aggregates that can reflect the realistic geometry such as shape, size and fracture surface of aggregate particles was developed using a user-defined procedure coded with FISH language in particle flow code in three-dimensions（PFC3 D）. The parallel-bond model（PBM）, linear contact model（LCM）, and slip model（SM）, whose sets of micro parameters were obtained by comparing experimental tests with numerical simulation results, were used to characterize the internal contact behavior of asphalt mixture. Digital asphalt mixture specimens were used to simulate the effects of aggregate size and specimen scale on the cracking behavior by the indirect tensile（IDT） test. Some conclusions can be drawn as follows： Both cracks and IDT strength decrease with increasing aggregate size. However, the heterogeneity of contact-force distribution augments with increasing aggregate size, especially with 13.2-16 mm aggregate. The aggregate size of 4.75-9.5 mm dominates in forming skeleton structure for asphalt mixture. The IDT strength decreases and cracks augment with increasing sample scale. The crack growth can be well interpreted from the perspective of energy analysis. The conclusions show that the proposed micromechanical model is suitable for the simulation of crack propagation. This study provides an assistant tool to further study the cracking behavior of particle-reinforced composites material such as asphalt mixture and Portland cement concrete.

Micromechanical Analysis of Thermal Expansion Coefficients

Thermal expansion coefficients play an important role in the design and analysis of composite structures. A detailed analysis of thermo-mechanical distortion can be performed on microscopic level of a structure. However, for a design and analysis of large structures, the knowledge of effective material properties is essential. Thus, either a theoretical prediction or a numerical estimation of the effective properties is indispensable. In some simple cases, exact analytical solutions for the effective properties can be derived. Moreover, bounds on the effective values exist. However, in dealing with complex heterogeneous composites, numerical methods are becoming increasingly important and more widely used, because of the limiting applicability of the existing (semi-)analytical approaches. In this study, finite-element methods for the calculation of effective thermal expansion coefficients of composites with arbitrary geometrical inclusion configurations are discussed and applied to a heterogeneous lightning protection coating made from Dexmet&#174 copper foil 3CU7-100FA and HexPly&#174 epoxy resin M21. A short overview of some often used (semi-)analytical formulas for effective thermal expansion coefficients of heterogeneous composites is given in addition.

INVESTIGATION OF SENSITIVITY FOR SILICON MICROMECHANICAL TUNING-FORK GYROSCOPE

Sensitivity is crucial to micromechanical gyro performance. The paper discusses how quality factors, resonant frequencies, driven vibration amplitude and sensor size, affect sensitivity of micromachined tuning fork gyro operating in an open loop mode. T

A MICROMECHANICAL ANALYSIS OF THE NONLINEAR ELASTIC AND VISCOELASTIC CONSTITUTIVE RELATION OF A POLYMER FILLED WITH RIGID PARTICLES

Micromechanical theory is applied to study the nonlinear elastic and viscoelastic constitutive relations of polymeric matrix filled with high rigidity solid particles. It is shown that Eshelby's method can be extended to the case of nonlinear matrix and Eshelby's tensor still exists provided that Poisson's ratio of the nonlinear matrix assumes constant value in deforming process and the rigidity of elastic filling particles is much higher than that of the matrix. A new method for averaging process is proposed to overcome the difficulty that occured in applying the ordinary equivalent inclusion method or the seff-consistant method to nonlinear matrices. A rather simple constitutive equation is obtained finally and the strengthening effect of solid particles to composites is investigated.

Micromechanical simulation and experimental investigation of aluminum-based nanocomposites

Ceramic reinforced metal matrix nanocomposites are widely used in aerospace and auto industries due to their enhanced mechanical and physical properties.In this research,we investigate the mechanical properties of aluminum/Nano-silica composites through experiments and simulations.Aluminum/Nanosilica composite samples with different weight percentages of silica nanoparticles are prepared via powder metallurgy.In this method,Nano-silica and aluminum powders are mixed and compressed in a mold,followed by sintering at high temperatures.Uniaxial tensile testing of the nanocomposite samples shows that adding one percent of Nano-silica causes a considerable increase in mechanical properties of nanocomposite compared to pure aluminum.A computational micromechanical model,based on a representative volume element of aluminum/silica nanocomposite,is developed in a commercial finite element software.The model employs an elastoplastic material model along with a ductile damage model for aluminum matrix and linear elastic model for nano-silica particles.Via careful determination of model parameters from the experimental results of pure aluminum samples prepared by powder metallurgy,the proposed computational model has shown satisfactory agreement with experiments.The validated computational model can be used to perform a parametric study to optimize the microstructure of nanocomposite for enhanced mechanical properties.